Fundamentals of Materials Science and Engineering: An Integrated Approach, 3e

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4.5 Molecular Weight • 107

Amount of polymer

Molecular weight

Number-average, Mn

Weight-average, Mw

Figure 4.4 Distribution of molecular

weights for a typical polymer.

degree of An alternative way of expressing average chain size of a polymer is as thedegree

polymerization of polymerization,DP, which represents the average number of repeat units in a

chain.DPis related to the number-average molecular weightMnby the equation

DP=

Mn

m

(4.6)

Degree of

polymerization—

dependence on

number-average and

repeat unit molecular

weights

wheremis the repeat unit molecular weight.

EXAMPLE PROBLEM 4.1

Computations of Average Molecular Weights and Degree

of Polymerization

Assume that the molecular weight distributions shown in Figure 4.3 are for

poly(vinyl chloride). For this material, compute(a)the number-average molec-

ular weight,(b)the degree of polymerization, and(c)the weight-average molec-

ular weight.

Solution

(a)The data necessary for this computation, as taken from Figure 4.3a, are

presented in Table 4.4a. According to Equation 4.5a, summation of all the

Table 4.4a Data Used for Number-Average Molecular

Weight Computations in Example Problem 4.1

Molecular Weight Mean Mi

Range(g/mol)(g/mol) xi xiMi

5,000–10,000 7,500 0.05 375

10,000–15,000 12,500 0.16 2000

15,000–20,000 17,500 0.22 3850

20,000–25,000 22,500 0.27 6075

25,000–30,000 27,500 0.20 5500

30,000–35,000 32,500 0.08 2600

35,000–40,000 37,500 0.02 750

Mn = 21,150