Statistical mechanics of helical wormlike chains. VII. Continuous limits of discrete chains

A discrete chain which tends to the helical wormlike chain in the continuous limit is studied. For this purpose, the physics of a generalized continuous chain is considered from the point of view of the theory of elasticity, and it is pointed out that the helical wormlike chain should be distinguished from the true Bugl–Fujita chain, which has the regular helix extreme but not the true wormlike case. Then, a hypothetical discrete chain corresponding to the generalized continuous chain is found. In particular, it is shown that the helical wormlike chain is a special limit of this discrete chain with coupled rotations of some kind, while the Bugl–Fujita chain is that of the chain with independent rotations. The derivation of the differential equation for the Green’s function for the generalized chain is discussed rather in detail in the Appendix.