Pressure-assisted filling of low-melting glasses into
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Pressure-assisted filling of low-melting glasses into microcapillaries
(Druckunterstütztes Füllen von Mikrokapillaren mit niedrigschmelzenden Gläsern)
Der Technischen Fakultät
der Friedrich-Alexander-Universität
Erlangen-Nürnberg
zur
Erlangung des Doktorgrades Dr.-Ing
vorgelegt von
Ning Da
aus Jiangsu, China
Als Dissertation genehmigt
von der Technischen Fakultät / vom Fachbereich Werkstoffwissenschaften
der Friedrich-Alexander-Universität Erlangen-Nürnberg
Tag der mündlichen Prüfung: 03th September 2013
Vorsitzende des Promotionsorgans: Prof. Dr.-Ing. habil. Marion Merklein
Gutachter/in: Prof. Dr.-Ing. Lothar Wondraczek
Prof. Dr.-Ing. habil. Aldo R. Boccaccini
Prof. Dr. Wilhelm Schwieger
Acknowledgements
Good time flies by fast. My four-year dissertation field research and study are coming to a
close. I have benefited from great help in so many ways from the following people:
First of all, I would like to express my deepest appreciation to my Ph.D advisor, Prof. Dr.-Ing.
Lothar Wondraczek. Without his unfailing support- both academic and personal, this
dissertation would not have been finished so smoothly. He gave me freedom while at the
same time also providing intellectual support on critical issues. His knowledge, perception,
inspiring ideas and optimistic attitude in research and scholarship always instilled in me great
interest in my project.
In addition, I would like to thank Prof. Dr. rer. nat habil. Markus Schmidt. I was able to get
through most of the difficulties and frustrations only with his assistance and guidance. What I
have learnt from him is not only the knowledge and the research methodology but also a
commitment to high scientific standards, which always inspires and motivates me.
I am also sincerely grateful to the Institute of Glass and Ceramics, especially the members of
my dissertation committee, for providing with me all the necessary facilities and a pleasant
working environment. I want to thank Prof. Dr. Peter Greil, Prof. Dr. Andreas Rossen, Dr.
Xin Jiang, Nicolai Granzow, and Howard Lee of Max-Plank Institute for their valuable
discussions and suggestions. Special thanks go to Dr. Mingying Peng and his wife Qin Li,
Sebastian Krolikowski, and Robert Meszaros, who offered me great help four years ago when
I had just started out on a new life journey in this beautiful country.
I thank my officemates Lorenz Schlier, Ingo Götschel for providing so much entertainment
and humor in what would otherwise have been a somewhat monotonous and stressful
laboratory environment. Lorenz’s taste in wine and Ingo’s interest in gliding drew me closer
to the native culture.
The financial support of the Cluster of Excellence Engineering of Advanced Materials and the
German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) is also gratefully
acknowledged.
Finally I come to the most personal gratitude. I thank my parents, my grandmother, my aunt,
and my cousins for their faith in me, their understanding, support and love.
III
Contents
Acknowledgements .................................................................................................................. III
Contents .................................................................................................................................... IV
List of figures ............................................................................................................................ X
List of tables .......................................................................................................................... XVI
Zusammenfassung ...................................................................................................................... 1
Motivation .................................................................................................................................. 2
1. Introduction ............................................................................................................................ 3
1.1 Glass rheology .............................................................................................................. 5
1.2 Confinement effects ..................................................................................................... 8
1.3 Structure, heterogeneity and anisotropy ..................................................................... 13
2. The μ-Infiltration Technique: Pressure- and surface-assisted infiltration ............................ 14
2.1 Fluid mechanics.......................................................................................................... 16
2.2 Wettability .................................................................................................................. 18
2.3 Analytic solutions for defined time stages ................................................................. 19
2.3.1 Purely inertial time stage ................................................................................. 19
2.3.2 Visco-inertial time stage .................................................................................. 20
2.3.3 Purely viscous time stage ................................................................................ 20
2.3.4 Viscous and gravitational time stage ............................................................... 20
2.4 Shear rate in pipes ...................................................................................................... 21
2.5 Pressure- and Surface-assisted Infiltration ................................................................. 21
2.6 Viscosity of polymers measured by infiltration method ............................................ 23
IV
3. Multi-material Assessment of Viscosity under Confinement ............................................... 25
3.1 Tellurite glasses .......................................................................................................... 25
3.1.1 Introduction of tellurite glass .......................................................................... 25
3.1.2 Experimental procedure .................................................................................. 27
3.1.3 Raman spectra of TeZnNa glass and glass in capillary ................................. 30
3.1.4 Results and discussion .................................................................................... 31
3.1.5 Viscosities and flow behaviour of alkali-free tellurite glass with suction
method ...................................................................................................................... 40
3.2 Interfacial reactions between tellurite melts and silica ............................................. 48
3.3 Sulfophosphate glasses ............................................................................................... 55
3.3.1 Introduction of sulfophosphate glasses ........................................................... 56
3.3.2 Experimental procedure .................................................................................. 56
3.3.3 Structure of sulfophoshate glasses .................................................................. 60
3.3.4 Rheology of phosphate and sulfophosphate glasses ....................................... 62
3.4 Germanate and sodium borate glass with suction method ......................................... 66
3.4.1 Introduction of germanate glasses ................................................................... 66
3.4.2 Introduction of borate glasses ......................................................................... 67
3.4.3 Experiments and discussion ............................................................................ 68
3.5 Conclusions ................................................................................................................ 72
4. Viscosity of chalcogenide glasses ........................................................................................ 74
4.1 Introduction of chalcogenide glasses ......................................................................... 74
4.2 Experiments and discussion ....................................................................................... 74
4.3 Non-Newtonian Flow ................................................................................................. 78
V
4.4 Conclusions ................................................................................................................ 83
5. Outlook: Fabrication of hybrid-all-solid PCF and their optical application ........................ 85
6. Conclusions and outlook ...................................................................................................... 86
6.1 Thesis conclusion ....................................................................................................... 86
6.2 Prospect ...................................................................................................................... 86
References ................................................................................................................................ 87
List of publications/Veröffentlichungen ................................................................................. 101
VI
Inhaltsverzeichnis
Danksagung .............................................................................................................................. III
Inhalt......................................................................................................................................... IV
Abbildungsverzeichnis .............................................................................................................. X
Tabellenverzeichnis ............................................................................................................... XVI
Zusammenfassung ..................................................................................................................... .1
Motivation .................................................................................................................................. 2
1. Einleitung ............................................................................................................................... 3
1.1 Glass Rheologie............................................................................................................ 5
1.2 Confinement Effekte .................................................................................................... 8
1.3 Structur, Heterogenität und anisotrope ....................................................................... 12
2. μ-Infiltration Technik: Druck-und Oberflächen-gestützte infiltration ................................. 14
2.1 Strömungsmechanik ................................................................................................... 16
2.2 Benetzbarkeit .............................................................................................................. 18
2.3 Analytische Lösungen für definierte Zeitstufen ......................................................... 19
2.3.1 Rein Inertial Zeitstufe...................................................................................... 19
2.3.2 Visco-Inertial Zeitstufe .................................................................................... 20
2.3.3 Rein viskosen Zeitstufe ................................................................................... 20
2.3.4 Viskose und Gravitations Zeitstufe ................................................................. 20
VII
2.4 Newtonsche und nicht-Newtonschen Strömung in Rohren ....................................... 21
2.5 Druck und Oberflächen-gestützte infiltration ............................................................ 20
2.6 Machbarkeit der Viskosität von Polymeren durch Infiltration Methode gemessen ... 22
3. Multi-Material Beurteilung der Viskosität unter Einschluss ................................................ 25
3.1 Telluritgläser ............................................................................................................... 25
3.1.1 Einführung von Telluritglas............................................................................. 25
3.1.2 Versuchsdurchführung ..................................................................................... 27
3.1.3 Raman-Spektren von TeZnNa Glas und Glas in der Kapillar ......................... 30
3.1.4 Ergebnisse und Diskussion.............................................................................. 31
3.1.5 Viskositäten und Fließverhalten von Alkali-freie Telluritglas mit saugen-InVerfahren .................................................................................................................. 40
3.2 Grenzflächen-Reaktionen zwischen Schmelzen und Tellurit Silica........................... 48
3.3 Sulfophosphat glas ..................................................................................................... 55
3.3.1 Einführung von Sulfophosphatglas ................................................................. 56
3.3.2 Versuchsdurchführung ..................................................................................... 56
3.3.3 Struktur sulfophoshate Gläser ......................................................................... 60
3.3.4 Rheologie von Phosphat und Sulfophosphatglas ............................................ 61
3.4 Germanate and sodium borate glass with suction method ......................................... 66
3.4.1 Einführung von Germanat Glas....................................................................... 66
VIII
3.4.2 Einführung von Boratgläser ............................................................................ 67
3.4.3 Ergebnisse und Diskussion.............................................................................. 68
3.5 Zusammenfassung ...................................................................................................... 71
4. Die Viskosität der Chalkogenidgläser .................................................................................. 73
4.1 Einführung von Chalkogenidgläser ............................................................................ 73
4.2 Ergebnisse und Diskussion......................................................................................... 74
4.3 Nicht-Newtonsche Durchfluss ................................................................................... 78
4.4 Zusammenfassung ...................................................................................................... 82
5. Ausblick: Herstellung von Hybrid-all-solid photonischen Kristall-Fasern .......................... 85
6. Zusammenfassung und Ausblick .......................................................................................... 86
6.1 Thesis Abschluss ........................................................................................................ 86
6.2 Aussicht ...................................................................................................................... 86
Referenzen ................................................................................................................................ 87
Veröffentlichungen ................................................................................................................. 101
IX
List of figures
Fig.1.1 Principle types of shear flow. ......................................................................................... 5
Fig.1.2 Three kinds of confinement geometries. (a) Porous confinement, (b) plate confinement,
and (c) capillary confinement ..................................................................................................... 9
Fig.1.3 A liquid droplet on a solid substrate ............................................................................. 11
Fig.2.1 Liquid droplets in equilibrium with a horizontal surface surrounded by a gas. The
wetting angle θ between the horizontal layer and the droplet interface defines the wettability
of the liquid. ............................................................................................................................. 19
Fig.2.2 Schematic representation of pressure cell used to fill silica PCFs and capillaries with
low-melting materials. (a) Pressure, (b) suction methods, and (c) an enlargement picture of
melt flowing into capillary with velocity and contact angle θ. ............................................ 23
Fig. 2.3 Viscosities of commercial honey and silicone oil byconventional rotational
viscometer and the proposed infiltration method. .................................................................... 24
Fig.3.1 Structure of TeO2: (a) α-TeO2, and (b) β-TeO2 ............................................................ 26
Fig.3.2 Structural units of (a) TeO4 trigonal bipyramid (TBP) and (b) TeO3 trigonal pyramid
(TP) in tellurite glass ............................................................................................................... 27
Fig.3.3 Glass transition temperature of TZN01 by calorimetry (A) and dilatometry (B),
respectively. .............................................................................................................................. 28
Fig.3.4 (a) Side-view of a homogeneously TZN01 filled silica capillary; (b) A filled capillary
containing cracks and bubbles; (c) SEM images of TZN01 in capillary with diameter of 15.0
µm ............................................................................................................................................ 30
X
Fig.3.5 Raman measurements of TZN01 filled silica capillaries (diameters 6.25µm).The
spectra have been recorded by illuminating the filling glass strands through the side of the
capillary. ................................................................................................................................... 31
Fig.3.6 (a) Microscopic picture of TZN01, and (b) close-up view ofthe area in red circle in (a),
blue circles are bubbles in glass after cooling. The scale bars are 100 and 20 μm in (a) and (b),
respectively............................................................................................................................... 32
Fig.3.7 Viscosity analysis of the tellurite filling process at different temperatures. The upper
four plots show the square of the filling length as a function of applied pressure and square of
capillary radius. (a)Experimental results at 700°C, (b) simulation at 700°C, (c) experimental
results at 840°C, (d) simulation at 840°C................................................................................. 33
Fig.3.8 Viscosity analysis of the tellurite filling process at different temperatures with VFT
equation. (a) Viscosity of the TZN01 glass as function of temperature. Three different
techniques (beam bending, sinking bar, pressure, suction method) and extrapolated data from
VFT equation have been used to determine the viscosity. (b) Comparison of viscosity data
measured with pressure and suction methods. ......................................................................... 34
Fig.3.9 Viscosities of TZN01 acquired by two data processing methods ................................ 38
Fig.3.10 (a) Parabolic and (b) linear fittings of filling length for TZN01 corresponding to the
filling times .............................................................................................................................. 38
Fig.3.11 Contact angle between silica and TZN01 as a function of temperature for a heating
rate of 3 K/min. Insets: Photographs of the TZN01 specimen on the silica wafer for selected
temperatures. ............................................................................................................................ 39
Fig.3.12 Viscosities of TZN02 at different temperatures. ........................................................ 38
Fig.3.13 Glass transition determined by calorimetry of TZL................................................... 41
XI
Fig.3.14 Side-view of an exemplary filling situation for a capillary with an inner diameter of
70 µm, filled with TZL at 700 °C for 36 s (a), and corresponding Raman spectrum of the
filled section ............................................................................................................................. 42
Fig.3.15 Viscosities of TZL corresponding to capillary diameters at (a) 700, (b) 750 and (c)
800 °C. Contact angles between melts and capillary wall were assumed for calculation. The
viscosity obtained from subtracting surface tension effect from the experiment is presented for
comparison ............................................................................................................................... 44
Fig. 3.16 Simulatively stable flow of Tellurite melt in capillary at various times ................... 46
Fig.3.17 Quadratic filling length as a function of the ratio between observation time and shear
relaxation time (±100Pa-1) for different capillary radii (a). Labels indicate capillary radius. In
(b), the resulting plot of RLW (obtained from the slopes of linear regression lines in (a) over
the real radius R is shown, together with the ratio between R LW and R. Lines in (b) are guides
for the eye, obtained from a fit of RLW/R data to first order exponential decay equation and,
respectively, from a fit of the RLW data to a line with slope 0.96 ............................................. 47
Fig.3.18 (a)Viscosities of TZL under different pressures, and (b) they are constantas a
function of shear rate at required temperatures, respectively. .................................................. 48
Fig.3.19 Viscosity data of TZL from pressure and suction methods, respectively................... 48
Fig.3.20 Schematic diagram of silica-tellurite-silica sandwich. .............................................. 49
Fig.3.21 Raman spectra of as-made bulk TZN and TZN in a silica-TZN-silica sandwich after
annealing for 80 min at 700 °C ................................................................................................ 50
Fig.3.22 Analyses of silica-tellurite interfaces after static contact experiments (sandwich
experiments) at 700 °C. (a) and (b) depict SEM micrographs after 20 and 80 min annealing
time, respectively. (c) is the result of EDS chemical analyses of the interface region shown in
(b). Lines serve as visual guides. (d) The diffusions of the three ions into the silica plate were
XII
fitted with Ficker’s Law (e): XRD diagram as taken of the tellurite-silica interface ex situ
after opening a sandwich which was annealed for 40 min. Labels mark peak positions and
assignment for β-quartz ............................................................................................................ 52
Fig.3.23 Raman spectra of TZN01 filled silica capillaries (strand diameters about 6 µm) and
bulk TZN01.Gaussian deconvolution of Raman peaks were conducted to show the bond
change of TZN01 by confinement............................................................................................ 54
Fig.3.24 Raman spectra of TZL filled silica capillaries (strand diameters about 8µm) and bulk
TZL. Gaussian deconvolution of Raman peaks were conducted. No obvious bond change of
TZL by confinement as that of TZN01 appears. ...................................................................... 55
Fig.3.25 Tg of SP glasses determined by (a) dilatometer and (b) DSC ................................... 58
Fig.3.26 Density and molar volume of (Na, Zn) sulfophosphate glasses as a function of SO42content [143]. © 2011 Published by Elsevier B.V ................................................................... 58
Fig.3.27 Raman spectra of (Na, Zn) sulfophosphate glasses for increasing SO42- content
(replacing P2O5 by SO3). Spectra of crystalline samples are shown for comparison............... 60
Fig.3.28 Deconvoluted Raman spectrum of a (Na, Zn) polyphosphate glass. ......................... 60
Fig.3.29 Cross sections of sulfophosphate glasses in capillaries (SEM pictures) (a) SP05,
(b)SP09, (c)SP14, and (d)SP22 ................................................................................................ 63
Fig.3.30 Viscosity analysis of the phosphate and sulfophosphate glasses measured with (a)
several viscometers at different temperatures (via beam bending, sinking bar, suction method)
and (b) enlargement diagram of melt viscosities (via suction method). .................................. 64
Fig.3.31 Illustration of kinetic fragility, using the Angell plot. Lines are guides for the eye. . 64
Fig. 3.32 The influence of shear stress on the apparent viscosity of sulfophosphate melts. .... 66
Fig. 3.33 Tetrahedra structure unit of GeO4 ............................................................................. 67
XIII
Fig.3.34 Boroxol group (a), layer structure of vitreous B2O3 (b), and chain structure of B2O3
(c) at high temperature ............................................................................................................. 68
Fig.3.35 (a) Viscosity of Ge.01 at respective temperature. Inset figure: microscope figures of
one end of capillary dipping in crucible, which shows the evidence for deviation from the real
viscosity of Ge.01. (top: 22 μm capillary at 1050℃, bottom: 35 μm capillary at 1100℃ after
filling) (b) Comparison of viscosities of Bo.01 proposed by different researchers. ................ 69
Fig.3.36 SEM of germanate glasses in different capillaries with radius (a)4 , (b)10, (c)20,
(d)35, and (e)75 μm. ................................................................................................................. 70
Fig.3.37 EDX results of composition concentration of Ge.01 in capillaries and diffusion or
corrosion of SiO2 in the glass ................................................................................................... 70
Fig.3.38 Raman spectrum of Ge.01 in capillaries and bulk Ge.01 .......................................... 71
Fig.3.39 Viscosities of Bo.01 measured by Leedecke and Sasek, respectively. ...................... 71
Fig.3.40 Phase diagram of Na2O-B2O3-SiO2 ternary system, The red arrow represents the
composition x(25Na2O-75B2O3)-(100-x)SiO2.......................................................................... 72
Fig.4.1 Viscosities of Ch.01(a), Ch.02(b), and Ch.03 (c) corresponding to external applied
pressure..................................................................................................................................... 76
Fig.4.2 Fitting curves
of Ch.03 with VFT, MYEGA, and AM models. Fitting with
macroscopic and microscopic viscosity(a) and with only macroscopic viscosity (b).
Microscopic viscosity in (b) shows the discrepancy with the fitting curves. ........................... 78
Fig.4.3 The square of the filling length as a function of the square of capillary radius
corresponding to different applied pressure for Ge3As52S45 at 250 °C(a) and 300 °C(b). The
slopes of the lines are proportional to 1/η of the glass, indicating the pressure dependence of
viscosity. ................................................................................................................................... 79
XIV
Fig.4.4 The square of the filling length as a function of the square of capillary radius for
different applied pressure for As40S60 at 600 °C(a) and 650 °C(b). The slopes of the lines are
proportional to 1/η of the glass, indicating the pressure dependence of viscosity. .................. 80
Fig.4.5 Viscosities of As40S60 corresponding to the shear rate of melts in capillaries at
respective temperatures ............................................................................................................ 81
Fig.4.6 Fitting curves of viscosity to shear rate by Yue-Brückner equation for As40S60 .......... 83
Fig. 4.7 Structure of As2S3 (a) and stretching under shear stress ............................................. 83
Fig. 5.1 SEM images of endlessly single mode silica fibres which have been filled with lowmelting glasses (hole diameters: 1.6 µm, center distances of neighboring holes: 3.7 µm). (a)
filling glass: tellurite. (b) Filling glass: chalcogenide. ............................................................. 85
XV
List of tables
Table 1.1 Critical cooling rate (K/s) by the impact of contact angle on heterogeneous
nucleation for glass formation. ................................................................................................. 11
Table 1.2 Influence of scale amplitude r of glass structure ...................................................... 11
Table 3.1 Capillaries (d = 4.0, 6.25, 10.2, and 15.0 μm) filled under temperatures and applied
pressures, and filling time. ....................................................................................................... 29
Table 3.2 Filling parameters and surface tensions for TZN01 glass at required temperatures 29
Table 3.3 Filling parameters and surface tension for TZN02 glass at required temperatures .. 30
Table 3.4 Viscosities of 75TeO2-10ZnO-15Na2O for different temperature regimes, obtained
by beam bending and sinking bar viscometry (macroscopic) and from infiltration technique
according to Eq. (2.2.6) (microscopic). .................................................................................... 36
Table 3.5 Tellurite alkali and alkali free glasses with their thermal properties ........................ 40
Table 3.6 Error controlling for using Eq. (2.2.8) to calculate viscosities of the TZL .............. 42
Table 3.7 Raman peak assignment of tellurite zinc sodium glasses ......................................... 53
Table 3.8 Composition and glass forming ability of examined materials (mol.%). ................. 59
Table 3.09 Assignment of experimentally observed Raman-active vibrations in sulfophosphate
glasses....................................................................................................................................... 61
Table 3.10 Theoretical fraction of Qi tetrahedron of sulfophosphate glasses .......................... 62
Table 3.11 Surface tension of sulfophoshpate glasses.............................................................. 63
Table 3.12 Surface tension of germanate and borate glasses. .................................................. 68
Table 4.1 Glass compositions selected for viscosity determination ......................................... 75
XVI
Table 4.2 Extrapolating log η∞ and fragility m of Ch.03 from the three viscosity-temperature
models ...................................................................................................................................... 77
Table 4.1 Viscosities and Re number of Ch.02 and Ch.03 under various externally applied
pressures for two temperatures, respectively. ........................................................................... 82
XVII
Zusammenfassung
In der vorliegenden Arbeit wurde die Infiltrationstechnik zur Untersuchung der Rheologie von
verschiedener
Glasschmelzen
in
Mikrokapillaren
angewandt.
