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
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
mV 2 3
A measure of kinetic energy of molecular motion E k =
= kT
2
2
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
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: 3695ԜK or 3422Ԝ°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:
dU = δQ − δA = δQ − pdV = TdS − pdV
U = f (S , V )
U – internal energy, Q – heat, A – work, T – temperature, V – volume, S - Entropy
„
Enthalpy
H = U + PV
„
dH = δQ + Vdp = TdS + VdP H = f (S , p )
Heat Capacity
dQ ⎛ ∂H ⎞
Cp =
=⎜ ⎟
dT ⎝ ∂T ⎠ p
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
http://www.msel.nist.gov/Nanotube2/
C+O2=CO2
Oxidation of catalyst
TGA+Spectroscopy/Chromatography
Combination
Gases, vapors
TGA
IR or MS or GC
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 preexponential 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)
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
Exothermal dQ/dT
Differential Scanning Calorimetry (DSC)
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)
„
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.
Heat flow
„
Heat δQ
=
Time
t
Heat Flow
Temperature
Heat flow
δQ t
δQ
=
⋅
=
= Cp
Temperature rate
t ΔT ΔT
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
⎛ ∂ 2 ΔG ⎞
⎛ ∂ΔG ⎞
⎟ ≠0
⎟ = −ΔS ≠ 0, ⎜⎜
⎜
2 ⎟
⎝ ∂T ⎠ p
⎝ ∂T ⎠ p
„
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
⎛ ∂ 2 ΔG ⎞
⎛ ∂ΔG ⎞
⎟ ≠0
⎜
⎟ = −ΔS = 0, ⎜⎜
2 ⎟
⎝ ∂T ⎠ p
⎝ ∂T ⎠ p
„
Examples: ferromagnetic – diamagnetic transition
Differential Scanning Calorimeter
Parts:
… Isolated
pans
box with 2
… Heating
element and
thermocouple
… Liquid
nitrogen
… Nitrogen
gas
… Aluminum
pan
Differential Scanning Calorimeter
Differential Scanning Calorimeter
Perkin Elmer DSC 7
Platinum sensors
Sample heater
„
Temperature range 110 –
1000 K
„
Heating rate 0.1 – 500 K/min
(normally 0.5 – 50 K/min)
„
Noise ± 4 μW
Reference heater „
Sample volume up to 75 mm3
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.,2001,3,1185-1195
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
Lamellar crystals
and Clusters
Crystallinity
concept
the molecules are
much larger than the
crystals
Chain folded
1. Fold length 5 -50 nm
2. Best grown from dilute
solution
3. Metastable lamellae
because of the large fold
surface area
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.
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.
Exothermal
Exothermal
How to observe Tg
Temperature
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).
Typical DSC Curve of a
Thermoplastic Polymer
DSC
Sample: PET80PC20_MM1 1min
Size: 23.4300 mg
Method: standard dsc heat
-cool-heat
Comment: 5/4/06
File: C:...\DSC\Melt Mixed1\PET80PC20_MM1.001
Operator: SAC
Run Date: 05-Apr-2006 15:34
Instrument: DSC Q1000 V9.4 Build 287
Tm
1.5
245.24°C
Heat Flow(W/g)
1.0
Tc
Tg
137.58°C
20.30J/g
79.70°C(I)
0.5
75.41°C
228.80°C
22.48J/g
81.80°C
Cycle1
144.72°C
0.0
-0.5
Exo Down
0
50
100
150
Temperature(°C)
200
250
300
Universal V4.2E TA Instruments
Heat Flow -> exothermic
Typical DSC Curve of a
Thermosetting Polymer
Cross-Linking
(Cure)
Crystallisation
Glass
Transition
Melting
Temperature
Oxidation
Differential Scanning Calorimetry
Melting
ENDOTHERMIC
Glass Transition
EXOTHERMIC
Crystallization
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 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)