Modeling of the Mass-Transfer Kinetics in Chromatographic Columns Packed with Shell and Pellicular Particles

Novel insights into the dependence of adsorption-desorption kinetics on particle geometry in chiral chromatography

The existence of slow adsorption-desorption kinetics in chiral liquid chromatography is common knowledge. This may significantly contribute to worsening the efficiency and kinetic performance of a chromatographic run, especially when high flow rates are employed. Many attempts and protocols have been proposed to access this term, the so-called c ads , but they are based on different (theoretical) assumptions. As a consequence, no official method is available for the estimation of the adsorption-desorption kinetics term. In this work, a novel approach to access c ads is presented. This procedure combines experimental results obtained with kinetic and thermodynamic measurements. The investigations have been performed on two zwitterionic teicoplanin chiral stationary phases (CSPs) based on 1.9 μ m fully porous and 2.0 μ m superficially porous particles (FPPs and SPPs), using Z-D,L-Methionine as probe molecule. Kinetic studies have been performed through the combination of both stop-flow and dynamic measurements, while adsorption isotherms have been calculated through Inverse Method. This study has confirmed that, on both particle formats, analyte diffusion on the surface of the particle is negligible, meaning that adsorption is localized, and it has been demonstrated that adsorption-desorption kinetics is strongly dependent on particle geometry and, in particular, on the loading of chiral selector. These findings are fundamental not only to unravel novel aspects of the complex enantiorecognition mechanism but also to optimize the employment of CSPs for ultra-fast and preparative applications.

Theoretical Investigation of the Nonlinear General Rate Model with the Bi-Langmuir Adsorption Isotherm Using Core-Shell Adsorbents

Core-shell particles enable the separation of intricate mixtures in a highly efficient and rapid manner. The porous shell particles increased the separation efficiency with expedited flow rates due to an abatement in the pore volume accessible for longitudinal diffusion and a decrease in diffusion path length. This study focuses on the numerical approximation of a nonlinear isothermal general rate model applied to stationary bed columns that are replete with inert core adsorbents featuring double adsorption sites. The transport of solute in heterogeneous porous media can be modeled by a nonlinear convection acquiescent partial differential equation system together with a specific nonlinear algebraic relation: the bi-Langmuir adsorption isotherm. Therefore, it is important to develop accurate and reliable numerical techniques that can perform accurate numerical simulations of these models. We extended and implemented a second-order, semidiscrete, high-resolution finite volume method to simulate the governing equations of the model. Single solute flow and multi component mixture flows are assessed through a series of numerical experiments to theoretically illustrate the repercussions of intraparticle diffusion, film mass resistance, axial dispersion, and the size of the inert core radius upon simulated elution curves. Standard performance criteria are assessed to determine the optimal core radius fraction range for optimizing the separation performance.

Absorption and escape kinetics of spherical biomolecules from fully porous particles utilized in size exclusion chromatography

The increasing demand for the characterization of large biomolecules such as monoclonal antibodies, double-stranded deoxyribonucleic acid (dsDNA), and virus-like particles (VLPs) is raising fundamental questions pertaining to their absorption (ingress) and escape (egress) kinetics from fully porous particles. The exact expression of their concentration profiles is derived as a function of time and radial position across a single sub-3 μm Bridge-Ethylene-Hybrid (BEH^TM) Particle present in size exclusion chromatography (SEC) columns. The boundary condition at the external surface area of the particle is a rectangular concentration profile mimicking the passage of the chromatographic zone. Four different BEH Particles were considered in the calculations depending on the molecular size of the analyte: 2.0 μm 100 Å BEH Particles for small molecules, 2.0 μm 200 Å BEH Particles for monoclonal antibodies, 2.0 μm 300 Å BEH Particles for dsDNA (100 base pairs), and 2.5 μm 900 Å BEH Particles for virus-like particles (VLPs). The calculated concentration profiles of small molecules and monoclonal antibodies confirm that all BEH Particles present in the column reach quasi-instantaneously thermodynamic equilibrium with the bulk mobile phase during the passage of the chromatographic band. This is no longer the case for larger biomolecules such as dsDNA or VLPs, especially when the SEC particle is located near the column inlet and for high velocities. The kinetics of biomolecule egress is slower than its kinetics of ingress leading to pronounced peak tailing. The mean concentration of the largest biomolecules in the SEC particles remains always smaller than the maximum bulk concentration. This persistent and transient intra-particle diffusion regime has direct implications on the theoretical expressions of the observed retention factors and plate heights. Classical theories of chromatography assume uniform spatial distribution of the analyte in the particle volume: this hypothesis is not verified for the largest biomolecules. These results imply that non-porous particles or monolithic structures are the most promising stationary phases for the separation and purification of the largest biomolecules in life science.

