Statistical Thermodynamics

12Helical Polymer

We apply what we learned in the preceding chapter to a helix‐forming polymer. The helicity, right‐handed or left‐handed, can be mapped onto a spin, and that is why we can consider the helicity in the Ising model (Section 12.1). Our interest is in how dominant one of the handedness is. There are experimental methods to estimate the mean helicity, which we review in Section 12.2. In the section that follows, we look at helical properties of the polymer consisting of repeat units that, on the average, have nearly zero handedness.

We learned in Section 11.5 two types of quenched local fields. Both types have a bearing on the polymer, which we examine in Section 12.4.

12.1 Helix‐Forming Polymer

Some polymers form a helix when dissolved in a solvent. There are two senses of the helix (see Figure 12.1). The sense is either right‐handed or left‐handed, named in the same way as screw threads are named. Nearly all screws we use are right‐handed; when turned clockwise, the screw moves forward. In a typical helical polymer, each turn consists of three or more repeat units of the polymer.

Figure 12.1 Two senses of helix. (a) Right‐handed helix, (b) left‐handed helix.

The helical polymers have either a predetermined helical sense or a dynamically reversible sense. Proteins and polypeptides have a predetermined sense, geometrically arranged by a chiral carbon in every residue ...