Materials Science and Engineering. An Introduction

William D. Callister

Chapter 14

Polymer Structures - all with Video Answers

Educators

Chapter Questions

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).

Ameer Said

Ameer Said

Numerade Educator

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).

Ameer Said

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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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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 .

Ameer Said

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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.
$$
\begin{array}{ccc}
\hline \begin{array}{c}
\text { Molecular Weight } \\
\text { Range }(\mathrm{g} / \text { mol })
\end{array} & \boldsymbol{x}_{\boldsymbol{i}} & \boldsymbol{w}_{\boldsymbol{i}} \\
\hline 10,000-20,000 & 0.03 & 0.01 \\
20,000-30,000 & 0.09 & 0.04 \\
30,000-40,000 & 0.15 & 0.11 \\
40,000-50,000 & 0.25 & 0.23 \\
50,000-60,000 & 0.22 & 0.24 \\
60,000-70,000 & 0.14 & 0.18 \\
70,000-80,000 & 0.08 & 0.12 \\
80,000-90,000 & 0.04 & 0.07 \\
\hline
\end{array}
$$

Ameer Said

Numerade Educator

Problem 6

Molecular weight data for some polymer are tabulated here. Compute (a) the numberaverage 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?
$$
\begin{array}{ccc}
\hline \begin{array}{c}
\text { Molecular Weight } \\
\text { Range }(\mathrm{g} / \text { mol })
\end{array} & \boldsymbol{x}_{\boldsymbol{i}} & \boldsymbol{w}_{\boldsymbol{i}} \\
\hline 8,000-20,000 & 0.05 & 0.02 \\
20,000-32,000 & 0.15 & 0.08 \\
32,000-44,000 & 0.21 & 0.17 \\
44,000-56,000 & 0.28 & 0.29 \\
56,000-68,000 & 0.18 & 0.23 \\
68,000-80,000 & 0.10 & 0.16 \\
80,000-92,000 & 0.03 & 0.05 \\
\hline
\end{array}
$$

Ameer Said

Numerade Educator

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

Ameer Said

Numerade Educator

Problem 8

High-density polyethylene may be chlorinated by inducing the random substitution of chlorine atoms for hydrogen.
(a) Determine the concentration of Cl (in $\mathrm{wt} \%$ ) 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)?

Ameer Said

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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.

Ameer Said

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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 $r=15 \mathrm{~nm}$.

Ameer Said

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Problem 11

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

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Problem 12

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

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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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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?

Ameer Said

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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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Problem 16

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

Ameer Said

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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 .

Ameer Said

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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?

Khoobchandra Agrawal

Khoobchandra Agrawal

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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,

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Problem 20

Crosslinked copolymers consisting of $35 \mathrm{wt} \%$ ethylene and $65 \mathrm{wt} \%$ 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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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.

Ameer Said

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Problem 22

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

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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.

Ameer Said

Numerade Educator

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, $V_{\text {tri }}$, is a function of these lattice parameters as
determine the number of repeat units per unit cell.

Ameer Said

Numerade Educator

Problem 25

The density and associated percent crystallinity for two poly(ethylene terephthalate) materials are as follows:
$$
\begin{array}{cc}
\hline \boldsymbol{\rho}\left(\mathrm{g} / \mathrm{cm}^{\mathbf{3}}\right) & \text { Crystallinity } \mathbf{( \% )} \\
\hline 1.408 & 74.3 \\
1.343 & 31.2 \\
\hline
\end{array}
$$
(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 $1.382 \mathrm{~g} / \mathrm{cm}^3$.

Manik Pulyani

Numerade Educator

Problem 26

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

Manik Pulyani

Numerade Educator

Problem 27

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

Ameer Said

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Problem 28

Carbon dioxide diffuses through a high density polyethylene (HDPE) sheet 50 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 kPa and 2500 kPa , which are maintained constant. Assuming conditions of steady state, what is the permeability coefficient at 325 K ?

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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 mm thick. The water vapor pressures at the two faces are 20 kPa and 1 kPa , which are maintained constant. Compute the diffusion flux [in $\left(\mathrm{cm}^3 \mathrm{STP}\right) / \mathrm{cm}^2$-s] at 350 K ? For this diffusion 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.

Ameer Said

Numerade Educator