Novel general expressions that describe the behavior of the height equivalent of a theoretical plate in chromatographic systems involving electrically-driven and pressure-driven flows

Novel general expressions are constructed and presented that describe the behavior of the height equivalent of a theoretical plate (plate height), H, as a function of the linear velocity, Vx, along the axis, x, of the column and the kinetic parameters that characterize the mass transfer and adsorption mechanisms in chromatographic columns. Open tube capillaries as well as columns packed with either non-porous or porous particles are studied. The porous particles could have unimodal or bimodal pore-size distributions and intraparticle convective fluid flow and pore diffusion are considered. The expressions for the plate height, H, presented in this work could be applicable to high-performance liquid chromatography (HPLC) and capillary electrochromatography (CEC) systems, and could be used together with experimental plate height, H, versus linear velocity, Vx, data to determine the values of the parameters that characterize intraparticle convective fluid flow and pore diffusion. Furthermore, chromatographic systems under unretained as well as under retained conditions are examined. The experimental values of the plate height, H, versus the linear velocity, Vx, for a CEC system involving charged porous silica C8 particles and an uncharged analyte are compared with the theoretical results for the plate height, H, obtained from the expressions presented in this work. The agreement between theory and experiment is good, and the results indicate that the magnitude of the intraparticle electroosmotic flow (EOF) in the pores of the particles is substantial while the pore diffusion coefficient was of small magnitude. But the overall intraparticle mass transfer resistance in these particles was low because of the significant contribution of the intraparticle EOF. Simulation results are also presented (i) for a hybrid HPLC-CEC system, and (ii) for different CEC systems involving open capillaries as well as packed columns having non-porous or porous particles. The analysis of the results indicates (a) the reasons for the superior performance exhibited by the hybrid HPLC-CEC system over the performance obtained when the system is operated only in the HPLC mode, and (b) the operational configuration and the properties that the structure of the porous particles would have to have in CEC systems involving uncharged or charged analytes under unretained or retained conditions in order to obtain high CEC efficiency (low values of the plate height, H).     

Investigation of the concentration dependence of mass transfer coefficients in reversed-phase liquid chromatography

In order to investigate the concentration dependence of mass transfer coefficients in RPLC, experimental breakthrough curves obtained by staircase frontal analysis (FA) were fitted to the simplified models such as multiplate (MP) model, equilibrium dispersive (ED) model, and transport model, and the sophisticated models such as lumped pore diffusion (POR) model and general rate (GR) model. The MP model was used to obtain the initial guesses of the parameters of the ED and the transport models. Then the best values were obtained by minimizing the differences between theoretical and experimental values with a nonlinear fitting procedure. The values of the parameters of the POR and the GR models can be calculated by using the expressions derived from the plate height equations, which was further validated by using the fitting method. It was found that the mass transfer coefficients would depend on the solute concentration. This can be ascribed to the surface diffusivity, which correlates with the concentration and is lumped into the mass transfer coefficients for both simplified and sophisticated models.     

Dynamics of capillary electrochromatography. II. Comparison of column efficiency parameters in microscale high-performance liquid chromatography and capillary electrochromatography.

In capillary electrochromatography (CEC) the flow of the mobile phase is generated by electrosmotic means in high electric field. This work compares band spreading measured experimentally in several packed capillaries with electrosmotic flow (EOF) and viscous flow under otherwise identical conditions. The data were fitted to the simplified van Deemter equation for the theoretical plate height, H = A + B/u + Cu, in order to evaluate parameters A and C in each mode of flow in the different columns. The ratio of these two parameters obtained with the same column in microscale HPLC (mu-HPLC) and CEC was used to quantify the attenuation of their contribution to band spreading upon changing from viscous flow (in mu-HPLC) to electrosmotic flow (in CEC). The capillary columns used in this study were packed with stationary phases of different pore sizes as well as retentive properties and measurements were carried out under different mobile phase conditions to examine the effects of the retention factor and buffer concentration. In the CEC mode, the value of both column parameters A and C was invariably by a factor of two to four lower than in the mu-HPLC mode. This effect may be attributed to the peculiarities of the EOF flow profile in the interstitial space and to the generation of intraparticle EOF inside the porous particles of the column packing. Thus, band spreading due to flow maldistribution and mass transfer resistances is significantly lower when the mobile phase flow is driven by voltage as in CEC, rather than by pressure as in mu-HPLC.     

