On The Structured Particles Lattice Gases

The statistical mechanics of structured particles with arbitrary size and shape adsorbed on discrete lattices presents a longstanding theoretical challenge, mainly due to complex spatial correlations and entropic effects that emerge at finite densities. Even for simplified systems like hard-core linear k-mers, exact solutions remain limited to low-dimensional or highly constrained cases. In this review, we present a comprehensive analysis of theoretical approaches developed to describe adsorption phenomena involving structured particles (also known as multisite-occupancy adsorption) on regular lattices. We examine classical models including the Flory–Huggins and Guggenheim–DiMarzio theories, modern extensions such as an extension to two dimensions of the exact thermodynamic functions obtained in one dimension, the Fractional Statistical Theory of Adsorption based on Haldane’s fractional statistics, and the so-called Occupation Balance based on the expansion of the reciprocal of the fugacity, and hybrid approaches like the Semiempirical model obtained by combining exact one-dimensional calculations and Guggenheim–DiMarzio approach. For interacting systems, statistical thermodynamics is explored within generalized Bragg–Williams and quasi-chemical frameworks. Particular focus is given to the recently proposed Multiple Exclusion statistics, which capture the correlated exclusion effects inherent to non-monomeric particles. Applications to monolayer and multilayer adsorption are analyzed, with relevance to hydrocarbon separation technologies. Finally, computational strategies, including advanced Monte Carlo techniques, are reviewed in the context of high-density regimes. This work provides a unified framework for understanding entropic and cooperative effects in lattice-adsorbed polyatomic systems and highlights promising directions for future theoretical and computational research.