Enhanced Kinetics and Free-Volume Universality in Dense Aggregating Systems

Aggregation kinetics and cluster-size distributions are studied with off-lattice, diffusion-limited cluster-cluster simulations. With increased cluster crowding (occurring at late times) as measured by the normalized free volume, $\Omega$, both the kinetics speeds up and the size distribution broadens. The exponents characterizing each, $z$ and $\lambda$, respectively, are found to be universal functions of $\Omega$. Moreover, the relation $z=(1-\lambda {)}^{-1}$ continues to hold up to $\Omega =0$ (the ideal gel point), implying mean-field kinetics still applies despite the crowding.