Simplification of Moment Analysis Procedure for Kinetic Study of Chromatographic Behavior of Core-shell Particles

The moment analysis method for chromatographic behavior in core-shell columns was simplified. Mass-transfer phenomena other than intra-stationary phase diffusion are analyzed while considering that the packing materials are spherical particles. The manner of intra-stationary phase diffusion is analyzed while assuming a hypothetical flat plate. For most core-shell particles commercially available, the geometry of a spherical thin layer can be supposed as a hypothetical flat plate with a relative error of less than ca. 2% because the thickness of the shell layer is sufficiently smaller than the diameter of whole particle. This supposition makes moment analysis easier because the moment equations for flat plates are simpler than those strictly developed for core-shell particles. Some chromatographic data measured using a core-shell column were analyzed by the simple moment analysis method to confirm its usefulness. It was demonstrated that the method is effective for a preliminary study of mass-transfer kinetics in core-shell columns.

Simple Moment Analysis for a Kinetic Study of the Chromatographic Behavior of Spherical Particles and Silica Monoliths

A simple procedure of moment analysis was proposed for a kinetic study of the rate processes in the columns packed with full-porous spherical particles and silica monoliths. Previous chromatographic data measured in reversed-phase HPLC systems using Mightysil and Chromolith columns were analyzed by a simple moment analysis. The surface of the packing materials is chemically modified with octadecyl alkyl ligands. A mixture of methanol and water (80/20, v/v) and alkylbenzene homologous series (C₆H₅C_nH_2n+1, n = 0 - 7) were used as the mobile-phase solvent and sample probes, respectively. More detailed information about the experimental conditions is provided in Supporting Information. The values of the intra-stationary phase diffusivity (D_e) and the surface diffusion coefficient (D_s), derived by the simple moment analysis, were almost the same as those by the conventional moment analysis. The simple moment analysis is effective for quantitative studies of mass transfer in chromatographic systems. The previous chromatographic data were also analyzed by assuming external porosity (ε_e) as typical values, i.e., 0.40 for spherical particles and 0.70 for silica monoliths. The resulting values of D_e and D_s were of the same order of magnitude as those derived by using ε_e experimentally measured. Even if ε_e is assumed to be typical values, the simple moment analysis is effective for preliminary studies of the mass-transfer kinetics in the columns.

Theoretical Analysis of Efficiency of Multi-Layer Core-Shell Stationary Phases in the High Performance Liquid Chromatography of Large Biomolecules

Modern analytical applications of liquid chromatography require columns with higher and higher efficiencies. In this work, the general rate model (GRM) of chromatography is used for the analysis of the efficiency of core-shell phases having two porous layers with different structures and/or surface chemistries. The solution of the GRM in the Laplace domain allows for the calculation of moments of elution curves (retention time and peak width), which are used for the analysis of the efficiency of bi-layer particles with and without a non-porous core. The results demonstrate that bi-layer structures can offer higher separation power than that of the two layers alone if the inner layer has smaller surface coverage (retentivity) and the pore size and pore diffusion of the outer layer is either equal to or higher than that of the inner layer. Even in the case of core-shell phases, there is an increase in resolution by applying the bi-layer structure; however, we can always find a mono-layer core-shell particle structure with a larger core size that provides better resolution. At the optimal core size, the resolution cannot be further improved by applying a bi-layer structure. However, in case of the most widely produced general-purpose core-shell particles, where the core is ∼70% of the particle diameter, a 15–20% gain of resolution can be obtained by using well-designed and optimized bi-layer core-shell phases.

Superficially porous particles with 1000Å pores for large biomolecule high performance liquid chromatography and polymer size exclusion chromatography

To facilitate mass transport and column efficiency, solutes must have free access to particle pores to facilitate interactions with the stationary phase. To ensure this feature, particles should be used for HPLC separations which have pores sufficiently large to accommodate the solute without restricted diffusion. This paper describes the design and properties of superficially porous (also called Fused-Core^®, core shell or porous shell) particles with very large (1000Å) pores specifically developed for separating very large biomolecules and polymers. Separations of DNA fragments, monoclonal antibodies, large proteins and large polystyrene standards are used to illustrate the utility of these particles for efficient, high-resolution applications.

