Physical evidence of two wall effects in liquid chromatography

Using optical on-column visualization for the study of the migration of sample bands, the radial variations of the local migration rate were studied in the region near the column wall. Photographs of small sample bands migrating along the column at various radial locations were obtained. On-column chromatograms extracted from these photographs showed evidence of two wall effects. The first of these effects was present only within the immediate vicinity of the wall. It is a direct result of the inability of the packing material to form a close packed configuration against the rigid column wall surface. The second wall effect causes a systematic variation of the migration rate of the sample band in the region of the wall, this rate increasing from the wall to the central region of the column. The corresponding images portrayed the classical "wall effect" that chromatographers have long discussed. They also show that this effect extends further into the column than anticipated. As to what are the relative contributions to the results of our observations of the wall effect and of a frit effect discussed in previous publications, this could not be ascertained.     

Nuclear magnetic resonance studies of solvent flow through chromatographic columns: effect of packing density on flow patterns

NMR (nuclear magnetic resonance) techniques have been used to measure and characterise solvent flow through chromatographic columns. NMR imaging was used to track an injection of D2O. PGSE (pulsed gradient spin echo) NMR was used to measure the flow-rate dependence of axial and transverse apparent diffusion. A combination of these two techniques (dynamic NMR imaging) gave the spatial distribution of the local velocity and apparent diffusion through a cross-section of the column. Significant column wall effects were observed and these effects were found to be highly dependent upon the column packing density. The column performance was assessed in terms of the HETP (height equivalent to a theoretical plate) determined by the NMR techniques employed.     

Visualization of sample introduction in liquid chromatographic columns. Contribution of a flow distributor on the sample band shape

The contributions to the radial distribution of the sample concentration across the column inlet and to the axial band dispersion resulting from a column header containing a distributor were evaluated using a band-visualization process entailing matching the refractive indices of the stationary and mobile phases in a glass column. This study illustrates graphically how a distributor fitted to the column can increase the axial dispersion of the sample band compared to an inlet containing only a frit. The distributor did not provide a uniform sample distribution across the column. In fact, for 17-mm inner diameter columns and high-porosity frits, the distribution was no better than with the frit having no distributor. However, when low-porosity frits were employed, improved peak shapes were obtained with a distributor. In addition, we observed that the inlet header configuration influenced dramatically the flow stream established along the column. The radial distribution of the efficiency of the columns was nearly homogeneous for those having only a frit but not for those having also a distributor. For the latter, the efficiency decreased from the column axis to its wall.     

Kinetic study of the mass transfer of S-Tr?ger's base in the system cellulose triacetate and ethanol.

A recent study of the mass transfer kinetics of (-)- or S-Tr?ger's base (TB) between ethanol and microcrystalline cellulose triacetate (CTA) allows an analysis of the concentration dependence of the mass transfer rate coefficient (k(m)). S-TB elutes before R-TB. The retention time of the both compounds decreases with increasing temperature. In this study, experimental data measured between 30 and 50 degrees C were analyzed to provide information on the kinetics of several mass transfer processes which take place in the chromatographic column, i.e., axial and intraparticle dispersion, the fluid-to-particle mass transfer, and the kinetics of adsorption/desorption at the actual adsorption sites. Intraparticle diffusion has the dominant contribution to band broadening at high flow-rates. Both intraparticle diffusivity and the surface diffusion coefficient exhibit a small concentration dependence. The positive dependence of k(m) on the concentration of S-TB seems to result from the properties of the adsorption/desorption kinetics and can be interpreted by considering the phase equilibrium properties. A quantitative analysis of the activation energy of the mass transfer kinetics of S-TB in the CTA column was also attempted.     

