Semiempirical Model for Adsorption of Polyatomics

Abstract

Multisite-occupancy adsorption is described by using a new formalism based on the occupation balance approximation (Roma, F.; Ramirez-Pastor, A. J.; Riccardo, J. L. J. Chem. Phys. 2001, 114, 10932). In this framework, the adsorption isotherm is characterized by a correction function C, which relates to the conditional probability of finding the ith empty site to a lattice with i - 1 already vacant sites. A simple semiempirical adsorption isotherm is proposed by approximating C as a combination of the correction functions corresponding to exact 1-D calculations and the Guggenheim-DiMarzio approximation, with adequate weights. Results are compared with corresponding ones from Monte Carlo simulations.

Configurational entropy of adsorbed rigid rods: Theory and Monte Carlo simulations

“…Detailed comparisons between theoretical and simulation results of adsorption [9] showed that the GD approach fits the numerical data very well at low coverage, while the EA model behaves excellently at high coverage. Based on these findings, the semiempirical model for adsorption of polyatomics (SE) was developed [8,9]. The SE model is a combination of exact calculations in one dimension, its generalization to higher dimensions and the GD approximation with adequate weights.…”

“…The model, hereafter denoted EA, is based on exact forms of the thermodynamic functions of linear adsorbates in one dimension and its generalization to higher dimensions [7,8]. Detailed comparisons between theoretical and simulation results of adsorption [9] showed that the GD approach fits the numerical data very well at low coverage, while the EA model behaves excellently at high coverage. Based on these findings, the semiempirical model for adsorption of polyatomics (SE) was developed [8,9].…”

Statistical Thermodynamics of Lattice Gas Models of Multisite Adsorption

“…The most well-known analytical approximation is: 1) the theory of Flory-Huggins [48,[55][56][57][58], which is a generalization of the theory of binary solutions of polymer molecules in a monomolecular solvent for the twodimensional case. The fact that in the framework of lattice gas model the problem of k-mer adsorption on homogeneous surfaces is isomorphic to the problem of binary solutions of polymer in a monomolecular solvent, 2) Guggenheim-DiMarzio approximation [59,60], which is based on calculating the number of possible ways of packaging rigid k-mers on lattices with different coordination numbers 3) the approximation based on the extension of the exact solution for a one-dimensional case [52,53] to higher dimensions [49,61], 4) well known quasichemical approximation [62] and mean-field approximation [63], 5) fractional statistical theory (FSTA) for the adsorption of polyatomic molecules, based on Holdan statistics [64], 6) semi-empirical model [61,65], etc. Unfortunately, none of these approximations is universal, and each shows quite good results, depending on the parameters of the model -a flexible or rigid k-mer, the length of k-mer, the presence or absence of lateral interactions between adsorbed molecules, etc.…”

“…Unfortunately, none of these approximations is universal, and each shows quite good results, depending on the parameters of the model -a flexible or rigid k-mer, the length of k-mer, the presence or absence of lateral interactions between adsorbed molecules, etc. A brief description of the approximations and compare them with each other can be found in [49,65]. Generally, more recent analytical approximations for the k-mers adsorption include earlier ones as special cases.…”

“…Analyzing the results deviations for various approximations from the results of Monte Carlo, it was shown that the most accurate approximation is the semi-empirical model, developed by Roma et al Semi-empirical model is a combination of the exact solution for one-dimensional approximation and Guggenheim-DiMarzio approximation [65]. A new theoretical approach is significantly better than other existing approximations and allows fairly simple explaining the experimental data.…”