Configurational probabilities for monomers, dimers and trimers in fluids

A new analytical approach is proposed to model aggregation of molecules with isotropic, nearest-neighbor, attractive interactions. By treating the clustering process as a chain reaction, equations with the exact high temperature limit are derived by evaluating the occupation probabilities of nearest neighbors based on the Ono-Kondo approach for a hexagonal lattice to calculate the configurational probabilities of i-mers (i = 1, 2, 3). Equilibrium constants for dimers and trimers are calculated based on the configurational probability data. The proposed model agrees well with Monte Carlo simulations at medium and high temperatures. At low temperatures, the model can be improved by considering the full set of site densities in the first shell of a central trimer. Approximate analytical solutions derived from exact calculations of the grand partition function for monomer adsorption on a 4 x N hexagonal lattice with cylindrical boundary conditions also are presented.