Stochastic models of disordered mesoporous materials for small-angle scattering analysis and more

Abstract Small-angle scattering of either x-rays (SAXS) or neutrons (SANS) is one of the few experimental techniques that can be used to study the structure of porous materials on the entire range from 1 to 100 nm, which makes it particularly suited for mesoporous materials. Because the information in scattering patterns is a correlation function, models are generally needed to convert data into structurally meaningful information. In this paper, we discuss five stochastic models that capture qualitatively different disordered structures, notably concerning the connectivity and the tortuosity of the phases. The models are two variants of the Boolean model, a dead leaves model, as well as two clipped Gaussian field models. The paper is illustrated with the SAXS analysis of a polymer xerogel, of a fumed silica as well as of a mesoporous alumina, and the fitted models are compared with pore size distributions derived from nitrogen adsorption. In the case of the xerogel and silica it is possible to pinpoint a single model that describes the structure best. In the case of the alumina, however, the scattering cannot discriminate the models. Even so, the models are useful because they enable one to quantitate the structural ambiguity of the SAXS data.

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