Isaac Kornhauser

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.

Pore network interactions in ascending processes relative to capillary condensation

It is currently accepted that domain interdependence in adsorption hysteresis (i.e. pore-blocking effects due to hindered liquid–vapour transitions in which the state of any domain depends on those adopted by its neighbours), occurs during the descending (desorption) processes associated with capillary evaporation. In contrast to this behaviour, network effects are thought to be absent during the ascending processes inherent in capillary condensation. However, we have considered the possibility of strong vapour–liquid transitions of an assisted kind taking place during capillary condensation. This situation seems to be the rule, rather than the exception, in a wide variety of porous materials. The interactive effect arises as a consequence of menisci coalescence at the meeting point of capillaries, and it becomes more important as the extent to which the network is filled with capillary condensate increases. When a critical proportion (which depends on the connectivity and geometry of the porous media) of filled elements in the network has been reached, the whole condensation occurs suddenly. This implies that the usual analysis of the ascending boundary curve does not lead to the true pore-size distribution. However, the ascending curve can be predicted from the size distribution and connectivity of the porous network.

Domain complexions in capillary condensation. Part 1.—The ascending boundary curve

A statement of the general principles of capillary condensation in porous networks and the ascertainment of its particularities for a given structure are difficult, since either independent or dependent vapour–liquid transitions arise at each point of the network and also because porous materials occurring in nature and in industrial processes possess extremely variable morphologies. However, the following stages enable one to achieve these objectives readily: (i) development of general expressions for the probability that the various elements fill with capillary condensate, according to their type (sites or bonds) and size, (ii) classification of all possible morphologies of porous structures into a few unambiguous types and (iii) for each of these types, simplification of the general expressions to obtain particular equations allowing a straightforward derivation of domain complexions and ascending boundary curves. It appears that, even if in one structural type, the less frequently encountered domains behave as though independent, for the other types, corresponding to most materials, an interdependence must be taken into account. As an extreme case of domain interactivity (also pertaining to structures represented fully, once a certain degree of filling is reached, a phenomenon arises in which the whole configuration of capillary condensate becomes unstable, the entire network then being filled.

Mechanistic and Experimental Aspects of the Structural Characterization of Some Model and Real Systems by Nitrogen Sorption and Mercury Porosimetry

Several mechanistic and phenomenological aspects of mercury intrusion and nitrogen sorption processes involving some model and real mesoporous systems were studied. The experimental pore systems examined consisted of two substrates: (a) a globular solid composed of monodisperse silica spheres in a perfect rhombohedral arrangement and (b) a controlled pore glass solid. Comparisons between the experimental nitrogen sorption and mercury porosimetry pore-size distributions demonstrated: (i) the existence of several mechanistic effects responsible of irreversible capillary behaviour that influences the calculation of pore structure parameters; (ii) the choice of the right sorption process (i.e. condensation or evaporation) suitable for comparison with either intrusion or extrusion results; (iii) the types of porous structures capable of convenient pore-size characterization by either nitrogen sorption and/or mercury porosimetry methods; and (iv) the nature of the pore entities (i.e. chambers or necks) that control the incumbent capillary process.

Domain complexions in capillary condensation. Part 2.—Descending boundary curve and scanning

The study of capillary condensation and evaporation in all possible types of porous structures leads to the following conclusions: blocking phenomena of the ‘network’ kind occurring in evaporation present several forms according to the degree of overlap between the site and bond size distributions. These phenomena are as follows: (i) intense, with a definite percolation threshold, for random structures pertaining to zero overlap; (ii) moderate, in the case of entities topologically correlated in size as the degree of overlap is medium; (iii) non-existent, for homotactic domains related to full overlap. Cooperative transitions during condensation are even more sensitive to porous morphology since for each type of structure there is a different set of equations to describe them. Each of these types also has its characteristic shape of boundary loop, and even particular forms of scanning curves. Starting from experimental data for a given solid, this property could permit one in principle to decide, according to the shape of its boundary and scanning curves, to which type of structure this solid belongs, and then to select the appropriate set of equations allowing the correct exploitation of these data.

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

Abstract 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.

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.

Fluid-Phase Morphologies Induced By Capillary Processes In Porous Media

Abstract A topological analysis of the phase-filled state of “sites” (cavities, antrae) and “bonds” (passages, windows), is presented graphically for several capillary processes in porous media. The originalities of this treatment consist in: (i) fundamental and technical aspects of the simulation of porous media, allowing topological size-correlations between neighbouring network elements, and (ii) consideration of menisci cooperative behaviour according to local network geometry and appropriate physical constraints for each process.