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Thermal Analysis
Yury Gogotsi, MatE 280
2011
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References
� Thermal Analysis, by Bernhard
Wunderlich Academic Press 1990.
� Calorimetry and Thermal Analysis of
Polymers, by V. B. F. Mathot, Hanser
1993.
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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
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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 -273.15°C
kTmV
Ek
2
3
2
2
==
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Temperature Scales
P. Atkins, Four Laws that drive the Universe, Oxford Univ. Press, 2007
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Maxwell-Boltzmann Distribution
P. Atkins, Four Laws that drive the Universe, Oxford Univ. Press, 2007
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Some Important Temperatures � Absolute zero (precisely by definition): 0 K or −273.15 °C
� Coldest measured temperature: 450 pK or –273.14999999955 °C
� Water’s triple point (precisely by definition): 273.16 K or 0.01 °C
� Water’s boiling point: 373.1339 K or 99.9839 °C
� Incandescent lamp: ~2500 K or ~2200 °C
� Melting point of tungsten: 3695 K or 3422 °C
� Melting point of carbon: 3773.15 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
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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 = 4.184 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
( )VSfUpdVTdSpdVQAQdU ,=−=−=−= δδδ
( )pSfHVdPTdSVdpQdHPVUH ,=+=+=+= δ
p
pT
H
dT
dQC
∂
∂==
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Thermal Analysis Instrument
Manufacturers � Perkin Elmer Thermal Analysis Systems
http://www.perkin-elmer.com/thermal/index.html
� TA Instruments
http://www.tainst.com/
� Mettler Toledo Thermal Analysis Systems
http://www.mt.com/
� Rheometric Scientific
http://www.rheosci.com/
� Haake
http://polysort.com/haake/
� NETZSCH Instruments
http://www.netzsch.com/ta/
� SETARAM Instruments
http://setaram.com/
� Instrument Specialists, Inc.
http://www.instrument-specialists.com/
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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
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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.
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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
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TGA Applications: Oxidation of SWCNT
Oxidation of amorphous carbon Oxidation of catalyst
C+O2=CO2
http://www.msel.nist.gov/Nanotube2/
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TGA+Spectroscopy/Chromatography
Combination
TGA IR or MS or GC
Gases, vapors
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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.
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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 67.54 kJ/mol
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Differential Thermal Analysis (DTA)
� 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
Can be conducted at the same time with
TGA
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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
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Differential Scanning Calorimeter
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Differential Scanning Calorimetry
(DSC)
t
Q
Time
Heat δ=
� 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
pCT
Q
T
t
t
Q
rateeTemperatur
flowHeat=
∆=
∆⋅=
δδ
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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)
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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
0,02
2
≠
∂
∆∂≠∆−=
∂
∆∂
pp T
GS
T
G
0,02
2
≠
∂∆∂
=∆−=
∂∆∂
pp T
GS
T
G
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Differential Scanning Calorimeter
Parts:
� Isolated box with 2 pans
� Heating element and thermocouple
� Liquid nitrogen
� Nitrogen gas
� Aluminum pan
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Differential Scanning Calorimeter
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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 µW
� Sample volume up to 75 mm3
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An Example of Phase Transitions
Studied by DSC
A.Schreiber et al. Phys.Chem.Chem.Phys.,2001,3,1185-1195
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
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An Example of Phase Transition in
DSC: Martensite/Austenite
Transition in Cu-Al-Ni Alloy
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DSC in Polymer Analysis
Main transitions which can be studied by DSC:
� Melting
� Freezing
� Glass transition
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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 5 -50 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
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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.
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How to observe Tg Exothermal
Experimental curves on heating after cooling at 0.0084 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).
Exothermal
Temperature
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79 . 70 °C ( I )
75 . 41 °C 81 . 80 °C
144 . 72 °C
137 . 58 °C 20 . 30 J / g
245 . 24 °C
228 . 80 °C 22 . 48 J / g
Cycle 1
- 0 . 5
0 . 0
0 . 5
1 . 0
1 . 5
Heat
Flo
w ( W
/ g )
0 50 100 150 200 250 300
Temperature ( °C )
Sample : PET 80 PC 20 _ MM 1 1 min Size : 23 . 4300 mg Method : standard dsc heat - cool - heat Comment : 5 / 4 / 06
DSC File : C :... \ DSC \ Melt Mixed 1 \ PET 80 PC 20 _ MM 1 . 001 Operator : SAC Run Date : 05 - Apr - 2006 15 : 34 Instrument : DSC Q 1000 V 9 . 4 Build 287
Exo Down Univ ersal V 4 . 2 E TA Instruments
Tg
Tc
Tm
Typical DSC Curve of a
Thermoplastic Polymer
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Temperature
Heat Flow -
> exothermic
Glass Transition
Crystallisation
Melting
Cross - Linking
(Cure)
Oxidation
Typical DSC Curve of a
Thermosetting Polymer
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Differential Scanning Calorimetry
PET
-1.5
-1
-0.5
0
0.5
1
1.5
2
0 50 100 150 200 250 300 350
Temperature (C)
Heat Flow (W/gm)
Melting
Glass Transition
Crystallization
ENDOTHERMIC
EXOTHERMIC
Sample: Polyethylene terephthalate (PET)
Temperature increase rate: 20°C/min
Temperature range: 30°C - 300°C
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The First law (Conservation of Energy)
We define Internal Energy, U, by:
dU = δδδδq - δδδδw
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)