Dabei
wurden
der
„Confinement-Effekt“ der Kapillare und der „Grenzflächeneffekt“ zwischen Schmelzen und
Kapillare berücksichtigt. Die Viskosität von handelsüblichem Honigs und des Silikonöls
wurde mittels der oben genannten Infiltrationsmethode analysiert und mit der Viskosität aus
rotationsrheometrischen Untersuchungen verglichen. In einem weiten Bereich der
Schergeschwindigkeit
war die durch die
Infiltrationstechnik
ermittelte scheinbare
Mikroviskosität konsistent mit der Makroviskosität. Dadurch ließ sich die Durchführbarkeit
dieser Infiltrationsmethode zur Bestimmung der Viskosität der Glasschmelzen, die nicht mit
der Kapillare in Wechselwirkung treten, nachweisen. Auf dieser Grundlage wurde die
Viskosität verschiedener Schmelzen untersucht und mit VFT-, MYEGA- und AM-Modellen
diskutiert.
Es wurden Tellurit- und Sulfophosphatglasschmelze, welche eine Grenzflächenreaktion mit
der Silicakapillare aufwiesen, wurden untersucht. Es zeigte sich, dass sowohl in der Phosphatals auch in der Sulfophosphatglasschmelze nicht newtonsches Flieβverhalten auftrat. Der
pseudoplastische Effekt ließ sich durch die Kettenverhakung erklären. Telluritschmelze mit
dreidimensionalen
Einheiten
und
Pyrophsophatschmelze
zeigten
im
untersuchten
Schergeschwindigkeitsbereich ein newtonsches Fließverhalten. Während die Germananteund
die
Boratschmelze
sehr
stark
die
Silicakapillare
korrodierten,
war
die
Chalkogenidschmelze, die keine Benetzung und keine Korrosion mit Silika zeigte, ein guter
Kandidat für die Untersuchung des Fließverhaltens. Bei der Chalkogenidschmelze wurde
jedoch nicht-newtonsches Fließverhalten in bestimmten Schergeschwindigkeits- oder
Viskositätsbereichen beobachtet. Dies ließ sich durch Entschlaufung oder Ausrichtung der
kettenförmigen Einheiten unter Scherung in der Chalkogenidschmelze erklären.
1
Motivation
Until now, comparatively little has been known about the rheology of glass melts, although
the material has been used for many centuries. There are several methods for determining
viscosity, but various disadvantages limit their applicability to glass melts. This work provides
a new technique which may be applied in the study of viscosity of glass melts. It is based on
infiltration of glass melts into a highly-confined micro geometry. The design of this new
technique may offer a facile way to investigate chalcogenide and other low-melting inorganic
liquids which are usually difficult-to-handle and easily oxidized. Intergrating the visicosity of
glass melts and undercooled liquids, a complete viscosity to temperature diagram can be
acquired, which facilitate to investigate the forming and cooling of glasses. In addition, the
diagram helps better understanding and optimizing viscosity models and theories. To
investigate the infiltration technique, several low melting-glasses were chosen as research
objects. The glasses were selected in consideration of two aspects: the interacting ability with
silica and the flow behaviour. Viscosities of these melts were then studied under external
forces and in confined conditions. The rheological properties of the confined melts are closely
linked with their structure but also with the surface and wetting behaviour at confinement
interfaces. Besides, question that whether and how the micro confinement influence on the
glass melts needs to be interpreted. First, the nano confinement on glass transition
temperature was reviewed, which demonstrated the depression of glass transition temperature
is proportional to the reciprocal of confinement. Then, the ignored micro confinement in the
research was expatiated both theoretically and experimentally.
On the other hand, infiltration of glass melts in micro-confinement geometries also offers
extensive applications. For instance, all-solid photonic crystal fibres (PCFs) can be fabricated
by infiltrating glass melts into a silica PCF template. This kind of all-solid PCF broadens and
optimizes the merits of silica PCF, ranging from super-continuum generation to optical filters
and polarizers. Another application is to fabricate dental ceramics by infiltrating glass into
ceramics. This process may effectively eliminate the pores during sintering, which can
improve visual appearance, strength and fracture toughness of the ceramics. Furthermore,
specific studies of relaxation, solidification, and, more generally, the frozen structure of
glasses after cooling in the confinement geometry can be performed.
2
1. Introduction
Glass has been applied extensively in art and is widely employed as ordinary commodity and
construction material. In the common understanding, glass does not bend or flow due to its
hardness and brittleness. However, artists and glass workers, and even scientists would argue
the state of the glass [1, 2]. For example, Philip Gibbs asked ‘Is glass liquid or solid?’ [1]. A
liquid has no determinate shape and depends on the form of container under certain pressure
and temperature, while a solid is rigid. To exploit this question, viscosity, a measure of the
resistance of the liquids to flow, is an important characteristic. Viscosity of glasses and
(supercooled) liquids spans dozens of orders of magnitude [2, 3]. Supercooled liquids are
materials below their melting point without existing solids [4]. The sharp increase in viscosity
may cause an undetectable flow, even of "solid" glasses. From the point of view of
thermodynamics, no obvious first-order phase transition can be observed when a supercooled
liquid turns to glass [5, 6]. This phenomenon confuses people, make it hard to judge whether
glass is liquid or solid. On the other hand, the surprisingly high viscosity of glass resulting
from little structural variation at the transition temperature (Tg) becomes one of the most
attractive research fields for scientists.
In this work, a new method has been developed and applied to infiltrate micro-capillaries with
glass melts, and to measure their viscosity, liquid flow behaviour and other properties inside
micro-confinement. In the past, various viscometers were developed and able to access a
viscosity range above 1 Pa·s [7]. However, attention has rarely been paid to its application on
high-viscosity liquids such as glass melts. The infiltration technique requires detailed
knowledge of the flow, relaxation and solidification behaviour of the glass that is to be
pumped into the capillary. More specifically, little is known about the properties of glass
melts in highly constrained micro-scale geometries and under mechanical load, and further
about the frozen structure after cooling inside confined geometry [8]. Phenomena like
viscosity and structure related to external pressure, crystallization and solubility of gases need
to be studied in the infiltration technique [8 - 19]. Compared to organic fluids (and
particularly polymer melts), these areas are typically difficult to assess for glass melts because
of experimental limitations [8, 20], such as complex equipment and low operating
temperatures. However, the knowledge influences not only PCF fabrication but also various
other applications such as micromechanical forming processes or the design of anisotropic
3
glasses [8, 20, 21]. With the new technique, we can overcome these previous boundaries but
several objects need to be studied and solved:
(1) How to treat the microscopic viscosity? Can it be regarded as bulk viscosity?
(2) What are the influences of the interfacial effects between confined glass melts and a
capillary?
(3) Does the micro confinement change the flow behaviour of melts, such as, from Newtonian
to non-Newtonian flow?
(4) Does this flow behaviour alter the structural rearrangement of melts after cooling down?
To solve these questions, the following experiments were designed. Firstly, viscosities of
polymers, which do not interact with silica capillary, were studied with the present technique
and compared to data obtained by conventional rotational viscometers. The results show that
the viscosities obtained from micro capillaries agree well with the bulk data. Based on this
observation, in the second step, several kinds of glasses were chosen to perform the viscosity
measurement according to two aspects: the interaction with silica and the flow behaviour.
Besides "inert" chalcogenide melts, tellurite and phosphate glasses were investigated in detail.
Some chalcogenide glasses were chosen and surveyed because of their perfectly non-wetting
property with silica, which excludes the influence of interfacial reactions. The technique is
shown to provide a convenient route to learn about the flow behaviour of chalcogenide melts.
However, close studies are still needed to answer questions (3) and (4).
In collaboration with colleagues Dr. Markus Schmidt and Nicolai Granzow in the Max Planck
Institute for the Science of Light, we have used the technique to fabricate as-yet impossible
all-solid PCFs in a new way, and this will open the path to various new applications, such as
optical filters and fibre polarizers. The approach was found to enable a novel route towards
optical fibre devices that combine the properties of glasses which are, usually, considered
incompatible because of significant differences in their thermomechanical and rheologic
properties. Exemplarily, photonic band-gap guidance has been demonstrated in the soprepared silica-tellurite PCF [22]. Various potential applications, ranging from supercontinuum generation to optical filters and polarizers have been discussed for silicachalcogenide as well as silica-tellurite waveguides [22 - 24].
This thesis consists of five chapters. Chapter 1 gives an introduction of the background of this
project. In addition, a literature review concerning glass rheology, confinement effects,
structure, heterogeneity and anisotropy of glasses is presented. Chapter 2 describes the
4
infiltration technique and theoretical background. Chapter 3 gives experimental procedures
and discusses viscosities of various glasses and the interfacial reaction between glass melts
and capillary. Chapter 4 describes the viscosity and flow of chalcogenide melts in capillaries
under different shear rates. Chapter 5 presents the outlook for optical application by the
infiltration technique.
1.1 Glass rheology
Viscosity is a property of a liquid which describes its resistance to shear flow. It is b ( )n ,
the proportionality between shear stress (σ) and shear rate ( )n. Viscosity is defined as η =
/ [6]. Then, Ostwald-de Waele's relationship turns to b ( )n1 [25]. The value of the
exponent n defines the type of flow in the respective liquid. It is n = 1 for ideal Newtonian
flow. If n < 1, viscosity decreases with increasing shear rate, which is called "shear thinning".
Shear thickening occurs when n > 1. The principal types of flow are illustrated in Figure 1.1.
Shearing stress,
Bingham plastic
Shear thinning
n<1
Newtonian
n=1
Shear thickening
n>1
Shear strain rate
Fig.1.1 Principle types of shear flow.
Most fluids exhibit non-Newtonian characteristics and this is often related to the influence of
the externally applied stress on the structure of a flowing medium [26]. Therefore, the
examination of non-Newtonian behaviour has often been used to explore the structural state
of a liquid. Several theories have been developed for investigating the relation between flow
behaviour and structure. For instance, the Grasseley theory proposes that entanglement of
structural units is responsible for the shear thinning effect in polymeric liquids [27]. Another
5
example is the non-Newtonian flow theory proposed by Bottinga, who finds a dependence of
the viscosity on applied shear stress [28].
In typical supercooled liquids, viscosity may vary with temperature over a large range. It
increases continuously and steeply when the supercooled liquid freezes into a glass. In
industrial glass fabrication, this behaviour being made use of as each forming process
(pressing, blowing, drawing, rolling, ...) can be performed only in a certain range of viscosity§
[29, 30]. Besides, the quality of glasses, such as homogeneity, striae, inclusions, and bubbles,
depends on the viscosity of glass melts during processing, as well. Viscosity has a direct
influence on whether bubbles or solid inclusions can be removed from the melt [31].
Viscosity theory and data on supercooled liquids have received much attention in recent years
[32 - 37]. Classical techniques, such as beam bending method (measuring range: 109 to 1013
Pa·s) [38, 39], sinking bar method (measuring range: 101 to 104 Pa·s) [40], and rotational
method (measuring range: 100 to 107 Pa·s) [29], were developed. Several empirical or semiempirical models have been established to describe the temperature dependence of viscosity.
——————————————————
§
Viscosity ranges for glass making operations, taken from [29, 30]
Glass melting
0.5 to 1.5
Sealing glasses to other glasses or to metals
2.5 to 2.8
Producing gobs for container forming
2.6 to 3.2
Glass pressing
3.0 to 5.3
Surface of a bottle during blowing
4.7 to 9.0
Sinter glass powder to a solid body
5.0
Sinter glass powder to form a porous body
7.0 to 7.8
Dilatometric softening point
10.3 to 0.7
Annealing range
11.0 to 3.0
Stress release occurs in a few seconds
11.8
Temperature for matching expansion curves for seals
13.0 to 3.5
Stress release too slow to be useful
Above13.6
Note: values are given as log (viscosity in Pa·s)
6
The most popular empirical model is Vogel-Fulcher-Tammann equation (VFT equation) [41 43],
log10 (T ) log10
B
T T0
(1.1)
where the empirical fit parameter T0 is often understood as the temperature at which the
majority of sub-Tg structural relaxations cease to exist. η∞, B, T0 are fitting constants specific
to a given glass. This model has been extensively employed for viscosity-temperature fitting
and industrial production, but it converges to infinity at T = T0. The alternative AvramovMilchev (AM) model [44] is derived from an atomic hopping consideration, where the
activation energy of viscosity changes with temperature. To account for this, a stretched
exponential is introduced,
(T ) 0 exp( )
(1.2)
T
where η0, α, τ are fitting parameters. VFT and AM models can only describe the temperature
and viscosity relationship at intermediate temperatures. The VFT equation overestimates the
viscosity below the glass transition temperature. Semi-empirical first principles approaches to
viscosity usually follow Adam and Gibbs [45]. They assumed that a liquid is a combination of
a number of cooperatively rearranging regions. The size of these regions grows as the liquid is
cooled down, being similar to the growth of a crystal. Therefore, the configurational entropy
of the system decreases until the cooperatively rearranging regions become one
configurational state [46 - 49]. This process induces sharply decreasing entropy of the liquid,
which leads to infinitely high viscosity.
log log
B
TS
(1.3)
where log η∞ is the logarithmic viscosity at infinite temperature, S is the entropy of the
material, B is a constant, and T is the temperature. Viscosity is inversely proportional to the
entropy of the materials determined by their configurational distribution. At a high (or low)
temperature, the Arrhenius equation is usually suitable to describe the viscosity with low
(high) activation energy Ea.
A·
exp E / RT
(1.4)
a
7
where A is a constant, and R is the ideal gas constant. Only a few supercooled liquids, such as
SiO2, GeO2, exhibit more or less Arrhenian behaviour. Most other supercooled liquids display
super-Arrhenius behaviour, that is, a hyperbolic curve of viscosity with regard to temperature.
The curvature extent that the viscosity η deflects from Arrhenius behaviour defines the liquids
as either strong or fragile [46]. Therefore, SiO2, and GeO2 are defined as strong glasses. There
are systematic or physical problems existing in the above models, even though they are
successful in fitting and predicting a viscosity to temperature relationship. Recently [47], the
Mauro-Yue-Ellison-Gupta-Allan (MYEGA) model was proposed to account for these
problems, in particular, for ‘the dramatic rise in viscosity as the supercooled liquid cools
towards the glass transition with very little change in structural features’. The model starts
from the Adam-Gibbs equation and is compared to the VFT and AM models. In short, it
circumvents convergence of the VFT equation as well as divergence of the configurational
entropy when approaching low or high temperature as in the AM model [47].
1.2 Confinement effects
With decreasing scale of devices, the behaviour of liquids in nano-confinement has received
wide attention [50 - 59]. While it should be noted that the present work reports on the flow of
melts in micro-capillaries, it is still worthwhile to have a brief look at the potential effects
which liquids are exposed to in sub-micrometric or even nanometric confinement. Figure 1.2
presents three confinement geometries. The dark regions in Fig.1.2 (a) indicate confining
walls. Two plates confine a fluid to flow between them in Fig.1.2 (b). The fluid is confined in
cylindrical space in Fig.1.2(c). Jackson and McKenna have found that the glass transition
temperature Tg of a supercooled liquid changes significantly when it is confined in pores with
r around ～1-3 nm [0]. A shift of glass transition temperature, both positive and negative, has
also been observed for supercooled liquids in nano-geometry [53]. Approaching the glass
transition temperature, there occurs a pronounced slowing down of structural unit motion of
supercooled liquid in nano-confinement. This slowing down is generally attributed to an
increasing length scale of cooperativity of units (ζ, 1 to 3 nm). Even given the comparability
between the ζ and r, the reasons for the pronounced change in glass transition temperature can
be either (i) the interfacial reaction between the supercooled liquid and the walls of nano
pores, or (ii) the exact finite size of the pores, or both. F. He et al. studied a molecular glassformer, 2-methyltetrahydrofuran (MTHF), infiltrating it into porous glass with pores of 2.5,
5.0, and 7.5 nm. The same procedure was also performed in a silanized porous glass [53]. The
comparison of these experiments displays the importance of the interfacial reaction between
8
the two contacting media and suggests that severe confinement does not necessarily
contribute to the variation in characteristic properties [53]. Other studies show that a glass
transition temperature depression increases linearly with the inverse of the pore radius [53,
54].
Fig.1.2 Three kinds of confinement geometries. (a) Porous confinement,
(b) plate confinement, and (c) capillary confinement.
The glass transition temperature of a liquid in a confined substance can be described by the
second Ehrenfest relation, which is an equation of irreversible thermodynamics[55],
dTg
dP
VTg
C p
(1.8)
where V, , and C p are the molar volume of the supercooled liquid, the isobaric changes
of the thermal expansion coefficient and heat capacity at Tg, respectively. Davies and Jones
have successfully investigated many pressure-related glass transition cases with the second
Ehrenfest relation[55,56]. Jonas et al. applied the second Ehrenfest relation to
phenomenologically explain the glass transition of a liquid in confined geometries. On the
other hand, the pressure reduction ∆P of liquid inside a cylindrical pore with the radius of r
could be derived by Kelvin equation[57],
P
2
r
(1.9)
where is the interfacial tension of the liquids. Therefore, by combing Eq.(1.8) and
Eq.(1.9), Jonas et al. derived an equation interpreting the depression of the glass transition of
liquid to the geometrical confined pore size r.
9
T VTg
2
C p r
(1.10)
The authors noted that the depression ratio of
T
is less than 5% for the smallest pore [55],
Tg
which is proportional to the reciprocal of confinement. Therefore, the depression ratio of
T
Tg
could be neglected if the glasses were restricted in the smallest micro confinement.
In addition to the influence on glass transition by confinement, crystallization of materials can
be significantly affected. J. C. Dore et al. reported the effects of confinement on the liquid-toplastic crystal transition and the plastic-to-brittle crystal phase transition for cyclohexane
confined in porous silica [58], in which the nucleation point of the plastic crystal phase is
depressed by over 30 oC [59]. Interfacial reaction or confinement effects need to be clarified
as they do on Tg. For bulk glasses, the interface impact on crystallization has been studied,
which is heterogeneous nucleation [60]. Wettability of a liquid droplet on a solid substrate
(Fig.1.3) affects the slowest cooling rate required for avoiding nucleation, as listed in Table
1.1 [60]. It can be deduced that the critical cooling rate of heterogeneous nucleation may be
lower than that of homogeneous nucleation, for example, for Na2O·2SiO2 and
CaO·Al2O3·2SiO2 when the contact angle is larger than 100°[60]. Under confinement, the
high surface-area-to-volume ratio will be a significant factor influencing the behaviour of
crystallization of materials. Therefore, other than the effect of confinement, the interfacial
reaction itself will either inhibit or promote the crystallization of materials depending on the
properties of the materials. Above noted Na2O·2SiO2 and CaO·Al2O3·2SiO2 glass can be
fabricated at a relatively slow cooling rate if confined in a small capillary, which has a contact
angle larger than 100°with the glass melt. With regard to the effect of confinement alone,
fabrication of a single crystal of organic materials along the axis of mico glass capillaries has
been successfully demonstrated [61].
10
Fig.1.3 A liquid droplet on a solid substrate
Table 1.1 Critical cooling rate (K/s) by the impact of contact angle on
heterogeneous nucleation for glass formation, taken from [60].
Materials
Homogeneous
Nucleation
(K/s)
Heterogeneous nucleation (K/s)
θ=100°
θ=80°
θ=60°
θ=40°
SiO2
9×10-6
1×10-5
2×10-4
8×10-3
2×10-1
GeO2
3×10-3
3×10-3
3×10-2
1
20
Na2O·2SiO2
6×10-3
8×10-3
3×10-1
10
3×102
CaO·Al2O3·2SiO2
3×102
3×102
5×103
2×105
2×106
Microfluidic motion in geometries with a characteristic scale length of between 1.0 and 100.0
μm has received much attention [62, 63], for example, because of the trend to miniaturization
in biotechnology, manufacturing all solid hybrid PCFs, and liquid flow in lab-on-a-chip
devices which all require detailed knowledge of liquids flowing in micro-scales.
Table 1.2 Influence of scale amplitude r of glass structure on the properties of glasses, taken from [64].