CFD modeling for flow and mass transfer in spacer-obstructed membrane feed channels

The effect of spacer geometry on fluid dynamics and mass transfer in feed channels of spiral wound membranes has been investigated. Three-dimensional computational fluid dynamics (CFD) simulations reveal significant influence of spacer geometric parameters such as filament spacing, thickness and flow attack angle on wall shear rates and mass transfer coefficients. The spacers with filaments in axial and transverse direction induce higher shear stresses at the top membrane surface when compared to the bottom; the mass transfer rates are almost equal. The distribution of mass transfer coefficients become uniform when the spacing between axial filaments is increased or transverse filament thickness is decreased. For spacers with filaments inclined to the channel axis, the flow structure depends on spacing and flow attack angle. The fluid follows a zigzag path when spacing is greater while it begins to line-up with the filaments when spacing is reduced or flow attack angle is increased. The flow when aligned with the filaments increases the wall shear stress but confines the region of higher mass transfer coefficient values to a narrower portion. The zigzag flow movement increases these values on a major portion of membrane surface which enhances the mass transfer rates.     

Radial distribution of the contributions to band broadening of a silica‐based semi‐preparative monolithic column

Using an on‐column local electrochemical microdetector operated in the amperometric mode, band elution profiles were recorded at different radial locations at the exit of a 10 mm id, 100 mm long silica‐based monolithic column. HETP plots were then acquired at each of these locations, and all these results were fitted to the Knox equation. This provided a spatial distribution of the values of the eddy diffusion (A), the molecular diffusion (B), and the resistance to the kinetics of mass transfer (C) terms. Results obtained indicate that the wall region yields higher A values and smaller C values than the central core region. Significant radial fluctuations of these contributions to band broadening occur throughout the exit column cross‐section. This phenomenon is due to the structural radial heterogeneity of the column.     

Visualization of sample introduction in liquid chromatography columns. The effect of the frit diameter.

A previously developed on-column detection technique using 35 mm SLR cameras [J. Chromatogr. A 826 (1998) 1] was employed to visualize colored sample bands as they elute through frits of differing diameter. Head fittings containing a 4.0 mm frit and a 15.9 mm frit were mounted in a 17 mm I.D. glass column packed with C18 silica with an average particle size of 21 microns. A carbon tetrachloride mobile phase of matching refractive index to that of the silica provides clarity along the column diameter during band migration. The photographs of the migrating sample zones were scanned and analyzed with appropriate imaging software. The smallest diameter frit induced severely parabolic sample distributions at the column inlet compared to the larger frit. Local axial dispersion coefficient values, expressed as local reduced plate height, were calculated as well as local zone velocities at the column inlet. The results demonstrate clearly the need to match the diameter of the inlet frit to the I.D. of the column so as to avoid the initial onset of zone broadening due to the frit.     

Multi-location peak parking method: an important new tool for the study of mass transfer kinetics in liquid chromatography

The peak parking (PP) method probes the longitudinal diffusion coefficient of a compound at a single location along the chromatographic column. We extended to a so-called multi-location peak parking (MLPP) method, in which a large number of axial locations along the column are selected in order to check the validity of the conventional PP method and to reveal possible defaults in the structure of the packed bed or pitfalls of the PP and the MLPP methods. MLPP was applied to a series of HILIC columns, including a 5.0 μm Venusil, a 3.0 μm Luna-diol, three 2.7 μm Halo, and a 1.7 μm Kinetex columns. The results demonstrate that the MLPP method may reveal local heterogeneities in the axial diffusion of small retained low molecular weight compounds along the column. Most importantly, experiments show that the sample zone should not be parked in the entrance of the column (i.e., at <1/10 th of the column length). The abrupt drop in the flow rate considerably affects the peak shape and prevents scientists from using the conventional PP method. Practical solutions to cope with that problem are proposed and their success/failure are discussed.     

