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)