Estimation of diffusion parameters in functionalized silicas with modulated porosity

Detailed analysis of the effective and intra-particle diffusion coefficient of proteins at elevated pressure in columns packed with wide-pore core-shell particles

To determine the efficiency that can be obtained in a packed-bed liquid-chromatography column for a particular analyte, a correct determination of the molecular and effective diffusion coefficients (Dm and Deff) of the analyte is required. The latter is usually obtained via peak parking experiments wherein the flow is stopped. As a result, the column pressure rapidly dissipates and the measurement is essentially conducted at ambient pressure. This is problematic for analytes whose retention depends on pressure, such as proteins and potentially other large (dipolar) molecules. In that case, a conventional peak parking experiment is expected to lead to large errors in Deff. To obtain a better estimate ofDeff, the present study reports on the use of a set-up enabling peak parking measurements under pressurized conditions. This approach allowed us to report, for the first time, Deff for proteins at elevated pressure under retained conditions. First, Deff was determined at a (average) pressure of about 105 bar for a set of proteins with varying size, namely: bradykinin, insulin, lysozyme, β-lactoglobulin, and carbonic anhydrase in a column packed with 400 Å core-shell particles. The obtained data were then compared to those of several small analytes: acetophenone, propiophenone, benzophenone, valerophenone, and hexanophenone. A clear trend between Deff and analyte size was observed. The set-up was then used to determine Deff of bradykinin and lysozyme at variable (average) pressures ranging from 28 bar to 430 bar. These experiments showed a decrease in intra-particle and surface diffusion with pressure, which was larger for lysozyme than bradykinin. The data show that pressurized peak parking experiments are vital to correctly determine Deff when the analyte retention varies significantly with pressure.

Comparative study of morphometric properties characterizing the complexity of silicate pore networks probed by adsorption of nitrogen and methanol

In this work, we compare the surface and morphometric properties of the pore networks in four silicas (code names Fr1428, Fr474, Fr1386, and MM1164) with different random porosities using the adsorption isotherms of two different probe adsorbents, nitrogen and methanol. The parent material Fr1428 was a pure silica 25 microm sample. The Fr474 sample was the same one with bonded electroneutral diol groups on its outer surface. Fr1386 was the parent material with bonded electroneutral diol groups on its outer surface and sulfonic groups on its inner surface, and the MM1164 sample was the original sample with external electroneutral diol groups and internal n-octadecyl groups. The properties examined were the specific surface area S(p) and the specific pore volume V(p), the pore connectivity c, the pore anisotropy b, the tortuosity tau, and the lacunarity lambda of the pore network as well as the percentage microporosity. These properties provide a complete characterization of complexity of the porous network. The surface areas of the solids were estimated via the traditional BET plots (S(BET)) and the I-point method (S(I)). The two sets of values S(BET) and S(I) were practically identical and they decrease as the size of the functional group increases. The values of percentage microporosity were also determined by the same I-point method using the variation of the C parameter of the BET equation. The total pore volume V(p) was found to be higher in the case of methanol adsorption, compared to nitrogen, which might be related to increase condensation. The networks of the pores were simulated using a dual site bond model (DSBM) and Monte Carlo (MC) techniques for achieving their proper arrangement into the solids. From the resulting simulating networks, the pore connectivity distributions (PCD) and their mean values c(mean) were estimated and favorably compared to the values of connectivity c(Seaton) determined according to the method of Seaton. Both values decrease with the size of the functional groups and are weakly affected by the adsorbent employed. From the simulation pore network, the mean values of tortuosity tau(mean) were also estimated and found to be lower when N2 was used as adsorbate compared to MeOH. The values of lacunarity lambda, estimated according to the method by Allain and Cloitre using the moving box technique in the DSBM/MC simulation matrix of the pore network, indicate that the distribution of the poreless mass into the matrix increases with the size of the functional group. Finally, the internal relationships observed between the pore anisotropy b and the percentage microporosity as well as between the tortuosity tau and the pore connectivity c are discussed.