Practical limits to column performance in liquid chromatography – Optimal operations
Introduction
Several column structures are used or are being investigated in liquid chromatography (LC) [1], [2], [3], [4], [5], [6], [7], [8], [9]. Their kinetic performance (briefly, performance) – the trade-off between separation, pressure, and time – depends not only on the structure but also on its implementation in each specific column. Objective performance metrics of the column structures have previously been evaluated [10], [11]. The focus of this study is on the development of objective characterization of specific differently structured columns rather than on their structures.
It has been previously shown [11] that, because they are based on particle size (dp), defined subjectively in many cases, the widely known dimensionless plate height (h) [12] and flow resistance parameter (ϕ) [5], [13], [14], [15], [16] can bring about misleading conclusions regarding the column's comparative performance. Among the objective metrics are the separation impedance (E) [15], the universal plate height (hc), and the kinetic performance factor (q) [10], [11] – all three are equivalent to each other with one uniquely defining the others and none adding information to the others. However, q has several advantages over the others and is the metric of choice in this report. It is the only metric proportional to peak capacity (n), resolution, and other metrics of separation performance of chromatographic systems.
Quantity q for a given column and solute depends on the solvent velocity and reaches its maximum (qmax) at optimal velocity. Different structures can have different qmax. Thus, under similar experimental conditions, qmax of an open-tubular column (OTC) is higher (better) than that of packed (not open-tubular) columns, qmax of pillar-array columns is higher than that of particulate and monolithic columns, and so on [10], [11]. Because the largest n attainable by a column at the same pressure in the same time is proportional to qmax, the latter was termed the structural quality factor [10], [11] of the column structure.
Being a parameter of a column structure, qmax does not incorporate all properties of specific columns. Owing to practical factors of design and manufacturing of the columns of each structure, a column of superior structure (larger qmax) may underperform its inferior counterparts (smaller qmax) in practical LC analyses. Thus, a column of superior structure might not be able to tolerate as high pressure as its counterparts of inferior structure can, or current manufacturing technology might not allow sufficiently narrow flow-through channels in the columns of superior structure and prevent realization of the full performance potential of their structures. Sorting out the effects of these and similar factors on performance of practically available columns is the topic of this report. The equations developed herein are tailored to address these issues.
The goal of this study is not to identify better- or worse-performing structures or specific columns but to develop a methodology of comparing the performance of differently structured columns, accounting for practically existing limits to that performance. In short, this report is not about specific columns and/or their structures but about the methodology of comparing the performance of practically existing columns.
It is assumed in this report that LC solvents are incompressible fluids, and, as its title indicates, only the optimal conditions with q = qmax are considered. Other assumptions introduced below are also highlighted by the bold face type.
Section snippets
Basic definitions
The following is a brief review of previously introduced [10], [11] performance metrics of LC columns. Additional details can be found in the sources.
Let tR and σ be retention time and standard deviation of a peak in a chromatogram, respectively. The latter is the only peak width metric herein, and the terms peak width and the peak standard deviation are treated as synonyms. Quantities Q and H below are, respectively, the transport efficiency and the apparent plate height [17] (briefly, plate
Experimental
The following discussion is based on the published data compiled in Table 2 for the columns of several structures abbreviated herein as:
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SWOT – solid-wall open-tubular columns having nonporous internal walls [1].
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PLOT – porous-layer open-tubular columns [2].
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PA – pillar-array columns [3].
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SCP – columns packed with solid-core particles [4].
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TPP – columns packed with totally porous particles [4].
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SM – silica monolithic columns [5].
The SWOT and PLOT columns are the OTC; all others are packed columns.
General considerations
Performance of LC analysis of a complex mixture can be expressed via its peak capacity (n) and analysis time (tanal). The latter is the price for the former and should be as small as possible. As shown in Supplementary material, n and tanal of generic gradient RPLC (reversed phase LC) analysis in a column with transport efficiency Q and void time tM at optimal mixing rate (approximately 5% increase in volume fraction of stronger solvent per tM in analyses of small molecules, down to 0.5% /tM
Conclusions
Kinetic properties of a column's internal structure are not the only factors affecting the performance (the trade-offs between separation, time, and pressure) of practically available columns. Because of constraints on its design, manufacturing, and other factors, a column might not be able to perform at its maximum potential represented by the quality factor (qmax) of its structure (or, equivalently, by the lowest separation impedance, Emin). The limiting factors evaluated in this report are
Declaration of Competing Interest
I declare that I have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this manuscript.
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