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Pore Size Distribution of Silica Colloidal Crystals from Nitrogen Adsorption Isotherms.

Silica colloidal crystals are face-centered cubic structures comprised of silica spheres with the diameters ranging between tens and hundreds of nanometers. The voids between the spheres form pores, which can be probed by nitrogen adsorption porosimetry. Here we prepared two mesoporous samples and a macroporous reference sample, then measured nitrogen adsorption and desorption isotherms for further characterization. We proposed a straightforward procedure for calculation of pore-size distribution of silica colloidal crystals from nitrogen adsorption isotherms. The procedure is based on the adsorption integral equation solution with a kernel of theoretical isotherms, consistent with the procedure used for many other porous materials. The solution is carried out using the non-negative least squares (NNLS) method with Tikhonov regularization. The kernel of mesoporous isotherms is build based on the macroscopic Derjaguin-Broekhoff-de Boer (DBdB) theory of capillary condensation considering the voids as a network of spheres. Application of our procedure to the analysis of the adsorption branches of experimental isotherms resulted in bi-modal distributions, where the modes matched well with the sizes of the voids in the colloidal crystals fcc structure: the main mode corresponds to the octahedral voids, and the second mode -- to the tetrahedral voids. Furthermore, we modified the surface of the samples with organics, and repeated the characterization procedure for the modified samples. The resulting pore size distribution for the samples with the modified surface matched the original one quite closely. It demonstrates the procedure as a simple and efficient technique to estimate the pore size distribution, and justifies the spherical shape approximation for the voids in the silica colloidal crystals.