1. Thermal Analysis
Yury Gogotsi, MatE 280
2011

2. References
Thermal Analysis, by Bernhard Wunderlich Academic Press 1990.
Calorimetry and Thermal Analysis of Polymers, by V. B. F. Mathot, Hanser 1993.

3. Common Definition of Thermal Analysis
A branch of materials science where the properties of materials are studied as they change with temperature.
Techniques:
Differential Scanning Calorimetry
Dynamic Mechanical Analysis
Thermomechanical Analysis
Thermogravimetric Analysis
Differential Thermal Analysis
Dilatometry
Optical Dilatometry
Dielectric Thermal Analysis
Evolved Gas Analysis
Thermo-Optical Analysis
Production Thermal Analysis of Metals
Thermal Analysis of Foods

4. Concepts of Thermal Analysis
Temperature
A measure of kinetic energy of molecular motion
Temperature Scales:
Newton (1701): freezing point of water 0, human body 12
Fahrenheit (1714): freezing point of water mixed with NaCl 0, human body 96, freezing point of water 32, boiling point of water 212
Celsius (1742): freezing point of water 0, boiling point of water 100
Kelvin (1848): absolute zero is the temperature at which molecular energy is a minimum and it corresponds to a temperature of °C

5. P. Atkins, Four Laws that drive the Universe, Oxford Univ. Press, 2007
Temperature Scales
P. Atkins, Four Laws that drive the Universe, Oxford Univ. Press, 2007

6. Maxwell-Boltzmann Distribution
P. Atkins, Four Laws that drive the Universe, Oxford Univ. Press, 2007

7. Some Important Temperatures
Absolute zero (precisely by definition): 0 K or − °C
Coldest measured temperature: 450 pK or –  °C
Water’s triple point (precisely by definition): K or 0.01 °C
Water’s boiling point: K or °C
Incandescent lamp: ~2500 K or ~2200 °C
Melting point of tungsten: 3695 K or 3422 °C
Melting point of carbon: K or 3500 °C
Sun’s visible surface 5778 K or 5505 °C
Lightning bolt’s channel 28,000 K or 28,000 °C
Sun’s core 16 MK or 16M°C
Thermonuclear weapon (peak temperature) 350 MK or 350M°C
CERN’s proton vs. nucleus collisions 10 TK or 10 trillion °C
Universe 5.391×10−44 s after the Big Bang 1.417×1032 K 1.417×1032 °C

8. Concepts of Thermal Analysis
Heat
A form of energy produced by the motion of atoms and molecules
Heat Units: J (Joule) [m2 kg s-2], Cal (Calorie) 1 cal = J
Heat is related to internal energy of a system and work done on or by a system through the First Law of Thermodynamics:
U – internal energy, Q – heat, A – work, T – temperature, V – volume, S - Entropy
Enthalpy
Heat Capacity

9. Thermal Analysis Instrument Manufacturers
Perkin Elmer Thermal Analysis Systems
TA Instruments
Mettler Toledo Thermal Analysis Systems
Rheometric Scientific
Haake
NETZSCH Instruments
SETARAM Instruments
Instrument Specialists, Inc.

10. Thermogravimetric Analysis (TGA)
A technique that permits the continuous weighing of a sample as a function of temperature and/or as a function of time at a desired temperature

11. TGA Applications: Inorganics
Hydrates decomposition, drying phenomena
Carbonates and other salts decomposition
Kinetics and mechanisms of oxidation, and other solid-gas reactions
Analysis of magnetic materials
Etc.

12. TGA Applications: Organics
Identification of polymers and pharmaceutical agents
Thermal stability of synthetic and natural polymers and other organics
Analysis of polymer-matrix composites
Kinetics and mechanism of solid organics – gas reactions
Residual solvent determinations

13. TGA Applications: Oxidation of SWCNT
C+O2=CO2
Oxidation of amorphous carbon
Oxidation of catalyst

14. TGA+Spectroscopy/Chromatography Combination
Gases, vapors
TGA
IR or MS or GC

15. Kinetic studies
The kinetic reaction mechanism can be determined from the Arrhenius equation,
K=A exp (-Ea/RT),
where Ea is the activation energy; R is the universal gas constant; A is the pre-exponential factor; T is the absolute temperature; and K is the reaction rate constant.
The above equation upon log transformation can be rewritten as
lnK= lnA - Ea/RT
The activation energy can be determined from the slope of the above plot, and the intercept value would yield the pre-exponential factor.

