On the mathematical model of capillary electrophoresis

Summary The influence of the electroosmotic flow profile on the efficiency of capillary electrophoresis for a wide range of buffer concentrations and capillary diameters is studied. Thermal effects in the capillary, the finite size of solute molecules and their interactions with the capillary wall are also taken into consideration. The dependence of capillary electrophoresis efficiency and resolution on the zeta-potential values is investigated.Presented at the 19^th ISC, Aix-en-Provence, France, September 13–18, 1992.     

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.     

Enantiomer separations on a vancomycin stationary phase and retention mechanism of pressurized capillary electrochromatography

Several chiral drugs, promethazine, carteolol, celiprolol, and albuterol, were resolved with vancomycin as the chiral stationary phase by pressurized capillary electrochromatography (pressurized CEC) and capillary HPLC. The effects of pressure and electrical field strength on efficiency, resolution, and capacity factor in pressurized CEC were investigated. A mathematical model describing the relationship of capacity factor in pressurized CEC with voltage, pressurized flow velocity, electroosmotic mobility, and electrophoretic mobility was established, which was in good agreement with the experimental data.     

Suppression of electroosmotic flow and its application to determination of electrophoretic mobilities in a poly(vinylpyrrolidone)-coated capillary

A hydrophilic polymer, poly(vinylpyrrolidone) (PVP), was employed for suppressing the electroosmotic flow (EOF). A capillary was filled with aqueous PVP solution for coating the capillary wall with PVP; the PVP solution was then replaced by a migration buffer solution containing no PVP. Three types of PVP with different molecular weights were examined. The EOF was suppressed more effectively as the molecular weight of PVP increased. The EOF in the coated capillary was approximately 10-fold smaller than that of a bare capillary and was constant in the pH range of 6-8. The suppressed EOF was stable even when no PVP was added to the migration buffer. However, the EOF increased significantly when sodium dodecyl sulfate was added into the migration buffer. The method was applied for determining the electrophoretic mobilities of inorganic anions that have negative electrophoretic mobilities larger than the electroosmotic mobility of the bare capillary. A novel method for determining the electrophoretic mobilities was proposed based on the linear relationship between electric current and electrophoretic mobility. The electrophoretic mobility was proportional to the electric current. Therefore, the intercept of the regression equation represents the electrophoretic mobility at room temperature. The electrophoretic mobilities were in good agreement with the absolute electrophoretic mobilities.     

Impact of organic solvents on the resolution of synthetic peptides by capillary electrophoresis

The effect of variations in the concentrations of different organic solvents, including acetonitrile, methanol, ethanol, propanol and isopropanol, with aqueous buffer electrolytes of defined composition and pH on the electroosmotic flow velocity, v(EOF), of uncoated fused silica capillaries and on the electrophoretic mobility, mu(e), of synthetic peptides in high-performance capillary electrophoresis (HPCE) has been systematically investigated. In these experiments, the volume fractions of the organic solvent in the aqueous buffer electrolyte were changed from psi = 0.0 to 0.80. The addition of these organic solvents to the aqueous buffer electrolyte reduced the electroosmotic flow (EOF) of the system, but to significantly different extents. For the protic solvents as the alkyl chain of the alcohol increased, at the same volume fraction the greater was the influence on the electroosmotic flow. However, for the aprotic solvent, acetonitrile, the EOF did not change substantially as the volume fraction was varied. The electrophoretic mobility of synthetic peptides under the different buffer electrolyte conditions showed similar trends, confirming that the content and type of the organic modifier can be rationally employed to subtly manipulate the separation selectivity of synthetic peptides. These results, therefore, provide fundamental insight into the experimental options that can be used to maximise resolution of synthetic peptides in HPCE with aqueous buffer-organic solvent mixtures as well as a basis to select optimal binary or ternary buffer electrolyte compositions for the analysis of peptides when hyphenated techniques, such as HPCE-electrospray ionisation mass spectrometry (ESI-MS), are contemplated for the analysis of peptide samples of low abundance as can often be experienced in proteomic investigations.     

The application of spline wavelet transform to the determination of electroosmotic mobility in capillary electrophoresis

The rule of current change was studied during capillary electrophoresis (CE) separation process while the conductivity of the sample solution was different from that of the buffer. Using a quadratic spline wavelet of compact support, the wavelet transforms (WTs) of capillary electrophoretic currents were performed. The time corresponding to the maximum of WT coefficients was chosen as the time of current inflection to calculate electroosmotic mobility. The proposed method was suitable for different CE modes, including capillary zone electrophoresis, nonaqueous CE and micellar electrokinetic chromatography. Compared with the neutral marker method, the relative errors of the developed method for the determination of electroosmotic mobility were all below 2.5%.     