Structure
Property
Short range
Colour, optical absorption
Ligand field effects: distortion-induced
violation of symmetry selection rules in rareearth and transition-metal ions
Electronic defect-like states, gap states
Electronic excitations
Ultraviolet absorption and transmission
Raman oscillations
Energetic contribution to thermal expansion
= nearest-neighbour interaction
r < 0.5 nm
Medium range
= atom-specific structure elements
and their interconnection
0.5 nm < r < 2.0 nm
Transport properties:
Diffusion, ionic conductivity, viscosity
Non-radiative heat conductivity
Relaxation
Vibrational excitations:
Infrared absorption and transmission
11
Brillouin light scattering
Boson peak
Nucleation
Stability against:
Phase separation/decomposition
Crystallization/devitrification
Low-temperature anomalies:
Specific heat
Heat conductivity
Transformation temperature
Fluctuations of concentration and density
Long range
Chemical durability
Phase separation/decomposition
Crystallization
Opacity, micro-porosity
Rayleigh and Mie light scattering
colour of “striking” glasses
photochromism, photosensitivity
>> ASE dimensions
2.0 nm < r < 100.0 nm
Structure insensitive
Density
Elastic moduli, strength, hardness
Refractive index, dielectric constant
Gas solubility
Radiative heat conductivity
Specific heat
= macroscopic
= averaging orientation and volume
(inhomogeneity)
r < 100.0 nm
In our case, the characteristic length-scale of confinement is just in the range of ~ 1.0 to 100.0
μm. In order to optimize the design and performance of the devices, a detailed understanding
of the flow of melts in such scales is necessary. For example, with our infiltration technology,
the structure of the undercooled liquids may remain after quick freeze. The structure of the
undercooled liquids, which affects the properties of glasses, is also influenced by the shear
rate. Therefore, by controlling the flow of the supercooled liquids, different structural
arrangements may be obtained, further optimizing the properties of glasses. Table 1.2 lists the
influence of scale amplitude r of glass structure on the properties of glasses [64]. It can be
found that optical performance of luminescent activators in glasses will change, if the
structure state is altered in a scale less than 0.5 nm; stability of glasses can be modified if
structure varies in the intermediate range. However, the ignored µm-confinement effect on
glasses has been theoretically demonstrated by Eq. (1.10). Furthermore, the glasses should
present more macroscopic distinctness comparing µm-confinement and nm-confinement if
there was. Analysis of different glasses reveals no properties dependence of glasses under
different µm-confinement conditions, such as undetected structure change of glasses and no
viscosity dependence on the scale of capillaries, which will be discussed in Chapter 3.
12
Therefore, different with nano-confinement, the research does not consider the µmconfinement.
1.3 Structure, heterogeneity and anisotropy
The structure of glasses lacks the periodicity of crystals, nevertheless, a short-range-order
remains. The composition of glasses can be extended to a much broader range than crystalline
materials as no building laws and laws of stoichiometry have to be taken into account - at
least in principle. Zachariasen proposed the random network theory to describe the tendency
of glass formation, which is the most used model for glass structure [6]. Structural units less
than 0.5 nm are the fundamental bricks for building a bulk glass. Together with adjacent
structural units, a short range ordered network is formed. Some parameters, such as bond
length, angle distribution, connectivity and coordination number, define the unit structure.
The structure of a larger dimension, the intermediate range order between 0.5 nm and 2.0 nm,
further contributes to the influence on transport properties, relaxation, nucleation, etc. of
glasses [64]. Some properties of glass are still structure sensitive until the research area
reaches above 100 nm. Various characterization techniques have been developed for revealing
the structure of glass from short order to long order scale. A. C. Wright [65] employed
neutron diffraction to vitrified silica and cristobalite at the short range, which testified the
same structural unit for both cases. The difference between glass and crystal was displayed
only at longer scale. On the other hand, glass is in a thermodynamic non-equilibrium state.
The structure of melts is frozen after supercooling, which results in the non-periodicity and
heterogeneity. The heterogeneity originates from the density fluctuation, which dissipates
within characteristic relaxation times. As Tg is approached, the characteristic relaxation times
become very long, which induces the freezing in of "dynamic" heterogeneity [66]. Techniques,
such as Brillouin scattering and small angle X-ray scattering, have been employed to study
the heterogeneity of glass at both intermediate and long range [67]. Since the glasses are
frozen to the structure of supercooled liquid at a certain temperature, which is denoted as
fictive temperature Tf, thermal history will influence the heterogeneity of glasses. Besides,
additional pressure added on supercooled liquid will change the structure of glasses, which
influence the heterogeneity of glasses as well. Y. Takahashi concluded that the denser regions
in the heterogeneity area are precursors of nuclei in the supercooled phase based on
investigating the Boson peak during crystallization [68]. As mentioned in section 1.3, under
nano confinement, a positive or negative shift of glass transition can be observed. This
confinement scale is in the range of heterogeneity of glasses, which is a possible reason for
13
the shift of glass transition. However, until now there has been no research on the influence of
micro confinement on supercooled liquids. It will in the future be interesting to study its
influence on heterogeneity of glasses, or investigate the crystallization of supercooled liquids.
Structural anisotropy may be induced in usually isotropic glasses as a result of unrelaxed flow
of supercooled liquids, such as in rapid drawing of a fibre. Anisotropy may be reflected in
various structural changes which are, however, still rather unexplored. For example, a fibre
drawn to the dimension of 10 μm may have an anisotropy expressed in birefringence of Δn =
10-5, which can be reduced by thermal treatment [69]. Here, nuclear magnetic resonance
(NMR) spectroscopy was used to show a coordination number shift from 3 to 4 of boron as a
result of fibre drawing [0]. However, such a coordination change may equally well be caused
simply by varying cooling rates [0].
2. The μ-Infiltration Technique: Pressure- and
surface-assisted infiltration
The dynamic flow of liquid inside a capillary had not been studied extensively until the
derivation of the Lucas and Washburn equation [70, 71]. The equation was derived based on
Poiseuille’s law [72] and proven through surveying the dynamic flow of water in given
capillaries under controlled time and external pressure. The coincidence between theoretical
derivation and experiments demonstrates the possibility of measuring the viscosity of liquid
based on this principle. The Lucas-Washburn equation is derived from Newton’s second law
14
without considering the chemical structure of liquids. Therefore, the Lucas-Washburn
equation should be effective in describing the flow of viscous glass melts as well. Researchers
in the polymer domain employed a capillary viscometer with external pressure for
determining viscosity based on the Lucas-Washburn equation [73, 74]. The critical conditions
of the viscometer, however, inhibit its application on viscous mineralic melts. For example,
the flow effects at the entrance to the capillary can only be neglected provided that long dies
have the length to radius ratio of less than 60 [73]. The aperture must be machined precisely,
since the tube radius has a remarkable influence on viscosity. Moreover, the pressure drop for
viscosity determination is difficult to measure directly because of the geometry of the
viscometer [73, 74]. The viscosity temperature range needs to be considered carefully for the
safety of the equipment, since inorganic glasses normally have much higher melting
temperatures than polymers. On the other hand, a conventional rotational viscometer can
measure a viscosity to as low as 1.0 Pa·s or less. It is currently the most popular viscometer
for measuring viscosity of glass melts in this regime [34, 36, 75]. However, a variety of
factors involving glass types, cost, required quantity the employed melt and safety in the case
of toxic or hazardous glasses must be taken into account. In my Ph.D project, I have applied
the infiltration technique, including pressure and suction methods, to measure viscosities of
different glass melts, such as, tellurite, sulfophosphate, chalcogenide, borate and germanate
glass melts. With the infiltration technique, a viscosity range of 0.01 to 10 Pa·s can be
covered. The experimental equipment system is designed according to the Lucas-Washburn
equation. Silica capillaries are chosen as flow matrix for glass melts. For the pressure method,
a pressure system with pressure as high as 200.0 bar is applied as external force to pump
melts into capillaries. For the suction method, a vacuum pump is used to suction the melts. In
the process of the pressure method, a suitable pressure and capillary size are chosen according
to pre-estimation of viscosity, for example, by choosing one capillary and filling it for a
certain time under pressure. After the filling procedure, the length of glass inside the capillary
is measured. Other parameters, (pressure, radius of the capillary, and filling time) are known
and used for calculating viscosity. Finally, we can use this pre-viscosity value to set the
appropriate filling length, pressure, and time to obtain more accurate results according to the
Lucas-Washburn equation. In the process of suction method, two forms of analysis, with and
without vacuum pump are performed: (1) The surface tension dominates the flow of melts
without evacuating. (2) With vacuum pumping, an unbalanced pressure less than one
atmosphere is introduced as external force. Now the surface tension and the unbalanced
pressure dominate the flow of melts. The surface tension effect can be subtracted from the
15
Lucas-Washburn equation. Then, an accurate value of viscosity will be acquired. Application
of the infiltration technique is discussed from both the theoretical and the experimental point
of view. Possible influences of the interfacial interaction between melts and silica capillaries
are considered and surveyed; for example, tellurite glasses, exhibit perfect wetting with silica,
and a stationary layer forms at the TeO2-SiO2 interface by interfacial reaction. This layer
causes a deviation of the effective radius in the Lucas-Washburn equation as it does on actual
viscosity. Nevertheless, this deviation becomes smaller as the radius of the employed capillary
increases. When capillary radii are ≥ 10 µm, the deviation of effective radii will be less than
5%, and the corresponding deviation of viscosity will be at most 10 %. Similar deviation may
be caused by interfacial reaction as with phosphate, borate, and germanate glasses. In order to
avoid interfacial reactions between the filling materials and the silica wall, chalcogenide
glasses are selected. It is well-known that chalcogenide glasses are perfectly non-wetting with
respect to silica; consequently, any viscosity deviation due to interfacial layer formation will
be excluded. Therefore, to find answers to the questions provided above, the following
chapters will be introduced and discussed: (1) Theory and technique of the infiltration method;
(2) Assessment of as-chosen glass melts and their interfacial reaction with silica matrix; (3)
Flow behaviour of chalcogenide melts under micro-confinement condition; (4) Application of
the infiltration method in fabricating all-solid PCFs and their optical applications.
2.1 Fluid mechanics
Jean Louis Marie Poiseuille experimentally derived, formulated and published the Poiseuille's
law, known nowadays as the Hagen-Poiseuille equation [76],
PR4
8L
(2.1.1)
where Π is the volumetric flow rate, ΔP is the pressure drop, R is the characteristic length of
the capillary (its radius for tabular capillary), η is the dynamic viscosity and L is the length of
the fluid column. To utilize this equation, laminar stationary flow of a uniformly viscous
liquid with zero compressibility is assumed (Newtonian flow). Lucas [70] and Washburn [71]
extended Eq. (2.1.1) by considering the dynamics of capillary rise:
d 2 L dL 2
8 L dL
P PE 2
2
R dt
dt
dt
(2.1.2)
16
This equation describes a typical experimental situation, where a capillary is dipped into a
liquid of density (ρ). As a result of the total effective pressure ΣP, over a certain time t, the
liquid will rise and form a column of height L. ΣP consists of hydrostatic pressure Ph=ρgL (g:
acceleration of gravity), the capillary pressure Pc=2γcosθ/R (with surface tension and
contact angle θ) and other applied body forces PA [8]. The right-hand side of Eq. (2.1.2)
includes the first term for viscous resistance and the second term for inertial effects. The
inertial effect is neglected for laminar flow. If the gravitational effect is neglected, in the
absence of any other forces, Eq. (2.1.2) reduces to
P Pc
2 cos 8 L dL
2
R
R dt
(2.1.3)
which yields, after integration,
L2
R cos
t
2
(2.2.4)
If an additional pressure PA is applied, the left side of Eq. (2.1.3) should be corrected by
ΣP=Pc+PA. Then, integration leads to
R cos R 2 PA
L2
t
4
2
(2.1.5)
Eq. (2.1.5) can be rearranged to yield the dynamic viscosity
(2 R cos R 2 PA )
t
4 L2
for 2 cos
(2.1.6)
RPA , body forces dominate over surface forces. For example, if the employed
capillary radius is larger than 10 μm, and an external pressure of 10 bar is applied, 2 cos
will be much less than RPA, since the surface tension of glass melts is much less than 1.0 N/m.
In the pressure technique, the calculation will be based on this simplification of Eq. (2.1.6) to
R 2 PA
t
4 L2
(2.1.7)
In the case in which an additional pressure PA is less than 1.0 bar, the gravitational and
surface tensional effect need to be considered. In order to obtain an estimate of the impact of
17
gravitational pressure PH, the column equilibrium length LE, which would be necessary to
compensate for capillary and atmospheric forces, can be estimated from the balance.
gLE PA +2 cos / R
(2.1.8)
If the experimentally obtained filling length is less than 3% of LE, the effect of PH can be
neglected. This is generally the case for R < 10.0 µm, which will generate a high equilibrium
length LE. If gravitational effects are not negligible, Eq. (2.1.2) becomes
PA
d 2 L dL 2
2 cos
8 L dL
gL 2
L 2
R
R dt
dt
dt
(2.1.9)
For laminar flow, neglecting inertial effects,
PA
2 cos
8 L dL
gL 2
R
R dt
(2.1.10)
and after integration,
2 cos RPA
gR 2
gRL
tL
ln(1
)
8
gR
2 cos RPA
(2.1.11)
if contact angle θ and surface tension are known, Eq. (2.1.11) can be employed to calculate
the apparent dynamic viscosity from the length of the filled capillary section obtained after a
certain filling time.
2.2 Wettability
Wettability or wetting of liquids within the capillary is a parameter that controls the kinetic
flow of the liquid inside the capillary. A contact angle is formed when a liquid droplet spreads
on the surface of a horizontally solid substrate. This angle is determined by a force balance
between adhesive and cohesive forces [77]. The contact angle θ varies from 0 to 180°, as
illustrated in Fig 2.1. The liquid is regarded as wetting when 0 < θ <90°and non-wetting
when 90° < θ < 180°. θ = 0, 180°correspond to perfect wetting and perfect non-wetting,
respectively [77, 78]. Perfect wetting means that the droplet spreads and forms a film on the
surface of the substrate. Perfect non-wetting means that the drop forms a sphere on the surface
of the substrate.
18
θ
θ
θ
Fig.2.1 Liquid droplets in equilibrium with a horizontal surface surrounded by a gas. The wetting angle θ
between the horizontal layer and the droplet interface defines the wettability of the liquid.
In fact, the interfacial tension of the liquid determines the wetting angle θ, which is a
thermodynamic variable [78]. With l , g denoting the interfacial tension due to the liquid-gas
surface, s ,l denoting the interfacial tension due to the solid-liquid surface and s , g denoting
the interfacial tension of the solid-gas surface, in thermodynamic equilibrium the wetting
angle θ is given by Young's law [79],
s , g s.l l , g cos
(2.2.1)
For two-phase flow in porous media or in capillary, the wetting angle influences the strength
of the capillary pressure Pc in a pore of size R [80],
Pc
2 l , g
R
cos
(2.2.2)
Therefore, the interfacial wettability between glass melts and the capillary should be
considered for obtaining an accurate viscosity value.
2.3 Analytic solutions for defined time stages
The dynamic flow of liquids in a capillary can be separated into several stages depending on
the development of various forces acting on liquids. The flowing states of the liquid will be
classified in the following parts [81, 82], where an external force PA is always considered.
2.3.1 Purely inertial time stage
At the moment of a capillary coming into contact with the liquid, the viscous and the gravity
terms in Eq.(2.1.2) can be neglected so that it becomes [83],
19
d 2 L dL 2
2 cos
PA
L 2
R
dt
dt
(2.3.1)
The length of the liquid column flowing into the capillary can be solved through this
differential equation when the liquid flows at a constant velocity.
2 cos PA R
R
Lt
(2.3.2)
2.3.2 Visco-inertial time stage
Later, the flow transfers into a transition stage. A solution is presented by Bosanquet [81],
which considers the inertial as well as viscous terms,
d 2 L dL 2 8 dL
RPA 2 cos
L 2 2 L
R
dt
dt R
dt
(2.3.3)
Solving this differential equation yields
R(2 cos RPA ) R 2
8
L
t
(1 exp( 2 t ))
8
8
R
2
(2.3.4)
It is noted that in a micro-capillary, if viscosity is too low, flow will become turbulent if one
certain pressure is applied. Thus, the obtained viscosity value is not a real but an apparent
value.
2.3.3 Purely viscous time stage
One period later, an equilibrium stage is reached where the Lucas-Washburn equation
becomes valid (inertia and gravity being neglected),
L2
R(2 cos RPA )
t
4
(2.3.5)
2.3.4 Viscous and gravitational time stage
With the increase in length of the liquid column inside the capillary, the gravity effect can no
longer be neglected. For example, 7.6 cm Hg is equal to 0.1 atmosphere pressure. Fries and
Dreyer [81, 82] show that gravity must be considered for L 0.1LE . An analytic solution
(neglecting inertia) was presented
20
2 cos RPA
gR 2
gRL
tL
ln(1
)
8
gR
2 cos RPA
(2.3.6)
The time from the purely inertial stage to the visco-inertial stage and from the visco-inertial
stage to the purely viscous time stage is proportional to R 2 / . Considering the dimension of
the capillaries (μm) and viscosities of the liquids (less than 10 Pa·s), the transition time is
much less than 1 min, which is shorter than our experimental time scale. Therefore, the
inertial effect can be neglected when deriving the Eq. (2.1.3) and the Lucas-Washburn
equation is applied for viscosities.
2.4 Shear rate in pipes
To define the flow behaviour of liquids, the viscosity as a function of shear rate in a pipe
needs to be surveyed. The shear rate follows the equation
4Q
R3
(2.4.1)
where Q is volumetric flow rate, R is the radius of the pipe or capillary. According to the
relationship between viscosity and shear rate discussed in section 1.1, the viscosity of a
Newtonian liquid will be constant. Otherwise, non-Newtonian flow is present.
2.5 Pressure- and Surface-assisted Infiltration
The design of the infiltration technique, including pressure and suction methods, is shown in
Fig.2.2 (a) and (b). The pressure method is to apply pressurized argon to press glass melts into
a capillary. The suction method is to employ a vacuum pump to suck glass melts into a
capillary. The advantages of the infiltration technique over conventional rotational
viscometers are:
(1) Requirement of only a small amount of as-melted samples;
(2) Safety in operating toxic or hazardous melts;
(3) A lower viscosity operating regime can be achieved.
In addition, it overcomes the drawbacks of the capillary viscometer as used for polymeric /
organic liquids. The procedure in the pressure technique involves the following steps:
(1) Setting a specialized furnace with a pressure system at a required temperature for
measuring viscosities;
21
(2) Preparing a silica crucible with inner radius of 2.00 mm that can contain the glasses;
(3) Placing capillaries into the silica crucible. The upper ends of the capillaries are sealed by
fusing;
(4) Placing the crucible and capillary into a steel tube;
(5) Transferring the steel tube into the furnace.
With the present system, a pressure up to 200 bar could be generated. As a result, a capillary
with a nanoscale inner diameter can be filled with melts within an acceptable experimental
duration [24, 84]. In contrast to the high pressure applied in the "pressure method", a vacuum
pump may be employed. For the "suction method", which has an unbalanced pressure less
than 1.0 bar, a capillary with pore size of several micrometers is placed vertically into a gold
crucible which contains the melts. The upper end of the capillary is connected to a mechanical
vacuum pump as shown in Fig 2.2 (b). Once the vacuum is turned on, with the assistance of
the surface tension the unbalance external pressure draws the glass melts into the capillary.
After preset filling-time, the capillary is taken out immediately. The length of melt filled into
the capillary is then measured with an optical microscope. Based on the Lucas-Washburn
theory, viscosities are calculated and plotted against temperatures. The difference in the
magnitude of external pressure between these two methods determines the choice of capillary
radius and experimental filling time, which is important for the viscosity measurement. For
example, less filling time means less interfacial corrosion between the glass melts and the
employed silica capillary. Chalcogenide glasses are measured with the pressure method for
safety reasons, and the chalcogenide melts are situated in a sealed silica tube as shown in
Fig.2.2 (a). Viscosities of some other glasses, such as tellurite, phosphate, borate glasses can
be measured with both the pressure and the suction methods. Fig.2.2(c) depicts the kinematic
behaviour of a glass melt flowing into a capillary.
22
(a)
exhaust
(b)
(c)
2R
pressurized
argon
connector
vacuum
capillary
sealed
capillary
s , g s,g
s ,l
silica tube
l,g
s ,l
L
furnace
glass melt
crucible
refractory
glass melt
Fig.2.2 Schematic representation of pressure cell used to fill silica PCFs and capillaries with low-melting
materials: (a) pressure, (b) suction methods, and (c) an enlargement picture of glass melt flowing into a
capillary with velocity and contact angle θ [8].
2.6 Viscosity of polymers measured by infiltration method
One commercial honey (Blüten honey, made by EUCO GmbH, Hamburg) and one silicone oil
(WACKER® AK 20), which are Newtonian fluids, were chosen for referencing the
infiltration technique to rotational viscometers. The structure formula of silicone oil is
(CH3)3SiO[Si(CH3)2O]nSi(CH3)3. Its kinematic and dynamic viscosity is 20 mm2s-1 and 19
mPa·s at 25 oC, respectively [85]. As there is no interfacial reaction between these two
materials and silica, the difference of viscosity between these two methods should be
attributed to the internal effects of the infiltration technique, or to confinement issues. The
experiments show consistent viscosities from both methods for honey (Fig.2.3).
