Electrophoretic mobility of a colloidal particle with constant surface charge density

When the electrophoretic mobility of a particle in an electrolyte solution is measured, the obtained electrophoretic mobility values are usually converted to the particle zeta potential with the help of a proper relationship between the electrophoretic mobility and the zeta potential. For a particle with constant surface charge density, however, the surface charge density should be a more characteristic quantity than the zeta potential because for such particles the zeta potential is not a constant quantity but depends on the electrolyte concentration. In this article, a systematic method that does not require numerical computer calculation is proposed to determine the surface charge density of a spherical colloidal particle on the basis of the particle electrophoretic mobility data. This method is based on two analytical equations, that is, the relationship between the electrophoretic mobility and zeta potential of the particle and the relationship between the zeta potential and surface charge density of the particle. The measured mobility values are analyzed with these two equations. As an example, the present method is applied to electrophoretic mobility data on gold nanoparticles (Agnihotri, S. M.; Ohshima, H.; Terada, H.; Tomoda, K.; Makino, K. Langmuir 2009, 25, 4804).     

Electrophoretic mobility of a spherical colloidal particle in a salt-free medium

A general expression as well as approximate expressions are derived for the electrophoretic mobility of dilute spherical colloidal particles in a salt-free medium containing only counter ions. It is shown that there is a certain critical value of the particle surface charge. When the particle surface charge is lower than the critical value, the electrophoretic mobility is proportional to the particle surface charge or the particle zeta potential, following Hückel's formula. When the particle surface charge is higher than the critical value, the electrophoretic mobility becomes independent of the particle surface charge. This is due to the effect of counter ion condensation in the vicinity of the particle surface.     

Individual electrophoretic mobilities of liposomes and acidic organelles displaying pH gradients across their membranes

This report focuses on measuring the individual electrophoretic mobilities of liposomes with different pH gradients across their membrane using capillary electrophoresis with laser-induced fluorescence detection (CE-LIF). The results from the individual analysis of liposomes show that, using surface electrostatic theories and the electrokinetic theory as the first approximation, zeta potential contributes more significantly to the electrophoretic mobility of liposomes than liposomal size. For liposomes with an outer pH 7.4 (pH(o) 7.4) and a net negative outer surface charge, the most negative electrophoretic mobilities occur when the inner pH (pH(i)) is 6.8; at higher or lower pH(i), the electrophoretic mobilities are less negative. The theories mentioned above cannot explain these pH-induced electrophoretic mobility shifts. The capacity theory, predicting an induced electrical charge on the surface of liposomes, can only explain the results at pH(i) > 6.8. In this report, we hypothesize that there is a flip-flop process of phospholipids, which refers to the exchange of phospholipids between the outer and inner layers of the membrane. This flip-flop is caused by the pH gradient and membrane instability and results in the observed electrophoretic mobility changes when pH(i) is <6.8. Furthermore, it is found that the mobilities of acidic organelles are consistent with the predictions of liposome models we used here.     

Effects of structural properties of the Stern layer on the electrophoretic migration of a highly charged spherical macroion

The electrophoretic migration of a highly charged spherical macroion suspended in an aqueous solution of NaCl is studied using the molecular dynamic method. The objective is to examine the effects of the colloidal surface charge density on the electrophoretic mobility (μ) of the spherical macroion. The bare charge and the size of the macroion are varied separately to induce changes in the colloidal surface charge density. Our results indicate that μ depends on colloidal surface charge density in a nonmonotonic manner, but that this relationship is independent of the way the surface charge density is varied. It is found that an increase in colloidal surface charge density may lead to the formation of new sublayers in the Stern layer. The μ profile is also found to have a local maximum for a bare charge at which a new sublayer is formed in the Stern layer, and a local minimum for a bare charge at which the outer sublayer becomes relatively dense. Finally, the electrophoretic flow caused by the migration of the spherical macroion is studied to find that one decisive factor causing the electrophoretic flow is the ability of the macroion to carry anions in the electrolyte solution.     

