Molecular sieve properties of mesoporous silica with intraporous nanocarbon.

Biporous carbon-silica materials (CSM) with molecular sieve properties and high sorption capacity were developed by synthesizing nano-sized carbon crystallites in the mesopores of Al-MCM-41.

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.

n- and isoalkane adsorption mechanisms on zeolite MCM-22.

Low-coverage adsorption properties (Henry constants, adsorption enthalpy, and entropy) of linear and branched alkanes (C3-C8) on zeolite MCM-22 were determined using the chromatographic technique at temperatures between 420 and 540 K. It was found that adsorption enthalpy and entropy of linear alkanes vary in a nonmonotonic way with carbon number. The adsorption behavior of alkanes was rationalized on the basis of the pore geometry. Short molecules prefer to reside in the pockets of the MCM-22 supercage, where they maximize energetic interaction with the zeolite. Longer molecules reside in the larger central part of the supercage. For carbon numbers up to six, singly branched alkanes are selectively adsorbed over their linear counterparts. This preference originates from the entropic advantage of singly branched molecules inside MCM-22 supercages, where these species have high rotational freedom because of their small length.

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.

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.

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.

Porous silicon as a stationary phase for shear-driven chromatography.

We report on the possibility to strongly increase the mass loadability and retention capacity of shear-driven chromatography (SDC) channels by growing a thin porous silicon layer on the stationary wall part. The thickness of the produced porous silicon layers was found to increase linearly with the anodisation time, and could easily be varied between 50 and 300 nm. Combining these layers with sub-microm thin flow-through channels, we believe it is the first time a sub-microm on-chip LC system with a phase ratio similar to that in packed column HPLC (i.e., Vs/Vm approximately equal to 1.5) is obtained. The chromatographic performance of the produced channels has been tested by separating binary mixtures of coumarin dyes under RP-LC conditions. The plate height measurements, yielding Hmin, approximately equal to 0.5 microm (corresponding to more than 2 x 10(6) plates/m) for a retained component with k" = 3, showed good agreement with the theoretical expectations. Due to the presence of some macroscopic defects in the prepared layers, the quality of the separations could however only be maintained over a few millimeters of the channel length. This length was however more than sufficient to separate the coumarin mixture, given the extremely small plate heights of the system.

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].

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.

Enhancement of DNA micro-array analysis using a shear-driven micro-channel flow system.

A very simple micro-channel flow system is used to investigate the potential gain in hybridization rate stemming from the induction of a convective flow past the surface of a DNA micro-array. Reporting on a series of preliminary experiments wherein a two-dimensional convective flow is created past the surface of a conventional micro-array slide, the analysis time could be brought down from overnight waiting (16 h) to some 10 to 30 min. The experiments open the road towards the development of novel, convection-driven hybridization systems yielding shorter analysis times, and/or lower detection limits.

Pore mouth versus intracrystalline adsorption of isoalkanes on ZSM-22 and ZSM-23 zeolites under vapour and liquid phase conditions.

Methylbranched C5-C9 alkanes do not adsorb in the intracrystalline void space of ZSM-23, neither from the vapour nor the liquid phase, but are adsorbed in ZSM-22, if only from the liquid phase, and this despite the small difference in pore size.

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.

Sub-second liquid chromatographic separations by means of shear-driven chromatography.

Utilizing the concept of shear-driven chromatography, we have been able to realize reversed-phase LC separations in flat rectangular nano-channels coated with a C8 monolayer and being as thin as 100 nm. At this scale, the separation kinetics are strongly enhanced, as is witnessed by the extremely short time (< 0.1 s) needed to separate a mixture of coumarin dyes. The observed plate numbers are still relatively small, because the experiments were conducted in ultra-short columns (< or = 1 mm) and under injection band width-limiting conditions.

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.

Experimental demonstration of the possibility to perform shear-driven chromatographic separations in micro-channels.

The possibility to perform shear-driven chromatographic separations in micro-channels is demonstrated, using a novel laser-jet printed microfluidic channel system. The obtained theoretical plate numbers are in fair agreement with the theoretical calculations. Theoretical extrapolations of the separation speeds and detection limits which can be achieved when further miniaturizing the current system are presented as well.

Simultaneous optimization of the analysis time and the concentration detectability in open-tubular liquid chromatography.

Scott's OT-LC minimal analysis time problem has been solved analytically and has been extended to thick-film and/or large diameter columns. The optimisation analysis has also been applied to a number of relative performance indexes (Cmax/t(anal), Cmax x d/t(anal) and Cmax x u x d2/t(anal) which provide a quantitative insight on the extent to which OT-LC allows to combine short analysis times with a large concentration detectability.

On the possibility of shear-driven chromatography: a theoretical performance analysis.

The use of shear forces for the generation of the mobile phase flow in chromatographic separations is proposed. This novel chromatographic operating principle, referred to as shear-driven chromatography (SDC), completely circumvents the pressure-drop limitation of conventional pressure-driven GC and LC without affecting the operational flexibility (choice of mobile and stationary phases, possibility of solvent and/or temperature programming, etc.). In the present paper, the expression for the height equivalent to a theoretical plate in SDC in a channel with a flat rectangular cross-section is established and is used to demonstrate the large gain in analysis speed under LC, GC and supercritical fluid chromatography conditions.

Simulation of growth of a filamentous fungus in 3 dimensions.

The tridimensional growth of a filamentous fungus was simulated, based on a model for the evolution of the microscopic morphology of Trichoderma reesei. When supplemented with a spatial representation of growth, the model correctly simulates the evolution from a single spore to a pellet. Diffusion of oxygen is included in the model. The simulated tridimensional structures have a fractal nature; and the fractal dimension, determined by a box-counting method, increases during growth. The fractal dimension only depends on the mass of the pellet and is not affected by model parameters such as tip extension rate and branching frequency. Realistic pictures are obtained and the radius of the pellet increases at a constant rate. The influence of model parameters (tip extension rate, branching frequency, minimum porosity) on dissolved oxygen concentration profiles, biomass concentration profiles, rate at which the pellet diameter increases, and the evolution of the fractal dimension was determined. The dissolved oxygen profiles were found to be very different from the profiles, obtained by assuming a homogenous biomass distribution within the pellet. Finally, the formation of pellets from spore aggregates is calculated and the size of the spore aggregate is found to only influence the time needed before the appearance of a pellet and not its morphology. (c) 1997 John Wiley & Sons, Inc.

Morphology of Trichoderma reesei QM 9414 in submerged cultures.

The microscopic morphology of Trichoderma reesei QM 9414, growing in submerged culture, was studied by image analysis. The morphology was characterized by the total hyphal length, the total number of tips, the number of actively growing tips, and the length of the main hypha. To describe the growth of a single mycelium a simple model is set-up. The main features of the model are: (1) saturation type kinetics for the tip extension of the individual branches within the mycelium; and (2) random branching with a frequency function, which is proportional to the total hyphal length. The model is used to simulate a population of mycelia, where spore germination is described with a log-normal distribution. From the simulation of the population, the average properties of the mycelia, e.g., the average total hyphal length, are calculated, and by fitting the model to experimental data the model parameters are estimated. Finally, the distribution function with respect to the mycelia properties, that is, number of tips and total hyphal length, is calculated, and it corresponds well with the experimental determination of the distribution function. (c) 1995 John Wiley & Sons Inc.