The thermodynamic properties of sI clathrate hydrates involving methane and carbon dioxide guest molecules have been investigated using Monte Carlo (MC) simulations in the grand canonical ensemble, and analytical cluster approximation (CA) theory. The CA approach is founded on the precise calculation of states within finite cells. Both the sI hydrate structure and the guest species were represented using a two-dimensional triangular lattice-gas model with single- and multiple-site occupancy. The investigation entailed monitoring the lattice coverage's dependence on the chemical potential (adsorption isotherm) and examining quantities like Helmholtz free energy, energy of the adsorbed phase, configurational entropy, and adsorption heat. Three distinct scenarios were considered, each dependent on the intra- and interspecies interactions. First, the study was restricted to an ideal clathrate hydrate, wherein lateral interactions were disregarded, and the system's properties are governed by entropy alone. Second, lateral interactions between the guest species and water molecules were introduced by employing the well-established Lorentz-Berthelot mixing rules. Lastly, repulsive lateral interactions were taken into account. In all cases, a remarkable agreement between the results obtained through CA and MC was observed, underscoring the significant potential of CA theory as a valuable tool for exploring cavity occupancy and selectivity in the sI clathrate hydrate formation process.

The problem of interacting binary mixtures adsorbed on triangular lattices has been studied by means of ground-state (GS) calculations, Monte Carlo (MC) simulations and exact counting of configurations on finite cells [the so-called cluster-exact approximation (CA)]. We focus on the case of repulsive intraspecies couplings and null interspecies interaction, where a rich variety of ordered phases is found in the adsorbed layer. Each surface structure is separated from a disordered state by a phase transition occurring at a finite temperature. The ordered phases are identified by means of GS analysis, and their dependence on temperature is studied by MC simulations and CA. Total and partial adsorption isotherms are obtained for values of the lateral interactions in the different regions of the phase diagram. MC results are compared with CA calculations. A very good coincidence is obtained between both methods, supporting the validity of the exact counting of states on finite cells as an adequate approach to describe the behavior of multicomponent competitive adsorption with adsorbate-adsorbate interactions.

The adsorption of interacting binary mixtures on triangular lattices is studied by combining theory and Monte Carlo (MC) simulations. Two theoretical approximations are used in the present work: (i) the cluster approximation (CA), based on exact counting of adsorption states on small lattices; and (ii) an extension of the standard quasi-chemical approximation (QCA) that includes two adsorbed species (a and b). In the case of CA, an own algorithm is developed to obtain the configurational grand partition function for small cells. Repulsive lateral couplings between adsorbate-adsorbate species are incorporated in the lattice-gas framework. Theoretical (CA and QCA) total and partial adsorption isotherms are compared with MC simulations. Quantitative and qualitative differences are shown and discussed, being CA the more accurate approach in all cases.

The systems H/Cu(100), H/Ag (100) and O/Cu(100) were analyzed theoretically by means of DFT calculations, Monte Carlo (MC) simulations and a Cluster-exact (CA) Approximation. To model these real systems, a two stages procedure was used. In a first stage, DFT calculations were performed in order to determine the adsorption energies corresponding to a hydrogen or oxygen atom in different environments. The obtained values depend on the number of first neighbors present in each adsorption site. For the systems H/Cu(100) and O/Cu(100), lateral interactions between adatoms were found to be repulsive, while for the H/Ag (100) system, the interactions are attractive, except for the case of four nearest neighbors. Then, with this information, MC simulations and CA approximation were applied for different temperatures. The process was monitored by following the surface coverage as a function of the chemical potential (adsorption isotherm). Interesting behaviors were observed and discussed in terms of the low-temperature phases formed in the adsorbed layer. In addition, a good agreement was found between MC and CA results, especially at high temperatures. At low temperatures, a chessboard-like phase was observed for the systems H/Cu(100) and O/Cu(100).