Electrophoretic mobility of a cylindrical colloidal particle in a salt-free medium

Approximate expressions are derived for the electrophoretic mobility of dilute cylindrical colloidal particles in a salt-free medium containing only counterions. The cylinder is assumed to be infinitely long. It is shown that as in the case of a spherical particle, there is a certain critical value of the particle surface charge separating two cases. When the particle surface charge is lower than the critical value (case 1), the electrophoretic mobility increases with increasing particle surface charge per unit length. When the particle surface charge is higher than the critical value (case 2), the mobility becomes constant (for a cylinder in a transverse field) or the increase in the electrophoretic mobility with the particle surface charge becomes suppressed (for a cylinder in a tangential field). These phenomena are caused by the effect of counterion condensation in the vicinity of the particle surface. The critical value of the particle charge is essentially independent of the particle volume fraction phi for the dilute case, unlike the case of a sphere, in which case the critical charge value is proportional to ln(1/phi).     

Smoluchowski equation and the colloidal charge reversal

Smoluchowski equation and the Monte Carlo simulations are used to study the conditions leading to the reversal of the electrophoretic mobility. Zeta (zeta) potential is identified with the diffuse potential at the shear plane which, we argue, must be placed at least one ionic diameter away from the colloidal surface. For sufficiently strongly charged colloids, zeta potential changes sign as a function of the multivalent electrolyte concentration, resulting in a reversal of the electrophoretic mobility. This behavior occurs even for very small ions of 4 A diameter as long as the surface charge density of the colloidal particles is sufficiently large and the concentration of 1:1 electrolyte is sufficiently low.     

Electrokinetics of charged spherical colloidal particles taking into account the effect of ion size constraints

The electrokinetic properties of suspended spherical particles are examined using a modified standard electrokinetic model, which takes into account the finite ion size and considers that the minimum approach distance of ions to the particle surface need not be equal to their effective radius in the bulk solution. We calculate the conductivity increment and the electrophoretic mobility and present a detailed interpretation of the obtained results, based on the analysis of the equilibrium and field-induced ion concentrations, as well as the convective fluid flow in the neighborhood of the particle surface. We show that when charge reversal takes place, the sign of the concentration polarization remains unchanged while the sign of the electrophoretic mobility only changes under favorable circumstances.     

Electrophoretic characterization of insulin growth factor (IGF-1) functionalized magnetic nanoparticles

The synthesis of composite nanoparticles consisting of a magnetite core coated with a layer of the hormone insulin growth factor 1 (IGF-1) is described. The adsorption of the hormone in the different formulations is first studied by electrophoretic mobility measurements as a function of pH, ionic strength, and time. Because of the permeable character expected for both citrate and IGF-1 coatings surrounding the magnetite cores, an appropriate analysis of their electrophoretic mobility must be addressed. Recent developments of electrokinetic theories for particles covered by soft surface layers have rendered possible the evaluation of the softness degree from raw electrophoretic mobility data. In the present contribution, the data are quantitatively analyzed based on the theoretical model of the electrokinetics of soft particles. As a result, information is obtained on both the thickness and the charge density of the surrounding layer. It is shown that IGF-1 adsorbs onto the surface of citrate-coated magnetite nanoparticles, and adsorption is confirmed by dot-blot analysis. In addition, it is also demonstrated that the external layer of IGF-1 exerts a shielding effect on the surface charge of citrate-magnetite particles, as suggested by the mobility reduction upon contacting the particles with the hormone. Aging effects are demonstrated, providing an electrokinetic fingerprint of changes in adsorbed protein configuration with time.     