For silicone oil, two viscosities were measured by the rotational method. The upper data is
first acquired by increasing the shear rate, then the lower one is obtained by decreasing the
shear rate, which are 28.0 and 18.3 mPa·s, respectively. The viscosities measured by the
infiltration method are marked with red half circles, which correspond to a shear rate above
240 s-1. There is a discrepancy between the data obtained from increasing and decreasing
shear rate by the rotational viscometer. The possible reason is that the molecular structure of
silicone oil is stretched out after employing shear stress because a molecule of silicone oil has
dozens of Si(CH3)2O [85]. Therefore, the molecules are entangled, which presents a
apparently higher viscosity. This entanglement is decreased when the shear stress is employed
23
for a certain time or when the shear rate exceeds a threshold value. Several glasses that have
been mentioned in the introduction will be classified and surveyed with regard to their flow
behaviour and interfacial reaction with silica capillary.
(a) 30
Viscosity (Pa·s)
Honey
rotational data
infiltration data
27
24
21
18
(b)
240
6
12
300
-1
360
0.04
Viscosity (Pa·
s)
18
Shear rate (s )
24
30
420
rotational results
infiltration results
increasing shear rate
0.03
0.02
decreasing shear rate
0.01
0.00
0
50
100
-1
150
Shear rate (s )
200
Fig. 2.3 Viscosities of commercial honey and silicone oil by
conventional rotational viscometer and the proposed infiltration method.
24
3. Multi-material Assessment of Viscosity under
Confinement
Four typical glass melts from tellurite, sulfophosphate, germanate, and borate, were chosen
and investigated. These glasses exhibit (1) well-defined polymerization grade, (2) preexisting
knowledge on their structural units, and (3) low melting temperatures for applicability of
silica capillaries. In addition, the optical properties of these glasses are also attractive for
further applications by using the infiltration technique. For borate glass, another goal was to
try to find structural change of borate units under micro-confinement because two structural
units, planar [BO3] and tetrahedral [BO4] units co-exist in borate glasses, depending on the
fraction of modifier ions. However, there is still one issue that needs to be taken into account,
that is, the interfacial reaction of the four studied melts with the silica matrix. In this chapter,
the following problems will be investigated and discussed:
(1) Can the microscopic viscosities be regarded as bulk viscosity?
(2) What is the influence of the interfacial effects between the as-confined glass melts and a
capillary?
(3) Does the micro confinement change the flow of melts from Newtonian to non-Newtonian
flow?
(4) Does the flow behaviour alter the structural state of glass melts after cooling?
3.1 Tellurite glasses
The tellurite glass was chosen as a research object for two reasons: (1) The well-defined
structure of bulk glass can be a reference and compared to the glass inside micro- capillary
when exploring potential changes due to confinement; and (2) excellent optical properties,
which will be of importance in the fabrication of all-solid PCFs.
3.1.1 Introduction of tellurite glass
Tellurite glasses have been extensively studied for several years. Their optical advantages
make them promising candidates for fabricating integrated optical amplifiers, fibre lasers,
chemical sensors etc. [86, 87]. They exhibit a high refractive index and optical nonlinearity, a
25
wide transmission range (0.35-5μm), good glass stability, and corrosion resistance [7, 86 - 88].
Compared to silicate and phosphate glasses, tellurite glasses have excellent rare-earth ion
solubility and relatively low phonon energy (780 cm-1), which are advantages for designing
efficient lasers and optical amplifiers [86]. Being different from other glass network formers
SiO2, GeO2, TeO2 itself cannot form glass without the addition of network modifiers [86].
From various spectroscopic measurements, it is found that two or more structure units may
exist in tellurite glasses [89 - 91]. These structure units are analogous to those of TeO2
crystalline, which consists of tetragonal α - TeO2, rhombic β - TeO2, etc. (Fig. 3.1) [91 - 93].
Fig.3.1 Structure of TeO2: (a) α-TeO2, and (b) β-TeO2 [90].
There are four coordination oxygens in pure TeO2: Two axial oxygen and two apical oxygen
atoms along the long axis [94]. There is still one pair of electrons according to Pauling’s
second rule. With the addition of network modifiers, which means that more oxygen atoms
are introduced, a TeO3 trigonal pyramid (TP) structural unit appears. Unlike TeO4, the
trigonal pyramid TeO3 has a non-bridging oxygen with a double bond, two bridging oxygen
atoms, and a lone pair of electrons. Therefore, according to the number and type of modifier
and intermediate ions, the oxygen coordination number of Te4+ is 3, 3+δ, and 4 [91, 92].
Figure 3.2 shows the structural units of TeO4 trigonal bipyramid (TBP) and TeO3 trigonal
pyramid (TP) [91].
26
Fig.3.2 Structural units of (a) TeO4 trigonal bipyramid (TBP)
and (b) TeO3 trigonal pyramid (TP) in tellurite glass [91].
3.1.2 Experimental procedure
Tellurite glasses with nominal compositions of 75TeO2-10ZnO-15Na2O (mol.%) (TZN01)
and 80TeO2-10ZnO-10Na2O (mol.%) (TZN02) were prepared by a conventional melting and
quenching technique. Reagent grade powders of TeO2, ZnO, and Na2CO3 were weighed,
mixed, and then melted in an Au crucible at 800 oC for 60 min. To improve the homogeneity
of the glasses, the melts were stirred manually with an alumina rod for ~ 1 min. Laboratory
glass transition temperatures Tg of TZN01 were determined by calorimetry (calorimetric Tg,
Tg-c, Netzsch DSC 404 F1), dilatometry (dilatometric Tg, Tg-d) and viscometry (beam bending
viscometer, T12, Bähr VIS402, assuming that Tg corresponds to the temperature at which the
viscosity equals 1012 Pa s [95). The heating rates are 20 and 10 K/min in the temperature
range of 50~430 and 30~300 °C, respectively for calorimetry and dilatometry. Figure 3.3
shows the glass transition temperature of TZN01 by calorimetry and dilatometry to be 273.5
and 271.1 °C, respectively [8].
The viscosity of TZN01 glass was measured by the pressure method and conducted in silica
capillaries with inner diameters (d) of 4.0, 6.25, 10.2, or 15.0 μm (drawn from Heraeus
Suprasil 301, outer capillary diameter 200.0 µm). It is noted that all the capillaries used in the
thesis are drawn from Heraeus Suprasil 301 with outer capillary diameter 200.0 µm. The
experimental setup is shown in Fig. 2.2(a). A small quantity of the TZN01 (< 0.25 cm 3) to be
pumped into the capillary was placed in a home-made 2 ml silica crucible. The silica crucible
was then placed inside a 70.0 cm long silica tube with inner diameter of 1.5 cm. A vertical
tubular resistance furnace accommodating the whole silica tube was used for further
pressurizing procedure at the required temperatures [8].
27
(a)
(b)
exo
0.0
0.6
-0.1
dL/L0 (%)
Heat flow (V/mg)
0.5
273.5
-0.2
274.4
271.1
0.4
0.3
0.2
0.1
-0.3
0.0
-0.4
50
100
150
200
250
300
350
400
-0.1
50
100
150
200
250
300
o
o
Temperature ( C)
Temperature ( C)
Fig.3.3 Glass transition temperature of TZN01 by calorimetry (a) and dilatometry (b), respectively.
Capillaries with lengths of ~ 50.0 cm were placed in the tube with one end immersed in the
TZN01 melt. The other end of these capillaries was sealed. Filling times were chosen with
reference to preliminary experiments in which the expected filling length was estimated.
Since one end of the capillary was sealed, depending on the degree of filling, a counter
pressure created by the residual air built up inside the capillary, acting opposite to the filling
pressure. The maximum filling length is in the range of 30.0 cm, which in the extreme case
corresponds to a counter pressure of ~ 2.0 bar. The average filling length was ~ 15.0 cm
corresponding to a counter pressure of ~ 1.4 bar. Therefore, compared to the filling pressure
larger than 10.0 bar, its presence can be neglected in all further calculations [8].
The whole set-up was stabilized at the temperatures for 1.0 min to allow the glass to be
melted, and then the silica tube was pressurized by argon. The pressure (1.0, 10.0, 20.0, and
30.0 bar) was monitored and held constant with an automated pumping system. During this
procedure, the glass melt was pressed into the hollow channels in the capillaries. The
microscopic viscosity of the filling melt was controlled by varying filling temperatures (700.0,
750, 800 and 840 °C for TZN01 as shown in Table 3.1). After a certain filling time, capillaries
were taken out of the hot tube and quenched in air, and thus became frozen filling state.
The suction method was employed for TZN01 (Table 3.2) as well. Filling experiments were
conducted in silica capillaries with inner diameter (d) of 20.0 μm. The experimental set-up
used for this filling procedure is similar to the pressure method employed above with one
major difference: instead of applying an elevated pressure to pump the melt into the capillary,
vacuum was used to suck in the melt (Fig. 2.2(b)). As a consequence, the filling dynamics are
28
Table 3.1 Capillaries (d = 4.0, 6.25, 10.2, and 15.0 μm) filled
under temperatures and applied pressures, and filling time.
Temperature (°C)
Pressure (bar)
Filling time (min)
700
10.0
20.0
30.0
2.0
3.0
4.0
5.0
750
10.0
20.0
30.0
1.0
2.0
3.0
5.0
800
10.0
20.0
30.0
1.0
2.0
3.0
840
10.0
20.0
30.0
1.0
2.0
3.0
dominated by capillary forces and, hence, surface tension and wetting behaviour of the
tellurite melt. Isothermal filling experiments were conducted at three different temperatures,
i.e. 700, 750, and 800 °C. About 5 g of glass was put into a 150 ml Au crucible and re-melted
at the targeted filling temperature, using a ~ 0.5×0.5×0.5 m3 furnace with a highly
homogeneous temperature distribution (calibrated with a thermocouple). An about 40 cm long
capillary section was then vertically dipped into the melt for a controlled duration of time by
using a stop watch. Vacuum (20 mbar) was applied and monitored on the other side of the
capillary, resulting in an unbalanced pressure of 960 mbar. After the respective filling time,
the capillary was rapidly removed from the furnace and quenched in air. For a better precision,
each filling procedure was carried out ten times.
Table 3.2 Filling parameters and surface tensions for TZN01 glass at required temperatures.
Temperature
(°C)
Pressure
(bar)
Surface tension*
(N/m)
Time
(s)
700
0.96
0
60
60
120
0.168
750
0.96
0
60
60
120
0.167
800
0.96
0
40
40
80
0.166
* Surface tension of the TZN01 glass taken from Sciglass [96].
The suction method was also employed for the TZN02 glass (Table 3.3). The experimental
procedure was the same as that for TZN01 glass. The isothermal filling temperatures were
500, 530, and 600 °C, and the employed capillary had an inner diameter of 44.0 μm. The
viscosities of the TZN02 melt would be higher at low temperatures. In order to save
experimental time and further reduce the effect of interfacial reaction between the glass melt
and silica capillary, capillaries with large diameter were used.
29
Table 3.3 Filling parameters and surface tension for TZN02 glass at required temperatures.
Surface tension*
(N/m)
Temperature
(°C)
Pressure
(bar)
500
0.96
200
400
600
0.16
530
0.96
100
200
300
0.16
600
0.96
20
40
60
0.16
Time
(s)
* Surface tension of the TZN01 cited from Sciglass [96].
The filling lengths of the glasses in capillary were then measured ex situ by imaging the
capillary from the side with an optical microscope (Nikon Eclipse LV100; Fig.3.4 (a) and (b)).
In addition to optical microscopy, dispersive Raman spectrometry (Nicolet Almega XR) was
employed to monitor the filled section of the capillary to confirm the existence of glasses and
structural rearrangement inside the capillary. For comparison with the microfluidic data
obtained by the infiltration technique, macroscopic viscosities of the TZN01 were determined
by beam bending viscometry within the range of 1013 to 109 Pa.s [97], and by the sinking bar
technique with the range of 103 to 101 Pa.s [98]. On selected capillaries, the cross-section was
monitored by electron microscopy (SEM, Fig. 3.4(c)). The SEM was operated at 20 kV with a
current of 1.24 nA.
Fig.3.4 (a) Side-view of a homogeneously TZN01 filled silica capillary; (b) A filled capillary containing
cracks and bubbles; (c) SEM images of TZN01 in capillary with diameter of 15.0 µm.
3.1.3 Raman spectra of TeZnNa glass and glass in capillary [8]
Raman spectrometry is a useful technique to investigate the structure of glasses. It was
performed systematically on the side-views of the TZN01 glass-in-capillary in order to
unambiguously confirm the presence of tellurite glass in the filled section (Fig. 3.5). The
Raman spectrum of the filled section of the capillary with TZN01 (diameter = 6.0 µm) clearly
matches that of the corresponding bulk reference. Three characteristic [94, 99, 100] scattering
peaks can be detected in the case of tellurite filling, corresponding to symmetric stretching
30
and bending vibrations of Te-O-Te linkages between TeO3, TeO3+δ and TeO4 structural units (~
460 cm-1), antisymmetric vibrations of Te-O-Te linkages (~ 660 cm-1) and Te-O-stretching
vibrations in TeO3+δ polyhedra or TeO3 pyramids (~770 cm-1). The shape and position of the
bands do not vary significantly between the bulk and confined glass at first consideration.
However, the peak at 660 cm-1 is a little sharper in the capillary than that of the bulk reference,
which implies that a structural change or crystallization may have happened during cooling.
This can be explained by (i) structural change induced by the confinement condition; (ii)
diffusion of ions caused by the interfacial reaction between SiO2 and TZN01, which further
affects the Raman spectrum. This will be discussed in detail in section 3.2. The structural
change is a result of freezing of the melts, while viscosities are obtained at melting
temperatures. Therefore it will not change the measuring accuracy of viscosity of melts.
Intensity (a.u.)
TZN01 in capillary
Bulk TZN01
300
400
500
600
700
800
900
-1
Raman frequency (cm )
Fig.3.5 Raman measurements of TZN01 filled silica capillaries (diameters 6.25µm).The spectra have
been recorded by illuminating the filling glass strands through the side of the capillary [8].
3.1.4 Results and discussion [8]
After the glass melt flows into the capillary, uncontrolled and/or fast cooling usually results in
the formation of cavities or cracks in the filled section (Fig. 3.4(b)). There are several reasons
for this. Firstly, the thermal expansion mismatch between silica and the filler is to be
considered. The thermal expansion coefficient of the filling glasses is about 30 times higher
than that of silica (0.6×10-6 K-1 for silica, and 17×10-6 K-1 for tellurite, respectively), which
means that a remarkable shrinkage of the tellurite glass will happen after cooling. At the
silica-filling glass interface, pronounced tensile stresses are to be expected after cooling. The
magnitude of these stresses depends primarily on the difference between Tg of the filling glass
31
from ambient temperature, on the applied cooling process and on the interface structure [19].
The subsequent procedures, such as removing the capillary from the furnace will cause the
formation of cracks. Besides thermally induced stresses and volume contraction, filling
defects may be induced by reboiling of dissolved gases, particularly argon (used as the
compression medium). If pressure is released too fast at too low a viscosity, oversaturation
may lead to gas release and bubble formation. This explanation would be supported by the
fact that the density of bubbles is much less by the suction method than by the pressure
method. Additionally, it is critical to melt a bubble free glass itself. These bubbles in glass
melts would probably be introduced into capillary during the filling procedures. To get rid of
the bubbles, a refining procedure has to be performed. In glasses, the distance (d) traveled by
a bubble follows the equation
d
2 gR 2
t
9
(3.1.1)
where g is the gravitational acceleration constant, R is the radius of the bubbles, ρ and η are
density and viscosity of the melts, respectively. It will take more than one hour for a bubble to
move 1.0 cm with the condition of R = 5µm, ρ = 5.0×103 kg/m3 and η = 0.1 Pa·s. Therefore, it
is very difficult to remove the bubbles formed in capillaries. Figure 3.6 presents the
microscopic picture of the TZN01 glass, which has many bubbles and cracks after quenching.
Fig.3.6 (a) Microscopic picture of TZN01, and (b) close-up view of
the area in the red circle in (a), blue circles are bubbles in glass after cooling.
The scale bars are 100 and 20 μm in (a) and (b), respectively.
Regardless of the length of the filled section, a single discontinuity (cavity or crack) will
strongly degrade the optical transmission of the waveguide. Therefore, in order to achieve
32
optical waveguiding, pressure release, cooling and a glass melting procedure must be
performed in a controlled way. In Fig. 3.7, the square of the filling length is plotted versus r2
and p for a constant filling time of 180 s for TZN01. Stable flow (approximately linear filling
speed) was obtained after an initial filling time of 2.0 min at 700 °C, 1.0 min at 750 °C, and <
1.0 min at higher temperatures. Since Eq. (2.3.5) is valid only for steady state conditions, the
Fig.3.7 Viscosity analysis of the tellurite filling process at different temperatures. The four plots show the
square of the filling length as a function of applied pressure and square of capillary radius. (a)
Experimental results at 700°C, (b) simulation at 700°C, (c) experimental results at 840°C,
(d) simulation at 840°C, taken from[8]. © 2010 Published by Elsevier B.V
length of the capillary section that was filled during this initial period was omitted from
further calculations. The ratio of inertial forces to viscous forces can be described by the
dimensionless Reynolds number Re,
Re
2 R
(3.1.2)
where ρ and η are density and viscosity of liquid, respectively, ν is the flow velocity, and R is
the radius of capillary. Here, values less than 20 are obtained for TZN01 filling over the
whole experimental temperature range, which clearly indicates laminar flow of the glass
inside capillary and PCF, respectively, during the filling process [102].
33
While filling kinetics were measured at various temperatures for TZN01 melts, in Table 3.4,
effective viscosity data as obtained from Eq. (2.3.5) are compiled together with macroscopic
information measured by beam bending and sinking viscometries. The most commonly used
function to fit the viscosity-temperature relationship of a glass melt is the Vogel-FulcherTamann (VFT) equation as mentioned in [41 - 43].
As already noted in the introduction section, it is now widely accepted that this formula starts
to break-down close to Tg and for η < 1.0 Pa·s [37]. It must therefore be noted that in the
following, the VFT equation is used only as an estimate for data interpolation. For the tellurite
glass used, the VFT fit produces A = −2.20, B = 1004 K and T0 = 475 K with regard to the
macroscopic viscosity data. From this, a glass transition temperature (η = 1012 Pa.s) of
272.6 °C is extrapolated, compared to the experimentally determined 271.1°C (dilatometer)
and 274.4°C (calorimeter), respectively. Figure 3.8 presents the viscosity as a function of
temperature for TZN01 glass. Through the VFT parameters, the viscosities were extrapolated
to glass melt. In Fig.3.8, two sets of viscosities for TZN01 melt were presented by the
pressure and suction methods, respectively.
(a)
(b)
-0.4
log in Pa·
s)
log (in Pa·
s)
9
6
3
-0.8
-1.2
-1.6
0
-3
500
pressure=10bar
pressure=20bar
pressure=30bar
suction method
75TeO2-10ZnO-15Na2O
suction in method
pressure method
VFT extrapolated data
12
600
700
800
900
1000
-2.0
960
1100
1000
1040
1080
1120
Temperature (K)
Temperature (K)
Fig.3.8 Viscosity analysis of the tellurite filling process at different temperatures with VFT equation. (a)
Viscosity of the TZN01 glass as a function of temperature. Three different techniques (beam bending,
sinking bar, pressure, suction method) and extrapolated data from VFT equation have been used to
determine the viscosity [8]. (b) Comparison of viscosity data measured with pressure and suction methods.
Compared to the extrapolated macroscopic viscosities, 3D plots in Fig. 3.7 were generated to
reveal the impact of confinement and pressure on the flow behaviour of the filling glasses. As
already noted, systematic Raman analyses did not reveal significant differences between bulk
glasses and glasses that were frozen-in under expectations provided that the lateral
confinement does not exceed a critical diameter (presently unknown, but certainly below 1.0
34
µm). However, Raman spectroscopy was performed ex situ. While it provides information on
the as-frozen state of the melt, it does not take into account kinetic data, long-range
anisotropy or fast relaxation processes that occur during freezing. For this reason, the
effective viscosity according to Eq. (2.2.6) was considered. The square of the filling length
that is plotted in Figs. 3.7 may be taken as a direct measure of this parameter. Then, an ideal
filling situation (L2(p, R2)) may be simulated by assuming a viscosity that is independent of
pressure and capillary diameter: using viscosity data as obtained for a given temperature
immediately enables the prediction of L2 for a given filling time and capillary diameter. If
these predicted values are compared to actual experimental data, deviations between
experimental viscosity (as a function of pressure and capillary diameter) and the assumed
constant value are revealed by changes in the symmetry of the 3D plots.