16. The Ea values are 66.45, 65.12, and 67.54 kJ/mol
Arrhenius plot
Determination of kinetic mechanism for volatilization of triacetin, diethyl phthalate, and glycerin from Arrhenius plots.
The Ea values are 66.45, 65.12, and kJ/mol

17. Differential Thermal Analysis (DTA)
Can be conducted at the same time with TGA
DTA measures temperature difference between a sample and an inert reference (usually Al2O3) while heat flow to the reference and the sample remains the same

18. Differential Scanning Calorimetry (DSC)
Exothermal dQ/dT
Temperature
DSC measures differences in the amount of heat required to increase the temperature of a sample and a reference as a function of temperature

19. Differential Scanning Calorimeter

20. Differential Scanning Calorimetry (DSC)
To heat a sample and a reference with the same heating rate requires different amount of heat for the sample and the reference. Why?
On the X-axis we plot the temperature, on the Y-axis we plot difference in heat output of the two heaters at a given temperature.
Temperature
Heat flow
Heat Flow

21. Major difference between TGA and DTA (DSC)
TGA reveals changes of a sample due to weight, whereas DTA and DSC reveal changes not related to the weight (mainly due to phase transitions)

22. Types of Phase Transitions
First order transitions, where first and second derivatives of thermodynamic potentials by temperature are not 0
Examples: crystallization and melting
Second order transitions where the first derivatives of thermodynamic potentials by temperature are 0 and the second derivatives are not 0
Examples: ferromagnetic – diamagnetic transition

23. Differential Scanning Calorimeter
Parts:
Isolated box with 2 pans
Heating element and thermocouple
Liquid nitrogen
Nitrogen gas
Aluminum pan

24. Differential Scanning Calorimeter

25. Differential Scanning Calorimeter Perkin Elmer DSC 7
Platinum sensors
Sample heater
Reference heater
Temperature range 110 – 1000 K
Heating rate 0.1 – 500 K/min (normally 0.5 – 50 K/min)
Noise ± 4 mW
Sample volume up to 75 mm3

26. An Example of Phase Transitions Studied by DSC
Melting and freezing of water in ordered mesoporous silica materials.
Pore size increases from 4.4 to 9.4 nm in the series SBA-15/1 to SBA 15/8
A.Schreiber et al. Phys.Chem.Chem.Phys.,2001,3,

27. An Example of Phase Transition in DSC: Martensite/Austenite Transition in Cu-Al-Ni Alloy

28. DSC in Polymer Analysis
Main transitions which can be studied by DSC:
Melting
Freezing
Glass transition

29. Polymers in Condensed State
Extended chain: presents equilibrium crystals.
1. Produced by annealing:
e.g. polyethylene
polytetrafluoroethylene
polychlorotrifluoroethylene
2. Produced by crystallization during polymerization:
e.g. polyoxymethylene
polyphosphates, selenium
Glassy amorphous
1. Random copolymers
2. Atatic stereoisomers
e.g. PS, PMMA, PP
3.Quenched slow crystallizing molecules
e.g. PET, PC
and others.
Chain folded
1. Fold length nm
2. Best grown from dilute solution
3. Metastable lamellae because of the large fold surface area
Lamellar crystals and Clusters
Crystallinity concept
the molecules are much larger than the crystals

30. Glass Transition
The glass transition temperature, Tg, is the temperature at which an amorphous solid, such as glass or a polymer, becomes brittle on cooling, or soft on heating.
More specifically, it defines a pseudo second order phase transition in which a supercooled melt yields, on cooling, a glassy structure and properties similar to those of cristalline materials e.g. of an isotropic solid material.

31. How to observe Tg
Exothermal
Exothermal
Temperature
Experimental curves on heating after cooling at K/min (1), 0.2 K/min (2)
0.52 K/min (3), 1.1 K/min (4), 2.5 K/min (5), 5 K/min (6), and 30 K/min (7).

32. Typical DSC Curve of a Thermoplastic Polymer79 . 70 °C ( I ) 75 41 81 80
144 72
137 58 20 30 J / g
245 24
228 22 48
Cycle 1 - 5
Heat Flow W 50
100
150
200
250
300
Temperature
Sample :
PET PC _ MM
1 1
min
Size 23
4300 mg
Method
standard dsc heat
cool
heat
Comment 4 06
DSC
File C
:... \
Melt Mixed
001
Operator
SAC
Run Date 05
Apr 34
Instrument
DSC Q
1000 V 9
Build
287
Exo Down
Universal V 2
E TA Instruments Tg Tc Tm

33. Typical DSC Curve of a Thermosetting Polymer
Oxidation
Cross -
Linking
Crystallisation
(Cure)
> exothermic -
Glass
Transition
Heat Flow
Melting
Temperature

34. Differential Scanning Calorimetry
Melting
Glass Transition
Crystallization
ENDOTHERMIC
EXOTHERMIC
Sample: Polyethylene terephthalate (PET) Temperature increase rate: 20°C/min Temperature range: 30°C - 300°C

35. The First law (Conservation of Energy)
We define Internal Energy, U, by:
dU = dq - dw
Can we measure the absolute value of the Internal Energy?
How is it stored?
Specific heat - increased atomic vibration
Making or breaking of atomic bonds
Latent heat
Chemical Reaction Heat - breaking and remaking chemical bonds
2Mg + O2 -> 2 MgO
Statement of First Law:
Internal Energy is a State Function:
U = f (T,P,…)
The same amount of work, however it is performed (motion, electrical current, friction, etc.) brings about the same change of the system (means, change of state is path independent)