Modeling Amorphous Porous Materials and Confined Fluids

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troduction Materials with pores of nanometer dimensions play a central role in many industrial separations technologies, catalytic processes, pollution control methods, and chemical, biochemical, and biological laboratory procedures.1–8 Most of these materials are generally microporous (pore size smaller than 2 nm) or mesoporous (pore size 2–50 nm); only with such small pores does one obtain the very high specific surface areas desired for adsorption-based processes. Such materials can be divided into two broad classes: those with regular or crystalline structure, such as zeolites, and those with irregular or amorphous structure. The latter class will be considered here. There are many amorphous porous materials with significant applications in science or industry, including sol-gel materials,1 activated carbons,6 phase-separated glasses,7 porous polymers.8 and others. These materials are primarily used in chromatographic (sepa-

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ration) processes, driven either by a preference of the material for adsorbing one component of a mixture (as in affinity chromatography, mercury removal from flue gas, or water purification) or by selective transport, as in gas chromatography or the kinetic separation of air into nitrogen and oxygen.9 The amorphous nature of these materials poses significant challenges to characterization, modeling, and design or optimization. In theoretical and computational studies of crystalline or otherwise very well-ordered materials, a unit cell structure obtained from x-ray diffraction or other experiments is usually available as a starting point, upon which a wide range of chemical theory and modeling methods may be brought to bear.10 Even for powdered materials with many surface sites and crystals with high defect concentrations, the “perfect” unit cell structure remains an important reference.

No such referents exist for amorphous materials, which can only be described using statistical measures. These may include chord-length distributions and other “stereological” measures obtained from microscopy,11 the structure factor extracted from small-angle scattering experiments, and the results of various spectroscopies. For porous systems, in particular, common characterizations include the pore volume, surface area, and pore size distributions inferred from gas adsorption or thermoporometry experiments.4,12 Note that all available methods for calculating these quantities are either implicitly or explicitly based on some assumed model for the adsorption process, the material morphology, or both, and that the validity of these characterizations depends on the applicability of the underlying assumptions. The characterization of amorphous porous materials is thus intertwined with their performance as sorbents, and therefore the various strategies available for modeling the behavior of fluids confined in such materials will be reviewed. In order to apply computational methods to understand the properties and performance of an amorphous porous material, one must nonetheless work with a particular mode