Monte Carlo simulation of the motions associated with a single Rouse segment

Abstract

The validity of the Monte Carlo simulation for studying the dynamics of a Rouse chain with a finite number of beads, N, is established by showing the close agreement between the simulation results and the analytical solutions for the time-correlation function of the end-to-end vector. Then, the Monte Carlo simulation is used to calculate the dynamic functions associated with the bond vector b(t) or direction u(t)=b(t)/(t) of an elastic dumbbell and a Rouse segment in a chain. The effect of chain connectivity on the motions of a single Rouse segment is studied. In particular, it is shown that the dynamic function < P-2[u(0). u(t)]>(2) over a wide dynamic range, which is the main region probed by the depolarized photon-correlation spectroscopy, is basically independent of the values of N greater than or equal to 8 in agreement with the experimental results. Furthermore, the line shape of the depolarized photon-correlation functions of the concentrated solutions (approximate to 60 wt. %) of polystyrene in cyclohexane at the theta point can be fully accounted for by including the effect of chain connectivity regardless of the crudeness of the Rouse segment relative to the chemical structure. From this study, the molecular weight for a Rouse segment of polystyrene in the concentrated solutions is estimated to be 1100, which is slightly larger than the values m=780-900 obtained for polystyrene in the melt state by other methods. (C) 2000 American Institute of Physics. [S0021-9606(00)50316-X].