Polymer coagulation is simulated on a lattice by a Monte Carlo diffusi
on process in which particles move according to the change in local en
ergy. Our model allows, for the first time, a description of the coagu
lation process beyond the initial quench state and a reproduction of t
he wide variety of polymer structures that can be obtained, ranging fr
om dustlike to fingerlike to spongelike morphologies. We show that the
se morphologies are fully controlled by the coagulation rate which its
elf depends on the miscibility between solvent and coagulant.