The development of a method for the prediction of the amounts adsorbed on a surface is of interest due to its application in various areas such as the recovery of gases and the transport thereof in porous beds. Various scientific contributions have been carried out on the adsorption under equilibrium conditions of gas mixtures. In the present work, a theoretical cluster approximation (CA) is analyzed against the experimental and simulation behavior of the adsorbed phase of a binary mixture of gases. The substrate is modeled as an heterogeneous surface and a combination of repulsive lateral interactions between adsorbed particles of the same species is considered. Under these conditions, a rich variety of structural orderings were observed in the adlayer. CA results were compared with Monte Carlo simulations, showing a very well agreement over the range of parameters investigated. Finally, the theoretical formalism was used to model experimental data of CO–O2 mixtures on a template-synthesized 5A zeolite. The study presented here has shown that CA model is a good one considering the complexity of the physical situation, which is intended to be described, and could be more useful in interpreting experimental data of adsorption of interacting binary mixtures on heterogeneous surfaces.

The adsorption of single particles with non-additive lateral interactions has been studied by combining Monte Carlo (MC) simulations and theoretical modeling. The traditional assumption of additive lateral interactions is replaced with a more general one including non-pairwise interactions. 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. Two theoretical models have been used in the present study: (i) the first, which we called cluster-exact approximation (CA), is based on exact calculations of configurations on finite cells. An efficient algorithm allows us to calculate the detailed structure of the configuration space for m=l×l cells; and (ii) the second is a generalization of the classical quasi-chemical approximation (QCA) in which non-additive lateral interactions have been included. The process is monitored by following the surface coverage as a function of the chemical potential (adsorption isotherm). Results from CA and QCA are compared with MC simulations. A good agreement is obtained between theoretical and MC results, with CA being the most accurate approximation in all cases. This finding supports the validity of the exact counting of states on finite cells as a starting point to predict the behavior of a system governed by non-additive lateral interactions.

The adsorption of binary mixtures containing particles A and B on homogeneous substrates is studied by Monte Carlo (MC) simulations, quasi-chemical approximation (QCA), and exact counting of states on finite cells (we call this approach cluster approximation, CA). The energies involved in the adsorption model are five: (1) \(\epsilon_A,\) interaction energy between an A particle and a lattice site; (2) \(\epsilon_B,\) interaction energy between a B particle and a lattice site; (3) \(w_{AA},\) nearest-neighbor interaction energy between two A particles; (4) \(w_{AB}\) (=\(w_{BA}\)), nearest-neighbor interaction energy between an A particle and a B particle and (5) \(w_{BB}\), nearest-neighbor interaction energy between two B particles. The process is monitored by following the coverage of both species with the simultaneous increasing of the individual chemical potentials of each mixture component. A non-trivial interdependence between the partial adsorption isotherms was observed and discussed in the context of the lattice-gas theory. The theoretical formalism is used to model experimental data of methane-carbon dioxide mixtures adsorbed on activated carbon. In addition, an excellent agreement was obtained between theoretical and MC simulation results. This finding evidences the usefulness of CA and QCA as a starting point to predict the behavior of a system governed by a large number of parameters.

The adsorption of binary mixtures on heterogeneous surfaces is studied by a cluster approximation (CA), based on the exact calculation of configurations on finite cells. The substrate is characterized by n types of sites, each with different adsorption energy. The process is monitored through the total and partial isotherms. The theoretical formalism is used to model experimental data of methane-ethane mixtures adsorbed on a template-synthesized carbon. The CA results are compared with the ones corresponding to the well-known Ideal Adsorbed Solution Theory (IAST). Even though a good fitting is obtained from IAST, it is found that CA is a more accurate model to estimate the binary data on the highly heterogeneous carbon sample. (C) 2016 Elsevier B.V. All rights reserved.

Collective diffusion of particles with repulsive nearest-neighbor interactions on bivariate surfaces is studied through Monte Carlo simulation, in the framework of the Kubo–Green theory. Shallow and deep adsorbing sites form l×l patches distributed at random or in chessboard-like ordered domains on a two-dimensional square lattice. The influence of the energetic correlation and the lateral interactions on the jump and collective diffusion coefficients are analyzed by simulating the coverage fluctuations in the grand canonical ensemble and the mean-square displacements of particles in the canonical ensemble. The combination of topography and lateral coupling is shown to produce interesting effects such as different filling regimes as well as strong effects on the coverage dependence of the transport coefficients.

