KTH ROYAL INSTITUTE
OF TECHNOLOGY
Degree Project in Electrical Power Engineering
Second cycle, 30 credits
Dielectric properties of
ion-exchanged electrotechnical
insulation papers
A study on the properties of novel papers
DAN SELSMARK
Stockholm, Sweden, 2023
Dielectric properties of
ion-exchanged electrotechnical
insulation papers
A study on the properties of novel papers
DAN SELSMARK
Master’s Programme, Electric Power Engineering, 120 credits
Date: February 21, 2023
Supervisors: Nathaniel Taylor, Xin Wang
Examiner: Hans Edin
School of Electrical Engineering and Computer Science
Host organization: RISE Research Institutes of Sweden
Swedish title: Dielektrisk respons hos jonbytta elektrotekniska isoleringspapper
Swedish subtitle: En studie om nya papperstypers egenskaper
© 2023 Dan Selsmark
Abstract | i
Abstract
Electrical insulation papers are a widely used group of papers in insulation
applications and has been used for more than 100 years. Common applications
include use as the dielectric medium in capacitors and insulation material
in cables, bushings and transformers. As new advances in the study of the
electrical properties of paper are made, the prospects of future applications
grow. One interesting prospect is the use of paper as a substrate in sensing
devices, biodegradable, printed and flexible electronics. Paper is a renewable
and recyclable material and it would therefor be desirable to replace nonrenewables materials such as plastics with paper as e.g., substrate in printed
electronics. For this to be feasible the paper must be able to meet the electric
and dielectric requirements of the intended application, among which low
dielectric losses is a key parameter. One way to alter and control the electric
and dielectric properties of a paper sample is through the selection of different
ions in the ion-exchange step of the paper making process.
In a collaboration between KTH Royal Institute of Technology and RISE Research Institutes of Sweden AB working within a greater Digital Cellulose
Center (DCC) project, this thesis aims to measure and characterise the
dielectric response of a set of novel ion-exchanged paper samples together with
a set of reference papers currently used in electrical applications. The greater
goal of RISE work is to understand and map the influence of ion choice in
order to better understand and control the dielectric properties of paper.
The samples were measured using an impedance spectroscopy method
from which capacitance and permittivity can be calculated. A parallel plate
Kelvin guard-ring capacitor consisting of two electrodes and a guard ring
placed in a custom made climate controlled chamber was used to measure
the samples in different environmental conditions. The results show that the
choice of ion used in the ion-exchanged papers heavily influence the samples
dielectric response, both its dielectric constant and dielectric losses. Further,
the choice of ion valence appears correlated with the change in responses;
monovalent ions had much greater influence than bivalent ions. This effect
appears to stem from monovalent ions having a greater mobility within the
bulk material, more research is however needed for a definite answer.
Keywords
Paper insulation, Frequency Domain Spectroscopy, Dielectric response, Karl
Fischer titration, Dielectrics
ii | Sammanfattning
Sammanfattning
Elektriska isoleringspapper är en flitigt använd grupp av papper i isoleringsapplikationer och har använts i mer än 100 år. Vanliga applikationsområden inkluderar användning som dielektriskt medium i kondensatorer
och isoleringsmaterial i kablar, genomföringar och transformatorer. I takt
med att nya framsteg görs inom olika pappers elektriska egenskaper växer
utsikterna för framtida tillämpningar. En intressant möjlighet är användningen
av papper som substrat för sensorer, biologiskt nedbrytbar, tryckt och
flexibel elektronik. Papper är ett förnybart och återvinningsbart material
och det vore därför önskvärt att ersätta icke förnybara material som plast
med papper som t.ex. substrat i tryckt elektronik. För att detta ska vara
genomförbart måste papperet kunna uppfylla de elektriska och dielektriska
kraven för den avsedda applikationen, bland vilka låga dielektriska förluster
är en nyckelparameter. Ett sätt att ändra och kontrollera de elektriska och
dielektriska egenskaperna hos ett pappersprov är genom valet av olika joner i
jonbytessteget i papperstillverkningsprocessen.
I ett samarbete mellan KTH Kungliga Tekniska Högskolan och RISE
Research Institutes of Sweden AB som arbetar inom ett större Digital Cellulose
Center-projekt, syftar denna avhandling till att mäta och karakterisera
den dielektriska responsen hos en uppsättning nya jonbytta pappersprover
tillsammans med en uppsättning referenspapper. Det övergripande målet i
RISE arbete är att förstå och kartlägga påverkan av jonval för att bättre förstå
och kontrollera pappers dielektriska egenskaper.
Proverna mättes med en impedansbaserad mätmetod från vilken kapacitans och permittivitet kan beräknas. En Kelvin plattkondensator bestående av
två elektroder och en skyddsring placerad i en skräddarsydd klimatkontrollerad kammare användes för att mäta proverna under olika miljöförhållanden.
Resultaten visar att valet av jon som används i jonutbytet kraftigt påverkar
provets dielektriska respons, både dess dielektriska konstant och dielektriska
förluster. Vidare verkar valet av jonvalens vara korrelerat med förändringen i
frekvenssvar; envärda joner hade mycket större inflytande än tvåvärda joner.
Denna effekt verkar bero på att envärda joner har en större rörlighet inom
bulkmaterialet, mer forskning krävs dock för ett definitivt svar.
Nyckelord
Pappersisolering, Frekvensdomänsspektroskopi, Dielektrisk respons, Karl
Fischer titrering, Dielektrika
Acknowledgments | iii
Acknowledgments
To everyone who has helped and supported me making thesis possible, a
heartfelt thank you.
I am especially grateful to my examiner and supervisor professor Hans
Edin and senior scientist Xin Wang, my supervisor from RISE. To Hans, for his
endless patience and support in matters both theoretical and practical, enabling
me to finalise this thesis. For always taking time from an otherwise eventful
workday or even vacations, to answer questions and discuss my work. To
Xin, for an abundance of insights and comments on theory and practice, and
a never ending support and encouragement. A seemingly endless source of
perspectives, knowledge and ideas on the topic of this work.
I would also like to thank associate professor Nathaniel Taylor, for
invaluable help in getting this project started and giving introductions of the
test equipment as well as providing scripts to read IDAX data files into Matlab
and knowledge of how to use the customisable version of the IDAX software.
I would like to also extend a grateful thank you to the lab staff, Patrick Janus,
Janne, Jesper and Elena for everything practical, from finding the correct
adapters to troubleshooting when equipment did not work as expected. A
special thank you to Patrick for his patience and teaching me many valuable
lessons in practical lab work, not least of all teaching me how to operate the
Karl Fischer equipment. I must give thanks to Mahidhar Durga Pawan Gorla,
working next to me in the lab for a time, lending great help in getting started,
answering questions on theory and practice and providing valuable discussions
on how to carry out the experiments in practice.
Additionally, I would like to thank RISE and DCC for both financing and
giving me the chance to carry out, and the patience to finish, this project and to
RISE Bioeconomy for giving me insights in the paper making processes and
giving me a very interesting tour of their lab.
Last but not least, my gratitude and blessings to friends and family for your
encouragement and support, through highs and lows, throughout not only my
thesis work but my time at KTH.
Stockholm, February 2023
Dan Selsmark
iv | Acknowledgments
Contents | v
Contents
1
2
3
Introduction
1.1 Dielectric measurement domains
1.1.1 Time domain . . . . . .
1.1.2 Frequency domain . . .
1.1.3 Choice of domain . . . .
1.2 Goals . . . . . . . . . . . . . .
1.3 Limitations . . . . . . . . . . .
1.4 The paper-making process . . .
1.5 Thesis outline . . . . . . . . . .
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Theoretical background
2.1 Basics of dielectrics . . . . . . . . . . . . .
2.1.1 Polarisation . . . . . . . . . . . . .
2.1.2 Relaxation . . . . . . . . . . . . .
2.1.3 Loss tangent . . . . . . . . . . . .
2.2 Dynamics of dielectric response . . . . . .
2.2.1 The effects of moisture in paper . .
2.2.2 The effect of voltage amplitude . . .
2.2.3 The effect of temperature . . . . . .
2.2.4 The effect of density . . . . . . . .
2.3 Interfacial polarisation . . . . . . . . . . .
2.3.1 The Maxwell-Wagner-Sillars effect .
2.3.2 Electrode polarisation . . . . . . .
2.4 Analysing and modelling dielectric response
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Measurement Setup
29
3.1 Hardware & Software . . . . . . . . . . . . . . . . . . . . . . 29
3.1.1 Low-frequency spectroscopy - The IDAX300 . . . . . 29
3.1.2 High frequency spectroscopy - The LCR-meter . . . . 32
vi | Contents
3.2
3.3
3.4
3.5
3.1.3 Equipment setup . . . . . . . .
Measurement procedure . . . . . . . . .
Sample preparation . . . . . . . . . . .
3.3.1 Sample geometry . . . . . . . .
3.3.2 Humidity control . . . . . . . .
3.3.3 Moisture content determination
Data collection and treatment . . . . . .
3.4.1 Model fitting . . . . . . . . . .
Assessing test setup accuracy . . . . . .
4 Results and Analysis
4.1 Medium moisture content . . .
4.2 Wet moisture content . . . . .
4.3 Dry moisture content . . . . .
4.4 Effect of moisture . . . . . . .
4.5 Dielectric response modelling
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5 Conclusions and Future work
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5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
References
113
A Measurement setup investigations
A.1 Equipment validation . . . . . . . . . .
A.2 Test cell comparisons . . . . . . . . . .
A.3 Pressure tests . . . . . . . . . . . . . .
A.4 Painted electrodes . . . . . . . . . . . .
A.5 Taped electrodes . . . . . . . . . . . .
A.6 Physical Vapor Deposition of electrodes
A.7 Water electrodes . . . . . . . . . . . . .
A.8 Summary . . . . . . . . . . . . . . . .
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B Resonance in RLC circuits
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147
C Karl Fischer titration
151
C.1 Emptying and cleaning measuring cell . . . . . . . . . . . . . 151
C.2 Coulometric titration with C10S on paper samples . . . . . . . 152
D Instrument control
154
List of acronyms and abbreviations | vii
List of acronyms and abbreviations
ADC
Analog to Digital Converter
DCC
DRS
DS
Digital Cellulose Center
Dielectric Response Spectroscopy
Dielectric Spectroscopy
EP
ESL
ESR
Electrode Polarisation
Effective Series Inductance
Effective Series Resistance
FDS
Frequency Domain Spectroscopy
IDAX
IS
Insulation Diagnostic System
Impedance Spectroscopy
KTH
KTH Royal Institute of Technology
LFD
Low-frequency Dispersion
MC
MWS
Moisture Content
Maxwell-Wagner-Sillars
RH
RISE
Relative Humidity
RISE Research Institutes of Sweden
SCPI
Standard Commands for Programmable Instruments
viii | List of acronyms and abbreviations
Introduction | 1
Chapter 1
Introduction
Electrical insulation papers are a widely used group of papers in electrical
insulation applications. The papers are made from mechanically and
chemically treated wood chips. Their dielectric properties depend on a
large number of parameters such a wood type, production method, humidity,
frequency and temperature. One of the most important aspects of paper as a
insulation, or dielectric, material is its ability to polarise in an external electric
field [1]. Another important aspect is low losses.
Paper has been used as an insulator for more than 100 years [2]. Common
applications of electrical insulation paper today are as oil-impregnated
insulators in transformers and bushing of a range of power ratings. Some
applications can also be found as an insulator in certain cables and capacitors.
As new advances in the study of the electrical properties of paper are made,
the prospects of future applications grow. These prospects include the use of
paper; as a substrate in sensing devices [3]; as a substrate for biodegradable
electronics [4] including cellulose film substrates, dielectric materials, OLEDs
(Organic Light-Emitting Diodes), OFETs (Organic Field-Effect Transistors),
ionic conductors, solar cells and light management layers [3] [5]; as a substrate
for printed electronics [2]; as a substrate for flexible electronics [3, 4, 5].
The studies include the dielectric response of paper to parameters such as
relative humidity, moisture content and temperature, as well as its anisotropic
properties and morphology.
Paper is a renewable environmentally friendly biopolymer as it is both
recyclable and made from renewable materials. For flexible electronics
applications, amongst others, it would be desirable to replace the commonly
used plastic substrates with paper. While many challenges remain to be solved,
both economical and functional ones, paper holds great promise in the advent
2 | Introduction
of both future active and passive biodegradable electronics. Common in most
applications, present and future, is the strive towards a low dielectric loss
material. Exchanging plastics for flexible papers would give rise to new design
options in a number of applications, one of them antenna design. However, for
this to be feasible the paper material needs to be able to meet the requirements
of the intended application. Low dielectric loss is a key parameter, one that
must be reduced for paper to viably replace plastics. This thesis aims to study
whether ion-exchange in the paper pulp during the paper making process can
reduce the paper’s dielectric losses. Several differently ion-exchanged papers
will be tested under different conditions to study the material’s behaviour. As
the moisture content in the paper is expected to have a significant impact on
the papers dielectric properties, the samples will be measured at three different
moisture contents. Likewise, the samples will be measured at four different
temperatures, as temperature is known to influence the dielectric properties.
Additionally, two different voltage amplitudes will be used, as amplitude will
impact the dielectric properties of papers with free ions. The samples will
be measured using Dielectric Response Spectroscopy (DRS) in order to study
the samples properties as a function of frequency, the parameter dominating a
dielectric response.
This project is a collaboration between KTH Royal Institute of Technology
(KTH) and RISE Research Institutes of Sweden (RISE), and is part of
RISEs studies into wood-fibre based materials in electrical applications as an
innovative, low cost and sustainable option. RISE is an independent, state
owned research institute with an explicit task to conduct research towards
creating a sustainable growth in Sweden by strengthening competitiveness
and innovation of trade and industry in concert with the public sector. Their
mission includes the promoting of cooperation between academia, industry
and the public sector as well as running test-beds of high relevance to industry.
As such, RISE has an interest in the development and research into electric
grade papers, with the possibility of both reducing losses, and replacing
unsustainable plastics with more sustainable paper materials in electronic
application. The outcome of the project at hand falls under the organizations
state mandated mission.
1.1
Dielectric measurement domains
There are two principal approaches to measuring dielectric response, namely
time domain and frequency domain measurements. While both approaches are
commonly used and based on measuring conduction, they deal with different
Introduction | 3
material parameters. In the time domain, parameters used to describe a linear,
homogeneous and isotropic material are the high-frequency component of the
relative permittivity ε∞ , conductivity σ and the dielectric response function
f(t). Parameters used in the frequency domain are the complex relative
permittivity ε̃(ω)[6].
In the time domain, common approaches are polarisation/depolarisation
current measurements and recovery voltage measurements. In the frequency
domain measurements are made of a complex impedance. In very high
frequencies such as the radio range, measurements are made of complex
transmission and reflection coefficients using a network analyser.
1.1.1 Time domain
Measurement of polarisation/depolarisation currents is one way to study the
slow polarisation processes of a material. Assuming the test object, of
known geometrical capacitance, at its initial state is completely discharged,
then applying a step voltage across it will give rise to a polarisation current
which can be measured. Likewise, removing the voltage will give rise to
a depolarisation current as the charges move to their equilibrium position.
The polarisation current contains two parts, one related to the test objects
conductivity, one related to activation of the different polarisation mechanisms
in the object. Having measured the currents, estimates can be made of both
response function and conductivity[6].
The recovery voltage method also investigates slow polarisation processes.
Again, a step voltage is applied over a discharged test object of known
geometrical capacitance, giving rise to a polarisation current during a charging
period. After the charging period, the object is short-circuited for a time,
known as the grounding period, giving rise to a depolarisation current. When
the grounding period is completed, a recovery voltage can be measured under
open circuit conditions. The relaxation process within the object produces an
induced charge on the electrodes, yielding the recovery voltage[6].
1.1.2 Frequency domain
Dielectric Spectroscopy (DS), or sometimes DRS, often used to study the
response of dielectric materials under a certain electric field and frequency.
DS can be used in a very wide range of frequencies, from µHz up towards
THz and provides information on both complex capacitance, permittivity,
loss factor and DC conductivity as well as on molecular dynamics giving
4 | Introduction
rise to a response [7]. There exists a number of different methods doing DS
measurements. In low frequencies, up to some MHz, Impedance Spectroscopy
(IS) is often used. By measuring the applied voltage across the sample and
the current through it, the samples impedance can be calculated as a function
of frequency from which its dielectric properties can be described. In higher
frequencies, more advanced methods are available, four of which are presented
in the application note from Rohde & Schwarz. As this thesis is limited to 1
MHz, no further discussion of these methods is done.
1.1.3 Choice of domain
Time domain methods have the advantage of being rather fast, requiring
shorter time to determine low frequency responses. Due to the bandwidth
of current measuring instruments, mechanical switching and rise time of high
voltage sources, the methods are often limited to frequencies up to about 1 Hz.
This means that time domain studies are best suited for low frequency studies.
Additionally, since time domain methods are wide-band measurements, they
are sensitive to noise, making them less reliable when applied to low loss
materials[6].
Frequency domain methods on the other hand often require at least two
full cycles to make a reliable measurement, thus taking increasingly long
time to complete with decreasing frequencies. On the other hand, these
methods are well suited for high frequency studies, where the completion time
of a measurement is very short. Additionally, since they are narrow-band
measurements, they are well suited for higher frequencies. These methods
are however suited for both low and high loss systems[6].
1.2
Goals
The goal of this project is to study and characterise the dielectric response
behaviour of a set of ion-exchanged and reference papers. The characterisation
is aimed at shedding light into whether a certain ion-exchange can result in
the paper having lower dielectric losses than the other measured papers, and
whether certain ion-exchanged papers are able to perform better under certain
conditions. This has been divided into the following sub-goals:
• Sub-goal 1: Measure the dielectric response of both ion-exchanged
papers and reference papers at different conditions
• Sub-goal 2: Characterise the dielectric response
Introduction | 5
1.3
Limitations
The project will focus only on a selection of different ion-exchanged and
reference papers, the reference papers acting as a means of comparison to
commercially available paper. The ion-exchanged papers will be measured at
three different moisture content levels in order to study the effect of moisture
on their frequency response. The two commercial papers, from AM and
Hitachi, will be limited to a frequency range of 1 Hz to 1 MHz at the driest
level in a compromise between time constraints and manufacturer interests.
Additionally, the effect of different amplitudes of applied voltage across the
papers will be studied using two different amplitudes.
The dielectric properties studied will be restricted to complex permittivity
and loss tangent. All paper samples were manufactured and provided before
the project start.
In order to try to fit this thesis work within the course schedule of 20
weeks, time is the greatest limiting factor. Several other parameters could be
of interest to study, such as the influence of density or oil-impregnation as well
as other ion-exchanged or reference papers. The measurements are restricted
to the frequency spectrum of 1 mHz to 1 MHz. Initially, the measurements
were planned to be done in a frequency spectrum of 1 mHz up to some GHz.
However, due to time constraints, this was later restricted down to 1 MHz, the
highest available frequency of the LCR meter.
All ion-changed papers are made from the same pulp, with different ionexchanges in the later stages of the paper-making process, all papers with the
exception of H+ have also been pressed at 400 bars for 5 minutes in order
to homogenise their densities. They are classified after, and in the following
report referenced as, the ion added:
• Al3+
• Ca2+
• H+
• Mg2+
• Na+
The reference papers are insulation papers from Hitachi and AhlstromMunksjö (AM). They are referenced as:
• AMetek - a commercial bushing paper
6 | Introduction
• AM400 - a special pulp, originally pressed at 400 bars for 5 minutes
after drying in the paper making process
• HTP - a thin pressboard from Hitachi
In this thesis the frequency domain is selected for all measurements, based
in part on the suitability of the intended frequency spectrum but mainly on the
equipment available.
1.4
The paper-making process
The ion-exchange was done, by RISE, by first washing the paper pulp carefully
to remove all metal ions. This was done by suspending the pulp in de-ionized
water adjusted to pH 1 for 30 minutes, after which the pulp was thoroughly
washed with de-ionized water with a pH of 1, followed an additional wash in
neutral de-ionized water. A counter-ion exchange to sodium (Na+) was then
done by a wash with de-ionized water by filtration. After this, the ion-exchange
was performed by suspending the pulp in water containing the counter-ion
of interest in excess, letting it react for 30 minutes and then washing by
filtration with de-ionized water. The paper sheets were made using a static
hand-sheet former. The papers were constrained dried in a climate-controlled
room of 23 °C and a relative humidity of 50 %. When dry, most papers were
mechanically compressed to achieve a homogeneous density.
1.5
Thesis outline
Chapter 2 reviews relevant literature and theory of dielectric response
studies. Chapter 3 describes hardware, software and measurement setup and
procedure, with the aim of transparency and repeatability. In chapter 4 the
results of the study are presented and analysed. Finally, a conclusion is
provided in chapter 5 followed by future work and some final words.
Theoretical background | 7
Chapter 2
Theoretical background
Both paper and pressboard are made of 3D-structured wood fibres, and
electrical grade paper are made from softwood fibres processed by the Kraft
pulp process. Wood fibres consists of three main components; cellulose,
hemicellulose and lignin in varying proportions, affecting the materials
dielectric constant and loss values. Paper is made by dewatering a dilute
suspension of cellulose fibres, called the pulp, which is then pressed and
dried. The pulp is mainly made from wood by separating the wood fibres
in a mechanical, thermomechanical or chemical process each giving the pulp
different characteristics. A paper made by the mechanical process is called
wood containing, while one made by the chemical process is called wood
free, or Kraft, paper. The chemical process also enables the removal of lignin,
the polymer giving the paper its ’woody’ properties, making the paper more
porous and hygroscopic (increased tendency to attract and bind water) [2].
The dielectric characteristics of paper materials depend, apart from
frequency and morphology, also on Relative Humidity (RH), temperature,
amplitude and direction of the applied field and paper contents, density and
homogeneity. While measurements of the dielectric constant of papers was
started already in the early 20th century, literature values are not always
granted to be correct for a given paper substrate a researcher has at hand. The
structure of the fibres as well as the contents of lignin and hemicellulose often
vary between different papers. Some guiding values are however available.
Dry paper typically has a dielectric constant of between 1.3 and 4 at 1 MHz
[2] or between 2 and 4 at 1 MHz [8] depending on e.g. fillers with different
constants and porosity since air has a constant of εair = 1. Morgan found
the dielectric constant of Kraft paper to be between 3.7 and 4 depending
on frequency, temperature and air pressure [9]. When used in insulating
8 | Theoretical background
Table 2.1: Reported values of the dielectric constant of paper and cellulose.
Type
Dielectric constant
Frequency
Reference
Dry paper
Dry paper
Dry Kraft paper
Dry cellulose
Dry cellulose
Regenerated cellulose
Cellulose
1.3-4
2-4
3.7-4
6-9
6.1
6.7
3.6-7.1
1 MHz
1 MHz
50 Hz - 20 kHz
1 MHz
constant
1 MHz
102 -1010
[2]
[8]
[9]
[2]
[10]
[11]
[12]
applications, paper is often impregnated, filling its voids, with a substance
of high constant, like oil or resin.
Cellulose makes up the largest volume fraction of fibres in paper, thus
having the greatest influence on the papers dielectric properties. Tobjörk and
Österbacka report dry cellulose to have a constant between 6-8 at 1 MHz
[2] while Luca et al found the constant to be 6.1 [10]. Stoops studying the
regenerated cellulose called cellophane found its constant to be 6.7 at 1 MHz
[11]. On the other hand, Torgovnikov found the dielectric constant of cellulose
to vary between 3.6 to 7.1 in the frequency range of 1010 to 10² [12]. Table 2.1
compiles the reported values on paper and cellulose.
Several factors influence the dielectric response of a paper of which some
of the most important ones will be discussed here after a presentation on the
basics of dielectrics. There are also a handful of different approaches to model
a dielectric response some of which will be discussed here.
2.1
Basics of dielectrics
In electromagnetism, a dielectric material is an electrical insulator that when
exposed to an electric field can be polarized. An ideal dielectric material does
not contain free charges. Bound charges in the material will align with the
applied field, so that positive charges will shift, or move, in the direction of
the field while negative charges will shift in the opposite direction of the field.
This shift of charges causes an internal electric field opposing the applied field,
thus reducing the overall field strength within the material [13].
When the electric field is removed, the bound charges will return to their
original state after some time, called the relaxation time. While this is the core
principle, the behaviour of dielectrics depends on a number of parameters,
such as whether the applied field is constant or time varying, whether the
Theoretical background | 9
material response depends on the direction of the applied field (that is, whether
the material is isotropic or anisotropic), whether the material is homogeneous
(the response being the same everywhere in the material) and whether the
response is linear or contains non-linearities. Insulation papers are highly
anisotropic, meaning that the dielectric response is dependent on the direction
of the field. This anisotropy is due to the form factor of the fiber and the paper
aligning phenomenon occurring during the paper making process. Simula et
al [8], studying the dielectric response of conventional copy paper, confirmed
that both the dielectric constant and losses differed greatly depending on the
direction of the applied field. Both parameters were greater in the machine
direction (parallel to the sheet) than in the thickness direction (normal to the
sheet). However, in most applications, such as transformers, the external field
is always applied perpendicular to the paper plane.
The permittivity of any dielectric material, including insulation paper, is
a measure of the material’s electric polarizability when exposed to an electric
field, measured in Farads per meter (F/m). The absolute permittivity, often
also called permittivity, denoted ε can also be described as a proportionality
constant between the electric displacement field D and the applied electric
field E [13]:
D = εE
(2.1)
The vacuum permittivity ε0 , sometimes also called the permittivity of
free space or the electric constant, is approximately 8.85 · 10−12 F/m. The
permittivity ε of any medium other than free space also contains a relative
permittivity εr , also known as the dielectric constant. For now the constant
is treated a single real number. The relative permittivity is a dimensionless
constant, specific to a medium introduced as a scalar to the permittivity of
free space to define the mediums absolute permittivity [13].
ε = εr ε0
(2.2)
The dielectric constant can also be described based on the principle of
polarisation. The electrical susceptibility, χe , is a unitless measure of how
easily the material polarises in an external field, which in turn defines the
materials permittivity. The susceptibility relates the polarisation, P, and the
electric field, E, as:
P = ε0 χ e E
(2.3)
In vacuum, the susceptibility is zero, while in any other medium it is
10 | Theoretical background
defined as:
χ e = εr − 1
(2.4)
It is also possible to relate the electrical displacement field, D, to
susceptibility as:
D = ε0 E + P = ε0 (1 + χe )E = εr ε0 E
(2.5)
The dielectric constant of a material is dependent on several factors, not
least among them the frequency of the applied electric field. The polarization
of a material is not instant, there exists a certain settling time for the charges to
align with the field. As the frequency increases, the inertia of the charges will
prevent their displacement to vary in phase with the applied field, giving rise
to a damping mechanism [14]. This out of phase polarisation can be described
by an (angular) frequency dependent complex permittivity. Consisting of two
terms, a real and an imaginary, the permittivity is in any practical application
no longer a single real number but rather a complex number.
