Considerations for the use of ultra-high pressures in liquid chromatography for 2.1mm inner diameter columns.

The current contribution investigates the effects of viscous heat dissipation in chromatographic columns (with an emphasis on so-called narrow bore columns with an inner diameter of 2.1mm) using numerical simulations of the temperature and velocity profiles and the resulting band broadening, for the first time at operating pressures up to 2000bar. When operating columns under well-thermostatted conditions to maintain a constant temperature of the mobile phase, a dramatic increase in plate heights can be observed that voids any advantage one could expect from the possibility to use smaller particles offered by the increased pressure limit. It is also clearly demonstrated that, even when the column is not temperature controlled, the backflow of heat along the wall can causes a significant loss in performance under standard operating conditions in a still air oven. It is found that for operating pressure above 1250bar, a significant (relative to the typical column performance) contribution to the observed plate height will be caused by viscous heating effects, which increases with increasing temperature dependency of the retention factor. In addition, unprecedented experimental measurements of the temperature effects at an operating pressure up to 2600bar were performed on a 10cm long, 2.1mm ID column showing a dramatic temperature increase up to 60°C relative to the inlet temperature when using methanol as a mobile phase.

Quantification aspects of constant pressure (ultra) high pressure liquid chromatography using mass-sensitive detectors with a nebulizing interface.

The present contribution investigates the quantitation aspects of mass-sensitive detectors with nebulizing interface (ESI-MSD, ELSD, CAD) in the constant pressure gradient elution mode. In this operation mode, the pressure is controlled and maintained at a set value and the liquid flow rate will vary according to the inverse mobile phase viscosity. As the pressure is continuously kept at the allowable maximum during the entire gradient run, the average liquid flow rate is higher compared to that in the conventional constant flow rate operation mode, thus shortening the analysis time. The following three mass-sensitive detectors were investigated: mass spectrometry detector (MS), evaporative light scattering detector (ELSD) and charged aerosol detector (CAD) and a wide variety of samples (phenones, polyaromatic hydrocarbons, wine, cocoa butter) has been considered. It was found that the nebulizing efficiency of the LC-interfaces of the three detectors under consideration changes with the increasing liquid flow rate. For the MS, the increasing flow rate leads to a lower peak area whereas for the ELSD the peak area increases compared to the constant flow rate mode. The peak area obtained with a CAD is rather insensitive to the liquid flow rate. The reproducibility of the peak area remains similar in both modes, although variation in system permeability compromises the 'long-term' reproducibility. This problem can however be overcome by running a flow rate program with an optimized flow rate and composition profile obtained from the constant pressure mode. In this case, the quantification remains reproducibile, despite any occuring variations of the system permeability. Furthermore, the same fragmentation pattern (MS) has been found in the constant pressure mode compared to the customary constant flow rate mode.

Kinetic performance comparison of fully and superficially porous particles with sizes ranging between 2.7 µm and 5 µm: Intrinsic evaluation and application to a pharmaceutical test compound.

The reintroduction of superficially porous particles has resulted in a leap forward for the separation performance in liquid chromatography. The underlying reasons for the higher efficiency of columns packed with these particles are discussed. The performance of the newly introduced 5 µm superficially porous particles is evaluated and compared to 2.7 µm superficially porous and 3.5 and 5 µm fully porous columns using typical test compounds (alkylphenones) and a relevant pharmaceutical compound (impurity of amoxicillin). The 5 µm superficially porous particles provide a superior kinetic performance compared to both the 3.5 and 5 µm fully porous particles over the entire relevant range of separation conditions. The performance of the superficially porous particles, however, appears to depend strongly on retention and analyte properties, emphasizing the importance of comparing different columns under realistic conditions (high enough k) and using the compound of interest.

Comparison of the quantitative performance of constant pressure versus constant flow rate gradient elution separations using concentration-sensitive detectors.

