Modeling of thermal processes in high pressure liquid chromatography

Prediction of overloaded concentration profiles under ultra-high-pressure liquid chromatographic conditions

In this study, overloaded elution profiles under ultra-high-pressure liquid chromatographic (UHPLC) conditions and accounting for the severe pressure and temperature gradients generated, are compared with experimental data. The model system consisted of an C18 column packed with 1.7-µm particles (i.e., a UHPLC column) and the solute was 1,3,5-tri‑tert-butylbenzene eluted with a mobile phase composed of 85/15 (v/v) acetonitrile/water. Two thermal modes were considered, and the solute was eluted at the very high inlet pressures necessary to achieve a highly efficient and rapid chromatographic process, as provided by using columns packed with small particles. However, the high inlet pressure and high linear velocity of the mobile phase caused the production of a significant amount of heat, and consequently, the formation of axial and radial temperature gradients. Due to these gradients, the retention and the mobile phase velocity were no longer constant. Thus, simple mathematical models consisting only of the mass balance equations are unsuitable to properly model the elution profiles. Here, the elution concentration profiles were predicted using a combined two-dimensional heat and mass transfer model, also including the calculation of the mobile phase velocity distribution. The isotherm adsorption model was the bi-Langmuir isotherm model with Henry constants that depended on the local temperature and pressure in the column. These adjustments allowed us to precisely account for changes in the shape and retention of the overloaded concentration profiles in the mobile phase. The proposed model provided accurate predictions of the overloaded concentration profiles, demonstrating good agreement with experimental profiles eluted under severe pressure and temperature gradients in the column even in the most extreme cases where the pressure drops reached 846 bar and the temperature gradients equaled 0.15 K mm-1 and 0.95 K mm-1 in the axial and the radial directions, respectively. In such cases 36 % decrease of the retention factor was observed along the column and 2 % increase in radial direction. These changes, combined with the velocity distribution, shifted the overloaded elution profile's shock towards the center of the column, advancing approximately 3 mm from its initial position close to the column wall. Ultimately, this resulted in the broadening of the elution band.

Improved Performance of UHPLC–MS Hyphenated Systems

An ultrahigh-pressure liquid chromatography–mass spectrometry (UHPLC–MS) research prototype instrument was built to improve the resolution power and the usability of conventional LC–MS hyphenated instruments for routine analyses in pharmaceutical applications. The improved characteristics of this UHPLC–MS system include: 1) the dramatic reduction of post-column sample dispersion; 2) the adoption of vacuum jacketed columns (VJC) for the reduction of undesirable radial temperature gradients across the column diameter; and 3) the presence of a column outlet end nut heater to refocus the distorted peaks prior to analyte ionization. The benefits of each of these added features are analyzed with a rigorous approach from a peak broadening perspective. A 2x improvement in peak capacities recorded with this prototype UHPLC–MS system compared to a standard system (Acquity UHPLC I-class/Xevo TQ-S) is illustrated for the gradient separation of seven small pharmaceutical compounds using a 2.1 mm x 100 mm column packed with sub-2-μm core-shell particles (1.6 μm Acquity UHPLC Cortecs C18 column).

Detailed computational fluid dynamics study of the parameters contributing to the viscous heating band broadening in liquid chromatography at pressures up to 2500 bar in 2.1 mm columns

Over the past years viscous heating band broadening occurring in high pressure liquid chromatography has been studied extensively. In the present numerical study, we investigate the fine details of this band broadening contribution under extreme high-pressure conditions (2500 bar). To analyze the results, we first show that viscous heating leads to two clearly distinguishable band broadening effects, one originating from the radial differences in the species migration velocity and the other from the axial variations. It was found that the radial contribution is independent of the intrinsic band broadening of the bed (i.e. band broadening in absence of viscous heating) while it strongly depends on the radial dispersion coefficient and the retention enthalpy of the analytes. On the other hand, the axial contribution is strongly dependent on the bed intrinsic band broadening and it is found to be 4 to 5 times lower than the radial contribution. We also show the strong effect of the endfittings on the temperature gradients inside the column thus on the resulting viscous heating band broadening.

Impact of changes in physicochemical parameters of the mobile phase along the column on the retention time in gradient liquid chromatography. Part A - temperature gradient

Gradient chromatography has been widely applied in analytical and preparative chromatography since it provides better peak shapes and the ability to elute analytes in a shorter time frame. Apart from changes in the composition of a mobile phase also alteration of process temperature can be applied during separation procedures to improve efficiency. However, proper mathematical modeling of the gradient chromatography and further correct prediction of solutes' retention behavior have become a serious challenge as it involves the need to develop computational procedures that accurately account for the time and spatial gradients of crucial parameters. In this work, a computational procedure including the equilibrium-dispersive two-dimensional mass transfer model, the two-dimensional (2D) heat transfer model together with Darcy's law and the continuity equation have been proposed. Additionally, the calculation procedure was simplified by replacing the 2D model with the one-dimensional (1D) mass transfer model in order to speed up the computations. Both proposed solutions were validated employing external experimental data of temperature gradient HPLC [1] as well as with predictions based on the linear elution strength (LES) model available therein. The proposed procedures made it possible to efficiently predict the concentration profiles with average relative errors of calculated retention times not exceeding 3.22%. Moreover, the effect of the axial dispersion coefficient determination method on the obtained peak shapes was examined involving the Gunn, the Wen-Fan, and the Chung-Wen correlations, indicating that the latter produces the most accurate results. Finally, the proposed mathematical procedures were tested under UHPLC conditions, and due to a significant difference in retention times found the 2D model is strongly advised.