ε̃r = ε′r − jε′′r (ω)
(2.6)
The real part of the complex permittivity signifies the dielectric constant
and gives rise to the energy stored in the polarisation of the material, as
previously described. The imaginary part of the complex permittivity is
related to the energy losses of the material due to the damping effect and ohmic
losses. In low loss media the damping losses are very small. It is also possible
to define an equivalent conductivity, representing all losses as:
σ = ωε′′
(2.7)
The overall conductivity, at low frequencies, may consist of different
conduction mechanisms. In moist materials, ionic conductivity dominates,
and is at low frequencies inversely proportional to frequency. Ionic
conductivity is characterised by the influence of free ions in a solvent, typically
water [15].
When a dielectric medium is exposed to an electric field small
displacements of bound charges in the medium occurs, resulting in a
polarisation of the material. If the field is strong enough, it can pull electrons
out of their bonds, giving rise to free electrons, and a dielectric breakdown
ensues. These electrons will accelerate in the electric field and will violently
collide with other molecules, causing damage to the insulation material.
Theoretical background | 11
Should the electrons be allowed to accelerate to speeds high enough, either
through a longer acceleration distance or due to a high field strength, they
may reach speeds high enough to knock electrons out of the molecules they
collide with, creating additional free electrons upon collision, thus causing
an avalanche effect. The dielectric strength of a material is defined as
the maximum electric field intensity the material can withstand, without a
dielectric breakdown occurring [13].
2.1.1 Polarisation
Polarisation is one of the fundamental mechanisms of dielectric materials.
There are however different kinds of polarisation taking place in a given
material, depending not only on the material but also on the frequency of
the applied electric field. Several polarisation effects may contribute to the
materials overall permittivity. The four fundamental mechanisms, in order of
increasing occurrence frequency are ionic polarisation, dipolar polarisation,
atomic polarisation and electronic polarisation. Figure 2.1 gives a good
overview of when the different mechanisms take place. In addition to these
mechanisms, an interfacial, or space charge, polarisation may occur at low
frequencies.
Figure 2.1: Polarisation mechanisms over frequency, adapted from [15].
Ionic polarisation is caused by the relative displacement of free positive
and negative ions, giving rise to an ionic conduction in the material.
Dipolar polarisation happens when an electric field causes the orientation
of dipoles to rotate in order to align with the field. The field exercises a torque
on the dipole, and when the field changes direction the dipole rotates to once
again align with the field. During rotation the dipole experiences friction
which gives rise to a dielectric loss. Water molecules for example, being
12 | Theoretical background
permanent dipoles rotating in an alternating electric field, produce a quite lossy
mechanism, which for example is why food heats in a microwave oven.
Electronic polarisation occurs in neutral atoms when an electric field
displaces the nucleus with respect to its surrounding electrons. The positive
nucleus will move towards the negative intensity of the field while the electron
could surrounding it will move towards the positive intensity of the field.
Electronic polarisation occurs at frequencies much larger than those used in
this thesis.
Atomic polarisation occurs when an electric field causes an atom or
molecule to stretch, displacing adjacent positive and negative ions creating a
dipole moment. This polarisation is also prevalent in frequencies much higher
than those used in this thesis, therefor it will not be discussed further.
Interfacial polarisation, unlike electronic, atomic and dipole polarisation
which are all due to locally bound charges, occurs due to charge carriers that
can migrate over a distance inside the material. At low frequencies interfacial,
also known as space charge, polarisation occurs when the movement of these
charges are hindered. This typically happens at the interface between two
different materials, where the charges become trapped at the interface. It may
also happen when charges cannot be discharged or replaced at the electrodes
giving rise to the field. When this mechanism occurs, charges will begin to
accumulate, causing a field distortion increasing the overall capacitance of the
material. This will affect the dielectric response by increasing the real part of
the complex permittivity, ε′r [15].
At low frequencies, a response mechanism called ”hopping charges” is
common. Hopping charges are a class of species somewhere between dipoles
and charge carriers, spending most of their time in a localised state, or zone.
Should the charge carrier be supplied enough energy, it may hop out of its
potential well, entering a new localised zone. These hopping charges could,
in very low frequencies, cause an increase in both imaginary and real parts of
the dielectric response [16].
2.1.2 Relaxation
The polarisation process can be described as an exponential function.
Dielectric relaxation is the delay of a polarised system or molecule returning
to a steady state after having been polarised in an external electrical field. The
relaxation process, which is not instant, can be described in its simplest form
as an exponential function of time. The relaxation time constant, τ , is the time
it takes for a polarised system to return to 1/e (≈ 37%) of its equilibrium state.
Theoretical background | 13
It can also be described as a measure of molecule mobility within a material
as it signifies the time required for a dipole to become oriented in an electric
field. In condensed matter, liquids and solids, molecules have limited freedom
to move, or align, under an applied field. Internal friction of material causes
the polarisation to take some time. Likewise, when the field is turned off and
the polarisation is reversed, it takes some time before the molecules reach their
initial state or position. A relaxation frequency, ω or f in Equation 2.8, can
also be defined as the inverse of the relaxation time constant [15]. The time
scale of the time constant is dependent on the relaxation frequency, and as
such may range multiple orders of magnitude.
τ=
1
1
=
ω
2πf
(2.8)
Permittivity is frequency dependent. At frequencies below a relaxation
frequency the polarisation process is able to keep pace with the alternating
field. This means the losses are directly proportional to frequency. As the
frequency increases slow polarisation mechanisms can no longer keep up
with the rapidly changing field, resulting in them relaxing and no longer
contributing to polarising the material. This can be seen as a decreasing real
part of the permittivity with increasing frequencies while the imaginary part
keeps increasing to reach a maximum at the relaxation frequency. Above the
relaxation frequency however, imaginary and real parts alike decrease [15].
2.1.3 Loss tangent
The complex permittivity can be represented in a simple vector diagram, see
Figure 2.2. a loss tangent, or loss factor, of the material can be defined as the
ratio of the imaginary and real part:
tan(δ) =
ε′′r
1
=D=
′
εr
Q
Figure 2.2: Vector representation of the complex permittivity.
(2.9)
14 | Theoretical background
Here δ denotes the phase angle between real and imaginary part. D is,
as commonly used, the materials dissipation factor, another name of the loss
tangent, and Q is called the quality factor. The loss tangent, being the ratio
of the energy lost and the energy stored in the material, describes the relative
lossiness of the material studied [15].
2.2
Dynamics of dielectric response
This section aims to briefly discuss the influence of the most important
parameters affecting a samples dielectric response, namely the moisture
content, voltage amplitude, temperature and sample density.
2.2.1 The effects of moisture in paper
RH is defined as the moisture content of the atmosphere expressed as a
percentage of the maximum amount of moisture the atmosphere can hold at
a given temperature and pressure before saturation. The RH, in percent, is
calculated as:
RH =
actual vapor density
· 100 (%)
saturation vapor density
(2.10)
The vapor density is typically defined in g/m³ and saturation densities for
a given temperature and pressure can be found in suitable tables. Often the
vapor pressure is given in units of torr, it is helpful to remember that 1 torr =
1/760 atm.
Moisture Content (MC) is defined as the amount of water in relation to the
amount of dry substance plus water in a sample. It can be calculated, in weight
percentage (wt%), as grams water over grams solid plus grams water:
MC =
g water
· 100 (%)
g dry solid + g water
(2.11)
When a paper, or pressboard, is exposed to an environment of some
humidity a sorption process is started, where water will diffuse into or out of
the paper until an equilibrium between environment and paper is reached. This
equilibrium is heavily dependent on temperature, as discussed in Section 3.3.2.
It is also the case that paper materials exhibit a form of hysteresis effect,
much like the magnetisation of a transform core, between adsorption and
desorption of water where it may have different moisture contents at a given
Theoretical background | 15
RH. The adsorption curve always lies below the desorption curve, the smallest
difference between being in very high or very low humidities [17].
Paper absorbs moisture quite quickly. Should both sides of a paper sample
be in contact with the surrounding air, the time constant of moisture diffusion
can be calculated as [18]:
τ=
d²
π²Ddif f
(2.12)
d is the sample thickness. D is the diffusion coefficient of moisture,
not to be mistaken for the dissipation factor, which can be calculated using
Equation 2.13 [18] where Cmoist is the moisture content of the paper in percent,
T0 is 298 K, the activation energy Ea is 8140 K, D0 is 2.62 × 10−11 m²/s for
paper. As an example. using Equation 2.12, a paper 150 µm thick left in room
temperature would require about 3 hours to reach an equilibrium of 7 % MC.
Ddif f = D0 e
0.5Cmoist +Ea ( T1 − T1 )
0
(2.13)
The MC of a paper sample has a great influence on its dielectric response.
With increasing MC the papers polarisability and conductivity increases,
′
′′
visible as sharp increases in both εr and εr [18, 19, 20] particularly at
low frequencies. Torgovnikov conluded [12] that the relation between MC,
dielectric constant and loss tangent varies depending on frequency range.
In very high frequencies, loss peaks were found to both shift towards lower
frequencies and reduce in magnitude with increasing MC.
The dielectric response of water itself has been the topic of several studies,
but as the ionic contents of the water samples differ between studies so does
its response curves. The dielectric constant of highly pure water is widely
accepted to be 80 at 20 °C, and 78 at 25 °C, based on the robust report by
Malmberg and Maryott [21] studying its temperature dependence below 100
kHz. Also the frequency dependence of highly pure water has been studied.
Batalioto et al [22], studying water in the frequency range of 10 mHz to
30 MHz, found a clear low frequency Debye-like relaxation process and a
dielectric constant tending to 80 at frequencies above about 1 kHz and about
3 · 107 at 10 mHz. In the GHz and THz ranges, at 25 °C, Ellison found pure
water to exhibit three relaxation processes, at 18.56 GHz, 167.83 GHz and
1.944 THz, and two resonance peaks at 4.03 THz and 14.48 THz [23]. A
study by Angulo-Sherman and Mercado-Uribe [24] found that there exists a
point in the frequency spectrum where the dielectric constant is independent
of temperature, at about 2.96 kHz. Below this point the constant increases
with temperature while it decreases with temperature below it.
16 | Theoretical background
2.2.2 The effect of voltage amplitude
When a sample, commonly liquids or liquid impregnated porous solids, is
exposed to an applied electric field mobile charge carriers will move with the
field. If the applied voltage is sufficiently high or the measurement done in
sufficiently low frequencies the carriers will have time to move and accumulate
at the sample boundaries where their movement is blocked, and given time the
bulk will be depleted of mobile charges [25]. This phenomenon, known as the
Garton effect, depend upon the path length i.e the thickness of the sample and
the drift speed of charge carriers in the sample which in turn depend not only
on voltage and frequency but also temperature.
Figure 2.3: (a) Short charge drift distance not enough for surface
accumulation, (b) Charge drift distance longer than sample thickness, giving
rise to charge accumulation. Adapted from [26].
The relation between sample thickness and applied stress is visualised in
Figure 2.3. If the distance the charges move during one cycle is lower than
the thickness of the sample, no significant reduction in conductivity due to
depletion will appear and its contribution to the dielectric loss is a straight line
with a slope of -1. If however the distance is larger than the thickness, charges
will accumulate until the voltage reverses. As accumulation appears dielectric
losses in the material are reduced as carrier movement is reduced. When
performing several consequent measurement sweeps at different voltages this
can be seen as a deviation of response in low frequencies where the imaginary
relative permittivity decreases with increasing amplitude, explained by the
Theoretical background | 17
reduction of carrier movement [26].
Another possible influence of the choice of voltage amplitude when
measuring liquids or solids is electrolysis of water. Electrolysis of water is
the decomposition of water molecules into hydrogen and oxygen gas when
exposed to a strong enough voltage and high enough temperatures. Typical
values of cell voltage in the production of hydrogen is in the range of 1.6 to
2.5 V in temperatures between 25 and 90 °C where higher temperatures allow
for lower voltages [27], while the authors neglect to specify whether AC or
DC is used, DC is assumed as it is standard practice. Thus, applying a high
voltage across a paper sample will induce electrolysis of water in the sample,
and so will the samples dielectric response change as water transforms into
oxygen and hydrogen gas.
2.2.3 The effect of temperature
The dielectric response of a paper sample depends to some degree on the
temperature at which the measurements are made. In general, an increased
temperature will decrease the restraints on the dipoles in the bulk, enabling
them to easier align with the electric field. This results in an increased
polarisability and so also an increased dielectric constant [8]. The effect is
however quite limited, about 5 % within the temperature interval 20 to 120 °C.
′′
ε however was found to decrease with increasing temperatures [9]. This
behaviour has also been observed in oil impregnated papers [28]. Additionally,
the mobility of ions increases with temperature meaning they will reach the
sample boundaries faster increasing the likelihood of boundary accumulation
[26].
Not only the magnitude of the response depends on temperature, the
frequency position of the response is also affected. In a log-log plot, the
response curve will often retain its shape but shift towards higher frequencies
with increasing temperatures [29]. If this shift is proportional to e−Ea /kT ,
T is the absolute temperature and k is Boltzmann’s constant, the relaxation
process can be described as thermally activated with an activation energy
Ea . An Arrhenius analysis is the study of this frequency shift by determining
the activation energies, where the common assumption is that the activated
process follows the Arrhenius relationship of Equation 2.14 where ωp is the
frequency of a loss peak at temperature T and ω0 refers to the same loss
peak at another temperature T0 . The higher activation energy of a process,
the stronger its temperature dependence is. It must be noted, that in a spectral
curve containing several processes, each process may have different activation
18 | Theoretical background
energies.
ωp = ω0 e
−Ea 1
(T
k
− T1 )
0
(2.14)
2.2.4 The effect of density
Both the dielectric constant and loss tangent of paper increases with increasing
density [8, 12, 30]. The effect is to be expected. Assuming no new type of
material is added to the paper, increasing its density will decrease its porosity
and thus reducing the volume fraction of air in the paper. The dielectric
constant is proportional to the density, and can be described by the ClausiusMossotti relation [31] where k ′ is the real part of the complex permittivity:
′
k −1
∝ρ
(2.15)
k′ + 2
Likewise, applying an increasing compressive stress on a paper sample will
increase its density. Morgan, studying Kraft paper, found that both real and
imaginary relative permittivity components to asymptotically increase with
′
increasing stress. If the stress increased high enough, εr will approach that of
pure cellulose as the fibres collapse [9]. It is of course possible to also increase
the density by impregnating a porous paper.
2.3
Interfacial polarisation
Charge carriers, prevalent in any conductive system, can under the influence
of an electric field move towards the electrode/sample interface where they are
blocked from further movement. On a mesoscopic scale, charges accumulate
at inner dielectric boundary layers, giving rise to what is known as MaxwellWagner-Sillars (MWS) polarisation. This may, for example, occur at the
boundaries of pores in porous material. On a macroscopic scale charges
may accumulate at the external electrodes contacting the dielectric sample,
giving rise to an Electrode Polarisation (EP). Both cases lead to a separation
of charges, in some cases over a considerable distance [32]. The separation
develops an ionic double layer, often called an electrical double layer, in
these regions creating a strong electrical polarisation and a near-absence of
electric field in the sample bulk in low frequencies [33]. These layers are
built over very small distances, down to nanometer thicknesses, creating very
high capacitances. The formation of electrical double layers is the basis of
supercapacitors [34, 35].
Theoretical background | 19
At low frequencies this effect can dominate the signal with very strong
′
′′
contributions to both εr and εr with decreasing frequencies, thus masking the
materials true response [32, 33]. Often the term Low-frequency Dispersion
(LFD) is used to describe phenomena of strongly dispersive behaviours of real
and imaginary components of a measured capacitance or impedance.
2.3.1 The Maxwell-Wagner-Sillars effect
Interfacial polarisation is observed in heterogeneous systems of two or more
phases and as an effect of differences in conductivities and permittivities in the
materials, leading to space charges accumulating at their interfaces. Contrary
to other types of polarisation, such as atomic, electric and dipolar polarisation
which are due to the displacement or orientation of bound charges in an electric
field, interfacial polarisation changes the electric field [36, 33].
The simplest model to describe interfacial polarisation in heterogeneous
materials is the electrical double layer arrangement, depicted in Figure2.4,
where each layer is characterised by a relative permittivity εi and a relative
conductivity σi [32]. The complex dielectric function then becomes a Debye
∆ε
response ε(ω) = ε∞ + 1+jωτ
with a relaxation time of:
MW S
εr1 + εr2
(2.16)
σr1 + σr2
Should the thickness of the two layers be equal, it holds that ε∞ =
ε1 ε2 /(ε1 + ε2 ) and:
τM W S = ε0
∆ε =
ε2 σr1 + ε1 σr2
(σr1 + σr2 )²(ε1 + ε2 )
(2.17)
Figure 2.4: Double dielectric layer model of the MWS effect: (a) diagram, (b)
equivalent circuit.
20 | Theoretical background
An example of dielectric response showing the MWS effect is discussed
by Schönhals and Kremer, see Figure 2.5. They studied a liquid crystalline
side group polymer, which has smectic layers (separated structures forming
a double layer). The layers create an internal phase boundary which can
block the movement of charges. Above a certain phase transition these
layers disappear, removing the double layer and no longer blocking charge
movement. The double layer can be seen to have a great influence on
the response, causing a sharp increase in real permittivity with decreasing
frequency at around 10 Hz, while this effect is largely non-present above the
phase transition. The losses are nearly ohmic below the phase transition while
they are less frequency dependent above the phase transition.
Figure 2.5: Example of the MWS effect, open circles below phase transition,
open squares above phase transition, inset shows dielectric loss, from
Schönhals & Kremer[32].
2.3.2 Electrode polarisation
Electrode polarisation is another unwanted phenomenon in DRS, most
common in highly conductive samples, which may hamper the analysis of
slow relaxation processes. The occurrence of EP effects can depend on
several factors such as the conductivity of the sample, sample temperature,
the structure of electrodes or even their composition and surface roughness
[33]. Similar to MWS polarisation, the molecular origin of EP is the build up
of charge creating an electrical double layer at the interface between sample
Theoretical background | 21
and electrode. This layer can give rise to a large capacitance in series with the
sample, which in low frequencies manifests as very large apparent dielectric
constants, typically in the range of 102 to 106 which clearly no longer reflect
any material properties of the sample, thus obscuring possible relaxations
processes. The effective thickness of the layer is given by the Debye length
(LD ) and both its relaxation strength and time scales linearly with the sample
thickness (L) [37]:
∆εEP
′′
L
=ε
;
2LD
′
′
τEP
ε ε0 L
=
σ 2LD
(2.18)
′′
The EP loss peak, εEP , appears as a frequency slope of -1 (or εEP ∝ ω −1 )
in a log-log plot, independent of sample thickness. Its derivative however,
′′
εderiv , appearing as a frequency slope of -2, shows a behaviour where an
increasing sample thickness (L) effectively shifts the EP peak towards lower
frequencies [37].
Figure 2.6: Electrode polarisation manifesting as a strong increase real part
(open circles) and imaginary part (open squares) of the complex permittivity,
adapted from [32].
In DRS one measures a system, the sum of what is connected between
the instruments output and input terminals. In order to study the dielectric
properties of the sample alone the measurements must be corrected for
phenomenon such as EP, which can be hard as the capacitance, and subsequent
impedance, of the polarisation layer can be extremely large in comparison
to that of the sample, especially in conductive samples. There are a
22 | Theoretical background
number of techniques to correct the measurements including both algorithmic
and hardware based corrections as well as comparison and substitution
methods, electrode coating techniques and the use of blocking electrodes [33].
Schönhals & Kremer suggests a fractal power law to describe the frequency
dependence of the complex dielectric function, Equation 2.19, in order to
correct measurements [32]. Here εs is the permittivity due to orientational
polarisation and λ, (0 < λ < 1), a parameter describing the fractal character
of the underlying process.
′
′′
εEP (ω) − εs = Aω −λ ;
εEP (ω) ∝ ω −λ for ω > 1/τEP
(2.19)
Other approaches to correct the measurements are to subtract the
conductivity term of dielectric response. This approach is based on the
′′
dispersion curves of the dielectric response, that is, the loss curves of ε (ω)
′
′′
[37]. Since ε and ε are related by the Kramers-Kronig relations, one of which
is Equation 2.20, both curves hold the same information about relaxation
processes, meaning that both parts of the complex permittivity ε̃ hold all
information on dielectric response.
∫
2 ∞ ′
ω0
σDC
′′
+
ε (ω0 ) 2
dω
(2.20)
ε (ω0 ) =
ε0 ω0 π 0
ω − ω02
′′
One of these techniques is based on the derivative εderiv , defined in
Equation 2.21, which approximately gives the dielectric loss of broad peaks.
For narrow relaxations, which are Debye-like, the derivative, Equation 2.22,
yields peaks narrower than the measured loss peaks, meaning that peaks in
tight proximity are more easily discriminated. A practical example of how
this technique can bring to light processes otherwise shrouded by EP is in
[37] by plotting the dispersion curve together with its derivative curve on a
frequency spectrum. Additionally, the paper provide an analytical expression
′
for the ∂εHN /∂lnω, see Equations 2.21 and 2.23 where a and b are unitless
shape parameters.
′
′′
εderiv
π ∂ε (ω)
′′
=−
≈ε
2 ∂lnω
(2.21)
′
−
∂ε (ω)
′′
∝ (ε )2
∂lnω
(2.22)
Theoretical background | 23
∆ε
}
(1 + (iωτk )a )b
′
ab∆ε(ωτ )a cos(aπ/2 − (1 + b)θHN )
∂εHN
=−
1+b
∂lnω
(1 + 2(ωτ )a cos(πa/2) + (ωτ )2a ) 2
θHN = arctan[sin(πa/2)/((ωτ )−a + cos(πa/2))]
′′
ε = Im{
(2.23)
The derivative approach has also been used to estimate the thickness of the
polarisation layers of MWS and EP induced double layers [38]. Both MWS
and EP dielectric effects show similar spectral features described by a set of
four characteristic frequencies:
′
• fon - the frequency of the onset of polarisation effects where ε begins to
increase with decreasing frequencies
• fmax - the frequency of the full development of polarisation effects, seen
′
as a saturation plateau in ε
′′
• fMWS - the frequency of a peak in ε , can also be calculated [38, 39, 34]
with sufficient knowledge of material parameters
′
• fi - the frequency position of the inflection point of the ε -curve, the
point where a curve goes from being concave to convex or vice versa
By studying the first and second derivative of dielectric response curves
both experimentally and analytically, the authors found that similar power
scaling laws can be derived for both MWS and EP effects. Additionally, a
discrimination criterion was found to distinguish between phenomena based
on the four characteristic frequencies. For MWS polarisation effects it was
found that fMWS is equal to the frequency position of the inflection point fi .
For EP effects, fMWS was found to be the same as frequency point of full
development of the polarisation effect, fmax . This means the type of effect
can be distinguished by analysing the interrelation governing the characteristic
frequencies of the responses. Additionally, as pointed out in [34], decreasing
the sample length shifts the positions of fon and fmax to higher frequencies,
similar to the effect described by Equation 2.18 and [37], without scaling the
responses.
24 | Theoretical background
2.4
Analysing and modelling dielectric response
The simplest model of a dielectric response is the Debye function, visible as
′′
a constant dielectric constant below and above the relaxation with a ε peak
at the relaxation frequency [15]. The function can be defined in time domain,
f (t), or in frequency domain, ε(ω), as a frequency dependent permittivity,
where εS is the static, or DC, permittivity, ε∞ is the high frequency limit
permittivity and τ is the characteristic relaxation time:
εS − ε∞ −t/τ
e
τ
εS − ε∞
ε(ω) = ε∞ +
1 + jωτ
1
χ∝
1 + jωτ
f (t) =
(2.24)
Debye responses are however rarely seen outside of the gas phase [14]
and polar liquids, in practice. Instead, experimental data can usually be
characterised by use of frequency dependent fractional power laws:
χ′r (ω) ∝ χ′′r (ω) ∝ ω n−1 ,
χ′r (0)
−
χ′r (ω)
∝
χ′′r (ω)
ω≫γ
∝ ωm,
ω≪γ
(2.25)
Here, γ denotes a loss peak frequency (refered to as a damping factor in
[14]), defined as the inverse of the relaxation time constant as in Equation 2.8,
describing the speed with which the material reverts to its equilibrium state.
n and m are fractional exponents, 0 < n, m < 1. This general form was first
defined empirically as the Havriliak-Negami function. Special cases have also
been identified. Setting n + m = 1 yields the Cole-Cole function; setting
m = 1 and 0 < n < 1 produces the Cole-Davidson form [14].
The Cole-Cole relaxation equation is defined as in Equation 2.26, and can
typically be found in water, PVC and pressboard. At α = 0 the response is the
same as the Debye response.
ε(ω) = ε∞ +
εS − ε∞
1 + (jωτC−C )1−α
(2.26)
Theoretical background | 25
Related to the Cole-Cole function is the Cole-Cole diagram. It is
sometimes a useful way of representing the imaginary and real parts of the
complex permittivity by plotting them on separate axises, keeping frequency
an independent variable. Materials with a single relaxation frequency will
appear as a semicircle with center on the x-axis. Materials with several
relaxation frequencies may appear as semicircles or arcs with center below
the x-axis. An example of a Cole-Cole diagram, of the permittivity of water
with a single relaxation frequency [15], can be seen in Figure 2.7.
Figure 2.7: Cole-Cole diagram of water, adapted from [15].
The equation of Davidson-Cole relaxation, typically found in mixtures of
liquids, is defined in Equation 2.27. At β = 1, the equation is the same as the
Debye response.
ε(ω) = ε∞ +
εS − ε∞
1 + (jωτD−C )β
(2.27)
The equation of the Havriliak-Negami relaxation is defined in Equation 2.28, including conduction term. At α = 0, β = 1 the equation is the
same as the Debye response.
ε(ω) = ε∞ +
εS − ε∞
σ
−j
1−α
β
(1 + (jωτH−N ) )
ωε0
(2.28)
All the models mentioned so far are based in physical principles and
assumptions in order to apply them by fitting curves, or equations, to empirical
data. It is also possible to model dielectric response using an equivalent circuit
approach. The dielectric material, viewed as an impedance is modeled as a
network of basic passive components like resistors and capacitors. Different
26 | Theoretical background
networks can be constructed, based on series and parallel RC circuits. As an
example, consider the simplified equivalent series RC circuit (valid only for a
certain frequency) of a dielectric material in Figure 2.8. The impedance of the
circuit is then:
Zeq = RS +
1
jωCS
(2.29)
Figure 2.8: Equivalent RC circuit.
The impedance of the dielectric, using C0 to denote its geometrical
capacitance, would be:
Z=
1
jωC0 (ε′ − ε′′ )
(2.30)
By equating both equations, ε′ and ε′′ can be described together with the
loss factor:
CS
C0 (1 + (ωRS CS )2
ωRS CS2
ε′′ =
C0 (1 + (ωRS CS )2
ε′′
tan(δ) = ′ = ωRS CS
ε
ε′ =
(2.31)
Among the functions, or models, mentioned the Havriliak-Negami
equation is the most versatile function for curve fitting, as it reduces to a Debye
equation when β = 1 and α = 0, a Cole-Cole equation when β = 1 and
α ̸= 0 or a Cole-Davidson equation when β ̸= 1 and α = 0 [40]. It is also
possible to describe complex curves consisting of several relaxation processes
as a superposition of several Havriliak-Negami equations, using one common
dc-conductivity term.
