GATE 2021 Question Paper XE F Engineering Sciences - Polymer Science and Engineering

Polymer Science and Engineering (XE-F)

Q.1 - Q.9 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong
answer: – 1/3).

Q.1 Linear low density polyethylene (LLDPE) is a copolymer of ethylene and a
small fraction of _______.

(A) butadiene

(B) isoprene

(C) butene

(D) hexadiene

Q.2 Binary polymer blends of polypropylene and polyamide 6 are immiscible.
From a thermodynamic viewpoint this is due to ___________.

(A) low enthalpy of mixing

(B) high entropy of mixing

(C) high enthalpy of mixing

(D) low entropy of mixing

Q.3 Which one of the following is an elastomer?

(A) Polyamide 6,6

(B) Poly(ethylene terepthalate)

(C) Vulcanized polybutadiene

(D) High density polyethylene

XE(F) - Copyright © GATE 2021 Page 1 of 7

Q.4 Compression moulded isotropic polypropylene film exhibits
________________ in X-ray diffraction analysis.

(A) spot pattern

(B) circular ring pattern

(C) circular ring and spot pattern

(D) arc pattern

Q.5 Which one of the following is an example of a biodegradable polymer?

(A) Polyethylene

(B) Polyamide 6,6

(C) Polypropylene

(D) Polylactic acid

Q.6 Polymer crystals show a range of melting points in contrast to single
melting point of crystals of small molecules, because ________.

(A) there is an absence of intermolecular interactions

(B) there is an absence of long range ordering

(C) the polymer chains are not in thermodynamic equilibrium in a metastable state

(D) the melting behavior of polymer crystal is independent of sample thermal
history

Q.7 When the rate of cooling is increased during the solidification process, the
glass transition temperature of a polymer ______.

(A) decreases

(B) increases

(C) stays unaltered

(D) shows a non-monotonic dependence

XE(F) - Copyright © GATE 2021 Page 2 of 7

Q.8 Equal and opposite forces of a constant magnitude F are applied at the two
ends of a thin elastomeric rod, which is held at a temperature T1 (Tg < T1 <
Tm), where Tg and Tm are the glass transition temperature and melting
temperature respectively. If the temperature is increased to T2 (Tg < T2 <
Tm and T2 > T1), the rod will _______________.

(A) expand along the loading direction and the transverse direction

(B) shrink along the loading direction

(C) remain dimensionally unaltered

(D) expand only along the loading direction

Q.9 The size of a coiled polymer chain in a dilute solution is RG in a good
solvent, RI in an ideal solvent and RP in a poor solvent. Select the correct
ordering of sizes.

(A) RG > RI > RP

(B) RG < RI < RP

(C) RP > RG > RI

(D) RP < RG < RI

XE(F) - Copyright © GATE 2021 Page 3 of 7

Q. 10 – Q. 12 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong
answer: – 2/3).

Q. 10 Match the Additive to its Function.

Additive Function

P. Tritolyl phosphate 1. Coupling Agent

Q. Triethoxy vinyl silane 2. Antioxidant

R. Azoisobutyronitrile 3. Plasticizer

S. 4-Methyl-2,6-di-t-butyl phenol 4. Blowing Agent

(A) P-3, Q-2, R-1, S-4

(B) P-3, Q-1, R-4, S-2

(C) P-4, Q-1, R-3, S-2

(D) P-1, Q-2, R-4, S-3

Q. 11 Match the polymer processing operation with respect to its typical range of
shear rate.

Processing Operation Shear rate (s-1)

P. Compression Moulding 1. 1000 - 10000

Q. Extrusion 2. 100 - 1000

R. Calendering 3. 1 - 10

S. Injection Moulding 4. 10 - 100

(A) P-3, Q-4, R-2, S-1

(B) P-1, Q-3, R-2, S-4

(C) P-2, Q-4, R-3, S-1

(D) P-3, Q-2, R-1, S-4

XE(F) - Copyright © GATE 2021 Page 4 of 7

Q. 12 Shear stress (𝝈) and shear viscosity (𝜼) are plotted as functions of the shear
rate, 𝜸̇ , for idealized “solid-like with yielding (1)” and “liquid-like (2)”
materials.

P
R

Q
σ η
S

𝜸̇ 𝜸̇

Associate the shear stress and viscosity plots with the appropriate material
responses.

