Valence Angle Model with Hindered Rotation

Figure 9.9: Valence Angle Model with Hindered Rotation

Source: Lauren Zarzar

In the valence angle model, we initially assumed that single bonds can freely rotate. But we know that not all orientations are created equal (recall Newman projections?) How can we account for that? In the valence angle model with hindered rotation, we not only account for the bond angles but also account for the fact that single bonds do not freely rotate to any angle, and depending on the substituents on the polymer, some bonds may be more hindered than others. We thus define the mean square end to end distance with a subscript of “0” meaning hindered rotation round a fixed bond angle:

$${\langle r^2\rangle }_0={\sigma }^{2}n{l}^2\frac{1-\cos \theta }{1+\cos \theta }$$

Notice we have introduced a new variable, σ, which is called the steric parameter. Steric parameters are usually determined experimentally from measured values of ${\langle r^2\rangle }_0$. The steric parameter represents how stiff or flexible the polymer is. A stiffer polymer with more hindered rotation will have a high steric parameter, and a more flexible polymer with freer rotation will have a lower steric parameter.

PROBLEM

Which polymer would you expect to have the highest steric parameter σ at a given temperature?

Click here for the answer.

ANSWER

B. The bulkiest substituent will give the most hindered rotation and largest steric parameter.