Pore structural characterization of monolithic silica columns by inverse size-exclusion chromatography

In this work, a parallel pore model (PPM) and a pore network model (PNM) are developed to provide a state-of-art method for the calculation of several characteristic pore structural parameters from inverse size-exclusion chromatography (ISEC) experiments. The proposed PPM and PNM could be applicable to both monoliths and columns packed with porous particles. The PPM and PNM proposed in this work are able to predict the existence of the second inflection point in the experimental exclusion curve that has been observed for monolithic materials by accounting for volume partitioning of the polymer standards in the macropores of the column. The appearance and prominence of the second inflection point in the exclusion curve is determined to depend strongly on the void fraction of the macropores (flow-through pores), (b) the nominal diameter of the macropores, and (c) the radius of gyration of the largest polymer standard employed in the determination of the experimental ISEC exclusion curve. The conditions that dictate the appearance and prominence of the second inflection point in the exclusion curve are presented. The proposed models are applied to experimentally measured ISEC exclusion curves of six silica monoliths having different macropore and mesopore diameters. The PPM and PNM proposed in this work are able to determine the void fractions of the macropores and silica skeleton, the pore connectivity of the mesopores, as well as the pore number distribution (PND) and pore volume distribution (PVD) of the mesopores. The results indicate that the mesoporous structure of all materials studied is well connected as evidenced by the similarities between the PVDs calculated with the PPM and the PNM, and by the high pore connectivity values obtained from the PNM. Due to the fact that the proposed models can predict the existence of the second inflection point in the exclusion curves, the proposed models could be more applicable than other models for ISEC characterization of chromatographic columns with small diameter macropores (interstitial pores) and/or large macropore (interstitial pore) void fractions. It should be noted that the PNM can always be applied without the use of the PPM, since the PPM is an idealization that considers an infinitely connected porous medium and for materials having a low (<6) pore connectivity the PPM would force the PVD to a lower average diameter and larger distribution width as opposed to properly accounting for the network effects present in the real porous medium.