Characterization of carboxylated nanolatexes by capillary electrophoresis

Poly(styrene-co-acrylic acid) (St/AA) and poly(styrene-co-methacrylic acid) (St/MA) nanolatexes with different acid contents were prepared by emulsion copolymerization and were analyzed by capillary electrophoresis (CE) and by laser doppler velocimetry (LDV). Due to the intrinsic differences in the methodologies, CE (separative technique) and LDV (zetametry, nonseparative technique) lead to very different electrophoretic mobility distributions. Beyond these differences, the variation of the electrophoretic mobility is a complex and nonlinear function of the hydrodynamic radius, the ionic strength, and the zeta potential. To gain better insight on the influence of the ionic strength and the acid content on the electrophoretic behavior of the nanolatexes, the electrophoretic mobility data were changed into surface charge densities using the O'Brien, White, and Ohshima modeling. This approach leads to the conclusion that the surface charge density is mainly controlled at high ionic strength (～50 mM) by the adsorption of anionic surfactants coming from the sample. On the contrary, at low ionic strength, and/or in the presence of neutral surfactant in the electrolyte, the acid content was the main parameter controlling the surface charge density of the nanolatexes.     

High‐resolution quantification by charge‐dominant electrophoretic mobility shift of quantum dots

Conjugation of biomolecules to colloidal nanoparticles, such as quantum dots (QDs), often leads to change in mobility. We discover that linking DNA molecules to quantum dots alters their surface charge density without significantly increasing the hydrodynamic radius, causing a prominent shift in electrophoretic mobility. In this study, a high‐resolution molecular quantification method named quantification by QDs electrophoretic mobility shift (qQEMS) is developed based on the charge‐dominant transformation that closely associates DNA quantity to QDs electrophoretic mobility. The versatility of qQEMS is demonstrated by a number of quantification assays in which DNA molecules functioned as enzyme substrates, target‐specific probes, and competitive charge carriers. qQEMS shows a great potential as a generic and versatile quantification platform for a wide range of applications.     

Changes in charge density and softness of a poly(l-lactide) microcapsule surface in the hydrolytic degradation process

The changes in surface properties of poly(l-lactide) microcapsules caused by hydrolytic degradation have been studied with electrophoretic mobility measurements. An electrokinetic model has been applied to examine the electrophoretic mobility data, which were previously analyzed with a model that does not take into account the liquid flow inside the microcapsule membrane [K. Makino, H. Ohshima and T. Kondo, J. Microencapsulation, 4 (1987) 47]. The present new model involves two parameters, the charge density in the microcapsule membrane and a softness parameter, the latter of which characterizes the reciprocal of the frictional coefficient of the polymer exerted on the liquid flow. Information about the changes in charge density and in the softness of the poly(l-lactide) microcapsule surface have been newly obtained. The surface charge density increases by the cleavage of ester bonds in the polymer chain in the initial stage of the degradation process. It then gradually decreases down to the value for intact poly(l-lactide) microcapsules as a result of the release of degraded polymer segments from the microcapsule surface. Also, as the degradation proceeds, the softness parameter value increases, suggesting that the surface of the microcapsules becomes softer, probably because the surface becomes porous. The above change in the softness and the decrease in charge density at the later stage of the degradation both imply liberation of charged polymer segments. The degradation of poly(l-lactide) microcapsules proceeds by alternate repetition of cleavage of the ester bonds in the polymer chains and liberation of the degraded polymer segments from the surface.     

Approximate analytic expressions for the electrophoretic mobility of spheroidal particles

Approximate analytic expressions are derived for the electrophoretic mobility of spheroidal particles (prolate and oblate) carrying low zeta potential in an electrolyte solution under an applied tangential or transverse electric field. The present approximation method, which is based on the observation that the electrophoretic mobility of a particle is determined mainly by the distortion of the applied electric field by the presence of the particle. The exact expression for the equilibrium electric potential distribution around the particle, which can be expressed as an infinite sum of spheroidal wave functions, is not needed in the present approximation. The electrophoretic mobility values calculated with these approximate expressions for spheroidal particles with constant surface potential or constant surface charge density are in excellent agreement with the exact numerical results of previous reports with the relative errors less than about 4%.     

