Monte Carlo description of A_f homopolymerization: Diffusional effects

We have developed a new algorithm that simulates the structure buildup process during homopolymerization of A_f monomers. The algorithm is an off lattice percolation solution on a cube with periodic boundary conditions. All monomers are treated as point particles. After choosing any two nodes at random, the probability of their reaction is computed and compared with a random number. We present results where the probability rule is a step function over the interunitary distance between the chosen pair. We reason that this simulates, in a simplistic but effective fashion, the importance of diffusion vs reaction times in the problem. Thus, the case where units react in immediate neighborhoods corresponds to a diffusion limited growth and where they react with equal probability with all other units to the mean field or kinetic limited growth. We present results for five step reactive potentials with careful analysis of finite size effects. We find that the gel conversion is delayed as a consequence of diffusion limitations. We find that cyclization is only partially responsible for this effect. We also find that small mobilities, such as might be available from rotational and translational degrees of freedom, give results realistically close to the mean-field results, thus explaining the experimental success of the mean-field theory. We find that the (effective) scaling exponent γ depends on the reactive radius and thus on diffusion. It is not entirely clear to us if this suggests nonuniversal behavior or is simply a crossover problem. We conclude that the dependence of the critical exponent on diffusion over a wide range of conversions suggests that some of the "nonuniversal" experimental observations might be due to diffusional effects.