A computational study of the porosity effects in silica monolithic columns

We report on a theoretical study of the influence of the through-pore porosity on the main chromatographic performance parameters (reduced theoretical plate height, flow resistance, and separation impedance) of silica monoliths. To investigate this problem devoid of any structural uncertainties, computer-generated structural mimics of the pore geometry of silica monolithic columns have been studied. The band broadening in these synthetic monoliths was determined using a commercial Computational Fluid Dynamics (CFD) software package. Three widely differing external porosities (epsilon = 0.38, epsilon = 0.60, and epsilon = 0.86) are considered and are compared on the basis of an identical intra-skeleton diffusivity (Ds = 5 x 10(-10)m2/s), internal porosity (epsilon(int) = 0.5), and for the same phase retention factor (k' = 1.25). Since the data are obtained for perfectly ordered structures, the calculated plate heights and separation impedances constitute the ultimate performance ever to be expected from a monolithic column. It is found that, if silica monoliths could be made perfectly homogeneous, domain size-based reduced plate heights as small as h(min) approximately 0.8 (roughly independent of the porosity) and separation impedances as small as Emin approximately 130 (epsilon = 0.60) and Emin approximately 40 (epsilon = 0.86) should be achievable with pure water as the working fluid. The data also show that, although the domain size is a much better reduction basis than the skeleton size, the former is still not capable of bringing the van Deemter curves of different porosity columns into perfect agreement in the C term dominated velocity range. It is found that, in this range, large porosity monoliths can be expected to yield smaller domain size-based reduced plate heights than small porosity monoliths.     

Model column structure for the analysis of the flow and band-broadening characteristics of silica monoliths

We report on the use of commercial computational fluid dynamics software to study the band broadening in a perfectly ordered three-dimensional model structure, the so-called tetrahedral skeleton column (TSC), selected for its close geometrical resemblance to the specific pore network topology of silica monoliths. Van Deemter plots are presented for the case of a species flow through a non-porous skeleton and for the case of a retained component (k' = 1) in a porous skeleton (mesopore porosity epsilon = 0.6 in both cases). Using the flow domain as the characteristic scaling dimension, the TSC model yields reduced plate heights as small as h(min) = 0.8 and separation impedances as small as Emin = 120 for a retained component with k' = 1. The very small reduced plate heights for the TSC model can without any doubt largely be attributed to the perfect homogeneity of the considered model structure: the B and C terms are similar to those obtained in real silica monoliths with similar external porosity, whereas the A term is significantly (about a factor of 10) smaller. The present study hence suggests that further experimental work to obtain more homogeneous silica networks could yield large gains in reduced plate height and separation impedance. Comparing the three-dimensional TSC model with a 2D array of cylinders, it was found that the use of the domain size as the characteristic dimension in the reduced plate height expression is much more appropriate than the use of the skeleton size, hence validating earlier approaches adopted in the literature.     

How does column packing microstructure affect column efficiency in liquid chromatography?

Full three-dimensional computer simulations of the fluid flow and dispersion characteristics of model nonporous chromatographic packings are reported. Interstitial porosity and packing defects are varied in an attempt to understand the chromatographic consequences of the packing microstructure. The tracer zone dispersion is calculated in the form of plate height as a function of fluid velocity for seven model particle packs where particles are selectively removed from the packs in clusters of varying size and topology. In an attempt to examine the consequences of loose but random packs, the velocities and zone dispersion of seven defect-free packs are simulated over the range 0.36< or =epsilon< or =0.50, where epsilon is the interstitial porosity. The results indicate that defect-free loose packings can give good chromatographic efficiency but the efficiency can vary depending on subtle details of the pack. When the defect population increases, the zone dispersion increases accordingly. For a particle pack where 6% of the particles are removed from an epsilon=0.36 pack, approximately 33% of the column efficiency is lost. These results show that it is far more important in column packing to prevent defect sites leading to inhomogeneous packing rather than obtaining the highest density pack with the smallest interstitial void volume.     

