Dynamic Monte Carlo Study of the Conformational Properties of Long Flexible Polymers .

In this paper we present results of Monte Carlo (MC) studies of long-chain polymers confined to a diamond lattice in which both repulsive and attractive interactions have been included. The hard-core repulsive part of the segment-segment interaction is modeled by the exclusion of multiple occupancy of lattice sites. Attractive inter- actions, t,, are associated with every pair of nonbonded nearest-neighbor segments. No preference for any of the three possible (one trans, t, and two gauche, g) rotational states of every internal bond is assumed. Thus the chain stiffness results only from lattice restrictions. The polymer occupies n lattice vertices, connected by n - 1 bonds; n - 3 conformational states define the chain conformation. A dynamic sampling method has been used, incorpo- rating reptation type and 3-bond kink motions of the chain backbone, together with 2-bond random flips of the chain ends. The details of the sampling procedure are similar to those in ref 1. We performed simulations on chains of length n = 100,200,400, and 800. The reduced temper- ature T* = kBT/t, was varied from infinity (the case of an athermal self-avoiding walk (SAW)) to unity, which is well below both the @point and the collapse transition. At a given P, (2-6) X lo6 ((1.5-4.5) X lo') iterations (one attempt at a reptation step plus several attempts at kink flips) have been performed for chains of n = 100 (800). Depending on n, the conformation of the polymer has been analyzed every 100-1000 cycles of the MC algorithm. Hence from 2 X lo4 to 6 X lo4 relatively independent "measurements" contributed to the ensemble averages, which were calculated as the appropriately weighted arithmetic mean of the quantity of interest. For some sets of the model parameters (n, P), the standard deviations from the mean have been evaluated on the basis of runs obtained with different streams of pseudo random num- bers.