Computer simulation of the entropy of continuum chain models: The two-dimensional freely jointed chain of hard disks

Abstract

A method for estimating the entropy of polymer chains from a sample of conformations has recently been proposed by Meirovitch and has been applied, up to now, only to lattice chain models. In this paper, the method is extended to continuum chains and applied to a two-dimensional model with excluded volume, the freely jointed chain of hard disks. As in the case of lattice models, the method is based on scanning ‘‘future’’ partial chains of b bonds (steps); however, it is necesary to approximate the continuum of directions of a bond by a finite number of directions l selected at random. Linear chains with a different number of bonds N, from N=11 to 35, are generated by the direct Monte Carlo (DMC) procedure, and their entropy is calculated by the present method. The results for the entropy are found to be very accurate, as compared to those obtained from an asymptotically exact formula based on the DMC procedure; even for the worst approximation of b=1 and l=3, for N=35, the error is only 1%. This provides strong suggestive evidence that the method can be employed for estimating the entropy of longer chains as well as that of much more complex chain molecules such as polypeptides and proteins.