Numerical modeling of the elution peak profiles of retained solutes in supercritical fluid chromatography

In supercritical fluid chromatography (SFC), the significant expansion of the mobile phase along the column causes the formation of axial and radial gradients of temperature. Due to these gradients, the mobile phase density, its viscosity, its velocity, its diffusion coefficients, etc. are not constant throughout the column. This results in a nonuniform flow velocity distribution, itself causing a loss of column efficiency in certain cases, even at low flow rates, as they do in HPLC. At high flow rates, an important deformation of the elution profiles of the sample components may occur. The model previously used to account satisfactorily for the retention of an unsorbed solute in SFC is applied to the modeling of the elution peak profiles of retained compounds. The numerical solution of the combined heat and mass balance equations provides the temperature and the pressure profiles inside the column and values of the retention time and the band profiles of retained compounds that are in excellent agreement with independent experimental data for large value of mobile phase reduced density. At low reduced densities, the band profiles can strongly depend on the column axial distribution of porosity.     

Fundamental chromatographic equations designed for columns packed with very fine particles and operated at very high pressures. Applications to the prediction of elution times and the column efficiencies

The wall temperatures of three Acquity-BEH-C18columns (2.1 mm x 50, 100, and 150 mm) and the temperature of the incoming eluent were maintained constant at 289 K, using a circulating water heat exchanger. The retention times and the band broadening of naphtho[2,3-a]pyrene were measured for each column as a function of the flow rate applied. Pure acetonitrile was used as the eluent. The flow rate dependence of neither elution volumes nor bandwidths can be accounted for by classical models of retention and HETP, respectively, since these models assume columns to be isothermal. Because the heat generated by friction of the eluent against the column bed increases with increasing flow rate, the column bed cannot remain isothermal at high flow rates. This heat is evacuated radially and/or longitudinally by convection, conduction, and radiation. Radial and axial temperature gradients are formed, which are maximum and minimum, respectively, when the temperature of the column wall is kept uniform and constant. The retention times that we measured match well with the values predicted based on the temperature distribution along and across the column, which we calculated and on the temperature dependence of the retention for the same column operated isothermally (i.e., at very low flow rate). The rate of band spreading varies along non-isothermal columns, so the HETP can only be defined locally. It is a function of the axial coordinate. A new contribution is needed to account for the radial thermal heterogeneity of the column, hence the radial distribution of the flow velocities, which warps the elution band. A new model, based on the general dispersion theory of Aris, allows a successful prediction of the unusually large bandwidths observed with columns packed with fine particles, operated at high flow rates, hence high inlet pressures.     

锥型与圆柱型液相色谱制备柱的比较研究

用可视化柱上图形分析对入口内径大于出口内径的锥型液相色谱制备柱的样品谱带流型进行了研究。在一定的实验条件下，锥型柱与圆柱型柱的流动相流型曲线相反。对与锥型柱有相同长度、相同容积的圆柱型色谱柱的柱效、样品容量及峰高的比较研究表明：锥型柱优于圆柱型柱。锥型柱的样品容量约为圆柱型柱的2倍，柱效比圆柱型的高36％，色谱流出曲线峰值高于圆柱型柱12％。     

Faster axial band dispersion in a monolithic silica column than in a particle-packed column

The contribution of molecular diffusion to peak broadening was studied in a reversed-phase HPLC system, consisting of a monolithic silica C18 column and methanol-water mobile phase. Study on the band broadening effect of holding a solute in a column or elution at very low linear velocity of mobile phase allowed facile determination of the contribution of the molecular diffusion term. Less obstruction against molecular diffusion, or the faster axial band dispersion in a monolithic silica column than in a particle-packed column, was found both in mobile phase and in stationary phase.     

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.     