Anomalous low-frequency electro-optic behavior of ferric oxide particles in the presence of poly(ethylene oxide)

Electro-optic techniques were used to investigate the influence of poly(ethylene oxide) (PEO) on the surface electric state of positively charged oxide particles. The variations in particle electrophoretic mobility of beta-FeOOH particles in the presence of PEO indicate significant changes in the surface electric state of the particles in the concentration interval of PEO 10(-2)-10(-1) g dm(-3). The electro-optic results for the same conditions were unexpected: no significant difference is observed in the value and the relaxation frequency of particle electric polarizability in the frequency domain of the alpha-relaxation (detected in the kilohertz range); particle rotational relaxation time also remains unchanged; considerable changes are detected only in the relaxation interval of particle rotation (detected in the hertz range). The obtained results reject the possibility of the formation on the particle surface of a thick polymer layer. A thin adsorption layer cannot explain the significant decrease in particle electrophoretic mobility. The variations in electrophoretic mobility are well correlated with the effects in the domain of particle rotation. A possible explanation of the observed effects is proposed, based on our previous investigations of the effects in the low-frequency domain. The presented results demonstrate that the important information on the electrokinetic charge distribution is not found in the domain of the alpha-dispersion, but in the domain of particle rotation.     

Dynamic electrophoretic mobility of spherical colloidal particles in a salt-free medium

A theory is proposed for the dynamic electrophoretic mobility mu(omega) of spherical colloidal particles in a salt-free medium containing only counterions in an oscillating electric field of frequency omega. The dynamic mobility depends on the frequency omega of the applied electric field and on the particle volume fraction as well as on the particle surface charge. It is found that as in the case of the static electrophoretic mobility mu(0) in salt-free media, there is a certain critical value of the particle surface charge separating two cases, that is, the low-surface-charge case and the high-surface-charge case (in the latter case the counterion condensation takes place near the particle surface). For the low-surface-charge case, the dynamic mobility agrees with that of a sphere in an electrolyte solution in the limit of very low electrolyte concentrations kappaa-->0 (Hückel's limit), where kappa is the Debye-Hückel parameter and a is the particle radius. For the high-surface-charge case, however, the dynamic mobility becomes constant independent of the particle surface charge, because of the counterion condensation effects. A simple expression for the ratio mu(omega)/mu(0) applicable for all cases is given.     

Protein binding onto surfactant-based synthetic vesicles

Synthetic vesicles were prepared by mixing anionic and cationic surfactants, aqueous sodium dodecylsulfate with didodecyltrimethylammonium or cetyltrimethylammonium bromide. The overall surfactant content and the (anionic/cationic) mole ratios allow one to obtain negatively charged vesicles. In the phase diagram, the vesicular region is located between a solution phase, a lamellar liquid crystalline dispersion, and a precipitate area. Characterization of the vesicles was performed by electrophoretic mobility, NMR, TEM, and DLS and we determined their uni-lamellar character, size, stability, and charge density. Negatively charged vesicular dispersions, made of sodium dodecylsulfate/didodecyltrimethylammonium bromide or sodium dodecylsulfate/cetyltrimethylammonium bromide, were mixed with lysozyme, to form lipoplexes. Depending on the protein/vesicle charge ratio, binding, surface saturation, and lipoplexes flocculation, or precipitation, occurs. The free protein in excess remains in solution, after binding saturation. The systems were investigated by thermodynamic (surface tension and solution calorimetry), DLS, CD, TEM, 1H NMR, transport properties, electrophoretic mobility, and dielectric relaxation. The latter two methods give information on the vesicle charge neutralization by adsorbed protein. Binding is concomitant to modifications in the double layer thickness of vesicles and in the surface charge density of the resulting lipoplexes. This is also confirmed by developing the electrophoretic mobility results in terms of a Langmuir-like adsorption isotherm. Charges in excess with respect to the amount required to neutralize the vesicle surface promote lipoplexes clustering and/or flocculation. Protein-vesicle interactions were observed by DLS, indicating changes in particle size (and in their distribution functions) upon addition of LYSO. According to CD, the bound protein retains its native conformation, at least in the SDS/CTAB vesicular system. In fact, changes in the alpha-helix and beta-sheet conformations are moderate, if any. Calorimetric methods indicate that the maximum heat effect for LYSO binding occurs at charge neutralization. They also indicate that enthalpic are by far the dominant contributions to the system stability. Accordingly, energy effects associated with charge neutralization and double-layer contributions are much higher than counterion exchange and dehydration terms.     