Modelling of the pore flow in capillary electrochromatography

Pore flow in capillary electrochromatography (CEC) on porous silica particles has been investigated. To that end the migration behaviour of narrow polystyrene (PS) standards dissolved in di-methylformamide (DMF) with lithium chloride in 1 and 10 mmol/l concentration has been measured. These data have been compared to theoretical predictions. The latter were based on a model comprising cylindrical pores of varying diameter as measured experimentally by porosimetry, while the flow in each set of pores was calculated with the expression given by Rice and Whitehead. A reasonable to good agreement between experimental and predicted data was observed, provided it was assumed that pores of differing diameter occur in series. It was found that the flow in pores with a nominal size of 100 A can be considerable compared to the interstitial flow, especially at 10 mmol/l ionic strength. It is concluded that pore flow within porous particles in CEC, of great importance for improved efficiency in both interactive and exclusion type CEC, can be predicted fairly reliably by means of the Rice and Whitehead expression.     

High Performance Size Exclusion Chromatography with Microparticulate Porous Silica Spheres. Influence of Flow Rate,Salute Mass Transfer and Polydispersity of Samples

Abstract

The contributions to peak broadening in Size Exclusion Chromatography with microparticles of porous silica spheres having narrow size distributions have been determined by measuring the plate height dependence on flow rate for toluene and for polystyrene standards covering a wide range of molecular weights. From these contributions, the diffusion coefficients of the macromolecules in the pore matrix and the polydispersities of the samples could be evaluated. It is shown that for permeating polymers the band broadening is determined by the eddy diffusion in the mobile phase, by the slow mass transfer of the solute in the stationary phase and by the polydispersity of the standards. In properly packed columns the eddy diffusion term is of minor importance compared to the other effects, whereas the solute mass transfer, which is a velocity dependent process, can be minimized only at extremely low flow rates.     

Capillary electrochromatography with macroporous particles.

The performance of macro-porous particles in capillary electrochromatography is studied. Three reversed-phase stationary phases with pore diameters between 500 A and 4000 A have been tested for separation efficiency and mobile phase velocity. With these stationary phases, a large portion of the total flow appears to be through the pores of particles, thereby increasing the separation efficiency through a further decrease of the flow inhomogeneity and through enhancement of the mass transfer kinetics. The effects of pore size and mobile phase composition on the plate height and mobile phase velocity have been studied. With increasing buffer concentrations and larger pore diameters, higher mobile phase velocities and higher separation efficiencies have been obtained. Columns packed with 7 microns particles containing pores with a diameter of 4000 A generated up to 430,000 theoretical plates/m for retained compounds. Reduced plate heights as low as 0.34 have been observed, clearly demonstrating that a significant portion of the flow is through the pores. For the particles containing 4000 A pores no minimum was observed in the H-u plot up to linear velocities of 3.3 mm/s, suggesting that the separation efficiency is dominated by axial diffusion. On relatively long (72 cm) columns, efficiencies of up to 230,000 theoretical plates/column have been obtained under non-optimal running conditions. On short (8.3 cm) columns fast separations could be performed with approximately 15,000 theoretical plates generated in less than 30 s.     

Determination of the intraparticle electroosmotic volumetric flow-rate, velocity and Peclet number in capillary electrochromatography from pore network theory

The results obtained from the pore network model employed in this work, clearly show that the magnitudes of the intraparticle electroosmotic volumetric flow-rate, Qintrap, and velocity, (v(intrap,x)), in the pores of the charged porous silica particles considered in this study are greater than zero. The intraparticle Peclet number, Pe(intra, of a solute in these charged porous silica particles would be greater than zero, and, in fact, the magnitude of the intraparticle Peclet number, Pe(intrap), of lysozyme is greater than unity for all the values of the pore connectivity, nT, of the intraparticle pores and of the applied electric potential difference per unit length, Ex, along the axis of the capillary column considered in this work. Furthermore, the values of the intraparticle electroosmotic volumetric flow-rate, Qintrap, and velocity, (v(intrap,x)), as well as the magnitude of the pore diffusion coefficient, Dp, of the solute increase as the value of the pore connectivity, nT, of the intraparticle pores increases. The intraparticle electroosmotic flow can contribute significantly, if the appropriate chemistry is employed in the mobile liquid phase and in the charged porous particles, in (i) decreasing the intraparticle mass transfer resistance, (ii) decreasing the dispersive mass transfer effects, and (iii) increasing the intraparticle mass transfer rates so that high column efficiency and resolution can be obtained.     

