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Materials Science and Engineering: An Introduction

William D. Callister, Jr. David G. Rethwisch

Chapter 14

Polymer Structures - all with Video Answers

Educators

Chapter Questions

01:12

Problem 1

On the basis of the structures presented in this chapter, sketch repeat unit structures for the following polymers:
(a) polychlorotrifluoroethylene, and (b) poly(vinyl alcohol).

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03:22

Problem 2

Compute repeat unit molecular weights for the following: (a) polytetrafluoroethylene (b) poly(methyl methacrylate), (c) nylon 6,6 and (d) poly(ethylene terephthalate)

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01:33

Problem 3

The number-average molecular weight of a polystyrene is $500,000 \mathrm{g} / \mathrm{mol}$. Compute the degree of polymerization.

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01:53

Problem 4

(a) Compute the repeat unit molecular weight of polypropylene.
(b) Compute the number-average molecular weight for a polypropylene for which the degree of polymerization is 15,000

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02:26

Problem 5

Below, molecular weight data for a polytetrafluoroethylene material are tabulated. Compute (a) the number-average molecular weight, (b) the weight-average molecular weight, and (c) the degree of polymerization.

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02:56

Problem 6

Molecular weight data for some polymer are tabulated here. Compute (a) the number average molecular weight, and (b) the weight-average molecular weight. (c) If it is known that this material's degree of polymerization is $477,$ which one of the polymers listed in Table 14.3 is this polymer? Why?

$$\begin{array}{ccc}
\hline \text {Molecular Weight} & & \\
\text {Range }(\mathrm{g} / \mathrm{mol}) & \boldsymbol{x}_{\boldsymbol{i}} & \boldsymbol{w}_{\boldsymbol{i}} \\
\hline 8,000-20,000 & 0.05 & 0.02 \\
20,000-32,000 & 0.15 & 0.08 \\
32,000-44,000 & 0.21 & 0.17 \\
44,000-56,000 & 0.28 & 0.29 \\
56,000-68,000 & 0.18 & 0.23 \\
68,000-80,000 & 0.10 & 0.16 \\
80,000-92,000 & 0.03 & 0.05 \\
\hline
\end{array}$$

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02:16

Problem 7

Is it possible to have a poly(vinyl chloride) homopolymer with the following molecular weight data, and a degree of polymerization of $1120 ?$ Why or why not?
$$\begin{array}{ccc}
\hline \text {Molecular Weight} & & \\
\text {Range }(\mathrm{g} / \mathrm{mol}) & \boldsymbol{w}_{\boldsymbol{i}} & \boldsymbol{x}_{\boldsymbol{i}} \\
\hline 8,000-20,000 & 0.02 & 0.05 \\
20,000-32,000 & 0.08 & 0.15 \\
32,000-44,000 & 0.17 & 0.21 \\
44,000-56,000 & 0.29 & 0.28 \\
56,000-68,000 & 0.23 & 0.18 \\
68,000-80,000 & 0.16 & 0.10 \\
80,000-92,000 & 0.05 & 0.03 \\
\hline
\end{array}$$

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03:00

Problem 8

High-density polyethylene may be chlorinated by inducing the random substitution of chlorine atoms for hydrogen.
(a) Determine the concentration of $\mathrm{Cl}$ (in wt\%) that must be added if this substitution occurs for $8 \%$ of all the original hydrogen atoms. (b) In what ways does this chlorinated polyethylene differ from poly(vinyl chloride)?

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03:25

Problem 9

For a linear polymer molecule, the total chain length $L$ depends on the bond length between chain atoms $d$, the total number of bonds in the molecule $N$, and the angle between adjacent backbone chain atoms $\theta,$ as follows:
$$L=N d \sin \left(\frac{\theta}{2}\right)$$
Furthermore, the average end-to-end distance for a series of polymer molecules $r$ in Figure 14.6 is equal to
$$r=d \sqrt{N}$$
A linear polyethylene has a number-average molecular weight of $300,000 \mathrm{g} / \mathrm{mol} ;$ compute average values of $L$ and $r$ for this material

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03:50

Problem 10

Using the definitions for total chain molecule length, $L$ (Equation 14.11 ) and average chain end-to-end distance $r$ (Equation 14.12), for a linear polytetrafluoroethylene determine:
(a) the number-average molecular weight for $L=2000 \mathrm{nm}$
(b) the number-average molecular weight for $r=15 \mathrm{nm}$

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04:29

Problem 11

Sketch portions of a linear polypropylene molecule that are
(a) syndiotactic
(b) atactic, and (c) isotactic.

