Concentration polarization and nonequilibrium electroosmotic slip in hierarchical monolithic structures

This article illustrates the appearance and electrohydrodynamic consequences of concentration polarization (CP) in hierarchically structured monolithic fixed beds used as stationary phases in CEC and related electrical-field-assisted separation techniques. Subject of the investigation are silica-based monoliths in capillary format with a bimodal pore size distribution. Ion-permselectivity in the intraskeleton pore space together with diffusive and electrokinetic transport induces depleted and enriched CP zones at the anodic and cathodic interfaces, respectively, of the cation-selective mesoporous skeleton. The extent of electrical-field-induced CP is shown to be governed by the fluid phase ionic strength, which tunes the ion-permselectivity of the mesoporous monolith skeleton via local electrical double layer overlap, and by the applied electrical field strength, which determines local transport. The analysis of quantitative confocal laser scanning microscopy data, resolving CP on the local skeleton scale, indicates that at sufficiently high field strength a transition from intraskeleton to interskeleton boundary-layer-dominated transport of charged species occurs. This transition is correlated to the onset of macroscopically measured, nonlinear EOF velocities, whose occurrence is explained in the framework of a nonequilibrium electroosmotic slip. It is shown that the onset of nonlinear electrokinetics in the system can be tuned by properties of the BGE, particularly buffer pH, which modulates the pH-dependent surface charge density and consequently the ion-permselective skeleton's charge selectivity. Finally, the CP dynamics of monolithic and particulate fixed beds are compared, and the observed differences are related to the specific morphologies of the two hierarchical fixed bed structures.     

Concentration polarization-based nonlinear electrokinetics in porous media: induced-charge electroosmosis

We have investigated induced-charge electroosmotic flow in a fixed bed of ion-permselective glass beads by quantitative confocal laser scanning microscopy. Externally applied electrical fields induce concentration polarization (CP) in the porous medium due to coupled mass and charge transport normal to the charge-selective interfaces. These data reveal the generation of a nonequilibrium electrical double layer in the depleted CP zones and the adjoining anodic hemispheres of the (cation-selective) glass beads above a critical field strength. This initiates CP-based induced-charge electroosmosis along curved interfaces of the quasi-electroneutral macropore space between glass beads. Caused by mutual interference of resulting nonlinear flow with (flow-inducing) space charge regions, an electrohydrodynamic instability can appear locally and realize turbulent flow behavior at low Reynolds numbers. It is characterized by a local destruction of the CP zones and concomitant removal of diffusion-limited mass transfer. More efficient pore-scale lateral mixing also improves macroscopic transport, which is reflected in the significantly reduced axial dispersion of a passive tracer.     

Electrohydrodynamics in hierarchically structured monolithic and particulate fixed beds

We have investigated the basic dependence of electroosmotic flow (EOF) velocity and hydrodynamic dispersion in capillary electrochromatography (CEC) on the variation of applied field and mobile phase ionic strengths employing silica-based particulate and monolithic fixed beds. These porous media have a hierarchical structure characterized by discrete intraparticle (intraskeleton) mesoporous and interparticle (interskeleton) macroporous spatial domains. While the macroporous domains contain quasi-electroneutral electrolyte solution, the ion-permselectivity (charge-selectivity) of the mesoporous domains determines the co-ion exclusion and counter-ion enrichment at electrochemical equilibrium (without superimposed electrical field) which depends on mesopore-scale electrical double layer (EDL) overlap and surface charge density. This adjustable, locally charge-selective transport realized under most general conditions forms the basis for concentration polarization (CP) induced by electrical fields superimposed in CEC. CP characterizes the formation of convective diffusion boundary layers with reduced (depleted CP zone) and increased (enriched CP zone) electrolyte concentration, respectively, at the anodic and cathodic interfaces in fixed beds containing the cation-selective, silica-based particles (or monolith skeleton). CP originates in the electrical field-induced coupled mass and charge transport normal to the charge-selective interfaces and has consequences for the EOF dynamics, hydrodynamic dispersion, and analyte retention in CEC. A secondary EDL with mobile counter-ionic space charge can be induced in the depleted CP zone leading to induced-charge EOF in the macroporous domains. It is characterized by a nonlinear dependence of the average EOF velocities on applied field strength and strong local velocity components tangential to the surface which enhance lateral pore-scale dispersion, thereby decreasing (axial) zone spreading. Differences in the pore space morphology of random-close sphere packings and monoliths criticially affect the intensity of CP and induced-charge EOF in these materials. CP is identified as a key phenomenon in CEC which also influences effective migration and the retention of charged analytes because the local intensity of CP inherently depends on applied field and mobile phase ionic strengths.     