Kinetic study of the mass transfer of bovine serum albumin in anion-exchange chromatography

A kinetic study was made on the mass transfer phenomena of bovine serum albumin (BSA) in two different anion-exchange columns (Resource-Q and TSK-GEL-DEAE-5PW). The analysis of the concentration dependence of the lumped mass transfer rate coefficient (km,L) provided the information about the kinetics of the several mass transfer processes in the columns and the anion exchangers, i.e., the axial dispersion, the fluid-to-particle mass transfer, the intraparticle diffusion, and the adsorption/desorption. In the Resource-Q column, the intraparticle diffusion had a dominant contribution to the band broadening compared with those of the other processes. The surface diffusion coefficient (Ds) of BSA showed a positive concentration dependence, by which the linear dependence of km,L on the BSA concentration seemed to be interpreted. On the other hand, in the TSK-GEL-DEAE-5PW column, the contribution of the adsorption/desorption was also important and almost same as that due to the intraparticle diffusion. There are some differences between the intrinsic properties of the mass transfer kinetics inside the two anion exchangers. It was likely that the positive concentration dependence of Ds was explained by the heterogeneous surface model.     

Effect of Modification on the Fluid Diffusion Coefficient in Silica Nanochannels

The diffusion behavior of fluid water in nanochannels with hydroxylation of silica gel and silanization of different modified chain lengths was simulated by the equilibrium molecular dynamics method. The diffusion coefficient of fluid water was calculated by the Einstein method and the Green–Kubo method, so as to analyze the change rule between the modification degree of nanochannels and the diffusion coefficient of fluid water. The results showed that the diffusion coefficient of fluid water increased with the length of the modified chain. The average diffusion coefficient of fluid water in the hydroxylated nanochannels was 8.01% of the bulk water diffusion coefficient, and the diffusion coefficients of fluid water in the –(CH₂)₃CH₃, –(CH₂)₇CH₃, and –(CH₂)₁₁CH₃ nanochannels were 44.10%, 49.72%, and 53.80% of the diffusion coefficients of bulk water, respectively. In the above four wall characteristic models, the diffusion coefficients in the z direction were smaller than those in the other directions. However, with an increase in the silylation degree, the increased self-diffusion coefficient due to the surface effect could basically offset the decreased self-diffusion coefficient owing to the scale effect. In the four nanochannels, when the local diffusion coefficient of fluid water was in the range of 8 Å close to the wall, Dz was greater than Dxy, and beyond the range of 8 Å of the wall, the Dz was smaller than Dxy.     

Simultaneous investigation of sedimentation and diffusion of a single colloidal particle near an interface

We describe here a new procedure for the simultaneous investigation of sedimentation and diffusion of a colloidal particle in close proximity to a solid, planar wall. The measurements were made using the optical technique of total internal reflection microscopy, coupled with optical radiation pressure, for dimensionless separation distances (gap width/radius of particle) ranging from 0.01 to 0.05. In this region, the hydrodynamic mobility and diffusion coefficient are substantially reduced below bulk values. The procedure involved measuring the mean and the variance of vertical displacements of a Brownian particle settling under gravity toward the plate. The spatially varying diffusion coefficient was calculated from the displacements at small times (where diffusive motion was dominant). The mobility relationship for motion normal to a flat plate was tested by measuring the average distance of travel versus time as the particle settled under the constant force of gravity. For the simple Newtonian fluid used here (aqueous salt solution), the magnitude of the diffusion coefficient and mobility, plus their dependence on separation distance, showed excellent agreement with predictions. This new technique could be of great value in measuring the mobility and diffusion coefficient for near-contact motion in more complex fluids for which the hydrodynamic correction factors are not known a priori, such as shear-thinning fluids.     

Experimental investigation of liquid chromatography columns by means of computed tomography

The efficiency of packed chromatographic columns was investigated experimentally by means of computed tomography (CT) techniques. The measurements were carried out by monitoring tracer fronts in situ inside the chromatographic columns. The experimental results were fitted using the equilibrium dispersive model (EDM) and varying the so called apparent axial dispersion coefficient. The additivity of the first and second central moments was exploited to estimate column efficiency in different regions of the column. The results showed that the columns under investigation offered a higher column efficiency in the centre compared to the wall region. Furthermore the void fraction in the vicinity of the walls was lower than that in the column core. For this reason the bands were conveyed faster in the central region of the column where the permeability was higher. This result is in good agreement with earlier findings.     