In addition to its systematic contributions, pressure may act on the flow in two different ways:
by actually (isotropically) impacting viscosity or by initiating non-Newtonian effects [8]. The
former effect is well-known in inorganic glasses, particularly silicates, when the applied
pressure approaches the GPa regime [19]. For example, a shift in the glass transition
temperature of ~ ±5-20 K/GPa is a reasonable estimate for most silicate glasses [10]. This
shift is more pronounced in low-melting (highly fragile) phosphate glasses with low network
connectivity, e.g. ~ +100K/GPa. Therefore the viscosity will change corresponding to this
shift,
log log (12.5 log )(
Tg ( p)
T
)
(3.1.3)
On the other hand, Fig.3.8 shows that these two infiltration methods present two sets of
viscosities at the same temperatures. The pressure induced data is almost ten times higher than
that measured by the suction method. Besides the possible reason of the shift of glass
transition, the liquid may become more viscous after densification by pressure. The free
volume theory has been employed to interpret the viscosity of a supercooled liquid in
dependence on pressure It states that the structure has a thermodynamic minimum volume
(V0). The specific volume (V) of a material will increase with increasing temperature. Then
the liquid will flow more easily, and be reflected in lower viscosity. Eq. (3.1.4) describes the
variation of viscosity corresponding to pressure at a constant temperature according to [9],
(
( p, T )
)T
( )
p
( p, T ) T p
(3.1.4)
35
Table 3.4 Viscosities of 75TeO2-10ZnO-15Na2O for different temperature regimes, obtained by beam bending and sinking bar viscometry (macroscopic) and from
infiltration technique according to Eq. (2.2.6) (microscopic) [8].
Infiltration techniques
Beam bending
Sinking bar
VFT extrapolated
Pressure method
Suction method
T (°C)
269
275
280
285
300
348
369
390
412
433
476
700
750
800
840
700
750
800
840
717
770
810
850
log (η/Pa·s)
12.4
11.3
10.7
10.2
9.0
4.2
3.4
3.1
3.0
2.1
1.4
- 0.2
-0.4
-0.5
-0.6
-0.6
-0.6
-1.0
-1.2
-1.6
-1.7
-1.9
-1.9
36
where κ is isothermal compressibility, α is isobaric thermal expansion coefficient. As κ > 0,
α<0 and (
) p 0 , ( )T 0 . Therefore, the viscosity measured by high pressure is
T
p
probably higher than that measured by the suction method.
L. H. Thamdrup et al. provided another possible explanation by studying the bubble formation
during capillary filling [103]. The results show that a small bubble may increase the fluidic
resistance, which reduces the filling speed of the liquid [103]. If lots of bubbles exist in the
glass melt during the filling process, they will correspondingly reduce the filling length, and
thus increase the apparent viscosity. J. Bico discussed the bubble formation and motion inside
the capillary and proposed designing the geometry of capillary so as to prevent bubbles from
being trapped, which often occurs in a circular capillary [104].
In the suction method, the filling dynamics are dominated by capillary forces and, hence, also
surface tension and wetting behaviour of the tellurite melt. From the equation
(2 R cos R 2 PA )
t , two data processing methods can be conducted to determine the
4 L2
apparent viscosities of melts, respectively. (1) Checking the part
R cos
closely. The
2
surface tension of melts is first identified from literature or the Sciglass database, then
viscosity is calculated assuming a constant dynamic contact angle. It is noted that the dynamic
contact angle here is not the same as the static contact angle, which is about zero for tellurite
melts at our experiment temperatures. Figure 3.9 shows the apparent viscosities by assuming
different dynamic contact angles with the surface tension of melts from Sciglass as shown in
Table 3.2. (2) Setting the part
R cos
as unity, and performing a separate filling procedure
2
without vacuum pump. This process means that the liquid flow is driven only by surface
tension,
L2
L12
R cos
t
2
will
be
measured.
The
L12
is
then
subtracted
from
2 R cos R 2 PA
R 2 PA
t as discussed in Chapter 2. A direct relationship L2 L12
t
4
4
between external unbalanced pressure PA and viscosity is established, where only PA is
responsible for the filling length. This data processing method is named the UP method in the
following. Assuming the equality of the viscosities calculated from these two methods, the
37
=
o
0
o
30
o
45
o
60
Viscosity (Pa·s)
0.028
0.024
UP method
0.020
0.016
0.012
680
720
760
800
o
Temperature ( C)
Fig.3.9 Viscosities of TZN01 acquired by two data processing methods.
(a)
(b)
8
60
2
L12(cm )
L (cm)
6
4
o
0
20
800 C
o
750 C
o
700 C
2
0
40
80
120
160
40
0
200
o
800 C
o
750 C
o
700 C
0
40
80
120
160
Time(s)
Time (s)
Fig.3.10 (a) Parabolic and (b) linear fittings of filling length for TZN01 corresponding to the filling times.
dynamic contact angle can be calculated as 50°, 43°, and 29° for 700, 750, 800 oC,
respectively. The result agrees with thermodynamics so we can expect that the contact angle
decreases with increasing temperature for wetting liquids. The filling length L1 and its square
L12 are presented in Fig.3.10, which obeys the characteristic of Lucas-Washburn equation
L12
R cos
t . In a further experiment, the macroscopic wetting behaviour of TZN01 was
2
observed in a hot-stage microscope (HT 04/17S, Nabertherm GmbH, Lilienthal, Germany). A
cubic TZN01 glass sample (5×5×5 mm³) was placed on a silica wafer. The wetting angles
between the tellurite glass and the wafer were observed during heating, using two digital
cameras. Comparative runs were conducted at two heating rates, 3 K/min and 1 K/min
between 200 and 500 °C, as shown in Fig. 3.11. The static contact angle decreases sharply
when the temperature increases. At around 430 °C, the static contact angle is about 24°.
38
Considering this trend, it can be deduced that the contact angle will be about zero with
increasing temperature, which agrees with the conclusion that the static contact angle is
smaller than the dynamic contact angle in the infiltration method. Not only in glass melts, this
discrepancy between dynamic and static contact angle has also been observed in polymer and
water [106, 107].
Fig.3.11 Contact angle between silica and TZN01 as a function of temperature for a heating rate of 3
K/min. Insets: Photographs of the TZN01 specimen on the silica wafer for selected temperatures, taken
from [109]. © 2011 Published by Elsevier B.V
Similarly, viscosities of TZN02 obtained with the suction method are shown in Fig.3.12. An
obvious deviation at 500 oC results from the crystallization of TZN02.
0.5
Viscosity (Pa·s)
0.4
0.3
0.2
0.1
500
520
540
560
580
600
o
Temperature ( C)
Fig.3.12 Viscosities of TZN02 at different temperatures.
39
3.1.5 Viscosities and flow behaviour of alkali-free tellurite glass with suction method
Replacing alkali ions (Na+) with lanthanide ions will improve certain properties of tellurite
glasses. M. R. Sahar et al. studied tellurite zinc erbium glasses and found that the glass
stability increases with the addition of Er2O3 [107]. Thermal properties, glass transition
temperature Tg, crystallization temperature Tc of TeO2-ZnO-RxOy (R=Na, or Er) are listed in
Table 3.5, which shows (i) the improvement in the glass stability and (ii) that tellurite glasses
containing lanthanide ions are more thermally stable than those containing alkali ions, since
Tc- Tg is used to assess the glass thermal stability. In the thesis, lanthanide compound Er2O3
was replaced by La 2 O 3 and a tellurite gl ass with a nominal composition of
Table 3.5 Tellurite alkali and alkali free glasses with their thermal properties, taken from [94, 107]
Temperature (oC)
Composition (mol.%)
TeO2
ZnO
Er2O3
Tg
Tc
Tc-Tg
79.5
20
0.5
321.0
420.0
99.0
79
20
1.0
322.0
442.0
120.0
78
20
2.0
323.0
460.0
137.0
77.5
20
2.5
335.0
475.0
140.0
TeO2
ZnO
Na2O
80
10
10
284.0
386.0
102
70
10
20
259.0
372.0
113
60
10
30
233.0
346.0
113
77TeO2-20.5ZnO-2.5La2O3 (mol.%) (TZL) was prepared by conventional melting and
quenching. Reagent grade powders of TeO2, ZnO, La2O3 were weighed, mixed and melted in
an Au crucible at 700 oC for 30 min. To improve homogeneity, the melts were stirred
manually with an alumina rod for ~ 1.0 min. Laboratory glass transition temperatures Tg of
the samples were determined by calorimetry (calorimetric Tg, Tg-c, Netzsch DSC 404 F1). The
heating rate is 20 K/min in the temperature range 50~430 oC for calorimetry. Figure 3.13
shows the glass transition temperature, which is 340.5 oC determined by calorimetry.
The viscosities of TZL glass melt were obtained through both pressure and suction methods.
In the suction method, filling experiments were conducted with silica capillaries having inner
diameters d of 4.0, 8.0, 20.0, and 44.0, 70.0, 160.0 μm. The experimental filling set-up and
procedure is the same as that of the TZN glasses. Capillary lengths were chosen with
reference to Eq. (2.2.6), using an estimation of the melt viscosity to obtain the expected filling
40
Heat flow (V/mg)
0.00
exo
-0.05
-0.10
340.5
-0.15
347.3
-0.20
-0.25
50
100
150
200
250
300
350
400
450
o
Temperature ( C)
Fig.3.13 Glass transition of TZL determined by calorimetry.
length. The experimental filling time was estimated according to an expected filling length of
~ 4.0 cm ( d ≤ 8.0 µm ), 10.0 cm ( 8.0 µm < d < 160.0 µm ) or 20.0 cm ( d = 160.0 µm ),
respectively. After the respective filling time, the capillary was rapidly removed from the
furnace and quenched in air, thus freezing-in the filling state. The data acquisition process is
the same as that of the TZN glasses. As there is applied pressure, a condition is defined at
which the hydrostatic pressure effect can be neglected. The condition is set at a hydrostatic
pressure not exceeding 3% of hE. hE is the equilibrium length of the liquid in capillary under
external and capillary pressure. In our case, the unbalanced atmospheric pressure PA is the
vacuum pressure, which is 0.96·105 Pa. We assume that the hydrostatic pressure equals the
applied external pressure plus the capillary pressure,
ρghE = 0.96·105 +2γcosθ/R
If the filling length is less than 3% of hE, the hydrostatic pressure is neglected; otherwise, the
hydrostatic pressure should be considered to calculate the viscosity of the glasses. Then, hE
and 3% hE for capillaries with different radii (assuming contact angle equals 30°) are
calculated in Table 3.6, where 10% hE is given as well. Surface tension and density of TZL
melts were cited from Sciglass for calculation §.
———————————————————
§
Surface tension and density of TZL glass melt at three temperatures [96]
Temperature (°C)
700
750
800
Surface tension (mN/m)
143.8
143
142.6
Density (g/cm3)
5.162
5.147
5.108
41
Table 3.6 Error controlling for using Eq. (2.2.8) to calculate viscosities of the TZL.
Radius R (µm)
2
Assumed
filling length (cm)
4
5
10
22
4
35
80
10
20
hE1 at 700°C (cm)
435.9
312.8
288.2
239
212.1
203.8
195.9
3% hE1 (cm)
13.1
9.4
8.6
7.2
6.4
6.1
5.9
10% hE1 (cm)
43.6
31.3
28.9
23.9
21.2
20.4
19.6
hE2 at 750°C (cm)
436.2
313.2
288.7
239.5
212.7
204.4
196.4
3% hE2 (cm)
13.1
9.4
8.7
7.2
6.4
6.1
5.9
10% hE2 (cm)
43.6
31.3
28.9
24.0
21.3
20.4
19.6
hE3 at 800°C (cm)
438.5
315.1
290.5
241.1
214.2
205.9
197.9
3% hE3 (cm)
13.2
9.5
8.7
7.2
6.4
6.2
5.9
10% hE3 (cm)
43.9
31.5
29.1
24.1
21.4
20.6
19.8
An exemplary filling situation is shown in Fig. 3.14(a) for a capillary with an inner diameter
of 70.0 µm, filled with TZL at 700 °C for 36 s (ex situ optical microscopy). The figure is the
upper end of the tellurite column (vacuum applied on the left side) which can be divided into
three sections: the not-yet-filled silica capillary (left), the tellurite meniscus (middle) and the
filled capillary section (right). In this example, the meniscus has a length of ~ 400 µm. From
the meniscus, the effective static wetting angle can be estimated. In practice, its very low
value leads to the occurrence of a thin tellurite film over the greater part of the meniscus
(~200 µm, due to the high refractive index of TZL visibly darker than the unfilled section to
(b)
Intensity (a.u.)
751cm
660cm
420cm
400
-1
-1
477cm
300
-1
500
-1
611cm
600
805cm
-1
700
800
-1
900
-1
Raman frequency (cm )
Fig.3.14 Side-view of an exemplary filling situation for a capillary with an inner diameter of 70 µm, filled
with TZL at 700 °C for 36 s (a), and corresponding Raman spectrum of the filled section (b) [109]. © 2011
Published by Elsevier B.V
42
the left side of Fig. 3.14(a). Importantly, Fig. 3.14 was taken ex situ after quenching the filled
capillary. Therefore, some viscous retraction of the tellurite column must be considered when
using Fig. 3.14 to discuss the wetting behaviour. The interior of the as-filled capillaries was
examined systematically by micro-Raman spectroscopy on side-views as shown in Fig.
3.14(b). The primary objective of these analyses was to confirm the presence of tellurite glass
in the filled section. Secondly, spectra were screened for eventual changes that might have
been induced by confinement or by chemical reactions between the filling melt and the silica
capillary. A best-fit of the spectra was obtained by deconvolution into six Gaussian peaks (Fig.
3.14(b)). These peaks correspond [94, 99, 100, 108] to symmetric stretching and bending
vibrations of Te-O-Te linkages between trigonal TeO3 pyramids, TeO3+δ polyhedral and
trigonal TeO4 bipyramids (~ 420 and 477 cm-1), vibration of the continuous network of TeO4
bipyramids (~ 611 cm-1), antisymmetric vibrations of Te-O-Te linkages (~ 660 cm-1),
stretching vibrations between tellurium and non-bridging oxygen sites(~ 751 cm-1), and Te-Ostretching vibrations in TeO3+δ polyhedral or TeO3 pyramids (~805 cm-1).
Figure 3.15 shows the apparent viscosities of the TZL melt obtained by employing capillaries
with various scales at 700, 750, and 800 oC, respectively. Generally, viscosity is understood as
a measure of the timescale of shear relaxation, τ, η = τ.G∞ (where G∞ is the shear modulus at
infinite shear frequency). Experimentally, a dependence of τ on lateral confinement has not
yet been demonstrated for inorganic glasses. It appears, however, that such dependence exists
already for µm-confinement. For capillary radii of ≥ 20 µm, we consider viscosity as
independent of capillary diameter. The deviation of viscosities corresponding to capillary
radius is observed at lower radii. In a first consideration, various effects, such as slip or
variation in surface tension, interfacial tension, and bubbles formed in the capillary are
Viscosity (Pa·
s)
(a) 0.13
0
30
45
UP method
0.12
0.11
o
T=700 C
0.10
0
10
20
Radius (m)
43
30
40
(b)
0
30
45
UP method
Viscosity (Pa·
s)
0.075
0.070
0.065
0.060
o
T=750 C
0
10
20
Radius (m)
Viscosity (Pa·
s)
(c) 0.050
30
40
0
30
45
UP method
0.045
0.040
o
T=800 C
0
10
20
Radius (m)
30
40
Fig.3.15 Viscosities of TZL corresponding to capillary diameters at (a) 700, (b) 750 and (c) 800 °C. Contact
angles between melts and capillary wall were assumed for calculation. The viscosity obtained from
subtracting the surface tension effect from the experiment is presented for comparison.
considered to be responsible for this deviation, whereas, an equilibrium viscosity can be
observed when the capillary radius is ≥ 20.0 µm. The obtained data were processed with the
same methods as those performed in TZN01. In the following, this value is taken as the actual
value of the dynamic viscosity of the tellurite melt at the respective temperature (viscosity
values of 0.111 Pa.s, 0.064 Pa.s, 0.040 Pa.s for TZL at 700, 750 and 800 °C, respectively),
which agree with the data processing method by experimentally subtracting the surface
tension filling length L12
2 R cos
t (discussed in section 3.1.4 in detail, and named the UP
4
method).
44
The software Fluent 6.3.26 was used to simulate the melt's flowing stage inside the capillary.
Melt flow under 700 oC was chosen as an example. The process parameters include radius of
capillary (10μm), viscosity (0.111 Pa.s) and unbalanced pressure (0.96 bar). The melt is
assumed to be a non-compressible and Newtonian fluid. The simulation is based on the (1)
law of conservation of mass and (2) Navier-Stokes momentum equation. Figure 3.16 presents
the inlet velocity distribution of the melt after flowing into a capillary at different times, 2.3,
9.1, 36.2, 227, and 910 μs, respectively. As mentioned in section 2.3, liquid flow in the tube
can be separated into several stages [80]. After 48 μs, the TZL melt will behave as purely
viscous [80]. The corresponding velocity distribution should be between Fig. 3.16 (a) and (d).
The simulation results show that the melt moves at laminar flow after 227 μs, which is higher
than 48 μs. Nevertheless, this time is much shorter than that of the experimental operation.
Therefore, the Lucus-Washburn equation can be applied. The y axis stands for the velocity
profile along the radius of the capillary.
In order to obtain a better view of the confinement effects on the rheologic behaviour of the
melt, the quadratic filling length was plotted over the ratio between filling time and the
timescale of shear relaxation (expressed as dynamic viscosity) for various filling lengths (Fig.
3.17 (a)). According to L2
2( L2 L12 )
2 R cos R 2 PA
R cos
t , R2
, the
t and L12
2
PAt
4
capillary radii can be extracted from the slope of the obtained curve. The thus obtained value
is denoted as the effective radius, RLW. Non-linear deviations between RLW and R directly
reflect deviations from the Lucas-Washburn equation. Figure 3.17(b) clearly illustrates nonlinear deviation for capillary radii below about 20.0 - 40.0 µm. For example, a deviation of
RLW -0.98R was found for a capillary diameter of 40.0 µm. According to Eq. (2.2.12), this
deviation may have several causes: (1) Gravitational effect. Given the designed filling length
corresponding to capillary radius and error estimation (Table 3.6), the gravitational effect
would be more obvious when the radius increases, that is, the deviation of RLW should be the
smallest for capillary with a radius of 2.0 μm. On the contrary, the deviation is largest for
capillary with the minimum radius. (2) The surface tension effect might change after
employing external pressure, which accelerates the kinetic movement of liquid flow. (3)
Confinement-induced pressure in wetting behaviour might have been present or, for instance,
non-Newtonian flow might have occurred during the experiment. For the present case,
however, the third aspect is excluded as dominant contributions to the deviation from LucasWashburn behaviour since no signs of a deviation from Newtonian flow could be found in the
45
Fig. 3.16 Simulated stable flow of Tellurite melt in capillary at various times.
previous experiments at least for filling pressures of up to 30.0 bars. It is assumed that the
tellurite melt follows Eq. (2.2.12), but the effective radius Re = RLW of the capillary is reduced
by the formation of a stationary layer at the TeO2-SiO2 interface. The thickness of this
reaction layer is dependent on the degree of confinement (capillary diameter). The diameter46
dependence decreases with increasing diameter and approaches value of about 2.5 µm at R =
80.0 µm. The comprehensive effect of the gravity and stationary layer induces the deviation
of effective radius.
(a) 0.05
1.00
(b)
80
0.04
0.02
0.01
0.96
40
0.94
20
0.00
0
2000
4000
6000
8000
0
10000
RLW/R
RLW(m)
0.03
2
L2- L1 (m2)
0.98
60
0
20
40
60
80
0.92
Radius(m)
-1
t/( Pa )
Fig.3.17 Quadratic filling length as a function of the ratio between observation time and shear relaxation
time (±100Pa-1) for different capillary radii (a). Labels indicate capillary radius. In (b), the resulting plot of
RLW (obtained from the slopes of linear regression lines) in (a) over the real radius R is shown, together
with the ratio between RLW and R. Lines in (b) are guides for the eye, obtained from a fit of RLW/R data to
first order exponential decay equation and, respectively, from a fit of the RLW data to a line with slope
0.96 [109]. © 2011 Published by Elsevier B.V
With the pressure method, external pressure of 10.0, 20.0, and 30.0 bar was applied (Figs.
3.18). The measured viscosities of TZL maintain a constant value with shear rate, implying
Newtonian flow of the TZL melt, at least for the range of the currently employed shear stress.
The consistence of viscosity acquired from both the pressure and the suction methods
indicates the feasibility of these two methods for measuring viscosity of TZL melts, though
there is diffusion of glass compositions and interfacial reaction. Differences of viscosity
behaviour under pressure between TZN glass and TZL glass may be caused by the
pronounced diffusion of Na+ ions, which is much more subtle for La3+ in TZL glass, or a
smaller free volume space in TZL glass, which significantly decreases the viscosity change
under pressure. The standard deviations shown in Fig. 3.19 are within experimental errors.
47
(b)
(a) -0.8
0.16
o
700 C
o
o
Viscosity (Pa·
s)
log ( in Pa·
s)
700 C
o
750 C
-1.0
o
800 C
-1.2
750 C
o
0.12
800 C
0.08
0.04
-1.4
0.00
10
15
20
25
30
0
300
600
900
Shear rate (s
1200
1500
)
-1
Pressure (bar)
Fig.3.18 (a)Viscosities of TZL under different pressures, and (b) they are constant
as a function of shear rate at required temperatures, respectively.
suction method
pressure method
log ( in Pa·s)
-0.90
-1.05
-1.20
-1.35
700
720
740
760
780
800
Temperature ( C)
o
Fig.3.19 Viscosity data of TZL from pressure and suction methods, respectively.