Study of the influence of the aspect ratio on efficiency, flow resistance and retention factors of packed capillary columns in pressure- and electrically-driven liquid chromatography

The influence of the aspect ratio, rho (rho = column diameter/particle diameter), on column parameters such as efficiency, retention factors and flow resistance was studied in both high-performance liquid chromatography and capillary electrochromatography with packed capillary columns. In order to compare the true efficiencies of different columns, a procedure to account for external band broadening was applied. High efficiencies (reduced plate height h approximately 2) were obtained with capillary columns with internal diameters of 150-, 100-, and 75-microm, packed with 10-microm particles. In contrast to previous reports in the literature, no significant improvements in efficiency or flow resistance were observed when the aspect ratio of such columns was decreased. Our observations suggest that the wall effect in these types of columns is not significant. When the aspect ratio was decreased by increasing the particle size, a decrease in reduced plate height was observed. However, the results of flow resistance measurements showed that the latter effect should be attributed to differences in packing and particle batch quality rather than to differences in the aspect ratio.     

Towards porous polymer monoliths for the efficient, retention-independent performance in the isocratic separation of small molecules by means of nano-liquid chromatography

We have investigated the free-radical copolymerization dynamics of styrene and divinylbenzene in the presence of micro- and macro-porogenic diluents in 100 μm I.D. sized molds under conditions of slow thermal initiation leading to (macro)porous poly(styrene-co-divinylbenzene) monolithic scaffolds. These specifically designed experiments allowed the quantitative determination of monomer specific conversion against polymerization time to derive the porous polymer scaffold composition at each desirable copolymerization stage after phase separation. This was carried out over a time scale of 3h up to 48 h polymerization time, enabling the efficient and repeatable termination of the polymerization reactions. In parallel, the porous and hydrodynamic properties of the derived monolithic columns were thoroughly studied in isocratic nano-LC mode for the reversed-phase separation of a homologous series of small retained molecules. At the optimized initiator concentration, polymerization temperature and time, the macroporous poly(styrene-co-divinylbenzene) monoliths show a permanent mesoporous pore space, which was readily observable by electron microscopy and indicated by nitrogen adsorption experiments. Under these conditions, we consistently find a polymer scaffold composition which suggests a high degree of cross-linking and thus minimum amount of gel porosity. These columns reveal a retention-insensitive plate height in the separation of small retained molecules which only slightly decreases at increased linear mobile phase velocity. As the polymerization progresses, a build-up of less-densely cross-linked material occurs, which is directly reflected in the observed consistent increase in retention and plate heights. This leads to a significant deterioration in overall isocratic separation performance. The decrease in performance is ascribed in particular to the increased mass transfer resistance governing the monoliths' performance over the whole linear chromatographic flow velocity range at polymerization times significantly higher than that of phase separation. The performance of the optimized monoliths only becomes limited by fluid dispersion due to the poorly structured macroporous pore space.     

Understanding and design of existing and future chromatographic support formats

The present contribution reviews the use of alternative support formats as a means to surpass the chromatographic performance of the packed bed of spheres. First, a number of idealized structures are considered to obtain a general insight in how the performance of a chromatographic support depends on its shape and size, using the isocratic peak-capacity generation speed as the main performance indicator. Using this criterion, it is found that the packing density or, equivalently, the external porosity, is the most important of all geometrical shape factors. Depending on whether the sample consists of weakly or strongly retained components, the optimal external porosity can be expected to vary between 60% and a value near 100%. The optimal exploitation of a high external porosity, however, also requires overall shrinkage of the domain size, towards and into the sub-micron range. With the current fabrication technologies, this requirement seems difficult to achieve. In the presence of a lower limit on the characteristic support size, each range of desired plate numbers or peak capacities has its own optimal external porosity, ranging from a very low value (high packing density) for high speed, small peak capacity applications, to very high external porosities (low packing density) for applications requiring a very large peak capacity. Subsequently, the obtained theoretical insights are used to review and discuss the past and current research on alternative support formats. Finally, a number of emerging micro- and nano-fabrication technologies are introduced and their potential for the future production of supports with improved shape and homogeneity is discussed.     

