Electrophoresis of a sphere along the axis of a cylindrical pore: effects of double-layer polarization and electroosmotic flow

The electrophoresis of a rigid sphere along the axis of a cylindrical pore is investigated theoretically. Previous analysis is extended to the case where the effects of double-layer polarization and electroosmotic flow can be significant. The influences of the surface potential, the thickness of the double layer, and the relative size of a pore on the electrophoretic behavior of a sphere are discussed. Some interesting results are observed. For example, if both a sphere and a pore are positively charged, then the mobility of the sphere has a local minimum as the thickness of its double layer varies. Depending upon the level of the surface potential of a sphere and the degree of significance of the boundary effect, the mobility of the sphere may change its sign twice as the thickness of its double layer varies. This result can play a significant role in electrophoresis measurements.     

Effect of multiple ionic species on the electrophoretic behavior of a charge-regulated particle

It is often assumed in the conventional electrophoresis analysis that the liquid phase contains only one kind of each cation and anion. That analysis is extended to the case where the liquid phase contains multiple ionic species in this study so that the conditions considered are closer to reality. Using a dispersion of SiO(2) particles, which is of a charge-regulated nature, as an example, where the dispersion pH is adjusted by HCl and NaOH, numerical simulation is conducted to examine the electrophoretic behaviors of the particle under various conditions. We show that the presence of multiple ionic species is capable of yielding profound and interesting electrophoretic behaviors, which are justified by the experimental data in the literature. In addition, we show that two types of double-layer polarization (DLP) are present that have not been reported previously in the electrophoresis analyses. Type I DLP, which reduces the mobility of a particle, occurs inside the double layer, and type II DLP, which raises that mobility, occurs immediately outside the double layer.     

Analytical expressions for the electroosmotic flow in a charge-regulated circular channel

Analytical expressions are derived for the flow velocity and ionic current for the electroosmotic flow (EOF) in a charge-regulated circular channel, focusing on the effect of types of ions and their concentrations. We show that the mean flow velocity for those two cases can be different both quantitatively and qualitatively, implying that the true charged conditions can be inferred by appropriately designed experiments. The types of ionic species and their concentrations are also found to play a significant role. Both the EOF velocity and the current density increase with increasing ionic concentration, in general. However, the reverse trend is also observed at a sufficiently high ionic concentration.     

Influence of polymer structure on electroosmotic flow and separation efficiency in successive multiple ionic layer coatings for microchip electrophoresis

The effect of successive multiple ionic layer (SMIL) coatings on the velocity and direction of EOF and the separation efficiency for PDMS electrophoresis microchips was studied using different polymer structures and deposition conditions. To date, the majority of SMIL studies have used traditional CE and fused-silica capillaries. EOF was measured as a function of polymer structure and number of layers, in one case using the same anionic polymer and varying the cationic polymer and in the second case using the same cationic polymer and varying the anionic polymer. In both situations, the EOF direction reversed with each additional deposited polymer layer. The absolute EOF magnitude, however, did not vary significantly with layer number or polymer structure. Next, different coatings were used to compare separation efficiencies on native and SMIL-coated PDMS microchips. For native PDMS microchips, the average separation efficiency was 4105 +/- 1540 theoretical plates. The addition of two layers of polymer increased the separation efficiency anywhere from two- to five-fold, depending on the polymer structure. A maximum separation efficiency of 12 880 +/- 1050 theoretical plates was achieved for SMIL coatings of polybrene (cationic) and dextran sulfate (anionic) polymers after deposition of six total layers. It was also noted that coating improved run-to-run consistency of the peaks as noted by a reduction of the RSD of the EOF and separation efficiency. This study shows that the use of polyelectrolyte coatings, irrespective of the polymer structure, generates a consistent EOF in the current experiments and dramatically improves the separation efficiency when compared to unmodified PDMS microchips.     

Electrophoresis of a charge-regulated spheroid along the axis of an uncharged cylindrical pore

Boundary effects can have a profound influence on the electrophoretic behavior of a charged entity, in particular, when the entity is nonspherical and its surface conditions are dependent upon the nearby environment. In this study, the electrophoresis of a spheroid along the axis of an uncharged cylindrical pore is analyzed for the case where the electrical potential is low and the applied electric field is weak. We consider the case where the surface of a particle contains dissociable acidic and basic functional groups, which simulate biological colloids and entities covered by an artificial membrane. This leads to a mixed-type boundary value problem, which extends the conventional constant-surface-potential and constant-surface-charge-density models to a more general case. The effects of the particle aspect ratio, the relative magnitudes of particle and pore, the thickness of the double layer surrounding a particle, and the pH of the liquid phase on the electrophoretic mobility of a particle are investigated. Several interesting results are observed; for example, if the volume of a particle is fixed, its mobility may have a local maximum as the relative magnitudes of its two axes vary.     