Further studies on solvent extraction with immobilized interfaces in a microporous hydrophobic membrane

Investigations on solvent extraction of acetic acid into xylene or methyl isobuty] ketone by using immobilized interfaces in microporous hydrophobic membranes have now been extended to a number of different membranes with a wide variation in pore size and porosity. Measured intrinsic membrane transfer coefficients of the solute are adequately described by the simple model of unhindered diffusion in tortuous pores developed earlier. Applied pressure difference did not influence the overall solute transfer coefficient as long as it was not close to that required for the breakthrough of aqueous phase into organic phase. Aqueous and organic boundary layer mass transfer coefficients in the flow type test cell have been determined with a known membrane and utilized to predict effectively the overall solute transfer coefficient observed with other membranes.     

Study of the mass transfer kinetics in a monolithic column

The purpose of this work is to investigate the mass transfer kinetics of butylbenzoate on a monolithic RPLC column, with methanol-water (65:35, v/v) as the mobile phase. We used the perturbation method, measuring the height equivalent to a theoretical plate (HETP) of the peaks obtained as the response to small pulses of solute injected on a concentration plateau. The equilibrium isotherm of butylbenzoate was previously determined by frontal analysis. It is well accounted for by a liquid-solid extended multilayer BET isotherm model. The equilibrium data derived from the pulse method are in excellent agreement with those of frontal analysis in the accessible concentration range of 0 to 8 g/dm3. Plots of the HETP of small pulses. injected on eight different plateau concentrations, were acquired in a wide range of mobile phase flow velocities. The axial dispersion and the mass transfer kinetic coefficients were derived from these data. The validity of these measurements is discussed. The mass kinetics of butylbenzoate depends strongly on the plateau concentration. Processes involving adsorptive interactions between the solute and the stationary phase, e.g. surface diffusion and adsorption-desorption kinetics, combine in series to the external mass transfer kinetics and to effective pore diffusivity.     

Characterization of Convection for Molecularly Imprinted Monolith

Convection of molecularly imprinted polymers monolith in LC mode was discussed in this paper. On the MIPs monolith reported here, a flat van Deemter plot of height equivalent to a theoretical plate (HETP) versus superficial velocity was observed. This typical behavior, similar to perfusion packings, suggests that the unique pore structure of the MIPs monolith allowed convection-enhanced mass transfer. Column parameters, e.g., external porosities, internal porosity, column permeability and equivalent sphere dimension, were obtained. Intraparticle Peclet number (λ) was used to characterize the convection in the monolith. In addition, a ratio of the numbers of transfer units, T, for diffusion in the micropores and through-pores has been introduced to quantify the relative importance of the contribution from convection and diffusion to mass transfer. The results show that the flow in a MIP monolith is extremely sensitive to pore size distribution and can be tuned by polymerization parameters.     

电色谱塔板高度方程的推导

比较了电色谱与高效液相色谱在动力学过程方面的异同。从热传导方程出发导出在有源无限长均匀圆柱体内温度场分布函数及组分移动速度径向分布函数,进而导出了温度场导致谱带弥散的弥散系数Ｄ热。提出了较全面地反映电色谱动力学过程的塔板高度方程,从而为改进柱型、选择电色谱分离条件提供了理论参考。     

Large-pore mesoporous SBA-15 silica particles with submicrometer size as stationary phases for high-speed CEC separation

A new mesoporous sphere-like SBA-15 silica was synthesized and evaluated in terms of its suitability as stationary phases for CEC. The unique and attractive properties of the silica particle are its submicrometer particle size of 400 nm and highly ordered cylindrical mesopores with uniform pore size of 12 nm running along the same direction. The bare silica particles with submicrometer size have been successfully employed for the normal-phase electrochromatographic separation of polar compounds with high efficiency (e.g., 210,000 for thiourea), which is matched well with its submicrometer particle size. The Van Deemeter plot showed the hindrance to mass transfer because of the existence of pore structure. The lowest plate height of 2.0 microm was obtained at the linear velocity of 1.1 mm/s. On the other hand, because of the relatively high linear velocity (e.g., 4.0 mm/s) can be generated, high-speed separation of neutral compounds, anilines, and basic pharmaceuticals in CEC with C18-modified SBA-15 silica as stationary phases was achieved within 36, 60, and 34 s, respectively.     