Theoretical study of the effect of frit quality on chromatography using computational fluid dynamics

Summary Frits at both ends of a chromatographic column, especially for a preparative column, have significant influence on the flow distribution within the column and thus the column efficiency. However, frits have received little attention from chromatographers in the past. Here a theoretical study was conducted with the aid of CFD software FLUENT to investigate the effect of frits on the performance of homogeneous and heterogeneous chromatographic columns. A dimensionless number,FQ, was applied to characterize frit quality. This study visualized how frit quality affects the flow distribution and the concentration band, the shape of eluted pulse at the colum exit and column efficiency. Simulation results show that the development length of the flow distribution is related toFQ but has nothing to do with the packing heterogeneity. The curvature of the concentration band in a column depends onFQ and packing quality. This study shows column efficiency can be improved significantly by increasingFQ and/or frit permeability.     

Band broadening in size-exclusion chromatography of polydisperse samples

Understanding and controlling the band broadening is essential to obtain accurate molar-mass distributions by size-exclusion chromatography (SEC). In this paper, band broadening in SEC is reviewed from a contemporary perspective. The observed band broadening is due to dispersion inside and outside the chromatographic column (undesirable band broadening) and to the polydispersity of the sample (desirable SEC selectivity). The various contributors to band broadening are discussed. Integrity plots are introduced as a tool to evaluate the performance of specific SEC columns at given experimental conditions. For narrow polymer standards on single SEC columns the observed peak width is dominated by the chromatographic dispersion. MALDI-ToF-MS is demonstrated as an alternative to determine the PDI of narrowly distributed samples. The plate heights encountered at very high reduced velocities are found to be lower than expected. This is advantageous for fast separations by SEC.     

Estimation of the instrumental band broadening contribution to the column elution profiles in open tubular capillary liquid chromatography

In comparison with conventionally packed HPLC columns, from a theoretical point of view, open capillary liquid chromatography (OTLC) systems offer a number of advantages like high plate numbers and short analysis times. On the other hand, drastic changes have to be made to the instrumentation. In particular, the contribution to band broadening by the chromatographic equipment must be considerably reduced. In the present study an OTLC system was developed and evaluated, which yields satisfactory results for 26 μm i. d. columns. The determination of the contribution of the chromatographic equipment to the total band broadening is discussed.     

Statistical analysis of packed beds,the origin of short-range disorder,and its impact on eddy dispersion

We quantified the microstructural disorder of packed beds and correlated it with the resulting eddy dispersion. For this purpose we designed a set of bulk (unconfined) monodisperse random sphere packings with a systematic, protocol-dependent degree of microstructural heterogeneity, covering a porosity range from the random-close to the random-loose packing limit (? = 0.366–0.46). With the precise knowledge of particle positions, size, and shape we conducted a Voronoï tessellation of all packings and correlated the statistical moments of the Voronoï volume distributions (standard deviation and skewness) with the porosity and the protocol-dependent microstructural disorder. The deviation of the Voronoï volume distributions from the delta function of a crystalline packing describes the origin of short-range disorder of the investigated random packings. Eddy dispersion was simulated over a wide range of reduced velocities (0.5 ≤  ν ≤ 750) and analyzed with the comprehensive Giddings equation. Transient dispersion was found to correlate with the spatial scales of heterogeneity in the packings. The analysis of short-range disorder based on the Voronoï volume distributions revealed a strong correlation with the short-range interchannel contribution to eddy dispersion, whereas transchannel dispersion was relatively little affected. The presented approach defines a strictly scientific route to the key morphology–transport relationships of current and future chromatographic supports, including their morphological reconstruction, statistical analysis, and the correlation with relevant transport phenomena. It also guides us in our understanding, comparison, and optimization of the diverse packing algorithms and protocols used in simulations and experimental studies.     

