Irreversible Growth Algorithm for Branched Polymers (Lattice Animals), and Their Relation to Colloidal Cluster-Cluster Aggregates

Abstract
We prove that a new, irreversible growth algorithm, Non-Deletion Reaction-Limited Cluster-cluster Aggregation (NDRLCA), produces equilibrium Branched Polymers, expected to exhibit Lattice Animal statistics [1]. We implement NDRLCA, off-lattice, as a computer simulation for embedding dimension d=2 and 3, obtaining values for critical exponents, fractal dimension D and cluster mass distribution exponent : ; in good agreement with theoretical LA values. The simulation results do not support recent suggestions [2] that BPs may be in the same universality class as percolation. We also obtain values for a model-dependent critical "fugacity", and investigate the finite-size effects of our simulation, quantifying notions of "inbreeding" that occur in this algorithm. Finally we use an extension of the NDRLCA proof to show that standard Reaction-Limited Cluster-cluster Aggregation is very unlikely to be in the same universality class as Branched Polymers/Lattice Animals unless the backnone dimension for the latter is considerably less than the published value.