Configurational probabilities for symmetric dimers on a lattice: An analytical approximation with exact limits at low and high densities

Abstract

A new approach is developed for lattice density functional theory of interacting symmetric dimers at high temperatures. Equations of equilibrium for two-dimensional square and three-dimensional cubic lattices are derived for the complete set of configurations in the first three shells around the central dimer, and rules of truncation for higher shells are based on exact results from the mathematical theory of domino tilings. This provides exact limits for both low and high densities. The new model predicts contributions of particular configurations which are in agreement with Monte Carlo simulations over the whole range of densities, including agreement with pocket Monte Carlo simulations at high densities.

Statistical thermodynamics of molecules with multiple adsorption states: Application to protein adsorption

“…However, the adsorption of the protein in the state II and the adsorption of a chain of length v are clear examples of multisite adsorption process, and consequently, multisite statistics should be considered. In this sense, it has been shown in numerous studies [33][34][35][36][37][38][39][40][41][42][43][44][45][46] that the entropic effects of structured molecules are significant in the monolayer regime when compared with monatomic adsorption. Moreover, in contrast to the statistic for the simple particles, the structure of lattice space plays a fundamental role in determining the statistics of particles occupying more than one site on the lattice.…”