MAT6102



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INSTRUCTIONS GIVEN ON THIS PAGE CAREFULLY BEFORE
ATTEMPTING ANY QUESTIONS





THE PHYSICS OF POLYMERS

Autumn Semester Exam 2019-2020

Duration of Exam: 3 Hours


There are SIX questions
Answer FOUR questions ONLY
Each Question is worth a possible total of 20 Marks


PLEASE WRITE YOUR ANSWERS IN THE ANSWER BOOK PROVIDED
NOT ON THE EXAM PAPER.

ANYTHING WRITTEN ON THIS PAPER WILL NOT BE CONSIDERED.







Department Of
Materials
Science &
Engineering.

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There are SIX questions - Answer FOUR questions ONLY

1. (a) Describe how the conformational entropy of an amorphous polymer molecule
changes with increasing end-to-end distance, and explain the entropic origin of
rubber elasticity. [3 marks]

(b) Explain why polystyrene and unplasticised PVC have much higher glass
transition temperatures than polypropylene, on the basis of their differences in
molecular structures. [4 marks]

(c) Describe the free volume theory of glass transitions, and define the terms
“occupied volume” and “free volume”. [4 marks]

(e) Use the free volume theory to explain the experimentally observed discontinuity
in the thermal expansion coefficient of amorphous polymers below and above the
glass transition temperature. [3 marks]

(f) A natural polymer –[-CH2C(CH3)=CH-CH2-]n– has on average 200 repeating
units between cross-links, and a density of 0.93 g cm-3. Calculate the number of
sub-molecules per unit volume, and estimate its shear modulus at 300K.

Note: Avogadro number: 6.02 x 1023 mol-1;
Boltzmann constant: 1.38 x 10-23 J K-1;
Relative atomic mass: C, 12; H, 1.
[6 marks]


2. (a) Define the stress relaxation modulus G(t) of a linear viscoelastic polymer.
[3 marks]

(b) Sketch, with as much detail as possible, the stress relaxation modulus curve of a
typical amorphous polymer as a function of log(time). Mark the “unrelaxed” and
“relaxed” relaxation moduli, and relaxation time on the sketch. [5 marks]

(c) Describe how the G(t) curve above would change at an increased temperature.
[2 marks]

(d) Describe the Boltzmann superposition principle, (which is useful e.g. in predicting
the strain induced in a linear viscoelastic polymer by applied stress that is
changing with time). [4 marks]

(e) The creep compliance of a linear viscoelastic polymer D(t) is given by
D(t) = (2.0 – exp(–0.10t)) GPa-1
Where time t is in hours. A stress of 1 MPa is applied at time t = 0 and then
removed at t = 10 hours. Calculate the strains at t = 5 hours and t = 15 hours
respectively. [6 marks]

TURN OVER
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3. (a) Draw the Zener (Standard linear solid) model of a linear viscoelastic polymer,
using spring(s) and dashpot(s) as its components. [4 marks]

(b) Use the Zener model, and how its parameters change with temperature, to
explain the temperature dependence of the relaxation time of linear viscoelastic
polymers, and the origin of the shift factor. [4 marks]

(c) The shift factor of a polymer with a glass transition temperature Tg = 250 K, can
be calculated using the WLF equation below:

= −
17.4(−)
51.6+(−)


Use the equation to calculate the shift factors for the polymer at 300 K and 350K
respectively. [4 marks]

(d) A creep experiment of the polymer in the previous section is carried out at 350 K
for 1 h. What is the equivalent time needed for the same amount of strain to be
produced under the same stress applied, if the experiment is carried out at 300 K?
[4 marks]

(e) Describe the time-temperature superposition principle of viscoelastic polymers.
How can it be used for predicting the viscoelastic behaviour of polymers at
temperatures and time scales that are not easily accessible experimentally?
[4 marks]



4. (a) Describe the differences in molecular structure between linear and branched low
density polyethylene. [4 marks]

(b) Explain why linear low density polyethylene has lower crystallinity, smaller crystal
size and better strength, which makes it a better candidate for thin transparent
films. [4 marks]

(c) Describe how the melt flow index of a polymer is measured. [3 marks]

(d) For different PE grades of the same crystallinity, describe how and explain why
the strength of the material is linked to its melt flow index. [4 marks]

(e) Taking PVC as an example, describe the external plasticisation process.
[3 marks]

(f) Describe how you choose plasticisers for PVC on the basis of their solubility
parameters for better resilience properties [2 marks]

CONTINUED


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5. (a) Describe how high Impact polystyrene (HIPS) is synthesized, and the chemical
components in the final product. [5 marks]

(b) Describe the typical morphology of HIPS observed under the microscope, and
how it arises from interactions of different components of the polymer.
[5 marks]

(c) On the basis of your answers to questions (a) and (b), explain the rubber
toughening mechanism in HIPS. [4 marks]

(d) Name another possible rubber toughening mechanism, and a polymer where
such a mechanism takes place. [2 marks]

(e) PET soft drink bottles are typically manufactured by injection moulding, followed
by stretch blow moulding. Explain how the crystallisation process is controlled in
the process, in terms of nucleation and crystal growth. [4 marks]



6. (a) Isotactic polypropylene (iPP) has a melting point of Tm ~ 170 °C, and a glass
transition temperature Tg ~ -10 °C. Draw schematically the rate of crystallisation
as a function of crystallisation temperature on cooling from the melt. Explain the
curve using the temperature dependence of the rate of nucleation and the rate of
crystal growth. [5 marks]

(b) On the basis of the curve you drew in answer to (a), explain briefly why iPP has
a high “after shrinkage” in injection moulding, and cannot be considered as a true
engineering polymer. [3 marks]

(c) What modifications can be made to the processing of iPP to reduce such “after
shrinkage” effects? [3 marks]

(d) Draw schematically the shear stress ̇ as a function of shear strain rate ̇ for a
polymer melt. Explain the molecular origin of the shear thinning phenomenon.
[5 marks]

(e) Explain, including examples, how the introduction of aromatic groups into the
polymer molecular backbone can produce better mechanical and processing
properties for structural applications. [4 marks]


END OF QUESTION PAPER


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