Axial development and radial non-uniformity of flow in packed columns

Flow inhomogeneity and axial development in low-pressure chromatographic columns have been studied by magnetic resonance imaging velocimetry. The columns studied included (a) an 11.7-mm I.D. column packed with either 50 microm diameter porous polyacrylamide, or 99 or 780 microm diameter impermeable polystyrene beads, and (b) a 5-mm I.D. column commercially packed with 10 microm polymeric beads. The packing methods included gravity settling, slurry packing, ultrasonication, and dry packing with vibration. The magnetic resonance method used averaged apparent fluid velocity over both column cross-sections and fluid displacements greater than one particle diameter and hence permits assessment of macroscopic flow non-uniformities. The results confirm that now non-uniformities induced by the conical distributor of the 11.7-mm I.D. column or the presence of voids at the column entrance relax on a length scale of the column radius. All of the 11.7-mm I.D. columns examined exhibit near wall channeling within a few particle diameters of the wall. The origins of this behavior are demonstrated by imaging of the radial dependence of the local porosity for a column packed with 780 microm beads. Columns packed with the 99-microm beads exhibit reduced flow in a region extending from ten to three-to-five particle diameters from the wall. This velocity reduction is consistent with a reduced porosity of 0.35 in this region as compared to approximately 0.43 in the bulk of the column. Ultrasonicated and dry-packed columns exhibit enhanced flow in a region located between approximately eight and 20 particle diameters from the wall. This enhancement maybe caused by packing density inhomogeneity and/or particle size segregation caused by vibration during the packing process. No significant non-uniformities on length scales of 20 microm or greater were observed in the commercially packed column packed with 10 microm particles.     

A first principles explanation for the experimentally observed increase in A-term band broadening in small domain silica monoliths and other chromatographic supports

The present computational study illustrates how the existence of a residual lower limit on the variance of the skeleton and through-pore size of monolithic columns can be expected to severely compromise the possibility to prepare well-performing small domain monolithic columns. Adopting rather conservative estimates for the minimal standard deviation on the pore and the skeleton size (0.2 and 0.04 microm, respectively), the presented calculations show that, if such a fixed lower limit on the size variance exists, it will be impossible to decrease the A-term band broadening below a given critical value, no matter how small the domain size is made. From a given critical domain size value on, any attempt to further decrease the domain size without being able to co-reduce the size variance can be expected to be counterproductive and leads to an increase instead of to a further decrease of the plate heights.     

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.     

Two‐dimensional chromatography as a tool for studying band broadening in size‐exclusion chromatography

Comprehensive 2‐D size‐exclusion chromatography (SEC×SEC) has been realized. SEC×SEC is not a useful technique for characterizing complex polymers. However, it is potentially an elegant tool to study band‐broadening phenomena. If narrow fractions can be collected from the first dimension, the band broadening in the second dimension is only due to chromatographic dispersion. This would allow a clear distinction to be made between chromatographic band broadening (column and extra‐column) and SEC selectivity (band broadening due to sample polydispersity). In comparison with MALDI‐MS, SEC×SEC allows the study of polymers across a much broader molar‐mass range.     

Axial and radial diffusion coefficients in a liquid chromatography column and bed heterogeneity

The axial and transverse diffusion coefficients of a band of iodine in a chromatographic column were measured optically as a function of time. It was found that the axial diffusion coefficient remains constant even when the edges of the sample band get close to the wall. By contrast, the radial diffusion coefficient decreases progressively with increasing time when the edges of the sample band leave the core region and begin to diffuse inside the wall region. The local axial and transverse diffusion coefficients of the band decrease from the column center toward the wall. Hence, the increase in local height equivalent to a theoretical plate observed in the region close to the wall must be explained by increasing mass transfer resistances and degree of heterogeneity of the bed.     

Visualization of solute migration in chromatographic columns influence of the frit porosity

The dual-perspective, on-column detection method previously described was used to observe the effects of the inlet frit on the profiles of chromatographic bands. Visualization of bands of iodine was achieved by injecting its dilute solutions in carbon tetrachloride into a glass column packed with a C18-bonded silica and eluted with carbon tetrachloride, which has the same refractive index as the packing material. The bands were photographed on-column with two standard 35-mm SLR cameras oriented at right angle. The photographs were scanned and the digitized images of the sample bands analyzed with proper software. A number of columns, as similar as possible, were fitted with different 2- and 10-microm porosity stainless steel frits. Subsequent analysis of the digitized band images revealed irregularities in the band shape resulting from frit contributions to band dispersion. The 2-microm frits produced more dramatic effects overall than the coarser frits. Local axial dispersion coefficient values, expressed as local reduced plate height, were calculated. The results demonstrate the possibly damaging effects of the frit on the band shape.     