La adsorción superficial de partículas interactuantes sobre superficies heterogéneas es estudiada mediante simulación de Monte Carlo. La topografía energética ha sido caracterizada en base a parches isoenergéticos de tamaño l, constituidos por sitios débiles o fuertes. Dichos parches se distribuyen al azar, o formando una estructura ordenada tipo tablero de ajedrez. Se identifican cantidades que escalean como leyes de potencia con la longitud característica l. Se discuten las consecuencias de estos resultados en relación con la determinación de la topografía energética superficial a partir de mediciones de adsorción.

En el presente trabajo se estudió la adsorción de una mezcla de dos gases monoatómicos sobre un sustrato homogéneo bidimensional, en presencia de interacciones laterales en el adsorbato y energías adsortivas diferentes para cada especie. Se calcularon isotermas de adsorción y calor isostérico de adsorción de la mezcla, en forma analítica mediante la implementación de técnicas de simulación de Monte Carlo. Se determinó la manera conecta de evaluar las cantidades de interés, comparándose los resultados teóricos con los correspondientes a simulaciones computacionales. Tanto isotermas de adsorción como calor isostérico mostraron comportamientos interesantes a bajas temperaturas e interacciones laterales repulsivas, ante la presencia de diferentes fases en el adsorbato.

Mediante la implementación de simulación de Monte Carlo en la asamblea Gran Canónica, se estudian las principales características del proceso adsortivo correspondiente a una gas en contacto con un sustrato sólido heterogéneo, en presencia de interacciones laterales en el adsorbato. Dicho proceso es monitoreado a través de la simulación computacional de isotermas de adsorción, energías media por partícula y por sitio, y calores diferenciales de adsorción. La superficie heterogénea es generada en el marco del modelo Dual Sitio-Enlace, asignando energías adsortivas y energías de puntos de silla entre sitios a partir de distribuciones energéticas uniformes. Se analiza la dependencia de las cantidades termodinámicas mencionadas con el grado de correlación energética superficial proporcionado por el solapamiento entre las distribuciones de energías de sitios y enlaces. Se observa además el efecto de las interacciones laterales en el adsorbato sobre tales cantidades, en función del cubrimiento superficial.Diferentes y novedosos comportamientos fueron observados y analizados en el contexto del modelo de Gas de Red.

En este trabajo se estudia la adsorción de moléculas monoatómicas con interacciones adsorbato-adsorbato (ads-ads) sobre superficies heterogéneas unidimensionales utilizando simulación numérica de monte carlo y aproximación de cluster. El substrato se modela como una red unidimensional de trampas con heterogeneidad energética, donde las trampas se agrupan en parches homogéneos alternantes con energías adsortivas e1, e2. Distintas cantidades termodinámicas como isotermas de adsorción, fluctuaciones del cubrimiento, energía por sitio y calores obtenidos mediante las dos técnicas empleadas son cotejeadas y se discute la validez de la aproximación de cluster en el rango de energías estudiadas. Los estudios realizados pueden ser aplicados a sistemas cuasi-unidimensionales como son los nanotubos de carbono, de muy reciente fabricación.

Mediante Simulación de Monte Carlo se estudia la difusión superficial de un trazador sobre un sustrato que presenta heterogeneidad energética y geométrica. En el contexto del modelo gas de red, el proceso difusivo de la partícula trazadora ocurre vía transiciones activadas a sitios primeros vecinos sobre una red bidimensional de sitios adsortivos. La topografía energética es construida en el marco del modelo Dual Sitio-enlace, introduciendo cierta fracción de enlaces cortados. Este modelo permite construir sustratos energética y geométricamente desordenados, de coordinación no-uniforme, y con cierto grado de correlación energética superficial. Los resultados obtenidos muestran como el desorden superficial afecta la dinámica del adsorbato

El proceso adsortivo superficial sobre superficies heterogéneas es estudiado en el contexto del modelo gas de red, mediante simulación de Monte Carlo en asamblea gran canónica. La topografía energética es modelada como un arreglo regular de sitios adsortivos, con geometría cuadrada, triangular o hexagonal, y condiciones de contorno periódicas. La heterogeneidad energética es introducida al considerar dos tipos de sitios (superficie bivariada), agrupados en parches homogéneos de tamaño l, determinando una topografía tipo "tablero de ajedrez". Las isotermas de adsorción muestran un comportamiento interesante, cuyas características dependen de la geometría de la red, la heterogeneidad, el tamaño del parche, y las interacciones laterales en el adsorbato. Los resultados de Monte Carlo son comparados con los obtenidos mediante la aproximación de "subestados efectivos", ESA.

