Thermal Analysis
1.
Introduction
Thermal Analysis is the term applied to a group of
methods and techniques in which chemical or
physical properties of a substance, a mixture of
substances or a reaction mixture are measured as
function of temperature or time, while the substances
are subjected to a controlled temperature programme.
References:
* Introdcution to Thermal Analysis, M.E. Brown -- Chapman
and Hall
* Thermal Analysis - Techniques and Applications, ed. E.L.
Charsley and S.B. Warrington -- Royal Society of Chemistry
* Thermal Analysis of Materials, Robert F. Speyer –Marcel
Dekker, Inc.
The following table is a list of the main thermal
analysis methods:
While carrying out these measurements, the
furnace atmosphere can either be static air or a
continuous flow of gas (purging). Examples are
inert conditions (nitrogen) to inhibit oxidation, or
reducing condition (e.g. purging hydrogen), etc.
General thermodynamic relationships
Thermal analyses are usually run under conditions of constant pressure, the
underlying thermodynamic equation is the Gibbs-Helmholtz expression:
G0=H0-TS0
where G=free energy of the system, H=enthalpy of the system, S=entropy
of the system, T=temperature in kelvins
The general chemical reaction
aA+bBcC+dD
Is spontaneous as written if G<0, is at equilibrium if G=0, and does
not proceed if G >0.
Thermal analysis involves the monitoring of spontaneous reaction.
Differentiating the Gibbs-Helmholtz equation with respect to
temperature (assuming S and H not vary with temperature):
d ( G )
  S
dT
Show how to move from a stable situation (G>>0) to one
where reaction will occur.
S>0, an increase in temperature cause G<0,
S<0, decreasing the temperature will achieve the desired
spontaneous reaction.
Once the reaction is made to occur, thermal analysis may be used
to detect the process, yielding different and complementary
information.
2.
Thermogravimetry
•Thermogravimetric analysis (TG) is the study of weight changes
of a specimen as a function of temperature. The technique is
useful strictly for transformations involving the absorption or
evolution of gases from a specimen consisting of a condensed
phase.
•A plot of mass versus temperature (thermogravimetric curves or
TG curves) permits evaluation of thermal stabilities, rate of
reaction, reaction processes, and sample composition.
* Measurements of changes in sample mass with temperature are
made using thermobalance. The balance should be in a suitably
enclosed system so that the atmosphere can be controlled.
General considerations
Suitable samples for TG are solids that undergo one of the two
general types of reaction:
Reactant(s)  Product(s)+Gas
Gas+Reactant(s)  Product(s)
(a mass loss)
(a mass gain)
Processes occuring without change in mass (e.g., the melting of a
sample) obviously cannot be studied by TG.
2.1
Instrumentation
LINSEIS L81
Thermogravimetric instrumentation should include several basic
components to provide the flexibility necessary for the
production of useful analytical data:
a) A balance,
b) A heating device,
c) A unit for temperature measurement and control,
d) A means for automatically recording the mass and
temperature changes,
e) A system to control the atmosphere around the sample.
2.1.1 The Thermobalance
Two typical designs of the thermobalance are shown in the following:
Balances must remain precise and accurate continuously
under extreme temperature and atmosphere conditions, and
should deliver a signal suitable for continuous recording.
* Null-deflection weighing mechanisms are favoured in TG as
they ensure that the sample remains in the same zone of the
furnace irrespective of changes in mass.
* Sensitivity of balance  1g for a 1g maximum load balance.
* The output weight signal may be differentiated electronically
to give a derivative thermogravimetric curve (DTG)
2.1.2
The Heating Chamber
The furnace is normally an electrical resistive heater;
Some basic requirements of the heating chamber are :
be non-inductively wound
be capable of reaching 100 to 200°C above the maximum desired working
temperature
have a uniform hot-zone of reasonable length
reach the required starting temperature as quickly as possible
not affect the balance mechanism through radiation or convection
In order to overcome the problem of possible temperature gradient, infrared
or microwave radiation have been used in some equipment.
infrared heating : use halogen lamp, temperature up to 1400°C, heating rate
can be as high as 1000°C/min, accuracy is about ±0.5°C.
