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.

On the 3-dimensional effects in etched chips for high performance liquid chromatography-separations.

In an attempt to quantify the potential of photolithographically etched micro-pillar arrays as a perfectly ordered alternative for the packed bed of spheres, the additional band broadening originating from the top and bottom plate has been investigated using computational fluid dynamics simulations. These calculations provide insight in the theoretical expectations that can be made for the experimental work that is currently being conducted by a number of groups. The calculations show that the additional band broadening contribution can be expected to go through a transient regime as a function of the axial distance along the array. In its fully developed regime and in the most relevant velocity range, the top and bottom wall contribution almost doubles the band broadening compared to the band broadening in a perfectly ordered array of non-porous, non-retentive pillars without top and bottom wall. Compared to the band broadening in an array of porous, retentive pillars on the other hand, the top and bottom wall-effect can be expected to become negligible. A simplified, phenomenological model yielding a first principles prediction of both the transient and the steady-state top and bottom wall band broadening as a function of the inter-pillar distance and the pillar height is proposed and shows good qualitative agreement with the exact calculations.

Use of the kinetic plot method to analyze commercial high-temperature liquid chromatography systems. II. Practically constrained performance comparison.

Using a set of experimentally determined plate height data obtained on three commercial high-temperature HPLC supports, and evaluating their isocratic separation speed potential under the application of a set of instrumental constraints, a qualitative map of the practically achievable critical pair separation speed potential of high-temperature HPLC has been established. The obtained data show that the gain in separation speed is more strongly affected by the instrumental limitations in the high-temperature range than it is for the low temperatures. For the presently considered case of alkylbenzene separations, the potential gain in analysis time that can be obtained by going from T=30 to 120 degrees C in the presence of a typical set of instrumental limitations nevertheless remains of the order of a factor of 2-4. The study also shows that improvements on the instrumentation side (increased detector frequency, pumping flow rate, smaller extra-column volumes, ...) are indispensable to fully benefit from the high temperature advantages for all separations requiring less than 10,000 effective theoretical plates.

Influence of the packing heterogeneity on the performance of liquid chromatography supports.

We report on a series of plate height and flow resistance data obtained via computational fluid dynamics simulations in a simplified two-dimensional (2D) mimic of real packed bed and monolithic columns. By varying the external porosity (0.4 < epsilon < 0.8) and the degree of packing randomness, a good qualitative insight in the relationship between the packing porosity and heterogeneity and the general chromatographic performance parameters is obtained, unbiased by any differences in phase retention factor k', mobile phase diffusivity or viscosity or intra-skeleton porosity. The results provide a quantitative support for the use of domain size reduced plate heights as a means to compare the performance of chromatographic beds with a different porosity, as it was found that packings with a similar degree of packing heterogeneity yield very similar domain size reduced h(min)-values, nearly completely independent of the porosity. The study also clearly shows that the presence of preferential flow paths (inevitably accompanied by the presence of more clustered regions) leads to a decrease of the flow resistance, but also leads to a strong increase of the band broadening if supports with the same porosity epsilon and the same radial width are compared. For the presently considered 2D system, the flow resistance reduction is too small to overcome the corresponding strong increase in band broadening, such that the presence of preferential flow paths always leads to an overall increase of the separation impedance.

On the optimisation of the bed porosity and the particle shape of ordered chromatographic separation media.

We report on a theoretical study wherein we considered a large number of ordered two-dimensional porous pillar arrays with different pillar shapes and widely varying external porosity and calculated the flow resistance and the band broadening (under retentive conditions) over the complete range of practical velocities using a commercial computational fluid dynamics software package. It is found that the performance of the small porosity systems is very sensitive to the exact pillar shape, whereas this difference gradually disappears with increasing porosity. The obtained separation impedances are very small in comparison to packed bed and monolithic columns and decrease with increasing porosity. If accounting for the current micromachining limitations, a proper selection of the exact shape and porosity even becomes more critical, and different design rules are obtained depending on whether porous or non-porous pillars are considered.

Computational fluid dynamics simulations yielding guidelines for the ideal internal structure of monolithic liquid chromatography columns.

A theoretical calculation of the separation performance of a (hypothetical) micro-structured monolithic LC column is presented, confirming that the polydispersity effect in parallel bundle columns can theoretically be eliminated to a very large extent by radially redistributing the mobile phase fluid at regular intervals. It is demonstrated that the flow can be redistributed in such a way that the advantage coming from the suppression of the polydispersity effect largely exceeds the losses caused by the additional pressure-drop and band broadening. The presently considered micro-structured column would allow to perform N > 100,000 plate separations in a few hundred of seconds, i.e., about an order of magnitude faster than the best possible packed bed and monolithic HPLC columns, while offering the same mass loadability. This clearly demonstrates that the currently available LC columns are still far away from the absolute resolution limit of the ideal, fully optimised LC column.

