Vrije Universiteit Brussel, Department of Chemical Engineering, Pleinlaan 2, Brussels 1050, Belgium.
KU Leuven, Department of Pharmaceutical Sciences, Pharmaceutical Analysis, Herestraat 49, Leuven 3000, Belgium.
J Chromatogr A. 2014 Jul 18;1351:46-55. doi: 10.1016/j.chroma.2014.04.099. Epub 2014 May 9.
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.
提出了整体柱和介孔骨架水平的单块二氧化硅柱 B 项带宽展宽的有效介质理论 (EMT) 表达式。鉴于整体柱的双连续性质，建立了 EMT 表达式的正则和反演形式。通过将建立的表达式应用于一组通过在若干第一代和第二代单块二氧化硅柱上进行峰停车获得的实验有效扩散 (Deff) 数据，以及一组在简化的单块柱表示形式（四面体骨架模型）中的数值扩散模拟，验证了所建立的表达式不同的外部孔隙率和内部扩散系数。可以使用建立的 EMT 表达式非常紧密地表示在非常宽的保留因子范围内（高达 k″=80）的数值模拟扩散数据，特别是当使用反演变体时。该表达式还可以非常紧密地表示实验测量的有效扩散数据。实验测量的 Deff/Dmol 值发现随着保留因子的增加而显著降低，通常从低 k″（k″≅1.5-3.8）时的约 Deff/Dmol=0.55 到 0.65 降低到非常高 k″（k″≅40-80）时的 Deff/Dmol=0.25。这些值明显大于在全多孔和核壳颗粒中观察到的值。骨架内扩散系数 (Dpz) 通常为 Dpz/Dmol=0.4，而在大多数基于颗粒的柱中观察到的 Dpz/Dmol=0.2-0.35。这些更高的 Dpz/Dmol 值是观察到更高的 Deff/Dmol 值的原因。此外，似乎更高的内部扩散与介孔骨架的更高孔隙率有关，介孔骨架具有相对开放的结构和相对较宽的孔。观察到的（弱）Dpz/Dmol 与区保留因子之间的关系似乎与直接在介孔骨架水平应用 EMT 表达式的正则变体时预测的关系非常吻合。
