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.     

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).     

Synthesis and structure of the grafted layer on silicas chemically modified by aminophosphonic acids

The synthesis and properties of three representatives of a new class of chemically modified silicas containing aminophosphonic acids, namely, (N-methyl-N-propylamino)methylenephosphonic,N-propylaminodi(methylenephosphonic), andN-[2-(propylamino)ethyl]-N,N-di(methylenephosphonic acids), covalently grafted on the silica surface are reported. The modified silicas were obtained by the two-step Kabachnik-Fields reaction in high yields. The concentrations of the grafted groups were determined by elemental analysis and pH-titration. The new materials were characterized by IR and³¹P and¹³C high resolution solid state NMR spectroscopy. The hydration of the modified silicas was found to result in a significant change in the structure of the grafted layer and to increase the mobility of the grafted groups. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 12, pp. 2340–2345, December, 1999.     

Electrophoretic motion of a slightly deformed sphere with a nonuniform zeta potential distribution

Electrophoretic motion is analyzed for a rigid, slightly deformed sphere with a nonuniform zeta potential distribution. Hydrodynamics and electrostatics solutions for the deformed sphere with an arbitrary double-layer thickness are determined by using the domain perturbation method. The surface shape and the zeta potential distribution for the deformed sphere are expressed by using the multipole expansion representation. In terms of monopole, dipole, and quadrupole moments of the surface shape and the zeta potential distribution, explicit expressions are obtained for the translational and rotational electrophoretic mobility tensors. The ensemble average for the mobility of the deformed sphere with a uniform orientation distribution is also derived. The utility of the general mobility expression is demonstrated by studying the electrophoretic motion of axisymmetric and ellipsoidal particles. The translational and rotational mobilities of axisymmetric particles are both affected by the monopole, dipole, and quadrupole moments of the zeta potential. For ellipsoidal particles, however, the dipole moment of the zeta potential does not affect the translational mobility, while the rotational mobility depends only on the dipole moment. The mobility of the deformed sphere with either a thick or a thin double layer is also derived.     

Dispersive evaluation and surface chemistry of advanced, multifunctional silica/lignin hybrid biomaterials

Advanced silica/lignin hybrid biomaterials were obtained using hydrated or fumed silicas (Aerosil®200) and Kraft lignin as precursors, which is a cheap and biodegradable natural polymer. To extend the possible range of applications, the silicas were first modified with N-2-(aminoethyl)-3-aminopropyltrimethoxsysilane, and then with Kraft lignin, which had been oxidized with sodium periodate. The SiO₂/lignin hybrids and precursors were characterised by means of determination of their physicochemical and dispersive-morphological properties. The effectiveness of silica binding to lignin was verified by FT-IR spectroscopy. The zeta potential value provides relevant information regarding interactions between colloid particles. Measurement of the zeta potential values enabled an indirect assessment of stability for the studied hybrid systems. Determination of zeta potential and density of surface charge also permitted the quantitative analysis of changes in surface charge, and indirectly confirmed the effectiveness of the proposed method for synthesis of SiO₂/lignin hybrid materials. A particularly attractive feature for practical use is their stability, especially electrokinetic stability. It is expected that silica/lignin hybrids will find a wide range of applications (polymer fillers, biosorbents, electrochemical sensors), as they combine the unique properties of silica with the specific structural features of lignin. This makes these hybrids biomaterials advanced and multifunctional.      

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.     

Structural and energetic characteristics of silicas modified by organosilicon compounds

Silica gels Davisil 633 and 643, and fumed silica Cab-O-Sil HS-5 with grafted 3-aminopropyl dimethylsilyl (APDMS), butyl dimethylsilyl (BDMS), octadecyl dimethylsilyl (ODDMS), and trimethylsilyl (TMS) groups of different concentrations were studied using the nitrogen adsorption method. Changes in the textural and energetic characteristics of modified silicas depend on features of the oxide matrices and grafted OSC.     

Polarization of the Electrical Double Layer. Time Evolution after Application of an Electric Field

Electrophoresis is one of the electrokinetic phenomena most widely investigated, both from a fundamental point of view and as a research tool in academia and industry. However, the dependence between electrophoretic mobility and zeta potential is, in a general case, far from simple, because of the many physical processes involved. In this work, we first describe qualitatively and (in some cases) quantitatively the time behavior of the dipole moment induced in the electrical double layer by an applied electric field. Further, a simple relationship is deduced between the dipole moment and the electrophoretic mobility. Through the analysis of the time dependence of the former, it is possible to resolve the different contributions to the stationary values of the mobility. Three characteristic relaxation times are distinguished in the time evolution of the dipole moment: tau(H) (the time needed for hydrodynamic flows to be established), tau(MW) (time for ionic electromigration to develop), and tau(VD) (after this time, diffusion flows are established in the system, and the double layer polarization is complete). This means that different mechanisms are operating on the double layer for different times after the application of the field, and that computing the mobility at such different times is equivalent to calculating the steady-state electrophoretic mobility under different approximations. A comparison is shown between estimated and computed mobility values as functions of time and of zeta potential, confirming the validity of the asymptotic calculations. Copyright 2000 Academic Press.     

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.     