Computational study of the band broadening in two-dimensional etched packed bed columns for on-chip high-performance liquid chromatography.

The chromatographic performance of several straightforward two-dimensional etched packed bed column lay-outs (equilaterally staggered arrays of, respectively, circular, hexagonal, and diamond-like pillars) has been compared using commercial computational fluid dynamics software. In all cases, the bed porosity was kept at epsilon = 0.4 and a retained component with zone capacity ratio k" = 2 was considered. Exploring the use of six different possible characteristic dimensions to bring the Van Deemter plots of the three different considered particle shapes into agreement, none of them yielded a perfect agreement. Using the pillar volume-based equivalent cylinder diameter (deq) as the characteristic dimension, the diamond-like pillars yielded a significantly smaller h(min) value than the cylinders and the hexagons (h(min) approximately equal to 0.74 for the former versus h(min) approximately equal to 0.83 for the two latter). Including the flow resistance into the analysis, it was found that the "hydrodynamic" shape of the particles has an important influence on the separation impedance E. The more axially elongated diamond pillars yielded an Emin number as small Emin = 180 (for a retained component with k" = 2), i.e. about 40% smaller than the cylinders and the hexagons (Emin = 300-330). The obtained h(min) and Emin values are also significantly smaller than the values often cited for the best possible packed bed HPLC columns. We believe this is a consequence of the assumed perfect homogeneity of the etched structures, and hence hints at the potential benefits of perfectly ordered chromatographic columns, as was already inferred by Knox [J. Chromatogr. A 831 (1999) 3; 960 (2002) 7] and He et al. [Anal. Chem. 70 (1998) 3790].

Shear-flow-based chromatographic separations as an alternative to pressure-driven liquid chromatography.

It is only by developing specially designed injection and detection systems that shear-driven chromatography can become a viable alternative to HPLC. In the present paper, a dedicated zero dead-volume injection procedure is presented with which sample volumes can be injected reproducibly in the required picoliter range. In addition, a transversal detection groove system is designed which should allow to perform on-line UV-VIS absorption measurements with path lengths in the millimeter range, with an acceptable theoretical plate loss (only 20% in a 5 cm long channel) and acting as a nearly perfect wave guide.

Advantages of perfectly ordered 2-D porous pillar arrays over packed bed columns for LC separations: a theoretical analysis.

A series of theoretical calculations is presented to quantify the gain in LC separation efficiency that can be expected if the traditionally used packed bed columns were replaced by columns with a perfectly ordered flow-through pore network. It is shown that a perfectly ordered 2-D array of porous cylindrical pillars could yield reduced plate heights as small as h = 0.65 (for k' ' = 0.75) to h = 0.85 (for k' ' = 2) and separation impedances as small as E = 200 (for k' ' = 0.75) to E = 300 (for k' ' = 2) without having to compromise on the porosity (epsilon = 0.4) and the retention capacity of the packed bed of spheres. Fitting the calculated van Deemter plots with Knox's equation especially shows a strong decrease of the A-term contribution, hence confirming that the improved column performance indeed stems from the increased homogeneity of the packing. The presented results, hence, provide a clear quantitative support for Knox's recent argumentation that the use of more uniform beds could greatly enhance the efficiency of pressure-driven LC.

Influence of the pillar shape on the band broadening and the separation impedance of perfectly ordered 2-D porous chromatographic media.

We report on a computational study assessing the effect of the pillar shape in perfectly ordered porous chromatographic media. Using computational fluid dynamics to compare the band broadening and flow resistance characteristics of a large number of different pillar shapes, it is found that the most axially elongated shapes yield the best chromatographic performance and that diamonds are to be preferred over ellipsoids. The former pack into a more uniform pore space and display a smaller C(s) value, whereas the latter pack into a locally constricted pore space and therefore generate a considerably larger flow resistance. For the presently considered case of a densely packed array (epsilon = 0.4), changing the pillar shape from a cylinder to a more elongated diamond, for example, reduces the minimal plate heights from h(min) = 0.84 to h(min) = 0.72, the C factor from C = 0.062 to C = 0.050, and the separation impedance from E(min) = 330 to E(min) = 220, without affecting the number of interchannel coupling points.