Lattice models for the collapse of branched polymers

Abstract

Randomly branched polymers in dilute solution in a good solvent can be modelled by lattice animals (i.e. connected clusters). Introducing attractive monomer—monomer interactions between nearest-neighbour sites causes the branched polymer to become more compact and a collapse transition, analogous to that in linear polymers, is expected to occur at low temperature. This model, and alternative lattice models for the collapse transition of branched polymers, will be described. In each of the models, the collapse is driven by some kind of near-neighbour fugacity, cycle fugacity or perimeter fugacity. In two and three dimensions and on several lattices, analytical results for the free energy and numerical results, using exact enumeration data, for the free energy and for the specific heat, will be presented with estimates of the cross-over exponentϕ and the collapse temperature Tc.