Perspective on concentration polarization effects in electrochromatographic separations

This work illustrates the appearance and electrohydrodynamic consequences of concentration polarization in the particulate and monolithic fixed beds used in capillary electrochromatography and related electrical-field assisted processes. Key property of most porous materials is the co-existence of bulk, quasi-electroneutral macroporous regions and mesoporous compartments which are ion-permselective (due to electrical double-layer overlap) causing different transport numbers for co-ionic and counterionic species, e.g., background electrolyte components, or the analytes. For a cathodic electroosmotic flow the (cation) permselectivity, together with diffusive and electrokinetic transport induces depleted and enriched concentration polarization zones at the anodic and cathodic interfaces, respectively, in dependence of the mobile phase ionic strength and applied electrical fields. At high field strength a secondary, nonequilibrium electrical double layer may be created in the depleted concentration polarization zones of a material stimulating electroosmosis of the second kind. The potential of this induced-charge electroosmosis with respect to nonlinear flow velocities and electrokinetic instability mixing (basically destroying the concentration polarization zones) is analyzed in view of the pore space morphology in random-close packings of spherical-shaped, porous particles and hierarchically structured monoliths. Possible applications based on a fine-tuning of the illustrated effects emerge for microfluidic pumping and mixing, or the intensification of sample recovery in adsorption processes. With this perspective we want to focus the attention on concentration polarization in electrochromatographic systems by presenting and discussing original data acquired on relevant microscopic as well as macroscopic scales, and point towards the importance of related effects in colloid and membrane science.*     

Fluid dynamics in capillary and chip electrochromatography

This review is concerned with the phenomenological fluid dynamics in capillary and chip electrochromatography (EC) using high-surface-area random porous media as stationary phases. Specifically, the pore space morphology of packed beds and monoliths is analyzed with respect to the nonuniformity of local and macroscopic EOF, as well as the achievable separation efficiency. It is first pointed out that the pore-level velocity profile of EOF through packed beds and monoliths is generally nonuniform. This contrasts with the plug-like EOF profile in a single homogeneous channel and is caused by a nonuniform distribution of the local electrical field strength in porous media due to the continuously converging and diverging pores. Wall effects of geometrical and electrokinetic nature form another origin for EOF nonuniformities in packed beds which are caused by packing hard particles against a hard wall with different zeta potential. The influence of the resulting, systematic porosity fluctuations close to the confining wall over a distance of a few particle diameters becomes aggravated at low column-to-particle diameter ratio. Due to the hierarchical structure of the pore space in packed beds and silica-based monoliths which are characterized by discrete intraparticle (intraskeleton) mesoporous and interparticle (interskeleton) macroporous spatial domains, charge-selective transport prevails within the porous particles and the monolith skeleton under most general conditions. It forms the basis for electrical field-induced concentration polarization (CP). Simultaneously, a finite and -- depending on morphology -- often significant perfusive EOF is realized in these hierarchically structured materials. The data collected in this review show that the existence of CP and its relative intensity compared to perfusive EOF form fundamental ingredients which tune the fluid dynamics in EC employing monoliths and packed beds as stationary phases. This addresses the (electro)hydrodynamics, associated hydrodynamic dispersion, as well as the migration and retention of charged analytes.     

