Impact of surface diffusion on transport through porous materials.

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.

Effect of the polydispersity on the dispersion of polymers through silicas having different morphologies (fully porous and core-shell particles and monoliths).

The effect of the polydispersity of polystyrenes on the dispersion through silicas having different morphologies (fully porous, core-shell particles and monoliths) was investigated. The heights equivalent to a theoretical plate (HETP) of those columns were measured for a small molecule (toluene) and a series of polystyrenes of different sizes in non-adsorbing conditions. The different contributions to the total HETP including polydispersity were determined experimentally. The longitudinal diffusion and the mass transfer resistance term were obtained from peak parking experiments. The eddy dispersion was obtained from models and experiments. The effect of polydispersity on the HETP values (Hpoly) can thus be calculated from the total HETP by substraction of the other contributions. The results were compared to the Knox model which surestimates the Hpoly values for porous and core-shell particles which is usually explained by an overestimation of the polydispersity index (PDI) given by the manufacturer. The PDI of two polymers (P02, Mw= 690 g.mol-1 and P03, Mw=1380 g.mol-1) was verified by liquid chromatography by separating each fraction of the polymer on the silica columns by using adsorbing conditions which are obtained with a mixture of heptane and THF. The PDI obtained are comparable to the PDI given by the manufacturer meaning that the assumptions made by Knox are not entirely valid. A direct method is proposed in this paper in order to determine Hpoly. In this method the excess of spreading as compared with a polymer with only one size corresponding to the average size is studied assuming the polymer size distribution is gaussian. The Hpoly values obtained by the direct method are comparable to the experimental values.