title: Experimental and numerical validation of the effective medium theory for the B-term band broadening in 1st and 2nd generation monolithic silica columns.
abstract: Effective medium theory (EMT) expressions for the B-term band broadening in monolithic silica columns are presented at the whole-column as well as at the mesoporous skeleton level. Given the bi-continuous nature of the monolithic medium, regular as well as inverse formulations of the EMT-expressions have been established. The established expressions were validated by applying them to a set of experimental effective diffusion (Deff)-data obtained via peak parking on a number of 1st and 2nd generation monolithic silica columns, as well as to a set of numerical diffusion simulations in a simplified monolithic column representation (tetrahedral skeleton model) with different external porosities and internal diffusion coefficients. The numerically simulated diffusion data can be very closely represented over a very broad range of zone retention factors (up to k″=80) using the established EMT-expressions, especially when using the inverse variant. The expressions also allow representing the experimentally measured effective diffusion data very closely. The measured Deff/Dmol-values were found to decrease significantly with increasing retention factor, in general going from about Deff/Dmol=0.55 to 0.65 at low k″ (k″≅1.5-3.8) to Deff/Dmol=0.25 at very high k″ (k″≅40-80). These values are significantly larger than observed in fully-porous and core-shell particles. The intra-skeleton diffusion coefficient (Dpz) was typically found to be of the order of Dpz/Dmol=0.4, compared to Dpz/Dmol=0.2-0.35 observed in most particle-based columns. These higher Dpz/Dmol values are the cause of the higher Deff/Dmol values observed. In addition, it also appears that the higher internal diffusion is linked to the higher porosity of the mesoporous skeleton that has a relatively open structure with relatively wide pores. The observed (weak) relation between Dpz/Dmol and the zone retention factor appears to be in good agreement with that predicted when applying the regular variant of the EMT-expression directly to the mesoporous skeleton level.
authors.affiliation: Vrije Universiteit Brussel, Department of Chemical Engineering, Pleinlaan 2, Brussels 1050, Belgium.
authors.forename: Sander
authors.initials: S
authors.lastname: Deridder
authors.affiliation: KU Leuven, Department of Pharmaceutical Sciences, Pharmaceutical Analysis, Herestraat 49, Leuven 3000, Belgium.
authors.forename: Alison
authors.initials: A
authors.lastname: Vanmessen
authors.affiliation: Kyoto University, Department of Chemistry, Sakyo-ku, Kyoto 606-8502 JAPAN.
authors.forename: Kazuki
authors.initials: K
authors.lastname: Nakanishi
authors.affiliation: Vrije Universiteit Brussel, Department of Chemical Engineering, Pleinlaan 2, Brussels 1050, Belgium. Electronic address: gedesmet@vub.ac.be.
authors.forename: Gert
authors.initials: G
authors.lastname: Desmet
authors.affiliation: KU Leuven, Department of Pharmaceutical Sciences, Pharmaceutical Analysis, Herestraat 49, Leuven 3000, Belgium.
authors.forename: Deirdre
authors.initials: D
authors.lastname: Cabooter
mesh_terms: D002845:Chromatography / Q000295:instrumentation*; D003198:Computer Simulation; D004058:Diffusion; D008956:Models, Chemical; D016062:Porosity; D015203:Reproducibility of Results; D012822:Silicon Dioxide / Q000737:chemistry*
chemical_list: D012822:Silicon Dioxide
keywords: Effective diffusion; Effective medium theory; Modeling; Monolithic porous medium; Peak parking