Probability distribution of the radius of gyration of freely jointed chains.
In this paper, we present a new approach to study the probability distribution of the radius of gyration of freely jointed chains. In this approach, we study the joint distribution P(N)(R(g) (2),R(G)), where R(g) is the radius of gyration and R(G) is the vector from the first bead to the center of the chain. We derive an iteration relation between the probability distributions of chains with lengths N and N+1. When the chain length is large, the iteration relation can be approximated by an evolution equation with integral determining condition. The equation is solved to obtain the probability distribution function, which yields the known result obtained by Fixman [J. Chem. Phys. 36, 306 (1962)] using the integral method. We hope the iteration method in this paper could be used to study the probability distribution of the structure factor of polymer molecules.
Lei
Jinzhi
J
Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing 100084, China. jzlei@mail.tsinghua.edu.cn