Thermal Analysis

Yury Gogotsi, MatE 280

2011

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

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

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

==

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 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

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

∂

∂==

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/

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 phenomena

� Carbonates and other salts decomposition � Kinetics and mechanisms of oxidation, and other solid-gas reactions

� Analysis of magnetic materials

� Etc.

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

TGA Applications: Oxidation of SWCNT

Oxidation of amorphous carbon Oxidation of catalyst

C+O2=CO2

http://www.msel.nist.gov/Nanotube2/

TGA+Spectroscopy/Chromatography

Combination

TGA IR or MS or GC

Gases, vapors

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.

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)

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

Differential Scanning Calorimeter

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

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 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

Differential Scanning Calorimeter

Parts:

� Isolated box with 2 pans

� Heating element and thermocouple

� Liquid nitrogen

� Nitrogen gas

� Aluminum pan

Differential Scanning Calorimeter

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

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:

� Melting

� Freezing

� Glass transition

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

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 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

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

Temperature

Heat Flow -

> exothermic

Glass Transition

Crystallisation

Melting

Cross - Linking

(Cure)

Oxidation

Typical DSC Curve of a

Thermosetting Polymer

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

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)