Are sub-2 μm particles best for separating small molecules? An alternative

Superficially porous particles (SPP) in the 2.5-2.7 μm range provide almost the same efficiency and resolution of sub-2 μm totally porous particles (TPP), but at one-half to one-third of the operating pressure. The advantage of SPP has led to the introduction of sub-2 μm SPP as a natural extension of this technology. While short columns of both SPP and TPP sub-2 μm particles allow very fast separations, the efficiency advantages of these very small particles often are not realized nor sufficient to overcome some of the practical limitations and disadvantages of such small particles. Advantages and disadvantages of columns packed with sub-2 μm particles are described for comparison with the characteristics of larger particles. The authors conclude that while sub-2 μm particles have utility in research studies, columns of larger particles are often better suited for most applications. A suggested 2.0 μm superficially porous particle diameter retains many of the advantages of sub-2 μm particles, but minimizes some of the disadvantages. The characteristics of these new 2.0 μm SPP are described in studies comparing some present sub-2 μm SPP commercial columns for efficiency, column bed homogeneity and stability.

Retention and bandwidths prediction in fast gradient liquid chromatography. Part 2-Core-shell columns

Recently, we confirmed that the well-established theory of gradient elution can be employed for prediction of retention in gradient elution from the isocratic data, method development and optimization in fast gradient chromatography employing short packed fully porous and monolithic columns and gradient times in between 1 and 2min, or even less. In the present work, we extended this study to short core-shell reversed-phase columns. We investigated the effects of the specification of the stationary phase in the core-shell structure on the prediction of gradient retention data. Two simple retention models describing the effects of the mobile phase on the retention by two-parameter equations yield comparable accuracy and can be used for prediction of elution times. The log-log model provides improved prediction of gradient bandwidths, especially for less retained compounds. A more sophisticated three-parameter model did not offer significant improvement of prediction. We compared the efficiency, selectivity and peak capacity of fast gradient separations of alkylbenzenes, phenolic acids and flavones on seven core shell columns with different lengths and chemistry of bonded shell stationary phase. Within the limits dictated by a fixed short separation time, appropriate adjustment of the range of the composition of mobile phase during gradient elution is the most efficient means to optimize the gradient separation. The gradient range affects sample bandwidths equally or even more significantly than the column length. Both 5-cm and 3-cm core-shell columns may provide comparable peak capacity in a fixed short gradient time.

UHPLC for the separation of proteins and peptides

There is increasing interest within the pharmaceutical industry in the development of proteins and peptides as drugs in addition to their use as biomarkers. Immunochemistry-based techniques have been traditionally used for the quantitation of proteins and peptides; however, LC-MS-based methodologies are being increasingly adopted as they offer several advantages. UHPLC is well established within the small-molecule community as a means to increase resolution and/or the speed of separations prior to MS detection; however, it is rarely applied to proteins or peptides separations. In this paper, current applications of UHPLC to such separations are reviewed, as well as considerations with regard to the effect of altering various chromatographic parameters.

Rapid determination of polycyclic aromatic hydrocarbons in rainwater by liquid-liquid microextraction and LC with core-shell particles column and fluorescence detection

Liquid-liquid microextraction coupled to LC with fluorescence detection for the determination of Environmental Protection Agency's 16 priority pollutant polycyclic aromatic hydrocarbons in rainwater has been developed. The optimization of the extraction method has involved several parameters, including the comparison between an ultrasonic bath and a magnetic stirrer as extractant apparatus, the choice of the extractant solvent, and the optimization of the extraction time. Liquid-liquid microextraction gave good results in terms of recoveries (from 73.6 to 102.8% in rainwater) and repeatability, with a very simple procedure and low solvent consumption. The reported chromatographic method uses a Core-Shell technology column, with particle size <3 μm instead of classical 5-μm particles column. The resulting backpressure was below 300 bar, allowing the use of a conventional HPLC system rather than the more expensive ultrahigh performance LC (UHPLC). An average decrease of 59% in run time and 75% in eluent consumption has been obtained, compared to classical HPLC methods, keeping good separation, sensitivity, and repeatability. The proposed conditions were successfully applied to the determinations of polycyclic aromatic hydrocarbons in genuine rainwater samples.