Thermal Transitions in Polymers

L4
• No polymer is completely crystalline
• Even the most crystalline polymers have lattice defect
regions containing unordered amorphous material.

• Crystalline polymers may exhibit both

• Tg corresponding to long range segmental

motions in the amorphous region and
• Tm crystalline melting temperature, at which
crystallites are destroyed and an amorphous,
disordered melt is formed.

The solid state properties of Polymers 2

• For many polymers
• Tg ≈ (½ - 2/3 ) Tm { when in K}
• Chemical structure of polymer determines
crystallanity in solid form.
• Eg: Linear PE, PTFE, Atactic PVC
• Specific interactions ( H bonding )
enhances crystallanity.
• Eg: Nylons
• Trans configuration ( geometric
isomerism if exists ) favors
crystallanity.

The solid state properties of Polymers 3

Crystalline melting temperature
• Free energy of fusion per RU of the polymer, ΔGu =
ΔHu – TΔSu
• At equilibrium melting temperature Tm0
ΔGu = 0
H u
T =
0

S u
m

In general, the observed crystalline melting

temperature Tm is always less than the
equilibrium value. Tmo ?????

The solid state properties of Polymers 4

• An approximate relation for the melting point
depression of a high molecular weight polymer by a
diluent.

1  R  Vu 
1
− 0 = 
Tm Tm  H u
(
  1 − 1212 )
 V1 
Vu: molar volume per RU
V1: molar volume of the diluent
Others: usual meanings

The solid state properties of Polymers 5

Example A polymer has a crystalline growth
parameter (n) of 2 and a rate constant (k) of 10-2
s-2 at 100°C. The polymer is melted and then
quenched to 100°C and allowed to crystallize
isothermally. After 10 s, what is the percent
crystallinity of the sample?
Avrami equation
• During the crystallization process, the fractional
crystallanity,  , at time t may be approximated
by Avrami equation

 = 1 − exp(− kt n )
k: temperature dependent growth rate parameter
n: temperature independent nucleation index
generally
1 n  4

The solid state properties of Polymers 7

Techniques to determine crystallanity
• Density measurements
Densities can easily be measured at some
standard temperature by means of a calibrated
density gradient column.

The solid state properties of Polymers 8

Once the density of the semicrystalline sample has
been measured, the fractional crystallanity φ can be
determined as

• --- If the densities of a totally amorphous (ρa) and

totally crystalline sample (ρc) are known.

The solid state properties of Polymers 9

Generally
• Amorphous density semicrystalline with very low
crystallanity

• Crystalline density crystalline low molecular

weight analogs

Table 4-5 shows amorphous and crystalline densities of

various polymers

The solid state properties of Polymers 10

X-Ray Diffraction

• Widely used technique for polymer characterization.

• X rays are high energy photons ( short wave λ≈0.5 to

2.5 )

• The scattering pattern provides info on the electron

density distribution and therefore the position of
atoms in the polymer.

The solid state properties of Polymers 11

• Thomson formula

intensity of unpolarized X ray beam

scattered intensity
r : distance b/w the electron and the detector where
scattered beam intensity is measured.
K : constant given by

The solid state properties of Polymers 12

Terms often used in X-ray scattering are

Wide angle X ray scattering (WAXS) ➔ used for small

scale structures (< 10 A0)

Small angle X ray scattering (SAXS) ➔ used for large

scale structures (10 - 104 A0)

WAXS is used for the determination of fractional

crystallanity as well as crystalline dimensions.

The solid state properties of Polymers 13

In many cases, the fractional crystallanity can be
measured by comparing the intensities or height of
the amorphous halo (Iam) of the crystalline sample
with the intensity (Iam0) of a totally amorphous
polymer as sometimes can be obtained by rapid
quenching from the melt as

wc is the weight fraction of the crystalline phase.

The solid state properties of Polymers 14

THERMAL TRANSITIONS
AND
PROPERTIES

Fundamental
Thermodynamic
Relationships

The solid state properties of Polymers 15

MEASUREMENT
TECHNIQUES

The solid state properties of Polymers 16

 Thermal Analysis Techniques
A group of techniques in which a physical property is
measured as a function of temperature, while the sample
is subjected to a predefined heating or cooling program.

