A Chord Distribution Description of Porous Glass
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A CHORD DISTRIBUTION DESCRIPTION OF POROUS GLASS M. Y. LINab and S. K. SINHAC,b a.NationalInstitute of Standardsand Technology, Gaithersburg,MD 20899 b. Exxon Research & Engineering Co., Annandale, NJ 08801 c. Brookhaven NationalLaboratory,Upton NY 11973
ABSTRACT Small angle neutron scattering data of Vycor is analyzed using a chord distribution model describing the microporous structure. In addition, the same model is applied in interpreting the data taken when capillary condensation takes place in the porous medium. In both cases, the results are in good agreement with other measurements, and shows a promising potential in describing such a bicontinuous system. INTRODUCTION Vycor glass has now become the subject of extensive studies since it provides a good example of a model bicontinuous porous medium. It has features in common with other granular materials of both scientific and technological interest such as polymer membranes, block copolymers, spinodally decomposed solids, etc. Quite often, as in the case of Vycor glass, the microstructure is on a length scale which are best probed by such techniques as small angle neutron (SANS) or x-ray (SAXS) scattering. A quantitative characterization of its micro structure is important for an understanding of the transport and phase behavior of fluids imbibed in such porous media. In this paper, we use a chord distribution model to characterize the microstructure of Vycor glass, which is widely used as a model system for the porous media. SANS data taken from the glass is analyzed using this model, and the parameters obtained are in good agreement with those measured independently. Also, qualitatively good agreement is seen between the chord distribution derived in the analysis and that experimently measured. In addition, we extend the model to the study of the process of capillary condensation, and show how the structure probed by SANS evolves as the liquid starts to condense in the pores. SYSTEM AND CHORD DISTRIBUTION Vycor is the trade mark of Coming Glass for its unique product of porous glass. The bicontinuous structure of silica and boron oxide is formed by spinodal decomposition during the annealing process of the glass. Afterwards the boron phase is leached out by acid, and the glass becomes solid-pore bicontinuous. For the samples we use, the porosity is 0.31, and the average minimum pore (neck) diameter is 67A, as measured by nitrogen desorption. Transmission electron microscopy (TEM) pictures taken from cross sections of the glass have shown that the structure is fairly random and isotropic.[1,2] In Fig. 1, we schematically show a similar picture, with the shaded area representing the solid (silica phase), and the empty area representing the pores. In general, they can be any two phases.
Let us impose a Cartisian coordinate, z-axis, on the porous structure. Assuming that the
structure is random, isotropic and bicontinuous, the direction and the origin of the axis are then arbitrary. This z-axis will intercept many interfaces of the two phases. We mark by a
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