Callister - An introduction - 8th edition

M w
542 • Chapter 14 / Polymer Structures
Weight-average,
Figure 14.4 Distribution of molecular
Number-average, M n
weights for a typical polymer.
Amount of polymer
Molecular weight
Weight-average
molecular weight
degree of
polymerization
Degree of
polymerization—
dependence on
number-average
and repeat unit
molecular weights
A weight-average molecular weight M w is based on the weight fraction of molecules
within the various size ranges (Figure 14.3b). It is calculated according to
M w ©w i M i
(14.5b)
where, again, M i is the mean molecular weight within a size range, whereas w i denotes
the weight fraction of molecules within the same size interval. Computations
for both number-average and weight-average molecular weights are carried out in
Example Problem 14.1. A typical molecular weight distribution along with these
molecular weight averages is shown in Figure 14.4.
An alternate way of expressing average chain size of a polymer is as the degree
of polymerization, DP, which represents the average number of repeat units in a
chain. DP is related to the number-average molecular weight by the equation
DP M n
m
where m is the repeat unit molecular weight.
M n
(14.6)
EXAMPLE PROBLEM 14.1
Computations of Average Molecular Weights and
Degree of Polymerization
Assume that the molecular weight distributions shown in Figure 14.3 are for
poly(vinyl chloride). For this material, compute (a) the number-average molecular
weight, (b) the degree of polymerization, and (c) the weight-average
molecular weight.
Solution
(a) The data necessary for this computation, as taken from Figure 14.3a, are
presented in Table 14.4a. According to Equation 14.5a, summation of all the
x i M i products (from the right-hand column) yields the number-average
molecular weight, which in this case is 21,150 g/mol.