Microwave heating : large sample can be used because uniform heating
generated within sample but temperature measurement and power control are
difficult.
Constant heating rate
Constant heating rate: lag behind of the sample temperature
During heating a temperature difference
between the furnace and the sample
temperature appears which means that
the sample temperature lags always
behind the furnace temperature.
Measurement of the melting point
of Di-tert.-biphenyle at different
heating rates.
Gradual raise of temperature
Thermal equilibrium is better reached by gradual raise of the
temperature.
2.1.3 The atmosphere
Sort, pressure and flow rate of the gas in the sample chamber
influence the following parameters:
•Sample reaction
Sample reactions with the gas (oxidation in the presence of oxygen).
•Heat transitions
Different heat conductivity of the gases used in an experiment.
•Buoyancy and current effects
Different density and flow rate of the gases used in an experiment.
For all thermoanalytical investigations it is very important to report
the sort, the pressure and the flow rate of the gases used in the
experiment.
Thermal decomposition temperatures for CaCO3 in different
gas atmospheres
* Thermbalance are normally housed in
glass or metal system to allow for operation
at pressures ranging from high vacuum (<
10-4 Pa) to high pressure (>3000 kPa) of
inert, oxidizing, reducing or corrosive gases.
* Care must be taken to correct for
buoyancy arising from the lack of symmetry
in the weighing system
* Thermal convection is responsible for
noise in the signal of TG. The use of dense
carrier gases at high pressures in hot zones
with large temperature gradients give the
most noise. Fitting of convoluted baffles
was found to be most successful in reducing
thermal convection.
2.1.4 The sample
Sample form, defect content, porosity and surface properties
has influence to the behaviour on heating, e.g. single crystal
sample give different response from powdered sample
Large sample size cause problems like heat transfer, and gas
exchange with the surrounding is reduced; in general, the use
of small (~ 20 mg) specimen is preferable if sensitivity of
balance permits
Sample should be powdered and spread thinly and uniformly
in the container
Crucibles
Decomposition temperatures of CaCO3 as function of crucibles
2.1.5 Temperature measurement and calibration
Platinum resistance thermometers or
thermocouples are used for temperature
measurement.
Large difference between sample
temperature (Ts) and furnace temperature
(Tf) can exist, sometime as high as 30°C.
Calibration is thus needed.
The difference or lag is more marked
when operating in vacuum or in fast
flowing atmosphere and with high heating
rate.
Temperature calibration for small furnace can be done by making use
of the melting point or Curie points of a range of metals and alloys.
A series of high purity wires may be
suspend in the region where the
specimen crucible would normally be
located. If the furnace temperature is
slowly raised through the melting point
of a particular wire, a significant weight
loss will be recorded when the wire
melts.
A series of fusible wire, such as :
indium (156.63°C), lead (327.5°C),
zinc
(419.58°C),
aluminium
(660.37°C), silver (961.93°C), and gold
(1064.42°C) should give a reasonable
calibration curve.
hanger of sample pan
furnace
different metal wires
thermocouple
Calibration can also be done by placing a series of
ferromagnetic materials in the specimen basket and a magnet
below or above it, external to the furnace. When each material
goes through its Curie temperature (ferro- to paramagnetic
transition), a sharp ‘weight’ change will be indicated.