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02:51

Problem 12

Sketch cis and trans structures for (a) butadiene, and (b) chloroprene.

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02:52

Problem 13

Make comparisons of thermoplastic and thermosetting polymers (a) on the basis of mechanical characteristics upon heating, and (b) according to possible molecular structures.

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01:38

Problem 14

(a) Is it possible to grind up and reuse phenol-formaldehyde? Why or why not?
(b) Is it possible to grind up and reuse polypropylene? Why or why not?

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02:50

Problem 15

Sketch the repeat structure for each of the following alternating copolymers: (a) poly (ethylene-propylene), (b) poly(butadienestyrene), and (c) poly(isobutylene-isoprene).

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01:24

Problem 16

The number-average molecular weight of a poly(acrylonitrile-butadiene) alternating copolymer is 1,000,000 g/mol; determine the average number of acrylonitrile and butadiene repeat units per molecule.

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03:12

Problem 17

Calculate the number-average molecular weight of a random poly(isobutyleneisoprene) copolymer in which the fraction of isobutylene repeat units is $0.25 ;$ assume that this concentration corresponds to a degree of polymerization of 1500

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04:15

Problem 18

An alternating copolymer is known to have a number-average molecular weight of 100,000 $\mathrm{g} / \mathrm{mol}$ and a degree of polymerization of 2210 If one of the repeat units is ethylene, which of styrene, propylene, tetrafluoroethylene, and vinyl chloride is the other repeat unit? Why?

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04:53

Problem 19

(a) Determine the ratio of butadiene to acrylonitrile repeat units in a copolymer having a number-average molecular weight of $250,000 \mathrm{g} / \mathrm{mol}$ and a degree of polymerization of 4640
(b) Which type(s) of copolymer(s) will this copolymer be, considering the following possibilities: random, alternating, graft, and block? Why?

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03:40

Problem 20

Crosslinked copolymers consisting of 35 wt $\%$ ethylene and 65 wt\% propylene may have elastic properties similar to those for natural rubber. For a copolymer of this composition, determine the fraction of both repeat unit types.

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03:00

Problem 21

A random poly(styrene-butadiene) copolymer has a number-average molecular weight of $350,000 \mathrm{g} / \mathrm{mol}$ and a degree of polymerization of 5000 . Compute the fraction of styrene and butadiene repeat units in this copolymer.

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00:57

Problem 22

Explain briefly why the tendency of a polymer to crystallize decreases with increasing molecular weight.

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02:33

Problem 23

For each of the following pairs of polymers, do the following: (1) state whether or not it is possible to determine whether one polymer is more likely to crystallize than the other; (2) if it is possible, note which is the more likely and then cite reason(s) for your choice; and (3) if it is not possible to decide, then state why.
(a) Linear and atactic poly(vinyl chloride); linear and isotactic polypropylene.
(b) Linear and syndiotactic polypropylene; crosslinked cis-isoprene.
(c) Network phenol-formaldehyde; linear and isotactic polystyrene.
(d) Block poly(acrylonitrile-isoprene) copolymer; graft poly(chloroprene-isobutylene) copolymer.

