Association of limited valence patchy particles in two dimensions

We report simulations of a simple model of particles with limited valence in two dimensions and compare the numerical results with recent predictions based on the application of the Wertheim theory. The predictions for the fraction of formed bonds are rather accurate, except at low densities and temperatures, where enhanced bonding is found. Such differences are traced-back to the break-down of the approximation of absence of intra-cluster bonding. The enhanced bonding is thus attributed to the growing entropic cost of merging different clusters when the density is low, compared to the free-energy gain of forming an intra-cluster bond. The presence of closed bond loops in finite size clusters affects the location of the percolation locus, which is located at temperature lower than expected on the basis of the Flory–Stockmayer theory. Similarly, the critical region is shifted to temperatures smaller than the ones accessible with present time numerical resources, despite the implementation of efficient cluster moves. Only a weak evidence of a low-T gas–liquid phase separation between a very dilute gas phase and a low-density percolating liquid phase is found.