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In the present paper, the adsorption thermodynamics of a lattice-gas model which mimics a nanoporous environment is studied by considering nonadditive interactions between the adsorbed particles. It is assumed that the energy linking a certain atom with any of its nearest neighbors strongly depends on the state of occupancy in the first coordination sphere of such an adatom. By means of Monte Carlo (MC) simulations in the grand canonical ensemble, adsorption isotherms and differential heats of adsorption were calculated. Their striking behaviors were analyzed and discussed in terms of the low temperature phases formed in the system. Finally, the results obtained from MC simulations were compared with the corresponding ones from Bragg-Williams approximation. [ABSTRACT FROM AUTHOR]

Monte Carlo simulations and finite-size scaling analysis have been carried out to study the critical behavior in a submonolayer lattice-gas which mimics a nanoporous environment. In this model, the adsorbent is modeled as one-dimensional channels of equivalent adsorption sites arranged in a triangular cross-sectional structure. Two kinds of lateral interaction energies have been considered: (1) wL interaction energy between nearest-neighbor particles adsorbed along a single channel and (2) wT interaction energy between particles adsorbed across nearest-neighbor channels. We focus on the case of repulsive transverse (wT>0) and attractive longitudinal (wL<0) lateral interactions, where a rich variety of structural orderings are observed in the adlayer depending on the value of the parameters kBT/wT (being kB the Boltzmann constant) and wL/wT. The results reveal the existence of a first-order phase transition in the adlayer between a low-temperature “condensed” phase and a high-temperature “disordered” phase. [ABSTRACT FROM AUTHOR]

Monte Carlo simulations and finite-size scaling analysis have been carried out to study the critical behavior in a submonolayer lattice-gas of interacting monomers adsorbed on one-dimensional channels arranged in a triangular cross-sectional structure. Two kinds of lateral interaction energies have been considered: (1) wL, interaction energy between nearest-neighbor particles adsorbed along a single channel and (2) wT, interaction energy between particles adsorbed across nearest-neighbor channels. We focus on the case of repulsive transverse interactions (wT>0), where a rich variety of structural orderings are observed in the adlayer, depending on the value of the parameters kBT/wT (being kB the Boltzmann constant) and wL/wT. For wL/wT=0, successive planes are uncorrelated, the system is equivalent to the triangular lattice, and the well-known (3×3) [(3×3)*] ordered phase is found at low temperatures and a coverage, θ, of 1/3 [2/3]. In the more general case (wL/wT≠0), a competition between interactions along a single channel and a transverse coupling between sites in neighboring channels leads to a three-dimensional adsorbed layer. Consequently, the (3×3) and (3×3)* structures “propagate” along the channels and new ordered phases appear in the adlayer. Each ordered phase is separated from the disordered state by a continuous order-disorder phase transition occurring at a critical temperature, Tc, which presents an interesting dependence with wL/wT. The Monte Carlo technique was combined with the recently reported free energy minimization criterion approach (FEMCA) [F. Romá et al., Phys. Rev. B 68, 205407 (2003)] to predict the critical temperatures of the order-disorder transformation. The excellent qualitative agreement between simulated data and FEMCA results allows us to interpret the physical meaning of the mechanisms underlying the observed transitions. [ABSTRACT FROM AUTHOR]

In the present paper, the connection between surface order-disorder phase transitions and the percolating properties of the adsorbed phase has been studied. For this purpose, four lattice-gas models in the presence of repulsive interactions have been considered. Namely, monomers on honeycomb, square, and triangular lattices, and dimers (particles occupying two adjacent adsorption sites) on square substrates. By using Monte Carlo simulation and finite-size scaling analysis, we obtain the percolation threshold θc of the adlayer, which presents an interesting dependence with w/kBT (w, kB, and T being the lateral interaction energy, the Boltzmann constant, and the temperature, respectively). For each geometry and adsorbate size, a phase diagram separating a percolating and a nonpercolating region is determined. [ABSTRACT FROM AUTHOR]

