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Thermal Analysis
References
Thermal Analysis, by Bernhard Wunderlich Academic Press 1990.Calorimetry and Thermal Analysis of Polymers, by V. B. F. Mathot, Hanser 1993.
Common Definition of Thermal AnalysisA branch of materials science where the properties of materials
are studied as they change with temperature.
Techniques:Differential Scanning CalorimetryDynamic Mechanical AnalysisThermomechanical AnalysisThermogravimetric AnalysisDifferential Thermal AnalysisDilatometryOptical DilatometryDielectric Thermal AnalysisEvolved Gas AnalysisThermo-Optical AnalysisProduction Thermal Analysis of MetalsThermal Analysis of Foods
Concepts of Thermal AnalysisTemperatureA 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
kTmVEk 23
2
2
==
Temperature Scales
P. Atkins, Four Laws that drive the Universe, Oxford Univ. Press, 2007
Maxwell-Boltzmann Distribution
P. Atkins, Four Laws that drive the Universe, Oxford Univ. Press, 2007
Some Important TemperaturesAbsolute zero (precisely by definition): 0 K or −273.15 °CColdest measured temperature: 450 pK or –273.14999999955 °CWater’s triple point (precisely by definition): 273.16 K or 0.01 °C Water’s boiling point: 373.1339 K or 99.9839 °CIncandescent lamp: ~2500 K or ~2200 °CMelting point of tungsten: 3695 K or 3422 °CMelting point of carbon: 3773.15 K or 3500 °CSun’s visible surface 5778 K or 5505 °CLightning bolt’s channel 28,000 K or 28,000 °CSun’s core 16 MK or 16M°CThermonuclear weapon (peak temperature) 350 MK or 350M°CCERN’s proton vs. nucleus collisions 10 TK or 10 trillion °CUniverse 5.391×10−44 s after the Big Bang 1.417×1032 K 1.417×1032 °C
Concepts of Thermal AnalysisHeatA 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
pp T
HdTdQC ⎟
⎠⎞
⎜⎝⎛∂∂
==
Thermal Analysis Instrument Manufacturers
Perkin Elmer Thermal Analysis Systemshttp://www.perkin-elmer.com/thermal/index.html
TA Instrumentshttp://www.tainst.com/
Mettler Toledo Thermal Analysis Systemshttp://www.mt.com/
Rheometric Scientifichttp://www.rheosci.com/
Haakehttp://polysort.com/haake/
NETZSCH Instrumentshttp://www.netzsch.com/ta/
SETARAM Instrumentshttp://setaram.com/
Instrument Specialists, Inc.http://www.instrument-specialists.com/
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
TGA Applications: Inorganics
Hydrates decomposition, drying phenomenaCarbonates and other salts decompositionKinetics and mechanisms of oxidation, and other solid-gas reactionsAnalysis of magnetic materialsEtc.
TGA Applications: Organics
Identification of polymers and pharmaceutical agentsThermal stability of synthetic and natural polymers and other organicsAnalysis of polymer-matrix compositesKinetics and mechanism of solid organics – gas reactions Residual solvent determinations
TGA Applications: Oxidation of SWCNTOxidation of amorphous
carbon Oxidation of catalyst
C+O2=CO2
http://www.msel.nist.gov/Nanotube2/
TGA+Spectroscopy/Chromatography Combination
TGA IR or MS or GCGases, vapors
Kinetic studiesThe 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/RTThe activation energy can be determined from the slope of the
above plot, and the intercept value would yield the pre-exponential factor.
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
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
Differential Scanning Calorimetry (DSC)
Exot
herm
al d
Q/d
T
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
Differential Scanning Calorimeter
Differential Scanning Calorimetry (DSC)
tQ
TimeHeat 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
Hea
t flo
w
Heat Flow
pCTQ
Tt
tQ
rateeTemperaturflowHeat
=Δ
=Δ⋅=
δδ
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)
Types of Phase TransitionsFirst 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
0,0 2
2
≠⎟⎟⎠
⎞⎜⎜⎝
⎛∂Δ∂
≠Δ−=⎟⎠⎞
⎜⎝⎛∂Δ∂
pp TGS
TG
0,0 2
2
≠⎟⎟⎠
⎞⎜⎜⎝
⎛∂Δ∂
=Δ−=⎟⎠⎞
⎜⎝⎛∂Δ∂
pp TGS
TG
Differential Scanning Calorimeter
Parts:Isolated box with 2 pansHeating element and thermocoupleLiquid nitrogenNitrogen gasAluminum pan
Differential Scanning Calorimeter
Differential Scanning CalorimeterPerkin Elmer DSC 7
Platinum sensors
Sample heater Reference heater
Temperature range 110 –1000 KHeating rate 0.1 – 500 K/min (normally 0.5 – 50 K/min)Noise ± 4 μWSample volume up to 75 mm3
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
An Example of Phase Transition in DSC: Martensite/Austenite Transition in Cu-Al-Ni Alloy
DSC in Polymer Analysis
Main transitions which can be studied by DSC:
MeltingFreezing Glass transition
Polymers in Condensed StateExtended chain: presents equilibrium crystals. 1. Produced by annealing:e.g. polyethylene
polytetrafluoroethylenepolychlorotrifluoroethylene
2. Produced by crystallization during polymerization:e.g. polyoxymethylene
polyphosphates, seleniumGlassy amorphous1. Random copolymers2. Atatic stereoisomers
e.g. PS, PMMA, PP3.Quenched slow crystallizing moleculese.g. PET, PCand others.
Chain folded1. Fold length 5 -50 nm2. Best grown from dilute
solution3. Metastable lamellae
because of the large fold surface area
Lamellar crystals and ClustersCrystallinity conceptthe molecules are much larger than the crystals
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.
How to observe TgEx
othe
rmal
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).
Exot
herm
al
Temperature
79.70°C(I)75.41°C
81.80°C
144.72°C
137.58°C20.30J/g
245.24°C
228.80°C22.48J/g
Cycle 1
-0.5
0.0
0.5
1.0
1.5
Hea
t Flo
w (W
/g)
0 50 100 150 200 250 300Temperature (°C)
Sample: PET80PC20_MM1 1minSize: 23.4300 mgMethod: standard dsc heat-cool-heatComment: 5/4/06
DSCFile: C:...\DSC\Melt Mixed 1\PET80PC20_MM1.001Operator: SACRun Date: 05-Apr-2006 15:34Instrument: DSC Q1000 V9.4 Build 287
Exo Down Universal V4.2E TA Instruments
Tg
Tc
Tm
Typical DSC Curve of a Thermoplastic Polymer
Temperature
Hea
t Flo
w - >
exo
ther
mic
GlassTransition
Crystallisation
Melting
Cross-Linking(Cure)
Oxidation
Typical DSC Curve of a Thermosetting Polymer
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
The First law (Conservation of Energy)
We define Internal Energy, U, by:dU = δq - δw
Can we measure the absolute value of the Internal Energy?How is it stored?
Specific heat - increased atomic vibrationMaking or breaking of atomic bondsLatent heatChemical 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)