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04:32

Problem 24

The density of totally crystalline nylon 6,6 at room temperature is $1.213 \mathrm{g} / \mathrm{cm}^{3} .$ Also, at room temperature the unit cell for this material is triclinic with lattice parameters
$$\begin{array}{ll}
a=0.497 \mathrm{nm} & \alpha=48.4^{\circ} \\
b=0.547 \mathrm{nm} & \beta=76.6^{\circ} \\
c=1.729 \mathrm{nm} & \gamma=62.5^{\circ}
\end{array}$$
If the volume of a triclinic unit cell, $V_{\mathrm{tri}}$, is a function of these lattice parameters as
$$\begin{aligned}
&V_{\mathrm{tri}}=a b c \sqrt{1-\cos ^{2} \alpha-\cos ^{2} \beta-\cos ^{2} \gamma+}\\
&2 \cos \alpha \cos \beta \cos \gamma
\end{aligned}$$
determine the number of repeat units per unit cell.

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06:35

Problem 25

The density and associated percent crystallinity for two poly(ethylene terephthalate) materials are as follows: $$\begin{array}{cc}
\hline \rho\left(g / c m^{3}\right) & \text { Crystallinity (\%) } \\
\hline 1.408 & 74.3 \\
1.343 & 31.2 \\
\hline
\end{array}$$
(a) Compute the densities of totally crystalline and totally amorphous poly(ethylene terephthalate).
(b) Determine the percent crystallinity of a specimen having a density of $1.382 \mathrm{g} / \mathrm{cm}^{3}$

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07:01

Problem 26

The density and associated percent crystallinity for two polypropylene materials are as follows:
$$\begin{array}{cc}
\hline \rho\left(g / c m^{3}\right) & \text {Crystallinity (\%)} \\
\hline 0.904 & 62.8 \\
0.895 & 54.4 \\
\hline
\end{array}$$
(a) Compute the densities of totally crystalline and totally amorphous polypropylene.
(b) Determine the density of a specimen having $74.6 \%$ crystallinity.

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03:04

Problem 27

Consider the diffusion of oxygen through a low density polyethylene (LDPE) sheet $15 \mathrm{mm}$ thick. The pressures of oxygen at the two faces are $2000 \mathrm{kPa}$ and $150 \mathrm{kPa}$, which are maintained constant. Assuming conditions of steady state, what is the diffusion flux $\left[\text { in }\left(\mathrm{cm}^{3} \mathrm{STP}\right) / \mathrm{cm}^{2}-\mathrm{s}\right]$ at $298 \mathrm{K} ?$

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03:15

Problem 28

Carbon dioxide diffuses through a high density polyethylene (HDPE) sheet $50 \mathrm{mm}$ thick at a rate of $2.2 \times 10^{-8}\left(\mathrm{cm}^{3} \mathrm{STP}\right) / \mathrm{cm}^{2}-\mathrm{s}$ at
325 K. The pressures of carbon dioxide at the two faces are $4000 \mathrm{kPa}$ and $2500 \mathrm{kPa}$, which are maintained constant. Assuming conditions of steady state, what is the permeability coefficient at $325 \mathrm{K} ?$

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03:26

Problem 29

The permeability coefficient of a type of small gas molecule in a polymer is dependent on absolute temperature according to the following equation:
$$P_{M}=P_{M_{0}} \exp \left(-\frac{Q_{p}}{R T}\right)$$
where $P_{M_{0}}$ and $Q_{p}$ are constants for a given gas-polymer pair. Consider the diffusion of water through a polystyrene sheet $30 \mathrm{mm}$ thick. The water vapor pressures at the two faces are $20 \mathrm{kPa}$ and $1 \mathrm{kPa}$, which are maintained constant. Compute the diffusion flux $\left[\text { in }\left(\mathrm{cm}^{3} \mathrm{STP}\right) / \mathrm{cm}^{2}-\mathrm{s}\right]$ at $350 \mathrm{K} ?$ For this dif-
fusion system
$$\begin{aligned}
P_{M_{0}} &=9.0 \times 10^{-5}\left(\mathrm{cm}^{3} \mathrm{STP}\right) / \mathrm{cm}^{2}-\mathrm{s}-\mathrm{Pa} \\
Q_{p} &=42.3 \mathrm{kJ} / \mathrm{mol}
\end{aligned}$$
Also, assume a condition of steady state diffusion.

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