RESUMO
The statistical thermodynamics of binary mixtures of polyatomic species was developed based on a generalization in the spirit of the lattice-gas model and the quasi-chemical approximation (QCA). The new theoretical framework is obtained by combining: (i) the exact analytical expression for the partition function of non-interacting mixtures of linear k-mers and l-mers (species occupying k sites and l sites, respectively) adsorbed in one dimension, and its extension to higher dimensions; and (ii) a generalization of the classical QCA for multicomponent adsorbates and multisite-occupancy adsorption. This process is analyzed using the partial adsorption isotherms corresponding to both species of the mixture. Comparisons with analytical data from Bragg-Williams approximation (BWA) and Monte Carlo simulations are performed in order to test the validity of the theoretical model. Even though a good fitting is obtained from BWA, it is found that QCA provides a more accurate description of the phenomenon of adsorption of interacting polyatomic mixtures.
RESUMO
The statistical thermodynamics of polyatomic species mixtures adsorbed on two-dimensional lattices was developed based on generalization of the semiempirical approximation for the adsorption of single components [Romá, F. et al., Langmuir, 2006, 22, 3192-3197]. In this scheme, the partial adsorption isotherms are obtained using a correction function C[combining tilde], which relates to the conditional probability of finding the ith empty site to a lattice with i- 1 already vacant sites. This approximation allows us to write a new theoretical model using a combination of the correction functions corresponding to exact 1-D calculations and the Guggenheim-DiMarzio approach. Finally, comparisons with MC simulations and experimental data of methane-ethane and ethane-propylene mixtures on activated carbon are used to test the accuracy and reliability of the proposed model. The obtained results indicate that the new thermodynamic description is significantly better than the existing theoretical models developed to treat adsorption of interacting binary mixtures of polyatomics.
RESUMO
The statistical thermodynamics of straight rigid rods of length k on triangular lattices was developed on a generalization in the spirit of the lattice-gas model and the classical Guggenheim-DiMarzio approximation. In this scheme, the Helmholtz free energy and its derivatives were written in terms of the order parameter, δ, which characterizes the nematic phase occurring in the system at intermediate densities. Then, using the principle of minimum free energy with δ as a parameter, the main adsorption properties were calculated. Comparisons with Monte Carlo simulations and experimental data were performed in order to evaluate the outcome and limitations of the theoretical model.
RESUMO
The adsorption of long, straight rigid rods of length k (k-mers) on 2D lattices is described by using a new theoretical approach based on a generalization of the classical Guggenheim-DiMarzio approximation. In this scheme, the Helmholtz free energy and its derivatives are written in terms of the order parameter δ, which characterizes the nematic phase occurring in the system at intermediate densities. Then, using the principle of minimum free energy with δ as a parameter, the main adsorption properties are calculated. Comparisons with Monte Carlo simulations are performed in order to test the validity of the theoretical model. The obtained results indicate that the new thermodynamic description is significantly better than the existing theoretical models developed to treat the polymer adsorption problem.
Assuntos
Simulação de Dinâmica Molecular , Polímeros/química , Termodinâmica , Adsorção , Método de Monte CarloRESUMO
The critical behavior of long straight rigid rods of length k (k-mers) on square and triangular lattices at intermediate density has been studied. A nematic phase, characterized by a big domain of parallel k-mers, was found. This ordered phase is separated from the isotropic state by a continuous transition occurring at an intermediate density theta(c). Two analytical techniques were combined with Monte Carlo simulations to predict the dependence of theta(c) on k, being theta(c)(k) proportional to k(-1). The first involves simple geometrical arguments, while the second is based on entropy considerations. Our analysis allowed us also to determine the minimum value of k (k(min) = 7), which allows the formation of a nematic phase on a triangular lattice.