Theoretical background | 27
As Dhar has pointed out in [40], there exists different ways to define
the Havriliak-Negami function in literature, some of them wrong, risking a
poor fit. Common errors include letting all superimposed equations share
common α and β parameters. As these parameters define the shape of a unique
relaxation peak, they are unique to a single relaxation process and thus unique
to a single superimposed equation k. Another is to reduce the exponent 1 − αk
to simply αk . The Havriliak-Negami model, in general form as a superposition
of several equations, is presented in Equation 2.32 as defined in [40].
It is possible to design a curve fitting algorithm to optimize the fitting,
not knowing much about the parameters. It is however also possible to do it
manually, with some knowledge of what physical and curve properties each
parameter signify. A middle way is also possible, entering some known
parameters manually and optimizing over others. A dielectric response of a
single relaxation time can easily be described by a single equation, with a
single set of parameters. Several relaxation processes, visible as several loss
peaks, requires several equations and parameters, superimposed upon each
other as in Equation 2.32 where the suffix k denotes the individual relaxation.
Some parameters can easily be read graphically from the response curves.
The static permittivity, εS , can be read as the permittivity of the very lowest
frequency measured, given that it indeed is near DC or ε(f ) = ε(0). ε∞ can
be read from the very highest frequency measured, given that it is indeed of
some largeness as ε(f ) = ε(∞). Likewise, the relaxation times τk can be
read graphically from the frequency of each loss peak. It can however be the
case that only parts of a relaxation process can be seen within the measured
frequency spectrum. This means that one can read an increase in loss, or
dielectric constant, towards the boundary of the measured spectra but the peak
lies outside of it at some unknown point. As such, one cannot see the loss peak
but an estimation can be made using different loss peak frequencies to find a
good fit. The conductivity in Equation 2.32, σ, dominates the imaginary part
of the response at low frequencies, and can easily be fitted manually.
ε̃ = ε∞ +
∑
k
σ
∆εk
−j
1−α
β
k
k
(1 + (jωτk )
)
ωε0
(2.32)
Other parameters are easier to fit using an optimizing algorithm. The
curve asymmetry parameter α, curve broadness parameter β and the dielectric
strength of a particular relaxation process ∆εk , are easily calculated. When
fitting a response function, one should take note to fit both real and imaginary
response simultaneously, so that the same model described both responses
sufficiently well.
28 | Theoretical background
As pointed out by Schönhals and Kremer [32], it cannot directly be
concluded that the molecular origin of a non-Debye response is a relaxation
of several independent processes all behaving like Debye responses. The
interpretation of a superposition of Debye responses can be correct in some
cases while questionable in others where a single relaxation process is at
work behaving non-exponentially due to the features of the process itself.
Using linear relaxation theory it is not possible to distinguish between these
interpretation schemes, it is however possible to do so experimentally using
specific techniques. In cases where two individual Debye-like processes are at
work in close proximity, i.e. with similar relaxation times, but with strongly
different relaxation strengths, situations may appear where the weaker process
seemingly disappears in the wing of the stronger process. These situations may
be hard to identify visually.
When phenomena such as MWS or EP are present, as discussed above, it
is prudent to correct the measurement data to better analyse the true material
response. Both the derivative and characteristic frequencies approaches
described in Section 2.3.2 are useful tools.
Measurement Setup | 29
Chapter 3
Measurement Setup
This chapter aims to describe both the hardware and software as well as the
measurement setup and procedure used in this thesis, with enough detail as to
enable repeatability.
3.1
Hardware & Software
Having settled for frequency domain spectroscopy, there are a number of
techniques available to measure dielectric response. This chapter introduces
the measurement techniques and hardware used in this thesis.
3.1.1 Low-frequency spectroscopy - The IDAX300
In insulation diagnostics of insulators for high and medium voltage
transmission and distribution network an Insulation Diagnostic System
(IDAX), is often used. The IDAX is a diagnostic system for analysis of
dielectric materials, most commonly insulators. By studying the materials
dielectric properties as a function of frequency, it is possible to distinguish
different phenomena such as polarisation losses and leakage currents.
By applying a sinusoidal voltage of desired amplitude and frequency
across the sample, a current through the sample is generated. With accurate
measurements of the voltage applied and current generated the sample
impedance can be calculated. Depending on the sample model, parameters
such as capacitance, loss and resistance can be derived from the impedance.
The IDAX300 from Megger AB, shown in Figure 3.1, is used in this
thesis. The choice of the IDAX300 was based on availability, strengthened
by knowledge of it being well calibrated. The system is fitted with two voltage
30 | Measurement Setup
sources, capable of delivering 10 Vpeak and 200 Vpeak respectively in the
range of 0.1 mHz to 10 kHz, although the voltage range can be increased by
adding an external high voltage unit to the system. The specified capacitance
range is defined as 10 pF to 100 µF, which is expected to be well suited for this
project work. Accuracy is defined as 0.5% + 1pF [41].
Figure 3.1: The IDAX300 from Megger AB.
The impedance of the sample is calculated using Ohm’s law, where all
quantities are complex:
U
(3.1)
I
The voltage is measured by an internal voltmeter in parallel with the
sample. The current is measured by an electrometer acting as a current-tovoltage converter. An Analog to Digital Converter (ADC) is used to convert
the analog voltages to digital signals for calculations. A simple graph of how
the IDAX300 measures impedance can be seen in Figure 3.2.
There are a few different ways to model the sample in the IDAX software.
An equivalent RC-circuit, more often used in circuit analysis than insulation
analysis, available as both series and parallel models. More often used
in insulation diagnostics is the complex capacitance model, as defined in
Equation 3.2. C is a complex capacitance [41].
Z=
Measurement Setup | 31
Figure 3.2: IDAX300 measurement circuit [41].
Complex capacitance:
1
Z=
jωC
1
1
′
′′
C = Re(
), C = −Im(
)
jωZ
jωZ
(3.2)
When interested in material characterisation a material model is often
used. In order to define material properties through the measured impedance,
the geometrical capacitance of the material sample must be known. Either
this value can be provided through the IDAX GUI, or the measurement data
can be exported to some other software for processing. Using the dielectric
model, the sample permittivity is defined as a complex function describing
both dielectric constant and loss described in Equation 3.3 where C0 denotes
the geometrical capacitance [41].
Dielectric:
1
)
jωC0 Z
1
′′
ε = −Im(
)
jωC0 Z
′
ε = Re(
(3.3)
All parameters of all models are derived from the same voltage and current
measurements, meaning that they are only different representations of the same
material. Thus, several models can be used simultaneously to describe any
32 | Measurement Setup
combination of parameters.
The hardware comes with a proprietary software, a GUI, for system
control and data representation. The software runs on a separate computer,
as the IDAX300 has no human machine interface. The latest GUI version,
5.0.xx, has however been optimized for field testing, restricting much of the
configurability found in the older version 4.1.xx, therefore the old version will
be used.
Using the older version, a measurement sequence is set up in a command
file (.icf), in which all parameters, such as frequency and voltage sweeps
and representation models relevant to the measurement are defined. The
representation models can be a good sanity check, plotting the data while
measuring will give an idea whether the data look reasonable. Both GUI
versions have a simple to use interface, the older one however has the added
feature to access the control file, fully configurable, in a text view providing
settings not available in the default view.
When a measurement is made, the command file is converted to a data
file (.idf), no longer configurable but holding all setup and measurement data.
It is also possible to access the .idf-file in text view to see all formatting and
settings made for that particular measurement. The .idf-file can also be read
by other software, such as Matlab, for data processing.
3.1.2 High frequency spectroscopy - The LCR-meter
While the IDA system has a frequency range of 0.1 mHz to 10 kHz, in higher
frequencies, typically up to the MHz range, an LCR-meter is used. The LCR
used in this thesis is the B&K Precision 895 LCR-meter, capable of measuring
inductance, capacitance and resistance with a basic accuracy of 0.05% with a
frequency range of 20 Hz to 1 MHz. It is able to generate a test signal level
between 5 mVrms and 2 Vrms with changing resolution, or a current signal
between 166.7 µA to 20 mA with appropriate resolutions. The meter comes
with both USB, RS-232, LAN and GPIB ports for data export and remote
control [42].
Much like the choices available in the IDA, LCR measurements are
based on an equivalent circuit model, choice being between a series and a
parallel circuit as in Figure 3.4. For low capacitances, the parallel model is
recommended as the impedance of a capacitor is inversely proportional to
its capacitance and will dominate at small capacitances. The series model is
recommended for large capacitances using the same reasoning. Regardless
of the choice of model, the LCR will measure a complex impedance, by
Measurement Setup | 33
Figure 3.3: BK Precision 895 bench LCR.
measuring applied voltage, sample current and their phases giving both
magnitude and phase of the impedance. From this, resistance and reactance
(impedance of an inductor or capacitor) are derived, in rectangular form, and
used in either model to derive all other parameters.
Before measurements are done, the meter needs some correction to
account for residual and stray elements of the test setup. There are three modes
of correction, a sweep mode, a point-frequency mode and no correction mode.
The sweep mode is typically used, and will be in this thesis. Correcting over 48
preset frequencies, with the possibility of interpolation between preset values
to correct at each and all frequency levels. An OPEN correction, performed by
removing removing the electrodes into an open circuit, corrects for any stray
admittances of the test setup. A SHORT correction, done by shorting the test
setup, corrects for any residual impedance within the setup. Most often, the test
leads are what need to be corrected for [42]. There is an additional correction
option, the LOAD correction, where a known load, or impedance, is measured.
By entering the known primary and secondary reference values manually
before measuring at selected frequencies, an accurate correction can be made.
Lastly, there is an option of cable length selection, and while the instrument
user manual does not clearly state exactly what is changed or corrected for
based on length selection, the instrument manual of the HP 4284A LCR meter
does. The HP manual indicates that the cable selection compensates for phase
shift errors induced due to the test leads, given that the HP 16048A/D test leads
34 | Measurement Setup
of specific lengths are used [43] ∗ . The 4284A meter has compensation data
for several cable lengths installed in its internal memory, the B&K 895 does
not.
Figure 3.4: Equivalent circuit model, [42].
Among the possible parameters derived from the measured impedance, a
pair of parameters can be selected for presentation and export, a primary and
a secondary parameter. Based of choice of series or parallel model, different
combinations of primary and secondary parameters are available, a complete
list of pairs can be found in the manual.
3.1.3 Equipment setup
The test cell used, shown in figure 3.7, is a custom made parallel plate Kelvin
guard-ring capacitor consisting of a high voltage electrode, a measurement
electrode and a guard-ring separated from the measurement electrode by a
narrow air gap. A schematic diagram of the test cell is presented in Figure 3.5
including the dimensions of the components, an air gap of 1 mm separates
measurement electrode and guard ring.
The measurement instrument output voltage is applied on the top electrode.
The guard ring is used to connect to instrument reference potential. The
measurement electrode is connected to the measurement instrument input
terminal. All electrodes are made of stainless steel and are encased in Teflon
discs. The measurement electrode can be spring loaded or supported by any
suitable elastic material to assert a fixed pressure on all samples.
∗
Understandably, it may seem odd to refer to a very old meter, of another brand, thinking the
inner workings are the same. Indeed, it is assumed that the fundamental working principles
of the two meters are the same, which seems very reasonable comparing manuals. It is also
the fact that an LCR of the old model is available at the KTH HV lab for practical comparison
between them. It can also be noted that the old LCR manual is four times as long (at an
impressive 460 pages), and much more detailed than the newer one.
Measurement Setup | 35
Figure 3.5: Schematic diagram of the Kelvin guard-ring parallel plate test cell,
measurement electrode can be spring loaded.
In order to achieve a constant humidity level, thus keeping the moisture
content of the samples constant, a sealed
plastic box was constructed, within
which the RH could be controlled and
the test cell placed. The box was fitted
with plugs to connect leads to the test
cell and measuring equipment, as well
as holes for rubber gloves for being able
to change samples and connect cables
without letting in any outside air. The
box can be seen in Figure 3.6, equipped
with test cell, a hygrometer, a stand
holding paper samples, torque wrench
and rubber pieces for pressure control.
The only piece of equipment not showing
in the figure is a Petri dish containing
either of the salt solutions. The hygrometer measures both temperature and
RH continuously, allowing its reader,
consulting the equilibrium charts, to
know the moisture content of the paper
sample, given that sufficient time has
elapsed for an equilibrium to settle. The
torque wrench was used together with the
rubber pieces and metal screws to assert
a constant force on the samples, higher
Figure 3.6: Plastic box constructed
to create a sealed environment.
Includes a) stand holding samples
for conditioning, from top to bottom Al3+, Ca2+, H+, Mg2+, Na+,
AMetek, AM400, HTP, b) hygrometer, c) bottom of measuring
electrode, d) brown rubber pieces
and e) torquemeter.
36 | Measurement Setup
than what the original spring loading of the cell could provide, see Section 3.5
for a further discussion. By applying a constant torque of 1 cm ∗ kg (the unit
of the torque meter) while tightening the screws, a constant force is applied
on the sample and thus a constant pressure, allowing for a measurable way to
assure all samples were measured under the same applied pressure.
During medium and wet MC level
measurements the test cell was placed
inside the climate container and was
connected to the measurement instrument using 1 m coaxial cables and plugs
mounted in the container wall. Short
cables on the inside of the box connects
the test cell with the wall mounted
plugs. The coaxial shield conductors are
connected for a common reference. An
example of the equipment setup can be
seen in Figure 3.8 which also presents
the climate chamber, further presented
in Figure 3.6. The LCR meter was
connected to a laptop computer using a
GPIB (General Purpose Interface Bus)
to USB connector, the IDAX300 was
connected to the laptop using a USB
cable. The test cell spring was replaced
by elastic rubber pieces in order to create Figure 3.7: The test cell used,
a higher pressure applied on the sample, spring loaded in the picture as indicated by the elevated measurement
see Section 3.5 for further discussion.
electrode. Includes a) measuring
electrode, b) guard ring, c) high
voltage electrode and d) encasing
teflon disks.
Measurement Setup | 37
Figure 3.8: Equipment setup with both measurement instruments and climate
chamber connected through coaxial cables and plugs mounted in the container
walls.
In order to condition the samples to a very dry MC level, a vacuum oven
was used, visible in Figure 3.9. The oven is fitted with a programmable
Eurotherm 3504 temperature PID controller, allowing the user to create
custom schedules including both ramping up and down temperatures over a
selected number of cycles with variable segment lengths as well as regulating
output power instead of temperature. However, the oven lacks active cooling
meaning the lowest temperature achievable is its ambient temperature, this
does not affect the thesis at hand as there is no need for lower temperatures.
The oven is connected to a separate pump standing on the floor beneath it
and not visible in the figure. In addition to the built in pressure gauge an
additional, digital, gauge was installed on top of the outlet visible to the top
left of Figure 3.9, giving both a confirmation of the built in meter as well as a
reading with higher resolution. In the figure the additional gauge is showing
2.67 Torr which equals about 3.6 mBar. The oven consistently achieves and
holds <5 mBar. As the test cell was placed, and all measurements at the
dry MC level performed, in the oven, it was interfaced with BNC connectors
on its backside to allow coax connection to the test instruments. Inside the
oven, coax cables connected to the interface were split, extended and fitted
with plugs to allow connection to the test cell. Care was taken to assure the
internal wiring were well insulated as the cables were bound to come into
contact with metallic surfaces on the inside of the oven, which were assumed
to be grounded through the oven chassis.
38 | Measurement Setup
Figure 3.9: Programmable vacuum oven used to condition the samples to a
very dry MC level. In additional to the built in pressure gauge an additional,
digital, gauge was used, visible in the top left, to get a more reliable pressure
reading.
3.2
Measurement procedure
Initial measurements were carried out on a selection of papers in room ambient
conditions, testing both that the setup worked as intended and giving the
possibility to adjust any parameters based on the initial results, see Section 3.5.
After the initial test, measurements were performed in a controlled
environment to study the effect of three different MC levels as well as four
different temperature levels under vacuum. All paper samples were studied
under three MC levels, a medium, a wet and lastly a dry level. At the dry level,
measurements were performed at four temperature levels of 115 °C, 85 °C,
45 °C and 26 °C where 26 °C was chosen due to ambient temperature of the
environment. Since very dry paper easily becomes brittle and may break or be
damaged, measurements at the driest level were performed last to minimize
the risk of ruining the samples or changing their material properties. Both
RH and temperature were logged at each measurement. At all MC levels,
measurements were done at two different voltage levels, 25 mV and 500 mV,
in order to study any effect of voltage amplitudes in this range. After this, a rerun of the lowest voltage level was done at to test for congruence between the
first and last measurements, detecting any possible material property change
Measurement Setup | 39
due to applying the higher voltage level.
The samples were prepared as described in Section 3.3, the setup
connected, corrections described in Section 3.1.2 were done and the
measurements run.
All measurements were done in the order of decreasing frequencies and
increasing voltage amplitudes in order to minimize the effect of any potential
sample influence, such as interfacial charge accumulation, of low frequencies
and high voltages. It is also advisable to perform measurements at as low
applied voltage as possible, unless the intended study demands otherwise,
limited of course by the instrument accuracy, signal stability and the influence
of noise, in order to avoid phenomena such as the Garton effect mentioned
in Section 2.2.2 and the onset of electrolysis of water in the sample. After a
successful measurement sweep, all data was exported to Matlab for processing
and graphical representation.
3.3
Sample preparation
The samples were prepared by first cutting them into 9 by 9.6 cm shapes, then
chamfering the corners to create octagons to better fit the test cell while still
being large enough to more than fully cover both electrodes. Then the sample
thickness was measured, the samples weighed and their densities calculated.
In order to measure the samples under both medium and wet MC levels, the
papers were conditioned in the climate chamber for at least 72 hours, deemed
enough to assure a stable equilibrium with air humidity. As a reference, the
example in Section 2.2.1 using Equations 2.12 and 2.13, found it would take
about 3 hours to reach a MC equilibrium of 7 % in room temperature. Salt
solutions were used to regulate the RH of the chamber, further described in
Section 3.3.2. All papers were conditioned simultaneously and since the total
time to measure all samples at a given RH takes several days, the samples
measured last were conditioned for about a week longer than the first one. The
climate chamber RH was controlled several times daily to assure it was steady
over the whole time period, thus guaranteeing that all papers were conditioned
to equilibrium in the same conditions. Since an equilibrium was assumed to be
reached after 72 hours, the increasing conditioning time of the later samples
compared to the ones measured first should have no effect on the dielectric
response. Together with the samples, paper strips cut from each corresponding
paper sheet as the samples were conditioned in the climate chamber. After
conditioning, the moisture content of a sample was determined by Karl Fischer
titration on its designated paper strip. This process was used for both the
40 | Measurement Setup
medium and the wet MC levels. A further description of the Karl Fischer
procedure is found in Section 3.3.3.
In order to achieve very dry samples, the programmable vacuum oven
presented in Section 3.1.3 was used. Two paper samples were conditioned
simultaneously, placed on Petri dishes next to the test cell inside the oven.
The papers were conditioned under vacuum at 115 °C for 24 hours before any
measurements were done. After conditioning, the vacuum was broken and
the oven door opened, a sample was mounted in the test cell after a lid was
placed on the Petri dish containing the other sample. After mounting, the
oven door was closed and vacuum restored after which the samples were reconditioned for an hour to draw out the moisture gathered during mounting.
After re-conditioning measurements were performed. After measurements
were finished, the oven was again opened and vacuum broken to change
sample, after which the samples again were re-conditioned for an hour before
starting any measurements. This procedure was repeated for four different
temperature levels, 115 °C, 85 °C, 45 °C, 26 °C, setting the oven controller to
the appropriate temperature each time.
All dry MC measurements were done inside the oven, at set temperatures
and vacuum. However, in order to determine the MC level of the samples after
conditioning, the vacuum must be broken and the sample removed from the
oven, weighed and placed in a methanol bath. As the papers would be very
dry, entering an atmosphere with some ambient RH, they would quickly absorb
an appreciable amount of moisture from the air during handling before being
placed in the bath. This means that, with the equipment at hand, there is no
reliable way to accurately measure the moisture contents of the samples after
the dry conditioning. Therefore, no MC determination was done at this MC
level. It was however expected that the samples would be dry to a level well
below 1 % MC. Consulting the Oommen charts in Figure 3.10, even without
vacuum, paper in an environment of 100 °C with 5% RH would have a MC
below 0.5 %.
3.3.1 Sample geometry
The geometrical capacitance formed by the sample was calculated as in
equation 3.4, where d denotes the sample thickness and r the measuring
electrode radius. 0.5 mm is added to the radius, corresponding to half the
air gap between measurement electrode and guard ring, in order to account
for the field lines emanating from the high voltage electrode above the air gap
ending in the measurement electrode. It is assumed that half of the field lines
Measurement Setup | 41
emanating from this area end in the measurement electrode while the other
half ends in the guard ring. See Section A.2 for a further discussion on this.
π(r + 0.5mm)²
(3.4)
d
Accurate measurements of sample thicknesses are crucial, as the
calculated dielectric constant is directly proportional to the sample thickness
through the geometrical capacitance, as indicated by Equation 3.5.
C 0 = ε0
Cmeasured
Cmeasured
=
d
(3.5)
C0
ε0 A
This relation implies that, for example, a 5 % error in measured thickness
will give an equally large error in dielectric constant, even though the
capacitance is measured perfectly correct. Since paper typically has a
somewhat rough surface, owing to being made out of unaligned fibres, a
true and constant thickness across the papers surface will be impossible to
determine. It is therefore useful to take an average of several measurements.
A micrometer, a Shahe Ip165 Digital Electronic Micrometer, was used to
measure the thickness. The ion-changed papers had pressed at 400 bar for
about 5 minutes after production to make their densities more uniform. It was
however expected that the papers would expand a bit over time, to regain some
of their original form. It was also expected that the thickness be somewhat
dependent of moisture content, which in turn depends on the environments
RH and temperature. Therefore, the thickness values used for all calculations
were measured just before starting the whole measurement produce, meaning
they were measured only once and not for example between conditioning
stages. The thicknesses were found as an average of 10 measurements.
Additionally, the thicknesses were measured at multiple dates to track any
possible expansion of the papers, but only the last measurement was used.
The grammage of all samples was also calculated, as the weight per surface
area. All thicknesses, densities and grammages can be found in Table 3.1.
εr =
3.3.2 Humidity control
In order to study the effect of moisture on the papers dielectric characteristics,
three MC levels at room temperature were deemed sufficient; a medium level
of about 6-8 % MC. A wet level of about 12-13 % MC, a dry level below
1 %. Two salts solutions were chosen to generate the medium and wet MC
levels, presented in Table 3.2, with their corresponding humidity levels at
temperatures around indoors climate. Dry MC was achieved using the vacuum
42 | Measurement Setup
Table 3.1: Sample thicknesses and densities.
Sample
Thickness [µm]
Density [g/cm3 ]
Grammage [g/m2 ]
Al3+
Ca2+
Mg2+
Na+
H+
AMetek
AM400bar
HTP
167.8
153.0
153.0
147.5
215.7
94.4
164.5
197
0.6227
0.6595
0.6634
0.6804
0.5657
0.6581
0.6351
1.2713
104.489
100.904
101.500
100.359
122.021
62.125
104.474
250.446
oven.
Table 3.2: Relative humidity values for different salts and temperatures, data
from [44].
RH [%]
T [◦ C]
20
25
30
Potassium Carbonate
43.16 ±0.33
43.16 ±0.39
43.17 ±0.50
Potassium Nitrate
94.62 ±0.66
93.58 ±0.55
92.31 ±0.60
Paper is a hydrophilic material, rather quickly absorbing water from the
surrounding environment which potentially poses a problem when wanting to
isolate some variable to study. Measuring the influence of moisture in paper
on the papers dielectric response, it is crucial that the moisture content remains
constant during measuring. In practice this means also a constant relative
humidity of the surrounding air.
A common way of accurately controlling the humidity is through the use
of a chemical system in a sealed environment. There are a number of chemical
systems available for this purpose, such as aqueous sulphuric acid solutions,
glycerine and water solutions and both single and binary salt solutions [44].
By changing the concentration of the solutions, the humidity can be adjusted.
There are however a number of problems with the chemical systems, for
example sources and sinks of moisture such as leakage through the system
boundaries must be controlled. The solution concentrations must also be
measured and controlled. At a given temperature, the concentration of a
Measurement Setup | 43
(a) Freundlich isotherm for Kraft (b) Moisture in wood pulp as a
paper, taken from Oommen [45].
function of relative humidity, drawn
by Oommen based on Jeffries data and
presented in Du et al.
Figure 3.10: Oommen charts on the relation between moisture content in Kraft
paper versus temperature and relative humidity of surrounding air.
saturated salt solution is fixed, and saturation is easily determined by the
presence of solid phase solute. By adding additional solute, the solution will
remain saturated even in the presence of minor sources or sinks. Due to this
chemical systems are often favored in humidity control.
A single solution offers a single RH value at a given temperature, different
salts however offer different RH values at the same temperature. Therefore,
by selecting different salts, different humidity levels can be achieved and thus
also different moisture contents in the paper. It must be mentioned, that the
solution referenced here is the mixture of a salt and distilled water. Wanting
a high accuracy in moisture conditioning, it is important not to dilute the salt
with ions and salts solved in the water added to create the solution as these
may change the moisture equilibrium levels of the solution. Distilled water
was produced and provided by the laboratory staff at KTH.
44 | Measurement Setup
For the purpose of this project, a single salt system was deemed sufficient,
providing known RH values at known temperatures. Greenspan [44] carried
out an extensive compilation and critical analysis of a wide range of commonly
used salts. At a certain RH each material will, over time, reach a moisture
equilibrium with its surroundings. Isotherm moisture equilibrium charts can
be used to determine the moisture content of a material as a function of RH
for a given temperature. In 1984 T. V. Oommen produced what would be
known as the Oommen curves, revising the legacy Piper charts which relate
the water content and vapour pressure of a selection of cellulose materials.
Oommen produced a set of charts, based only on data from Kraft paper, from
which the moisture content of Kraft paper could be read knowing the vapour
pressure and temperature, known as isotherm equilibrium charts or Freundlich
isotherm charts. Oommen produced charts for both Kraft paper and paper-oil
systems, his chart for Kraft paper is presented in Figure 3.10a.
Oommens chart is however restricted to somewhat low vapour pressures,
which stands to reason considering they’re made for transformer applications.
Wanting a broader range of vapour pressure and or water contents, some
complementary chart is needed. Du et al [18], in their article on moisture
in paper-oil systems, reviews a set of equilibrium charts. Among the charts
presented is a Moisture in paper vs Relative Humidity chart, drawn by
Oommen based on Jeffries [46] data, ranging from 0 % to 100 % RH. The
chart, presented in Figure 3.10b, is not very useful for very low humidity
or moisture values, but serves its purpose as a complement to the chart in
Figure 3.10a well.
