Fractal surface and cluster structure of controlled-pore glasses and Vycor porous glass as revealed by small-angle x-ray and neutron scattering

Analysis of small-angle x-ray-scattering data from a series of controlled-pore glasses (nominal 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 irregularity, 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 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 an average diameter of 300 and 450 A{} for the controlled-pore glasses of pore size 75 and 170 A{}, respectively, and units with an average diameter of 350 A{} for Vycor glass.