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Methane clathrate hydrates, particularly those with an sI structure, are significant due to their potential as energy resources and their impact on gas pipelines. In this study, a two-dimensional (2D) lattice-gas model is employed to investigate the main thermodynamic properties of methane clathrate hydrates. The proposed framework is validated through comparison with experimental data and more advanced three-dimensional (3D) simulations. Adsorption isotherms, dissociation enthalpy and phase stability of the sI structure are evaluated using Monte Carlo (MC) simulations in the grand canonical ensemble. The 2D adsorption isotherms closely align with both experimental data and 3D simulations, demonstrating the 2D model's ability to precisely represent both rigid and flexible sI structures. The dissociation enthalpy calculated using our approach (76.4 kJ/mol) excellently matches the experimental value (78 kJ/mol), confirming the model's accuracy. Furthermore, the phase diagram obtained from the Clausius-Clapeyron equation shows very good agreement with experimental data between 260 and 290 K, though deviations are observed above 290 K. These findings underscore the effectiveness and robustness of the 2D model in studying methane clathrate hydrates and suggest its potential applicability for investigating other guest species and hydrate structures.

Irreversible adsorption of objects of different shapes and sizes on Euclidean, fractal and random lattices is studied. The adsorption process is modeled by using random sequential adsorption (RSA) algorithm. Objects are adsorbed on one-, two-, and three-dimensional Euclidean lattices, on Sierpinski carpets having dimension $d$ between 1 and 2, and on Erdos-Renyi random graphs. The number of sites is $M=L^d$ for Euclidean and fractal lattices, where $L$ is a characteristic length of the system. In the case of random graphs it does not exist such characteristic length, and the substrate can be characterized by a fixed set of $M$ vertices (sites) and an average connectivity (or degree) $g$. The paper concentrates on measuring (1) the probability $W_{L(M)}(\theta)$ that a lattice composed of $L^d(M)$ elements reaches a coverage $\theta$, and (2) the exponent $\nu_j$ characterizing the so-called "jamming transition". The results obtained for Euclidean, fractal and random lattices indicate that the main quantities derived from the jamming probability $W_{L(M)}(\theta)$ behave asymptotically as $M^{1/2}$. In the case of Euclidean and fractal lattices, where $L$ and $d$ can be defined, the asymptotic behavior can be written as $M^{1/2} = L^{d/2}=L^{1/\nu_j}$, and $\nu_j=2/d$.

A new distribution for systems of particles in equilibrium obeying exclusion of correlated states is presented following the 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. The Haldane's statistics and Wu's distribution are recovered in the limit of non-correlated states of the multiple exclusion statistics. In addition, an exclusion spectrum function $\mathcal{G}(n)$ is introduced to account for the dependence of the state exclusion on the occupation-number $n$. Results of thermodynamics and state occupation are shown for ideal lattice gases of linear particles of size $k$ ($k$-mers) where multiple exclusion occurs. Remarkable agreement is found with Grand-Canonical Monte Carlo simulations from $k$=2 to 10 where multiple exclusion dominates as $k$ increases., Comment: 5 pages, 3 figures. Final version to be published in Physical Review Letters

The monolayer adsorption process of interacting binary mixtures of species $A$ and $B$ on square lattices is studied through grand canonical Monte Carlo simulation in the framework of the lattice-gas model. Four different energies have been considered in the adsorption process: 1) $\epsilon_0$, interaction energy between a particle (type $A$ or $B$) and a lattice site; 2) $w_{AA}$, interaction energy between two nearest-neighbor $A$ particles; 3) $w_{BB}$, interaction energy between two nearest-neighbor $B$ particles; 4) $w_{AB}=w_{BA}$, interaction energy between two nearest-neighbors being one of type $A$ and the other of type $B$. The adsorption process has been monitored through total and partial isotherms and differential heats of adsorption corresponding to both species of the mixture. Our main interest is in the repulsive lateral interactions, where a variety of structural orderings arise in the adlayer, depending on the interaction parameters ($w_{AA}$, $w_{BB}$ and $w_{AB}$). At the end of this work, we determine the phase diagram characterizing the phase transitions occurring in the system. A nontrivial interdependence between the partial surface coverage of both species is observed.

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 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 $\theta_c$ of the adlayer, which presents an interesting dependence with $w/k_BT$ (being $w$, $k_B$ and $T$, the lateral interaction energy, the Boltzmann's constant and temperature, respectively). For each geometry and adsorbate size, a phase diagram separating a percolating and a non-percolating region is determined., Comment: 25 pages, 12 figures, figures missing in previous version

In this paper the percolation of monomers on a square lattice is studied as the particles interact with either repulsive or attractive energies. By means of a finite-size scaling analysis, the critical exponents and the scaling collapsing of the fraction of percolating lattice are found. A phase diagram separating a percolating from a non-percolating region is determined. The main features of the phase diagram are discussed in terms of simple considerations related to the interactions present in the problem. The influence of the phase transitions occurring in the system is reflected by the phase diagram. In addition, a scaling treatment maintaining constant the surface coverage and varying the temperature of the system is performed. In all the considered cases, the universality class of the model is found to be the same as for the random percolation model., Comment: 19 pages, 8 figures

The deposition of a metal on a foreign substrate is studied by means of grand canonical Monte Carlo simulations and a lattice-gas model with pair potential interactions between nearest neighbors. The influence of temperature and surface defects on adsorption isotherms and differential heat of adsorption is considered. The general trends can be explained in terms of the relative interactions between adsorbate atoms and substrate atoms. The systems Ag/Au(100), Ag/Pt(100), Au/Ag(100) and Pt/Ag(100) are analyzed as examples., Comment: 26 pages, 9 figures