Electrophoretic mobility, zeta potential, and fixed charge density of bovine knee chondrocytes, methyl methacrylate-sulfopropyl methacrylate, polybutylcyanoacrylate, and solid lipid nanoparticles

The electrophoretic mobility and zeta potential of bovine knee chondrocytes (BKCs), methyl methacrylate-sulfopropyl methacrylate (MMA-SPM) nanoparticles (NPs), polybutylcyanoacrylate (PBCA) NPs, and solid lipid nanoparticles (SLNs) were investigated under the influences of Na+, K+, and Ca2+ with various ionic strengths. The fixed charge density in the surface layers of the four biocolloidal particles was estimated from the experimental mobility of capillary electrophoresis with a theory of soft charged colloids. The results revealed that, for a specific cationic species, the absolute values of the electrophoretic mobility, the zeta potential, and the fixed charge density decreased with an increase in ionic strength. For a constant ionic strength, the effect of ionic species on the reduction in the absolute values of the electrophoretic mobility, the zeta potential, and the fixed charge density followed the order Na+>K+>Ca2+ for the negatively charged BKCs, MMA-SPM NPs, and SLNs. The reverse order is true for the positively charged PBCA NPs.     

Electrophoretic mobility of a liquid drop in a salt-free medium

A theory is proposed for the electrophoretic mobility mu of dilute spherical liquid drops of radius a in salt-free media containing only counterions (e.g., nonaqueous media). As in the case of the electrophoretic mobility of rigid particle in salt-free media, there is a certain critical value of the drop surface charge separating two cases, that is, the low-surface-charge case and the high-surface-charge case. For the low-surface-charge case, mu coincides with that of a drop in an electrolyte solution in the limit of very low electrolyte concentrations kappaa-->0 (Hückel's limit), where kappa is the Debye-Hückel parameter. For the high-surface-charge case, however, mu becomes constant independent of the drop surface charge, since the counterion condensation takes place near the drop surface.     

Effect of background electrolyte on the estimation of protein hydrodynamic radius and net charge through capillary zone electrophoresis

Two physicochemical models are proposed for the estimation of both hydrodynamic radius and net charge of a protein when the capillary zone electrophoretic mobility at a given protocol, the set of pK of charged amino acids, and basic data from Protein Data Bank are available. These models also provide a rationale to interpret appropriately the effects of solvent properties on protein hydrodynamic radius and net charge. To illustrate the numerical predictions of these models, experimental data of electrophoretic mobility available in the literature for well-defined protocols are used. Five proteins are considered: lysozyme, staphylococcal nuclease, human carbonic anhydrase, bovine carbonic anhydrase, and human serum albumin. Numerical predictions of protein net charges through these models compare well with the results reported in the literature, including those found asymptotically through protein charge ladder techniques. Model calculations indicate that the hydrodynamic radius is sensitive to changes of the protein net charge and hence it cannot be assumed constant in general. Also, several limitations associated with models for estimating protein net charge and hydrodynamic radius from protein structure, amino acid sequence, and experimental electrophoretic mobility are provided and discussed. These conclusions also show clear requirements for further research.     

Electric migration of α‐hemolysin in supported n‐bilayers: A model for transmembrane protein microelectrophoresis

Proteome analysis involves separating proteins as a preliminary step toward their characterization. This paper reports on the translational migration of a model transmembrane protein (α‐hemolysin) in supported n‐bilayers (n, the number of bilayers, varies from 1 to around 500 bilayers) when an electric field parallel to the membrane plane is applied. The migration changes in direction as the charge on the protein changes its sign. Its electrophoretic mobility is shown to depend on size and charge. The electrophoretic mobility varies as 1/R², with R the equivalent geometric radius of the embedded part of the protein. Measuring mobilities at differing pH in our system enables us to determine the pI and the charge of the protein. Establishing all these variations points to the feasibility of electrophoretic transport of a charged object in this medium and is a first step toward electrophoretic separation of membrane proteins in n‐bilayer systems.