Dual Site-bond Model Research Articles

On the characterization of heterogeneous surfaces through the dual site–bond model

Abstract The statistical description of the energetic topography of heterogeneous solid surfaces and the problem of its determination from experimental results are discussed in terms of the dual site–bond model. The effects of the topography on surface processes such as adsorption and thermal desorption, as predicted by the model, are obtained through Monte Carlo simulations. It is shown that adsorbate–adsorbate interactions and adsorptive energy topography may compete with each other in such a way as to produce an indetermination in the characterization from experimental adsorption isotherms and that such an indetermination can be overcome through the analysis of thermal desorption experiments.

Mixed wettability: a numerical study of the consequences of porous media morphology

Four types of 2-D numerical networks have been used as models of porous media, in order to derive capillary pressure curves in the case of two immiscible fluids competing for the possession of the porous space under mixed-wetting conditions. The porous networks were constructed using a variation of the dual site bond model (DSBM) framework, which allows a substrate to have an adequate geometrical and topological distribution of its pore elements. For the same pore-size distribution, the DSBM can provide simulated porous media of different topological structures. Just taking into account thermodynamics aspects, it is possible to calculate some wetting indices for the special case involving spontaneous water imbibition, forced water drive, oil imbibition, and forced oil drive within each one of the above topologically different substrata, i.e. the main flooding sequences characteristic of wettability experiments have been studied in a variety of porous media. In this work, Amott–Harvey and US Bureau of Mines wetting indices are calculated from simulated capillary pressure curves describing the water–oil and oil–water immiscible displacements occurring in these topologically different porous structures.

Simulation of three-dimensional porous networks

Simulation of porous networks, with characteristics similar to those of real media, is essential for the study of capillary processes that take place within these substrata. The dual site-bond model (DSBM) provides a theoretical basis from which it is possible to adequately describe and simulate porous networks of diverse structural properties. Following the DSBM principles, heterogeneous 3-D cubic porous networks have been built by a Monte Carlo method. The desired topological properties of these substrata have been introduced by considering: (i) different sizes of the void entities (sites or cavities and bonds or throats); (ii) different connectivities ( C) of the pore elements with their neighbours, i.e. the number of throats (bonds) that surround and connect a pore cavity (site) with its homologous entities is not constant throughout the network; (iii) geometrical restrictions, in the sense that the sizes of the bonds that meet into a site must be of such values as to avoid any mutual interference. The overlapping ( Ω) between the site and bond distribution functions, the connectivity ( C) and the geometrical restrictions ( G), are the three fundamental factors that promote segregation effects in the substrate. For regular networks (i.e. those of constant C) subjected to G and high Ω, it is found that big sites: (i) prefer big bonds as neighbours, and (ii) are less affected by geometrical restrictions than small ones. In turn, for irregular networks of varying C subjected to G and large Ω it is found that: (i) the smallest sites are linked to the biggest possible bonds thus acquiring a low connectivity, and (ii) the biggest sites adopt the maximum possible connectivity and allocate small and medium size bonds rather than large ones. All these particularities strongly influence the topology of a porous network and hence the repartition of fluids inside the pores during a capillary process.

Everett’s sorption hysteresis domain theory revisited from the point of view of the dual site-bond model of disordered media

The classical and elegant independent sorption domain theory introduced by Everett marked a milestone in the field of adsorption, since it allowed via their famous complexion diagrams a straightforward visualization of the state of individual pores, i.e. filled or emptied of condensate according to their sizes, of an adsorbent in contact with a vapor. The principal results of the independent domain theory are comprised in a series of theorems. The applicability of these theorems is now examined from the point of view of the dual site-bond model, a non-independent pore domain approach that has been proved to be very useful to simulate porous networks and capillary phenomena occurring wherein.

Monte Carlo simulation of collective diffusion on heterogeneous media: Dual Site-Bond Model

The Dual Site-Bond Model is an important tool in order to describe porous media and heterogeneous energetic substrates. This statistical description has proved to be useful to analyze topography effects on several molecular processes that occurs on correlated heterogeneous systems. In the context of the Kubo–Green approximation, we have performed a Monte Carlo simulation study of the thermodynamic factor on heterogeneous media, in order to understand the influence of the topography on the collective diffusion process. The adsorbent has been generated by using the Dual Site-Bond Model. The effects of temperature, lateral pairwise interactions in the adsorbate, and energy correlation on the thermodynamic factor have been analyzed.

Determination of the pore size distribution of correlated mesoporous networks

In the present work we study how the adsorption desorption hysteresis loop of a mesoporous disordered medium represented by a 3-dimensional Dual Site-Bond Model (DSBM) is affected by percolation. Site and bond distributions are assumed to be gaussians. The behavior of the threshold pressure for the evaporation processe suggests a method to determine the site and bond distributions from experimental adsorption-desorption hysteresis curves. Traditional methods developed for non-correlated networks are tested and evaluated against our simulation results showing the discrepancy mainly for highly correlated networks. Results of the prediction capability of our method are shown.

