Detailed analysis of the effective and intra-particle diffusion coefficient of proteins at elevated pressure in columns packed with wide-pore core-shell particles.

To determine the efficiency that can be obtained in a packed-bed liquid-chromatography column for a particular analyte, a correct determination of the molecular and effective diffusion coefficients (Dm and Deff) of the analyte is required. The latter is usually obtained via peak parking experiments wherein the flow is stopped. As a result, the column pressure rapidly dissipates and the measurement is essentially conducted at ambient pressure. This is problematic for analytes whose retention depends on pressure, such as proteins and potentially other large (dipolar) molecules. In that case, a conventional peak parking experiment is expected to lead to large errors in Deff. To obtain a better estimate ofDeff, the present study reports on the use of a set-up enabling peak parking measurements under pressurized conditions. This approach allowed us to report, for the first time, Deff for proteins at elevated pressure under retained conditions. First, Deff was determined at a (average) pressure of about 105 bar for a set of proteins with varying size, namely: bradykinin, insulin, lysozyme, ß-lactoglobulin, and carbonic anhydrase in a column packed with 400 Å core-shell particles. The obtained data were then compared to those of several small analytes: acetophenone, propiophenone, benzophenone, valerophenone, and hexanophenone. A clear trend between Deff and analyte size was observed. The set-up was then used to determine Deff of bradykinin and lysozyme at variable (average) pressures ranging from 28 bar to 430 bar. These experiments showed a decrease in intra-particle and surface diffusion with pressure, which was larger for lysozyme than bradykinin. The data show that pressurized peak parking experiments are vital to correctly determine Deff when the analyte retention varies significantly with pressure.

Taylor-Aris methodology for the experimental determination of molecular diffusion coefficients: Tutorial with focus on large biomolecules.

High-Performance Liquid Chromatography (HPLC) is a key technique in the evaluation of biopharmaceuticals. To improve the separation of biopharmaceuticals, it is crucial to improve the fundamental understanding of the parameters governing their band broadening behavior. This can be obtained by a detailed assessment of the individual contributions to their mass transfer. For this purpose, a precise knowledge of the molecular diffusion coefficient (Dm) of biopharmaceuticals is required. Only little experimental data is available for the Dm-values of biopharmaceuticals under HPLC relevant conditions. Furthermore, none of the available equations that can be used to calculate Dm-values, allows to account for any conformational changes that might occur. The Taylor-Aris method is a very simple and absolute method that is often employed to determine Dm-coefficients. The Taylor-Aris method measures the band broadening of an analyte in an open tube under laminar conditions, wherein (1) longitudinal diffusion can be ignored, (2) the sample is fully radially equilibrated and (3) the contribution of the extra-column variance to the total variance is negligible. Moreover, since the open tubes are typically coiled for practical reasons, (4) the influence of secondary flows on the band broadening should be insignificant. In this tutorial paper, the impact of the four conditions mentioned above on the accuracy of the obtained Dm values is revisited. For this purpose, Dm values are measured for two representative compounds (Bovine Serum Albumin and Thiourea), and the obtained values are compared with literature data and theoretical recommendations. Based on these observations, a set of 'rules' for accurate and fast Dm measurements is put forward. Finally, an Interactive Tool (IT), combining these rules in a comprehensive way, is introduced and can be used to set up TA experiments.

Measurement and modelling of the intra-particle diffusion and b-term in reversed-phase liquid chromatography.

In an ongoing effort to better understand the underlying mechanisms of band broadening in particle-packed reversed-phase liquid chromatography columns, new models for intra-particle diffusion, representing an adsorption- and partition-type retention behavior, are proposed. These models assume the mesoporous zone inside the particles is subdivided in four distinct regions: a fraction f1 filled with bulk mobile phase, a fraction f2 enriched in pure organic modifier extending outside the stationary phase layer, a fraction f3 comprising the liquid surrounding the alkyl chains and a fraction f4 consisting of the stationary phase alkyl chains. Intra-particle diffusion is calculated as a residence time weighted average of the diffusion in these different regions. Experimental procedures and models are proposed to determine the volumes of these four regions and applied to three reversed-phase liquid chromatography columns with different pore sizes (80 Å versus 300 Å) and different stationary phase types (C18 versus C8). The newly proposed models are then applied to predict the intra-particle diffusion of butyrophenone across a wide range of retention factors (1 ≤ k" ≤ 40) in each of these columns. These predictions are compared to experimental data that are extracted from the effective diffusion coefficients of butyrophenone obtained via peak parking experiments. It is demonstrated that both adsorption- and partition-type models for intra-particle diffusion model the actual behavior of the test compound well, and require the determination of only one (partition) or two (adsorption) fitting factors: the obstruction to free movement the analytes experience from the alkyl chains in the retained state (partition and adsorption) and in the unretained state (adsorption). Finally, it is demonstrated that the major contributor to the intra-particle diffusion of retained compounds (k" > 2) is the diffusion these analytes undergo when retained in the organic-modifier enriched zone surrounding the alkyl chains (partition model) or when adsorbed onto the alkyl chains (adsorption model), confirming that surface diffusion plays an important role in the mass transfer of retained compounds in reversed-phase liquid chromatography columns.

Methodologies to determine b-term coefficients revisited.

The accuracy of the longitudinal diffusion term (b-term) plays a vital role in the study of mass transfer mechanisms in high performance liquid chromatography (HPLC). In this study, three commonly used methodologies (peak parking; fitting of an experimental van Deemter curve; and the so-called dynamic method) for the determination of the b-term constant were investigated in detail. The three methods were compared based on their mutual agreement, the intra- and inter-day variation of the obtained values and the time required to measure them. Whereas the dynamic method was found to be plagued by impractically long waiting times and concomitant baseline variations compromising accurate measurements of the band broadening, the two other methods lead to very similar b-values, i.e., well within the 1% RSD inter-day variation typically marking both methods in the present study. The best way to study the agreement of the peak parking and plate height fitting method is in a plot of h.ν versus ν, providing a much better zoom on the b-term region of the van Deemter curve than the customarily employed h versus ν-curve and hence allowing to identify any anomalous measurement values (usually related to measurements with a long experimentation time). Verifying the mutual agreement between both methods is proposed here as an additional accuracy check of the obtained data.