Waters Corporation, Instrument/Core Research/Fundamental, Milford, MA 01757, USA.
J Chromatogr A. 2018 Jan 19;1533:112-126. doi: 10.1016/j.chroma.2017.12.030. Epub 2017 Dec 14.
The general dispersion theory of Aris is applied to predict the virtual asymptotic dispersion behavior of packed columns. The derived model is also used to estimate the actual pre-asymptotic dispersion behavior of modern 2.1 mm × 50 mm columns packed with sub-2 μm fully porous particles (FPPs) during the transient dispersion regime. The model accounts for the actual radial distribution of the flow velocity across the column diameter. From the wall to the center of the column, focused-ion-beam scanning electron microscopy (FIB-SEM) experiments were recently performed to reveal the existence of a thin (0.15d wide, d is the average particle diameter) hydrodynamic boundary layer (THBL), a thin (3d wide) and loose orderly packed layer (TLOPL), a 60d wide and dense randomly packed layer (WDRPL), and a large (≃460d) randomly packed bulk central region [1]. The theoretical calculations of the actual pre-asymptotic reduced van Deemter curves (2.1 mm × 50 mm column, sub-2 μm BEH-C FPPs, n-hexanophenone analyte, acetonitrile/water eluent, 80/20, v/v, flow rate from 0.05 to 0.35 mL/min) confirm that the impact of the sole THBL on column dispersion can be neglected. In contrast, the contribution of the TLOPL to the reduced plate height (RPH) is about 0.2 h unit at optimum reduced velocity. Most remarkably, the negative impact of the TLOPL on column performance may be fully compensated by the presence of the adjacent WDRPL if the depth of the velocity well were to be 5% of the bulk velocity. In actual 2.1 mm × 50 mm columns packed with sub-2 μm FPPs, this velocity depth is as large as 25% of the bulk velocity causing a significant RPH deviation of 0.7 h unit from the RPH of the bulk packing free from wall effects. Maximum column performance is expected for a reduction of WDRPL density. This suggests optimizing the packing process by finding the proper balance between the stress gradient across the WDRPL (responsible for the deep velocity well) and the friction forces between the packed particles (responsible for the rearrangement of the particles during bed consolidation). Past and recently reported RPH data support the theoretical insights: the stress gradient/particle friction balance in the WDRPL is better realized when packing superficially porous particles (SPPs) rather than FPPs in 2.1-4.6 mm i.d. columns (the RPH deviation is reduced to 0.4 h unit) or sub-2 μm particles in 100 cm × 75 μm i.d. capillaries combining high slurry concentrations and sonication (the RPH deviation is reduced to only 0.15 h unit).
阿里斯（Aris）的一般扩散理论被应用于预测填充柱的虚拟渐近扩散行为。所得到的模型也用于估计在瞬态扩散阶段，现代 2.1mm×50mm 柱中使用亚 2μm 全多孔颗粒（FPP）填充时的实际渐近前的扩散行为。该模型考虑了柱径内实际的流速径向分布。最近通过聚焦离子束扫描电子显微镜（FIB-SEM）实验从壁到柱中心揭示了存在一个薄（0.15d 宽，d 是平均粒径）的流体动力边界层（THBL），一个薄（3d 宽）且松散有序填充层（TLOPL），一个 60d 宽且密集随机填充层（WDRPL）和一个大（≃460d）的随机填充中心区域[1]。对实际渐近前的降低范德米尔曲线（2.1mm×50mm 柱，亚 2μm BEH-C FPP，正己烷酮分析物，乙腈/水洗脱液，80/20，v/v，流速从 0.05 到 0.35mL/min）的理论计算证实，单独的 THBL 对柱扩散的影响可以忽略不计。相比之下，在最佳降低速度下，TLOPL 对降低板高（RPH）的贡献约为 0.2h 单位。最值得注意的是，如果速度阱的深度为主体速度的 5%，则 TLOPL 对柱性能的负面影响可能会被相邻的 WDRPL 完全补偿。在实际的填充有亚 2μm FPP 的 2.1mm×50mm 柱中，该速度深度高达主体速度的 25%，导致与无壁效应的主体填充的 RPH 偏差为 0.7h 单位。最大的柱性能预计是降低 WDRPL 密度。这表明通过在 WDRPL 中的应力梯度（负责深的速度阱）和填充颗粒之间的摩擦力（负责床固结过程中颗粒的重新排列）之间找到适当的平衡，优化填充过程。过去和最近报道的 RPH 数据支持理论见解：在 2.1-4.6mm 内径柱中填充表面多孔颗粒（SPP）而不是 FPP 时（RPH 偏差减小到 0.4h 单位），或者在 100cm×75μm 内径毛细管中使用亚 2μm 颗粒并结合高浆料浓度和超声处理（RPH 偏差减小到仅 0.15h 单位），在 WDRPL 中实现了更好的应力梯度/颗粒摩擦平衡。