Quantitative analysis and synthesis of the electrokinetic mass transport and adsorption mechanisms of a charged adsorbate in capillary electrochromatography systems employing charged adsorbent particles.

The dynamic mathematical model of Grimes and Liapis [J. Colloid Interf. Sci. 234 (2001) 223] for capillary electrochromatography (CEC) systems operated under frontal chromatography conditions is extended to accommodate conditions in CEC systems where a positively charged analyte is introduced into a packed capillary column by a pulse injection (analytical mode of operation) in order to determine quantitatively the electroosmotic velocity, electrostatic potential and concentration profiles of the charged species in the double layer and in the electroneutral core region of the fluid in the interstitial channels for bulk flow in the packed chromatographic column as the adsorbate adsorbs onto the negatively charged fixed sites on the surface of the non-porous particles packed in the chromatographic column. Furthermore, certain key parameters are identified for both the frontal and analytical operational modes that characterize the performance of CEC systems. The results obtained from model simulations for CEC systems employing the analytical mode of operation indicate that: (a) for a given mobile liquid phase, the charged particles should have the smallest diameter, d(p), possible that still provides conditions for a plug-flow electroosmotic velocity field in the interstitial channels for bulk flow and a large negative surface charge density, deltao, in order to prevent overloading conditions; (b) sharp, highly resolute adsorption zones can be obtained when the value of the parameter gamma2min, which represents the ratio of the electroosmotic velocity of the mobile liquid phase under unretained conditions to the electrophoretic velocity of the anions (0>gamma2.min>-1), is very close to negative one, but the rate at which the solute band propagates through the column is slow; furthermore, as the solute band propagates across larger axial lengths, the desorption zone becomes more dispersed relative to the adsorption zone especially when the value of the parameter gamma2,max, which represents the ratio of the electroosmotic velocity of the mobile liquid phase under retained conditions to the electrophoretic velocity of the anions (0>gamma2,max>-1), is significantly greater than gamma2,min; (c) when the value of the equilibrium adsorption constant, K(A),3, is low, very sharp, highly resolved adsorption and desorption zones of the solute band can be obtained as well as fast rates of propagation of the solute band through the column; (d) sharp adsorption zones and fast propagation of the solute band can be obtained if the value of the mobility, v3, of the analyte is high and the value of the ratio v1/v3, where v1 represents the mobility of the cation, is low; however, if the magnitude of the mobility, v3, of the analyte is small, dispersed desorption zones are obtained with slower rates of propagation of the solute band through the column; (e) good separation of analyte molecules having similar mobilities and different adsorption affinities can be obtained in short operational times with a very small column length, L, and the resolution can be increased by providing values of gamma2,min and gamma2,max that are very close to negative one; and (f) the change in the magnitude of the axial current density, i(x), across the solute band could serve as a measurement for the rate of propagation of the solute band.     

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.     

Langevin dynamics simulations of the diffusion of molecular knots in tensioned polymer chains

Motivated by recent experiments, in which knots have been tied in individual biopolymer molecules, we use Langevin dynamics simulations to study the diffusion of a knot along a tensioned polymer chain. We find that the dependence of the knot diffusion coefficient on the tension can be non-monotonic. This behavior can be explained by the model, in which the motion of the knot involves cooperative displacement of a local knot region. At low tension, the overall viscous drag force that acts on the knot region is proportional to the number N of monomers that participate in the knot, which decreases as the tension is increased, leading to faster diffusion. At high tension the knot becomes tight and its dynamics are dominated by the chain's internal friction, which increases with the increasing tension, thereby slowing down the knot diffusion. This model is further supported by the observation that the knot diffusion coefficient measured across a set of different knot types is inversely proportional to N. We propose that the lack of tension dependence of the knot diffusion coefficients measured in recent experiments is due to the fact that the experimental values of the tension are close to the turnover between the high- and low-force regimes.