Sorption characteristics and visualization of the state of porous entities in simulated porous networks

Cubic porous networks are computer simulated by a Monte Carlo method implemented under the premises of the Dual Site-Bond Model of complex media. Topological properties of the networks (size and connectivity) are visualized from cross-sectional planes of the substrata. Sorption characteristics of these media are evidenced through their hysteresis loops. Visualization of the state (liquid or vapour-filled) of porous entities during a particular sorption process is made directly from cross-sectional planes of the porous media or indirectly from domain complexion diagrams.

Percolation Effects on Adsorption−Desorption Hysteresis

In the present work we study how the adsorption−desorption hysteresis loop of a mesoporous-disordered medium represented by a three-dimensional dual site-bond model is affected by percolation for different kinds of site and bond distributions. The behavior of the threshold pressure for the evaporation process, as a function of the separation between the site and bond distributions and their dispersions, suggests a method to determine them from experimental adsorption−desorption hysteresis curves.

Correlated Site−Bond Ensembles: Statistical Equilibrium and Finite Size Effects

This work presents a Monte Carlo analysis of the propagation of correlation strength in site−bond square lattices generated through the dual site−bond model (DSBM), where the values of the property assigned to sites and bonds are sampled from two uniform density distributions that may have some overlapping area with each other. Correlations appear when a construction principle is established. Although this model has been extensively used in many physical applications, such as adsorption and surface diffusion on heterogeneous surfaces and percolation and transport processes in porous media, a careful study of the way correlated topology is settled on through the system was lacking. The dependence of the relaxation time needed to reach equilibrium and of the minimum size of the network to be used is established for different correlation strengths, represented by the overlapping parameter Ω. A more accurate empirical equation, relating the characteristic correlation length l0, corresponding to the spatial correlation function, and Ω, is found, than the one used in former applications of the DSBM.

Effects of the heterogeneous energetic topography on the collective motion of adsorbed particles

Collective surface diffusion of adsorbed particles on correlated heterogeneous surfaces is studied by Monte Carlo simulation, in the framework of the Kubo–Green theory. The energetic disordered surface is described through the dual site-bond model (DSBM) introduced by Mayagoitia et al. [Surf. Sci. 221, 394 (1989)]. The influence of the energetic correlation on the jump (DJ) and collective (D) diffusion coefficients is analyzed by simulating the coverage fluctuations in the grand canonical ensemble and the mean-square displacements of particles in the canonical ensemble. The topography is shown to strongly affect the coverage dependence of the transport coefficient. The effects of nearest-neighbor lateral interactions is also discussed.

Probabilistic Analysis of the Dual Site−Bond Model: The Self-Consistent Case

A probabilistic analysis of the generation of dual site-bond models for the energy landscape of adsorbents is presented, focusing attention on the self-consistent case. To generate an uncorrelated site-bond energy landscape with prescribed distribution functions F S * (E) and F S * (E) consistent with the two basic laws of the dual site-bond model, the random variables associated wit the site and bond energies should possess the local distribution functions F S (E) and F S (E), which are related to F S * (E) and F B * (E) through a nonlinear integral equation. In particular, the inverse problem in two dimensions is solved in closed form. The analytical solution for the inverse problem provides a clear description of the intrinsic correlation in the energy landscape induced by the fulfillment of the construction principle.

Role of Size Correlations in Fluid Displacement in Porous Solids

A 3-dimensional simulation of fluid displacement in a disordered porous solid is performed. The solid heterogeneities are characterized by two pore size distributions in the context of the dual site−bond model (DSBM). It is shown how invasion patterns and relevant quantities in invasion percolation are affected by the disordered porous matrix confirming and also contrasting previous results in 2-dimensional networks. Deeper understanding of the problem is achieved by allowing the presence of anisotropy in the porous space.

Structure Characterization of Disordered Porous Media — A Memorial Review Dedicated to Vicente Mayagoitia

We present a review of the description of disordered porous media according to the Dual Site-Bond model introduced by Vicente Mayagoitia. The model formulation, percolation properties and applications to problems of practical interest are discussed.

Molecular Processes on Heterogeneous Solid Surfaces

The dual site-bond model (SBM) to describe heterogeneous surfaces with different energetic topographies is reviewed and applied to the study of molecular processes on solid surfaces such as adsorption, surface diffusion, reactions, and diffusion limited aggregation. It is found that all these processes are strongly affected by the energetic topography, and the observed behaviors are discussed.

Temperature behavior of tracer diffusion on heterogeneous surfaces

The behavior of a tagged particle on a generalized heterogeneous surface is studied by Monte Carlo simulation. Using the dual site-bond model (SBM), the energetic properties of the heterogeneous substrates can be appropriately described through the site and bond energy distributions and the overlapping degree between them. The effect of the adsorptive energy topography on the tracer diffusion coefficient, as well as on the time behavior of the mean-square displacement of the adparticle, are analyzed for different temperatures and energy correlation degrees. The short-time behavior of tracer diffusion is highly sensitive to the surface energy structure. The possibility of using tracer diffusion analysis for a better characterization of the energetic topography of heterogeneous surfaces is discussed.

Characterization of energetic surface heterogeneity by a dual site-bond model

Characterization of energetic surface heterogeneity by a dual site-bond model

On the topology of correlated energies on heterogeneous surfaces

The authors comment on the topology of correlated energies on heterogeneous surfaces. A large effort is being dedicated to the characterization of the adsorptive energy topography of heterogeneous surfaces. The authors discuss here the dual site-bond model.