Diffusion In Stationary Phase Research Articles

Assessment of intra-particle diffusion in hydrophilic interaction liquid chromatography and reversed-phase liquid chromatography under conditions of identical packing structure

A recently developed stripping protocol to completely remove the stationary phase of reversed-phase liquid chromatography (RPLC) columns and turn them into hydrophilic interaction liquid chromatography (HILIC) columns with identical packing characteristics is used to study the underlying mechanisms of intra-particle diffusion in RPLC and HILIC. The protocol is applied to a column with a large geometrical volume (250×4.6mm, 5μm) to avoid extra-column effects and for compounds with a broad range in retention factors (k” from ∼0.6 to 8). Three types of behavior for the intra-particle diffusion (Dpart/Dm) in RPLC versus HILIC can be distinguished: for nearly unretained compounds (k”<0.6), intra-particle diffusion in HILIC is larger than in RPLC; for compounds with intermediate retention behavior (k”∼0.9–1.2), intra-particle diffusion in HILIC and RPLC are similar; and for well retained compounds (k”>1.8), intra-particle diffusion in RPLC is larger than in HILIC. To explain these observations, diffusion in the stationary phase (γsDs) and in the stagnant mobile phase in the mesopore zone (γmpDm) are deduced from experimentally determined values of the intra-particle diffusion, using models derived from the Effective Medium Theory. It is demonstrated that the larger intra-particle diffusion obtained for slightly retained compounds under HILIC conditions is caused by the higher mesopore diffusion in HILIC (γmp=0.474 for HILIC versus 0.435 for RPLC), while the larger intra-particle diffusion obtained for strongly retained compounds under RPLC conditions can be related to the much higher stationary phase diffusion in RPLC (γsDs/Dm=0.200 for RPLC versus 0.113 for HILIC).

Errors involved in the existing B-term expressions for the longitudinal diffusion in fully porous chromatographic media: Part II: Experimental data in packed columns and surface diffusion measurements

Peak parking experiments have been performed on three RP-HPLC different columns, using two different components and a variable mobile phase composition. The aim of the study was to investigate whether the B-term diffusion expressions currently used in the literature (which are all Knox-type models) should be replaced by the effective diffusion expressions that have been developed in the frame of the effective medium theory (EMT). Although the EMT-expressions are not fully accurate either (the mathematics of the complex interactions between different diffusion zones that are in close contact are too demanding to catch them in an exact analytical expression), they at least are physically sound and do not violate Maxwell's basic law of diffusion. Further they also provide a much better approximation of the numerically calculated effective diffusivity in the theoretical test situation considered in part I. The present study shows that the values of the surface or stationary phase diffusion coefficient that are derived from peak parking models can depend heavily on the employed B-term model. The EMT-based B-term expressions lead to values of the surface diffusion coefficient that vary much less strongly with the phase retention factor than if one of the Knox-type models is used to analyze the data. This implies that, since all peak parking experiments that have been performed in the past have all been interpreted with a Knox-type model, the conclusions that have been drawn from these studies should all be moderated or at least revisited.

Errors involved in the existing B-term expressions for the longitudinal diffusion in fully porous chromatographic media: Part I: Computational data in ordered pillar arrays and effective medium theory

Numerically solving the effective diffusion in a simplified representation of a chromatographic bed, it was found that the B-term expressions that have up to now been used in the literature, and which can all be reduced to either D eff = ( γ m D m + k′ γ s D s)/(1 + k′) or D eff = ( γ me D m + k″ D part)/(1 + k″), can no longer be considered to be unconditionally valid. This could be demonstrated by showing that the simulated diffusion data are in agreement with the mathematically sound effective medium theory (EMT), whereas the B-term expressions used up to now in literature are in conflict with the EMT, a theory that is widely accepted in all other fields of science. It is also shown that the use of the existing B-term expressions can lead to very large measurement errors (up to a 100% and more) for the determination of the stationary phase diffusion coefficient γ s D s from peak parking experiments. The representation of the B-term diffusion should in the future hence be based on the D eff expressions that can be derived from the EMT. These are physically sound and are also more accurate than the classical B-term expressions used up to now.

Computer Tool for Calibration of Chromatography Models

Model based engineering require good models to make analysis, optimisation and design. There is a need of tools for systematic parameter estimation and model calibration. In this paper a computer tool that supports the calibration of chromatography models for protein purification is presented. A model for protein purification has to describe a set of behaviours that can be present during the optimisation. Examples of behaviours are mobile phase dispersion, diffusion in stationary phase, multi component adsorption and elution dependency. A systematic model calibration procedure is needed to find all these parts in the model. Each step in the procedure involves a parameter estimation application for a given model structure and specific experimental data. There is a need for using both single data responses and multiple data responses to calibrate the given model structure. Experimental data is imported to the computer tool directly from a chromatography set-up. The model response is computed in a simulator solving a set of partial differential equations. A regression method is used to minimize the residuals to find the best parameter set. The tool is developed in MATLAB and has a graphical user interface to support the user through a model calibration activity.

Performance and preparation of immobilized polysiloxane stationary phases in 5–55 μm I.D. open-tubular fused silica columns for liquid chromatography

Cross-linked non-polar polysiloxanes were evaluated as stationary phases in open-tubular column reversed-phase liquid chromatography. Coating of 5–55 μm I.D. fused-silica capillaries with stationary phase films of a well defined thickness in the range 0.03–1.96 μm is described for the two polysiloxane gum phases PS-255 (methylvinyl silicone) and SE-54 (methylphenylvinyl silicone). The chromatographic properties of these columns were investigated using split injection and on-column laser-induced fluorescence detection. Gas chromatography was used complementarily in the evaluation of column stability, retention and inertness. A retentive layer thickness to column diameter ratio up to 1:27 could be prepared. A retentive layer thickness to column diameter ratio up to 1:27 could be prepared, and a linear relationship was observed between the retention and the stationary to mobile phase volume ratio. The selectivity was related to the polysiloxane structure and was constant for films thicker than 0.25 μm. The column band-broadening was studied regarding the contribution from stationary phase diffusion, and compared with theory. Depending on film thickness, the stationary phase diffusion coefficient D s was in the range 10 −8-10 −6 cm 2/s. The highest efficiency, 351 000 plates ( k′ = 0.16), was obtained with a 1.97 m × 11.7 μm I.D. open-tubular-column. An application to the gradient separation of fluorescence labelled amino acids is presented. Preliminary results are also reported on a new type of stationary phase, created by swelling the immobilized polysiloxane with n-heptane. A nearly ten-fold increase in retention and a change in selectivity were obtained.