The localized monolayer adsorption of interacting particles onto heterogeneous surfaces has been studied through Monte Carlo simulation in the framework of the lattice-gas model. The substrate was modelled as a collection of finite homotatic patches, each one characterized by an adsorption energy arising from a discrete energy density function. Patches were distributed spatially, either in a deterministic alternate way (ordered topography) or in a non-overlapping random way (random topography). The adsorption process was analyzed by following the behaviour of surface coverage versus chemical potential (adsorption isotherm) and the differential heat of adsorption as a function of the coverage. These quantities depend on the size of the patch as well as on the topological distribution of the patches on the surface. The consequences of these findings are discussed for the determination of the energetic topography of the surface from adsorption measurements. [ABSTRACT FROM AUTHOR]

The adsorption of polyatomics on one- and two-dimensional lattices is studied by combining theoretical modeling, Monte-Carlo (MC), simulations and their correspondence with experimental results. In one dimension, the rigorous statistical thermodynamics of interacting chains has been presented. With respect to two-dimensional adsorption, six different models to study non-interacting adsorbates have been discussed: (i) an extension to two dimensions of the exact thermodynamic functions obtained in one dimension; (ii) the Flory–Huggins's approximation and its modification to address linear adsorbates; (iii) the well-known Guggenheim–DiMarzio approximation; (iv) the fourth one is a new description of adsorption phenomena, based on Haldane's fractional statistics; (v) the so-called Occupation Balance, based on the expansion of the reciprocal of the fugacity; and (vi) a simple semi-empirical model obtained by combining exact one-dimensional calculations and Guggenheim–DiMarzio approach. In addition, the statistical thermodynamics of interacting polyatomics has been developed on a generalization in the spirit of the Bragg–Williams and the quasi-chemical approximations. Comparison with MC simulations and experimental adsorption isotherms are used to test the accuracy and reliability of the proposed models. Finally, applications to heterogeneous systems and multilayer adsorption are discussed. [ABSTRACT FROM AUTHOR]

The configurational entropy of interacting linear molecules (k-mers) absorbed on a regular lattice is addressed through analytical as well as numerical methods. The general definitions for computational exact calculations of k-mers lattice-gas entropy are presented. In addition, theoretical basis for accurate analytical estimations of the entropy of reference states are given. The coverage and temperature dependence of the configurational entropy of interacting adsorbed dimers on one and two-dimensional lattices are obtained. A novel phase behavior of k-mers lattice-gas is shown and discussed. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The phase behavior of interacting rigid rods of length k (k-mers) on two-dimensional square and triangular lattices has been studied by theoretical calculations in the framework of the lattice-gas model. The process was analyzed by comparing the dependence on coverage of the free energy per site of an isotropic submonolayer of interacting k-mers fiso(θ) with that corresponding to a fully aligned (nematic) system fnem(θ). The existence of an intersection point between the curves fiso(θ) and fnem(θ) which is indicative of the occurrence of an isotropic-nematic phase transition in the adlayer, allowed us to obtain the complete (temperature, coverage, k-mer size) phase diagram of the system. [ABSTRACT FROM AUTHOR]

A new distribution for systems of particles in equilibrium obeying the exclusion of correlated states is presented following Haldane's state counting. It relies upon an ansatz to deal with the multiple exclusion that takes place when the states accessible to single particles are spatially correlated and it can be simultaneously excluded by more than one particle. Haldane's statistics and Wu's distribution are recovered in the limit of noncorrelated states of the multiple exclusion statistics. In addition, an exclusion spectrum function G(n) is introduced to account for the dependence of the state exclusion on the occupation number n. The results of thermodynamics and state occupation are shown for ideal lattice gases of linear particles of size k (k-mers) where the multiple exclusion occurs. Remarkable agreement is found with grand-canonical Monte Carlo simulations from k=2 to 10 where the multiple exclusion dominates as k increases. [ABSTRACT FROM AUTHOR]