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.     

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 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.     

Noncovalent coatings for the separation of synthetic polypeptides by nonaqueous capillary electrophoresis

Recently, we demonstrated the possibility to extend the range of capillary electrophoresis (CE) applications to the separation of non-water-soluble synthetic polymers. This work focuses on the control of the electro-osmotic flow (EOF) and on the limitation of the solute adsorption in nonaqueous electrolytes. For these purposes, different strategies were investigated. For the initial, a viscous additive (ethylene glycol or glycerol) was used in the electrolyte in order to decrease the EOF magnitude and, possibly, to compete with solute adsorption. A second strategy was to modify, before separation, the fused-silica capillary wall by the adsorption of poly(ethylene oxide) (PEO) via hydrogen bonding. The influence of the molecular mass of the adsorbed PEO on the EOF magnitude and direction was studied in electrolytes based on methanol/acetonitrile mixtures containing ammonium ions. For PEO molecular masses above 1000 g/mol, reversed (anodic) EOF were reported in accordance with previous results obtained with PEO covalently bonded capillaries. The influence of the nature and the concentration of the background electrolyte cation on the EOF magnitude and direction were also investigated. A third strategy consisted in modifying the capillary wall by the adsorption of a cationic polyelectrolyte layer. Advantageously, this polyelectrolyte layer suppressed the adsorption of the polymer solutes onto the capillary wall. The results obtained in this work confirm the high potential and the versatility of CE for the characterization of ionizable organic polymers in nonaqueous media.     

Influencing electroosmotic flow and selectivity in open tubular electrochromatography by tetrakis(pentafluorophenyl)porphyrin as capillary wall modifier

A physically adsorbed and covalently bonded porphyrin derivative, 5,10,15,20-tetrakis(pentafluorophenyl)porphyrin, H₂TPFPP, has been used as a fused-silica capillary wall modifier in open tubular capillary electrochromatography (OT-CEC), and its influence on the electroosmotic flow (EOF) velocity and on the selectivity of OT-CEC separations of a set of model aromatic carboxylic acids has been tested. Whereas most of the coatings of this category bring about an increase in selectivity with a concomitant slow down of the EOF, H₂TPFPP coating, depending on pH of the background electrolyte used, resulted both in decreasing of EOF at pH 8.5 by 5% and in increasing of EOF by 10–43% at pH 6 and 5, respectively. The separation efficiency and the resolution of aromatic carboxylic acids separation in coated capillaries, namely in that one with covalent coating, were better than in the bare fused-silica capillary. The perspectives of H₂TPFPP as capillary wall modifier are visualized in introducing well defined electroosmotic properties of materials used for miniaturized separation channels preparation in chip-based electromigration devices.     

Electrostatic potential and electroosmotic flow in a cylindrical capillary filled with symmetric electrolyte: analytic solutions in thin double layer approximation

The electrostatic potential in a capillary filled with electrolyte is derived by solving the nonlinear Poisson-Boltzmann equation using the method of matched asymptotic expansions. This approach allows obtaining an analytical result for arbitrary high wall potential if the double layer thickness is smaller than the capillary radius. The derived expression for the electrostatic potential is compared to numerical solutions of the Poisson-Boltzmann equation and it is shown that the agreement is excellent for capillaries with radii greater or equal to four times the electrical double layer thickness. The knowledge of the electrostatic potential distribution inside the capillary enables the derivation of the electroosmotic velocity flow profile in an analytical form. The obtained results are applicable to capillaries with radii ranging from nanometers to micrometers depending on the ionic strength of the solution.     

Diffusioosmosis of electrolyte solutions in a fine capillary tube

A theoretical study is presented for the steady diffusioosmotic flow of an electrolyte solution in a fine capillary tube generated by a constant concentration gradient imposed in the axial direction. The capillary wall may have either a constant surface potential or a constant surface charge density of an arbitrary quantity. The electric double layer adjacent to the charged wall may have an arbitrary thickness, and its electrostatic potential distribution is determined by an analytical approximation to the solution of the Poisson-Boltzmann equation. Solving a modified Navier-Stokes equation with the constraint of no net electric current arising from the cocurrent diffusion, electric migration, and diffusioosmotic convection of the electrolyte ions, the macroscopic electric field and the fluid velocity along the axial direction induced by the imposed electrolyte concentration gradient are obtained semianalytically as a function of the radial position in a self-consistent way. The direction of the diffusioosmotic flow relative to the concentration gradient is determined by the combination of the zeta potential (or surface charge density) of the wall, the properties of the electrolyte solution, and other relevant factors. For a prescribed concentration gradient of an electrolyte, the magnitude of fluid velocity at a position in general increases with an increase in its distance from the capillary wall, but there are exceptions. The effect of the radial distribution of the induced tangential electric field and the relaxation effect due to ionic convection in the double layer on the diffusioosmotic flow are found to be very significant.     