3.2 Interfacial reactions between tellurite melts and silica [109]
In section 3.1, the apparent microscopic viscosities of tellurite melts identified using
infiltration techniques have been measured and discussed. It is demonstrated that an
interfacial reaction between as-filled melts and silica capillaries more or less influences the
precision of the viscosities of melts The particular interfacial reactions that occur at the filling
temperature between the filling medium and the silica matrix must be controlled. In the case
of tellurite-filling, such reactions may involve diffusion of tellurite species into the silica
matrix, dissolution of silica in the tellurite melts, interfacial crystallization and phase
separation. Secondly, process-induced volume reactions may occur such as the generation of
structural anisotropy as a result of shear flow [13, 14], isotropic changes in the network
topology as a result of the applied body forces [12], solution and re-boiling of gases [18, 110],
or pressure and confinement-dependent crystallization or phase-separation processes [111]. In
a first consideration, especially the interfacial reactions would lead to the occurrence of
48
scattering centers inside the waveguide and, hence, to very high optical loss. While such
reactions are less critical for chalcogenide melts (which typically do not wet silica), they are
of significant importance for the fabrication of tellurite-silica hybrid devices [22].
TZN01 was used to study the interaction with silica glass in the temperature regime of about
400 °C to 800 °C. Production and isothermal annealing of silica-tellurite-silica sandwiches
was conducted according to the following procedure: a small amount of tellurite glass was
crushed and milled. The obtained glass powder was then compressed to the form of thin
sheets (thickness of 300 µm) using a hydraulic press. As depicted in Fig. 3.20, sandwiches
were prepared by placing one such tellurite sheet in between two silica wafers (Heraeus
Suprasil SU 1). These sandwiches were then placed into an electric furnace and preheated in
the desired isothermal reaction temperature (400-700 °C, 20.0 - 80.0 min). During this
procedure, the tellurite sheet re-melted to form an approximately 40 µm thick film between
the two silica wafers. On the reacted sandwiches, Raman spectra were collected (Fig.3.21). In
addition, electron microscopy was performed, using EDS for chemical analyses of the film
and the silica-tellurite interface.
Fig.3.20 Schematic diagram of silica-tellurite-silica sandwich.
A result of macroscopic analyses (optical dilatometry) of the wetting angle of tellurite on
silica is shown in Fig.3.11 for TZN01 glass. At a heating rate of 3 K/min, the onset of
softening was found at 323 °C, the maximum wetting angle of ~ 120°at 370 °C. Subsequently,
the wetting angle decreases rapidly to < 10°at 500 °C. These data lead to an assumption of
total wetting at the respective filling temperature.
The observation of a deviation between RLW and R discussed in section 3.1.5 and the
occurrence of a stationary interfacial layer between silica and the tellurite melts is in good
agreement with ex situ analyses of static contact experiments. A typical result of such an
49
experiment is summarized in Fig.3.22, which is representative of a silica-TZN01-silica
sandwich heat-treated at 700 °C for various periods of time.
bulk TZN
o
Intensity (a.u.)
sandwich, 700 C 80 min
300
400
500
600
700
-1
800
900
Wavelength (cm )
Fig.3.21 Raman spectra of as-made bulk TZN and TZN in a silica-TZN-silica sandwich after annealing
for 80 min at 700 °C [109]. © 2011 Published by Elsevier B.V
Figure 3.22(b) shows a close-up view at the interface region after prolonging the annealing
time to 80 min. EDS chemical analyses were performed on the interface regions as well as on
the different precipitates which are visible in the tellurite layer. These led to three principal
observations: (1) for both treatment times, observed precipitates are silica-rich, (2) diffusion
of sodium ions from the tellurite melt into the silica wafer occurs to a depth of about 8 - 10
µm (80 min) and silicon ions into tellurite layers diffuse to a depth of about 6 – 8 µm (80 min),
and (3) for the longer treatment time, the presumable crystalline interfacial precipitates are
replaced by a continuous silica-rich interfacial tellurite layer and almost homogeneously
distributed spherical precipitates of narrow size distribution throughout the tellurite layer.
Notably, while on the SEM micrograph, the size distribution appears broad, the fact that the
image reflects the cross-section of particles which are embedded at different depths must be
considered. A statistical analysis reveals practically equivalent diameter for all spheres. In Fig.
3.22(c), an EDS line scan of the interfacial region is shown. Notably, a clear dependence of
the diffusion depth on ion size and charge is detected, which means the smaller the ions, the
more deeply the ions diffuse. The diffusions of the three ions into the silica plate were fitted
with Ficker’s Law (Fig.3.22 (d)). The distributions of the three ions follow the equation
y C1 exp( x2 / C2 ) , where C1 and C2 are related to the diffusion coefficient. Actual probing
locations are marked in Figs. 3.22(a) and (b). In terms of reaction time, a typical capillary
50
filling experiment is best reflected by the faster sandwich experiments. However, if a
diffusion process is assumed to be the dominating interface reaction, and if sodium ions are
assumed to be the most mobile species, reaction times of stationary sandwich experiments
(representing a non-infinite sodium source) and the dynamic filling process can not readily be
compared. Rather, all three cases of Fig. 3.22 must be considered. Generally, Fig. 3.21(b)
indicates a reaction layer thickness of about 2 µm. With respect to the composition and
regardless of whether or not this layer is crystalline, it exhibits a significantly higher viscosity
than the tellurite filling glass and, hence, should be practically stationary at 700 °C. Spherical
precipitates in Fig. 3.22(b) seem to exhibit the same composition as the reaction layer and
presumably result from liquid-liquid separation of a silica-rich phase after silica dissolution in
the tellurite melt. For the interface region, the ex situ XRD pattern (Fig. 3.22(e)) indicates the
(b)
(a)
(c)
Element concentration (at.%)
3
e
2
e
1
e
0
Silica plate
e
-1
e
TeZnNa film
-2
e
Na
Zn
Si
Te
-3
e
-4
e
Interface
-10
-8
-6
-4
-2
0
Position (m)
51
2
4
6
8
(d) 20
Na
Zn
Te
Element diffusion (at.%)
16
12
8
4
0
0
2
4
6
Position (m)
8
10
Intensity (a.u.)
(e)
15
20
25
30
35
40
2 (
45
o
50
55
60
65
70
)
Fig.3.22 Analyses of silica-tellurite interfaces after static contact experiments (sandwich experiments) at
700 °C. (a) and (b) depict SEM micrographs after 20 and 80 min annealing time, respectively. (c) is the
result of EDS chemical analyses of the interface region shown in (b). Lines serve as visual guides. (d) The
diffusions of the three ions into the silica plate were fitted with Ficker’s Law (e): XRD diagram as taken of
the tellurite-silica interface ex situ after opening a sandwich which was annealed for 40 min. Labels mark
peak positions and assignment for β-quartz [109]. © 2011 Published by Elsevier B.V
presence of β-quartz crystallites, while no other crystalline species can be detected. In contrast,
no crystalline species could be found on samples which were treated at the same temperature
for 80 min, i.e. the sample shown in Fig. 3.22(b). Interfacial precipitates seen in Fig. 3.22(a)
are therefore assigned as β-quartz crystallites, which are further indicated also by their
morphology. Spherical precipitates in Fig. 3.22(b) are presumably glassy. It is assumed that
interfacial crystallization is triggered by the diffusion of alkali species into the silica layer.
52
This is well-known to strongly facilitate devitrification of silica. For example, while at 700 °C,
practically no devitrification can be observed from pure vitreous silica for any observation
time, at the same temperature, the crystallite growth rate approaches about 20 µm/min for a
Na2O-content of 0.69 mol.%. Notably, under the same experimental conditions, the
crystallization reaction could not be observed in alkali-free TZL while phase separation
occurs in a similar manner.
As mentioned in section 3.1, at first consideration, the Raman spectrum of the bulk TZN01 is
similar to that of the glass in the capillary. However, variation of scattering peaks can be
observed by investigating the spectra closely. The Raman peaks of bulk TZN01 and glass in
the capillary were deconvoluted by assuming that the overlapping peaks are all Gaussian
distribution. The resulting separate peaks are presented in Figs.3.23(a)-(c). An obvious shift of
peaks and a strong difference in intensity imply a structural change in the TZN01 glass after
being frozen inside the capillary. In the tellurite zinc sodium glasses, the five peaks at 455,
610, 669, 720, and 780 cm-1 are assigned in Table 3.7.
Table 3.7 Raman peak assignment of tellurite zinc sodium glasses.
Frequency
Assignment
~ 455 cm-1
Symmetric stretching and bending vibrations
of Te-O-Te linkages
~ 610 cm-1
Vibration of the continuous network composed of TeO4 TBP
~ 660 cm-1
Antisymmetric vibrations of Te-O-Te linkages
~ 720 cm-1
Stretching vibration between Te and
non-bridging oxygen (NBO) sites
~ 780 cm-1
Vibration of the continuous network composed of a Te-Ostretching vibration of TeO3+δ polyhedra or TeO3 TP
(a)
Intensity (a.u.)
TZN01 in capillary
Bulk TZN01
300
400
500
600
700
-1
Raman frequency (cm )
53
800
900
(b)
Intensity (a.u.)
Bulk TZN01
300
450
600
750
-1
900
Raman frequency (cm )
(c)
Intensity (a.u.)
TZN01 in capillary
300
450
600
750
Raman frequency (cm
-1
)
900
Fig.3.23 Raman spectra of TZN01 filled silica capillaries (strand diameters about 6 µm)
and bulk TZN01.Gaussian deconvolution of Raman peaks were conducted to show
the bond change of TZN01 by confinement.
Firstly, the peak at around 455 cm-1 has generally been attributed to the deformation vibration
modes of the glass network's bridging oxygens. Not only has the intensity increased, the
frequency has also shifted to a higher value of 478 cm-1. In addition, the shape becomes
asymmetric. The peak at 455 cm-1 is assigned to symmetric stretching and bending vibrations
of corner sharing units of TeO4, TeO3+δ, and TeO3. The increase in intensity and frequency
shift reflect reduction of TeO3+δ and TeO3 relative to TeO4. The ratio of (I720+I780)/I660 present
the ratio of the fractions of TeO3 TP/ TeO4 TBP, which is 1.60 and 1.46 for bulk TZN01 and
TZN01 in capillary, respectively. It agrees with the analysis of the increase of the peak at 455
cm-1. Peaks at 720 and 780 cm-1 correspond to the stretching vibration between tellurium and
non-bridging oxygen and the vibration of the continuous network composed of Te-Ostretching vibration of TeO3+δ polyhedra or TeO3 TP, respectively. Intensities of the peaks at
54
720 and 780 cm-1 behave oppositely for bulk glass and glass in the capillary, which may be
influenced by the diffusion of Si atoms into TZN01 in capillary.
The alkali free glass TZL, however, has no Raman spectral difference on intensity and
frequency position as shown in Fig. 3.24 (a) and (b), which has less ions exchange. The
comparable Raman spectra between TZN01 and TZL glasses suggest that the interfacial
reaction has a significant influence on the glass structure. It is concluded that all structural
changes observed here result from this reaction, and not from confinement.
(a)
Intensity (a.u.)
Bulk TZL
300
450
600
750
900
-1
Raman frequency (cm )
(b)
-1
751cm
Intensity (a.u.)
TZL in capillary
-1
660cm
-1
420cm
-1
-1
477cm
300
450
-1
805cm
611cm
600
750
900
-1
Raman frequency (cm )
Fig.3.24 Raman spectra of TZL filled silica capillaries (strand diameters about 8µm)
and bulk TZL. Gaussian deconvolution of Raman peaks was conducted. No obvious
bond change of TZL by confinement as that of TZN01 appears.
3.3 Sulfophosphate glasses
Sulfophosphate melts of the type ZnO-P2O5-SO3-Na2O may form stable ionic glasses [112].
The melt becomes increasing depolymerized when replacing P2O5 with SO3. Correspondingly,
the chemical heterogeneity on short length scale can be detected in the sulfophosphate melts.
55
Reibstein et al. investigated the heterogeneity of this system and found that density fluctuation
increases with increasing amount of SO3 [112]. On the other hand, the structural change by
modifying the compositional ratio of P2O5 to SO3 must have some impact on the rheology of
sulfophosphate melts.
3.3.1 Introduction of sulfophosphate glasses
To vitrify sulfate-rich ashes, Arkhipov and Mamoshin et al. first investigated the
sulfophosphate glass system in the early 1980s [113 - 119]. Later, potential applications were
proposed and studied by employing sulfur-containing iron phosphate glasses or polymersulfophosphate blends for immobilization of nuclear waste and moulding, respectively [120 126]. Recently, sulfophosphate glass ceramics were introduced, which acts as an effective
matrix for some luminescent species [127]. In a more general way, low melting inorganic
glasses - glasses with a glass transition temperature Tg well below 400 °C and a softening
temperature below 500 °C – are receiving extensive attention, such as for organic-inorganic
hybrid systems [128, 129], moulding [130], sealing and melt-infiltration of rigid preforms
[129]. Compared to some typical glass forming systems ranging from phosphates, particularly
zinc [131 - 133] and tin phosphates [134], to bismuthates, tellurites and chalcogenides [135],
sulfophosphate glasses can overcome some drawbacks such as the presence of toxic or rare
components, weak chemical durability and high reactivity with water and a strong
devitrification tendency [136, 137]. Sulfophosphate glasses can be easily prepared below
800 °C with Tg below 330 °C [136]. Additionally, with the substitution of P2O5 by SO3 in
Na2O-ZnO-P2O5-SO3, kinetic fragility and Tg generally decreases [136, 137]. Rheologic
properties of sulfophosphate melts appear to be related to topology and topological
heterogeneity [112]. Brückner et al. investigated the rheologic properties of phosphates by
choosing the composition range around the transition from the three-dimensionally connected
ultra phosphates to the one-dimensionally connected polymetric chain-like polyphosphates. It
was found that Newtonian flow of ultra phosphates transforms to non-Newtonian flow in
poly-phosphates [139]. In the sulfophosphate glasses we studied here, the glass type
transforms from polyphosphate to orthophosphate.
3.3.2 Experimental procedure
Glass formation in the system ZnO-P2O5-SO3-Na2O was studied by varying the ratio of SO3
to P2O5 (Table 3.9). The SP0x (x=0, 5.1, 9.1, 14.1, 19.1, 22.1) is the abbreviation of the
sulfophosphate glasses with the composition of 42.2ZnO-19.6Na2O-xSO3-(38.2-x)P2O5.
56
Batches of ZnO, Na2CO3, ZnSO4•7H2O and NH4H2PO4 were first calcinated at 300 °C for 3 h,
then melted at 800 °C for 30 min (heating rate of 2.8 K/min). Glass slabs of about 300 g were
produced by pouring the melt onto a pre-heated graphite plate and subsequent annealing for
one hour at 300 °C. Melting was performed in Pt crucibles. Viscosities of the six glass
compositions were measured with beam bending, sinking bar, and suction methods. Glass
slabs (5.0 cm × 0.6 cm × 0.3 cm) were cut for the beam bending viscometer. 30 g of each
glass were chosen for the sinking viscometer. 2.0 g of each glass were put into platinum
crucible for the suction viscometer. Capillaries with a diameter of 70.0 μm were employed.
Laboratory glass transition temperatures Tg of the glasses were determined by calorimetry
(calorimetric Tg, Tg-c, Netzsch DSC 404 F1) and dilatometry (dilatometric Tg, Tg-d). The
heating rates are 20 and 10 K/min in the temperature range 50 ~ 430 ℃ and 30 ~ 360 ℃,
respectively for calorimetry and dilatometry as shown in Fig.3.25. Chemical composition of
as-melted glasses was verified by ICP-OES with an accuracy of 0.1 mol.% or better
(Spectroflame Modula FTM 08, Spectro Analytical Instruments), revealing a systematic
absolute volatilization loss of SO3 of about 2.0-3.0 mol.%. The chemical composition of the
filled glasses in capillaries was detected by Energy Dispersive Spectrometer (EDS) (Table
3.8). Starting from the eutectic pyrophosphate and gradually (nominally) replacing P2O5 by
SO3, structural characterization was performed on the basis of density measurements (He
pycnometer Accu-Pyk 1330, Micromeritics, employing bulk glass samples of ~ 2 g), Raman
spectroscopy (Nicolet Almega XR, employing SiC/isopropanol polished glass disks of 10 mm
× 10 mm × 1 mm). For the employed sample mass, the accuracy of density measurements was
± 0.01 g/cm3. Following substitution of P2O5 by SO3, density increased from 3.13 to 3.22 ±
0.01 g/cm3, and molar volume was found to decrease from about 34.9 to 27.3 ± 0.1 cm3/mol
(Fig.3.26).
57
(a) 0.7
SP00
SP05
SP09
SP14
SP19
SP22
0.6
dL/L0 (%)
0.5
0.4
0.3
0.2
0.1
0.0
50
100
150
200
250
300
350
Temperature ( C)
o
Heat flow (mV/mg)
(b)
0.0 exo
SP09
SP14
SP19
SP22
-0.1
-0.2
-0.3
-0.4
-0.5
50
100
150 200 250 300
Temperature (oC)
350
400
Fig.3.25 Tg of SP glasses determined by (a) dilatometer and (b) DSC .
3.24
36
34
-3
32
3.16
30
V (cm3 mol-1)
(gcm )
3.20
28
3.12
0
5
10
15
26
20
SO42- (mol.%)
Fig.3.26 Density and molar volume of (Na, Zn) sulfophosphate glasses as a function of SO42- content [137].
© 2011 Published by Elsevier B.V
58
Table 3.8 Composition and glass forming ability of examined materials (mol.%) [137].
ZnO
Ref.
Na2O
#
ICP
EDX
(±0.1 mol%)
(capillary)
SO3
*
ICP
EDX
(±0.1 mol%)
(capillary)
P2O5
*
ICP
EDX
(±0.1 mol%)
(capillary)
nom. chem. chem.
sd¶
nom. chem. chem.
sd
nom.
SP00
43.0
42.78
27.7
13.3
21.0
20.04
36.8
8.6
0
0.2
SP05
42.2
44.27
38.8
1.5
19.8
19.40
26.1
1.2
5.1
SP09
42.2
43.5
34.7
2.9
19.8
20.5
30.2
2.7
SP14
42.2
43.9
34.3
1.0
19.8
20.6
31.6
SP19
42.2
44.1
37.1
0.2
19.8
20.1
24.4
SP22
42.2
43.9
19.8
19.7
EDX*
(±0.1 mol%)
(capillary)
sd
nom. chem. chem.
sd
0
0
38.0
37.18
35.5
4.7
3.98
3.7
0.5
32.9
32.35
31.3
0.5
9.1
6.4
6.7
0.8
28.9
29.6
28.3
0.8
1.3
14.1
10.8
9.8
0.1
23.9
24.7
24.2
0.3
3.4
19.1
15.9
17.3
0.7
18.9
19.9
21.3
0.9
22.1
18.8
15.9
17.7
# (4.0±2.0)% SiO2 in SP00 filled into capillary
* 1.0% - 2.0% SiO2 is found in glasses filled into capillaries.
¶sd is the standard deviation of EDX analysis.
59
chem. chem.
ICP
3.3.3 Structure of sulfophoshate glasses
Vibration bondings of the series of sulfophosphate glasses were detected with Raman
spectrometer (Fig.3.27). For the SO42--free polyphosphate glass, contributions from nine
individual vibrations can be detected after best-fit deconvolution of the experimental
spectrum into multiple Gaussian peak functions (600 - 1300 cm-1, Fig.3.28).
SP22
Intensity (a.u.)
SP19
SP14
SP09
SP05
SP00
-1
999cm
-1
Na2SO4, cryst.
634cm
-1
993cm
-1
618cm
400
600
800
ZnSO47H2O, cryst.
1000
1200
-1
Wavenumber (cm )
Fig.3.27 Raman spectra of (Na, Zn) sulfophosphate glasses for increasing SO42- content
(replacing P2O5 by SO3). Spectra of crystalline samples are shown for comparison,
taken from [137]. © 2011 Published by Elsevier B.V
Fig.3.28 Deconvoluted Raman spectrum of a (Na, Zn) polyphosphate glass,
taken from [137]. © 2011 Published by Elsevier B.V
60
These can be assigned to various P-O-related vibrations (Table 3.10 [140, 141]. Note that the
Q0-resonance at 790 cm-1 could not be resolved in the polyphosphate glass because only a
very small amount of Q0-species is present in this case, which is presented in detail as
follows).
Table 3.09 Assignment of experimentally observed Raman-active vibrations
in sulfophosphate glasses, taken from [137].
Frequency
Assignment
~ 702cm-1
(POP)sym stretch (bridging oxygen), Q2 species
~ 758cm-1
(POP)sym stretch (bridging oxygen), Q1 species
~ 910cm-1
(POP)asym stretch (bridging oxygen), Q2 species
~ 970cm-1
(PO4)sym stretch (non-bridging oxygen), Q0 species
~ 1010cm-1
P-O stretch, Q1 chain terminator
~ 1052cm-1
(PO3)sym stretch (non-bridging oxygen), Q1 species
~ 1138cm-1
P-O stretch, Q1 chain terminator
~ 1206cm-1
(PO2)sym stretch (non-bridging oxygen), Q2 species
~ 1252cm-1
(PO2)asym stretch (non-bridging oxygen), Q2 species
~ 614cm-1
(SO42-)asym bending
~ 997cm-1
(SO42-)sym stretch
When SO42- species are added, two new resonances appear at 614 and 997 cm-1 (Fig.3.27).