Advective flow in a sludge floc

The interior of sludge floc is highly heterogeneous, while the large pores in the floc control the advective flow. This work for the first time numerically details fluid flow and mass transfer processes in pores of activated sludge floc. The dimensionless permeabilities and mass dispersion coefficients were contoured against pore size ratio and the floc Reynolds number. With a pore size less than 20% of the floc size, the commonly adopted homogeneous model overestimates the floc permeability, and pore velocity is less than 2% of the bulk velocity. This is particularly true for flocs with low porosity. Although the convective flux is low, the dispersive mass transfer rate can be much higher than the diffusional rate, attributable to the strong Taylor dispersion effect. The three-dimensional pore structures in waste activated-sludge floc were identified using confocal laser scanning microscope (CLSM) images. Large pores were used to numerically estimate the permeability and dispersion coefficient for these pores. The permeability and the dispersion coefficient of the tortuous pores can be one order of magnitude lower than those for the equivalent straight pores. Besides the dispersion effect, the pore tortuosity appeared as the most important geometrical factor retarding the advective flow in the sludge pores. In addition, the small side pores connected to the large pore had only a mild effect on the flow process, and can be neglected in analysis.     

Continuous‐Bed Columns Containing Sol‐Gel Bonded Packing Materials for Capillary Electrochromatography

Sol‐gel bonded packing materials in continuous‐bed columns have been prepared for capillary electrochromatography (CEC). Three packing materials were investigated: small‐pore Spherisorb ODS1 (3 μm, 80 Å) with octadecyl as stationary phase, small‐pore mixed‐mode Spherisorb ODS/SCX (3 μm, 80 Å) with octadecyl and propyl sulfonic acid as stationary phases, and large‐pore Nucleosil ODS (7 μm, 1 400 Å) with octadecyl as stationary phase. The characteristics of these columns were compared in terms of electroosmotic flow, efficiency, inertness, and retention factors. In contrast to columns containing sol‐gel bonded ODS, columns containing sol‐gel bonded mixed‐mode ODS/SCX generated nearly pH independent electroosmotic flow (EOF) over pH 2–9. Columns containing sol‐gel bonded large‐pore ODS produced nearly three times lower reduced plate height than those containing small‐pore ODS. Efficiencies of 220,000 plates per meter and 175,000 plates per meter were obtained from columns containing sol‐gel bonded 7 μm, 1 400 Å ODS and columns containing sol‐gel bonded 3 μm, 80 Å ODS, respectively, which are among the highest reported efficiencies for continuous‐bed columns. In CEC, over one million plates per meter and pH independent EOF are expected from continuous‐bed columns containing sol‐gel bonded 1.5 μm particles with large pores and mixed‐mode stationary phases.     

亚微米中孔SBA-15 棒状固定相在毛细管电色谱分离中的应用(英文)

采用中孔SBA-15棒状硅胶颗粒填充毛细管柱用于毛细管电色谱(CEC)分离。这一亚微米材料直径为400 nm并具有沿相同方向伸展的高度有序、均一的圆柱形中孔。棒状的特殊形态使得填充柱的通透性良好,简化了尺寸微小的CEC柱的填充过程。修饰后的棒状SBA-15填充毛细管柱成功应用于反相和离子交换电色谱分离非极性和极性样品,获得了较高柱效(140000理论塔板/m)。流速3.2cm/min时获得最低理论塔板高度为7.1 mm。范迪米特曲线说明了SBA-15孔结构的传质阻力特征。分别以芳香酸、人参、天麻提取物为样品,对亚微米固定相毛细管电色谱柱加以评价。该固定相显示出了较高的分离能力,为纳米材料在色谱固定相中的应用提供了一个新的思路。     

Film Mass Transfer Coefficient Expressions for Electroosmotic Flows

Expressions are developed and presented that could be used to determine the film mass transfer coefficient of a solute in electroosmotic flows. In contrast to pressure-driven flows at low Reynolds numbers where the film mass transfer coefficient is independent of the linear characteristic dimension of the channel for flow, in electroosmotically driven flows at low Reynolds numbers the film mass transfer coefficient is shown to be a function of the ratio R/lambda, where R is the channel radius and lambda is the Debye length. This result implies that for electroosmotically driven flows in a packed bed or porous monolith with channels for flow having similar geometry but different sizes, the film mass transfer coefficient would vary with the size of the interstitial channels for bulk flow while in pressure-driven flows the film mass transfer coefficient would be the same for all interstitial channels. From the expressions presented in this work, one can show that for the same volumetric flow rate the film mass transfer coefficient of electroosmotically driven flows is proportional to that for pressure-driven flows. Copyright 2000 Academic Press.     

