PHYSICAL REVIEW B VOLUME 38, NUMBER 2 15 JULY 1988-I Fractal surface and cluster structure of controlled-pore glasses and Vycor porous glass as revealed by small-angle x-ray and neutron scattering Axel Hohr, Hans-Bernd Neumann, Paul W. Schmidt, and Peter Pfeifer Physics Department, University of Missouri, Columbia, Missouri 65211 David Avnir Department of Organic Chemistry and F Hab. er Research Center for Molecular Dynamics, The Hebrew University of Jerusalem, Jerusalem 91904, Israe! (Received 16 November 1987) Analysis of small-angle x-ray-scattering data from a series of controlled-pore glasses (nominal 0 pore sizes from 75 to 2000 A) and from Vycor porous glass has revealed the fractal nature of the surfaces of these materials. The controlled-pore glasses show a relatively low degree of surface irre- gularity, with a surface fractal dimension of D =2. 20+0. 05, regardless of pore size. Vycor glass, the fractal properties of which have been under some debate, has a rougher surface, with D =2.40+0. 10. The D value for Vycor has been verified by small-angle neutron scattering. The 0 fractal dimensions refer to surface irregularity in the range 10-100 A. The scattering data suggest that the carriers of the fractal surface properties are interconnected units (particles, clusters) with 0 0 an average diameter of 300 and 450 A for the controlled-pore glasses of pore size 75 and 170 A, re- 0 spectively, and units with an average diameter of 350 A for Vycor glass. I. INTRODUCTION Many physical and chemical processes in nature, in in- dustry, and in the laboratory occur in porous environ- ments. The long and continuous interest in these sys- terns' has gained much rnomenturn in recent years, one of the reasons being the advent of new ideas which simplified the analysis of complex geometries. In this paper we focus our attention on a group of ma- terials known as controlled-pore glasses (CPG's), of which Vycor porous glass (VPG) is one example. This class of Si02 materials has the unique feature of having pore-size distributions (PSD's) which are much narrower than those found in silica gels. The most important use of controlled-pore glasses is in chromatography, where these glasses have offered practical solutions to many chemical, biochemical, biological, and medicinal chroma- tographic problems. Another important application of both CPG and VPG is as intermediates in the prepara- tion of silica glasses and optical fibers of high purity. ' '" The narrow pore-size distribution of VPG has made it the material of choice for many studies of the effects of a porous environment on diffusion, reaction, and physical 0 properties. Because the pore size is of the order of 40 A, many of these studies employed probes which during their lifetime can diffuse distances of this magnitude. Ex- amples are studies which involved photochemical' and photophysical processes. ' Among the electronic ground-state processes investigated in these porous envi- ronments are the superAuid behavior' '" of He and the kinetics of isotopic exchange, ' ' ' and of water adsorption. ' " There has been considerable interest in the question of whether or not VPG has fractal structural properties & 2( ' ), & 3( ), & s — & 8 Values of the fractal dimension D in the range 1. 7-2. 45 have been suggested for this ma- terial. In particular, small-angle x-ray- and neutron- scattering (SAXS and SANS, respectively) data gave' D =2. 0 and D =2.45. ' Here we report a study of a series of CPG's of various average pore sizes (APS) in the range 75-2000 A by SAXS, and of VPG by both SAXS and SANS. We obtained the following results: All of the CPG's which we studied have a fractal surface, with D =2. 20+0. 05, regardless of APS. For VPG we find that D =2. 40+0. 10; in the ongoing debate on the fractal properties of this material, our result is close to that of Sinha et al. ' These fractal dimensions refer to a regime of length scales of approximately 10-100 A. On length scales larger than about 100 A, we find that VPG and the small-APS CPG's have a nonfractal structure that can be modeled as a random-packed assembly of particles or clusters with average diameters from 300 to 450 A. (We conjecture a similar structure for the larger-APS CPG's, with an increasing particle diameter as the APS in- creases. In order to confirm this conjecture about these CPG's, however, one would have to measure intensities at smaller angles than those accessible in the present study. ) This cluster structure agrees with the model for VPG proposed by Kadokura' " and amplified by Yang et al. , ' ' ' except that (a) the particles are not smooth but have a fractally rough surface, as borne out by our D values, and (b) the particle diameter is larger. As we ex- plain in Sec. IV, the clusters and their fractal surface structure are in keeping with the mechanism of formation of these glasses. Our results about the cluster structure, as well as those in Ref. 15, leave little room for the idea' ""3" that VPG has a fractal pore network on length scales above 40 A. 38 1462 1988 The American Physical Society