Electrophoresis of an ellipsoid along the axis of a cylindrical pore: effect of a charged boundary

The influence of a charged boundary on the electrophoretic behavior of a particle is investigated by considering the electrophoresis of a nonconducting ellipsoid along the axis of a cylindrical pore at the level of the linear Poisson-Boltzmann equation ignoring the polarization effect. The problem considered simulates the electrophoresis conducted in a narrow space such as capillary electrophoresis and electrophoresis through a porous medium. Here, because the effect of electroosmotic flow can be important the electrophoretic behavior is much more complicated than that for the case where a boundary is uncharged. The influences of the thickness of double layer, the aspect ratio of an ellipsoid, the relative radius of a pore, and the charge conditions on the ellipsoid and pore surfaces on the mobility of the ellipsoid are discussed. Several interesting but nonintuitive electrophoretic behaviors are observed.     

Influence of boundary on the effect of double-layer polarization and the electrophoretic behavior of soft biocolloids

The electrophoresis of a soft particle comprising a rigid core and a charged porous membrane layer in a narrow space is modeled. This simulates, for example, the capillary electrophoresis of biocolloids such as cells and microorganisms, and biosensor types of device. We show that, in addition to the boundary effect, the effects of double-layer polarization (DLP) and the electroosmotic retardation flow can be significant, yielding interesting electrophoretic behaviors. For example, if the friction coefficient of the membrane layer and/or the boundary is large, then the DLP effect can be offset by the electroosmotic retardation flow, making the particle mobility to decrease with increasing double layer thickness, which is qualitatively consistent with many experimental observations in the literature, but has not been explained clearly in previous analyses. In addition, depending upon the thickness of double layer, the friction of the membrane layer of a particle can either retard or accelerate its movement, an interesting result which has not been reported previously. This work is the first attempt to show solid evidence for the influence of a boundary on the effect of DLP and the electrophoretic behavior of soft particles. The model proposed is verified by the experimental data in the literature. The results of numerical simulation provide valuable information for the design of bio-analytical apparatus such as nanopore-based sensing applications and for the interpretation of relevant experimental data.     

Prediction of Migration Times of Organic Ions in Capillary Zone Electrophoresis

The electrophoretic mobility ratio (R value) of any two ions is constant and independent of the capillary type and electrophoretic conditions if their electrical charges and hydration radii are constant. The use of strong acid salts and quaternary ammonium salts is therefore proposed for the determination of R values. Such analytes are called markers. The following determinations can be carried out: (i) the determination of the migration time corresponding to the electroosmotic flow (EOF) in any capillary under any electrophoretic condition by measuring the migration times of two markers in the condition studied (useful when the EOF is weak); (ii) the determination of the migration time of an analyte in any capillary by knowing the migration time of the markers in the capillary studied. If the pH is changed and the ionization of the analyte is pH dependent, the resulting migration time for the analyte can be calculated. The constancy of the mobility ratios of seven markers was checked experimentally at eight different pH values (between pH 3 and 10), at three temperatures, and for two buffer concentrations. The predicted and experimental migration times were also compared in two different types of capillaries.     

毛细管电泳分离I^—和IO3^—中的电渗流的控制与调节

毛细管电泳分离是基于带电粒子在电场下的电动现象，当电场加到带电粒子所处的介质上时，存在电泳和电渗两种电动现象，其中电泳与带电粒子的大小、电荷和形状有关，而电渗与毛细管的表面及电泳介质的组成有关．由于电渗流能显著地影响分析时间和分离效率，因此，控制电渗流在毛细管电泳分离中是一个重要的环节［‘·‘j．此外，调节PH值、离子强度和缓冲液的粘度也是常用的控制电渗流的方法［’j．Ewing［‘与1入一个附加电场来控制电渗流．在缓冲液中加入足够浓度的阳离子表面活性剂将改变电渗流的方向．与通常的电渗流相比，人们对反向…     

毛细管电色谱中双电层叠加的研究

通过流动相中电解质浓度对毛细管电色谱柱效能的流动相平均线速度的影响，研究了ＣＥＣ中双电层叠加现象。提出选择合适电解质组成的浓度及在制备色谱柱过程中避免细小和破碎的固定相颗粒进入柱中，以有效地减小双电层叠加作用。     

Cyclodextrin-assisted capillary electrophoretic resolution of 1,1'-bi-2-naphthol atropisomers.