Nonlinear electroosmosis in hierarchical monolithic structures

We studied the dependence of electroosmotic flow (EOF) velocity and separation efficiency for neutral analytes in 100 microm ID capillary monoliths on a variation of the mobile phase ionic strength and applied electrical field strength, i.e., we covered a range for the concentration of Tris buffer from 10(-5) to 10(-2) M and applied electrical field strengths up to 10(5) V/m. The silica-based monoliths are hierarchically structured having intraskeleton mesopores and interskeleton macropores. While a linear dependence of the average EOF velocity on applied field strength could be observed with 5 x 10(-3) M Tris (turning slightly nonlinear at a higher concentration due to thermal effects), this dependence becomes systematically nonlinear as the Tris concentration is reduced towards 10(-4) M. Increased velocities by more than 50% compared to those expected from linear behavior are realized at 10(5) V/m. Concomitantly, as the Tris concentration is reduced from 10(-3) to 10(-4) M, we notice an improvement in plate heights by a factor of more than 2 (they approach 2 microm for ethylbenzoate). We complementary analyzed the onset of the nonlinear EOF dynamics in a hierarchical monolith and the significantly reduced axial dispersion in view of nonequilibrium electrokinetic effects which may develop in porous media due to the presence of ion-permselective regions, e.g., the mesoporous monolith skeleton. In this respect, a decreasing mobile phase ionic strength favors the formation of nonequilibrium concentration polarization in strong electrical fields, and a coupling of the electrostatics and hydrodynamics then may explain nonlinear EOF velocities and increasing separation efficiencies depending on the Tris concentration and applied field strength.     

Nonequilibrium electrokinetic effects in beds of ion-permselective particles

Electrokinetic transport of fluorescent tracer molecules in a bed of porous glass beads was investigated by confocal laser scanning microscopy. Refractive index matching between beads and the saturating fluid enabled a quantitative analysis of intraparticle and extraparticle fluid-side concentration profiles. Kinetic data were acquired for the uptake and release of electroneutral and counterionic tracer under devised conditions with respect to constant pressure-driven flow through the device and the effect of superimposed electrical fields. Transport of neutral tracer is controlled by intraparticle mass transfer resistance which can be strongly reduced by electroosmotic flow, while steady-state distributions and bead-averaged concentrations are unaffected by the externally applied fields. Electrolytes of low ionic strength caused the transport through the charged (mesoporous) beads to become highly ion-permselective, and concentration polarization is induced in the bulk solution due to the superimposed fields. The depleted concentration polarization zone comprises extraparticle fluid-side mass transfer resistance. Ionic concentrations in this diffusion boundary layer decrease at increasing field strength, and the flux densities approach an upper limit. Meanwhile, intraparticle transport of counterions by electromigration and electroosmosis continues to increase and finally exceeds the transport from bulk solution into the beads. A nonequilibrium electrical double layer is induced which consists of mobile and immobile space charge regions in the extraparticle bulk solution and inside a bead, respectively. These electrical field-induced space charges form the basis for nonequilibrium electrokinetic phenomena. Caused by the underlying transport discrimination (intraparticle electrokinetic vs extraparticle boundary-layer mass transfer), the dynamic adsorption capacity for counterions can be drastically reduced. Further, the extraparticle mobile space charge region leads to nonlinear electroosmosis. Flow patterns can become highly chaotic, and electrokinetic instability mixing is shown to increase lateral dispersion. Under these conditions, the overall axial dispersion of counterionic tracer can be reduced by more than 2 orders of magnitude, as demonstrated by pulse injections.     

Perfusive flow and intraparticle distribution of a neutral analyte in capillary electrochromatography

The relevance and magnitude of an electroosmotic perfusion mechanism in electrochromatography is analyzed. To systemize our studies we first considered the transport of an electroneutral and nonadsorbing tracer. Based on the refractive index matching in a microfluidic setup containing fixed spherical porous particles, we conducted a quantitative analysis in real time of the spatio-temporal distribution of fluorescent tracer molecules during their uptake by (and a release from) single particles using confocal laser scanning microscopy. Even under conditions of a significant electrical double layer overlap the intraparticle electroosmotic flow produces due to its unidirectional nature and in striking contrast to the symmetric (spherical) distributions typical for purely diffusive transport strongly asymmetric concentration profiles inside spherical particles as the locally charged pore liquid begins to respond to the externally applied electrical field. The profiles retain an axisymmetric nature, i.e., rotational symmetry with respect to the field direction. Results of our measurements could be successfully interpreted and further analyzed by a compact mathematical model. Intraparticle Peclet numbers of up to 150 have been realized and found to significantly enhance the mass transport on particle scale towards the convection-dominated regime when compared to a conventional (diffusion-limited) kinetics.     