Having decided what moisture content in the papers are desired, one then
consults the isotherm equilibrium charts to read what RH value is needed.
Since different papers are structured differently all unique papers will have
unique isotherm charts. The papers to be studied in this thesis are novel and
no such charts exists, it is however expected that they roughly will follow the
Kraft paper charts discussed here. Thus, the Kraft paper charts will be used
as an indicator of what MC and RH pairs to use. Knowing the RH value,
one can then decide upon which salt solution is best suited, based on tables
such as those provided in the work of Greenspan, showing which salt solution
yield what RH. Additionally, consulting the isotherm equilibrium charts, the
temperature can be altered in order to reach the desired moisture content using
for example a climate chamber.
Equilibrium charts can often hard be to read precisely, offering a
comparatively low degree of accuracy. For more exact readings, more accurate
methods are needed. They are however very useful for getting a good
Measurement Setup | 45
indication of the moisture content of the sample, telling the reader when to
perform more accurate measurments. Karl Fischer titration offers an easy
and quick method of determining the moisture content precisely but requires
a bit of the paper sample to be lost at each titration process. The combination
of charts and titration is therefore an effective method, reducing the need for
several titrations and thus reducing the amount of samples lost.
3.3.3 Moisture content determination
Karl Fischer titration is a commonly used method of moisture content
determination, using either volumetric or coulometric titration. Both
techniques operate based on the same working principle, a chemical reaction
between iodine, water and sulphur dioxide, described by R. W. Bunsen:
I2 + SO2 + 2H2 O → 2HI + H2 SO4
(3.6)
In 1935 Karl Fischer discovered that this reaction could be used for
water determination in a non-aqueous system containing an excess of sulphur
dioxide. He used methanol as a solvent and pyridine to neutralise the acids,
needed to achieve an equilibrium shift to the right. The formula was later
improved upon and generalised, as it was discovered that methanol can be
replaced by other alcohols and pyridine replaced by other bases. A general,
standard, formula for the Karl Fischer reaction was proposed by E. Scholz,
presented in the Karl Fischer GTP∗ brochure from Mettler Toledo [47], where
different alcohols (ROH) and bases (RN) can be used:
ROH + SO2 + 3RN + I2 + H2 O → (RNH) · SO4 R + 2(RNH)I
(3.7)
The choice of technique depends on the expected water content.
Volumetric titration is suitable for samples where water is present as the main
component, while coulometric titration is suitable when water is present only
in trace amounts, in the magnitude of some percents. Since the water content is
expected to be low in the paper samples under study in this thesis, coulometric
titration is preferable.
In coulometric titration, a two electrode setup, the iodine is generated
electrochemically by anodic oxidation in the coulometric cell, at a generator
electrode:
∗
Good Titration Practice (GTP) brochure
46 | Measurement Setup
2I− → I2 + 2e−
(3.8)
The negative iodide ions release electrons at the anode forming iodine
which reacts with the water in the cell. At the cathode, or measuring electrode,
positive hydrogen ions are reduced to hydrogen, and a salt is added to promote
hydrogen production. Ammonium ions (NH+
4 ) are reduced with the formation
of hydrogen and a free amine. In this thesis, a Coulomat AD solution from
HYDRANAL is used as titration solvent, allowing the user to only add the
sample and run a chosen titration method to find the water content. The amount
of water titrated by this technique is determined by the amount of electrical
current, measured in Coulomb (ampere seconds), used to generate iodine.
Knowing the current needed to produce one mole of a substance requiring
one electron and measuring both time and current, it can be calculated how
much water has reacted with the iodine.
Figure 3.11: Coulometric Karl Fischer titrator C10S from Mettler Toledo and
precision scale also from Mettler.
Both titration techniques use a bipotentiometric indication, or a two
electrode potentiometry. A small constant AC current, called a polarisation
current, is applied to a double pin platinum electrode. As long as iodine reacts
with water, there is no free iodine in the titration solution. When all water
has reacted with iodine, free iodine will appear in the solution, causing ionic
conduction requiring the applied voltage to be reduced in order to keep the
Measurement Setup | 47
polarisation current constant. When the voltage drops below a certain value,
the titration is terminated and the water content deemed determined [47].
The titration method is possible only when the water in the sample is freely
available, which is not the case with solids when water is bound. Bound
water may occur in different ways, for example entrapped in the substance,
part of crystallisations such as sugar or bound in capillaries (which is often
the case with biological samples). To free the water bound in solids, they
can be crushed, dissolved and or bathed in a dry extraction solution for a
sufficient amount of time for the solution to absorb all moisture from the
solid. The solution, for example methanol, can then be used in the titrator.
It is important that the solution is dry, so that only, and all, water from the
solid is measured [48]. Since Karl Fischer titration is a destructive method,
any solid measured is ruined. In order to not ruin the whole paper samples,
small pieces of them were cut from the sheets not needed in the test cell, and
placed alongside the main sample in the moisture conditioning process. The
small designated paper strips could then be used in the titration procedure
without harming the sample to be used in the test cell. The titration equipment
used is the Coulometric KF Titrator C10S from Mettler Toledo, presented in
Figure 3.11, and a brief component declaration is presented is Figure 3.12.
The basic titration procedure was performed in the steps described below, a
full procedure together with a procedure on how the equipment was emptied
and cleaned when the solvent bottle was full can be found in Appendix C:
1. Two identical dry beakers were prepared with an equal and known
amount of methanol solvent.
2. A paper sample were cut, weighed and bathed in the solvent containing
beaker for between 12 and 13 hours to extract all water from the sample.
3. After extraction time, a titration was performed on the solvent from the
beaker with no paper sample as reference (even dry liquids will contain
some amount of water, and some will drift in during extraction).
4. Titration was performed on the solution containing solvent and paper.
5. Knowing the amount of paper and solvent (in grams) and both the
residual water in the solvent and the water content of the solution
of solvent and paper (in grams) the water content of the sample was
calculated in ppm or %.
An Excel spreadsheet, provided by the lab staff, for calculating the
moisture contents of the samples, as either ppm or % was used, in which the
48 | Measurement Setup
titration results and measured weights were used as input. The principle for
external extraction of water from solids is that the water amount in the solution
(in grams) after extraction is equal to the water amount before extraction,
which can be described as:
Wtot · (mL + (mp · Wp )) = WP · mp + WL · mL
(3.9)
Where Wtot denotes the water content of the supernatant extraction solvent,
in percent or ppm. Wp denotes the water content in the sample gathered from
the Karl Fischer method while WL is the water content of the solvent (methanol
in this case), both either in percent or ppm. mL is the amount of solvent and
mp the amount of sample used in the extraction, both in grams. From this,
rearranging the terms, an expression for the moisture content of the sample
can be defined. In ppm the following equation, where x denotes the measured
water content WT OT , is found:
Wp (ppm) =
106
mL WL mL
(x
−
) = MC (ppm)
6
10 − x mp
mp
(3.10)
Figure 3.12: Coulometric Karl Fischer titrator C10S components, from [49].
Measurement Setup | 49
3.4
Data collection and treatment
Data collection for the lowest frequencies, using the IDAX300, was done
using the IDAX 4.1.64 software. A control file was written for use in all
measurements using the IDAX, in which amplitude and frequency range
could easily be adjusted when needed. The IDAX data file, the .idffile, was saved to later be read in Matlab. The LCR meter can also be
controlled remotely, meaning that only the circuit connections of OPEN and
SHORT corrections needs to be done manually. The meter was controlled
using a simple Matlab script using Standard Commands for Programmable
Instruments (SCPI) commands over the GPIB using a GPIB-USB-HS device
IEEE 488.2 compatible, and measurement data was saved as .mat-files.
Both instruments measure impedance, from which capacitance and
dissipation factor are derived by the instrument. In Matlab, permittivity was
calculated, curves plotted and models fitted. All measurement files and their
corresponding conditions were logged in a run card in Excel for keeping track
of measurements and environmental conditions. An example of the .icf file
configuration can be seen in Section D of the Appendix. The Matlab files are
multiple and cumbersome to present in an easy-to-read fashion but are gladly
supplied upon request.
3.4.1 Model fitting
In order to model the measured dielectric responses, the Havriliak-Negami
function was chosen due to its versatility. The function, described in
Section 2.4, allows its user to both choose the number of processes to
superimpose and to enter certain parameters manually while others can be
defined by a curve fitting process. By first defining the function, with an
appropriate number of relaxation terms, one can then fit this function to the
measured response curves of a given sample using a fitting algorithm. In this
thesis, the built-in Matlab nonlinear least-squares solver called lsqcurvefit was
used. By default the solver will use a trust-region-reflective algorithm to solve
an optimisation problem minimising the sum of squares of the components.
When the sum of squares is zero, the system of equations is solved. The solver
requires an input function, an array of start guesses and an array to fit against
e.g. of measurement data. For a more detailed description of the algorithm
the interested reader is referred to the Matlab documentation.
When curve fitting complex functions one must fit both real and imaginary
parts of the function simultaneously, when both parts share at least some
50 | Measurement Setup
parameters which are optimize for. In this thesis, the complex HavriliakNegami function, as defined in Equation 2.32 was split into a real and an
imaginary function, both passed to the curve fitting algorithm, separately.
With two arrays of parameter estimates, the best fitting one, or a combination
thereof, can be chosen as parameter start guesses to be passed again to the
algorithm to create a final fit. The Havriliak-Negami function depends on a
number of parameters, of which a subset are entered manually and others are
optimized for, passed as variables to the solver algorithm. Both εS , ε∞ , σ and
the time constants τk were entered manually while αk , βk and the dielectric
strengths ∆εk were optimised for. The curve fitting Matlab script runs as
follows:
• Prompt user which sample to fit, read medium MC data files of that
′
′′
sample and calculate ε and ε arrays
• Prompt user how many relaxation processes to use, define HavriliakNegami function with corresponding number of relaxation terms and
start guesses and parameters bounds
′
• Find εS from lowest frequency data point of ε array and ε∞ from
′
highest frequency data point of ε array, find dc-conductivity from
′′
lowest frequency data point of ε array
• Enter relaxation time constants
• Pass function, start guesses, frequency array and measurement data
array to lsqcurvefit-function, enter output parameters into HavriliakNegami function and plot fitted curves
• If fit not good enough, adjust number of relaxation time processes or
their time constant values
3.5
Assessing test setup accuracy
In order to verify the accuracy and reliability of the test setup, initial
measurements were performed in ambient conditions on some of the ionchanged and reference samples using the original spring loading of the
test cell, as in Figure 3.7, where a spring is placed beneath the measuring
electrode in order to assert a constant pressure on all samples. The results
raised some concerns as the measured permittivities were significantly lower
than expected, especially on the polymer reference samples used, Kapton
Measurement Setup | 51
from DuPont with well defined reference values available in manufacturer
datasheets. No reference values were available for the paper samples. This
led to an investigation as to what the cause of the poor results could be.
Measurement instruments, test cell and test setup up were investigated and it
was concluded that both instruments and the test cell itself were not the issue.
However, it was found that the most likely cause of the measurement errors was
a poor contact between sample and electrodes. Additionally, it was found that
the original spring loading of the test cell could be exchanged for rubber pieces
placed underneath the measuring electrode in order to increase the pressure
asserted on the sample, which both alleviated the issue of poor contact to some
degree and gave better results. Therefore the spring, previously mounted on
the measuring electrode as in Figure 3.7 was removed and 6 rubber pieces
were used to generate pressure henceforth, as in Figure 3.6. It was concluded
that, while this correction did not entirely solve all problems it showed two
important things. Firstly, the cause of the poor initial measurement values was
most likely an issue of poor contacting, and secondly, that the issue worsens
the thinner the sample thickness is. With thinning samples, the ratio between
air gap between sample and electrode increases if the sample and or electrode
roughness is constant, thus increasing the error introduced by poor contacting.
It must however be noted, that generating a higher compressive force on the
sample introduces new uncertainties. Unless the sample thickness can be
accurately measured while mounted in the test, with a certain compressive
force applied, it cannot be made certain that at least part of what is seen as an
alleviated issue of poor contact is not due to an overestimation of the sample
thickness. An overestimation of thickness would results in an equally large
overestimation of dielectric constant. It is not expected that the thickness of the
polymer samples would decrease very much. However this might be more of
an issue with the paper samples due to the fibrous nature of cellulose materials
and the porosity in the paper construction.
The polymer samples should ideally give very accurate measurement
results, perhaps with some slight deviations through different measurement
conditions between manufacturer and what was performed in this thesis, such
as ambient RH. These are also the only samples where one can confidently
say that the measurement data is off and as the polymer data is off, it is safe
to assume that the paper data is also off, how much so is unclear as there are
no reference values available. However, the papers are generally a fair bit
thicker than the polymers, and as the issue appears to lessen with growing
thicknesses it can be assumed that the paper data should be somewhat less
off than the polymer data. Paper is a naturally porous material, and a perfect
52 | Measurement Setup
contact will never be achieved unless the sample somehow is mechanically
altered and/or smoothened out or different electrodes or methods are. Dealing
with impregnated paper is much easier, as the impregnation will grant a good
contact.
While the correction using rubber pieces did alleviate the issue, it did
not solve it completely. With the equipment and time left available it was
decided to proceed with the thesis regardless. Ideally, another test setup and
or method, such as the non-contact method proposed in [26], should be used
when measuring very thin and porous samples, such as those in this thesis. The
interested reader is implored to read Appendix A where the study leading up to
these conclusions is presented. This is somewhat of a result in and of itself, as
both test setup and method were expected to be suitable for the measurements
intended in this thesis.
While the investigations on the test setup showed the data is not entirely
reliable, that is, whether it actually is a measure of the quantity to be
measured or only a partial measurement or even a measurement of the
quantity plus some additional components, the accuracy of the data can still
be good. When the data is reproducible, it is accurate. However, there
still may be constraints as to what conclusions can be drawn from the data
as the data is dependent of e.g. test setup and method. The instruments
measure more than simply a sample, they measure a system consisting of
everything connected between input and output terminals as well as for
example stray capacitances to grounded elements in the test setup vicinity
or even background noise. The measurements of the known capacitors, of
Appendix A, does indicates a good accuracy, and some additional steps can
be taken. Before any measurements are done using the LCR meter both OPEN
and SHORT corrections are performed, no cable length correction was used,
to increase accuracy. The meters test speed was to the slowest setting using
the SCPI command ”LONG”∗ as measurements are generally more stable and
accurate at slower speeds. The test speeds is determined by several factors,
both the Analog-Digital conversion integration time, average test time per
test, measurement delay (between start up and start of measurement) and the
display time of test results. Both fast and medium test speed settings will
automatically be slowed down below 10 kHz [42]. It is also possible to set
the number of samples to use for averaging before a measurement is done,
i.e. how many samples are taken at a certain frequency point. This setting
∗
”LONG” is actually never specified in the instruments programming manual, which
specifies ”FAST”, ”MED” and ”SLOW”. ”LONG” however also sets the speed to ”SLOW”
and is compatible with the older LCR meter.
Measurement Setup | 53
can also be set remotely, but due to output buffer issues a work-around was
used where the instrument was set to repeat and export measurements at a
given frequency point so that the averaging could be done manually in Matlab.
Three samples per frequency point were used for averaging. In the IDAX
control files, the ”IntegrationMode” parameter was set to ”Auto”, meaning
multiple measurements are taken until satisfied with stability. On ”Auto” the
tolerance is set by the ”Accuracy” parameter, which was set to ”High”. It is
also possible to do averaging of several samples at each data point, but due to
the high time demands of low frequency measurements only one sample per
point was utilised.
54 | Results and Analysis
Chapter 4
Results and Analysis
In this chapter the measurement results are presented and analysed. The results
are divided into five sections the first three of which present the measured
′
′′
response, in the shape of ε , ε and tan(δ) curves, based on MC level. To
′
easier compare responses at a given MC the ε curves are plotted together,
′′
likewise the ε and tan(δ) curves are gathered into one plot respectively. In the
following section the influence of MC on dielectric response is presented. The
section on dry MC also contains responses measured at different temperatures
in the dry condition. In the last section the measured responses are modelled
by curve fitting.
4.1
Medium moisture content
Medium MC conditioning was performed with the use of a potassium
carbonate salt solution placed in the climate chamber. The expected RH of
43% was achieved and stable during the whole measuring period, varying
at most 1% for short times. In connection to initializing a measurement
sweep, Karl Fischer titration was performed on the designated paper strips of
the corresponding sample. Two paper strips per sample were used, bathed
in separate beakers of dry methanol, weighing between 120 and 520 µg
depending on sample density, all strips were of similar sizes. 40 ml dry
methanol was used per beaker. Two titrations were performed per strip,
totalling four titrations per sample, giving four MC data points to average over.
All moisture contents are presented in Table 4.1.
The gap between the lowest MC, measured in weight percentage (wt%)
AMetek at 6.31 wt%, and the highest, Al3+ at 9.08 wt%, is 2.77 percentage
points. All strips went through the same process, bathed in methanol from the
Results and Analysis | 55
Table 4.1: Medium MC levels of all samples, temperature was kept at 23 °C
and RH at 44 % during the conditioning period. Sample sequence from to
bottom is the same as the measurement sequence.
Sample
MC beaker 1
[wt%]
MC beaker 2
[wt%]
∆ MC
Average MC
[wt%]
Al3+
Ca2+
H+
Mg2+
Na+
AMetek
AM400
HTP
8.88
7.77
7.99
8.51
6.53
5.95
6.74
6.53
9.28
7.97
7.32
7.05
6.51
6.67
6.82
7.23
0.4
0.2
0.67
1.46
0.02
0.72
0.08
0.7
9.08
7.87
7.66
7.78
6.52
6.31
6.78
6.88
same bottle for an equal amount of time. It might be the case that different
papers, especially the ion-exchanged papers, both or either absorb moisture
from the air to different degrees and bind this moisture with different strengths
thus releasing it to the methanol to varying degrees. The interaction between
cellulose, porosity, ion contents and methanol is not known, nor is it known
whether exactly the same amounts, either in volume, number or weight, of ions
were used in the ion-exchange. However, the use of two strips, two beakers
and four total titrations per sample should ensure robust results, minimizing
the risk that some disturbance during the Karl Fischer procedure introduce
substantial errors. It is therefore concluded that the differences in MC level
of the ion-exchanged samples likely are due to the ion-exchange and not the
Karl Fischer procedure, even though the paper samples originate from the
same pulp. In other words, the ion-exchange also likely changes the papers
hydrophilicity, i.e. its capacity to interact with water.
It is also worth noting that, for most of the samples, the differences in
measured MC between beakers, ∆MC, is relatively small, < 1%. Ideally
there would be no difference at all, but that is hard to achieve in practice as
all quantities are small, the titration method sensitive and even minor external
influences may have a large impact on the outcome. The largest difference can
be found in the Mg2+ sample, where ∆MC is 1.46 percentage points, or about
17 % of the lower value. It is not clear what the cause of this difference may
be, likely is some external influence during the titration procedure. It can also
be that the difference would shrink if larger paper strips were used, resulting
in more moisture in the methanol solvent and thus more moisture to react with
56 | Results and Analysis
during titration.
The medium MC response curves of all samples, presented in Figures 4.1
through 4.11, exhibit similar behaviour and some features are common
between them. In the high frequency region the dielectric constant flattens out,
approaching a constant value, or a curve with zero slope, as may be expected.
The settled values are all around 2 with the exception of the HTP sample with
a dielectric constant of slightly over 4. Additionally, in the medium frequency
region of all samples a diffusion process is noticed through its characteristic
slope of -0.5. Both ε∞ and εS values of all samples can be found in Table 4.3
′′
in Section 4.5. The measured loss curves, ε curves, exhibit a small increase
towards the highest frequencies in most samples, much as was experienced
measuring the known capacitors of Appendix A. This is not an expected
behaviour and likely due to the test setup rather than a true material response.
In the low frequency region two parallel phenomena are present, a
low frequency dispersion adhering to a power law behaviour and a strong
conduction term. The conduction term is visible as a linear loss curve
segment towards the lowest frequencies, present in all samples. The dispersion
behaviour is prominent in the dielectric constant curves of all samples. While
the spectral onset of dispersion varies between samples, it appears to begin in
′
′′
′
the vicinity of where ε ≈ ε . Additionally, the low frequency ε value, of all
curves, are orders of magnitudes larger than what can be expected of a true
material response. The dielectric constant of a dry paper is expected to have a
flat frequency response in the range of 101 , similar to the values presented in
Table 2.1 while the measured low frequency dielectric constant is in the range
of 102 to 103 .
It is likely that the build up of an electrical double layer is the correct
explanation of the observed behaviour, caused by an interfacial polarisation.
This can be modelled as the build up of capacitances in series with the
sample. As these layers build up, the applied voltage across them drops
rapidly, implying a large polarisation in the material and a rapidly decreasing
electrical field in the bulk material in low frequencies. Thus, these layers
will dominate the response. It is plausible this formation is due to the
moisture and ion contents of the ion-exchanged samples having a mobility
large enough to move to the electrode interfaces well within a half-cycle.
As mentioned in Section 2.3.2, electrode polarisation may cause apparent
dielectric constants in the range of 102 to 106 . However, also the MWS
polarisation may cause large constants and the observed curve shapes appears
similar to both types of phenomenon. It is, in theory, possible to discriminate
between EP and MWS effects with sufficient knowledge of material properties
Results and Analysis | 57
and or the characteristic frequencies. In the medium MC measurement data
all four characteristic frequencies are not present, and thus this method cannot
be utilized to distinguish between EP and MWS. No saturation plateau is
′′
developed in either sample and no ε peaks are present, needed to define fmax
and fM W S . Should a broader spectrum be measured, with a few additional
low frequency decades, it is possible that both a plateau and loss peak will
appear. The samples can be described as heterogeneous systems, due to their
porosity, and charges can accumulated at the pore interfaces, giving rise to a
MWS effect. What is more likely however, is that the mobile charge carriers
are mobile enough, due to both moisture and ionic contents, to reach and
accumulate at the electrode interfaces, causing EP.
′
′
A common feature, among all samples, is a subtle peak in ε where ε ≈
′′
ε . This has been described by Barsoukov [39] as a MWS peak caused by
dielectric discontinuities within a sample. Using Equation 2.21, where σdc is
removed, he finds a weak but clear MWS loss peak at this point. It is expected
that also the measured samples of this thesis exhibit this kind of weak loss
peak.
Interpreting the tan(δ), referred to as TD in all following plots, is difficult,
′′
′
when interfacial polarisation processes dominate, the ratio of ε and ε is no
more than a mathematical construct, not necessarily saying anything about the
′
material response. TD is a good indicator of losses as long as ε is constant, or
′′
close to constant, meaning that the curve shape is dictated by ε . An advantage
of using TD to represent losses in this case is that the division of permittivities
removes the geometrical parameters inherent in the capacitances. However,
all samples show a loss tangent peak above the interfacial polarisation onset,
albeit with varying strengths. The HTP sample provides the best example
of this, where a clear local maximum is reached at 10 Hz before polarisation
onset. In the other samples, this peak appear present, visible in the slopes of the
curves, but its lower frequency wing is overshadowed by the polarisation effect
thus making the peak less clear. Most curves also plateau at low frequencies,
′
′′
′
indicating parallel ε and ε curves. The slopes were calculated for all ε and
′′
ε curves as ∆ε/∆f using the 500 mV data.
58 | Results and Analysis
Figure 4.1: Al3+ conditioned to a medium MC in 43 %RH at 23 °C. Upper
graph plots dielectric constant and loss curves, lower graph plots tan delta.
The Al3+ sample, presented in Figure 4.1, exhibit a power law behaviour of
′
′′
ε ∝ ω −0.9 from about 10 mHz down and ε ∝ ω −0.9 from about 200 mHz. In
the region below 10 mHz both curves are parallel. The interfacial polarisation
′
onset frequency, fon is about 200 mHz, the point where ε starts to heavily
′
increase with decreasing frequency. No saturation plateau of ε is present in
the measurement data, so no fmax can be defined. Neither can any fM W S be
′′
defined as no peak in ε is visible. Calculating the slope along the entire curve,
′
a possible ε inflection point at 5 mHz can be seen, but another decade of lower
frequency data would be needed to draw any sure conclusion. The slope data
′
′′
also indicates a small relaxation peak around 1 Hz, the point where ε = ε ,
and loss tangent peak at ≈ 10 Hz. The measured 1 mHz dielectric constant εS
is 374.45 and the high frequency constant ε∞ at 1 MHz is 2.00.
Results and Analysis | 59
Figure 4.2: Ca2+ conditioned to a medium MC in 43 %RH at 23 °C. Upper
graph plots dielectric constant and loss curves, lower graph plots tan delta.
The Ca2+ sample, presented in Figure 4.2, also exhibit a low frequency
′
power law behaviour where ε ∝ ω −0.9 from about 5 mHz to about 2 mHz
′′
where the slope increases to -0.95. The loss curve exhibits a ε ∝ ω −0.5 slope
between 100 Hz and 1 Hz, preceding a sharp increase at where the slope is
-0.9. Like the Al3+ sample, this is indicative of an interfacial polarisation
effect. The onset of polarisation, fon occurs at roughly 10 mHz, however
neither saturation nor inflection points are present in the visible spectra. The
′
slope of ε continuously increase with decreasing frequencies. A loss tangent
peak is indicated around 2 Hz. The measured 1 mHz dielectric constant εS is
134.41 and the high frequency constant ε∞ at 1 MHz is 2.11.
60 | Results and Analysis
Figure 4.3: H+ conditioned to a medium MC in 43 %RH at 23 °C. Upper
graph plots dielectric constant and loss curves, lower graph plots tan delta.
Only two samples exhibit any noteworthy response to change in voltage
amplitude between frequency sweeps. Both the H+ and Na+ samples show an
increase in both dielectric constant and loss in the low frequency region with
an increased voltage amplitude. Additionally, both exhibit a decrease in tan(δ)
in the low frequency region at the 25 mV rerun sweep. This can be explained
by a depletion of ions in the sample bulk. As mentioned in Section 2.2.2, when
running consecutive sweeps of varying amplitude, a depletion of ions in the
sample may occur as the distance charge carriers can travel are longer than
the bulk distance. Running a higher amplitude sweep charges reaching the
bulk electrode interface may accumulate and stick there. During a following
lower amplitude sweep, the ion density of the bulk is reduced causing lower
measured losses. Ionic losses occur due to ion movement. This indicates that
the H+ and Na+ samples both have higher ion mobility than other samples.
Both curves also have markedly earlier onset frequencies, H+ at about
1 Hz and Na+ at about 10 Hz, than the other ion-exchanged and reference
′
′′
samples. They also have lower low frequency slopes of both ε and ε . Both
′
′′
H+ ε and ε curves have a slope of -0.8 while the Na+ curves have slope of
Results and Analysis | 61
-0.7 to -0.5 and -0.7 to -0.6 respectively. The H+ response is presented in
Figure 4.3 and the Na+ response in Figure 4.5. This also indicates that both
samples have a higher ion-mobility than the other samples, meaning losses
and potential interfacial polarisation can occur at higher frequencies. As with
the other samples, interfacial polarisation is present in both samples but to
a greater degree, visible as much larger dielectric constant and loss values.