毛细管反相电色谱法分离行为的研究

对乙睛-水-磷酸二氢销体系毛细管反相电色谱分离行为进行了研究。采用柱上紫外检测,在75μmi.d.×30cm的毛细管ODS（3μm）填充柱上获得了小于2.0的折合培板高度。同时还研究了乙睛的比例、电解质的浓度和电场强度等因素对电渗流和往效的影响。     

Pore network modelling: determination of the dynamic profiles of the pore diffusivity and its effect on column performance as the loading of the solute in the adsorbed phase varies with time

A three-dimensional pore network model for diffusion in porous adsorbent particles was employed in a dynamic adsorption model that simulates the adsorption of a solute in porous particles packed in a chromatographic column. The solution of the combined model yielded the dynamic profiles of the pore diffusion coefficient of beta-galactosidase along the radius of porous ion-exchange particles and along the length of the column as the loading of the adsorbate molecules on the surface of the pores occurred, and, the dynamic adsorptive capacity of the chromatographic column as a function of the design and operational parameters of the chromatographic system. The pore size distribution of the porous adsorbent particles and the chemistry of the adsorption sites were unchanged in the simulations. It was found that for a given column length the dynamic profiles of the pore diffusion coefficient were influenced by: (i) the superficial fluid velocity in the column, (ii) the diameter of the adsorbent particles and (iii) the pore connectivity of the porous structure of the adsorbent particles. The effect of the magnitude of the pore connectivity on the dynamic profiles of the pore diffusion coefficient increased as the diameter of the adsorbent particles and the superficial fluid velocity in the column increased. The dynamic adsorptive capacity of the column increased as: (a) the particle diameter and the superficial fluid velocity in the column decreased, and (b) the column length and the pore connectivity increased. In preparative chromatography, it is desirable to obtain high throughputs within acceptable pressure gradients, and this may require the employment of larger diameter adsorbent particles. In such a case, longer column lengths satisfying acceptable pressure gradients with adsorbent particles having higher pore connectivity values could provide high dynamic adsorptive capacities. An alternative chromatographic system could be comprised of a long column packed with large particles which have fractal pores (fractal particles) that have high pore connectivities and which allow high intraparticle diffusional and convective flow mass transfer rates providing high throughputs and high dynamic adsorptive capacities. If large scale monoliths could be made to be reproducible and operationally stable, they could also offer an alternative mode of operation that could provide high throughputs and high dynamic adsorptive capacities.     

Capillary electrochromatography with bare silicas of different pore sizes as stationary phases

Bare silica can be used with reversed phase eluents for the chromatographic separation of basic analytes. It provides high surface charge density within a certain pH range, thus generating a high electroosmotic flow (EOF) when applied in electrochromatography. The influence of pore size on EOF velocity and mass transport is demonstrated. High EOF and fast mass transfer were encountered with 100 nm and 200 nm material and related to a pore perfusion mechanism. On a silica with 200 nm average pore size at pH 7, an EOF velocity of 2 mm/s was obtained at 600 V/cm. Silicas with pore diameters between 6 nm and 200 nm, corresponding to surface areas between 500 m/g and 10 m/g (data calculated from inverse size exclusion chromatography experiments), were used for CEC and HPLC separation of strongly basic solutes. On separation of tricyclic antidepressants by CEC, “normal” and “abnormal” efficiencies were achieved and were found to vary with the charge density within the separation column.     

Modelling of the pore size distribution of ultrafiltration membranes

A dilute aqueous solution of polydisperse neutral dextrans was used to determine the sieving properties (flux and rejection) of porous polyacrylonitrile membranes. Gel ermeation chromatography was used to measure the solute mole and concentration in the permeate. From these data, rejection coefficients were calculated as a function of solute molecular size. A mathematical model was then developed to relate the flux and solute rejection to pore size distribution and the total number of pores, based upon the assumption that solute rejection was the result of purely geometric considerations. As a first approximation, a solute molecule was considered either too large to enter a membrane pore, or if it entered, its concentration in the permeate from that pore, as well as the solvent flux through the pore, were not affected. This model also considered the effects of steric hindrance and hydrodynamic lag on the convection of solute through a membrane. The shape and sharpness of pore size distributions were found to be useful in comparisons of ultrafiltration membranes.