For a linear, freely rotating polymer molecule, the total chain length L depends on the bo...

For a linear, freely rotating 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 u, as follows:

Furthermore, the average end-to-end distance for a series of polymer molecules r in Figure 14.6 is equal to

A linear polyethylene has a number-average molecular weight of 300,000 g/mol; compute average values of L and r for this material.

Figure 14.6 Schematic representation of a single polymer chain molecule that has numerous random kinks and coils produced by chain bond rotations.

(From Physics of Rubber Elasticity, 2nd edition, by Treloar (1958), Fig. 3.3, p. By permission of Oxford University Press.)

Figure 3.3 For the simple cubic crystal structure, (a) a hard-sphere unit cell, and (b) a reduced-sphere unit cell.