Influence of moderate Joule heating on electroosmotic flow velocity, retention, and efficiency in capillary electrochromatography

The influence of Joule heating on electroosmotic flow velocity, the retention factor of neutral analytes, and separation efficiency in capillary electrochromatography was investigated theoretically and experimentally. A plot of electrical current against the applied electrical field strength was used to evaluate the Joule heating effect. When the mobile phase concentration of Tris buffer exceeded 5.0 mM in the studied capillary electrochromatography systems using particulate and monolithic columns (with an accompanying power level of heat dissipation higher than 0.35 W/m), the Joule heating effect became clearly noticeable. Theoretical models for describing the variation of electroosmotic flow velocity with increasing applied field strength and the change of retention factors for neutral analytes with electrical field strength at higher Tris buffer concentrations were analyzed to explain consequences of Joule heating in capillary electrochromatography. Qualitative agreement between experimental data and implications of the theoretical model analysis was observed. The decrease of separation efficiency in capillary electrochromatography with macroporous octadecylsilica particles at high buffer concentration can be also attributed to Joule heating mainly via the increased axial diffusion of the analyte molecules and dispersion of solute bands by a nonuniform electroosmotic flow profile over the column cross-section. However, within a moderate temperature range, the contribution of the macroscopic velocity profile in the column arising from radial temperature gradients is insignificant.     

Modeling the velocity field of the electroosmotic flow in charged capillaries and in capillary columns packed with charged particles: interstitial and intraparticle velocities in capillary electrochromatography systems

Mass transfer systems based on electrokinetic phenomena (i.e., capillary electrochromatography (CEC)) have shown practical potential in becoming powerful separation methods for the biotechnology and pharmaceutical industries. A mathematical model has been constructed and solved to describe quantitatively the profiles of the electrostatic potential, pressure, and velocity of the electroosmotic flow (EOF) in charged cylindrical capillaries and in capillary columns packed with charged particles. The results obtained from model simulations (i) provide significant physical insight and understanding with regard to the velocity profile of the EOF in capillary columns packed with charged porous particles which represent systems employed in CEC, (ii) provide the physical explanation for the experimental results which indicate that the velocity of the EOF in capillary columns packed with charged porous particles is a very weak function (it is almost independent) of the diameter of the particles, and (iii) indicate that the intraparticle velocity, nu(p,i), of the EOF can be greater than zero. The intraparticle Peclet number, Pe(int rap), for lysozyme was found to be greater than unity and this intraparticle convective mass transfer mechanism could contribute significantly, if the appropriate chemistry is employed in the mobile liquid phase and in the charged porous particles, in (a) decreasing the intraparticle mass transfer resistance, (b) decreasing the dispersive mass transfer effects, and (c) increasing the intraparticle mass transfer rates so that high column efficiency and resolution can be obtained. Furthermore, the results from model simulations indicate that for a given operationally permissible value of the applied electric potential difference per unit length, Ex, high values for the average velocity of the EOF can be obtained if (1) the zeta potential, zeta(p), at the surface of the particles packed in the column has a large negative magnitude, (2) the value of the viscosity, mu, of the mobile liquid phase is low, (3) the magnitude of the dielectric constant, epsilon, of the mobile liquid phase is reasonably large, and (4) the combination of the values of the concentration, C(infinity), of the electrolyte and of the dielectric constant, epsilon, provide a thin double layer. The theoretical results for the velocity of the EOF obtained from the solution of the model presented in this work were compared with the experimental values of the velocity of the EOF obtained from a fused-silica column packed with charged porous silica C8 particles. Systems with four different particle diameters and three different concentrations of the electrolyte were considered, and the magnitude of the electric field was varied widely. The agreement between theory and experiment was found to be good.     

Effect of skimming layer in an electroosmotically driven viscoelastic fluid flow over charge modulated walls

We report a numerical study on the effect of the skimming layer in an EOF of Oldroyd-B fluid over charge modulated walls. Three types of flow conditions were identified on the basis of the relative thickness of the skimming layer and the electrical double layer. We observe maximum slip velocity magnitude when the skimming layer thickness is very less than the thickness of the electrical double layer. For higher skimming layer thickness compared to the thickness of electrical double layer, slip velocity magnitude attenuates, and the polymeric stress inside the skimming layer becomes zero. Enhanced fluid elasticity generates asymmetric flow structures inside the microchannel, which can also be achieved by imposing an asymmetric surface charge along the channel walls. Our present analysis highlights the complex flow dynamics of the EOF of biofluids/polymeric fluids with a near-wall region depleted of macro-molecules.     

