Abstract
The thermodynamics of pure and mixed adsorption in idealised narrow pore solids was investigated. A narrow pore was defined as one in which no two adjacent molecules can slide past each other. The molecules confined within such a pore were idealised as a one-dimensional assembly subject to a homogeneous external field. An exact statistical mechanical analysis of this assembly was performed and the exact equation of state derived for a one-dimensional adsorbate with arbitrary nearest-neighbour lateral interactions. The one-dimensional model was shown to be thermodynamically exact with the correct low and high coverage behaviour. The transition between pure and mixed adsorption and "localised" to "mobile" adsorption were also naturally secured by this model. A systematic sensitivity analysis was conducted to separate the influence of the vertical and lateral interactions and the non-idealities of the bulk fluid on the thermodynamics of mixed adsorption. This was found to depend on the affinity of the solid for the various species which was defined as the difference between the initial isosteric heat of adsorption and the latent heat of vapourisation. The thermodynamics of a system with high affinities was primarily governed by the relative strength of the vertical interactions, the lateral interactions and the non-idealities of the bulk fluid played a secondary role. However, the behaviour of the mixed adsorbate was strongly moderated by the lateral interactions when one or more of the species exhibited a low affinity. In particular, the mixed adsorbate could exhibit positive deviation, no deviation or negative deviation from ideality depending on the strength of the mixed lateral interactions. The one-dimensional model does not rely on the random mixing assumption and could provide a measure of the local composition which obviates the need for the definition of adsorbed phase activity coefficients. This model was used to explore the consequences of employing approximate standard states in the Adsorbed Solution Theory analysis of saturated liquid adsorption. It was clearly demonstrated that the unjustified use of the approximate standard states could lead to a catastrophic misinterpretation of the thermodynamics of the mixed adsorbate. Furthermore, a key parameter was identified which could be extracted from the pure vapour adsorption isotherm and serve as an a priori indicator for the validity of the approximate standard states often employed. On a more practical note, the thermodynamically exact one-dimensional model reproduced many of the experimentally observed features of mixed liquid adsorption on narrow pore solids. It also predicted the occurrence of maxima in the individual uptake of the species which is yet to be observed experimentally. The liquid phase adsorption characteristics of the ethanol-water/silicalite system was well described by the one-dimensional model without taking a detailed view of either the pore structure or the energetic heterogeneity of silicalite. In particular, the parameters derived from the pure liquid adsorption data could be simply combined to predict the mixed liquid adsorption. However, a good prediction of the vapour adsorption isotherm could only be obtained close to saturation. The energetic heterogeneity and the detailed structure of the microporous solid exert a more critical influence in adsorption from a vapour. A systematic procedure for "subtracting out" the influence of localised energetic heterogeneity was presented. The overall adsorption was deconvoluted into separate contributions from "local sites" and the underlying "decontaminated" one-dimensional solid; thus enabling a direct comparison between different samples of "nominally" the same solid. This model gave an good description of the vapour adsorption isotherm and the differential heat of adsorption of water on silicalite. In particular, the lateral interaction potential recovered from the pure vapour and pure liquid data measured on different samples of silicalite were remarkably similar. The one-dimensional model with local sites gave a good description of the initial sharp fall in the differential heat of adsorption of ethanol on silicalite but systematic deviations were observed at intermediate to high loadings. This is due to the intrusion of the structural heterogeneity caused by the local variations in the pore structure which affect the adsorption characteristics of the larger and more strongly adsorbed ethanol molecule. A good description for this system was obtained through an approximate treatment of structural heterogeneity which distinguished between the pores and their larger intersections. Evidently, for a larger and more strongly adsorbed species it may also be necessary to allow for the difference between the two types of pore in silicalite. A rigorous treatment of such effects requires a model of an adsorbate in an inhomogeneous external field which is complicated even in one-dimension.