Detecting deviations from pure EOF during CE separations

CE separations are known for their high separation efficiencies. In systems with EOF, the high efficiencies benefit from the flat, plug profile that is characteristic of EOF. When a velocity gradient is present, such as in separations which have nonuniform buffer ionic strength, surface adsorption or differences in the height of the ends of the capillary, a parabolic flow component is introduced. This deviation from purely EOF yields increased peak dispersion and a subsequent decrease in separation performance. This work details a rapid method for detecting deviations from ideal plug flow during the course of a separation using the radially averaged flow profile of a photobleached fluorophore added to the BGE. By comparing the ratio of two different data analysis procedures, deviations from ideal plug flow can be detected. This method allows rapid measurement of flow character and does not interfere with the concurrent separation. We demonstrate easy detection of the onset of hydrodynamic flow induced by both gravity siphoning and an ionic strength buffer discontinuity. A brief analysis of the radially averaged peak shapes is also presented.     

Fluorinated ethylenepropylene copolymer as a potential capillary material in CE

In this work, a new generation UV-transparent polymer, fluorinated ethylenepropylene copolymer (FEP) exhibiting a low degree of crystallinity, extruded in dimensions similar to the most commonly used CE capillaries of approximately 80 mum id and about 360 mum od was investigated for its use as a CE capillary. FEP is transparent down to the low-UV region, and as fluorinated polymers in general are good electrical insulators and exhibit reasonable heat conductivity, it has considerable potential as a material for electrodriven analysis in capillary or microchip formats. The FEP capillary has been characterised with regard to some important aspects for its use as a CE capillary, including its profile of EOF versus pH, as well as procedures for manipulating EOF by coating the inner capillary wall with various semipermanent and dynamic layers. The FEP capillaries were tested and compared with fused-silica capillary for the separation of inorganic and small organic ions using conditions involving direct and indirect detection in the low-UV region. Finally, advantages of the use of the FEP capillary for simultaneous detection of a mixture containing nine inorganic cations and anions using indirect photometric detection with a movable light-emitting diode (LED) detector and a novel electrolyte are demonstrated.     

Electrokinetic flow in a capillary with a charge-regulating surface polymer layer

An analytical study of the steady electrokinetic flow in a long uniform capillary tube or slit is presented. The inside wall of the capillary is covered by a layer of adsorbed or covalently bound charge-regulating polymer in equilibrium with the ambient electrolyte solution. In this solvent-permeable and ion-penetrable surface polyelectrolyte layer, ionogenic functional groups and frictional segments are assumed to distribute at uniform densities. The electrical potential and space charge density distributions in the cross section of the capillary are obtained by solving the linearized Poisson-Boltzmann equation. The fluid velocity profile due to the application of an electric field and a pressure gradient through the capillary is obtained from the analytical solution of a modified Navier-Stokes/Brinkman equation. Explicit formulas for the electroosmotic velocity, the average fluid velocity and electric current density on the cross section, and the streaming potential in the capillary are also derived. The results demonstrate that the direction of the electroosmotic flow and the magnitudes of the fluid velocity and electric current density are dominated by the fixed charge density inside the surface polymer layer, which is determined by the regulation characteristics such as the dissociation equilibrium constants of the ionogenic functional groups in the surface layer and the concentration of the potential-determining ions in the bulk solution.     