Electrophoresis of a spherical particle along the axis of a cylindrical pore: effect of electroosmotic flow

The electrophoresis of a spherical particle along the axis of a cylindrical pore is investigated under conditions of low surface potential and thick double layer. In particular, the effect of electroosmotic flow is taken into account. The results of numerical simulation reveal that if both particle and pore are positively charged, the variation of the mobility of a particle may have a local minimum as the thickness of the double layer varies, which is not reported in the literature. This is mainly due to the charge induced on the particle surface, which arises from the presence of the charged boundary. Depending upon the level of the surface potential of the pore, the presence of the local minima may lead to a reversal in the direction of particle movement as the thickness of the double layer surrounding it varies: if the surface potential is either too low or too high, reversal does not occur; if it has a medium level, reversal occurs twice. This interesting observation can play a role in electrophoresis measurements. Previous analysis predicts that reversal always occurs once, regardless of the level of the surface potential of the pore.     

Boundary effect on electrophoresis: finite cylinder in a cylindrical pore

The boundary effect on electrophoresis is investigated by considering a finite cylindrical particle moving along the axis of a long cylindrical pore under conditions of low surface potential and weak applied electric field. The influence of the thickness of the double layer, the aspect ratio of a particle, the ratio particle radius/pore radius, and the charged conditions of the surfaces of the particle and pore on the electrophoretic behavior of a particle are investigated. We show that the effect of the aspect ratio of a particle on its electrophoretic behavior for the case where the particle is charged and the pore is uncharged is larger than that for the case where the particle is uncharged and the pore is charged. Also, depending on the parameters chosen, increasing the aspect ratio of a particle can either promote or hinder its movement, which is not reported in previous studies, and can play a role in electrophoresis measurements. Because both the electric and the flow fields in the gap between the particle and the pore are mediated by those near the top and the end of the particle, the end effect is large when the double layer is thick.     

Electrophoresis of two identical rigid spheres in a charged cylindrical pore

The electrophoresis of two identical spheres moving along the axis of a long cylindrical pore under the conditions of low surface potential and weak applied electric field is investigated. The geometry considered allows us to examine simultaneously the effects of boundary and the presence of a nearby entity on the behavior of a particle. The influences of the separation distance between two spheres, the thickness of a double layer, the ratio (radius of sphere/radius of pore), and the charged conditions on the surfaces of the spheres and the pore on the mobility of a particle are investigated. Several interesting results that are not reported in the literature are observed. For instance, although for the case of two positively charged spheres in an uncharged pore the qualitative behavior of a sphere depends largely on its size relative to that of a pore and the thickness of the double layer, this might not be the case when two uncharged spheres are in a positively charged pore. In addition, in the latter, the mobility of a sphere increases with the increases in the separation distance between two spheres, and this effect is pronounced when the ratio (radius of sphere/radius of pore) takes a medium value or the thickness of the double layer is either sufficiently thin or sufficiently thick.     

Mobilization of electroosmotic flow markers in capillary zone electrophoresis

UV-absorbing neutral substances are commonly used as markers of mean electroosmotic flow in capillary electrophoresis for their zero electrophoretic mobility in an electric field. However, some of these markers can interact with background electrolyte components and migrate at a different velocity than the electroosmotic flow. Thus, we tested 11 markers primarily varying in their degree of methylation and type of central atom in combination with five background electrolyte cations differing in their ionic radii and surface charge density, measuring the relative electrophoretic mobility using thiourea as a reference marker. Our results from this set of experiments showed some general trends in the mobilization of the markers based on the effects of marker structure and type of background electrolyte cation on the relative electrophoretic mobility. As an example, the effects of an inadequate choice of marker on analyte identification were illustrated in the electrophoretic separation of glucosinolates. Therefore, our findings may help electrophoretists appropriately select electroosmotic flow markers for various electrophoretic systems.     

Effects of double-layer polarization and electroosmotic flow on the electrophoresis of an ellipsoid in a spherical cavity

The electrophoresis of a rigid, positively charged ellipsoidal particle at the center of a spherical cavity is investigated theoretically under the conditions where the effects of double-layer polarization and the presence of an electroosmotic flow can be important. The equations governing the problem under consideration and the associated boundary conditions are solved numerically, and the influences of the key parameters on the electrophoretic mobility of the particle are discussed. We show that if the cavity is uncharged, the effect of double-layer polarization yields a local minimum in the electrophoretic mobility as the thickness of the double layer varies. This local minimum disappears if the cavity is also positively charged. In addition to reducing the scaled mobility of an ellipsoid, the presence of the boundary is also capable of influencing the relative magnitudes of the scaled mobility for particles of various shapes. For instance, if the volume of an ellipsoid is fixed, the scaled mobility ranks as prolate > sphere > oblate if the boundary effect is unimportant, but that order is reversed if the boundary effect is important.     

