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

The validity of the Monte Carlo simulation for studying the dynamics of a R ouse 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 Mont e Carlo simulation is used to calculate the dynamic functions associated wi th the bond vector b(t) or direction u(t)=b(t)/\b(t)\ of an elastic dumbbel l and a Rouse segment in a chain. The effect of chain connectivity on the m otions of a single Rouse segment is studied. In particular, it is shown tha t the dynamic function < P-2[u(0). u(t)]>(2) over a wide dynamic range, whi ch is the main region probed by the depolarized photon-correlation spectros copy, is basically independent of the values of N greater than or equal to 8 in agreement with the experimental results. Furthermore, the line shape o f the depolarized photon-correlation functions of the concentrated solution s (approximate to 60 wt. %) of polystyrene in cyclohexane at the theta poin t can be fully accounted for by including the effect of chain connectivity regardless of the crudeness of the Rouse segment relative to the chemical s tructure. From this study, the molecular weight for a Rouse segment of poly styrene in the concentrated solutions is estimated to be 1100, which is sli ghtly larger than the values m=780-900 obtained for polystyrene in the melt state by other methods. (C) 2000 American Institute of Physics. [S0021-960 6(00)50316-X].