Diffusioosmosis of electrolyte solutions along a charged plane wall

The steady diffusioosmotic flow of an electrolyte solution along a dielectric plane wall caused by an imposed tangential concentration gradient is analytically examined. The plane wall may have either a constant surface potential or a constant surface charge density of an arbitrary quantity. The electric double layer adjacent to the charged wall may have an arbitrary thickness, and its electrostatic potential distribution is determined by the Poisson-Boltzmann equation. The macroscopic electric field along the tangential direction induced by the imposed electrolyte concentration gradient is obtained as a function of the lateral position. A closed-form formula for the fluid velocity profile is derived as the solution of a modified Navier-Stokes equation. The direction of the diffusioosmotic flow relative to the concentration gradient is determined by the combination of the zeta potential of the wall and the properties of the electrolyte solution. For a given concentration gradient of an electrolyte along a plane wall, the magnitude of fluid velocity at a position in general increases with an increase in its electrokinetic distance from the wall, but there are exceptions. The effect of the lateral distribution of the induced tangential electric field in the double layer on the diffusioosmotic flow is found to be very significant and cannot be ignored.     

Separation of organic cations using novel background electrolytes by capillary electrophoresis

A background electrolyte for capillary electrophoresis containing tris(-hydroxymethyl) aminomethane (THAM) and ethanesulfonic acid (ESA) gives excellent efficiency for separation of drug cations with actual theoretical plate numbers as high as 300,000. However, the analyte cations often elute too quickly and consequently offer only a narrow window for separation. The best way to correct this is to induce a reverse electroosmotic flow (EOF) that will spread out the peaks by slowing their migration rates, but this has always been difficult to accomplish in a controlled manner. A new method for producing a variable EOF is described in which a low variable concentration of tributylammonium- or triethylammonium ESA is added to the BGE. The additive equilibrates with the capillary wall to give it a positive charge and thereby produce a controlled opposing EOF. Excellent separations of complex drug mixtures were obtained by this method.     

Characteristics of the electroosmotic flow of electrolyte systems for nonaqueous capillary electrophoresis

Nonaqueous capillary electrophoresis (NACE) is a powerful tool for the analysis of surface-active substances, which represent a broad class of analytes containing cationic and anionic species, such as surfactants, phosphoric acid esters, and amines. In order to conduct an efficient method development in NACE, the influence of the electrolyte composition on the electroosmotic flow (EOF) of organic separation systems was systematically investigated. Background electrolytes and background chromophores appropriate for direct and indirect UV-detection were considered, as the majority of surface-active substances do not absorb UV-light. It was found that theoretical models developed to describe the EOF in aqueous electrolyte systems are insufficient for organic electrolyte systems. Experimental data on electroosmosis in a variety of organic solvents and mixtures of methanol and acetonitrile applying different background chromophores and basic or acidic additives are given. Differences between them are discussed with relation to the physicochemical properties of the organic solvents.     

Change of migration time and separation window accompanied by field-enhanced sample stacking in capillary zone electrophoresis.

When field-enhanced sample stacking was used in capillary zone electrophoresis (CZE) analysis of cations, the decrease of migration time and the reduction of separation window was observed with increase of sample plug length. A simple equation expressing the migration velocity in the stacking process was derived to explain the above phenomenon. From experiments and theoretical consideration, we confirmed that this effect was caused by the higher potential gradient and larger eletroosmotic flow (EOF) mobility at the sample plug than those at the supporting electrolyte. A mathematical model appropriate for the computer simulation of such a system was studied considering the experimental results, and it was concluded that electroosmotic velocity (v(eof)) should be introduced to the equation of continuity as a constant.     

Diffusioosmosis of electrolyte solutions in a fine capillary slit

The steady diffusioosmotic flows of an electrolyte solution along a charged plane wall and in a capillary channel between two identical parallel charged plates generated by an imposed tangential concentration gradient are theoretically investigated. The plane walls may have either a constant surface potential or a constant surface charge density. The electrical double layers adjacent to the charged walls may have an arbitrary thickness and their electrostatic potential distributions are determined by the Poisson-Boltzmann equation. Solving a modified Navier-Stokes equation with the constraint of no net electric current arising from the cocurrent diffusion, electric migration, and diffusioosmotic convection of the electrolyte ions, the macroscopic electric field and the fluid velocity along the tangential direction induced by the imposed electrolyte concentration gradient are obtained semianalytically as a function of the lateral position in a self-consistent way. The direction of the diffusioosmotic flow relative to the concentration gradient is determined by the combination of the zeta potential (or surface charge density) of the wall, the properties of the electrolyte solution, and other relevant factors. For a given concentration gradient of an electrolyte along a plane wall, the magnitude of fluid velocity at a position in general increases with an increase in its electrokinetic distance from the wall, but there are exceptions. The effect of the lateral distribution of the induced tangential electric field and the relaxation effect in the double layer on the diffusioosmotic flow are found to be very significant.     