The measured 1 mHz H+ dielectric constant is 4168 while the high frequency
constant is 2.03 at 1 MHz. The measured 1 mHz Na+ constant is 4416 and the
high frequency constant is 2.30. Loss tangent peaks are indicated around 100
Hz in the H+ data and 460 Hz in the Na+ data.
Unlike any other sample, the Na+ sample exhibits a low frequency slope
′
′′
peak, where both ε and ε curves becomes concave towards the lowest
′
frequencies. An inflection point of ε is observed at around 300 mHz.
Figure 4.4: Mg2+ conditioned to a medium MC in 43 %RH at 23 °C. Upper
graph plots dielectric constant and loss curves, lower graph plots tan delta.
The response of the Mg2+ sample is presented in Figure 4.4. The low
′
frequency Mg2+ ε curve follows a power law behaviour with a slope of -0.9
′′
from about 5 mHz, parallel to it is ε with the same slope from about 100
′
mHz down. Unlike the other samples, the Mg2+ ε slope approaches -1.0
62 | Results and Analysis
towards the very lowest frequencies, a slope characteristic of EP. An onset
frequency of 10 mHz is observed while both saturation and inflection points
are absent. The measured 1 mHz dielectric constant εS is 125.66 and the high
frequency constant, ε∞ at 1 MHz is 2.11. A loss tangent peak is indicated by
the calculated slopes at 2 Hz.
Figure 4.5: Na+ conditioned to a medium MC in 43 %RH at 23 °C. Upper
graph plots dielectric constant and loss curves, lower graph plots tan delta.
The commercial AMetek sample is the only sample to exhibit a consistent
′
low frequency ε slope of -1.0, from 20 mHz down, presented in Figure 4.6.
The onset frequency is found at 50 mHz. A possible inflection point is
indicated by calculated slope at 10 mHz where it begins to slowly decrease.
′′
The ε slope, from 2 Hz down, is between -0.8 and -0.9 with a peak value at
200 mHz. The measured 1 mHz dielectric constant εS is 559.63 and the high
frequency constant, ε∞ at 1 MHz is 1.95. A loss tangent peak is indicated by
the calculated slopes at 20 Hz, outside of the EP area.
Results and Analysis | 63
Figure 4.6: AMetek conditioned to a medium MC in 47 %RH at 23 °C. Upper
graph plots dielectric constant and loss curves, lower graph plots tan delta.
Figure 4.7 presents the response curves of the AM400 sample. The onset
′
of interfacial polarisation of the AM400 sample occurs at about 3 Hz and the ε
slope reaches -0.9 at 10 mHz increasing towards an inflection point at 5 mHz.
′′
ε reaches a slope of -0.9 at 200 mHz and reaches a maximum at 50 mHz of
-0.93 before starting to plateau. The measured 1 mHz dielectric constant εS is
263.34 and the high frequency constant, ε∞ at 1 MHz is 2.07. A loss tangent
peak is indicated at 5 Hz, outside of the EP area.
64 | Results and Analysis
Figure 4.7: AM400 conditioned to a medium MC in 47 %RH at 23 °C. Upper
graph plots dielectric constant and loss curves, lower graph plots tan delta.
The HTP sample, presented in Figure 4.8, has an onset frequency of about
′
40 mHz and ε reaches a slope of -0.9 at about 5 mHz, from onset the slope
′′
increases through the measured spectra. Much like the AMetek sample, the ε
slope reaches a maximum to then decrease towards the end of the spectrum. A
slope peak of -0.9 is found at 40 mHz, decreasing to -0.8 at lower frequencies.
A clear loss tangent peak is present at 10 Hz. The measured 1 mHz dielectric
constant εS is 525.69 and the high frequency constant ε∞ at 1 MHz is 4.25.
Results and Analysis | 65
Figure 4.8: HTP conditioned to a medium MC in 44 %RH at 23 °C. Upper
graph plots dielectric constant and loss curves, lower graph plots tan delta.
It is possible to group the responses into three groups, consisting of an
upper group including H+ and Na+, a middle group including only HTP and
a lower group including all ion-exchanged papers plus AMetek and AM400.
The upper group of H+ and Na+, star and cross marked respectively in
Figure 4.9, both exhibit a polarisation onset decades earlier and a dielectric
constant about an order of magnitude larger than the bottom group. It is
likely that these samples have markedly higher ion-mobility than the rest,
allowing earlier and stronger EP. It could be that the ion and what it binds
to makes a smaller compound than the others, allowing for easier movement.
Ion-mobility depends on the interaction between ion and paper contents
including cellulose, hemicellulose, lignin, water and potential impurities.
These interactions are a complex matter however, beyond the range of this
thesis.
The second and middle group, containing only HTP, are formed by their
unique response curves. The high frequency dielectric constant is to be
expected as the sample have a density about twice that of the other samples
meaning it is less porous, see Table 3.1. It also exhibits a much more developed
66 | Results and Analysis
′
′′
relaxation peak in both ε and ε before the onset of EP. It is not expected that
the unique response is attributed to its MC, as it is close to the mean of 7.36
%. Rather it is likely due to the fiber contents and density of the sample. The
exact contents are not known.
Figure 4.9: Collected dielectric constant curves at medium MC.
The third and bottom group, containing Al3+, Ca2+, Mg2+, AMetek
′
′′
and AM400, all show similar response curves of both ε and ε . While
slightly shifted in frequency, they all show a small relaxation peak before the
onset of a strong EP. In both real and imaginary parts the Ca2+ and Mg2+
follow each other surprisingly close. This indicates that the choice of ion,
between these two, for an ion-exchange is of no great importance, both lends
the paper the same dielectric properties at least at a medium MC. AMetek
stands out however with a much smaller relaxation peak yielding a smaller
dielectric constant at around 0.5 Hz, before the EP onset. The entire groups
high frequency constants are all close to 2. While all samples exhibit a low
frequency dispersion, the magnitude vary between samples. AMetek exhibit
the largest dielectric EP effect while Mg2+ and Ca2+ exhibit the weakest
effect.
The sample MC values vary significantly and do not correlate with the
grouping based on response curves. Al3+ has the highest MC level but does
Results and Analysis | 67
not exhibit the strongest EP effect. AMetek has the lowest MC level but
exhibit one of the third strongest EP effects. AMetek is the thinnest sample
which could explain the high EP magnitude. A thinner sample means a shorter
distance any charge carrier have to travel before reaching the sample electrode
interface. This means that interfacial accumulation of charge carriers will
begin to build up at higher frequencies and will create a stronger double layer
effect at lower frequencies than thicker samples. This behaviour is visible in
Figure 4.9.
The categorisation of responses into three groups is also relevant for the
′′
ε curves. The upper group of H+ and Na+ both exhibit much greater losses
than the bottom group in all but the very highest frequencies. Both samples
approach the bottom group in the high end spectrum but with different speeds
and Na+ remains markedly higher. These greater losses are most likely due to
a greater ion-mobility causing greater ionic conduction than what is seen in
the other samples. It is noteworthy, that while Na+ exhibit the highest losses
for most of the spectrum H+ overtakes it at 50 mHz after the Na+ slope begins
to decline. It appears that H+ and Na+, both experiencing a much earlier EP
onset than the other samples also begins to plateau in low frequencies meaning
they are approaching an EP saturation. Also the HTP sample, of the middle
group, exhibit greater losses than the bottom group before the onset of EP. The
magnitude of EP in HTP is comparable to the bottom group.
The bottom group consistently show lower losses than the top group. In
general, within this group, there is a tendency for samples with high relative
low frequency losses to hold relatively low high frequency losses. This
behaviour can be seen in the Ca2+ and Mg2+ curves showing the lowest losses
from 1 mHz to 1 kHz from where they proceed to hold the highest in-group
losses in higher frequencies. Likewise, AMetek has the lowest high frequency
losses from 1 MHz down to 7 kHz and exhibit the highest in-group losses in
the lowest frequencies along with Al3+.
The data also indicates that the exchange ions valence influence the papers
losses. The upper group of H+ and Na+ exhibit higher losses than the bottom
group. The upper group are ion-exchanged with ions of lower valence than the
bottom group. This is further strengthened by the very similar responses of the
Ca2+ and Mg2+ samples. One theory could be that larger valence ions allow
for larger compounds bound to it, reducing mobility. However the Al3+ data
contradicts this, as it is single highest valence ion and also exhibits large losses
compared to the other members of the bottom group. It can also be that the
higher losses of Al3+ is explained by its much higher MC content, the highest
among all samples. It is not known what the ions bind to in paper samples. Ions
68 | Results and Analysis
may for example bind to either cellulose which is slightly negatively charged
and fixed in position in the bulk. They may also bind to water molecules which
can be either free or trapped in position.
Figure 4.10: Collected loss at medium MC.
Naturally, the grouping is still relevant in the tangent delta curves, as they
′
′′
depend on the ε and ε curves. The lowest frequency peaks of both the bottom
group and the HTP sample are well defined and easy to read. They are however
present in the frequency region of a well developed EP effect and therefor
do not necessarily correspond to tangent delta peaks in the sample materials
themselves. The Na+ curves show an EP peak 10 Hz after which it forms a
trough and a possible second peak in frequencies lower than was measured.
The H+ sample however does not exhibit such a well formed EP peak but
rather reach a plateau at 10 mHz before again rising at 1 mHz. It could be
the case that the bottom group and HTP would form a similar behaviour as
the Na+ sample in frequencies below 1 mHz as they all form a clear peak and
subsequent decrease.
Results and Analysis | 69
Figure 4.11: Collected loss tangent curves, at medium MC.
70 | Results and Analysis
4.2
Wet moisture content
All paper samples and designated paper strips were conditioned simultaneously. After having initiated a measurement, Karl Fischer titration was
performed on the strips, having been bathed in dry methanol for approximately
13 hours prepared the evening prior. The potassium nitrate salt solution used
to regulate the chamber RH is expected to yield a humidity of 95 %, however
only 86 % was reached. The discrepancy is attributed to the chamber not
being entirely air tight, allowing for some drift or leakage of moisture to and
from the surrounding environment, which was roughly stable at 45 to 50 %
RH. However, since the chambers achieved a stable 86%, varying only some
decimal points, it was deemed moist enough for a wet environment and all
measurements were performed at this RH. The temperature was stable at 23 °C,
varying at most 1 to 1.5 degrees for very short durations.
Table 4.2: Wet MC conditioning values, temperature was stable at 23 °C with
minor deviations and RH at constant 86 %. Sample sequence from to bottom
is the same as the measurement sequence.
Sample
MC beaker 1
[wt%]
MC beaker 2
[wt%]
∆ MC
Average
[wt%]
Al3+
Ca2+
H+
Mg2+
Na+
AMetek
AM400
HTP
12.53
11.95
11.82
14.82
11.07
11.40
12.83
13.23
14.8
14.97
13.65
14.79
11.70
11.20
11.58
13.99
2.27
3.02
1.83
0.03
0.63
0.20
1.25
0.76
13.67
13.46
12.73
14.81
11.39
11.30
12.21
13.61
All measured moisture contents are presented in Table 4.2. Some samples
show very consistent MC levels between beakers, such as the Mg2+ and
AMetek samples, while others vary rather much, such as the Ca2+, Al3+ and
H+ samples. Ideally, the results should be the same, as the strips are both
conditioned in the same environment and bathed in methanol from the same
bottle an equal time duration. There can be a number of possible sources of
error causing this. Since all beakers were washed after used, oven dried at
100 °C for an hour and left over night before next use, it is not expected that
residual water in the beakers would be the cause. More likely are errors in the
extraction of moisture from the samples. Since two paper strips were used,
Results and Analysis | 71
it could be that the strips hold on to moisture to different degrees, while they
were of similar size one piece may have been cut from closer to the edges of the
paper where the sheet is generally thicker due to the pressing procedure during
the paper making process. Unlikely, but possible, are errors in the weighing
of either paper strips or titration sample, both of which influence the result. It
could, also unlikely but possible, be due to some disturbance during titration.
It is not clear why the results differ. It is however always recommended to do
several titrations on several samples of the same kind to minimize the impact
of potential errors. Consulting the Oommen charts for Kraft paper, which
indicates an expected MC level of between 11.5 and 12 %, the results appear
reasonable at about 12.5±2%. It cannot however be said whether the moisture
uptake is evenly distributed in the bulk material.
As at the medium MC level, AMetek is the sample that absorbed the
smallest amount of moisture. While Al3+ absorbed the highest amount at the
medium MC level it was the second wettest sample at the wet MC level, Mg2+
absorbed the most. This is assuming all absorbed moisture was released in the
methanol bath and detected during titration.
It is clear that a high MC level has a great influence on the papers dielectric
response. As at the medium MC, there are some commonalities between
samples also at the wet MC. All samples exhibit an early onset of EP which
reaches low frequency amplitudes several orders of magnitude larger than the
medium MC curves. In fact, the EP effect dominates much of the measured
spectrum overshadowing any true material response.
Unlike at the medium MC, all wet MC curves are influenced by the voltage
amplitude, visible in both 500 mV and 25 mV re-run curves. Both of these
effects are attributed to the higher MC in the samples. It appears that moisture
increases the ion-mobility within the samples leading to an earlier and stronger
interfacial accumulation of charge carriers and possibly also to the start of an
ion-depletion in the bulk. A complete ion-depletion is however expected to
generate a stronger voltage dependence. An increased ion mobility leads to
an earlier ion depletion in the bulk, explaining the prevalence of diverging
curves between sweeps. With a higher mobility, a lower frequency is required
to begin the formation of a double layer and ion depletion of the bulk. A
subsequent sweep of higher voltage amplitude will further increase the number
of ions accumulating at the interface by exerting a stronger electric field. This
will increase losses and the strength of the double layer. At some frequency
however, the bulk starts to deplete and fewer ions will move along the field,
thus generating lower losses. As the double layer remains and the losses
′′
′
decrease, this can be seen as a decrease in tangent delta (the ratio of ε over ε ).
72 | Results and Analysis
The 25 mV re-run curve also exhibiting a diverging low frequency behaviour
indicates that the entire double layer formation, and thus ion depletion, has
not been restored to equilibrium between sweeps. The sample bulk exhibits a
certain memory. The overtake of the 500 mV tangent delta curve in the very
lowest frequencies is attributed to the stronger electric field exerting a stronger
pull than the 25 mV. It could also be that as MC increases the content of free
water in sample increases, allowing for a higher water mobility and influence
in polarisation processes.
Comparing wet and medium MC curves, it appears that the wet curves
follow a similar behaviour as the medium curves but are shifted towards
higher frequencies. The high frequency response of approaching a fixed
dielectric constant value remains, as expected, and the low frequency response
appears like a continuation of the medium MC low frequency response. After
′
′′
separating at the point where ε ≈ ε the curves again converge at a lower
frequency before once again separating. It is interesting to note that neither of
′
the ε curves reaches any plateau characteristic of interfacial polarisation [38].
Figure 4.12: Al3+ conditioned to a wet MC in 86 %RH at 23 °C. Upper graph
plots dielectric constant and loss curves, lower graph plots tan delta.
The Al3+ response, presented in Figure 4.12, exhibit an onset frequency of
′
about 300 Hz with an ε slope of -1 until 10 Hz where it decreases to between
Results and Analysis | 73
-0.4 and -0.5. An inflection point is found around 30 Hz. The measured 25
′
′
mV static ε value is 194 790 and the high frequency ε value is 2.48. No loss
peak outside of the EP range is easily discernible in neither graph nor slope
data. A tangent delta peak is however indicated in the slope data at 7 kHz.
Well developed tangent delta peaks inside the EP range are present at 100 Hz
and 10 mHz in the 500 mV data. An influence of voltage magnitude begins to
′
develop at about 200 Hz. While the 500 mV ε curve follows the 25 mV curve
closely, the 25 mV re-run curve has a noticeably smaller magnitude. Likewise,
′′
the ε 500 mV and 25 mV re-run curves slightly overshoot the 25 mV from
about 200 Hz to about 20 mHz. From 20 mHz down they both have a markedly
lower magnitude than the 25 mV curve.
Figure 4.13: Ca2+ conditioned to a wet MC in 86 %RH at 23 °C. Upper graph
plots dielectric constant and loss curves, lower graph plots tan delta.
The Ca2+ response, presented in Figure 4.13, has an onset frequency of
′
about 200 Hz and ε inflection point at about 50 Hz. The measured 25 mV
′
′
static ε value is 83 458 and the high frequency ε value is 3.02. No loss peak
outside of the EP range is easily discernible in neither graph nor slope data. No
tangent delta peak outside the EP range is detected. Well developed tangent
delta peaks inside the EP range are present at 200 Hz and 2 mHz in the 25 mV
data. At 1 kHz the curves of different sweeps diverge, this is most easily seen
74 | Results and Analysis
in the tangent delta curves. The Ca2+ tangent delta curves are a good example
of ion depletion. The re-run curve exhibit lower low frequency losses except
for the very lowest frequency points. This indicates that the two preceding
sweeps have depleted the bulk to a high degree, meaning that some charges
have not returned to an equilibrium but rather remains at the bulk interfaces.
Figure 4.14: H+ conditioned to a wet MC in 86 %RH at 23 °C. Upper graph
plots dielectric constant and loss curves, lower graph plots tan delta.
The H+ and Na+ samples exhibited the strongest responses at the medium
MC level, likely due to an higher ion-mobility. It could therefore be expected
that they would also exhibit a stronger ion-depletion effect at the wet MC
level. This however appears not to be the case. The H+ sample, presented
in Figure 4.14, exhibit a depletion effect much like the Ca2+ sample, visible
in the 25 mV re-run curves. The Na+ sample, presented in Figure 4.16, exhibit
a low frequency 25 mV re-run curve more similar to the AMetek sample. Both
samples do however experience both early and strong EP effects.
′
H+ has an onset frequency of about 1 kHz, its measured ε value is 187 390
at 1 mHz and 2.83 at 1 MHz. A tangent delta peak outside of the EP region
is indicated by the slope data around 28 kHz. Na+ has an onset frequency of
′
about 14 kHz, its measured ε value is 183 360 at 1 mHz and 4.29 at 1 MHz.
No tangent delta peak outside of the EP region is present. Neither of them
Results and Analysis | 75
show any loss peak before the EP onset. Both show prominent tangent delta
peaks within the EP region.
Figure 4.15: Mg2+ conditioned to a wet MC in 86 %RH at 23 °C. Upper graph
plots dielectric constant and loss curves, lower graph plots tan delta.
The Mg2+ response, presented in Figure 4.15, includes an onset frequency
′
of about 200 Hz. The measured ε value 67 359 at 1 mHz and 3.04 at 1
MHz. No loss peak or tangent delta peak is discernible outside the EP region.
The sample exhibits a strong low frequency response to voltage amplitude and
number of sweeps.
76 | Results and Analysis
Figure 4.16: Na+ conditioned to a wet MC in 86 %RH at 23 °C. Upper graph
plots dielectric constant and loss curves, lower graph plots tan delta.
The AMetek response, presented in Figure 4.17, includes an onset
′
frequency of about 400 Hz. Its measured ε values are 25 126 at 1 mHz and
2.61 at 1 MHz. No loss peak is discernible outside the EP region. A tangent
delta peak outside the EP region is however indicated by the calculated slope
data around 22 kHz, but is hard to discern in figure.
Results and Analysis | 77
Figure 4.17: AMetek conditioned to a wet MC in 86 %RH at 23 °C. Upper
graph plots dielectric constant and loss curves, lower graph plots tan delta.
The onset frequency of the AM400 sample, presented in Figure 4.18, is
′
about 200 Hz. Its measured ε value at 1 mHz is 49 438 and 2.54 at 1 MHz. No
loss peak is present outside the EP region. A weak tangent delta peak outside
the EP region is indicated by the slope data at about 6.7 kHz. Compared
to other samples, AM400 is not much influenced by voltage amplitude or
subsequent sweeps. The dielectric constant, losses and tangent delta are only
slightly increased at 500 mV and slightly decreased at the 25 mV re-run. This
indicates that no strong depletion appears in the sample.
78 | Results and Analysis
Figure 4.18: AM400 conditioned to a wet MC in 86 %RH at 23 °C. Upper
graph plots dielectric constant and loss curves, lower graph plots tan delta.
The HTP response, presented in Figure 4.19 is, similar to the medium MC
level, unique among the wet MC responses in that it exhibits a clear tangent
delta peak outside of the EP region. The onset frequency is about 200 Hz, and
′
its measured ε value is 30 582 at 1 mHz and 4.99 at 1 MHz. Both a loss peak
and a tangent delta peak are indicated by the slope data at 14 kHz, and a weak
′
ε peak is indicated around 2.6 kHz, all outside the EP region. Additionally, in
the lowest frequency range, it exhibits a strong increase of losses and tangent
delta at the higher voltage amplitude. No such behaviour appear in the re-run
data, indicating that no significant depletion occurs in this sample.
Results and Analysis | 79
Figure 4.19: HTP conditioned to a wet MC in 86 %RH at 23 °C. Upper graph
plots dielectric constant and loss curves, lower graph plots tan delta.
Figure 4.20 plots all dielectric constants at wet MC. The data shows that
the grouping made of the samples at medium MC is not entirely relevant at
wet MC. An upper group, of H+ and Na+, can still be defined. Both exhibit
earlier and stronger EP and thus higher constants which interestingly converge
at 1 Hz. This indicates a build up of very similar double layers even though
the onset in Na+ appears significantly earlier than an in H+. It also strengthens
the idea that these ions have a greater mobility within the sample bulk.
The HTP sample can be grouped with the former bottom group consisting
of Al3+, Ca2+, Mg2+, AMetek and AM400. HTP holds a relatively high
dielectric constant in high frequencies, attributed to its higher density. It
does however not experience an EP as strong as most other samples, in fact
only the AMetek EP is weaker. While AMetek exhibited one of the strongest
EPs at the medium MC, it exhibits the weakest EP at the wet MC. AMetek
is also the sample with the lowest MC. Unlike the other members of the
bottom group, HTP is the only sample with a clearly defined relaxation peak
outside the EP region. It is also noteworthy that while HTP and Al3+ have
very similar moisture contents, the magnitude of EP varies greatly between
samples. In fact, AMetek, HTP and AM400 are the samples exhibiting the
80 | Results and Analysis
three weakest EP, indicating that the ion-exchange of the ion-exchanged papers
has a significant impact on EP potential in wet environments.
Mg2+ is the sample with the highest MC, it is however not the sample with
the strongest EP, indicating that choice of ion in the ion-exchange has a greater
impact than the MC of the paper when comparing different samples. The high
moisture contents are likely what dominates the overall responses, both of loss
and dielectric constant, due to the consistently high curve amplitudes.
Figure 4.20: Collected dielectric constant curves at wet MC.
Figure 4.21 plots all loss curves at wet MC. The grouping of responses into
two groups is relevant also for the loss curves. H+ and Na+ has the greatest
losses until about 20 - 50 mHz where Al3+ takes over. In high frequencies,
outside of the EP region, Na+ has significantly higher losses than any other
sample. However, it must be noted that all samples exhibit exceedingly high
losses, especially in the medium and low frequency ranges. This is attributed
to the high ion-mobility and moisture contents.
As with the dielectric constants, AMetek consistently has the lowest losses.
This cannot solely be explained by having the lowest MC as the Na+ sample
with only a marginally higher MC exhibit the highest losses in the majority
of the spectrum. Likewise, Mg2+ with the highest MC does not exhibit the
highest losses.
Results and Analysis | 81
Figure 4.21: Collected loss at wet MC.
The tangent delta curves are all plotted in Figure 4.22. All samples exhibit
well developed tangent delta peaks within the EP region. However only HTP
exhibit a distinct peak outside the region. While Na+ has the earliest onset
of EP, H+ has the highest tangent delta peak, at about 500 Hz, slightly after
its onset at 1 kHz. H+ has a peak at about 10 kHz, slightly after its onset at
14 kHz. Two samples, Al3+ and Ca2+, reaches a second tangent delta peak
inside the EP region. The Na+ curve is the only one to flatten out into a low
frequency plateau.
82 | Results and Analysis
Figure 4.22: Collected loss tan delta at wet MC.
Results and Analysis | 83
4.3
Dry moisture content
The dry MC conditioning was performed in a vacuum oven. All samples were
measured at 4 different temperatures, first at 115 °C then at 85 °C, 45 °C and
26 °C while cooling. The AMetek and HTP samples were measured only
between 100 mHz and 1 MHz, as the primary interest in these samples lie
around 50 Hz. This was decided in consensus with RISE and DCC. The oven
held a constant temperature, at all four set points, and a pressure stable within
2-4 millibar. Before initiating any measurement sequence both test cell, rubber
pieces and cabling inside the oven was tested at 140 °C for 40 min to ensure
they would withstand the needed temperatures. It was expected that it would
be hard to get reliable MC results from Karl Fischer titration on the very
dry papers as they quickly absorb moisture from the surrounding air during
processing before titration. This includes weighing and transport to a methanol
bath. Additionally, if the paper is very dry its moisture might be relatively
highly diluted by the residual moisture of the dry methanol (which will always
contain some small amount of water). One paper strip of the Al3+ sample
was however used as a test, conditioned together with the other samples. After
removing the strip from the oven, it was placed in a sealed plastic bag in which
it was also weighed. After this it was removed from the bag and placed in
a methanol bath for about 13 hours in a sealed beaker. Two titrations were
performed on the solution. An average of 1.30 % MC was found. While this
is considered dry in some applications, in cases such as transformers it would
be considered wet. While the processing of the strip only took 1-2 minutes,
and the strip was contained in a plastic bag most of the time, it is expected to
have absorbed a considerable amount of water still. After conditioning at a
high temperature in close to vacuum the MC of all samples is expected to be
well below 1 %.
The medium curves did not show any profound influence of voltage
magnitude or subsequent sweeps. Likewise the Al3+ sample, presented in
Figure 4.23, measured first at this MC level, showed no significant difference
between 25 mV and 25 mV re-run sweeps. Neither was such a dependence
expected in the absence of moisture in the samples. Therefore, it was decided
to do the remaining measurement sweeps only at 25 and 500 mV without any
low amplitude re-runs.
The Al3+ data also differ from the others in that part of the data is missing.
The 500 mV data in Figure 4.23 is missing between 1 kHz and 1 MHz.
Likewise, the 115 °C 500 mV data in Figure 4.24 is missing between 1 kHz
and 1 MHz. Between 1 mHz and 10 mHz the 85 °C, 45 °C and 26 °C data is
84 | Results and Analysis
Figure 4.23: Al3+ conditioned to a dry MC. Upper graph plots dielectric
constant and loss curves, lower graph plots tan delta.
missing. An unfortunate misunderstanding led to these data series not being
measured with the others. An attempt was made to fill in the measured gaps
by new measurements. The new data was however non-conforming with the
old data. It is clear that the procedure of keeping the sample very dry for an
extended time, and under a certain compressive force when mounted in the
test cell, affected its physical properties. This could be seen not only in the
dielectric response data, but also visually as the sample had become brittle and
shriveled. This effect is commonly known to occur when drying wet paper.