Native beta- and gamma-cyclodextrin (CD), neutral beta-CD derivatives and ethylcarbonate derivatives of beta- and gamma-CD were used as stereoselective additives for CD-capillary zone electrophoresis (CZE) resolution of atropisomers of 1,1'-bi-(2-naphthol) (BN). CZE experiments at variable CD concentration allowed calculating binding constants from electrophoretic mobility data, corrected for electroosmotic flow (EOF) and running buffer viscosity variations. The CDs were chosen on the basis of geometric examination of molecular models of BN and CDs that suggested the possibility of inclusion complexes formation. Optimum concentrations, with aqueous 25 mM phosphate running buffer at pH 10.5, 36 cm x 50 microm capillary and 10 kV applied potential, were 3.6, 3.9, 2.1, 2.2, 1.9 mM for beta-CD, gamma-CD, ethylcarbonate-beta-CD, methyl-beta-CD and hydroxypropyl-beta-CD, respectively.     

Continuous microfluidic DNA and protein trapping and concentration by balancing transverse electrokinetic forces

Sample pre-concentration can be a critical element to improve sensitivity of integrated microchip assays. In this work a converging Y-inlet microfluidic channel with integrated coplanar electrodes was used to investigate transverse DNA and protein migration under uniform direct current (DC) electric fields to assess the ability to concentrate a sample prior to other enzymatic modifications or capillary electrophoretic separations. Employing a pressure-driven flow to perfuse the microchannel, negatively charged samples diluted in low and high ionic strength buffers were co-infused with a receiving buffer of the same ionic strength into a main daughter channel. Experimental results demonstrated that, depending of the buffer selection, different DNA migration and accumulation dynamics were seen. Charged analytes could traverse the channel width and accumulate at the positive bias electrode in a low electroosmotic mobility, high electrophoretic mobility, high ionic strength buffer or migrated towards an equilibrium position within the channel in a high electroosmotic mobility, high electrophoretic mobility, low ionic strength buffer. The various migration behaviours are the result of a balance between the electrophoretic force and a drag force induced by a recirculating electroosmotic flow generated across the channel width due to the bounding walls. Under continuous flow conditions, DNA samples were concentrated several-fold by balancing these transverse electrokinetic forces. The electrokinetic trapping technique presented here is a simple technique which could be expanded to concentrate or separate other analytes as a preconditioning step for downstream processes.     

Separation of the positional isomers of phthalic acids in hydroorganic solvents using capillary electrophoresis

The positional isomers of phthalic acids (ortho-, meta-, and para-) and benzoic acid could be completely separated by capillary electrophoresis (CE). A simple CE method employing direct detection in mixed methanol/water buffers is presented. The effect of the electrolyte buffer system, including pH, buffer concentration, and organic solvent on the electrophoretic mobility of the analytes, is investigated. The electroosmotic flow is reversed using cationic surfactant and cetyltrimethylammonium bromide so that anions are separated under the co-EOF mode. The resolution of the analytes and selectivity could be improved by the adjustment of the methanol content. Ion association with the surfactant in methanol/water buffer is discussed. The validity of the method in terms of sensitivity, reproducibility, and linearity is also reported. The text was submitted by the authors in English.     

Study of the selectivity of inorganic anions in hydro-organic solvents using indirect capillary electrophoresis

In capillary electrophoresis (CE) analysis of small inorganic anions, the ability to control the electroosmotic flow (EOF) and the ability to alter the electrophoretic mobility of the ions are essential to improve resolution and separation speed. In this work, a CE method for separation of small inorganic anions using indirect detection in mixed methanol/water buffers is presented. The suitability of different UV absorbing probes commonly used for indirect detection including chromate, iodide, phthalate, benzoate, trimellitate, and pyromellitate, in mixed methanol/water buffers is examined. The effect of the electrolyte buffer system, including the pH, buffer concentration and the organic solvent on the electrophoretic mobility of the probes and analytes are also investigated. The EOF was reversed using cationic surfactant, cetyltrimethylammonium bromide (CTAB) so ions were separated under co-EOF mode. The organic solvent alters the electrophoretic mobility of the probes and the analytes differently and hence choice of the appropriate probe is essential to achieve high degree of detection sensitivity. Separations of six anions in less than 2.5 min were accomplished in buffers containing up to 30% MeOH. Adjustment of the methanol content helps to improve the selectivity and resolution of inorganic anions. Limit of detection, reproducibility and application of the method for quantification of anions in water samples will also be discussed.     

Theoretical study on potential distribution and electroosmotic flow velocity in microscale channel

A developed mathematical model for calculating potential distribution inside the electrical double layer is explored in this paper based on the Poisson-Boltzmann equation. By modifying the ion concentration, we numerically simulated the potential profile inside the actual electrical double layer according to the zeta potential. Then a theoretical analysis on the streamwise electroosmotic velocity in microscale channel is presented. Furthermore, the expression of the electroosmotic velocity is significantly suppressed after considering the Helmboltz-Smolucbowski equation boundary conditions. The results show that the calculated electroosmotic values basically agree with the experimental ones. Therefore, this provides the data for micro- and nano-channels’ electrophoretic transport, as well as separation of neutral and charged electrolyte.     

