Brownian motion with stiff bonds and rigid constraints

Abstract

Brownian systems with stiff elastic bonds of nearly constant length, such as long chain polymer molecules, behave differently when the stiff bonds are replaced by rigid bonds of exactly constant length, i.e. in statistical mechanics real stiff systems cannot be idealized by theoretical rigid ones. It is shown that a potential force can be applied to the rigidly constrained system in order to make it behave like the limit of a very stiff elastic system. A simple explicit expression for the required potential, suitable for computer simulations of the Brownian motion, is given for general constraints and also in the particular case of a trumbbell or trimer.