Due to these issues, the response of the Al3+ sample is plotted at 115 °C while
all other samples are plotted at the intended 26 °C, which is much closer to a
normal room temperature. The responses while cooling are plotted in the same
manner for all samples.
In general, the quality of the data varies considerably. All samples exhibit
choppy loss curves, and consequently tangent delta curves, where one would
expect much smoother curves. The quality is consistently worse at 25 mV than
at 500 mV. This can be explained by a weaker signal at 25 mV, sensitive to
noise and disturbances. In addition to a low voltage amplitude, the very dry
Results and Analysis | 85
Figure 4.24: Al3+ conditioned to a dry MC, measured at different
temperatures while cooling.
samples are highly non-conductive, resulting in a signal testing the limits of
the measuring instruments. In addition to being choppy, several data points are
missing in the loss curves of the majority of the sample, no dielectric constant
data is missing however. The majority of the data points are missing in the
low frequency region of the 25 mV curves. Missing data corresponds to a
measured negative imaginary impedance, which is unreasonable and indicates
a measurement error and thus is discarded. A 500 mV amplitude is high
enough to generate a signal capable of producing a reasonably smooth curve
in most samples. That is, a curve smooth enough that a trend can identified if
there is one. The 25 mV data is, in most samples, not good enough to draw
any conclusions from even though some trends might be indicated.
The Ca2+, Mg2+ and AM400 samples suffered multiple interruptions
of the IDAX measurement sweeps, which consequently had to be redone
until successful. These interruptions could be due to a relatively high stray
capacitance to ground, causing the instrument to react. One could expect these
issues to be most prominent in the samples with lowest conductivity and not
so prominent in the, relatively, highly conductive samples. Na+, proved to be
conductive in previous measurements and showed no significant problems of
weak signals. However, the H+ sample, also previously proven to be highly
86 | Results and Analysis
Figure 4.25: Ca2+ conditioned to a dry MC. Upper graph plots dielectric
constant and loss curves, lower graph plots tan delta.
conductive, provided very poor results at dry MC with choppy curves and
several missing data points at 25 mV.
It is clear that an amplitude of 25 mV is too low to generate reliable
results, neither is 500 mV quite enough as the loss curves of all samples show
substantial interference in their choppiness. It is expected that 1 V would
provide more reliable data. Still, these amplitudes were used for conformity
between MC levels, so that the same amplitudes were consistently used in all
measurements.
With the exception of Al3+ and Na+, presented in Figure 4.23 and 4.31
respectively, which exhibit a small increase in dielectric constant in the
mHz range, all samples have flat dielectric constant responses throughout the
measured spectra. The Al3+ curve is however measured at 115 °C meaning it is
not directly comparable to the other samples. The Al3+ 26 °C curve indicates
a flatter response more inline with the other samples. Additionally, all ionexchanged samples have a defined lowest loss point from where the losses
increase with both increasing and decreasing frequency.
All samples were measured at four temperatures, to study their behaviour
Results and Analysis | 87
Figure 4.26: Ca2+ conditioned to a dry MC, measured at different
temperatures while cooling.
while cooling. Only the 500 mV data is used in plotting the cooling curves.
A common feature among all samples is an apparent low frequency thermal
activation, likely following an Arrhenius activation. With the data available,
the activation energy of each sample should be possible to calculate using the
Arrhenius equation, Equation 2.14. Due to time constraints this is not done.
In this way a thermal activation could be argued for. Unfortunately, no loss
peaks are visible in measured spectra. While the data does indicate a thermal
activation, it is also the case that ion-mobility increases with temperature,
affecting both losses and potential interfacial accumulation.
Both losses and dielectric constants exhibit a strong low frequency
response, increasing with temperature. This behaviour can be seen in the
cooling curves of each respective sample. Both onset frequency and amplitude
differ between samples. The dielectric constants of all samples are, to a
varying degree, shifted upwards with increasing temperature through the
entire frequency range. In the low frequency region, all loss curves increase
with temperature. However, the high frequency loss curves decrease with
increasing temperature in all samples. Additionally, the loss curves of
88 | Results and Analysis
Figure 4.27: H+ conditioned to a dry MC. Upper graph plots dielectric
constant and loss curves, lower graph plots tan delta.
all samples appear to shift in frequency while retaining a convex shape.
The minimum loss point shifts towards higher frequencies with increasing
temperatures. These results are consistent with what was found in [29].
A high frequency increase in dielectric constant is detected in all samples,
at all temperatures, to a varying degree. The increase is present in all curves,
but more prominent in the cooling graphs of each sample as they are of a
higher resolution. AMetek, see Figure 4.34, and HTP, see figure Figure 4.38,
are good examples exhibiting strong increases at around 500 kHz. The
phenomenon, while not expected, was noticed during the test setup validation
in Appendix A. The increase is not expected to be a material response as
paper, and most materials, exhibit a constant decreasing with frequency.
Rather, the likely explanation lies with either the test setup or specifically the
instrumentation or fringe effects. The exact cause in this case not certain.
At 26 °C the dielectric constant of all samples, while increasing in both
ends of the spectra, is still fairly constant, varying only on the first decimal
point. The 26 °C 50 Hz constant of Al3+, Figure 4.24, is 1.84. Ca2+,
Figure 4.26, has a 50 Hz value of 1.83. H+, Figure 4.28, has a 50 Hz value of
1.81. Mg2+, Figure 4.30, has a 50 Hz value of 1.81. Na+, Figure 4.32, has a
Results and Analysis | 89
Figure 4.28: H+ conditioned to a dry MC, measured at different temperatures
while cooling.
50 Hz value of 1.85. AMetek, Figure 4.34, has a 50 Hz value of 1.71. AM400,
Figure 4.36, has a 50 Hz value of 1.77. HTP, Figure 4.38, has a 50 Hz value
of 3.08.
It is however harder to draw any conclusions of at which frequency the
samples generate the lowest losses. This is due to the loss curves not being
smooth enough to indicate such a point even when a general trend indicates
that such a point exists. The loss curves of all samples, with the exception of
Na+, exhibit a discontinuity at 1 kHz where the losses suddenly decrease when
the frequency increases at 115 °C and 85 °C. This is where the LCR and IDAX
data are concatenated. The only thing changed in the test setup when switching
instrument is disconnecting the LCR and connecting the IDAX using the same
cables. The Mg2+ data, Figure 4.30, is a good example of this. This behaviour
is attributed to some noise or disturbance and not a material response. It does
however indicate a false loss minimum in e.g. the Mg2+ curves.
90 | Results and Analysis
Figure 4.29: Mg2+ conditioned to a dry MC. Upper graph plots dielectric
constant and loss curves, lower graph plots tan delta.
Figure 4.30: Mg2+ conditioned to a dry MC, measured at different
temperatures while cooling.
Results and Analysis | 91
Figure 4.31: Na+ conditioned to a dry MC. Upper graph plots dielectric
constant and loss curves, lower graph plots tan delta.
Figure 4.32: Na+ conditioned to a dry MC, measured at different temperatures
while cooling.
92 | Results and Analysis
Figure 4.33: AMetek conditioned to a dry MC. Upper graph plots dielectric
constant and loss curves, lower graph plots tan delta.
Figure 4.34: AMetek conditioned to a dry MC, measured at different
temperatures while cooling.
Results and Analysis | 93
Figure 4.35: AM400 conditioned to a dry MC. Upper graph plots dielectric
constant and loss curves, lower graph plots tan delta.
Figure 4.36: AM400 conditioned to a dry MC, measured at different
temperatures while cooling.
94 | Results and Analysis
Figure 4.37: HTP conditioned to a dry MC. Upper graph plots dielectric
constant and loss curves, lower graph plots tan delta.
Figure 4.38: HTP conditioned to a dry MC, measured at different temperatures
while cooling.
Results and Analysis | 95
Figure 4.39 plots all 500 mV 26 °C dielectric constants. HTP stands out
with the by far highest constant throughout its measured spectra. The density
of HTP is about twice that of other samples, explaining the larger constant in
the absence of moisture. The figure also includes the re-measured missing high
frequency Al3+ data, showing a significant jump at 1 kHz from 1.74 to 1.84.
This was chosen as an example of the mismatch between the measurements,
indicating the effect of the samples altered physical properties after having
already been conditioned and measured once.
It is clear that only the Na+ sample exhibit any strong increase in low
frequency dielectric constant. While the trend is strong and the percent
increase is high, the values are still low. The H+ sample also show an
inclination towards higher constant in the millihertz range, although it is still
very weak. All other samples appear stable even in the lowest of frequencies.
The ion-mobility increases with temperature, and it is likely that this pared
with an already higher mobility in mainly the Na+ sample, as has been shown
at both medium and wet MC, but also the H+ sample is the cause of this rise.
Figure 4.39: Collected dielectric constant curves at dry MC.
Comparing the 500 mV 26 °C loss curves of all samples, plotted in
Figure 4.40, a few things stand out. In the low frequency region Na+ dominates
with a markedly higher loss than both other ion-exchanged and reference
samples. This is not surprising as it has done so also in medium and wet MC.
96 | Results and Analysis
However, HTP exhibits the greatest losses from 10 Hz upwards, greater than
both Na+ and H+.
While all loss curves are choppy to some degree, comparing them shows
a similarity in choppiness. The region of 100 mHz to 1 Hz is particularly bad,
where erratic local maximums and minimums appear seemingly not based in
a true material response. Likewise, the 1 kHz point where instrument data
series are concatenated present several discontinuities. Also the region around
10 kHz show similar unexpected jumps in losses with increasing frequencies.
These phenomena is likely explained by low signal strengths paired with
the switching of internal feedback components within the measurement
instruments at these frequencies. This is strengthened by the fact that the
curves tend to smoothen out outside these regions.
In order to more easily draw any conclusions from the loss data, least
square fitted curves could be plotted instead of the measured loss curves and
the deviation between fitted and measured curves calculated. Due to the time
restrictions of this thesis this was not done.
Figure 4.40: Collected loss at dry MC.
′
As the 500 mV 26 °C ε curves are flat, the tangent delta curves of
′′
Figure 4.41 will be shaped by the somewhat erratic ε curves. The most
′′
important features of the tangent delta curves are also present in the ε curves.
Results and Analysis | 97
Since no loss peaks are present, no tangent delta peaks are either. The loss
curves rather indicate a loss minimum within the measured spectra, and indeed
also tangent delta minimums are indicated. It is worth mentioning again, that
due to the poor data, one must be careful to draw any conclusion about optimal
operating points, i.e., a point of minimum losses, with regards to frequency in
any possible future application of these papers.
Figure 4.41: Collected tangent delta at dry MC.
98 | Results and Analysis
4.4
Effect of moisture
The dielectric response of the studied papers are heavily influenced by the
amount of moisture in the papers. To see the effect of moisture in each sample,
the response curves at different moisture contents of each sample are plotted
together. In all figures, Figure 4.42 through 4.49, only the 500 mV responses
′
′′
are plotted, as they provided the best signal stability. ε , ε and tangent delta
are plotted separately for easier comparison.
In the high frequency region no interfacial charge accumulation will form.
Thus this is the region most clearly showing the influence of moisture on
′
′′
both ε and ε in the absence of such effects. As shown in previous sections,
the measured losses are very high at wet MC and both substantially lower
and flatter at dry MC. Noticeable is a clear high frequency convergence in
all three response curves of all samples. The medium and dry MC curves
converge especially close in the range of 100 kHz to 1 MHz. This indicates
that, in the absence of interfacial polarisation and at high frequencies, the
influence of moisture content diminishes. Still, wet paper, unsurprisingly,
exhibit significantly greater dielectric losses even in this region.
Figure 4.42: Dielectric response curves of Al3+ under different MCs.
′
′′
Increasing moisture contents in all samples shifts both ε and ε , and
Results and Analysis | 99
subsequently tangent delta, curves towards higher frequencies. Additionally,
′
′′
increasing moisture content increases the amplitude of both ε and ε . This
effect is established in the literature on dielectrics. The measured response
curves presented here do however not entirely show this as a pure shift and
magnitude increase. The measured curves also, to varying degrees, change
shape with varying MC. This change is subtle in terms of permittivity, but
′′
′
can be seen in the ε of H+ and the ε of Na+. It is however prominent in the
tangent delta curves, of e.g. H+ and HTP. This shape change could be due to
interfacial polarisation. At network frequencies (50/60 Hz) the influence of
moisture is very large in all samples.
The dry MC responses are of particular interest, as the absence of moisture
hinders interfacial polarisation. Thus, the response curves reflect the true
material response of the samples where the fibre and ion contents as well as
porosity dictate the measured responses.
Figure 4.43: Dielectric response curves of Ca2+ under different MCs.
100 | Results and Analysis
Figure 4.44: Dielectric response curves of H+ under different MCs.
Figure 4.45: Dielectric response curves of Mg2+ under different MCs.
Results and Analysis | 101
Figure 4.46: Dielectric response curves of Na+ under different MCs.
Figure 4.47: Dielectric response curves of AMetek under different MCs.
102 | Results and Analysis
Figure 4.48: Dielectric response curves of AM400 under different MCs.
Figure 4.49: Dielectric response curves of HTP under different MCs.
Results and Analysis | 103
4.5
Dielectric response modelling
The dielectric response modelling of the measured samples was performed by
curve fitting the medium MC curves to a Havriliak-Negami function consisting
of one or more relaxation terms. The medium MC curves was chosen as a fair
representation of the responses in a normal indoors climate where the samples
contain some degree of moisture without being wet or very dry. The fitting
process is described in Section 3.4.1, this section presents the results of this
fitting processes. The modeled curves are plotted together with the measured
response curves. While straightforward in theory, achieving a good curve fit
proved hard in practice. The measurement data indicate a relaxation process
′
in all samples, as can be seen for example in the increase of ε around 2 Hz in
Figure 4.50, but, as previously discussed, there exist some EP effect in the low
frequency region also in the medium MC curves. This will overshadow any
possible additional relaxation processes in this region, making them harder to
model. Therefor, the measured responses are plotted with the corresponding
conduction term subtracted, defined in the fitting process. The conduction
term is the pure conduction of the bulk and is not attributed to any relaxation
processes. Thus, removing it filters out the bulk conduction leaving only
relaxation and polarisation effects in the response, making them much easier
to distinguish. Removing the conduction terms reveals, in the samples H+,
Na+, AMetek and HTP, well defined low frequency loss peaks not previously
visible. The peaks appear correlated to relaxation processes, exhibiting a
Debye-like response. In the dielectric constant curves it is not possible to easily
distinguish between the effect of interfacial polarisation, which is indicated by
unexpectedly high values, and a Debye-like response. The loss curves sans
conduction term align with the measured loss curves in the medium to high
frequency regions, as expected.
The development of the fitting processes were iterative. First, the clearly
visible relaxation process of each sample was chosen as a basis for fitting.
The fit was however not good enough with only a single process, therefore
additional processes were added to create better fits. It is however debatable
whether this is actually good practice, as this region exhibits a behaviour
different from what one might expect with only relaxation processes. It is
worth repeating, that while based off of physical processes, the HavriliakNegami function is a purely mathematical construct only ideally modelling
physical reality. As mentioned in Section 2.4, it is prudent to first, if possible,
filter out any unwanted polarisation effects such as MWS or EP in order to
model only the true polarisation and relaxation of the bulk material. This was
104 | Results and Analysis
attempted using the approach described in Section 2.3.2 and Equations 2.21
through 2.23 without success. Again, the theory proved harder than initially
thought to put into practice, and it was decided that no more time could be
spent on filtering out these effects as the thesis work had already exceeded
its time budget. Therefore, the models are defined by curve fitting against
measurement data still including unwanted polarisation effects. The bounds
of both αk and βk was set to [0,1].
Figure 4.50: Al3+ fitted curves.
In order to get a better fit, a low frequency relaxation term was added
to the functions. This term was defined with a bit of trial and error, as no
relaxation process is visible in this region. Thus it does not necessarily model
any physical bulk process. Likewise, in order to improve the fit in the high
frequency region, an additional term was added to the ion-exchanged samples.
Additionally, fine tuning of the time constants was needed to produce good
fits. A time constant defined far from a reasonable value will produce either
a function term tending to zero as it lacks relevance or a function that had no
possible good fit with the measurement data.
Noticeable in the fitted curves of all samples are two things. A very good
curve fit is achieved of the dielectric constants throughout the entire frequency
spectrum of all samples; the measured and fitted curves are hard to separate
for much of the spectrum. AMetek is the sample where the fit is worst, with a
obvious discrepancy around 7 to 70 mHz, visible in Figure 4.55. The other is
a very good fit of the loss curves throughout the low and medium spectrum, in
which they are hard to distinguish between, deviating to a rather poor fit in the
high frequency region where the measured loss curve aligns very tightly to the
loss sans conduction curve. This poor fit is due to the fitting algorithm used.
The least square algortithm, lsqcurvefit, works to minimise the square of the
Results and Analysis | 105
Figure 4.51: Ca2+ fitted curves.
Figure 4.52: H+ fitted curves.
error between fitted and measured curve at each data point through the entire
input arrays. As the results are plotted on a log-log scale and the curves tend to
decrease with increasing frequency, what at first glance appears to be a large
fitting error in the high frequency region is in reality a very small number. And
as the algorithm will minimise the absolute value of the error over the whole
spectrum this will produce a larger deviation by relation, or ratio, in the parts
of the curve where the measured and fitted values are very small. This means
that the fitted curves, and absolute values, follow the measured curves rather
well, while doing so rather poorly in a log-log scale or when plotted as a ratio
between curves.
The increase of the loss curves towards the very high frequencies cannot
easily be fitted by a relaxation term. As the term is complex with a real
numerator an increase in the imaginary part will also generate an increase in
106 | Results and Analysis
Figure 4.53: Mg2+ fitted curves.
Figure 4.54: Na+ fitted curves.
the real part which cannot be accommodated as the fit of the real part would
deteriorate. Such a term is also nonphysical, as no such response is present
in the response’s real part. It is worth considering other fitting algorithms, or
designing a tailored one, to avoid the issue of poor fitting in regions of small
absolute values. This however, due to time constraints, must be part of possible
future work.
All manually entered and fitted parameters are presented in Table 4.3.
From the shape parameters, α and β, it is clear that among the proposed
relaxation terms there exist different characteristic modelling equations. For
example, relaxation term 2 of Al3+, H+, Mg2+ and AMetek with a β2 = 1.00
and α2 = 0 describes the Debye equation. Relaxation term 1 of AMetek with
a α1 = 0 and β1 ̸= 1 corresponds to a Cole-Davidson equation and relaxation
term 1 of H+ and Na+ with a α1 ̸= 0 and β1 = 1 corresponds to a ColeCole equation. Further study is needed to investigate whether these parameter
Results and Analysis | 107
Figure 4.55: AMetek fitted curves.
Figure 4.56: AM400 fitted curves.
Figure 4.57: HTP fitted curves.
108 | Results and Analysis
equation pairs accurately describes the bulk polarisation process or if these
results stem from the design of the fitting process itself.
The bounds of ∆εk was set to [0,1000] for all samples except H+ and
Na+, the most conductive samples, with needed increased upper bounds
of [0,10000] in order to achieve good fits. Additionally, using the lowest
′′
frequency ε value to define the conductivity σ proved inadequate as the
fitted loss curves would exceed the measured loss curves in the very lowest
frequencies where the conduction term is dominant. Therefore conduction
values were multiplied by a scalar between 0.75 and 0.9 in order to find a
good fit. For Al3+ a scalar of 0.9 was used, for Ca2+, H+, Mg2+, Na+ and
AM400 0.8 was used, for AMetek 0.85 was used and for HTP 0.75 was used.
The H+ and Na+ samples were previously deemed the most conductive, in
that they both exhibit early and strong EP onset and high loss curves. This is
also reflected in the conductivity values in Table 4.3, where they together with
Al3+ hold the highest σ values even after scaling.
Table 4.3: Curve fitted Havriliak-Negami parameters characterising the dielectric response of measured samples.
Manually entered
Sample
εS
Al3+
Ca2+
H+
Mg2+
Na+
AMetek
AM400
HTP
374.45
134.41
4168
125.66
4416
559.63
263.34
525.69
ε∞
τ1
τ2
2.00
2.11
2.03
2.11
2.30
1.95
2.07
4.25
1.00 100
2.00 100
0.035 10
1.67 100
0.0357 10
2.083 72.99
0.5 142.86
0.10 142.86
Fitted
τ3
σ
∆ε1
∆ε2
∆ε3
10 000
10 000
200
1667
200
-
1.14e-10
3.83e-11
6.61e-10
3.59e-11
3.27e-10
9.95e-11
6.22e-11
6.71e-11
0.52
5.63
5.21
4.68
8.28
6.96
8.04
16.68
378.53
138.86
98.78
91.72
1264
623.78
405.07
787.39
999.91
1000
7620
1000
7329
-
α1
α2
α3
β1
β2
β3
0.69
0.10
0.42
0.01
0.64
0.00
0.49
0.52
0.00
0.00
0.00
0.00
0.30
0.00
0.00
0.00
0.19
1.00
0.09
0.17
0.27
-
0.66
0.39
1.00
0.32
1.00
0.39
1.00
1.00
1.00
0.29
1.00
1.00
1.00
1.00
0.87
0.84
0.60
1.00
0.79
1.00
1.00
Results and Analysis | 109
110 | Conclusions and Future work
Chapter 5
Conclusions and Future work
5.1
Conclusions
The goal of this thesis was to measure and characterise the dielectric response
of a set of eight samples. These goals are met and new insights into the effects
of ion-exchanges in paper materials have been gained to further the research
of RISE and DCC in their work to develop new renewable materials for a more
sustainable future. While there is room for both improvement and further data
analysis, an extensive set of measurement data and a good basis for further
analysis has been achieved.
It is clear that the choice of ion used in the ion-exchanged paper samples
has a significant impact on the dielectric response of the papers. Both
dielectric constant and loss curve shape and position in a frequency spectrum is
affected. The measurements performed in this thesis unambiguously show that
the ion-exchanged H+ and Na+ samples exhibit the highest losses, an unwanted
property. Higher losses could be due to these ions having a higher mobility
within the bulk than the other ions. It could be that the size of ion and what
binds to it is small enough to afford high mobility. Likewise, stronger ions
might create larger compounds with what binds to it, thus restricting their
movement. Higher mobility leads to higher ionic conduction and increased
likelihood of interfacial polarisation onset. The H+ and Na+ samples were
found to be the most conductive samples and also exhibit the earliest and
strongest EP. They are also the only monovalent samples. Likewise, the
responses of the bivalent ions Ca2+ and Mg2+ follow each other rather
closely, almost to the point of interchangeability, distinguished from the other
samples, at medium MC. At wet and dry MC however the difference between
them increases somewhat. This indicates that the choice of ion valence is
Conclusions and Future work | 111
significant, impacting both the samples dielectric constant and losses, possibly
through the mechanisms of ion-mobility.
Humidity control and moisture determination was successfully implemented, but some conclusions can be drawn. The Oommen curves,
constructed for Kraft paper, proved not to entirely reflect the moisture
absorption of the paper materials studied in this thesis, with the exception
of AMetek which is close to a Kraft paper. The difference in measured
MC levels of the ion-exchanged papers indicate that the choice of ion also
influence the ability of the papers to absorb and bind moisture. While the
ion-exchanged papers originate from the same pulp, their MC at a given RH
varies significantly. It could be that certain ions enables the paper to absorb
more water, which is then released during the methanol bath and determined
during titration. It could also be that the papers ability to absorb moisture
is unaffected, but that the choice of ion influences its ability to hold water
so that different samples release absorbed water to different degrees during
the methanol bath. The Karl Fischer titration method is accurate but also
very sensitive and requires some practice, the titration procedure is a possible
source of error that at least partially could explain the differences in MC.
An important conclusion from this work is the issues of measuring very
thin samples using this kind of contact method and test cell. The issue is one of
poor contacting and was alleviated to a good degree, but some uncertainty of
the results remains. The instruments measure more than simply a sample, they
measure a system consisting of everything connected between input and output
terminals as well as e.g. stray capacitances to grounded elements in the test
setup vicinity and can even pick up background noise in very high frequency
measurements. With this in mind, this work has aimed for repeatability.
However, it can be said with certainty that with this test setup, these samples
and conditions, these are the dielectric properties including EP effects of these
samples.
5.2
Future work
This thesis has been heavily focused on the measurement of the samples, which
has both presented unexpected difficulties and has been, as expected, time
consuming. To some degree this has come at the expense of the analysis of the
measurement data; there is plenty of possible future work to better understand
both different aspects of measuring very thin samples and in the analysis of
the measurement data.
It will be worthwhile to look into non-contact methods of measuring
112 | Conclusions and Future work
capacitances of very thin samples as an alternative to the contact method
used in this thesis. A non-contact method would eliminate the issues of
poor contacting between sample and electrodes, but will introduce other
potential difficulties that could affect its performance in comparison to a
contact method.
There are several aspects of the samples measured in this thesis that
have not been characterised. The Arrhenius activation energy, crucial in
constructing master curves used in temperature correction functions used in
e.g. transformer and bushing insulation testing, should be possible to define
with the current measurement data. Additionally, as the DCC project this
thesis has been a, albeit small, part of look into several different possible
applications for ion-exchanged papers there is a high demand for extending
the measured frequency range into the GHz. This will require additional test
setups, instrument and methods. A suitable test cell should be designed to
be used with a network analyser capable of atleast several GHz. A network
analyser will use a different measuring method compared to the impedance
methods used in this work. Another avenue of application is as oil impregnated
insulation paper. The ion-exchanged papers could be impregnated before
measuring their responses to study the effect of ion-exchange also in this state.
In order to facilitate a more reliable data analysis an algorithm must be
used to filter out double layer capacitances formed by interfacial polarisation
which have a very strong influence on the measured responses. An attempt
was made in this work, but was not successfully implemented. Having filtered
the measurement data, the bulk polarisation processes will be easier to identify
and a response model, in this case the Havriliak-Negami model, can be defined
that much closer reflects the physical processes taking place. Thus providing
a model closer to the true material response. Likewise, the curve fitting
algorithm should be looked over in order get a better fit in both absolute
values but also in ratio between fitted and measured curves throughout the
whole frequency range. Different algorithms should be tested to select the one
producing the best fit. It would also be interesting to apply different analysis
models on the existing data, such as the Cole-Cole plots to better understand
the materials measured, first and foremost the ion-exchanged papers.
It is with interest and confidence in the further study of ion-exchanged
papers and their applications that this author hands over data and results to
RISE for future research.
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Appendix A: Measurement setup investigations | 119
Appendix A
Measurement setup investigations
Performing the initial measurements on both ion-changed and reference papers
raised some concerns of the validity of the data. Therefore two additional,
polymer, reference samples of different thicknesses were used. both Kapton
films from DuPont. Although there were no reference values of dielectric
constants or dissipation factors for the paper samples the manufacturers of
the plastic samples provides an extensive technical datasheet. The DuPont
polyimide, called Kapton HN, datasheet specifies a dielectric constant of 3.4
for a 50 µm sheet and 3.5 for a 125 µm sheet, both at 1 kHz. It also specifies
a dissipation factor, but only the dielectric constants have been studied in
this investigation. A dissipation factor is not always specified in all reference
material, the dielectric constant however almost always is.
