Nanometer Pore Size Dependence of Intraparticle Diffusion in Silica Gel

Abstract

The sorption of rhodamine 6G into single silica gel microparticles possessing pore sizes of 3, 6, 15, and 30 nm was analyzed using single microparticle injection and microabsorption methods. The intraparticle diffusion of the solute was highly influenced by the pore size of the silica gel. The relationship between the intraparticle diffusion coefficient and a hindrance parameter for the diffusion in the pores is discussed on the basis of a pore and surface diffusion model.

Analysis of Distribution and Intraparticle Diffusion of a Fluorescent Dye in Mesoporous Silica Gel by Confocal Fluorescence Microspectroscopy

“…In previous reports, the intraparticle diffusion of Rh6G in silica gel was analyzed by a spherical diffusion equation based on the Fick's second law as the external diffusion is assumed to be very fast. 7,8,15 In the present model, both the external diffusion including the restricted external diffusion at the lower side of the microparticle and the intraparticle diffusion of Rh6G are considered. The t dependence of a concentration profile of Rh6G (Ci(r, θ, t), i = p or w) in the microparticle (Cp(r, θ, t)) or water (Cw(r, θ, t)) is given by the diffusion equation (Eq.…”

“…We previously reported the intraparticle diffusion of rhodamine 6G (Rh6G) in silica gel/water systems using an absorption microspectroscopy method combined with a single microparticle injection technique. 7,8,15 Based on the absorption microspectroscopy, however, we could only determine the total concentration of the dye in the single microparticle, so the intraparticle diffusion was indirectly analyzed as the particle size dependence of the diffusion coefficient. Recently, we have developed the confocal fluorescence microspectroscopy method combined with the single microparticle injection technique.…”

External and Intraparticle Diffusion of Coumarin 102 with Surfactant in the ODS-silica Gel/water System by Single Microparticle Injection and Confocal Fluorescence Microspectroscopy

“…As Ke = 5 × 10 3 , Dp is estimated to be much greater than 2 × 10 -9 cm 2 s -1 . According to the pore and surface diffusion model, on the other hand, Dp is given by the equation for Ke >> 1: Dp = DwH/{τp(1+Ke)}+Ds/τs, 14,30 where H is the hindrance parameter and estimated to be 0.69 by the Renkin equation as the coumarin 102 diameter is 1 nm. 31 Ds is the surface diffusion coefficient of coumarin 102.…”

“…[14][15][16] In those reports, as the mass transfer rate in the microparticle/solution system was assumed to be limited by the intraparticle diffusion, the intraparticle diffusion coefficient (Dp) was estimated. When the supposed Dp value was independent of the microparticle diameter (d), the intraparticle diffusion was analyzed in detail on the basis of the pore and surface diffusion model.…”

“…When the supposed Dp value was independent of the microparticle diameter (d), the intraparticle diffusion was analyzed in detail on the basis of the pore and surface diffusion model. [14][15][16] For mass transfer of perylene as a water-insoluble organic compound in the presence of Triton X-100 (nonionic surfactant) in an ODS-silica gel/water system, however, the supposed Dp value depended on d, indicating that the mass transfer rate cannot be analyzed as the intraparticle diffusion. 17 From the d dependence of mass transfer rate, we concluded that the rate-determining step was the micelle-mediated solubilization of the dye at the microparticle surface.…”