2.2 Interpretation of TG and
DTG curves
Resolution of stages can be improved by
recording DTG or by digital differentiation
of TG data.
i.The sample undergoes no decomposition with
loss of volatile products over the temperature
range shown but solid phase transformation,
melting ,etc can not be detected by TG,
ii.The rapid initial mass loss is characteristic of
desorption or drying. If it is true, then re-run the
sample should result in type (i) curves,
iii.Single stage decomposition,
iv.Multi-stage decomposition with relatively
stable intermediates : provide information on the
temperature limit of stability of reactants and
intermediate products and also stoichiometry,
v.Multi-stage decomposition with no stable
intermediate product. However heating-rate
effect must be considered. At low heating rate,
type (v) resemble type (iv). At high heating rate,
type (iv) and (v) resemble type (iii) and lose all
the details,
vi.Gain in mass due to reaction with atmosphere,
e.g. oxidation of metals,
vii.Oxidation product decompose again at higher
temperature; this is not often encountered.
2.3 Preparing the measurement
General advices:
•Exact characterization of the starting materials (purity, grain size)!
•Large amount of the starting material for repeated and further
measurements
•Removal of absorbed water by drying (m must be constant)
•Use samples with narrow grain size distribution (Sieving)
•For measurement in vacuum no sample with a grain size below 60
mesh (0.25 mm) (a part of the sample can be lost)
2.4 Applications of TG
only for studying thermal events accompanied by mass change
provide valuable information for desorption, decomposition and oxidation.
e.g. dehydration of CuSO4·5H2O
TG curve for CuSO45H2O
TG curve for CaSO42H2O at
different water-vapour pressure
knowledge of thermal stability can give information on problems like
the hazards of storing explosives, shelf life of drugs, etc.
TG curves can also be used for 'fingerpring' purpose.
The thermal balance in a TG equipment can also be used to measure
vapour pressure of a sample and magnetic susceptibility, etc.
ATTN:
Three factors should be noted when you get a TG curve:
1. General shape,
2. The particular temperatures at which changes in mass occur
(severely affected by many experimental conditions),
3. The magnitudes of the mass changes (much more use directly
related to the specific stoichiometries of the reactions,
independent of the many factors that affect the shape of the
curves. Can be used for precise quantitative analysis).
Analytical calculations
Under controlled and reproducible conditions, quantitative data
can be extracted from the relevant TG curves. Most commonly,
the mass change is related to sample purity or composition.
Example: A pure compound may be either MgO, MgCO3, or MgC2O4. A
thermogram of the substance shows a loss of 91.0 mg from a total of 175.0 mg
used for analysis. What is the formula of the compound? The relevant possible
reactions are
MgO  No reaction
MgCO3  MgO+CO2
MgC2O4  MgO+CO2+CO
Solution:
% Mass loss Sample=(91.0/175.0)(100%)=52.0
% Mass loss if MgCO3=(44/84.3)(100%)=52.2
% Mass loss if MgC2O4=((44+28)/112.3)(100%)=64.1
If the preparation was pure, the compound present is MgCO3.
3. Dynamic Mechanical Analysis
3.1 Viscoelastic Properties of Polymers
* A polymer may exhibit mechanical behaviour characteristic
of either an elastic solid or a viscous liquid, depending upon
temperature, in relation to the glass-transition temperature
(Tg) of the polymer and the time scale of the deformation.
* Two extremes types of stress-strain curves are those for
elastic solid ( , Hooke’s law) and fluid (  d/dt,
Newton’s law)
relationship between moduli: E = 3B(1-2) = 2(1+)G
E: Young’s modulus; B: bulk modulus; G: shear modulus; : Poisson’s ratio
*For polymer, if d/dt = constant, a curve like the following will be observed
3.2 Periodic stress and DMA
* In DMA, the sample is subjected to a sinusoidally varying
stress of angular frequency . The strain is also sinusoidal but
out of phase with the stress by an angle  due to internal
damping effects.
The response of the sample to this treatment can provide information on the
stiffness of the material (quantified by its elastic moduli) and its ability to
dissipate energy (measured by its damping). For a viscoelastic material, the
strain resulting from the periodic stress will also be periodic, but will be out
of phase with the applied stress owing to energy dispersion as heat, or
damping.
If an elastic sample is vibrated over a range of frequencies and the amplitude
of vibration is measured, the resonance frequency is that which produces a
maximum in a plot of amplitude against frequency. Young's modulus (of
elasticity), E, is related to the square of the resonance frequency, Vr.
