Multilayer adsorption of rigid and flexible k -mers: Theoretical modeling, Monte Carlo simulations, and experimental validation

Abstract

This work examines multilayer adsorption of rigid and flexible 𝑘-mers (rod-like molecules of variable length)on homogeneous lattice surfaces. A combination of theoretical models, Monte Carlo (MC) simulations, and experimentalcomparisons captures the complexity of the process. The models include multisite occupancy andallow bending or stretching, enabling diverse microscopic adsorption mechanisms. Adsorbed rods may: (a) forma monolayer directly above an underlying object (stack model); (b) form a monolayer atop previously adsorbedstructures (brick model); or (c) adopt stretched/bent conformations to follow prior layer topography when neighboringsites are within√2 lattice constants (flexible model). For the stack model, an exact analytical solutionis obtained via statistical mechanics for finite and infinite layering. For the brick and flexible models, MC simulationsare combined with a cluster-based approximation using exact enumeration of configurations in finitelattice cells. Comparison of adsorption isotherms with the Brunauer-Emmett-Teller (BET) model shows that bothmonolayer capacity (𝑣 𝑚 ) and the BET constant (𝑐) strongly depend on molecular size and microscopic adsorptionpathways. The results improve the accuracy of surface property characterization, a key factor in catalysis,materials science, and surface chemistry.