Expressions for evaluating the possibility of slip at the liquid-solid interface in open tube capillary electrochromatography

In this work, expressions are constructed and solved that describe the velocity field of electroosmotic flow (EOF) in open tube capillary electrochromatography (CEC) systems when the possibility of having unequal tangential velocities at the liquid-solid interface is considered and a slip condition is employed as a boundary condition for the velocity of the EOF at the capillary wall. The coupled equations of hydrodynamics (momentum balance equation) and electrostatics (Poisson equation) are solved numerically in order to obtain the distribution of the velocity field as well as the value of the volumetric flow rate in the open tube. Also, expressions for the velocity field and the volumetric flow rate of the EOF are presented that are valid for certain electrolytic systems and for certain parameter values for which analytical solutions to the momentum balance and Poisson equations could be obtained. The results presented in this work indicate that having slip in the velocity of the EOF at the wall of the capillary could (i) substantially increase the electroosmotic velocity in the plug-flow region of the radial domain of the open capillary tube and (ii) increase the portion of the radial domain of the open capillary tube where the velocity of the EOF has a plug-flow profile, which in turn could increase the average velocity and volumetric flow rate of the EOF in the open capillary tube. Furthermore, the modeling approach and the results presented in this work indicate a method for experimentally evaluating the possibility of having slip in the velocity of the EOF at the capillary wall.     

Ability of porous graphitic carbon to support electroosmotic flow in capillary electrochromatography

The existence of a cathodic EOF (electroosmotic flow) in the case of a porous graphitic carbon (PGC) partially packed column has been demonstrated. Then, the ability of PGC to afford electroosmosis has been brought to the fore with a fully PGC packed column. Experimental data have shown that PGC particles are negatively charged and their electrophoretic mobility has been evaluated. In order to investigate the conditions of existence of EOF different mobile phases have been tested. An EOF occurs when the conductivity of the PGC packed column is larger than the conductivity of an empty fused-silica capillary operating in the same conditions i.e. when the PGC participates in the electric conduction. Since the local electric fields in the two segments of the column are different, an evaluation of the electroosmotic mobility is not possible and the effect of the operational parameters such as the composition of the mobile phase (acetonitrile ratio and total ionic strength) has been studied in term of electroosmotic velocity V(eo).     

Inherent peak compression of charged analytes in electrochromatography

This work resolves peak compression of charged analytes in CEC with strong cation‐exchange stationary phase particles. By combining electrochromatographic peak shape analysis with the results of numerical simulations and confocal laser scanning microscopy in the packed capillaries, we identify electrical field‐induced concentration polarization as the key physical phenomenon responsible for the inherent existence of local electrical field gradients on the scale of an individual support particle. Consequently, positive and negative field gradients exist between and inside the particles along the whole packing. Their intensity depends on the particles cation‐selectivity (governed by the particles volume charge density and the mobile phase ionic strength) and the applied field strength. The interplay of these local field gradients with the analytes retention (intraparticle adsorption) determines whether fronting, tailing, or spiked analyte peaks are observed, and it provides a mechanism by which strongly retained analytes can be eluted over long distances with little zone dispersion. Our analysis explains the “anomalous” peak compression effects with strong cation‐exchange particles, which have been reported more than a decade ago (Smith, N. W., Evans, M. B., Chromatographia 1995, 41, 197–203) and since then remained largely unresolved.     

The influence of membrane ion-permselectivity on electrokinetic concentration enrichment in membrane-based preconcentration units

The performance of nanoporous hydrogel microplugs with varying surface charge density is described in concentrating charged analytes electrokinetically in a microfluidic device. A neutral hydrogel plug with a mean pore size smaller than the size of charged analytes acts as a simple size-exclusion membrane. The presence of fixed charges on the backbone of a nanoporous hydrogel creates ion-permselectivity which results in charge-selective transport through the hydrogel. This leads to the development of concentration polarization (CP) in the adjoining bulk electrolyte solutions under the influence of an applied electrical field. CP strongly affects the distribution of the local electrical field strength, in particular, in the vicinity of the hydrogel plug which can significantly reduce the concentration enrichment factors compared to the neutral hydrogel. A theoretical model and simulations are presented, together with experimental data, to explain the interplay of hydrogel or membrane cation-selectivity, electrical field-induced CP, and the distribution of the local electrical field strength with respect to concentration enrichment of negatively charged analytes at the cathodic membrane-solution interface.     

