Separation Speed and Power in Isocratic Liquid Chromatography: Loss in Performance of Poppe vs Knox-Saleem Optimization

But Why Doesn’t It Get Better? Kinetic Plots for Liquid Chromatography, Part III: Pulling It All Together

Choosing a liquid chromatography (LC) column for a particular application can be a surprisingly challenging task. On one hand, column manufacturers give us many options to choose from, including particle types, pore sizes, particle sizes, and different lengths and diameters. On the other hand, we usually don’t have time to experimentally evaluate many combinations of these parameters, and sometimes we end up picking something similar to the columns that are already in the drawer. The “kinetic plot” is a powerful graphical tool that can help leverage the best available theory to help us understand how different combinations of parameters (that is, particle size and length) will perform in terms of the time needed to get to a particular column efficiency (and thus resolution), and therefore make well-informed decisions when choosing columns.

But Why Doesn’t It Get Better? Kinetic Plots for Liquid Chromatography, Part I: Basic Concepts

Choosing a liquid chromatography (LC) column for a particular application can be a surprisingly challenging task. On the one hand, column manufacturers give us many options to choose from, including particle types, pore sizes, particle sizes, and different lengths and diameters. On the other hand, we usually do not have time to experimentally evaluate many combinations of these parameters, and sometimes we end up picking something similar to the columns that are already in the drawer. The “kinetic plot” is a powerful graphical tool that can help leverage the best available theory to help us understand how different combinations of parameters (such as particle size and length) will perform in relation to the time needed to get to a particular column efficiency (and thus resolution), and therefore make well-informed decisions when choosing columns.

Measurement of optimal flow rate in gradient elution liquid chromatography

Method development in gradient LC relies upon the selection of a solvent time program and a mobile phase flow rate. The flow rate, optimal for gradient separation cannot be inherently predicted by the isocratic value optimal for a given analyte, and rather should be identified independently to ensure the highest separation performance of gradient analysis. The optimal flow rate (F_opt) is defined herein as the solvent volumetric flow rate (F) maximizing the separation (Δs) of a predetermined peak-pair or the separation capacity (s_c) of the entire LC analysis. The theoretical background and the experimental technique of measurement of F_opt in gradient elution analysis were considered and experimentally demonstrated. The technique of measuring F_opt is based on translatable changes of F where the product Ft_G (t_G is the gradient time) was the same for all values of F. The F_opt was found as F corresponding to the maximum in Δs or in s_c.

Column length is a structure-independent measure of solvent consumption in liquid chromatography

Column length (L) is a measure of solvent consumption in LC analysis. In its latter role, L is the specific solvent consumption - the void time (t_M) solvent consumption per unit of the column flow-area (A_F) which is the cross-sectional area of the column open space (external and internal pores). In t_anal-long LC analysis (isocratic or gradient), the solvent consumption (V_S) is V_S = A_FLt_anal /t_M regardless of flow rate (F) as long as all changes in column dimensions and operational parameters are translatable (in gradient analysis, the ratio of the gradient time (t_G) to t_M remains fixed).

Three-dimensional graphing representing six variables for speed and separation performance in liquid chromatography

The two variables, flow rate and column length, enable naive determination of the number of theoretical plates (N) in isocratic elution; this, in turn, enables the formation of a three-dimensional graph with N as the z-axis. An alternate three-dimensional graph with N as the z-axis can be drawn, then, with the alternate basal plane illustrating the pressure drop and hold-up time. In this article, the pressure drop and hold-up time are formulated so as to be represented unitarily in the former graph, because the flow rate and column length interact simultaneously as operational variables. This formulation manipulates both the pressure drop and the hold-up time as logarithmic axes, to evaluate the landscape. Also of use is the representation, in the same graph, of the height equivalent to a theoretical plate, as the fundamental property of the packing supports. For this purpose, the number of theoretical plates per unit length are here introduced as the sixth variable, instead of the height equivalent to a theoretical plate. Representing the six variables in three-dimensional graphs enables a clear understanding both of the separation condition optimization methods and the relation among variables for the speed and separation performance. The linear velocity, column length, N, velocity-length product, hold-up time, and number of theoretical plates per unit length, are here selected as the six elementary variables for the three-dimensional graphs; and, based on the packing supports of 2, 3, and 5-μm particle and monolithic columns. Finally, the usage of logarithmic three-dimensional graph is illustrated for understanding the speed and separation performance.

