1) Discuss numerous methods to characterize the properties of polymers and of the materials
formed by polymers.
Match each of the scenarios below with the most appropriate technique by choosing a method from
the box below, and explain your answer. Each method may be matched to only one scenario, so
choose wisely!
a) You are measuring the properties of fibers of poly(paraphenylene terephthalamide), branded
Kevlar, under mechanical stress. To determine how the crystalline orientation of the polymers
change with applied stress, what technique would be best? (4 points)
b) You have synthesized a block copolymer and need to assess the polydispersity of your
synthesized product. What technique would be best? (4 points)
c) You need to assess the structures of spherulites formed in a semicrystalline polypropylene
sample. What technique would be best? (4 points)
d) You need to determine the glass transition temperature of a sample of polycarbonate. What
technique would be best? (4 points)
e) You have fabricated a thin polymer membrane with 10 nm pores for filtration and need to assess
the uniformity of pore size. Which technique would be best? (4 points)
transmission electron microscopy (TEM), wide-angle X-ray scattering (WAXS),
gel permeation chromatography (GPC), atomic force microscopy (AFM),
differential scanning calorimetry (DSC)
MSE 151: Polymeric Materials Prof. Stacy Copp
UC Irvine Materials Science and Engineering
© Stacy Copp 2020

2. Improving strength with polymer blending. (18 points total)
   The figure below displays stress-strain curves for poly(lactic acid) (PLA, black), poly(methyl
   methacrylate) (PMMA, red), polybutadiene-g-poly(styrene-co-acrylonitrile) (PB-g-SAN, dark
   red), and blends of these polymers (green, pink, and blue curves). For each blend, the two polymers
   in the blend are separated by a slash (/).
   a) PLA is a biodegradable polymer which can be sourced from renewable feedstocks, but PLA
   has mechanical shortcomings, as shown by the black stress-strain curve above.
   (i) What type of failure is PLA exhibiting? (2 points)
   (ii) What does this suggest about the degree of crystallinity of PLA? In other words, is PLA
   likely to be amorphous or crystalline? (2 points)
   b) Which of the curves above is an elastomer? How can you tell? (4 points)
   c) Which of the polymer blends displays ductile deformation? How can you tell? (4 points)
   d) Estimate �!” and �!” at the onset of necking for the PMMA/PB-g-SAN blend. (4 points)
   e) DSC of both PLA and PLA/PB-g-SAN show a crystallization transition. Adding PMMA
   (which is amorphous) into the blend makes the material significantly more resistant to fracture.
   Given that the tri-blend PLA/PMMA/PB-g-SAN is more resistant to fracture, would you expect
   DSC measurements to observe a crystallization transition or not? (2 points)
   MSE 151: Polymeric Materials Prof. Stacy Copp
   UC Irvine Materials Science and Engineering
   © Stacy Copp 2020
   3) Polymeric materials: states of matter
   (19 points total)
   a) Crystalline and amorphous polymers.
   (i) Which graph corresponds to a semicrystalline polymeric material (right)?
   Explain your answers in the context of
   phase transition thermodynamics. (3 points)
   (ii) Which graph corresponds to an amorphous polymeric material? Explain your answers in the
   context of phase transition thermodynamics. (3 points)
   (iii) On graphs (1) and (2) above, mark the glass transition temperature Tg or the melting
   temperature Tm, depending on which is relevant for each type of polymeric material. (4 points)
   b) Rate of cooling. The graph to the right shows volume of a polymeric
   material as it is cooled from a liquid state to a glassy state at three
   different cooling rates a, b, and c.
   (i) Which curve corresponds to the slowest rate of cooling? How can you
   tell? (2 points)
   (ii) Why does V(T) depend on the cooling rate for glassy polymeric
   materials? (2 points)
   c) Thermal cycling. Consider a semi-crystalline polymeric material with crystallinity �# at
   temperature T1 below the melting temperature, Tm.
   (i) This polymer is heated up to T2 (T1 < T2 < Tm), and held at constant T2 for a certain time before
   cooling back to T1. On the graph below (or a graph you draw yourself), sketch �(�) for this
   polymeric material over the entire thermal cycle, from T1 to T2 and back to T1. (3 points)
   (ii) Does the final crystallinity increase or decrease after
   thermal cycling? Why? (2 points)
   MSE 151: Polymeric Materials Prof. Stacy Copp
   UC Irvine Materials Science and Engineering
   © Stacy Copp 2020
   4) Nucleation of polymer crystals. (22 points total) The change in free energy ∆� upon formation
   of a crystalline nucleus within an amorphous polymer is:
   ∆� = ��
   � (�$ − �#) + ��
   � and � are volume and surface area of the nucleus, respectively; � and � are density and
   molecular weight of the material, respectively; �# is molar free energy of the liquid polymer; �$
   is molar free energy of the crystalline polymer; � is coefficient of surface tension.
   Most polymers crystallize into thin layers like
   the diagram below of a square “lamella” with
   side length ℓ and thickness ℎ. Because the
   sides (shown by the green squiggly lines) and
   the top/bottom of the crystal have different
   crystalline planes, the coefficient of surface
   tension of the top and bottom, �%&’, differs from that of the sides, �()+. a) Write an expression for ∆� of this lamella in terms of ℓ and ℎ. (6 points) b) In this case, ∆� is a function of both ℓ and ℎ, and there exist some critical point(s) (ℓ∗, ℎ∗) for which ∆� is a local maximum. Derive the critical length and thickness of the nucleus, (ℓ∗, ℎ∗), and state which values of ℓ∗, ℎ∗ are physically relevant (8 points) c) Write an expression for the corresponding height of the energy barrier at this critical point, ∆�∗, in terms of �%&’ and �()+. (Simplify this expression – don’t just write a messy answer!) (4 points)
   d) Now write ∆�∗ in terms of ℓ∗ and/or ℎ∗. (Note: you can pick multiple ways to do this.) What
   does your expression tell you about how the height of the energy barrier relates to one of the terms
   in the expression for (a) above? (Hint: see lecture on this topic for example of how this was done
   for a spherical nucleus.) (4 points)
   MSE 151: Polymeric Materials Prof. Stacy Copp
   UC Irvine Materials Science and Engineering
   © Stacy Copp 2020
3. Polymer blends and composites. (16 pointstotal) Flory-Huggins theory can be used to describe
   how a polymer dissolves in a solvent (as discussed in lecture) and can also be used to predict
   whether two different polymers will form a miscible blend or will phase-separate upon mixing.
   a) What must be true about the change in Gibbs free energy upon blending two polymers if the
   two polymers are miscible? (3 points)
   b) Consider a mixture of n1 moles of polymer 1 with volume fraction �# and n2 moles of
   polymer 2 with volume fraction �$. Write the expression for the change in entropy ∆� upon
   mixing two polymers together. (3 points)
   c) For polymer blends, the enthalpy of mixing can be expressed as �#�$� (this differs slightly
   from the case of a polymer dissolved in a solvent). � is the Flory-Huggins parameter which
   describes the interaction between polymers 1 and 2. Write the expression for the change in Gibbs
   free energy upon mixing. (4 points)
   d) What is the sign (positive or negative) of the two entropic terms in ∆�? Why? (3 points)
   e) The point at which miscibility becomes possible for a polymer blend is called �-.)%. Derive an
   expression for �-.)% for polymers 1 and 2, using your answer from (c). (3 points)

Sample Solution

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