The problem of characterization
The characterization of amorphous materials is problematic because the structure of the materials is enormously complex, and a ``complete'' characterization requires no less than the location of every atom in a macroscopic sample. While the periodicity of crystalline materials (such as zeolites) reduces this problem to locating every atom in a microscopically-sized unit cell, no such symmetry is present in amorphous materials, and determining their structure at this level is impossible. Rather, average properties (or simple property distributions) may be defined which one hopes will still be usable in the application and categorization of the materials.
Porous media are generally characterized by a number of simple measures, the most common of which are the porosity, surface area, mean pore size and the more complex pore size distribution. Generally speaking, values of these measures are obtained by fitting experimental data to one of many models and reporting the corresponding property of the model. The models used may be either explicitly defined (as is the case for most methods of obtaining pore size distributions) or implicit in the data analysis procedure (common in methods for surface area such as alpha-plot analysis.) In all cases, there are significant ambiguities in the definition of the quantity being measured and significant approximations in the model being used.
The standard classification of pore sizes is given by:
The porosity of a materials ought to be relatively straightforward to define; it is just the volume of the pores divided by the volume of the material. This simple definition obscures two difficulties, which can be significant in pores of atomic dimension. The first is that parts of the void volume may not be accessible to any external probe molecule. This ``dead space'' is not be counted towards the true porosity of the material, but does make a contribution to the porosity if it is reported in [volume]/[mass] units, since it reduces the ``effective'' density of the material. The second difficulty is that, in pores of near-atomic dimension, the void volume itself is not well-defined, because the position of the atomic surface is not well-defined. This issue will be revisited in the consideration of surface area which follows. Porosity is often measured gravimetrically by filling the material with a gas or liquid and obtaining the volume of the pores from the mass of the adsorbed fluid. This procedure, while certainly accurate for large pore materials, requires assuming a constant adsorbate density throughout the pore system. In microporous and ultramicroporous materials where the ratio of surface area to volume is very high, the influence of the pore walls on the packing of gas or liquid molecules may not be negligible and will lead to systematic errors in these determinations.
The surface area of a microporous material is also a somewhat ambiguous concept, for two reasons. Firstly, the microscopic definition of the molecular surface is arbitrarily defined, and there are several sensible and intuitive definitions available, which can yield significantly different results under certain circumstances. Secondly, once a suitable surface definition has been chosen, the roughness of the surface must be accommodated. All surfaces are highly corrugated at the atomic scale, which can give higher than expected surface areas if microscopic definitions are used; this is a continuing source of difficulty in comparisons of simulated and experimental results on porous materials.
Experimental surface areas are most commonly obtained through the analysis of adsorption isotherms of nitrogen or some other gas. In the case of explicit-model analyses such as the Brunauer-Emmett-Teller (BET) method the experimental isotherm is fit to a theoretically-obtained adsorption model, from which is extracted a monolayer capacity of the material. This capacity is a well-defined quantity and can be used compare experimental and simulated systems. In order to convert to a surface area, a value for the monolayer density is needed, which is obtained experimentally using a reference system of known surface area. The accuracy of this method requires that the monolayer density be transferable; that it is not dependent on the surface curvature or pore structure, and not strongly dependent on the chemistry of the underlying surface. In previous work we have shown that in at least one mesoporous system there are significant systematic errors in this approach, that the monolayer density is not constant with surface curvature, and that this behavior can occur even when the fit of the BET model to the isotherm is of very high quality.
(Discuss implicit-model analyses here?)
