Statistical properties of multi-theta polymer chains

Abstract

We study statistical properties of polymer chains with complex structures whose chemical connectivities are expressed by graphs. The multi-theta curve of m subchains with two branch points connected by them is one of the simplest graphs among those graphs having closed paths, i.e. loops. We denoted it by , and for m = 2 it is given by a ring. We derive analytically the pair distribution function and the scattering function for the -shaped polymer chains consisting of m Gaussian random walks of n steps. Surprisingly, it is shown rigorously that the mean-square radius of gyration for the Gaussian -shaped polymer chain does not depend on the number m of subchains if each subchain has the same fixed number of steps. For m = 3 we show the Kratky plot for the theta-shaped polymer chain consisting of hard cylindrical segments by the Monte-Carlo method including reflection at trivalent vertices.