This contribution discusses the difference in chromatographic performance when switching from the customary employed constant flow rate gradient elution mode to the recently re-introduced constant pressure gradient elution mode. In this mode, the inlet pressure is maintained at a set value even when the mobile phase viscosity becomes lower than the maximum mobile phase viscosity encountered during the gradient program. This leads to a higher average flow rate compared to the constant flow rate mode and results in a shorter analysis time. When both modes carry out the same mobile phase gradient program in volumetric units, normally identical selectivities are obtained. However, small deviations in selectivity are found due to the differences in pressure and viscous heating effects. These selectivity differences are of the same type as those observed when switching from HPLC to UHPLC and are inevitable when speeding up the analysis by applying a higher pressure. It was also found that, when using concentration-sensitive detectors, the constant pressure elution mode leads to identical peak areas as the constant flow rate mode. Also the linearity is maintained. In addition, the repeatability of the peak area and retention time remains the same when switching between both elution modes.

Kinetic performance limits of constant pressure versus constant flow rate gradient elution separations. Part I: theory.

We report on a general theoretical assessment of the potential kinetic advantages of running LC gradient elution separations in the constant-pressure mode instead of in the customarily used constant-flow rate mode. Analytical calculations as well as numerical simulation results are presented. It is shown that, provided both modes are run with the same volume-based gradient program, the constant-pressure mode can potentially offer an identical separation selectivity (except from some small differences induced by the difference in pressure and viscous heating trajectory), but in a significantly shorter time. For a gradient running between 5 and 95% of organic modifier, the decrease in analysis time can be expected to be of the order of some 20% for both water-methanol and water-acetonitrile gradients, and only weakly depending on the value of V(G)/V0 (or equivalently t(G)/t0). Obviously, the gain will be smaller when the start and end composition lie closer to the viscosity maximum of the considered water-organic modifier system. The assumptions underlying the obtained results (no effects of pressure and temperature on the viscosity or retention coefficient) are critically reviewed, and can be inferred to only have a small effect on the general conclusions. It is also shown that, under the adopted assumptions, the kinetic plot theory also holds for operations where the flow rate varies with the time, as is the case for constant-pressure operation. Comparing both operation modes in a kinetic plot representing the maximal peak capacity versus time, it is theoretically predicted here that both modes can be expected to perform equally well in the fully C-term dominated regime (where H varies linearly with the flow rate), while the constant pressure mode is advantageous for all lower flow rates. Near the optimal flow rate, and for linear gradients running from 5 to 95% organic modifier, time gains of the order of some 20% can be expected (or 25-30% when accounting for the fact that the constant pressure mode can be run without having to leave a pressure safety margin of 5-10% as is needed in the constant flow rate mode).

Kinetic performance limits of constant pressure versus constant flow rate gradient elution separations. Part II: experimental.

We report on a first series of experiments comparing the selectivity and the kinetic performance of constant flow rate and constant pressure mode gradient elution separations. Both water-methanol and water-acetonitrile mobile phase mixtures have been considered, as well as different samples and gradient programs. Instrument pressures up to 1200 bar have been used. Neglecting some small possible deviations caused by viscous heating effects, the experiments could confirm the theoretical expectation that both operation modes should lead to identical separation selectivities provided the same mobile phase gradient program is run in reduced volumetric coordinates. Also in agreement with the theoretical expectations, the cP-mode led to a gain in analysis time amounting up to some 17% for linear gradients running from 5 to 95% of organic modifier at ultra-high pressures. Gains of over 25% were obtained for segmented gradients, at least when the flat portions of the gradient program were situated in regions where the gradient composition was the least viscous. Detailed plate height measurements showed that the single difference between the constant flow rate and the constant pressure mode is a (small) difference in efficiency caused by the difference in average flow rate, in turn leading to a different intrinsic band broadening. Separating a phenone sample with a 20-95% water-acetonitrile gradient, the cP-mode leads to gradient plate heights that are some 20-40% smaller than in the cF-mode in the B-term dominated regime, while they are some 5-10% larger in the C-term dominated regime. Considering a separation with sub 2-µm particles on a 350 mm long coupled column, switching to the constant pressure mode allowed to finish the run in 29 instead of in 35 min, while also a larger peak capacity is obtained (going from 334 in the cF-mode to 339 in the cP-mode) and the mutual selectivity between the different peaks is fully retained.

