Adsorption in sparse networks I. Cylinder model

Materials with very low density, such as aerogels, are networks with polymers or chains of particles joined at nodes, where the spacing of the nodes is large compared to the thickness of the chains. In such a material, most of the solid surface has positive curvature, so condensation of an adsorbate is more difficult than condensation in a body containing cavities whose surfaces have negative curvature. A model is presented in which the network is represented by straight cylinders joined at nodes with coordination numbers 4, 6, or 12. The shape of the adsorbate/adsorptive interface is obtained for each network by minimizing its surface area. The adsorption behavior is found to depend on the ratio of the node separation, l, to the radius of the cylinders, a: if l/a exceeds a critical value (which depends on the coordination of the node), then the curvature of the adsorbate/adsorptive interface approaches zero while the adsorbate occupies a small fraction of the pore volume; if l/a is less than the critical value, then condensation occurs. Even in the latter case, interpretation of the adsorption isotherm in terms of cylindrical pores (as in the BJH model) yields apparent pore sizes much greater than the actual spacing of the nodes. In a companion paper (J. Colloid Interface Sci. 202, 412 (1998).) this model is applied to silica aerogels and found to give a good fit to both the adsorption and desorption curves with a single distribution of node spacings.