E  cL4 vr2 / d 2
where c is a constant, L is the sample length between clamps, d is the sample
thickness and  is the sample density.
3.3 The resonance frequency
If a sample is vibrated over a range of frequencies and the the amplitude of
vibration can be measured, the resonance frequency is that which produces a
maximum in a plot of amplitude against frequency. Modulus is related to the
resonance frequency.
Free oscillation with damping
Damping: log10(A1/A2)=log10(A2/A3)
For elastic materials, the modulus E is simply the constant
ratio between the stress and the resulting strain, but for
viscoelastic materials, the modulus is a complex quantity:
E* = E' + iE"
where E' is the storage modulus or in-phase component
and E" is the loss modulus or out-of-phase component. The
ratio E" / E' is the tangent of the phase angle, .
* For this forced-vibration situation, complex variables (i.e. ) is used for
analysis The modulus can also be written as G* = G + iG where G is
called the storage modulus and G is called the loss modulus.
* The outputs of the test are usually temperature variation plots of either tan
, G and/or G or some other combinations of these parameters.
DMA response of
polystyrene cross-linked
with 2% divinyl benzene
DMA spectrum of polysulfone.
o : storage_modulus;  : loss-modulus. (Tg 480K)
3.3
Apparatus
* The sample is set in cyclic tensile load, a linear variable differential transformer
(LVDT) is used to monitor the frequency and the amplitude of vibration.
* The preset oscillation amplitude is maintained by a feedback control loop and the
driving force required to do so is a measure of the energy dissipation of the sample
3.4
Applications
* change in E (or G) indicate changes in rigidity and hence
strength of the sample (cure behaviour)
*damping measurements give practical information on glass
transitions, change in crystallinity, the occurrence of crosslinking and also show up the features of polymer chains
* damping information can be useful in studies of vibration
dissipation impact resistance and noise abatement.
* Stress relaxation behaviour of polymer
Typical DMA results on two different samples of polyethylene
(a) Linear polyethylene
(b) branched polyethylene.
The damping curve for linear polyethylene (a) shows peaks at -95°C and 65°C. The lower temperature
peak has been attributed to long chain (-CH2-)n crankshaft relaxations in the amorphous phase and the
higher temperature peak to similar motion in the crystalline phase. The temperatures and relative sizes
of the two peaks can be related to the degree of crystallinity of the sample.
The damping curve for branched polyethylene (b) has features at -112°C, -9°C and 45°C. The -112°C
and 45°C peaks are explained as above, while the -9°C peak is attributed to (-CH3) relaxations in the
amorphous phase.
The thermal behaviour of styrene-butadiene-rubber (SBR)
Various formulations of SBR are used in tyre manufacture. Different styrenebutadiene ratios may be used, or different butadiene isomers, or different
additives e.g. carbon black. A high cis-butadiene content (a) lowers the glass
transition temperature, Tg, (to as much as -110°C compared to -50°C) giving
greater flexibility at low temperatures. The addition of carbon black (c) increases
the modulus of elasticity. The Tg is also slightly increased. The complex damping
curve at low temperatures indicates polymer-carbon black interactions and may
lead to adverse properties e.g. heat build-up.
4. Differential Scanning Calorimetry
In power-compensated DSC, the sample and a reference material
are maintained at the same temperature throughout the controlled
temperature programme. The difference in the independent
energy supplies to the sample and the reference is then recorded
against the programme temperature
DSC can be used to study heats of reaction, kinetics, heat
capacities, phase transitions, thermal stabilities, sample
composition and purity, critical points, and phase diagrams.
Circuitry of a DSC
Two separate heating circuits:
•The average-heating controller
(the temperatures of the sample (Ts)
and reference (Tr) are measured
and averaged and the heat output is
automatically adjusted to increase
the average temperature of the
sample and reference in a linear
rate)
•Differential-heating circuit
(monitor the difference in Ts and
Tr, and automatically adjust the
power to either the reference or
sample chambers to keep the
temperatures equal)
x-axis: temperature, y-axis: the difference in power supplied to the
two differential heater (calories per unit time).