The kinetic plot method applied to gradient chromatography: theoretical framework and experimental validation.

The kinetic plot method, originally developed for isocratic separations, was extended to the practically much more relevant case of gradient elution separations. A set of explicit as well as implicit data transformation expressions has been established. These expressions can readily be implemented in any calculation spread-sheet program, and allow to directly turn any experimental data set representing the relation between the separation efficiency and the flow rate measured on a single column into the kinetic performance limit curve of the tested separation medium. Since the kinetic performance limit curve is based on an extrapolation to columns with a different length, it should be realized that the curve is only valid under the assumption that the gradient time and the delay time (if any) are adapted such that the analytes are subjected to the same relative mobile phase history when the column length is changed. Both experimental and numerical data are presented to corroborate the fact that the kinetic performance limit curves that are obtained using the proposed expressions are indeed independent of the column length the experimental data were collected in. Deviations might arise if excessive viscous heating occurs in columns with a pronounced non-adiabatic thermal behaviour.

Towards a solution for viscous heating in ultra-high pressure liquid chromatography using intermediate cooling.

A generic solution is proposed for the deleterious viscous heating effects in adiabatic or near-adiabatic systems that can be expected when trying to push the column operating pressures above the currently available range of ultra-high pressures (i.e., 1200 bar). A set of proof-of-principle experiments, mainly using existing commercial equipment, is presented. The solution is based on splitting up a column with given length L into n segments with length L/n, and providing an active cooling to the capillaries connecting the segments. In this way, the viscous heat is removed at a location where the radial heat removal does not lead to an efficiency loss (i.e., in the thin connection capillaries), while the column segments can be operated under near-adiabatic conditions without suffering from an unacceptable rise of the mobile phase temperature. Experimental results indicate that the column segmentation does not lead to a significant efficiency loss (comparing the performance of a 10 cm column with a 2 cm x 5 cm column system), whereas, as expected, the system displays a much improved temperature stability, both in time (because of the shortened temperature transient times) and in space (reduction of the average axial temperature rise by a factor n). The method also prevents a large backflow of heat along the column wall that would lead to large efficiency losses if one would attempt to operate columns at pressures of 1500 bar or more. A real-world pharmaceutical example is given where this improved temperature robustness could help in moderating the changes in selectivity during method transfer from a low to a high pressure operation, although the complex non-linear behavior of the viscous heating and high pressure effects result in lower than expected improvement.

Numerical and analytical solutions for the column length-dependent band broadening originating from axisymmetrical trans-column velocity gradients.

Trans-column velocity gradients arising from radial variations in packing density or mobile phase temperature lead to a plate height contribution that, in the case of for example a 4.6mm column, may increase over several tens of centimeters before it reaches a constant value. Considering a wide variety of different trans-column velocity profiles, including Giddings' general polynomial expression and several simplified partially flat profiles, and performing a set of analytical calculations (to establish an expression for the long time-limit constant value H(infinity)) and numerical simulations (to calculate the band broadening in the transient regime), it was found that the column length-dependent variation of this plate height contribution can be very closely approximated by a simple exponential-law expression. The availability of the latter will greatly simplify the experimental analysis of radial column heterogeneity effects, especially considering that this expression is independent of the radial dispersion, the column diameter, and the average velocity and maximum velocity difference. Surprisingly, the exponential-law expression is to a first approximation also independent of the shape of the velocity profile, provided the velocity profile does not become flat over a substantially large part of the cross-section. In the latter case, the transient curve obeys a more complex law, but can nevertheless still be approximated by an exponential-law expression, though with a different (larger) decay constant.

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 Deff=(gamma mDm+k'gamma sDs)/(1+k') or Deff=(gamma meDm+k''Dpart)/(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 gamma sDs from peak parking experiments. The representation of the B-term diffusion should in the future hence be based on the Deff 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.