Salomón Cordero

Capillary condensation in heterogeneous mesoporous networks consisting of variable connectivity and pore-size correlation

Heterogeneous three-dimensional mesoporous networks (A. J. Ramirez-Cuesta, S. Cordero, F. Rojas, R. J. Faccio and J. L. Riccardo, J. Porous Mater., 2001, 8, 61, ) constructed under the premises of the dual site–bond model have been used as probe substrates to study the effects of variable connectivity and pore-size correlation on the aspects of both hysteresis loops and primary sorption scanning curves. The shapes of the hysteresis loops obtained from sorption simulation in networks of diverse morphologies are compared and discussed. It is found that the precursor structural parameters of the Monte Carlo simulated networks together with the sorption algorithm used in this work, can lead to IUPAC types H1, H2 and H3-like hysteresis loops, depending on the values chosen for the pore-size distribution parameters and mean connectivity. Network morphology also influences greatly the mechanisms of sorption processes in poorly or highly size correlated porous substrates. Sorption results on these 3-D porous specimens help to visualize the extents of pore blocking (vapour percolation) and delayed adsorption (liquid percolation) phenomena and also to foresee the most appropriate methods to ascertain the structure of porous materials.

On comparing BJH and NLDFT pore-size distributions determined from N2 sorption on SBA-15 substrata

SBA-15 silica materials consisting of a collection of non-intersecting cylindrical pores of varying diameters have been utilized to try to reconcile the pore-size distribution results proceeding from the classical Barrett–Joyner–Halenda (BJH) and modern non-local density functional theory (NLDFT) approaches. To assess such pretended concordance, it is necessary to perform BJH pore-size estimates on the basis of a modified Kelvin equation that makes allowance for the adsorption potential field emanating from the solid walls of the adsorbent towards the adsorbate molecules. Under this context, critical conditions for capillary condensation and evaporation to happen in cylindrical pores have been specifically calculated via a treatment previously developed by Broekhoff and de Boer (BdB). In this way, BJH-BdB pore-size distribution results, obtained from the analyses of both ascending and descending boundary curves of N2 sorption isotherms at 76 K on a series of model SBA-15 substrata that have been synthesized in this work, are compared with homologous curves proceeding from a NLDFT treatment performed on the descending boundary curve and very reasonable agreement has been found.

Simulation of three-dimensional porous networks

Abstract 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.

Effect of the Drug-Excipient Ratio in Matrix-Type-Controlled Release Systems: Computer Simulation Study

The main objective of this work is to study the drug release behavior from inert matrix systems by using computer simulation. This study allowed us to propose a new statistical method to evaluate the drug percolation threshold as a function of the exposed surface area of the device. The matrix system was simulated as a simple cubic lattice. The sites of the lattice were randomly occupied at various drug–excipient ratios. By simulating a diffusive process, the drug was delivered from the matrix system. The obtained release profiles were fitted to two different models: near the excipient percolation threshold, the square root of the time was well fitted, whereas close to (but above) the drug percolation threshold, the power law described accurately the release data. A relationship between the initial drug load and the amount of drug trapped inside the matrix system at infinite time was found. This relationship was conveniently described by an error function. Percolation thresholds in the matrix systems were determined from the latter relationship by using a nonlinear regression method. The assessment of percolation thresholds depends on the exposed surface area of the matrix systems. Moreover, estimated percolation thresholds were in agreement with the predicted values stated in the percolation theory.

On Modeling, Simulation and Statistical Properties of Realistic Three Dimensional Porous Networks

The basis for modeling and simulation of self-consistent porous networks encompassing pore and throat-size distributions, size correlation and non-uniform connectivity are given. The framework is a straightforward generalization of the Dual Site–Bond Description (DD) of Ref. (J. Chem. Soc. Faraday Trans I 84, 801 (1988)), which considers heterogeneity (size distribution of entities), correlation and connectivity as interdependent characteristics of the porous space. A general and technically simple method for Monte Carlo simulation of three-dimensional networks is presented and exemplified. Statistical and topological properties of simulated networks are shown and analyzed.

Pore-blocking and pore-assisting factors during capillary condensation and evaporation

Abstract Thirty-four years ago Everett [The Solid–Gas Interface, Vol. 2, Marcel Dekker, New York, 1967, p. 1055] proposed a pore-blocking factor when establishing the foundations of a non-independent domain theory (IDT) of sorption hysteresis. Such pore-blocking factor was defined as the ratio between two desorbed volumes within the same pressure range. The first volume arose from a non-independent pore structure. The second quantity was a virtual one since it represented the volume desorbed if the pores of the substrate had acted as independent domains. In fact, Everett calculated the ratio between pore-blocking factors, while not their absolute values, from experimental data proceeding from sorption results on porous glasses. The astonishing conclusion of all this preliminary work, was that blocking factors depended upon the total amount of condensate at a certain stage of a desorption process rather than on the distribution of it within the porous network. In this way, a unique pore-blocking factor curve ensued from different sorption processes such as boundary and scanning curves. Now, through the aid of simulated heterogeneous 3-D porous networks and the sorption curves thereon developed, an assessment of the above mentioned important assertion has been undertaken. Besides, a pore-assisting factor that may arise during an ascending sorption process has been treated under a similar context.

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.

Is the Alexander–Orbach Conjecture Suitable for Treating Diffusion in Correlated Percolation Clusters?

How does a particle diffuse inside a percolation cluster? This question is of both scientific and practical importance, e.g. in drug-controlled release and vapour adsorption. Diffusion in fractal media is characterized by the fracton dimension, ds. The Alexander and Orbach conjecture indicates that ds = 4/3 for diffusion in classical percolation clusters and, after much research on the subject, it is still provides a very good approximation for ds in the case of uncorrelated percolation cluster structures. However, what happens to the value of ds when a particle is moving inside a correlated percolation cluster? In this work, this problem is studied via Monte Carlo computer simulation. Our results show that the Alexander and Orbach conjecture is not always fulfilled.

Determination of pore size distributions using the Dual Site-Bond Model: experimental evidence

Abstract In previous papers, we have described a suitable method to obtain pore size distributions for voids and necks using the Dual Site-Bond Model (DSBM) and Monte Carlo simulations. This method basically consists in the determination of the corresponding size distributions by using adsorption–desorption hysteresis data. Void size frequency functions are featured from the ascending curve. From the descending curve, we obtain a characteristic pressure value that will give us, via a quasi-universal curve, information about the neck size distribution function. In this work, we use our method to predict, using experimental hysteresis loops, the size distributions of several mesoporous samples. Once these functions are determined, we simulate the adsorption–desorption isotherms on a simple cubic network of voids and necks whose radii are sampled from the obtained size distributions. Comparison with experimental data is performed, drawing out fruitful conclusions and future perspectives based on the simplicity and predictive capability of the method.

On the universal behavior of sorption isotherms in disordered mesoporous solids

Abstract Adsorption–desorption isotherms in disordered mesoporous solids, described by the Dual Site-Bond Model, are obtained through Monte Carlo simulations and their behavior is correlated to the topological properties of the porous networks and to their percolation properties, extending previous results to the general case of variable connectivity networks. A quasi-universal curve is found which may be useful in the problem of obtaining pore size distributions from the analysis of experimental Adsorption–desorption isotherms.