Effect of tortuosity on diffusion of polystyrenes through chromatographic columns filled with fully porous and porous –shell particles and monoliths

The tortuosity parameter, essential in the prediction of molecular transport properties, is determined for several materials with multiscale porosities: interparticular/interskeleton macropores and intraparticular/intraskeleton mesopores for beds of spherical porous particles and monoliths. Electrical measurements (impedance spectroscopy) and peak parking experiments are used. The former measures the electrical resistance between two electrodes surrounding the porous material impregnated with a concentrated electrolyte, while the latter uses a set of polystyrene molecules in non-adsorbing conditions within a chromatographic setup. Tortuosity measurements as well as characterization via mercury porosimetry, nitrogen adsorption and inverse size exclusion chromatography (ISEC) are performed on four materials: fully porous silica and alumina particles, core-shell silica particles and silica monoliths. The tortuosity determined by electrical measurements is in agreement with the value determined by peak parking with the smallest probe (toluene). For molecules which size is not negligible as compared to pore size, the apparent particle tortuosity is determined from the intraparticle diffusion coefficient obtained by the Maxwell model estimating the hindrance factor via the Renkin correlation. The apparent particle tortuosity is estimated from the Weissberg equation τp[rm] = l-pln(εp[rm]), where εp[rm] is the particle porosity accessible to a molecule of size rm and p a parameter depending on the material topology. A model with just one adjustable parameter p can thus estimate the intraparticle diffusion coefficient in non-adsorbing conditions.