J. Phys. I France
Volume 6, Numéro 3, March 1996
Page(s) 357 - 371
DOI: 10.1051/jp1:1996161
J. Phys. I France 6 (1996) 357-371

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

R.C. Ball and J.R. Lee

Theory of Condensed Matter, Cavendish Laboratory, Madingley Road, Cambridge, CB3, 0HE, England

(Received 19 October 1995, accepted 28 November 1995)

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 $\tau$: $d=2,\,D\approx 1.53\pm 0.05,\,\tau = 1.09\pm 0.06$; $d=3,\,D=1.96\pm 0.04,\,\tau =1.50\pm 0.04$ 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", $z_{\rm c}$ 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.

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