Power difference
 Thermal events in the sample appear as deviation from the DSC baseline, in
either an endothermic or exothermic direction (marked on DSC curves). In
DSC, endothermic responses are usually represented as being positive, i.e.
above the base line.
DSC trace of poly(ethylene terephthalate-co-p-oxbenzoate)
4.2 Sample containers and sampling
DSC cell
* T<500°C : usually contained in aluminium sample pans
which can be sealed either by crimping or by cold-welding for
holding volatile samples
* T>500°C :
pans
use quartz, alumina (Al2O3), gold or graphite
* the reference material in most DSC applications is simply an
empty sample pan
* purging of gas into the DSC sample holder is possible, e.g.
N2, O2, etc.
* the mass of (sample+pan+lid) should be recorded before and
after a run so that further information about the processes can
be deduced
The reference sample
For all difference methods (DTA, DSC) reference samples like Al2O3 are
needed to ensure that the heat flow from the furnace to the sample and from
the furnace to the reference sample is identical!
The thermal behavior of the reference sample is included in the measured
signal.
Requirements for the reference sample:
•Known temperature behavior
•No discontinuity in the temperature curve
•If possible a similar thermal behavior as the sample (similar heat capacity)
For small weights of the sample and when no precise measurements are
required an experiment without a reference sample is possible.
In such case an empty crucible can be used as reference.
4.3 Interpretation of DSC curves
* aim at correlating the features recorded with the thermal
events taking place in the sample
* after baseline correction, the peak area is proportional to
enthalpy change,
AK
H 
m
where K is a constant and m is the mass of the sample
K can be obtained by melting a known amount of a pure metal
 reversibility can be monitored by cooling and reheating
Heating and cooling curves for a partially
crystallized polymer.
4.4
4.4.1
Applications
Measurement of heat capacity
H   Cp dT
T2
T1
S  
G = H - TS
T2
T1
 Cp 
  dT
T
4.4.2
Measurement of thermal conductivity
* The temperature at the
bottom of the sample (T1) is
measured via the output of
the
DSC,
while
the
temperature at the top of
sample is measured with a
separate thermocouple in
the contact rod.
* The DSC cell is brought to the desired measurement
temperature, T, and when the output to the recorder is steady
with time, the temperature difference across the sample Ts and
the displacement of baseline, hs, is recorded. The same is then
go through for a standard calibrant, e.g. a standard glass.
 hs Rs ls d c2 Tc 

s  c 
2
 hc Rclc d s Ts 
where Ri = recorder sensitivity
li = length of sample/calibrant
di = diameter of sample/calibrant
4.4.3 Determination of phase diagrams
 melting point can be determined from the DSC curve
* Melting point of pure components are easily determined
* DSC curves for slow cooling of mixture
* If heating is done instead of cooling, the curve should
ideally be endothermic mirror image of that shown and the
problem of supercooling is avoided.
* From a series of this kind of curves, a phase diagram can be
constructed.
4.4.4 General Applications
* Temperature and enthalpy changes for the thermal events
enthalpy  area of peak after baseline correction
Corresponding
TG curve
* Detection of solid-solid phase transition and the measurement
of H for these transitions
DSC curve of carbon tetrachloride
 Tracing the ferromagnetic to paramagnetic transformation.
Most rewarding applications is in study of polymer
•Most solid polymers are formed by rapid cooling to low temperatures
(quenching) are thus in glassy state; by heating above Tg, glass transition,
with change in cp but no change in enthalpy, is observed, therefore no peak
is observed, only discontinuity results
•degradation or oxidation of polymers can be study with DSC in isothermal
mode
•for recycling plastics, identification is important and DSC curves provide
'fingerprint'of the materials.