Vicente Mayagoitia

Mechanistic study of surface processes on adsorbents: I. Statistical description of adsorptive surfaces

Abstract A dual description based on a network of “sites” and “bonds” is developed for the characterization of the adsorptive energy of a heterogeneous surface. This description is more complete than previous ones based on only one of those elements. The joint site-bond energy distribution is determined through a correlation function in such a way that the maximum degree of randomness is attained in the network. The degree of randomness is limited by the “Construction Principle”: according to this, the adsorptive energy at a site must be deeper than that of any bond connected to that site. This correlation function contains valuable information about the topology of the energy surface, which plays an important role in adsorption equilibrium and dynamics.

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 studies of capillary processes in porous media. Part 1.—Probabilistic description of porous media

Prior to the proper study of any capillary process, it is absolutely necessary to describe correctly the porous medium in which the process is supposed to occur. This description can be made on the basis of a network consisting of alternate sites and bonds. The originality of the present treatment consists in introducing the following constraints, which are absent in netweks other than those which are porous in nature: for a porous network (i) to be self-consistent it must obey the ‘construction principle’, i.e. the size of any site must be greater or at least equal to the size of any of its delimiting bonds, and (ii) to be verisimilar the randomness in size-topology must be shared alike between sites and bonds and raised to a maximum. From these constraints there arise topological size correlations and statistical properties which are analysed in detail. Our description allows the construction of adequately porous networks by analytical (probabilistic), digital (Monte-Carlo) or analogical (micromodel) methods, which must all conform to the above constraints. In this part, emphasis is made on the probabilistic description. It appears that simple models used by previous authors, e.g. for treating capillary condensation and evaporation, are in fact extreme cases of ours, and some of them are revealed as unable to represent real media.

Mechanistic studies of capillary processes in porous media. Part 2.—Construction of porous networks by Monte-Carlo methods

We reveal that present Monte-Carlo representations of porous networks are very unsatisfactory, since either (i) they are limited to the simulation of fully random networks corresponding to zero overlap between the site and the bond size distributions, a rather less frequent situation in natural and industrial materials, or (ii), in the more general case of overlapped distribution, they merely avoid any bond becoming bigger than any one of its two delimiting sites. In the case of a substantial degree of overlap it is absolutely necessary to observe the laws of self-consistency which were stated in Part 1 (J. Chem. Soc., Faraday Trans. I, 1989, 85, 2071). To disregard them would lead to (i) a certain departure of the size distributions of the resultant network, compared to those initially proposed and, much more importantly, (ii) an incapability to represent the morphology of topologically correlated structures (which play a major role in the characteristics of phase invasion and retraction during the course of capillary processes). A straightforward method for simulating porous media is proposed and its results, which agree with the considerations given in Part I are analysed, especially those dealing with (i) the size segregation arising as the overlap increases and (ii) the periodical properties of the network.

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.

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.

The Five Types of Porous Structures and Their Hysteresis Loops

Abstract Porous materials are classified within five types according to the relative positions of their site- and bond- size distributions. This leads to a better understanding of the morphological aspects of the porous medium as well as an assessment of the different mechanisms arising during capillary condensation and evaporation. For each one of these types of materials, relevant characteristics can be recognised in their hysteresis loops.

Description of Heterogeneous Surfaces in Activated Chemisorption

Abstract The adsorbent surface is considered as a collection of independent sites, each one possessing a certain energy of adsorption as well as an activation energy of adsorption. The correlation between these two parameters is found by means of a general treatment similar to that formerly applied by us in other fields, e.g.: (i) porous media (models, capillary condensation and evaporation, textural determinations), (ii) heterogeneous adsorbents (models, physical adsorption equilibria and surface diffusion, surface analysis). This correlation is useful to describe and characterize the solid surface, and to predict the adsorption equilibrium and the rate of activated chemisorption.

Twofold Description of Percolation in Porous Media

Most porous networks are not merely fully random media: their elements are strongly correlated. A deep reformulation of the original theory of percolation is then undertaken, based on the “Twofold Description” of porous media. This new development renders considerable advantages: (i) the mean- field approximation is exempted in some extent (ii) mean quantities are calculated only at the last stage, concomitantly assuring a greater accuracy of results, and (iii) domain complexions, which constitute a precious information about the state of elements as function of their size, are readily obtained.