Impact of surface diffusion on transport through porous materials

•Model of surface diffusion using Brownian motion.•Surface diffusion depends on chain length and surface chemistry.•Model and experimental results are comparable. The peak parking method was applied to evaluate the surface diffusivity Ds of polystyrenes dissolved in a THF/heptane mixture and transported through porous silica materials with various morphologies. With this method, the overall effective diffusivity D is measured experimentally with coarse-grained models like Maxwell equation allowing one to infer the particle diffusivity Dpz. Such particle diffusivity has two main contributions: in-pore diffusivity Dp and surface diffusivity Ds. The diffusion within the pores is determined experimentally using either non-adsorbing conditions or calculated from particle porosity, particle tortuosity, and hydrodynamic hindrance. The surface diffusion coefficient Ds is usually determined using models considering parallel diffusion in the pores and at the surface but this assumption is rather crude. In this paper, to address this problem, another approach is proposed using the Brownian motion of molecules in the pore space. These two approaches lead to similar equations relating the effective diffusion coefficient D, the in-pore diffusion Dp and surface diffusion Ds. The surface diffusion is analyzed as a function of the surface affinity of the probes considered here (polystyrenes of different molecular weights/lengths). Such surface affinity depends both on the probe chain length and surface chemistry of the host solid (the latter being characterized here through the silanol surface density). For short chain lengths, a non-monotonic change in the surface diffusion with affinity (i.e. retention factor) is observed in some cases. Yet, generally, as expected, surface diffusion decreases upon increasing the surface affinity. In contrast to short chain lengths, the longest chain lengths are less sensitive to the silanol surface density.