Initial measurements were taken of all paper samples, the results of the
Ca2+ sample is presented in Figure A.1 as an example. First thing to notice,
is that quite high voltages were used to test any effect of voltage amplitudes,
140 Vrms is the maximum output of the IDAX. The old LCR meter has a
maximum output of 20 Vrms and was used here to increase the amplitude
range. Measurements were taken at 24 ± 3-4 %RH at 23 °C. A slight
increase in dielectric constant was noticed at the highest amplitude, and a
slight decrease in loss factor in the frequency range of the IDAX. No amplitude
dependence could be seen between 2 and 70 Vrms. In high frequencies, from
about 400 kHz and upwards, the a sharp increase in dielectric constant is
noticed. While the slope is high, the resolution is great and the increase is only
visible in the second decimal. It would been interesting to see how the curve
evolves an addition couple of decades, but this was unfortunately not available.
120 | Appendix A: Measurement setup investigations
This trend is, as later shown and discussed, visible also in measurements of
known capacitors and the majority of the other paper samples. Measurement
data from IDAX and LCR meter are exported to MATLAB where they are
processed and concatenated into a single vector for plot, the interface, at 1 kHz,
where the LCR data ends and the IDA data begins, sometimes produces a small
notch in the curve. This notch is due to measurement discrepancies between
instruments, typically though they are very small and cannot be amended. A
substantial notch would indicate that something is wrong and the setup must
be reviewed, as both data series ideal should consistent resulting in no notch
at all. The notch visible in Figure A.1 is deemed acceptable. Most noticeable
is the quite small dielectric constant values, raising some concern.
Figure A.1: Initial test measurements on the Ca2+ sample, using different high
voltages.
The initial measurements, in ambient conditions, yielded a dielectric
constant in the range of 1.5-1.6 for the 50 µm Kapton film and 2 for the 125 µm.
It should be noted, that the 125 µm film is unlabeled, hence it cannot be certain
exactly which version of Kapton it is, there are about a dozen different versions
optimized for different applications with some variations in dielectric constant
and dissipation factor. These results raised some serious concern, if the plastic
sample data is this low the paper sample data is not reliable either. The paper
data seemed a bit low at first glance, but not far outside of what is reasonable
for a very porous sample conditioned in a fairly dry environment. But, if the
test setup cannot produce good data of known materials, then clearly there
is something wrong with the setup, automatically eliminating the validity of
Appendix A: Measurement setup investigations | 121
the paper sample data. These errors needed to be investigated and addressed
before any proper study of the ion-changed papers could be carried out.
A.1
Equipment validation
The first thing to come to mind was that there might be some issues with
the measurement instruments, the IDAX and the LCR-meter, even though
they are all, supposedly, calibrated and both OPEN, SHORT corrections are
performed in the LCR meter before measurements. It is easy to test whether
the equipment gives good data on known materials to an accuracy of atleast a
handful of percent. Very high accuracy is of course harder to establish. The
measurements of the thinner Kapton samples were off by about a factor of 2,
clearly outside any errors such as dust particles on the electrodes or a slight
calibration error.
In order to test that the equipment was reliable, measurements of known
capacitors were made, both a set of three through-hole capacitors as well as an
air capacitor, without the use of any test cell in order to test only the equipment.
Additionally, tests were done on free space, introducing an air gap of known
thickness between electrodes. The capacitors tested are shown in Figure A.2,
the air gap was created by stacking plastic pieces of known thickness around
the electrodes. The through-hole capacitor were rated 1000 nF, 4700 nF and
6800 nF while the air capacitor were rated 100 nF.
(a) Capacitors of known rating.
(b) Air capacitor used to validate
equipment.
Figure A.2: Known capacitances used to test equipment accuracy.
Two LCR meters were used in addition to the IDAX, the BK895 referenced
as the new LCR and an older, HP4284A LCR meter referenced as the old
LCR, both allowing a frequency spectrum of 20 Hz to 1 MHz. Both new
and old LCR meters as well as the IDAX300 all perform reasonably well
measuring known capacitors. The through-hole capacitors were all measure
slightly above their rating, they are all manufactured to their rating with some
122 | Appendix A: Measurement setup investigations
accuracy which could explain the deviance between ratings and measured
values. It should be noted that LCR meters sometimes perform poorly towards
their very lowest frequency rating, in this case below a few hundred Hertz, as
can been seen in the data of the old LCR in Figure A.3. The capacitances were
connected through test leads of two 1 meter coax cables, crocodile clips were
used on the pins of the through-hole capacitors.
Figure A.3: Measurements on known capacitors, a way to validate measured
capacitance.
The graphs in Figure A.3 indicates that all three instruments, with test
leads, are working as expected. The slight variation in between the curves is
in the order of a couple of pico Farads. Since both LCR meters performed
good, and the older one is significantly more cumbersome to work with, it was
decided to proceed only with the new LCR as the problem did not appear to
lie with the instruments themselves.
The air capacitor was measured using the IDAX and the BK895, the new
LCR, and the results are presented in Figure A.4. The air capacitance is said
to be leaky at low frequencies, which was not noticed in these measurements.
Notable is the runaway capacitance in towards higher frequencies and the
choppiness of the curve. The choppiness is likely attributed to a somewhat
low signal strength in combination with the switching of internal components
of the measuring circuit of the meter. The runaway capacitance could be to
resonance phenomenon, discussed in Appendix B. While the numbers of the
increasing capacitance are low, single digit pico Farads, the trend is clear.
This trend was also noticed when measuring the other knowh through-hole
Appendix A: Measurement setup investigations | 123
capacitors. These issues can however not explain the low initial measured
paper permittivities, and the LCR meter is deemed to be working as expected.
Figure A.4: Measurements on an air capacitor rated at 100 pF, a way to validate
measured capacitance.
While the capacitance in both IDA and LCR systems are derived from
measurements of a phase valued voltage and current, and not measured
directly, the results of testing the equipment indicates that they are indeed in
good working order. Therefore it can be concluded that whatever the source of
the error in measuring the Kapton samples, it does not lie with the equipment
itself, nor with the test leads attached to it which was used during all tests.
A.2
Test cell comparisons
Having concluded the problem did not lie with the equipment or test leads,
the test cell itself was tested. The geometry of the test cell will affect a 2electrode test setup, where it could be assumed that an increased height of
electrodes would increase the fringe effect of field lines not passing through
the sample but rather around it through air. It might also be the case that there
is something with either electrodes or connectors that might cause an issue
with thin samples.
As a first way of controlling that the test cells was not an issue tests were
done on free space, presented in Table A.1 where an air gap of 3.75 mm was
124 | Appendix A: Measurement setup investigations
used in the spring loaded cell. Additionally, a three electrode brass cell with
a measuring electrode diameter of 77 mm and a 1 mm air gap between guard
and measuring electrode was used with an air gap of 11.75 mm between high
voltage and measuring electrodes. Ideally a very small air gap should also
have been tested, in order of micro meters, however due to practical reasons
this was not realised.
Table A.1: Air gap measurements using both the spring loaded and threeelectrode brass cell, using 50 Hz and 200 Vpeak.
Cell
Measured capacitance C (pF)
Spring loaded
4.637
Three-electrode brass 3.553
Geometrical
capacitance C0
(pF)
Ratio C/C0
4.636
3.509
1.0002
1.0125
Both cells tested with this method performed well, providing no
explanation for the poor values of the Kapton measurements. Therefore,
additional test cells were tested in order to get a better understanding of the
effect of test cell design on the results. All cells have different geometries,
and some additional features. All test cells are contact cells, where the sample
is placed between two electrodes. The first cell is the original spring loaded,
three electrode, 50 mm diameter stainless steel measuring electrode cell with
an air gap of 1 mm to guard. Second is a similar cell, using three electrodes but
77 mm diameter brass measuring electrode, also with 1 mm air gap to guard.
Third is a simple brass, 87 mm diameter brass two electrode cell, unguarded.
Lastly is a Kiethley 6105 Resistivity Adapter, originally designed to measure
surface resistivity. This guarded test fixture is housed in a shielding metal
case, uses a three electrode setup utilising a 50 mm diameter stainless steel
measuring electrode and a 3 mm air gap to guard.
Both brass electrodes are much heavier than the spring loaded cells,
asserting a higher pressure on the sample than that of the springs. Both
brass cells are also encased in epoxy so that only the electrode surface facing
the sample is exposed. The electrodes of both spring loaded cells however
have surfaces exposed to the environment even when a sample is introduced
between electrodes.
It should be noted that the electrodes of both the two-electrode brass cell
and the Kiethley cell are both a bit dirty and scratched, with a high degree of
wear and tear from years of use. The three-electrode brass was polished up by
hand, using a very fine sand paper together with water and a bit of soap and a
Appendix A: Measurement setup investigations | 125
(a) Spring loaded test cell.
(c) Two electrode brass cell.
(b) Three electrode brass cell.
(d) Kiethley test fixture.
Figure A.5: Four different test cells used to investigate the effect of design.
fair amount of time and effort. It was polished until a somewhat smooth surface
was achieved and all dirt and various coats were removed, which is about what
can realistically be achieved by hand. The two-electrode brass and Kiethley
cells were not polished. A good finish is both time and effort consuming, and
126 | Appendix A: Measurement setup investigations
a very good finish will require some machinery and finesse. In addition to the
Kapton samples, three paper samples were measured, of varying thicknesses.
A commercial bushing paper was used, called Labetek, provided by the lab
inventory. It is thinner than the other paper samples, at 100 µm.
Table A.2: A comparison of dielectric constants in different materials
using different test cells, all measurements are done in stable room ambient
conditions, 50 Hz and 200 Vpeak.
Sample
AMetek
AM400bar
Labetek
Kapton 125 µm
Kapton 50 µm
Spring
loaded
1.40
1.54
1.72
2.01
1.54
3 electrode
brass
2 electrode
brass
1.39
1.74
1.81
2.1
1.63
0.90
1.06
1.02
1.14
0.61
Kiethley
6105
1.26
1.8
1.2
Both the two-electrode brass cell and the Kiethley cell were quickly
discarded due to poor results. Perhaps they would provide a better results
after a thorough cleaning, but it was deemed unfeasible weighing the very
poor initial results and time, effort and machinery needed to complete. An
unguarded test cell should at any case be less accurate than a guarded one.
The three-electrode brass cell yields slightly higher constants than those
of the spring loaded cell, possibly an effect of its heavy weight squeezing
the samples both removing air gaps and thinning the sample. Notable is
that the results of the commercial paper from Ahlström-Munksjö is largely
unaffected comparing the spring loaded and the three-electrode brass cell. The
AM paper pressed in 400 bar for 5 minutes is quite porous, more so than the
other samples, and an increased pressure upon it could explain the increase in
constant between spring loaded and three-electrode brass cell.
It was expected that the constants of the Kapton samples would also be
largely unaffected by the heavier brass cell, as the they can be assumed to
hold very little air in the bulk. The increase in constant can be explained by
either the design of the brass cell or its heavier weight. A simple COMSOL
model, presented in Figure A.6 was design to investigate the effects of test cell
geometries, looking only at guarded test cells.
Appendix A: Measurement setup investigations | 127
Figure A.6: COMSOL model of the three electrode design, zoomed in towards
the area of the air gap to guard and the edge of the sample, 2D-axisymmetrical
view.
The Maxwell capacitance between high voltage and measuring electrodes
(C21 component) was evaluated at different air gaps between guard ring and
measuring electrode as well as different air gaps between high voltage and
measuring electrodes. The air gap representing the area where a possible
sample would be placed is called sample thickness in Table A.3 where the ratio
of the simulated capacitance over a theoretical pure geometrical capacitance
between high voltage and measuring electrodes, calculated using MATLAB,
is presented. The pure geometrical capacitance was calculated as:
C0 =
ε0 Area
Sample thickness
(A.1)
[F]
Table A.3: Ratio of simulated capacitance to theoretical capacitance of
air using a simple three electrode COMSOL model. Air gap and sample
thicknesses in millimeter.
Sample thickness
Air gap
0.1
0.5
1
1.5
0.5
1
1.5
2
1.0116
1.0150
1.0171
1.0227
1.0245
1.0366
1.0459
1.0530
1.0327
1.0494
1.0624
1.0737
1.0382
1.0567
1.0726
1.0877
128 | Appendix A: Measurement setup investigations
The ratio provides an idea of how good the assumption of a pure
geometrical capacitance is. The data in Table A.3 clearly shows, no matter the
thickness of the sample, that the error of assumed capacitance increases with
an increasing air gap to guard. Likewise, the error increases as the sample
grows in thickness for a given air gap. This shows two things, firstly that
there should be no issue with a very thin sample thickness in a test cell of this
geometry, the paper samples to be studied in this thesis range roughly between
0.1 and 0.2 mm. Secondly, it shows that for a 1 mm air gap, the geometry of
the test cell is not able to explain the large deviations in measurement data
for the Kapton samples, even though the error sharply rises with an increasing
sample thickness of air. Additionally, it proves that at most the error, for all
tested geometries is below 10 %, and only 1.5 % for a thin sample and 1 mm
air gap.
It must be noted, that the field lines originating from the high voltage above
the air gap to guard splits between measuring electrode and guard. To get more
accurate results of the assumed geometrical capacitance, it can be assumed
that the field lines splits in equal parts, so that half of them would terminate in
the measuring electrode. This means that the effective area of the measuring
electrode increases by half of the area of the air gap, as in Equation A.2.
rairgap
)
(A.2)
2
Correcting the area of the geometrical capacitance yields ratios between
simulated capacitances and assumed capacitances as presented in Table A.4.
Ae = π(r +
Table A.4: Ratio of simulated capacitance to corrected theoretical capacitance
of air using a simple three electrode COMSOL model. Air gap and sample
thicknesses in millimeter.
Sample thickness
Air gap
0.1
0.5
1
1.5
0.5
1
1.5
2
0.9916
0.9756
0.9587
0.9417
1.0043
0.9963
0.9857
0.9734
1.0115
1.0067
1.0001
0.9914
1.0177
1.0153
1.0096
1.0029
It is noteworthy, that including the correction factor results in an over
estimation of capacitance when the sample is thin in relation to the air gap.
For thin sample thicknesses and a wide air gap, the error even increases, as
Appendix A: Measurement setup investigations | 129
can been seen when comparing the results for an air gap of 2 mm and a sample
thickness of 0.1 mm. This correction factor has been used in previous works
[50], but does not always necessarily increase the accuracy of measured data,
this can be comparing the data for the thinnest sample thickness and air gaps
wider than 0.5 mm. It can also be noticed, that for the thickest sample size,
the accuracy increases with increasing air gap while the inverse holds true
without the correction factor. Apart from the thinnest sample size, accuracy
is increased across the board compared to not using the correction factor. The
samples to be measured in this thesis range between about 100 µm to 200 µm
and the air gap of the test cell is 1 mm, meaning that the estimated accuracy of
the geometrical capacitance is off by less than 2.5 %. The thicker the sample,
the smaller this error becomes.
After having tested different test cells on a selection of materials, and
having done some simple simulations of geometries, it is concluded that the
issue with poor measurement data does not stem from the test cell itself, unless
of course they all share the same problem but to a varying degree, which
is highly unlikely. It is also concluded that the spring loaded cell, while
not providing as good results as the three-electrode bass cell, should suffice
going forward. This cell is preferable for practical reasons, as the spring is
replaceable, it has screws to create a tight and secure fit and as it both smaller
and lighter to work with. Its electrodes also have a smoother surface, which
should give more accurate measurement data.
It appears that the issue is largely unaffected by choice of cell and material,
although the cells provide different results none of them are correct. A
common culprit in issues like this could be a problem of poor contact between
sample and electrode. A poor contact means that the electrode is not in full
contact with the sample, leaving small air gaps between them and can often
arise when either sample or electrode is not entirely flat but rather rough to
some degree.
A.3
Pressure tests
If a contact problem is at hand, increasing the pressure applied on the sample
should smooth the contact surface and reduce potential air gaps. Paper, which
is made from fibres of cellulose, lignin and hemi-cellulose, will have a rough
surface at a micro scale. The roughness is dependent on the size of the fibres
and their positions when the paper is made. Cutting the fibres into nano-size
one can achieve a much smoother surface, much like grains of sand compared
to pieces of rock produce a smooth or rough surface when placed on a plane.
130 | Appendix A: Measurement setup investigations
The papers in this study have an uneven surface and the fibres are not nanosized, placing them in a test cell will yield some air gaps between paper and
electrode as a function of the roughness of the paper.
Whenever an air gap between any of the electrodes and the sample appears,
it can be described as a capacitance in series with the sample between the
electrodes. A rough sample surface, where only the highest points on the
surface is in contact with the electrode will create a sequence of parallel
capacitances consisting of a sample capacitance and a series air and sample
capacitance, as in Figure A.7. Since air has a relative permittivity of 1, lower
than any paper insulation material, the sequence of series air gap capacitances
will lower the total permittivity seen by any measurement.
Figure A.7: A rough surface can be modeled as a sequence of a sample
capacitance in parallel with a series are and sample capacitance.
One way of investigating whether there is an issue of poor contacts creating
air gaps is to increase the pressure on the sample, so that the sample is
somewhat squeezed, minimizing any air gaps in the contact interface making
it smoother. And then, comparing these results with those using a lower and
or higher pressure. There will however be a trade off in accuracy, as too
much pressure will reduce the thickness of the sample, needing a re-measuring
of sample thickness while the pressure is applied. A too high pressure will
also not be representative of the material behaviour itself, as it will likely not
be applied under such conditions. Too little pressure however, and contact
problems are prone to arise.
Three different levels of pressure were asserted on a selection of samples
by using three different springs of different stiffnesses in the spring loaded test
cell. The heavy three-electrode brass cell was included for comparison. In
addition to the paper and Kapton samples, three sheets of poly-carbonate (PC)
from Nordbergs Tekniska AB of different thicknesses was used as these all
have well defined reference values in the manufacturer datasheets. The results
are presented in Table A.5.
Appendix A: Measurement setup investigations | 131
Table A.5: A comparison of dielectric constants applying different pressure
on the sample in an attempt to amend issues of poor sample contacts. All
measurements except on Kapton performed at 50Hz, 200Vpeak, 23% RH and
22 °C. Kapton measured at 1 kHz, 200 Vpeak, 50% RH and 23 °C for datasheet
comparison.
Spring loaded test cell
Sample
Original
spring
Stiff
spring
Stiffest
spring
Threeelectrode
brass cell
Reference
AMetek
95 µm
AM400bar
162 µm
Labetek
100 µm
PC-film
140 µm
PC-film
250 µm
PC-film
475 µm
Kapton
125 µm
1.4
1.48
1.48
1.4
−
1.55
1.61
1.67
1.75
−
1.68
1.82
1.96
1.8
−
1.88
2.14
2.23
2.02
3.0
2.66
2.65
2.6
2.53
3.0
2.77
2.81
2.85
2.76
3.0
2.13
2.45
2.32
−
3.5
The results in Table A.5 show a few things. Firstly, all samples show an
increase in dielectric constant with increasing pressure, except for the 250 µm
PC-film, regardless of thickness of the sample. This strengthens the idea of a
problem of poor contact. It also shows, surprisingly, that this effect can also
be seen in the PC-film samples, which was assumed to be much smoother than
the rather rough paper surfaces. This could be due to an unevenness in either
sample or electrodes.
The increase in dielectric constant could also be due to the fact that the
samples are squeezed, reducing their thickness to the point where thickness
of the sample, measured before the samples were placed in the test cell at
1 atm of pressure, is a gross overestimation resulting in an overestimation of
the constant. The constant is directly proportional to the thickness of the
sample through the geometrical capacitance. Ideally, the thickness of the
132 | Appendix A: Measurement setup investigations
sample should be measured while under pressure, this is however hard to do
in practice.
There is an alternative way of creating a high pressure on the sample,
namely the use of electrostatic force. When two plates of different potential,
U , are separate by a distance d, with some plate charge Q, an electrostatic force
F , is generated. The force will act in a way as to close the distance between the
plates, thus applying a force and subsequent pressure on the sample between
the plates. Equation A.3 indicates how this force can be calculated.
1
F = QE
2
E = U /d
QU
F =
2d
Q = CU
(A.3)
A DC power supply, a RND 320-KA3005D, was connected to a x2000
amplifier, a Trek 20/20C-HS, to generate a high DC voltage. The amplifier
was connected to the high voltage electrode of the test cell. An electrometer, a
Kiethley 6514, was connected to the measurement electrode. The electrometer
was protected using two transient voltage suppression diodes rated at 100 V,
shunt connected to ground with opposite orientation in order to protect against
different polarity overvoltages.
Increasing the applied voltage from 1 kV to 12 kV in steps of 1 kV, the
plate charge was read from the electrometer a few seconds after the voltage
step in order to get a steady reading, capacitance and permittivity were both
calculated. After having reached 12 kV, the applied voltage was decreased
back to 1 kV in steps of 1 kV in order to also measure any hysteresis. The
results are presented in Figure A.8.
Appendix A: Measurement setup investigations | 133
Figure A.8: High voltage DC on Kapton 125 µm, top graph shows measured
plate charge, bottom graph shows permittivity and applied electrostatic force.
Reference permittivity of Kapton is 3.5 at 1 kHz.
The results in Figure A.8 shows a couple of interesting things. First of
which is a clear pressure dependency, as the applied voltage increases the
applied force increases, and the calculated permittivity slowly climbs towards
the expected reference value of 3.5. At 12 kV DC the permittivity is calculated
as 3.29. At this voltage level the force is great, about 140 N, which equals about
14 kg.
Another interesting result is a clear hysteresis. It appears that the polymer
sample accumulates charge linearly with increasing voltage, but has trouble
releasing charge when the voltage is decreased. This results in a higher
calculated capacitance and corresponding permittivity. It could also be the
case that the polymer, after having experienced such a high compressing force,
has trouble expanding again, affecting its behaviour. It must be noted that the
geometrical capacitance was assumed constant at all voltage levels, meaning
that the assumed thickness of the sample was constant.
Both tests using different springs and a high electrostatic force indicate
a pressure sensitivity in the measurement results: higher pressure gives, as
expected, a higher measured dielectric constant. The springs used were not
very stiff, providing a pressure much lower than that of the electrostatic force.
No stiffer, but still able to fit, springs were immediately available, although new
ones could have been bought. Therefore, in order to generate a higher pressure
134 | Appendix A: Measurement setup investigations
without the need of high voltages, an elastic rubber sheet was used. Pieces of
the rubber sheet was cut and placed beneath the measurement electrode plate
so that the plate would have a height about 1 mm greater than the guard ring.
This way, when the high voltage electrode is pressed onto the sample, the
measurement electrode is pressed downwards compressing the rubber sheet
pieces. The pieces are elastic and will expand, asserting a pressure upwards
while to trying to regain their original form, generating a fairly high pressure
on the sample. In order to compress the pieces, and the whole setup, nylon
screws was placed in the Teflon sheets, the white discs in Figure A.5a, were
tightened. While compressing the pieces an equal height, the use of more
pieces will generate a higher pressure. Setups using three, four and six pieces
were used while measuring the 125 µm Kapton sample at 1 kHz, the results are
presented in Table A.6.
Table A.6: Measured dielectric constant of the 125 µm sample while varying
applied pressure using different amounts of elastic rubber pieces. Measured
at 1 kHz, 23 °C and RH48%, reference value claimed at 1 kHz, RH50% and
23 °C.
Pieces
εr
Reference
3
4
6
2.64
2.72
2.75
3.5
3.5
3.5
Using a torque meter to apply a known torque when tightening the screws
it is possible to further control the pressure applied on the sample. Different
torque levels were tried on the 125 µm Kapton sample and the Na+ paper
sample. The nylon screws were exchanged for metal screws as they would
risk being damaged by a high torque. The metal screws will not be damaged,
but may rather cut into the Teflon threads at high torque, care was taken to not
risk this. From the results in Table A.7 it’s apparent that the Kapton sample
was not affected by different torque levels, indicating that 1 cm*kg is enough.
The Na+ paper sample indicates that 2 cm*kg, is enough. While 3 cm*kg
could possible give a slightly better result, again running the risk of simply
compressing the sample too much, 2 cm*kg was deemed enough.
It is clear, from this test as well, that a higher pressure generates a higher
measured dielectric constant. It is also clear that the setup of rubber pieces
gave a much higher pressure applied on the sample. The highest constant
measured, using the stiff spring, was 2.45, while the lowest measured constant
using rubber pieces was 2.64 and the high 2.75. 2.75 is still only about 80%
Appendix A: Measurement setup investigations | 135
Table A.7: Torque levels and dielectric constant of Kapton 125 µm and Na+
paper. Measured at 23 °C, 200 Vpeak and RH48%.
Torque
Kapton 50 Hz
Kapton 1 kHz
Na+ 50 Hz
Na+ 1 kHz
1 cm*kg
2 cm*kg
3 cm*kg
4 cm*kg
2.66
2.65
2.65
2.65
2.65
2.64
2.64
2.64
5.52
5.62
5.65
-
3.52
3.53
3.52
-
of the reference value, but is the highest value achieved so far with AC.
The trials of different pressures strongly indicates a pressure sensitivity in
the test setup. However, not only does the results move towards the reference
values with increased pressure, looking at Table A.5, it appears that the thinner
the sample the worse result. Both of these factors indicate that an issue of poor
contacting is at hand. An air gap of fixed, or semi-fixed, dimensions would
have an increasingly strong impact on the measurements as it would make up
an increasingly large portion of the combined sample and air gap thickness.
An increased applied pressure on the sample would both smoothen out any
surface roughness of the sample as well as minimize any potential air gap due
to poor contacting, assuming the sample is not completely rigid.
The results are all still lower than expected, albeit better with higher
pressures. One often used method to assure good contact is to paint the
electrodes directly onto the sample with a highly conductive paint, so that
the paint will even out any roughness of the surface. Comparing results of
using painted electrodes with non-painted contact electrodes is a good way
to determine if there is a contact issue, assuming that the paint is conductive
enough to pose a negligible impedance and that all other parameters are equals.
A.4
Painted electrodes
Silver paint is often used to paint electrodes, as silver is a very good conductor.
Two different silver paints were available, an older paint from DuPont and one
silver ink, CI-1036 from Nagase ChemteX.
Five samples were chosen to be painted, each were measured in three ways.
First they were measured unpainted in the original spring loaded test cell, then
using only the painted electrodes connected to the test leads with copper tape,
and lastly measured in the test cell with painted electrodes.
A steel pipe, 1 mm thick with an inner diameter of 50 mm was used as a
template to paint around, creating a painted electrode of the same dimensions
136 | Appendix A: Measurement setup investigations
as the spring loaded cell. Examples of the painted cells on the 125 µm Kapton
and PET-film can be seen in Figure A.9.