Modeling the zeta potential of silica capillaries in relation to the background electrolyte composition

A theoretical relation between the zeta potential of silica capillaries and the composition of the background electrolyte (BGE) is presented in order to be used in capillary zone electrophoresis (CZE). This relation is derived on the basis of the Poisson-Boltzmann equation and considering the equilibrium dissociation of silanol groups at the capillary wall as the mechanism of charge generation. The resulting model involves the relevant physicochemical parameters of the BGE-capillary interface. Special attention is paid to the characterization of the BGE, which can be either salt or/and buffer solutions. The model is successfully applied to electroosmotic flow (EOF) experimental data of different aqueous solutions, covering a wide range of pH and ionic strength. Numerical predictions are also presented showing the capability of the model to quantify the EOF, the control of which is relevant to improve analyte separation performance in CZE.     

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。     

Separation of atropisomers of anti-hepatitis drug dimethyl diphenyl bicarboxylate analogues by capillary electrophoresis with vancomycin as the chiral selector

Separation of atropisomers of analogues of the anti-hepatitis drug dimethyl diphenyl bicarboxylate (DDB) by capillary electrophoresis with vancomycin as the chiral selector is described. Among several tested chiral selectors, including various cyclodextrin derivatives as well as vancomycin, only the latter displayed the enantioselectivity to the studied atropisomers. However, relatively poor separation efficiency was obtained due to the adsorption of vancomycin on the capillary wall. This problem was overcome by modifying the capillary wall with a polycationic electrolyte named hexadimethrine bromide (HDB) to produce a positively charged coating, which minimized the adsorption of vancomycin on the capillary wall by electrostatic repulsion. Moreover, the positively charged coating could shorten the separation time by reversing the EOF because the reversed EOF migrated to the same direction as the negatively charged analyte. Effects of buffer pH, vancomycin and buffer concentrations and applied voltage on the separation were investigated and the optimal conditions were established as follows: 40 mM Tris-phosphate buffer (pH 6.0) containing 6.0 mM vancomycin and 0.001% HDB. Baseline separation of three racemic DDB analogues was obtained within 12 min under the optimal conditions.     

Chiral separation of six diastereomeric flavanone-7-O-glycosides by capillary electrophoresis and analysis of lemon juice

Inexpensive and disposable polyester microchips were fabricated through photolithographic and wet-chemical etching procedure, followed by replication using an imprinting method at room temperature. Laboratory-scale laser-induced fluorescence equipment was employed as a detection system. The generation of electroosmotic flow (EOF) on the polyester channels was discussed in this paper. Surfactants in the running buffer had a significant effect on the EOF depending on their types. The epsilon potential of the electric double layer formed by adsorbing sodium lauryl sulfate molecules on the wall of polyester channels seemed to be constant within the buffer pH investigated. EOF could also be suppressed to zero by adding polyoxyethylene 23 lauryl ether into the running buffer. The separation of two laser dyes was obtained using polyester chips through both micellar electrokinetic chromatography and capillary zone electrophoresis. The polyester channels modified with 10-undecen-1-ol exhibited a dramatically high-separation efficiency compared with the conventional fused-silica capillary tubes.     

Comparison of different capillary isoelectric focusing methods--use of "narrow pH cuts" of carrier ampholytes as original tools to improve resolution

Two capillary isoelectric focusing (CIEF) systems have first been optimized: one uses a bare silica capillary and 30% (v/v) of glycerol in the separation medium while the other uses a coated capillary and an aqueous background electrolyte. To perform permanent capillary coating, two neutral polymers have been compared: hydroxypropylcellulose (HPC) and polyvinylalcohol (PVA). HPC coating gave best results for electroosmotic flow (EOF) limitation on a wide pH range: as compared to a bare silica capillary, it allowed to decrease EOF by 96% at pH 7.2 after acidic and basic treatments, whereas PVA coating lead only to a 76% decrease. The glycerol CIEF system was more satisfying for the separation of model proteins classically used as pI markers. Finally, the use of "narrow pH cuts" of carrier ampholytes added to commercial ampholyte mixtures allowed increasing resolution up to a factor 2.4 at a chosen pH for the separation of pI markers and milk proteins.