Electrokinetics of concentrated suspensions of spherical colloidal particles with surface conductance, arbitrary zeta potential, and double-layer thickness in static electric fields

In this paper the electrophoretic mobility and the electrical conductivity of concentrated suspensions of spherical colloidal particles have been numerically studied under arbitrary conditions including zeta potential, particle volume fraction, double-layer thickness (overlapping of double layers is allowed), surface conductance by a dynamic Stern layer model (DSL), and ionic properties of the solution. We present an extensive set of numerical data of both the electrophoretic mobility and the electrical conductivity versus zeta potential and particle volume fraction, for different electrolyte concentrations. The treatment is based on the use of a cell model to account for hydrodynamic and electrical interactions between particles. Other theoretical approaches have also been considered for comparison. Furthermore, the study includes the possibility of adsorption and lateral motion of ions in the inner region of the double layers (DSL model), according to the theory developed by C. S. Mangelsdorf and L. R. White (J. Chem. Soc. Faraday Trans.86, 2859 (1990)). The results show that the correct limiting cases of low zeta potentials and thin double layers for dilute suspensions are fulfilled by our conductivity formula. Moreover, the presence of a DSL causes very important changes, even dramatic, on the values of both the electrophoretic mobility and the electrical conductivity for a great range of volume fractions and zeta potentials, specially when double layers of adjacent cells overlap, in comparison with the standard case (no Stern layer present). It can be concluded that in general the presence of a dynamic Stern layer causes the electrophoretic mobility to decrease and the electrical conductivity to increase in comparison with the standard case for every volume fraction, zeta potential, and double-layer thickness.     

Separation of Basic Proteins in Bare Fused-Silica Capillaries with Diethylentriamine Phosphate Buffer as the Background Electrolyte Solution

The effectiveness of diethylentriamine (DIEN) phosphate buffer at separating basic proteins in bare fused-silica capillaries at various pH values was examined. Such a buffer consists of an aqueous solution of DIEN titrated to the desired pH value with phosphoric acid. The study was conducted by investigating the effect of DIEN phosphate buffer on the electrophoretic mobility and efficiency of four basic proteins at various pH values within the ranges over which the phosphate salts of DIEN are effective at controlling the protonic equilibrium on the basis of the acidic pKa values of either diethylentriamine or phosphoric acid. The ranges were taken as one pH unit below and above the acidic pKa values of either DIEN or phosphoric acid. Electrophoretic separations of the four basic proteins performed at the selected pH values, ranging from pH 3.0 to pH 8.0, showed well-resolved efficient and symmetric peaks, demonstrating the capability of DIEN phosphate buffer at inhibiting untoward interactions of basic proteins with the active sites on the inner wall of bare fused-silica capillaries. Such effect is ascribed to the absorption of DIEN ions at the interface between the capillary wall and the electrolyte solution resulting in drastic variations of the positive charge density in the compact region of the electric double layer that, however, are is not suppressing completely the negative charges due to the ionization of silanol groups. Consequently, the net charge within the immobilized region of the electric double layer is negative as evidenced by the cathodic electroosmotic flow measured at any pH value within the range 3.0–8.0, indicative of negative zeta potential.     

Theory of capillary electrochromatography

The present state of the theory of capillary electrochromatography (CEC) is reviewed. Emphasis is placed on electroosmosis and the electrical double layer, and the generally good understanding of the factors affecting the electroosmotic flow in CEC columns. The relation of CEC to other electrically driven separations are described, along with band broadening, and the influence of column temperature in CEC. The theoretical potential of CEC is assessed from the standpoint of current and future column technology, and likely future application areas are described.     

Transient electrophoresis of dielectric spheres

The dynamic electrophoretic response of a spherical dielectric particle suspended in an electrolyte solution to a step change in the applied electrics field is analytically studied. The electrical double layer surrounding the particle may have either a small but finite thickness or a very large thickness relative to the particle radius. For the case of electrophoresis of a particle with a thin double layer, the local electroosmotic velocity at the outer edge of the double layer evolving with time after the external field is imposed is used as an apparent slip boundary condition at the particle surface so that the unsteady equation of motion for the fluid flow outside the double layer is solved. Closed-form formulas for the transient electrophoretic mobility of the particle are derived as functions of relevant parameters. The results demonstrate that, when the double layer surrounding the particle is relatively thin, the normalized electrophoretic mobility at a given dimensionless time decreases monotonically with a decrease in the parameter kappaa, where kappa(-1) is the Debye screening length and a is the particle radius. When the double layer of the particle is relatively thick, the particle mobility can have magnitudes comparable to those for a particle with a thin double layer in the initial stage, but will become much smaller afterward. In general, the effect of the relaxation time for transient electrophoresis is negligible, regardless of the value of kappaa.