(a) High voltage electrode on Kapton.
(b) Guard and measuring electrodes on Kapton.
(c) High voltage electrodes on
PET-film.
(d) Guard and measuring electrode on
PET.
Figure A.9: Electrodes painted with silver paint on Kapton and PET-film.
Appendix A: Measurement setup investigations | 137
Table A.8: A comparison of dielectric constant using silver painted electrodes
to amend issues of poor sample contacts. Measured at 22 °C and RH22-23%,
frequency was set to that of the reference values.
With test cell
Sample
Painted
Without test cell
Unpainted
Painted
PC 140 µm
−
1.997
2.77
Kapton
50 µm
3.3
1.31
3.14
Kapton
125 µm
3.41
2.13
3.39
PET-film
100 µm
3.35
2.03
3.21
Hitachi
thin board
197 µm
7.42
3.06
7.5
Reference
2.9
@1 MHz
23 °C
RH50%
3.4
@
50 µm,1kHz,
23 °C,
RH50%
3.5
@
125 µm,
1kHz,
23 °C,
RH50%
3.2
@1 MHz
RH50%
Unknown,
50 Hz
The thicker Kapton sample, along with he PC and PET-film, were painted
with the old DuPont paint, the thinner Kapton sample and the Hitachi thin
board were painted with the silver ink from Nagase ChemteX.
Using the samples with painted electrodes in a test cell works well in
theory. As long as the conductivity of the silver paint is good enough, which is
a fair assumption, any air gaps between electrodes and sample will not matter
as long as the silver is in contact with the electrodes. That is, the painted
measuring electrode has contact only with the measuring electrode of the test
cell, and likewise for the guard ring. If this is not achieved, the assumed
geometrical capacitance will be off. In practice however, it turned out to be
quite hard to fit the painted samples properly into the test cell. This because
neither paint nor electrodes are transparent. There was a bit of trial and error
138 | Appendix A: Measurement setup investigations
getting good readings, placing the sample carefully, reading the meter and
adjusting the sample position if the reading were far from the expected value
which would point towards poor positioning. Several test were run to ensure
that the results were reproducable.
The fact that one cannot see whether the measuring electrodes are in
contact with each other, so that the measurements correspond to the assumed
geometrical capacitance of the setup, does introduce some new sources of
error. In Table A.8 one can see that the PET-film has a slightly high constant
both compared to the reference value as well as the painted sample measured
outside the test cell. This is most likely due to the problem of perfect
positioning, but was deemed good enough to show that the test cell itself works
well with this thin painted sample.
The kind of positioning issue is the most likely explanation also for the
125 µm Kapton sample, which shows very similar results with and without the
test cell when painted.
Unfortunately, the silver paint did not adhere well to the PC-film. The
paint would crack and release at the smallest bend, and removing the copper
tape holding the plugs to the paint would also remove large portions of the
paint. Therefore, only one reliable measurement could be taken of this painted
sample, one outside of the test cell.
The measurements of painted samples are all considerably closer to
the reference values than those of unpainted samples. The discrepancy to
reference values could be due to different environmental conditions, humidity
and temperature, between reference and lab environment. Additionally, both
silver paint and copper tape could have some small influence on results.
Assuming that the paint is in very good contact with the sample, without
penetrating into it, effectively removing any small air gaps between electrode
and sample, any issues of poor contact should be removed. Comparing the
painted results, with and without the test cell, to the reference values, again
indicates that indeed there is a contact issue at hand.
Using painted electrodes is however not viable on paper samples, as the
paint solvent would penetrate the paper. This can easily be seen in the test
on the Hitachi thin board, as all the painted results are surprisingly high, most
likely due to sample penetration. This begs the question, can the measurement
method used in this project be adjusted to correct for this contact problem, or
will another method have to be utilised?
Appendix A: Measurement setup investigations | 139
Figure A.10: Copper tape was used to create electrodes, here examples of
Kapton 125 µm, Kapton 50 µm and Hitachis thin board can be seen.
A.5
Taped electrodes
Conductive tape can sometimes be an alternative to conductive paint in order
to get around the uncertainties and issues introduced when the paint solvent is
absorbed into to the paper substrate bulk. Conductive tape, such as copper or
aluminium tape, consists of a metal film coated with an adhesive on one side,
typically a conductive or non-conductive pressure sensitive acrylic adhesive.
∗
The adhesive, being nonreactive, should not penetrate the substrate bulk
while simultaneously assuring a good fit on the substrate filling any troughs
and unevenness on a rough surface.
Square shaped pieces of tape was cut out to form a two electrode setup
when fitted on the samples, the polymer and Hitachi thin board samples can
be seen in Figure A.10. The test leads were connected in the same way as for
the painted cells. Enough pressure was applied, by hand, on the tape as to
ensure a good fit on the samples. The taped electrodes were measured using
the BK895 LCR meter, and the results can be seen in Table A.9.
It is clear that the taped electrode did not perform well on the polymer
substrates, although the setup did provide a substantial increase in measured
permittivity compared to the measurments of the polymers using the test cell
without paint or tape, see Table A.8. Caution should be observed when making
a direct comparison however, as the relative humidity of environment when
∗
Pressure sensitive adhesives is a type of nonreactive adhesives, forming a bond with the
surface when pressure is applied. No water, solvent etc is needed.
140 | Appendix A: Measurement setup investigations
Table A.9: Measured relative permittivity using conductive copper tape as
electrodes. Measured using the BK895 LCR meter at 2 Vrms, RH 45% and
22 °C.
Sample
Taped electrodes
Reference
Kapton 50 µm
Kapton 125 µm
Hitachi thin board 197 µm
Na+ 147 µm
1.82
2.52
5.24
3.2
3.4, 1kHz 23 °C RH50%
3.5, 1kHz 23 °C RH50%
Unknown, 1kHz
Unknown, 1kHz
measuring was very different. Even though the sample had been stored in
a sealed container and left out in the ambient environment for only about an
hour, the increased humidity levels of the taped electrode measurements could
explain atleast part of the observed increase in measured permittivity.
The sodium paper permittivity was measured, at RH 22% and equal
temperature, to be about 2.25. The taped electrode test show a significant
increase in permittivity. However, whether this is due to a better contact due
to a good fit of the tape or due to an increase in humidity is hard to tell. Most
likely, both factors are at play.
The results do hold some promise for the paper substrates. However,
ideally, the taped papers would be fitted inside the test cell when performing all
measurements. This in part due to the test cell having a guard ring, improving
accuracy of measurement data. A guard ring can however also be made out of
tape. Fitting the taped sample inside the test cell is troublesome, as you need a
perfect placement to get each electrode in full contact and only in contact with
its respective electrode of the test cell. This can be hard to achieve, as there is
no way to visibly assure a good fit.
A.6
Physical Vapor Deposition of electrodes
Another alternative to conductive paint and tape is to evaporate metal
electrodes onto a substrate, called Physical Vapor Deposition. There are
different techniques to achieve this, of which one is Thermal Evaporation, a
type of Thin Film Deposition. In short, Thermal Evaporation involves heating
a solid material inside a vacuum chamber to temperatures producing a vapor
pressure. Heating the material in vacuum means that even a relatively low
vapor pressure produces a vapor cloud inside the chamber and continuous
heating creates a vapor cloud stream which is directed at the substrate. The
Appendix A: Measurement setup investigations | 141
vapor stream then condenses on the substrate creating a coating or film. A
diagram of evaporation process can be seen in Figure A.11.
Figure A.11: Diagram of the Thermal evaporation process [51].
There are two primary techniques to heat the material, namely Filament
Evaporation and Electron Beam Evaporation. Filament evaporation involves
placing the material to be evaporated in a ”boat” or trough, essentially thin
sheets of metal capable of sustaining very high temperatures. A relatively low
voltage is then applied across the boats, generating a very high current, often
several hundred amps, heating and evaporating the material inside it. Electron
beam evaporation involves shooting a very high energy electron beam at the
material, thus heating it. This method requires much greater voltages however,
in the range of 10 kV, but very small currents. Since a metal can be evaporated
in pure form, no solvent is needed in evaporation techniques meaning that only
the desired metal will come into contact with the substrate when creating the
electrodes, thus in theory lowering the risk of bulk penetration.
142 | Appendix A: Measurement setup investigations
Figure A.12: Deposited thin film electrodes of Au on trafo paper? to the left
and Ag on Hitachi thin board to the right.
The thermal evaporation technique was used on two paper substrates from
Hitachi, courtesy to RISE for providing finished and ready to use samples,
seen in Figure A.12. Gold electrodes were evaporated onto a 100 µm winding
paper and silver was used to created electrodes on a thin board of the same kind
as previously used. At 1 kHz, 22 °C and 44 %RH, the permittivity of the thin
board was measured to be εthinboard = 8, and at 50 Hz to 11.35. The winding
paper was measured as εwindingpaper = 6.1. The results appear high, even
without a reliable reference, and it seems plausible that a bulk penetration of
some degree has occurred also with this technique. For reference, the Hitachi
thin board permittivity was measured to about 3 at 1 kHz using the test cell in
ambient conditions of about 22-33 % RH, which is expected to be a bit low
due to the contacting issues.
A.7
Water electrodes
One way to ensure a perfect contact is to use a conductive solution which will
not penetrate the sample but fill every roughness of the surface. Water fits this
criteria when used on certain samples, such as Kapton which will not absorb
any water, atleast not in the time it takes to setup and conduct a measurement.
The idea of using water electrodes is to exchange regular metallic electrodes
with conductive energized water. There are, of course, some practical issues
which need be overcame in order to achieve this, one of which is to make sure
there are no air bubbles in contact with sample. Another issue to ensure there
is no leakage of water in the interface between water and sample. Another
Appendix A: Measurement setup investigations | 143
issue to construct suitable vessels to hold the water while remaining in a fixed
position, should the setup be allowed to even just slightly move one risks
leakage of water.
A water electrode test setup was constructed with what material was
immediately at hand in the lab, visible in Figure A.13. Two plastic containers
was used as water holders, holes were cut into their sides to both pour water
through and act as holes to put cables through in order to apply a voltage. The
cans were put on a wooden pallet, and pieces of wooden planks were screwed
on the pallet to hold the containers in place in a horizontal plane. Straps
were strapped across the containers to fix their vertical position. The sample
to be measured was placed between container openings and the containers
were aligned such that their openings met each other precisely as to created
aligned electrode areas. The alignment was fine tuned by used of distances
between container and planks. The containers were carefully filled with
regular tap water∗ at a fairly slow pace as to avoid creation of air bubbles.
A first test showed heavy leakage around the sample, therefore a layer of
water proof silicone was introduced around the sample and container interface.
The voltage across the sample was applied through dipping banana contacts
connected to the IDAX300 through BNC connectors.
Figure A.13: Water electrode test setup.
The silicone was water proof for a fairly short amount of time, around 15
∗
One might at first thought think of using distilled water, which would be a mistake as it’s
the salt and ions solved in the water which gives it its needed conductivity.
144 | Appendix A: Measurement setup investigations
minutes. A first measurement was started, but towards the end of the short
sweep a small and slow leakage was noticed. It was expected that the leakage
would increase with time, but was deemed stable enough to allow for one
additional sweep. The measured capacitance of the two measurements were
almost identical, 262 pF and 263 pF, measured at 200 Vpeak and 100 Vpeak
respectively. No air bubbles could be noticed, although the silicone layer did
cover almost all surface area from view.
The inner diameter of the water container openings were measured to be
34 mm, giving a relative permittivity of 4.07 at 1 kHz at both measurements.
The fact that both sweeps measured the capacitance to be, almost, the same
although the second sweep had a slow drip of water leakage through the whole
sweep shows that this leakage has already started during the first sweep, but
not yet pushed through the silicone layer. The reference value of the Kapton
sample is 3.5 at 1 kHz, meaning that the measured value is high. This can very
likely be explained by the fact the water surface on the sample had increased to
be slightly larger than the container opening, creeping over the container edge
while still being in contact with the sample. A slightly larger effective area
than the one used to calculated the geometrical capacitance would results in
a slightly higher calculated permittivity. Increasing the radius of the surface
area by 1 mm yields a permittivity of 3.64, an increase of 1.5 mm yields a
permittivity of 3.44. Table A.10 collects these data. An increase between one
and two millimeter is very plausible, although the surface area would no longer
be perfectly circular any more due to gravity pulling the leakage water down.
Table A.10: Permittivity of Kapton 125 µm using water electrodes. Varying
water surface radius due to uncertainty of true radius value when water leakage
starts.
Radius
εr
17 mm 4.07
18 mm 3.63
18.5 mm 3.44
The results show that the theory of using water electrodes to solve contact
issues works in practice. It also provides a good reference to show that the
manufacturers claimed permittivity can be reproduced. Additionally, this
test too points towards poor contacting in the original test cell being the
source of the very low measured capacitances and subsequent permittivity
values. It must however, perhaps a needless reminder, be remembered that
water electrodes cannot be used on the paper samples due to them being very
Appendix A: Measurement setup investigations | 145
hygroscopic.
A.8
Summary
In Appendix A several different test setups has been tried in an attempt to
understand the poor initial measurement results. By testing both different test
cells, including 2 and 3 electrode cells, different levels of applied pressure,
as well as alternative electrodes including water, tape and painted electrodes,
some conclusions can be drawn.
From tests using different test cells, it can be concluded that no other
contact-method cell available gave much better results, indicating that it
would not be the test cell itself that was the issue. Likewise, tests on
known capacitors, including the 100 pF air capacitor, shows that neither
the BK895 LCR nor IDAX300 devices are at fault. By applying different
levels of pressure on the sample, it can be concluded that the measurement
results appear better with increasing pressure and that the measurement errors,
compared to reference values, increases with thinner samples. This indicates
that the cause of the poor initial measurement results are poor contacting
between sample and electrodes.
Different alternative electrodes were tried, where the contact issue could
be addressed. The combined results of the test using taped, painted and
water electrodes supports the idea that there is a poor contact between sample
and electrode. The results of both water and painted electrodes on polymer
samples, where the paint and water would be liquid enough as to achieve
a close to perfect contact, are close to the reference values. Remaining
differences could perhaps be due to different humidity and voltage levels. The
reference values are collected from manufacturer data sheets, and produced
by different measurement standards not available to the author of this thesis.
Evaporated test cells should in theory also be a way to achieve very good
contact, but the results indicate that the paint might have penetrated the bulk
when condensing. The results of the different setups are summarized in
Table A.11 including the three most tested samples.
146 | Appendix A: Measurement setup investigations
Table A.11: Summary table of measured dielectric constant using different test
setups, including the three most tested samples. Kapton samples measured
at 1 kHz, Hitachi thin board measured at 50 Hz with 1 kHz values inside
parentheses when available.
Sample
Kapton 50 µm
1kHz
Kapton 125 µm
1kHz
Hitachi thin board
50 Hz (1 kHz)
Test cell
Painted
Taped
Evaporated
Water
electrodes
Electrostatic
force
Rubber
Reference
1.31
3.14
1.82
-
2.13
3.39
2.52
3.4-3.6
3.06
7.5
6.4 (5.24)
11.35 (8)
-
-
3.29 (DC)
-
3.4
2.75
3.5
-
The conclusion drawn from the study performed within Appendix A is
that there is an issue of poor contacting. This issue has, to the knowledge
of this author, not been experienced to this extent in other students studies
on similar topics and while using the very same test cell. The fact that this
issue is so apparent in this thesis might be explained by the second conclusion
drawn, which is that this issue increases, rather quickly, with thinning samples.
Previous studies, both MSc and PhD, have all either studied impregnated
papers or samples thicker that 1 mm. The papers to be studied in this thesis
are all around 150 µm to 200 µm thick.
While this sub-study has not been able to provide a good alternative to the
test cell originally intended to be used it has shed some light on the cause of the
poor initial measurement values. The cause can now, with good confidence, be
explained. What remains however, is a study of how and when this contacting
air gap affects a dielectric response. It can safely be assumed that the air gap
does not simply add a scalar to the all measurement points, but rather also
changes the response curves shape in addition to shifting the curve down in an
ε − f plot.
Appendix B: Resonance in RLC circuits | 147
Appendix B
Resonance in RLC circuits
Looking at Figure A.4 it is clear that some unexpected phenomenon occurs at
higher frequencies, starting at around 100 kHz. First of all, the curve becomes
very choppy with three sharp spikes. This is most likely due to the switching
of components of the measuring bridge in the LCR meter, and while neither
wanted nor expected can be explained and accounted for. Another example
of component switching can be seen as a small notch around 15 kHz. The
other unexpected trend is a sharp increase in measured in capacitance. The
test object, an air capacitor of known and stable capacitance, is expected to
hold a constant value over the entire measured frequency range.
Figure B.1: Varying the test lead length impacts the observed behaviour of
increasing measurement error.
148 | Appendix B: Resonance in RLC circuits
Because of this assumption, the test leads was deemed the probable cause
of the observed behaviour, as the equipment itself provided good results on
the other capacitors. In order to try this, different cable lengths were tried, as
can be seen in Figure B.1, performing both OPEN and SHORT corrections for
each new cable lengths.
Introducing very long test leads, of course unrealistic in any proper
measurement but a good illustrative test, also introduces heavy measurement
errors. The test leads are coaxial cables which always comes with both
stray capacitance, residual resistance and some inductance. Increasing the
lead length will increase the leads contribution to these parameters of the
measured circuit. The self inductance of a coaxial cable (Lcoax ) depends
upon its geometry, cable length (L) and the diameter of inner (d) and outer
(D) conductors, as well as the relative permeability of the dielectric medium
between conductors (µr ). The RG058 uses polyethylene (PE) as a dielectric,
which can be assumed to have a relative permeability of 1. The inner diameter
of the M17/028 RG058 cable used is 0.90 mm, the shielding diameter is
3.50 mm. The self inductance can be calculated as [52]:
µ0 µr L D
ln( )
(B.1)
2π
d
Additionally, measuring any capacitive sample, be it a sheet of paper
or an expensive capacitor used in electronics, no capacitor is ideal. There
is always a small amount of resistance in series with any ideal capacitor
(known as Effective Series Resistance (ESR)), as well as a small amount of
series inductance due to its conductor geometry (known as Effective Series
Inductance (ESL)), as well as a very large leakage resistance between the
capacitor plates. These three parasitic effects causes an ideal capacitor to in
reality become an RLC network, as in Figure B.2. At the resonant frequency,
a capacitive component will shift and start to behave rather as an inductive
component than an capacitive one.
Lcoax =
Figure B.2: A real capacitor can be described as an RLC network.
Appendix B: Resonance in RLC circuits | 149
Together a capacitive, or inductive for that matter, sample and the test
leads, along with any plugs and connectors, create a RLC circuit to be
measured. Any RLC circuit will exhibit resonance behaviour. In a simple
series RLC circuit, at a certain frequency resonance between the inductive and
capacitive element will occur as the collapsing magnetic field of the inductor
charges the capacitor, and the discharging capacitor rebuilds the magnetic
field in the inductor. As resonance occurs, the reactance of the inductor
and capacitor are equal, canceling each other out resulting in a near zero
impedance in a series circuit (in a parallel RLC circuit the impedance would
reach infinity). All circuits contain some resistance however, damping this
oscillation. By equating inductive and capacitive reactances, the resonance
frequency of any circuit can be solved for:
1
√
(B.2)
2π L · C
In a circuit without resistance, plotting the impedance of a series RLC
circuit would exhibit a sharp spike towards zero at the resonance frequency.
The damping effect of resistances will decrease the magnitude of this as well
as broadening the spike into a curve of increasing width. As the impedance
decreases, an LCR meter applying a constant voltage magnitude will see an
increasing current and an increasing capacitance. It could be the fact that
what was observed in Figures A.4 and B.1 is just this, a damped decrease
of impedance resulting in an increasing apparent capacitance with a peak
somewhere outside of the measured frequency spectrum.
Assuming that the ESL of the air capacitor and the stray capacitance
of the test leads are small, and neglecting any mutual inductance between
test leads, the capacitance of the capacitor and inductance of test leads will
dominate. Calculating the inductance of the test leads using Equation B.1 and
the resonance frequency using Equation B.2, the resonance frequency of a
simple equivalent RLC circuit was found as in Table B.1.
fresonance =
150 | Appendix B: Resonance in RLC circuits
Table B.1: Resonance frequencies of an (R)LC circuit, fr = f (L, C) in MHz.
L (nH)
C (pF)
100e-12
200e-12
300e-12
400e-12
500e-12
272 (1m)
543 (2m)
815 (3m)
2720 (10m)
30.5
21.6
17.6
15.3
13.6
21.6
15.3
12.5
10.8
9.7
17.6
12.5
10.2
8.8
7.9
9.7
6.8
5.6
4.8
4.3
Measuring the 100 pF air capacitor using in total two meters of coaxial
test leads creates a circuit with a resonance frequency of about 22 MHz. A
heavily damped circuit will have show an impedance curve with a peak at
the resonance frequency with a broad slow slope on either side. It appears
plausible that what is visible in Figures A.4 and B.1 is precisely this, the slow
slope of a resonance peak. The LCR meter stops at 1 MHz, another LCR meter
or a network analyser could be used reach higher frequencies.
Taking into account also the ESL of the test subject, slightly increasing the
total series inductance, will lower the resonant frequency. In fact, any increase
in capacitance and series inductance will lower the resonance frequency.
Appendix C: Karl Fischer titration | 151
Appendix C
Karl Fischer titration
The aim of this chapter is simply to provide the interested reader with a more
detailed description on how the titrations were performed.
C.1
Emptying and cleaning measuring cell
• Turn titrator off if on and put on rubber gloves
• Prepare some paper towels to place removed components on, avoiding
dirt
• Prepare some waste vessel to empty cell into
• Remove drying tube (the one with marbles)
• Carefully remove tube ending in platina mesh (same stack as drying
tube), careful to no damage the mesh
• Lift and unscrew the electrode (double pin)
• Remove the cell and empty into waste vessel (don’t empty in sink!)
• Wash cell with heptane (can use gloved hand as lid for cell to shake it)
• Empty heptane into waste vessel (take care not to drop magnetic stirrer
into waste vessel)
• Remove magnetic stirrer
• Wash cell with a drop of washing up liquid and water
152 | Appendix C: Karl Fischer titration
• Rinse with water
• Dry the cell
– Optimally - dry the cell in an oven for about 5-6 hours or until
completely dry
– Else – use a small amount of methanol in the cell, shake and stir.
Methanol will attract most of the water in the cell. Empty into
waste vessel! Any remaining water can be removed using pretitration before next measurement
• Fill cell with titration reagent (Coulomat AD for the coulometric C10S
titrator) until about half full (platina mesh must be fully immersed in the
reagent when reassembled)
• Reassemble – check mesh is fully immersed
• Done
C.2 Coulometric titration with C10S on paper samples
Always use rubber gloves and protective eyewear when doing Karl Fischer
titration!
• Prepare sample
– Cut a small piece of paper sample and weigh it
– Use two identical dry beakers
– Fill both beakers with an equal and known amount of methanol,
in grams, from the same bottle (enough for the paper sample to be
fully immersed), and cork them to minimize water ingress
∗ If the methanol bottle is not new, it’s a good idea to measure
the amount of water in it before proceeding. A high amount
of moisture in the methanol could potentially ‘drown out’ the
moisture extracted from the paper sample, ruining the titration
results. If the amount is high, use a new bottle of dry methanol
Appendix C: Karl Fischer titration | 153
– Place paper sample in one of the beakers and cork it
– Bathe sample in methanol for at least 2-3 hours (preferably 4-6
hours) in one of the prepared beakers. May use ultrasonic bath for
better/faster extraction
– After bathing time has elapsed, run titration on reference methanol
to find its moisture content (even new “pure” methanol will have
some moisture content, and some will have drifted in during
bathing time)
– Export reference result in ppm to excel sheet
– Run titration measurement on sample solution and export result to
excel, in ppm
• Turn titrator on and press ‘paper sample’, pre-titration initializes
• When pre-titration is done, run drift determination (button in bottom
right)
• Prepare syringe and needle from supplies cabinet
• Use syringe to extract a sample (a volume of a few ml is enough) from
the sample solution
• Weigh the syringe, now including the sample (wait until stable reading)
• Set zero
• Tap “Start sample” on titrator
• Add sample to cell (piercing the membrane)
– Make sure not to dip the needle in the reagent
– Draw a bit of air into needle after emptying it to avoid any drop
forming on the end point which would get stuck in the membrane
interfering with later titrations
• Weigh syringe (now emptied) again
• Enter sample size (in grams) and note in excel sheet
• Run measurement
• Read and export results (in ppm) to excel sheet for easy water content
(ppm or %) calculation
154 | Appendix D: Instrument control
Appendix D
Instrument control
The IDAX is controlled through writing a control file, .icf, with appropriate
settings and definitions. The LCR meter is controlled using a custom Matlab
file. This chapter presents the .icf file format used, Matlab files are the
interested reader supplied upon request.
[Header]
FileType = ’C-file’
SpecVersion = ’3.0’
[Info]
Date = ’2022-08-08’
Time = ’15:33:00’
Description = ’description of test sequence’
[Measurement]
% May choose between 10 Vpeak or 200Vpeak internal voltage
sources
Voltagesource = ’Internal10Vpeak’
% Set test mode configuration, UST -1 = Ungrounded Specimen
Test channel 1
Appendix D: Instrument control | 155
Configuration = ’UST-1’;
AmplitudeScale = ’PEAK’
% Set voltage sweeps, left to right in array
Amplitude = [ 0.025 0.5 0.025 ]
% Set frequency sweeps
Frequency = LogSweep(1000, 0.001, 3)
% Inner loop variable - automatically sets amplitude
to outer
SweepVar = ’Frequency’
MeasurementsPerPoint = 1
TimeLog = ’Point’
MinSpecimenC = 1e-12
MaxSpecimenC = 100e-6
MaxDCCurrent = 1e-6
MaxHumCurrent = 1e-3
Presentation(’AddModel = ’’ComplexC’’’)
Presentation(’AddModel = ’’Dielectric’’’)
Presentation(’Showview = ’’graphview’’’)
Presentation(’AmplitudeScale = ’’Peak’’’)
Presentation(’AngularUnit = ’’Degrees’’’)
Presentation(’AutoScale = ’’on’’’)
% May set C0, geometrical capacitance, to display permittivities
Presentation(’C0 = 118.22e-12’)
Presentation(’Xscale = ’’log’’’)
Presentation(’Yscale = ’’log’’’)
InterferenceFrequency = 50
AutoDetect = ’ON’
InitAmplitude = 5
InitFrequency = 33
InitMaxDCTime = 30
156 | Appendix D: Instrument control
FeedbackMode = ’Auto’
CapacitiveFeedback = 0.01
MaxNoCFeedback
MinNoCFeedback
MaxNoRFeedback
MinNoRFeedback
=
=
=
=
6
1
9
0
IntegrationMode = ’Auto’
Accuracy = ’High’
MaxIntegrationTime = 40
MinTime = 1
MinCycles = 1
MinSkipTime = 1
MinSkipCycles = 1
% Initiate measurement
MeasureZ
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