Major Techniques:
Differential Thermal Analysis (DTA)
Differential Scanning Calorimetry (DSC)
Thermal Gravimetric Analysis (TGA)
Dynamic Mechanical Analysis (DMA)
Thermo-mechanical Analysis (TMA)
 Thermal Analysis Techniques
Differential Thermal Analysis (DTA)
• the temperature difference between a sample and an inert
reference material, DT = TS - TR, is measured as both are
subjected to identical heat treatments

Differential Scanning Calorimetry (DSC)

• the sample and reference are maintained at the same
temperature, even during a thermal event (in the sample)

• the energy required to maintain zero temperature

differential between the sample and the reference, dDq/dt,
is measured
 Thermal Analysis Techniques
Thermogravimetric Analysis (TGA)
• The change in mass of a sample on heating is measured

Thermo-mechanical Analysis (TMA)

• Dimensional changes of the sample are monitored
as a function of temperature or time, while the
sample may be subjected to an additional mechanical load.

Dynamic Mechanical Analysis (DMA)

• Mechanical behavior of a sample subjected to a specific
temperature program is investigated under the effect of a
load which changes with time.
 Basic Principles of Thermal Analysis
Modern instrumentation used for thermal analysis usually consists of four
parts:
1) sample/sample holder
2) sensors to detect/measure a property of the sample and the
temperature
3) an enclosure within which the experimental parameters may be
controlled
4) a computer to control data collection and processing

heat flux DSC

DTA power compensated DSC
 Differential Thermal Analysis
alumina block
Sample holder heating
• sample and reference cells (Al) coil

Sensors
• Pt/Rh or chromel/alumel
thermocouples sample reference
pan pan
• one for the sample and one for
the reference
• joined to differential
temperature controller inert gas
Furnace vacuum
• alumina block containing sample
and reference cells Pt/Rh or chromel/alumel
Temperature controller thermocouples

•controls for temperature program and furnace atmosphere

 Differential Thermal Analysis

Applications:
• Characteristic temperatures identification
• Glass transitions
• Melting and crystallization behavior
• Heat of melting and crystallization
• Solid-liquid ratio
• Specific heat capacity & heat of reaction
• Reaction kinetics & reaction behavior
• Oxidative stability & thermal stability
Differential Thermal Analysis
 Differential Thermal Analysis

Advantages:
Instruments can be used at very
high temperatures
Instruments are highly sensitive
Flexibility in crucible volume
/form
Characteristic transition or
reaction temperatures can be
accurately determined
Disadvantages:
Uncertainty of heats of fusion, DTA
transition, or reaction estimations
is 20-50%
 Differential Scanning Calorimetry (DSC)

➢DSC differs fundamentally from DTA in that the sample

and reference are both maintained at the temperature
predetermined by the program.

➢During a thermal event in the sample, the system will

transfer heat to or from the sample pan to maintain the
same temperature in reference and sample pans

➢Two basic types of DSC instruments: power compensation

and heat-flux
DSC
DSC System for a polymer sample
Differential Scanning Calorimetry (DSC)

Heat flux DSC

Power compensation DSC
 Power Compensation DSC
individual controller P
heaters

sample reference
pan pan
Sample holder
• Al or Pt pans
inert gas inert gas
Sensors vacuum vacuum

• Pt resistance thermocouples thermocouple T = 0

• separate sensors and heaters for the sample and reference

Furnace
• separate blocks for sample and reference cells

Temperature controller
• differential thermal power is supplied to the heaters to maintain
the temperature of the sample and reference at the program
value
 Heat Flux DSC heating
coil

Sample holder sample reference

• sample and reference are connected byconstantan pan pan

a low-resistance heat flow path

chromel/alumel
• Al or Pt pans placed on constantan disc wires
inert gas
vacuum thermocouples
Sensors chromel wafer
• chromel®-constantan area thermocouples (differential heat flow)
• chromel®-alumel thermocouples (sample temperature)

Furnace
• one block for both sample and reference cells
Temperature controller
• the temperature difference between the sample and reference is
converted to differential thermal power, dq/dt, which is supplied to
the heaters to maintain the temperature of the sample and
reference at the program value