These can be assigned to asymmetric bending and symmetric stretching vibrations,
respectively, of the SO42- - group [140]. No S-O-P links can be detected. To confirm the
assignment of SO42--related vibrations, comparative data on crystalline Na2SO4 and
ZnSO4•7H2O (analytical grade) were added to Fig.3.26. In the sulfate-containing glass, the
relevant resonance energies appear to lie between those of the crystalline zinc and sodium
sulfate species. The degree of polymerization can hence be described by the relative quantity
of [POO3/2]0, [POO2/2O]–, [POO1/2O2]2 –, and [POO0/2O3]3 – groups, respectively, where x in
Ox/2 stands for the number of bridging oxygens ions and y in Oy for the number of nonbridging oxygens (NBO) in each tetrahedron. For simplicity, [POO3/2]0, [POO2/2O]–,
[POO1/2O2]2–, and [POO0/2O3]3– are denoted Qi (i = 3, 2, 1, 0), respectively, where ‘i’
represents the number of bridging oxygens per tetrahedron.
Raman spectroscopy clearly shows a transition in predominance from Q1 groups to Q0 groups
with an increasing amount of SO3. At the same time, no indication can be found in Raman
data that SO42--species contribute to network formation, or indeed link in any way to
61
phosphate groups. This indicates that SO42- groups are incorporated into the structure as
isolated ions. This assumption is confirmed by the observation of strongly decreasing molar
volume and increasing density with increasing amount of SO3. Then, the depolymerization of
the phosphate network can be calculated on the basis of subsequent pseudo-reactions [131],
starting from a completely polymerized fictive network of PO43- - tetrahedra and accounting
for compensation of cation charges by formation of NBO:
2 [POO3/2] 0+Na2O(ZnO) 2 [POO2/2O]– +2 Na+(Zn2+)
2 [POO2/2O] – + Na2O (ZnO) 2 [POO1/2O2]2 –+2 Na+( Zn2+)
2 [POO1/2O2] 2 –+ Na2O (ZnO) 2 [POO0/2O3]3 – +2 Na+( Zn2+)
In this calculation, eventual partitioning of 2Q1 → Q2 + Q0 is neglected. SO42- is treated as
completely ionic, requiring two cation charges which do not consequently contribute to
phosphate depolymerization. We conservatively assume an absolute error of 5 % for this
estimation. Derived data are shown in Table 3.10.
Table 3.10 Theoretical fraction of Qi tetrahedron of sulfophosphate glasses.
Glass types
Q2 (%)
Q1 (%)
SP00
31.6
68.4
SP05
27.1
72.9
SP09
17.0
83.0
Q0 (%)
SP14
99.6
0.4
SP19
73.0
27.0
SP22
49.1
51.9
Substitution of P2O5 by SO3 clearly results in further depolymerization of the pyrophosphate
network until a state is reached in which essentially only Q0 and Q1 species are present in the
glass, both of them in equal amounts. Accordingly, the glass must then be understood as
purely ionic, being built-up by an assembly of [SO4]2-, [POO1/2O2]2 –, [POO0/2O3]3 –, Na+ and
Zn2+.
3.3.4 Rheology of phosphate and sulfophosphate glasses
The micro-viscosities of the melts were obtained through the suction method. Surface tension
of sulfophosphate glasses was listed in Table 3.11 [96]. The EDS results demonstrated that
about 1.0% - 2.0% SiO2 diffused into the as-filled glasses in the capillary. Figures 3.29 shows
62
the cross section of the glasses in the capillary by SEM. In Fig.3.29(d), there is a big bubble,
which has been discussed above.
Table 3.11 Surface tension of sulfophosphate glasses cited from Sciglass, taken from [96].
Surface tension (N/m)
Temperature
(oC)
SP00
SP05
SP09
SP14
SP19
700
0.267
0.266
0.268
0.271
0.271
750
0.266
0.265
0.267
0.270
0.273
800
0.264
0.264
0.266
0.268
0.272
Fig.3.29 Cross sections of sulfophosphate glasses in capillaries (SEM pictures)
(a) SP05, (b) SP09, (c) SP14, and (d) SP22.
A complete viscosity-temperature diagram is shown in Fig.3.30(a). Fig.3.30(b) shows the
enlargement of viscosities of melts by the suction capillary filling method shown in
Fig.3.30(a). With increasing SO3 content, the steepness of the viscosity curve decreases;
glasses become longer. The kinetic glass transition temperature, T12, the temperature at which
the viscosity equals 1012 Pa·s, varies from 329 oC (SP09; S: P=0.11) to 310 oC (SP22;
S:P=0.54; note that high-temperature data on composition of SP22 could not be obtained
because of the occurrence of devitrification during sinking bar experiments; in other samples,
63
(b)
12
10
log ( in Pa·s)
5
SP00
SP05
SP09
SP14
SP19
SP22
8
6
Viscosity (Pa·s)
(a)
4
2
SP00
SP05
SP09
SP14
SP22
4
3
2
1
0
600
700
800
900
1000
0
1100
700
720
740
760
o
780
800
Temperature ( C)
Temperature (K)
Fig.3.30 Viscosity analysis of the phosphate and sulfophosphate glasses measured with (a) several
viscometers at different temperatures (via beam bending, sinking bar, suction method) and (b)
enlargement diagram of melt viscosities (via suction method).
no signs of devitrification could be detected by visual inspection). Similarly, the dilatometric
softening point T10.3 (maxima of the expansion curves, Fig.3.25(a)) decreases from 348 oC to
330 oC. Plotting viscosity versus the normalized temperature T12/T reveals decreasing kinetic
fragility for increasing SO3 content (Fig.3.31). Notably, while this occurs at the same time,
the relative amount of network formers drops from 44 at.% to 39 at.%. Using the VFT fit, the
steepness index m= d / d (T12 / T ) |T T12 was found to shift from 107 to 78 [136]. The viscosity
of liquid melts decreases from SP00 to SP19 corresponding to the increasing ionic
characteristic of sulfophosphate glasses.
log (in Pa·s)
12
8
SP00
SP05
SP09
SP14
SP19
4
0
-4
0.0
0.2
0.4
0.6
0.8
1.0
Tg/T (K/K)
Fig.3.31 Illustration of kinetic fragility, using the Angell plot.
64
Building on Brückner’s classical study [137], the investigation of viscosity as a function of
shear rate for sulfophosphate glasses was performed in microcapillaries, Fig. 3.32. In this
experiment, two kinds of capillaries with radius of 20 and 35 μm were employed, respectively.
In order to produce lower shear rates, the capillaries with radius of 20 μm were used. The data
in the red frames in Fig.3.32 were obtained from the capillaries with radius of 20 μm. Only
investigating the data obtained from the capillaries with a radius of 35 μm, a decrease of
viscosities to shear rate can be observed for SP00, which becomes much less obvious in SP09
and SP14. This non-Newtonian flow for SP00 can be explained by: (1) the interfacial reaction.
However, the interfacial reaction does not affect the flow behaviour of tellurite melts. Besides,
no silica-phosphate layer was observed in the as-filled capillaries, which will not influence
viscosities too much as discussed in tellurite glasses. Among the as-studied glasses, SP14 has
the highest proportion of modifier ions. Therefore, the diffusion of the modifier ions into the
silica capillary should be strongest, resulting in fewer modifier ions in the glasses. Fewer
modifier ions in phosphate glasses means that possible Q2 structural units may be formed for
SP14 in capillaries, which do not exist in bulk SP14 glass (Table 3.10). If so, the SP14 may
exhibit non-Newtonian flow. (2) Chain-like polyphosphates inducing the non-Newtonian flow.
Among these three kinds of glasses, SP00 and SP09 are polyphosphates. They have networks
based on Q2 chains (– P – O – P –) terminated by Q1 tetrahedra as discussed in section 3.3.3.
While the network structure of SP14 is dominated by phosphate dimers, two Q1 tetrahedra are
linked by a common bridging oxygen [131]. In SP00 melts, Q2 chains which are coiled and
entangled at low shear rate gradually become disentangled. This change in micro-structures
facilitates flow, leading to the decrease of the apparent viscosity with shear. With the breakage
of Q2 chains to Q1 in SP09 and SP14, the coiled and entangled chains gradually disappear and
only phosphate dimers exist in the melts. In our shear range, the external shear stress cannot
change the structure of SP14 melts, therefore, the apparent viscosity does not vary with shear
rate, which represents Newtonian flow behaviour. It is assumed that the shear thinning
behaviour may happen when shear stress is high enough to break the bridging oxygen,
decreasing the size of the fluid units.
65
2.2
5.0
Viscosity (Pa·s)
SP09
2.0
4.5
1.8
4.0
SP14
3.5
1.6
SP00
3.0
4
8
12
16
-1
Shear rate (s )
20
24
1.4
Fig. 3.32 The influence of shear stress on the apparent viscosity of sulfophosphate melts.
3.4 Germanate and sodium borate glass with suction method
Germanate glasses are well known for fabricating optical waveguides in the infrared region.
Similar to the tellurite glass, the germanate glass has a high refractive index, however, the
germanate glass is more stable than the tellurite glass. Various fibre lasers and amplifiers
were studied by doping rare earth ions and transition metals into germanate glasses because
they have a much lower melting temperature compared with silicate glasses [144, 145]. As for
borate glasses, the influence of micro confinement is interesting because of its potential effect
on the distribution of planar [BO3] and tetrahedral [BO4] units.
3.4.1 Introduction of germanate glasses
The dioxide of germanium, GeO2, forms glass consisting of a 3D framework with a
continuous random network of GeO4 tetrahedra linked by corner shared oxygens, somewhat
similar to the network former SiO2 as shown in Fig. 3.33. To satisfy the requirements of
optical applications, many modifier species have been added to pure GeO2 [145 - 153].
Especially Bi4Ge3O12 (so called “BGO”) crystals have received attention as a scintillator [154]
due to their high optical density and radiation hardness. The difficulty and high cost of
fabricating large single crystals have motivated the development of glassy systems. These
may exhibit properties similar to those of crystals with the advantages of lower cost and easier
fabrication. In the Bi2O3-GeO2 binary glass system, the composition ratio determines glass
transitions and crystallization temperatures. After heat treatment, two main crystalline phases
Bi4Ge3O12 and Bi2GeO5 were observed [155 - 156]. The infiltration technique provides a
route for post-processing such glasses into hybrid fibre form. The confinement in 2D may
66
either restrict the crystal growth, which is prone to grow along the axis of the capillaries, or
lower devitrification and phase separation of the glass system.
Fig. 3.33 Tetrahedra structure unit of GeO4.
3.4.2 Introduction of borate glasses
The structure of vitreous B2O3 has been studied with X-ray diffraction, which proved the
existence of planar [BO3] triangles [156]. The planar [BO3] units connect with each other and
form a boroxol group, a planar, six-membered ring of alternate boron and oxygen atoms, as
shown in Fig. 3.34(a). The vitreous B2O3 itself has poor chemical stability and a large
expansion coefficient, even though the bonding energy of B-O is a little larger than that of SiO. The reason may be due to its particular structure. The layer structure of vitreous B2O3 is
formed by connections between boroxol groups and planar [BO3] units through bridging
oxygens. At high temperature, the layers disconnect and break to transform to a chain
structure, shown in Fig. 3.34(b) and(c). The layers or chains are linked to each other by the
weak Van der Waal’ s forces. A coordination change of boron from three to four occurs with
the addition of alkali oxides. The oxygen atoms provided by alkali ions behave as bridging
oxygen instead of the non-bridging role which they have in silicate glasses. The addition of
bridging oxygens then transforms the layer structure of vitreous B2O3 into a framework
structure. This is known as boron anomaly. However, the bridging oxygens no longer appear
in the structure when the amount of alkali oxide reaches a certain value. The excess oxgyen
ions will then be non-bridging, which again depolymerizes the framework of borate glasses
and makes them behave as usual silicate glasses above a certain threshold value of modifier
species.
67
Fig.3.34 Boroxol group (a), layer structure of vitreous B2O3 (b),
and chain structure of B2O3 (c) at high temperature.
3.4.3 Experiments and discussion
Germanate glasses with nominal compositions of 60GeO2-5WO3-35Bi2O3 (mol.%) (Ge.01)
and borate glass 75B2O3-25Na2O (mol.%) (Bo.01) were prepared by conventional melting
and quenching. Reagent grade powders of GeO2, WO3, Bi2O3, HBO3, and Na2CO3 were
weighed, and mixed. Ge.01 was melted in an alumina crucible at 1100oC for 30 min and
Bo.01 was melted in a Pt crucible at 900 oC for 60 min. To improve the homogeneity of the
glasses, the melts were stirred manually with an alumina rod for ~ 1 min. 2 g of each glass
were put into platinum crucible for the suction viscometer. Capillaries with inner radius of 22
μm and 35 μm for Ge.01, and 35 μm for Bo.01 were employed, respectively. Surface tensions
of both glasses were taken from SciGlass (Table 3.12)[96].
Figures 3.35 present the apparent viscosities of Ge.01 and Bo.01. It can be seen that glass
corrosion has a non-negligible effect on the viscosity of Ge.01. As the temperature increases,
an inflection point appears at 1100 oC. The end of the capillary dipping into the melt was
strongly corroded after this process as shown in the inset figure of Fig.3.35(a) by optical
microscopy. The problem becomes much more serious as the temperature increases. Good
accordance with literature data was obtained only up to a maximum filling temperature of
about 1150 °C.
Table 3.12 Surface tension of germanate and borate glasses cited from [96].
Surface tension (N/m)
Glass
types
800°C
850°C
900°C
950°C
Bo.01
0.156
0.155
0.154
0.154
0.153
0.152
Ge.01
0.244
0.243
0.242
0.241
0.239
0.238
68
1000°C 1050°C 1100°C
0.237
(a) -0.4
log in Pa·
s)
60GeO2-5WO3-35Bi2O3
-0.5
-0.6
-0.7
-0.8
1250
1300
1350
1400
1450
1500
Temperature (K)
(b) 1.5
log in Pa·s)
1.0
0.5
0.0
-0.5
-1.0
Li
Leedecke
Matusita
Sasek
Frumin
Our work
1080
1140
1200
1260
1320
Temperature (K)
Fig.3.35 (a) Viscosity of Ge.01 at respective temperatures. Inset figure: microscope figures of one end of
capillary dipping in crucible, which shows the evidence of deviation from the real viscosity of Ge.01 (top:
22 μm capillary at 1050 °C, bottom: 35 μm capillary at 1100 °C after filling), (b) Comparison of viscosities
of Bo.01 proposed by different researchers.
EDX was performed on the cross section of glasses in capillaries with different radius
(Fig.3.36). The results in Fig. 3.37 show that a very high concentration of SiO2 is present in
the germanate core glass when the radius of the capillary is ≤ 35 μm. It can be seen that in a
capillary with radius of 10 μm, the glass inside the capillary exhibits a Ge/Si molar ratio of
100/80. When a larger capillary is used, e.g. 75 μm, the concentration of SiO2 in germanate
glass becomes much less because of the much reduced filling time and the much higher
quantity of germanate glass inside the capillary. Raman spectra provide a confirmation of the
significant dissolution of SiO2 (Fig. 3.38).
69
Fig.3.36 SEM of germanate glasses in different capillaries with radius
(a) 4, (b) 10, (c) 20, (d) 35, and (e) 75 μm.
Composition concentration
1.0
4m
10m
22m
35m
75m
0.8
0.6
0.4
0.2
0.0
GeO2
WO3
Bi2O3
SiO2
Glass compositions
Fig.3.37 EDX results of composition concentration of Ge.01 in capillaries
and diffusion or corrosion of SiO2 in the glass.
70
Intensity (a.u.)
Glass
22m
35m
200
400
600
800
1000
1200
-1
Raman frequency (cm )
Fig.3.38 Raman spectrum of Ge.01 in capillaries and bulk Ge.01.
Viscosities of Bo.01 were presented and compared to available data (Fig.3.35(b)) [157].
Leedecke and Sasek measured the temperature at viscosity from 101 to 104 Pa·s with
rotational viscometers, as shown in Fig. 3.39. It is found that the same viscosity corresponds
to different temperatures. Meanwhile the difference between the two temperatures increases
with increasing temperature. The distinct results may be caused by the gradually rising
temperature of the sample after the measurement starts [158].
4.0
Leedecke
Sasek
log in Pa·s)
3.5
3.0
2.5
2.0
1.5
1.0
900
1000
1100
1200
1300
Temperature (K)
Fig.3.39 Viscosities of Bo.01 measured by Leedecke and Sasek, respectively.
With regard to our results, the viscosities are higher than the other data. This can be explained
through investigating the phase diagram of Na2O-B2O3-SiO2 (Fig. 3. 40). The red arrow in Fig.
3.40 represents the composition x(25Na2O-75B2O3)-(100-x)SiO2. The liquid temperatures are
from 700 to 1000 oC, when the molar amount of SiO2 is from 0 to 70%. The interfacial
71
reaction between Bo.01 melt and silica capillary, or the corrosion of capillary by Bo.01
happens when the infiltration measurement starts. This corrosion or interfacial reaction
becomes strong when the infiltration temperature increases. So the difference between our
results and others grows larger with the increase of infiltration temperature.
Fig.3.40 Phase diagram of Na2O-B2O3-SiO2 ternary system, The red arrow represents the composition
x(25Na2O-75B2O3)-(100-x)SiO2, taken from [159]. © 1993 Published by John Wiley & Sons
3.5 Conclusions
The apparent viscosities of various melts were obtained with the infiltration technique. Flow
behaviour of several glass melts was investigated as well. For mild corrosion glass melts,
tellurites and sulfophosphates, Newtonian as well as non-Newtonian flow was observed. The
strong corrosion for germanate and borate melts on silica prevents study of their flow
behaviour at high temperature. With regard to the extent of the effect of the interfacial
reaction between melts and silica, the detail needs to be studied.
Interfacial reactions between silica glass and tellurite melts were studied under confined
conditions. Isothermal heat-treatment was performed on tellurite film, confined in a
silica/tellurite/silica – sandwich. For temperatures > 500 °C, the reaction process between the
two compounds can be described as follows: Silica is completely wet by the considered
tellurite melts. Tellurite melts attack the silica substrate, leading to gradual dissolution of
silica. Ahead of the reaction front, cationic diffusion of Na+ and Te4+ into the silica substrate
72
occurs to a depth of several µm per hour. At 700 °C, the thickness of the stationary silicatellurite reaction layer is about 2 µm. In a capillary filling experiment, this leads to an
apparent deviation of the filling dynamics from Lucas-Washburn behaviour. Dissolved silica
was observed to re-precipitate from the tellurite melt by liquid-liquid phase separation. When
an alkali-containing tellurite glass is used as the reaction medium at 700 °C, in the early
reaction stages, as a result of alkali diffusion into the silica substrate, β-quartz crystallizes at
the silica-tellurite interface. With respect to fabrication of microstructured silica-tellurite
optical waveguides, TZL was preferred over TZN for two reasons: interfacial crystallization is
largely avoided by the absence of alkali species and, as demonstrated here, the glass exhibits a
lower viscosity and can thus penetrate the silica matrix at significantly lower temperature.
Raman spectra of TZN and TZL were resolved and analyzed. A significant peak variation was
found on intensity and position comparing TZN01 in capillary to bulk glass. The results of
TZN01 and TZL glasses suggest that the interfacial reaction or ion exchange has a
predominant influence on the structural change of some glasses in capillary.
73
4. Viscosity of chalcogenide glasses
Chapter 4 discussed the interfacial reaction between the filled melts and silica capillary, and
its impacts on viscosities of melts. In order to avoid interfacial reactions between the filling
materials and the silica wall, chalcogenide glasses are selected and investigated. Indeed, it is
well-known that some chalcogenide glasses are perfectly non-wetting on silica. Any apparent
viscosity deviation from real viscosity due to interfacial layers will therefore be excluded.
4.1 Introduction of chalcogenide glasses
Chalcogenide glasses have been extensively studied due to their advantages in the far infrared
(IR) transmission range, and semiconductor properties. They contain one or more of the
chalcogen elements sulphur (S), selenium (Se) or tellurium (Te), in conjunction with other
electropositive elements such as As, Ge, P, Sb, Bi, Si, Sn, Pb, B, AI, Ga, In, T1, Ag,
lanthanides,and Na [160]. In simple S, Se and Te melts, rings and chains are the basic
structural morphology. The vitrification of chalcogen compounds is realized through the
bridging ability of chalcogen elements. Heteropolar links, such as in Ge-S, As-S bonds can
form when other elements are added to simple S melts. Therefore, chalcogenide glasses can
contain elements from groups IVA (Si, Ge, Sn) and VA (P, As, Sb, Bi), which are not limited
to the chalcogen elements [60]. The molecular formula of elemental sulphur is S8, which has a
ring structure. Each S atom has a sp3 bonding state, resulting in two covalent bonds. The ring
structure of S molecules will open and form a chain-like structure when S is heated. Vitreous
S can be prepared after quenching in cold water. The chain lengths can exceed 106 atoms. Se
and Te contain shorter chains [6, 60]. Addition of elements such as Ge and As can result in a
highly cross linked structure [6, 60, 135]. Stable glass compositions As2S3 and As2Se3 are the
most important systems [135]. However, chalcogenide glasses typically exhibit also a high
thermal expansion coefficient and low chemical and mechanical stability [8]. Recently, N.