Basic Structure-Independent Equations of Kinetic Performance of Columns in Liquid Chromatography

The lowest dimensionless plate height (h_min) of the liquid chromatography (LC) column is a subjective metric that cannot be found from measurements of parameters of a column as a separation device and is not suitable for comparison of kinetic performance of differently structured columns. In some cases (monolithic, pillar-array columns), there is no correlation between h_min (as it is currently understood) and the column performance. The same is true for the flow resistance parameter (ϕ). Recently introduced measurable effective diameter and structural quality factor (q_max) of a column are objective replacements for ϕ and h_min. Metric q_max, the maximum of the flow-dependent kinetic performance factor (q), is suitable for comparison of differently structured columns. Structure-independent basic equations binding kinetic performance of LC column with its q and other parameters and operational conditions were developed. It has been shown that previously known and new equations of a column kinetic performance can be derived from the basic ones. An example of using the equations for solving a known practical problem of column selection is provided.

Three approaches to improving performance of liquid chromatography using contour maps with pressure, time, and number of theoretical plates

Attempts to improve HPLC performance often focus on increasing the speed or separation performance. In this article, both the flow rate and column length are optimized as separation conditions, while observing the number of theoretical plates and hold-up time with isocratic elutions. In addition, the upper pressure limit must be simultaneously considered as the boundary condition. Approaches based on the optimal velocity (Opt.) are often adopted; but the kinetic performance limit (KPL) in Desmet's method can also be utilized for three-dimensional graphing with axes of pressure, time, and number of theoretical plates. Here, two approaches involving pressure increase are introduced, beginning with the condition of optimal linear velocity: one aimed at greater speed and the other at higher resolution. Coefficients of pressure-application are derived to measure the effectiveness of the intermediate conditions between the Opt. and KPL methods. In the third approach, the hold-up time is extended while maintaining a fixed pressure. Coefficients of time-extension are also derived, to determine the effectiveness to improve the separation performance.

Methods to determine the kinetic performance limit of contemporary chromatographic techniques

By combining separation efficiency data as a function of flow rate with the column permeability, the kinetic plot method allows to determine the limits of separation power (time vs. efficiency) of different chromatographic techniques and methods. The technique can be applied for all different types of chromatography (liquid, gas, or supercritical fluid), for different types of column morphologies (packed beds, monoliths, open tubular, micromachined columns), for pressure and electro-driven separations and in both isocratic and gradient elution mode. The present contribution gives an overview of the methods and calculations required to correctly determine these kinetic performance limits and their underlying limitations.

Graphical Method for Choosing Optimized Conditions Given a Pump Pressure and a Particle Diameter in Liquid Chromatography

The general limitations on liquid chromatographic performance in isocratic and gradient elution are now well understood. Many workers have contributed to this understanding and to developing graphical methods, or plots, to illustrate the capabilities of chromatographic systems over a wide range of values of operational parameters. These have been invaluable in getting a picture, in broad strokes, about the value of changing an operational parameter or the value of one separation approach over another. Here we present a plotting approach more appropriate for determining how to use chromatography most efficiently in one's own laboratory. The axes are linear: column length vertical and mobile phase velocity horizontal. In this coordinate system, straight lines with intercept zero correspond to different values of t₀. Hyperbolas correspond to values of pressure as the product of length and velocity is proportional to pressure. For a given relationship between theoretical plate height and velocity (e.g., van Deemter), the number of theoretical plates as a function of column length and mobile phase velocity is a surface (z direction) to the x and y of velocity and length. By representing the surface as contours, a two-dimensional plot results. Any point along a constant pressure hyperbola represents the best one can do given the particle diameter, solute diffusion coefficient, and temperature. The user can quickly see how to use the pressure for speed or for more theoretical plates. Sets of such plots allow for comparisons among particle diameters or temperatures. Analogous plots of peak capacity for gradient elution are equally revealing. The plots lead instantly to understanding liquid chromatographic optimization at a practical level. They neatly illustrate the value (or not) of changing pump pressure, particle diameter, or temperature for fast or slow separations in either isocratic or gradient elution. They are illustrated with a focus on maximizing plate count with a given analysis time (isocratic), the effect of volume overload (isocratic), and separations of a limited number of peptides with a peak capacity coming from statistical peak overlap theory (gradient).