Yiming Chen1, Timothy E. Wetzel1, Gregory Aranovich2, and Marc Donohue2. (1) Chemical and Biomolecular Engineering, Johns Hopkins University, 3400 N Charles Street, Baltimore, MD 21218, (2) Chemical & Biomolecular Engineering, Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218
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. Exact solutions derived from calculations of the grand partition function on a 4xN hexagonal lattice with cylindrical boundary conditions also are presented.