Granzow et al. fabricated a chalcogenide-silica waveguide for supper-continuum generation
employing the high nonlinear properties of chalcogenide glasses and using the infiltration
technique described in this study [24].
4.2 Experiments and discussion
Chalcogenide glasses were provided from J. Troles (University of Rennes 1, Rennes, France).
The glass compositions and melting temperatures are listed in Table 4.1. Laboratory glass
74
transition temperatures Tg of the samples were determined by calorimetry (calorimetric Tg,
Netzsch DSC 404 F1, heating rate: 20K/min).
Table 4.1 Glass compositions selected for viscosity determination.
glass compositions
(in mol.%)
Tg(°C)
Tm(°C)
Ch.01
Ga4Ge21Sb10S65
315.0
-
Ch.02
Ge3As52S45
39.0
-
Ch.03
As40S60
176.6
-
Filling experiments were conducted in silica capillaries with inner radius R of 2.0, 4.0, 10.0,
and 22.0, 35.0, 70.0 μm (outer diameter: 200.0 µm). The experimental setups used for the
filling procedure are those employed previously for the production of all-solid PCFs,
including the pressure and suction methods [22, 24]. The pressure method, with external body
force (from 10.0 to 60.0 bar), was employed to acquire the viscosity of chalcogenide glasses
[22, 24]. Viscosities of a series of chalcogenide melts were acquired with the pressure method
(Figs.4.1).
(a) 1.5
O
630 C
log in Pa·s)
1.2
O
680 C
0.9
0.6
O
730 C
0.3
0.0
10
20
30
40
Pressure (bar)
75
50
60
(b)
0.6
T=
o
250 C
o
300 C
Viscosity(Pa·s)
0.5
0.4
0.3
0.2
0.1
0.0
10
20
30
40
50
60
Pressure (bar)
(c) 7
6
12
Viscosity(Pa·s)
5
o
500 C
4
10
3
o
650 C
2
8
1
0
-1
10
15
20
30
6
Pressure (bar)
Fig.4.1 Viscosities of Ch.01(a), Ch.02(b), and Ch.03 (c) corresponding to external applied pressure.
An obvious viscosity pressure dependence of Ch.02, and Ch.03 above a certain temperature
has been observed, which will be discussed in section 4.3. As already noted, in past decades,
VFT (Eq.(4.2.1)) and AM (Eq.(4.2.2)) models have been extensively applied to interpolate
viscosity results with sufficient accuracy within a certain temperature range, even though,
systematic errors and physically non-realistic values exist in these two models,
log( / Pa s) A
B
T T0
(4.2.1)
log( / Pa s) C ( ) x
T
(4.2.2)
76
where A, B, T0, and C, , x are fitting parameters for VFT and AM models, respectively. As
the glass transition occurs when the viscosity is about 1012 Pa·s, and the fragility index m is
defined as m
log
|T Tg , the MYEGA equation can also be used for viscosity interpolation
Tg / T
[47],
log log (12 log )
Tg
Tg
m
exp[(
1)( 1)]
T
12 log
T
(4.2.3)
where log η∞ and m are first taken from the fitting data. Fig.4.2 shows the fitting curves
corresponding to these three models for the viscosity of Ch.03. The curves in Fig.4.2(a) are
calculated by fitting the combined viscosity of macroscopic and microscopic viscosity, the
latter being obtained from the infiltration technique. Macroscopic data are obtained from A. S.
Tverjanovich [164]. Viscosity log η∞ tends to be extremely low when microscopic viscosity is
not taken into account (Fig.4.2(b)), because the microscopic viscosity constrains the
divergence of fitting curves. Note that all of these three models present a good fitting in the
low temperature range, when considering only macroscopic viscosity, but split at high
temperatures. Viscosity log η∞ at infinite temperature and fragility index m is listed in Table
4.2.
Table 4.2 Extrapolating log η∞ and fragility m of Ch.03 from the three viscosity-temperature models.
log η∞
model
Fragility m
Fig.4.1(a)
Fig.4.1(b)
Fig.4.1(a)
Fig.4.1(b)
VFT
-5.4
-11.6
41.2
35.9
AM
-2.2
-7.1
39.1
35.7
MYEGA
-3.85
-10. 4
40.0
35.8
According to the Maxwell equation [165], η∞ can be deduced from G , where is
atomic vibration and G is shear modulus of glass at infinite frequency [165]. G v 2p is
less than 6.5 GPa for Ch.03, where ρ is the density and v p is the velocity of shear acoustic
waves at infinite frequency [164, 165]. Note that the ρ and v p employed for calculation, are
estimated at glass transition, and will be less at high temperature. is between 10-12 and 1014
s. log η∞ will be lower than -2.2. With current microscopic viscosities, log η∞ derived from
all models coincides with the Maxwell equation, while many other glasses derived from the
AM model present higher logη∞ [166]. We note that no dependence of viscosity on radius was
77
observed with two capillary dimensions (radii of 10.0 μm and 22.0 μm) for acquiring the
microscopic viscosity data.
Note that viscosity of Ch.03 at 500 °C is 11.6 Pa·s with a
standard deviation of 0.5 Pa·s, which is 10 Pa·s in [167]. Therefore, it is possible to regard the
microscopic viscosity as bulk viscosity and integrate with macroscopic data for model fitting.
(a) 12
log in Pa·s)
8
VFT model
MYEGA model
AM model
experimental viscosity
4
0
-4
0.0
0.2
0.4
0.6
0.8
1.0
0.8
1.0
Tg/T (K/K)
(b) 12
log in Pa·s)
8
4
VFT model
MYEGA model
AM model
macroscopic viscosity
microscopic viscosity
0
-4
-8
-12
0.0
0.2
0.4
0.6
Tg/T (K/K)
Fig.4.2 Fitting curves of Ch.03 with VFT, MYEGA, and AM models. Fitting with macroscopic and
microscopic viscositiy (a) and with only macroscopic viscosity (b). Microscopic viscosity in (b) shows the
discrepancy with the fitting curves.
4.3 Non-Newtonian Flow
In section 4.2, the viscosities of three kinds of chalcogenide glasses in molten state have been
discussed. It can be seen that viscosities of Ga4Ge21Sb10S65 keep a constant value at a
temperature when the externally applied pressure is in the range of 10.0 to 60.0 bar, which
indicates Newtonian flow. However, a pressure dependence of viscosity was detected for
78
Ge3As52S45 and As40S60 samples (Table 4.1 and Fig.4.2). The apparent viscosities of
Ge3As52S45 decrease by about a factor of two and three at 250 and 300 °C, respectively, when
the pressure increases from 10 to 30 bar. Figures 4.3 and 4.4 show the square of the filling
length as a function of the square of capillary radius corresponding to different applied
pressure for Ge3As52S45 at 250 °C (Fig.4.3(a)) and 300°C (Fig.4.3(b)), and As40S60 from 550
(a)
o
250 C
60bar
1200
800
50bar
30bar
2
2
L (cm )
40bar
400
20bar
10bar
0
0.0
0.4
0.8
2
6
1.2
1.6
2
PR t (10 bar·m ·s)
(b) 400
o
300 C
30bar
2
L (cm )
300
2
200
20bar
100
0
0.00
10bar
0.02
0.04
2
0.06
6
0.08
0.10
2
PR t (10 bar·
m ·
s)
Fig.4.3 The square of the filling length as a function of the square of capillary radius corresponding to
different applied pressure for Ge3As52S45 at 250 °C(a) and 300 °C(b). The slopes of the lines are
proportional to 1/η of the glass, indicating the pressure dependence of viscosity.
to 650 °C, respectively. The slopes of the lines are proportional to 1/η of the glass. It is
obvious that the viscosity of the glass varies under different applied pressures for Ge3As52S45
at 250 °C and 300 °C, respectively, which means a non-Newtonian flow of Ge3As52S45 melt
appears at temperature above 250 °C at least. On the other hand the pressure dependence of
viscosity occurs in As40S60 when the temperature is above 600 °C.
79
(a)
700
o
600 C
600
2
400
2
L (cm )
500
300
o
550 C
o
650 C
200
o
500 C
100
0
0
1
2
3
4
6
2
PR t (10 bar·m ·
s)
2
5
6
(b) 90
o
650 C
80
30bar
70
2
2
L (cm )
60
50
20bar
40
30
10bar
20
10
0.00
0.02
0.04
0.06
0.08
0.10
PR t (10 bar·
m ·
s)
2
6
2
Fig.4.4 The square of the filling length as a function of the square of capillary radius for different applied
pressure for As40S60 at 600 °C(a) and 650 °C(b). The slopes of the lines are proportional to 1/η of the glass,
indicating the pressure dependence of viscosity.
Two possibilities could be responsible for the pressure dependence of viscosity: (1) Shear
thinning, i.e. a negative dependence of viscosity on directional stresses and deformation rate.
A viscosity to shear rate diagram can be figured to demonstrate the flow behaviour of liquids.
Figure 4.5 shows the viscosities of As40S60 and Ge3As52S45 corresponding to the shear rate. At
500 and 550 oC, no shear thinning phenomena can be found. It is possible that the shear rate is
not high enough to initiate a shear thinning. In another words, shear stress cannot rearrange
the structure of As40S60 in this condition. However, a shear thinning becomes obvious when
the shear rate is higher than 100 s-1.
80
3.5
14
o
500 C
o
550 C
o
600 C
o
650 C
2.5
13
12
2.0
1.5
11
1.0
Viscosity (Pa·s)
Viscosity (Pa·
s)
3.0
10
0.5
0.0
0
100
200
300
400
9
500
Shear rate (s )
-1
Fig.4.5 Viscosities of As40S60 corresponding to the shear rate of melts
in capillaries at respective temperatures.
(2) Turbulent flow of the liquid. The Reynolds number Re
2 vR
2 PRt
is frequently
l
used to characterize and differentiate laminar and turbulent flow, where R is the radius of the
capillary, Δt, Δl are time of the moment that the applied pressure acts on the liquid melt and
the glass length in the capillary before applying pressure, and ρ and η are the density and
viscosity of the liquid, respectively. If Re was less than 2300, the flow would be laminar.
Turbulent flow occurs when Re > 4000. In the interval between 2300 and 4000, laminar and
turbulent flows are both possible. Considering the pressure and capillary dimension in our
case, Re is calculated in Table 4.1. Re would be less than 2300, the value defined as the upper
boundary for laminar flow in a pipe of radius R, for the Ge3As52S45 and As40S60 samples at
temperatures of 250 - 300 and 600 - 650 °C, respectively (Table 4.1), assuming Δt = 0.01 and
Δl = 5.0 mm. It can be seen that Re is less than 2300 for As40S60, which implies that the
turbulent flow would not happen. Therefore, shear thinning is responsible for the pressure
dependence of viscosity of As40S60 glass, given that the applied pressure is lower than 30.0 bar.
For Ge3As52S45, if Δt = 0.01 s, Re is less than 2300 as well and laminar flow dominates,
namely, shear thinning causes the pressure dependence of viscosity.
To understand the mechanics of non-Newtonian flow, several physical equations were
proposed and discussed several decades ago. Based on configurational entropy theory,
Bottinga developed a model explaining the shear thinning effect [168, 169]. As mentioned in
Chapter 1, rheology on polymer materials has been surveyed extensively. From the molecular
81
Table 4.1 Viscosities and Re number of Ch.02 and Ch.03 under various
externally applied pressures for two temperatures, respectively.
Ge3As52S45
Temp. (250°C)
As40S60
Temp. (300°C)
Temp. (600°C)
Vis.
(Pa·s)
Re
Δt (s) =
0.01
Vis.
(Pa·s)
Re
Δt (s) =
0.01
10
0.60
66.9
0.20
59.3
1.66
24.0
0.68
23.4
20
0.38
211.0
0.13
182.3
1.08
74.0
0.28
111.9
30
0.32
377.0
0.06
587.3
0.83
143.5
0.25
188.0
40
0.31
510.0
0.11
50
0.38
523.0
60
0.32
760.5
Press.
(bar)
Vis.
(Pa·s)
Re
Δt (s) =
0.01
Temp. (650°C)
Vis.
(Pa·s)
Re
Δt (s) =
0.01
0.83
theory, Grasseley proposed an entanglement principle to describe the shear thinning effect of
polymers [27]. Yue and Brückner derived one set of phenomenological equations, which
presents a good fit of experiment results with regard to non-Newtonian flow. Viscosities vary
with the shear rate of liquids as follows [170],
(0 ) exp( / g )
(4.3.1)
where η0 is the Newtonian viscosity, η∞ is the ultimate Binghamian viscosity at → ∞, g is the
flow relaxation rate [170]. Viscosities of As40S60 at 600 and 650 oC are fitted with Eq. (4.3.1)
as shown in Fig. 4.6. A best fit can be obtained. These three parameters (η0, η∞, g ) for 600
and 650 oC are (2.75, 0.35, 187.84) and (1.23, 0.25, 91.11), respectively.
It is known that rings and chains are the basic structural element that interacts to form a
vitreous structure (Fig. 4.7(a)). The entangled structural units of the melts were stretched to
oriented chains under shear, which facilitates the flow of melts (Fig. 4.7(b)). Therefore, the
apparent viscosity decreases under shear. The resistance of the structural units to realignment
is high at low temperatures, which explains why the shear thinning happens easily above a
certain temperature. It can be deduced that the melts with rings and chains as basic structural
units will show non-Newtonian flow as long as shear stress reaches a certain value.
82
3.0
o
600 C
o
650 C
Viscosity (Pa·s)
2.5
2.0
1.5
1.0
0.5
0.0
0
100
200
300
400
500
Shear rate ( s )
-1
Fig.4.6 Fitting curves of viscosity to shear rate by Yue-Brückner equation for As40S60.
Fig. 4.7 Structure of As2S3 (a) and stretching (b) under shear stress.
4.4 Conclusions
The presented infiltration technique has been applied to chalcogenide melts. The absence of
corrosion and interfacial reaction of the chalcogenide melts with the silica capillary promotes
a reliable viscosity determination at high temperature. Furthermore, the absence of capillary
dimension dependence of the as-obtained viscosity indicates that the microscopic viscosity
can be regarded as bulk viscosity, which means that the infiltration technique can be
employed as a reliable method to determine the melt viscosity of glasses. Viscositytemperature models VFT, AM, and MYEGA have been used to fit complete viscosity data.
The high log η∞ of chalcogenide glass indicates either the incompleteness of the employed
fitting model or illustrates that viscosities at high temperature are required for realistic fitting.
An apparent viscosity dependent on shear rate was observed in chalcogenide glasses. As there
is no interfacial reaction between chalcogenide glass and silica, this dependence can be
83
regarded as a result of shear thinning. The structural disentanglement and orientation of
chalcogenide melts are responsible for the viscosity decrease under shear. Yue and Brückner’s
equation was used to describe the extrapolated shear thinning behaviour of As40S60 melts.
84
5. Outlook: Fabrication of hybrid-all-solid PCF
and their optical application
In a collaboration with colleagues at the Max Planck Institute for the Science of Light,
Erlangen, the presented infiltration technique was employed to prepare all-solid PCFs where a
silica matrix fibre is infiltrated with a low-melting glass.
As examples, silica solid core PCFs with a hexagonal array of holes (diameter of 1.6 µm,
spacing between holes 3.7 µm) are depicted, filled with tellurite (Fig. 5.1(a)) and
chalcogenide (Fig. 5.1(b)) glass. The optical properties and applications of such devices are
numerous. Corresponding studies are ongoing [22 - 24, 171, 172].
Fig. 5.1 SEM images of endlessly single mode silica fibres which have been filled with low-melting glasses
(hole diameters: 1.6 µm, center distances of neighboring holes: 3.7 µm). (a) Filling glass: tellurite. (b)
Filling glass: chalcogenide, taken from [8]. © 2011 Published by Elsevier B.V
85
6. Conclusions and outlook
6.1 Thesis conclusion
This thesis introduced the infiltration technique for investigating the rheology of various glass
melts in micro capillaries. The confinement effect of capillaris and interfacial effects between
filled melts and capillaries were considered. Viscosities of commercial honey and silicon oil
were studied and compared with conventional rotation viscometers in order to initially judge
the infiltration technique. Over a wide range of shear rates, the apparent micro-viscosities
obtained from the infiltration technique are consistent with the macro-viscosities of bulk
liquids, demonstrating the feasibility of the infiltration technique for measuring the viscosities
of melts which do not interact with the capillary. On that basis, the viscosities of various melts
were measured and discussed using VFT, MYEGA and AM models. Tellurite and
sulfophosphate melts that exhibit pronounced interfacial reactions with silica capillaries are
also studied. It was found that non-Newtonian flow can be observed in sulfophosphate melts.
The chain entanglement is responsible for the shear thinning. Tellurite melts with 3D structure
units and pyrophosphate melts show Newtonian flow under the investigated shear rate range.
At temperatures above about 1100 °C, a strong corrosion effect (shown for germanate and
borate melts) prevents application of the capillary viscometer. Non-Newtonian flow was also
observed in chalcogenide melts. This can be explained by the disentanglement or orientation
of the chain-like structural units under shear. The infiltration technique provides a route for
fabricating all-solid glass-glass PCFs. This kind of PCFs can take advantage of the properties
of the filled glasses that silica does not possess.
6.2 Prospect
The infiltration technique offers a method of correlating the rheology of melts with the
structure of glasses in confinement. This correlation will enable us to know the origin of
glasses better. With these results, all-solid glass-glass PCFs could be fabricated. Furthermore,
the structure of glasses could be modified in PCFs to improve the performance of the fibres.
For example, the structure of chalcogenide melts could be modified under the shear rate. The
structure under a certain shear rate could be maintained under fast cooling. Consequently, the
properties of chalcogenide glasses can change. In addition, the crystallization of melts in
micro-confinement is also an interesting aspect.
86
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List of publications/Veröffentlichungen
1, S. Striepe, N. Da, J. Deubener, Lothar Wondraczek. Micromechanical properties of
(Na,Zn)- sulfophosphate glasses, J. Non-Cryst. Solids 358(2012)1032-1037.
2, N. Da, O. Grassmé, K.H.Nielsen, G.Peters, L.Wondraczek. Formation and structure of
ionic (Na, Zn) sulfophosphate glasses, J.Non-Cryst. Solids, 357(2011)2202-2206.
3, N. Da, A. A. Enany, N. Granzow, M. A. Schmidt, P. St. J. Russell, L. Wondraczek.
Interfacial reactions between tellurite melts and silica during the production of
microstructured optical devices, J. Non-Crystal. Solids, 357(2011)1558-1563.
4, M. A. Schmidt, L. Wondraczek, H. W. Lee, N. Granzow, N. Da, P. St. J. Russell. Complex
Faraday rotation in microstructured magnetooptical fibre waveguides, Adv. Mat., 23(2011)
2681-2688.
5, S. Reibstens, N. Da, J.- P. Simon, E, Spiecker, L. Wondraczek. Phase separation and
crystal precipitation in supercooled sulphophosphate ionic melts, Phys. Chem. Glass 53(2012)
61-67
6, Q. Yan, Y. Liu, G. Chen, N. Da, L. Wondraczek. Photoluminescence of Mn2+ centers in
chalcohalide glasses, J. Am. Ceram. Soc., 94(2011)660 - 662.
7, W. Wang, Q. Yan, J. Ren, G. Chen, N. Da, L. Wondraczek. Ultrabroad near-infrared
photoluminescence from Bi/Dy/Tm co-doped chalcohalide glasses, Phys. Chem. Glasses: Eur.
J. Glass Sci. Technol. B 52(2011)221 - 224.
8, N. Da, L. Wondraczek, M. A. Schmidt P. St. J. Russell. High index-contrast all-solid
photonic crystal fibres by pressure-assisted melt infiltration of silica matrices, J. Non-Crystal.
Solids 356(2010)1829-1836.
9, N. Da, S. Krolikowski, L. Wondraczek. Viscosity and softening behaviour of alkali zinc
sulfophosphate glasses, J. Am. Ceram. Soc. 93(2010)2171-2174.
10, N. Da, M. Peng, S. Krolikowski, L. Wondraczek. Intense red photoluminescence from
Mn2+-doped (Na+;Zn2+) sulfophosphate glasses and glass ceramics as LED converters, Optics
Express 18(2010)2549-2557.
101
11, G. Gao, N. Da, S. Reibstein, L. Wondraczek. Enhanced photoluminescence from mixedvalence Eu-doped nanocrystalline silicate glass ceramics, Optics Express 18(2010)A575A583.
12, M. Peng, N. Da, L. Wondraczek. Luminescence from Bi2+-activated alkali earth
borophosphates for white LEDs, Optics Express 17(2010)21169-21178.
13, M. A. Schmidt, N. Granzow, N. Da, L. Wondraczek, P.St. J. Russell. All-solid bandgap
guiding in tellurite-filledsilica photonic crystal fibres, Optics Letters 34(2010)1946~1948.
102