The pore size, whether quoted as a mean or most probable pore size or as part of a pore size distribution, is the least well-defined characterization of a material, but often considered the most useful and the most informative. Defining a pore size (or pore size distribution is generally a matter of selecting both a surface definition and a pore shape definition, and fitting some experimentally obtained quantity to a distribution of similar pores. In principle, the shape could be controlled by several independent variables, leading to a distribution of size and shape, but in practice this is never attempted. Practically, the pores are generally assumed to be either slit-shaped or cylindrical, leading to a single variable size parameter (wall spacing or cylinder radius). While these procedures may be fraught with small approximations introduced to make the models tractable, the central question of the meaning of these pore size distributions is difficult to address. Pore size distributions (PSDs) are generally interpreted qualitatively, in order to determine how regular a material is (how sharp is its PSD) or whether the PSD is unimodal or bimodal. Certainly, increasingly complex material structures result in increasingly complex pore size distributions, but in general these measures cannot be reliably interpreted at a microscopic level without additional information on the morphology of the material.
Nearly all amorphous porous materials consist of a pore network, rather than a collection of individual ``independent'' pores. Quantitative (or even qualitative) descriptions of the properties of this network are rare in the literature, despite the (presumed) importance of the network topology to both the thermodynamics of confined fluids and the transport of fluid through a material. Indeed, the much-discussed phenomenon of adsorption hysteresis is often discussed in terms of ``pore-blocking'' (see the comprehensive discussion in , and references therein) resulting from particular pore network structures, which themselves are hardly understood.
The relationship of structure and function
In nearly all applications of porous media the choice of material used is made based on this kind of information, combined with previous experience (e.g., trial and error.) It is often the case that the essential physics and chemistry involved in the use of porous materials in applications (chromatography, gas and liquid purification, liquid crystal displays) is not completely understood, and is is therefore difficult to correlate the useful properties of the materials with the standard characterization measures. As a result, choosing the optimal material for a given application cannot be done in a systematic way, and previous experience is invaluable. Generally speaking, for novel applications many trials are made before a suitable material is found.
Towards materials design
Recent developments in the preparation of templated materials and other micro-patterning technologies afford the possibility of rational design of porous media for different applications, in much the same way that rational design of pharmaceuticals and of optical and electronic materials are now topics of great interest. Without considerably better understanding of the behavior of fluids confined in these materials, and without efficient and sensible characterization methods, this type of rational design is not possible: if one cannot predict what material properties are required for a given task, the ability to prepare precisely specified materials is much less valuable! What is clearly needed are predictive, quantitative relationships between a material's microscopic (atomic) structure, its average structural properties, and its useful physical and chemical properties.
Computer simulation studies afford a unique way to investigate both the characterization issues described above and the functional meaning of those characterizations. In addition, they offer an environment where it is possible to test hypotheses which are not easily accessible to experiment, and may further advance our understanding of the fundamental physics of fluid confinement.
In a realistic computational model, the position of every atom is known (by definition), so a 'complete' and non-arbitrary characterization is available a priori. This data can be used to critically evaluate the performance, utility, and specific shortcomings of nearly any standard characterization technique, provided that the data necessary for the technique can be obtained through simulation. In the case of methods based on gas adsorption, thermoporometry, scattering, diffraction, (mercury) porosimetry, direct microscopy (such as AFM) and many other methods, this is true, at least in principle. By applying a standard analysis to simulated data, we obtain an analogue of the experimental characterization, which can be compared with exact results from analyses based on the exactly known atomic positions. This type of critical study of characterization methods is generally not possible through experiment.
The utility and reliability of conclusions drawn from this type of study will depend on the realism of the model system under investigation. The more convincing the model of the material, the more likely it will be that quantitative results from computer simulation studies can be carried over to help improve experimental characterization methods. While many qualitative results will be insensitive to the details of the model (and can be obtained from quite coarse descriptions of the porous matrix), reliable quantitative information will require the development of more sophisticated models that have yet been developed. For instance, it has long been known from simple thermodynamic arguments that PSD methods based on the Kelvin equation should lead to systematically low pore sizes (ALSO some DFT stuff?), but the first quantitative determination of the size of this error in a complex geometry was only achieved very recently .
References Sorry - until I learn how to do full reference translation automagically, using LaTeX2HTML, these pages won't have bibliographic data
Department of Materials Science and Engineering
The University of Texas at Dallas
Fri Aug 27 16:29:16 2010