Computational fluid dynamics study of potential solutions to alleviate viscous heating band broadening in 2.1 millimeter liquid chromatography columns

We report on a numerical simulation study of a number of potential column technology solutions to minimize the plate height contribution (H_vh) originating from the use of ultra-high pressures and their concomitant viscous heating effect. Looking as far as possible into the future of UHPLC, all main results are obtained for the case of a 2500 bar pressure gradient. However, to generalize the result, a correlation is given that can be used to interpolate the results to lower pressures with some 10% accuracy. For the considered case of a 2.1mm column, a liquid flow rate of 0.45 ml/min, an analyte with retention factor k(25°C)=3 and a retention enthalpy chosen such that ΔH_R/R= -1000 K, it is found that, in order to keep the global plate height as measured at the column outlet (H_vh,glob,out) below 1 μm, the bed conductivity would need to be raised to λ_bed=2.4 W/m•K, i.e., 4 times higher than a typical packed bed of fully-porous or core-shell silica particles. An equivalent effect on the band broadening could be obtained if it would be possible to replace the steel column wall with a low conductivity material. In this case, a wall conductivity of 0.25 W/m•K, i.e., 64 times smaller than the conductivity of steel, would be needed to keep H_vh,glob,out below 1 μm. Results are also interpreted based on contour plots of the axial and radial velocity variation of a retained analyte.

Evaluating the advantages of higher heat conductivity in a recently developed type of core-shell diamond stationary phase particle in UHPLC

In recent studies, the nature and magnitude of the temperature gradients developed in ultra-high pressure liquid chromatography (UHPLC), were found to be dependent on the heat conductivity properties of the column matrices, but also, on the principle used for controlling the temperature over the column. Here, we investigated the potential of using highly heat conductive diamond-based stationary phases (85 times higher than silica), for reducing the temperature gradients. The stationary phases investigated were a (i) Diamond Analytics FLARE column, based on particles comprised of a graphite core surrounded by a very thin diamond shell, and two silica hybrid columns: (ii) a core-shell silica Kromasil Eternity Shell column and (iii) a fully porous silica Kromasil Eternity XT column. Models were developed based on two-dimensional heat transfer theory and mass transfer theory, which were used to model the temperature profiles and the migration of an analyte band accounting for column efficiencies at different flow rates. For the silica-based columns, using water-controlled temperature mode, the temperature gradients along the column axes are suppressed whereas temperature gradients in the radial direction prevails resulting in decreased column efficiencies. Using these columns with air-controlled temperature mode, the radial temperature gradients are reduced whereas temperature gradients along the column prevails resulting in decreased retention times. With the Diamond FLARE column, there was no loss in column efficiency using the water-controlled temperature mode and the van Deemter curves are almost identical using both temperature control modes. Thus, for the Diamond FLARE column, in contrast to the silica-based columns, there are almost no losses of column efficiencies due to reduced radial temperature gradients independent on how the column temperature was controlled.

The mass transfer kinetics in columns packed with Halo-ES shell particles

The average mesopore size of the new Halo-ES-Peptide shell particles is 160 Å, markedly larger than that of the classical Halo shell particles (90 Å). We found that this change causes a considerable decrease of the film mass transfer resistance measured for columns packed with these particles. We analyze data obtained by systematic measurements of the C term of the van Deemter equation for the peptide β-lipotropin (MW = 769 Da), the protein insulin (MW = 5800 Da), and a series of non-retained polystyrene standards (MW = 6400 and 13,200). The improvement in column performance is explained by an increase of the fraction of the external surface area of the shell that allows the entrance of the sample molecules inside the particle. The fraction of the shell surface accessible to a probe controls the rate of its external film mass transfer, i.e. its rate of transfer between the interstitial and the stagnant eluent. Although measurable, the increase in sample diffusivity through the porous shells does not account for the better performance of Halo-ES-peptide columns. Furthermore, the analysis of the HETPs data of small molecules (uracil, acetophenone, toluene, and naphthalene, MW< 150) reveals that the eddy diffusion (A) term of these new columns is 25% lower than that of the classical Halo columns. This result is consistent with the impact of intra-particle diffusivity on the eddy diffusion mechanism in packed columns. As shell diffusivity increases, so does the rate of transfer of sample molecules between the eluent stream-paths flowing through the packed particles and across the column diameter. Dispersion through short-range inter-channel and trans-column eddies is reduced.