(A) P-2, Q-1, R-2, S-1

(B) P-1, Q-2, R-1, S-2

(C) P-1, Q-2, R-2, S-1

(D) P-2, Q-1, R-1, S-2

XE(F) - Copyright © GATE 2021 Page 5 of 7

Q. 13 – Q. 22 Numerical Answer Type (NAT), carry TWO marks each (no negative
marks).

Q. 13 The plateau modulus of polystyrene has a value of 0.2  106 Pa at 150 °C.
Given, the density of polystyrene is 1.05 g/cm3, the universal gas constant,
R = 8.3 J K-1 mol-1, and the monomer molecular weight is 104 g/mol. The
molecular weight between entanglements (rounded off to the nearest
integer) of polystyrene chains is _____________ g/mol.

Q. 14 A unidirectional composite of epoxy and carbon fiber of 50% by volume is
made. The elastic modulus of epoxy and carbon fiber are 3.5 GPa and 350
GPa, respectively. The ratio (rounded off to one decimal place) of the
modulus of the composite to the matrix modulus is __________.

Q. 15 A single screw extruder is operating at a rotational speed of 2 revolutions
per second for the extrusion of a Newtonian polymer under open-discharge
conditions (in absence of a die, the pressure drop, ∆p = 0). The extruder has
a screw diameter, D = 5 cm, a channel depth, H = 0.4 cm, distance between
flights, W = 1 cm, and a helix angle, θ = 20°. Assume the value of  =
3.14. The volumetric flow rate (rounded off to 2 decimal places) is
____________ cm3/s.

Q. 16 At 215 oC, the viscosity of a polystyrene of molecular weight 250  103
g/mol is 8.0  103 Pa.s. The critical molecular weight of polystyrene, Mc =
35  103 g/mol. For a similar polystyrene of molecular weight 500  103
g/mol, the viscosity (rounded off to nearest integer) will be __________  103
Pa.s.

Q. 17 There are two different PTFE polymer specimens of the following density
() and % crystallinity. For PTFE-specimen-1,  is 2.144 g/cm3 and %
crystallinity is 50. For PTFE- specimen-2,  is 2.215 g/cm3 and %
crystallinity is 75. Assuming the polymer is pure and defect free, the
density (rounded off to 3 decimal places) of 100% amorphous PTFE
specimen will be _______ g/cm3.

XE(F) - Copyright © GATE 2021 Page 6 of 7

Q. 18 The behavior of a polymer is described by a Maxwell model consisting of a
spring element of modulus 1010 Pa in series with a dashpot of viscosity 1012
Pa.s. In the solid, 50 s after the sudden application of a fixed strain of 1%,
the stress (rounded off to 2 decimal places) will be _________  107 Pa.

Q. 19 A particular free radical polymerization process yields a polymer with a
number averaged degree of polymerization, 𝒙 ̅𝒏 = 𝟏𝟎𝟎. The monomer
concentration is doubled and the initiator concentration is increased by
four times. Assuming that all rate coefficients and other parameters remain
unchanged, the value of 𝒙̅𝒏 (rounded off to the nearest integer) is
___________.

Q. 20 A polymer is synthesized from 2 moles of terephthalic acid (molecular
weight of the repeat unit, (-OCC6 H4 CO-), is 132 g/mol), 1 mol of ethylene
glycol (molecular weight of the repeat unit, (-OCH2 CH2 O-), is 60 g/mol), and
1 mol of butylene glycol (molecular weight of the repeat unit, (-O(CH2)4O-),
is 88 g/mol). The reaction is terminated at 99% conversion of the acid. The
number averaged molecular weight, 𝑴 ̅ 𝒏 (rounded off to the nearest integer)
is _________ g/mol.

Q. 21 A sample of natural rubber (cis-1,4-polyisoprene) is vulcanized such that
one of every 240 chain carbon atoms is cross-linked. The formula unit of
the isoprene monomer is C5 H8 (molecular weight = 68 g/mol). The average
molecular weight (rounded off to the nearest integer) between cross-links is
___________ g/mol.

Q. 22 A sample of an oriented semi-crystalline polymer is subjected to uniaxial
tensile stress, σ, in an X-ray diffractometer. The wavelength of X-ray
radiation (Cu K α) is λ = 1.542 Å. The position of the (002) peak, which was
found initially at a Bragg angle of 37.50° at σ = 0 MPa shifted to 37.45° at σ
= 160 MPa. Assuming elastic deformation, the strain (rounded off to three
decimal places) in the sample along the direction of applied stress is
__________ × 𝟏𝟎−𝟑.

END OF THE QUESTION PAPER

XE(F) - Copyright © GATE 2021 Page 7 of 7