Relations between kinetic parameters of different column models for liquid chromatography applying core-shell particles

Abstract

This article presents analytical solutions of the general rate model (GRM), the lumped kinetic model (LKM), and the simpler equilibrium dispersive model (EDM) for core-shell particles and linear adsorption isotherms. The solutions in the Laplace domain are applied to derive analytical expressions for the temporal moments of these models. The results provide relations between the model specific kinetic parameters by matching one or more of the temporal moments. Several case studies are considered for illustration. The results show that simpler models are in many cases as good as the most detailed GRM if their kinetic parameters fulfill the matching relations. Thus, it is possible to reliably predict elution profiles using the simpler models. The derived analytical expressions can also be utilized to efficiently estimate model parameters from experimentally observed elution profiles to further optimize core-shell particles and to identify suitable column sizes and operating conditions. GRAPHICAL ABSTRACT 0 10 20 30 40 50 60 70 80 90 0 0.1 0.2 0.3 0.4 0.5 t [min] c [g/l] GRM LKM EDM u = 1 cm/min KEYWORDS Core-shell particles; Liquid chromatography; mathematical models; moment analysis; matching relations; semi-analytical solutions rate model (GRM), the lumped kinetic model (LKM), and the equilibrium dispersive model (EDM). [1,2] Hereby, the GRM is the most detailed model, while the LKM and EDM have less degrees of freedom and are simpler. It accounts for various mass transfer kinetics that influence the band profiles, namely external mass transfer resistance and intraparticle diffusion. In addition axial dispersion is

Recent advances in modelling and control of liquid chromatography

“…This is achieved by two additional equations describing the radial solute concentration profiles inside the porous particles (Figure 2c) and the mass transfer between the stationary and mobile phases at the stationary particle surfaces. For some kinetic parameters, the GRM reduces to a lumped kinetic model which can be considered as an intermediate between EDM and GRM [50]. Since computational power is no longer a bottleneck for the more demanding GMR models, and because these models provide the highest accuracy, they are now used more commonly, although their application is mostly limited by the amount of parameters that have to be estimated using additional models or experiments.…”

Numerical Approximation of the Nonequilibrium Model of Gradient Elution Chromatography Considering Linear and Nonlinear Solvent Strength Models

“…It is generally known that under some fundamental assumptions simpler models may be obtained from the comprehensive general rate model. 19 , 20 …”

“…The EDM is the simplest and basic, combining all kinetic effects into a single apparent dispersion value. It is generally known that under some fundamental assumptions simpler models may be obtained from the comprehensive general rate model. , …”

“…It is generally known that under some fundamental assumptions simpler models may be obtained from the comprehensive general rate model. 19,20 While gradient elution studies frequently require the use of tiny and dilute samples, in preparative gradient elution chromatography, the column is frequently overloaded. As a result, the adsorption isotherms are nonlinear and competitive, and interference effects become significant.…”

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“…On the other hand, the chromatographic processes and subsequent technologies used in the industry for product purification are well-understood and established. Thus, mechanistic modeling of biochromatography has, as of today, reached a considerable maturity level. , A wide range of mechanistic models with different complexities are available, with the Generalized Rate Models (GRMs) − being the most detailed and the equilibrium dispersive models being the simplest. ,, The pore-based and lumped kinetic models are mechanistic models with intermediate complexity. These mechanistic models provide the ability to learn and predict the chromatographic behavior of proteins in terms of how the different phases (liquid and solid) interact and how the concentration of the protein of interest is distributed along the column and in time.…”