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).     

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.     

Numerical analysis of electroosmotic flow in dense regular and random arrays of impermeable, nonconducting spheres

We present a numerical scheme for analyzing steady-state isothermal electroosmotic flow (EOF) in three-dimensional random porous media, involving solution of the coupled Poisson, Nernst-Planck, and Navier-Stokes equations. While traditional finite-difference methods were used to resolve the Poisson-Nernst-Planck problem, the (electro)hydrodynamics has been addressed with high efficiency using the lattice-Boltzmann method. The developed model allows simulation of electrokinetic transport under most general conditions, including arbitrary value and distribution of electrokinetic potential at the solid-liquid interface, electrolyte composition, and pore space morphology. The approach provides quantitative information on a spatial distribution of simulated velocities. This feature was utilized to characterize EOF fields in regular and random, confined and bulk packings of hard (i.e., impermeable, nonconducting) spheres. Important aspects of pore space morphology (sphere size distribution), surface heterogeneity (mismatch in electrokinetic potentials at confining wall and sphere surface), and fluid phase properties (electrical double layer thickness) were investigated with respect to their influence on the EOF dynamics over microscopic and macroscopic spatial domains. Most important is the observation of a generally nonuniform pore-level EOF velocity profile in the sphere packings (even in the thin double layer limit) which is caused by pore space morphology and which is in contrast to the pluglike velocity distribution in a single, straight capillary under the same conditions.     

Modeling of electroosmotic and electrophoretic mobilization in capillary and microchip isoelectric focusing

Our dynamic capillary electrophoresis model which uses material specific input data for estimation of electroosmosis was applied to investigate fundamental aspects of isoelectric focusing (IEF) in capillaries or microchannels made from bare fused-silica (FS), FS coated with a sulfonated polymer, polymethylmethacrylate (PMMA) and poly(dimethylsiloxane) (PDMS). Input data were generated via determination of the electroosmotic flow (EOF) using buffers with varying pH and ionic strength. Two models are distinguished, one that neglects changes of ionic strength and one that includes the dependence between electroosmotic mobility and ionic strength. For each configuration, the models provide insight into the magnitude and dynamics of electroosmosis. The contribution of each electrophoretic zone to the net EOF is thereby visualized and the amount of EOF required for the detection of the zone structures at a particular location along the capillary, including at its end for MS detection, is predicted. For bare FS, PDMS and PMMA, simulations reveal that EOF is decreasing with time and that the entire IEF process is characterized by the asymptotic formation of a stationary steady-state zone configuration in which electrophoretic transport and electroosmotic zone displacement are opposite and of equal magnitude. The location of immobilization of the boundary between anolyte and most acidic carrier ampholyte is dependent on EOF, i.e. capillary material and anolyte. Overall time intervals for reaching this state in microchannels produced by PDMS and PMMA are predicted to be similar and about twice as long compared to uncoated FS. Additional mobilization for the detection of the entire pH gradient at the capillary end is required. Using concomitant electrophoretic mobilization with an acid as coanion in the catholyte is shown to provide sufficient additional cathodic transport for that purpose. FS capillaries dynamically double coated with polybrene and poly(vinylsulfonate) are predicted to provide sufficient electroosmotic pumping for detection of the entire IEF gradient at the cathodic column end.     

Micellar electrokinetic capillary chromatography using polymeric hollow fibers

Summary In this paper, polymeric hollow fibers prepared from pH-stable polypropylene were used as columns for micellar electrokinetic capillary chromatography (MECC). The electroosmotic flow (EOF) for polypropylene hollow fibers was evaluated in the pH range of 5.0–12.0. With untreated polypropylene hollow fibers a stabilized but enhanced EOF was achieved when SDS was used in the buffer, decreasing the separation window for uncharged substances in MECC to impractical levels. Uncharged acrylamide and charged 2-acryloylamido-2-methylpropane sulfonic acid surface modifications were used to lower the strength of the EOF, increase the separation window and prevent local overheating that could melt the column wall.