Approximate transient and long time limit solutions for the band broadening induced by the thin sidewall-layer in liquid chromatography columns

Using a combination of both analytical and numerical techniques, approximate analytical expressions have been established for the transient and long time limit band broadening, originating from the presence of a thin disturbed sidewall layer in liquid chromatography columns, including packed, monolithic as well as microfabricated columns. The established expressions can be used to compare the importance of a thin disturbed sidewall layer with that of other radial heterogeneity effects (such as transcolumn packing density variations due to the relief of packing stresses). The expressions are independent of the actual velocity profile inside the layer as long as the disturbed sidewall layer occupies less than 2.5% of the column width.     

Extended thermodynamic approach to ion interaction chromatography: a thorough comparison with the electrostatic approach,and further quantitative validation

Based on a simple, chromatography-based analogy, a quantitatively exact explanation for the strong additional band broadening induced by the presence of the side-walls in flow channels with a large aspect-ratio rectangular cross-section is given and validated for two different flow types: pressure-driven and shear-driven flow.     

Effect of steric exclusion on the separation of proteins by hydrophilic size-exclusion chromatography

On the basis of studying the retention and band broadening of proteins on the TSK SW column, diffusion coefficients (Ds) of solute in stationary phase were obtained which elucidate the hydrodynamic process of chromatographic resolution of proteins by hydrophilic size-exclusion chromatography (SEC). After calculating the correlation between Ds and the molecular weight of the solute, the molecular dimensions of proteins in the process of chromatographic separation can be predicted. Deviations in diffusion coefficient of a protein from the calculated value reflect differences of measured molecular dimensions from molecular volumes predicted from the calibration curve of the SEC column. This study illustrates a convenient method for estimating the purity of proteins by SEC. Deviations from 2 lambda dp (where dp is the particle diameter) in the intercept of the theoretical plate height (H) versus flow-rate (U) curve from the band broadening equation H = CsU + 2 lambda dp + f(alpha M)T (where CsU represents mass transfer resistance caused by solute diffusion in the stationary phase and f(alpha M)T an added term for polydisperse solutes as proposed by Knox and McLennan [Chromatographia, 10 (1977) 75]) reflect impurities in the proteins.     

The effect of shell side hydrodynamics on the performance of axial flow hollow fibre modules

Fluid flow and mass transfer experiments have been performed on axial flow hollow fibre modules of varying packing density (32 to 76%). Shell-side pressure drop was found to be proportional to (flowrate)ⁿ, where n varied from about 1.1 at high packing density to 1.5 at low packing density, for shellside Reynolds numbers < 350. Assuming an Ergun-type pressure drop relationship it was found that for packing densities < about 50% the inertial (turbulent) losses exceeded the viscous (laminar) losses. Inspection of cross-sections taken from the middle of modules revealed non-uniform fibre packing with regions of high and low packing density. The cross-sections also change along the length of the module. It is inferred that, in addition to axial flow along fibres, there is also a degree of stream splitting which provides transverse flow across fibres as fluid continuously seeks preferential paths through regions of lower packing density. The presence of transverse flow would explain the higher than expected velocity exponent. Mass transfer experiments involving the removal of oxygen from water flowing through the shell to a sweep gas in the fibre lumens produced higher than expected shell-side mass transfer coefficients. The results are correlated within ± 15% by Sh = (0.53 − 0.58φ)Re^0.53Sc^0.33. The exponent on Re is consistent with entry region conditions, caused by repeated stream splitting and transverse flow. Compared with mass transfer predicted for axial flow through a uniformly packed shell the experimental results are up to 2× higher, with the most significant enhancement at the lower packing densities. The implication of this work is that module design requires a more sophisticated approach than the traditional assumption of laminar flow through parallel axial ducts.