Investigation of the electroosmotic flow effect on the efficiency of capillary electrophoresis.

The influence of the electroosmotic flow profile on the efficiency and resolution of capillary electrophoresis is studied. The mathematical model is formulated and the set of equations is solved numerically. The results of the analysis are applicable to a wide range of buffer concentrations and capillary diameters. The temperature dependence of electrophoretic mobility, viscosity and thermal conductivity and the dependence of electrical conductivity on temperature and ion concentration in the double layer are taken into account. It is shown that there exists a region of buffer concentrations and capillary diameters where the influence of the electroosmotic flow profile on the efficiency and resolution is much greater than that of the temperature dependence of the electrophoretic mobility. The results are especially essential for small buffer concentrations or capillary diameters comparable with the double electrical layer thickness.     

Modification of electroosmotic flow for a polydimethylsiloxane electrophoresis microchip via polyelectrolyte coating

Polydimethylsiloxane has been dominantly employed as the substrate material for microchip capillary electrophoresis. The poor surface chemistry, however, generates inconsistent electroosmotic flow under the electrophoretic condition, limiting its broader applications. In this work, different polyelectrolytes, including polydiallyldimethylammonium chloride, polyvinyl sulfate, and dextran sulfate, were successfully deposited onto polydimethylsiloxane microchannel surfaces. The polyelectrolyte coated polydimethylsiloxane microchannel showed improved consistency and reproducibility in electroosmotic flow under an electric field over the uncoated native microchannel.     

Fluid mechanics of electroosmotic flow and its effect on band broadening in capillary electrophoresis

Electroosmotic flow (EOF) usually accompanies electrophoretic migration of charged species in capillary electrophoresis unless special precautions are taken to suppress it. The presence of the EOF provides certain advantages in separations. It is an alternative to mechanical pumps, which are inefficient and difficult to build at small scales, for transporting reagents and analytes on microfluidic chips. The downside is that any imperfection that distorts the EOF profile reduces the separation efficiency. In this paper, the basic facts about EOF are reviewed from the perspective of fluid mechanics and its effect on separations in free solution capillary zone electrophoresis is discussed in the light of recent advances.     

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.     

Hydrodynamic suppression of the electroosmotic flow in capillary electrophoresis with indirect spectrophotometric detection

A version of capillary electrophoresis with indirect spectrophotometric detection and the hydrodynamic suppression of electroosmotic flow is studied. It is shown that, to improve the reliability of ion identification, one should calculate electrophoretic mobilities of ions or migration times corrected with regard to the electroosmotic flow rate. Correlations between electrophoretic peak areas of ions and their electrophoretic mobilities are derived. In the studied version of capillary electrophoresis, the accuracy of measuring anion concentrations can be improved using the internal standard method.     

Electrophoresis of a charge-regulated sphere at an arbitrary position in a charged spherical cavity

The electrophoresis of a charge-regulated spherical particle at an arbitrary position in a charged spherical cavity is modeled under conditions of low surface potential (<25 mV) and weak applied electric field (<25 kV/m). The charged cavity allows us to simulate the effect of electroosmotic flow, and the charge-regulated nature of the particle permits us to model various types of surface. The problem studied previously is reanalyzed based on a more rigorous electric force formula. In particular, the influences of various types of charged conditions on the electrophoretic behavior of a particle and the roles of all the relevant forces acting on the particle are examined in detail. Several new results are found. For instance, the mobility of a particle has a local minimum as the thickness of a double layer varies, which is not seen in the cases where the surface of a particle is maintained at a constant potential and at a constant charge density.     

Effect of ionic size on the deposition of charge-regulated particles to a charged surface

The deposition of charge-regulated particles to a rigid, planar charged surface is modeled theoretically, taking the effects of the excluded area arising from deposited particles and finite ionic sizes into account. Here, a particle comprises a rigid core and an ion-penetrable charged membrane layer, which represents a general type of particle. If the membrane layer has a negligible thickness, the particle simulates a regular inorganic particle, and if the membrane layer has a finite thickness, it simulates biocolloids such as cells. The results of numerical simulation reveal that the rate of particle deposition is faster under the following conditions: (1) lower potential of the planar surface, (2) thicker membrane, (3) higher counterion valance, (4) lower fixed charge density, (5) smaller counterions, (6) larger co-ions, (7) larger functional group, and (8) lower pH. Neglecting the sizes of ionic species may lead to an appreciable deviation in both the electrical repulsive force between particle and surface and the rate of deposition. Typical deviation for the former is approximately 20%, and that for the latter is approximately -75%.