El proceso adsortivo superficial sobre sustratos heterogéneos fuertemente correlacionados es estudiado mediante simulación de Monte Carlo en la asamblea gran canónica. En el marco del modelo "gas de red", la superficie es representada por una red cuadrada de sitios adsortivos, con condiciones de contorno periódicas. La heterogeneidad es introducida en base a dos tipos de sitios con diferentes energías de adsorción (superficie bivariada). Sitios fuertes y débiles son agrupados en parches homogéneos de tamaño lxl sitios, distribuidos en forma de tablero de ajedrez. Se analiza la dependencia de las características principales del proceso superficial con el tamaño de parche, la energía de interacción lateral y la heterogeneidad energética, encontrándose dos diferentes regímenes de adsorción según la relación entre la energía de interacción repulsiva y la diferencia de energía adsortiva entre parches débiles y fuertes.

The reversible adsorption process occurring on patchwise heterogeneous bivariate surfaces is studied by Monte Carlo simulation and mean-field approximation. These surfaces are characterized by a collection of deep and shallow adsorbing patches with a typical length scale l. Patches can be either arranged in a deterministic chessboard structure or in a random way. Previous studies showed that the topography of a given surface can be obtained from the knowledge of the corresponding adsorption isotherm and a reference curve. In the present work, we discuss the advantages and disadvantages of using different reference curves. One of the main consequences of this analysis is to provide an improved method for the determination of the energetic topography of the surface from adsorption measurements.

A simple model for amorphous solids, consisting of a mixed bond triangular lattice with a fraction of attenuated bonds randomly distributed (which simulate the presence of defects in the surface), is studied here by using computational simulation. The degree of disorder of the surface is tunable by selecting the values of (1) the fraction of regular [attenuated] bonds ρ [1−ρ] (0≤ρ≤1) and (2) the factor r, which is defined as the ratio between the value of the conductivity associated to an attenuated bond and that corresponding to a regular bond (0≤r≤1). The results obtained show how the percolation properties of the disordered system are modified with respect to the standard random bond percolation problem (r=0).

A simple model for amorphous solids, consisting of a triangular lattice with a fraction of attenuated bonds randomly distributed (which simulate the presence of defects in the surface), is used here to find out, by using grand canonical Monte Carlo simulations, how the adsorption thermodynamics of repulsively interacting monomers is modified with respect to the same process in the regular lattice. The degree of disorder of the surface is tunable by selecting the values of (1) the fraction of attenuated bonds ρ (0 ≤ρ≤ 1) and (2) the attenuation factor r (0 ≤r≤ 1), where r is defined as the ratio between the value of the lateral interaction associated to an attenuated bond and that corresponding to a regular bond. Adsorption isotherm and differential heat of adsorption calculations have been carried out showing and interpreting the effects of the disorder. A rich variety of behavior has been observed for different values of ρ and r, varying between two limit cases: bond-diluted lattices (r = 0 and ρ≠ 0) and regular lattices (r = 1 and any value of ρ). In addition, the critical behavior of the system was studied, showing that the order-disorder phase transition observed for the regular lattice survives, though with modifications, above a critical curve (ρ-r-temperature).

The adsorption process of interacting binary gas mixtures containing particles A and B on triangular substrates is studied through grand canonical Monte Carlo simulation in the framework of the lattice-gas model. The energies involved in the adsorption process are four: (1) ϵ0, interaction energy between a monomer (type A or B) and a lattice site; (2) wAA, nearest-neighbor interaction energy between two A particles; (3) wAB (=wBA), nearest-neighbor interaction energy between an A particle and a B particle and (4) wBB, nearest-neighbor interaction energy between two B particles. The process is monitored through partial and total isotherms, differential heats of adsorption and energy of the system, which appear as very sensitive to all lateral interactions. We focus on the case of repulsive lateral interactions, where a rich variety of structural orderings are observed in the adlayer, depending on the value of the parameters wAA, wAB and wBB. Results are rationalized through the determination of the phase diagrams characterizing second order phase transitions in the system. A nontrivial interdependence between the partial surface coverage of both species is observed.