Electrophoretic mobility of latex particles: effect of particle size and surface structure

The influence of particle size on the electrophoretic mobility of negatively charged latex particles was examined by a comparison between theory and experiment. Theoretical values for the dependence of the mobility on electrolyte concentration were calculated by a modified White–O’Brian model (Hidalgo-Alvarez et al., Adv. Coll. Interf. Sci. 67 (1996) 1) which enables the consistent calculation of the zeta (ζ) potential. For three polystyrene latexes of different size but similar surface charge density the measured mobilities increased with increasing radius for the electrolyte range under consideration. The theoretical calcalations resulted in a qualitatively correct prediction of the experimental data. The experimental comparison of the mobilities of hydrophobic and hydrophilic particles of similar size and surface charge density lead to the conclusion that hydrophilic surfaces lower the electrophoretic mobility. The same theoretical model was able to describe correctly this observed behavior by assuming a greater distance of the plane of shear. The effect of a spatial distribution of the charges was examined by characterizing an electrosterically stabilized latex. Contrary to all standard latices with surface charges this latex didn't show any mobility maximum as a function of electrolyte concentration.     

The characterization of silica microparticles by electrophoretic mobility measurements

Summary Electrophoretic mobility measurements in the pH 2‐10 range are described for several commercial HPLC silica microparticles and a laboratory-produced product. The content of metal impurities for the silicas was also determined by AAS. An acidic/hydrothermal treatment was used to generate a more homogenous surface for some of the silicas. The zero points of charge (zpc) for both a native and a treated silica plus several commercial HPLC silicas were compared. The electrophoretic mobility method may be useful in predicting the utility of certain types of silica supports for chromatographic separations.     

Electrokinetic characterization of superparamagnetic nanoparticle–aptamer conjugates: design of new highly specific probes for miniaturized molecular diagnostics

With the view of designing new nanoparticle (NP)–aptamer conjugates and proving their suitability as biorecognition tools for miniaturized molecular diagnostics, new maghemite–silica core–shell NP–aptamer conjugates were characterized for the first time in terms of grafting rate and colloidal stability under electrophoretic conditions using capillary electrophoresis. After the grafting rate (on the order of six to 50) of the lysozyme-binding aptamer had been estimated, the electrophoretic stability and peak dispersion of the resulting oligonucleotide–NP conjugates were estimated so as to determine the optimal separation conditions in terms of buffer pH, ionic strength and nature, as well as temperature and electric field strength. The effective surface charge density of the NPs was close to zero for pH lower than 5, which led to some aggregation. The NPs were stable in the pH range from 5 to 9, and an increase in electrophoretic mobility was evidenced with increasing pH. Colloidal stability was preserved at physiological pH for both non-grafted NPs and grafted NPs in the 10–100 mM ionic strength range and in the 15–60 °C temperature range. A strong influence of the nature of the buffer counterion on NP electrophoretic mobility and peak dispersion was evidenced, thus indicating some interactions between buffer components and NP–aptamer conjugates. Whereas an electric field effect (50–900 V cm^?1) on NP electrophoretic mobility was evidenced, probably linked to counterion dissociation, temperature seems to have an appreciable effect on the zeta potential and aptamer configuration as well. This information is crucial for estimating the potentialities of such biorecognition tools in electrophoretic systems.     

On the limiting electrophoretic mobility of a highly charged colloidal particle in an electrolyte solution

The electrophoretic mobility of a spherical charged colloidal particle in an electrolyte solution with large kappaa (where kappa= Debye-Hückel parameter and a= particle radius) tends to a nonzero constant value in the limit of high zeta potential. It is demonstrated that this is caused by the fact that counterions condensed near the highly charged particle surface do not contribute to the electrophoretic mobility and only co-ions govern the mobility. A simple method to derive the limiting electrophoretic mobility expression is given. The present method is also applied to cylindrical particles, showing that the leading term of the limiting electrophoretic mobility of a cylindrical particle in a transverse field with large kappaa is the same as that of a spherical particle. The electrophoretic mobility of a cylindrical particle in a tangential field, on the other hand, is proportional to the particle zeta potential and does not exhibit a constant limiting value for high zeta potentials.     

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.     

Electrophoretic mobility of a highly charged colloidal particle in a solution of general electrolytes.

For a highly charged particle in an electrolyte solution, counterions are condensed very near the particle surface. The electrochemical potential of counterions accumulated near the particle surface is thus not affected by the applied electric field, so that the condensed counterions do not contribute to the particle electrophoretic mobility. In the present paper we derive an expression for the electrophoretic mobility mu(infinity) of a highly charged spherical particle of radius a and zeta potential zeta in the limit of very high zeta in a solution of general electrolytes with large ka (where k is the Debye-Hückel parameter) on the basis of our previous theory for the case of symmetrical electrolytes (H. Ohshima, J. Colloid Interface Sci. 263 (2003) 337). It is shown that zeta can formally be expressed as the sum of two components: the co-ion component, zetaco-ion, and the counterion component, zetacounterion (where zeta = zetaco-ion + zetacounterion) and that the limiting electrophoretic mobility mu(infinity) is given by mu(infinity) = epsilonr epsilon0 zetaco-ion(infinity)/eta + 0(1/ka), where zetaco-ion(infinity) is the high zeta-limiting form of zetaco-ion, epsilonr and eta are, respectively, the relative permittivity and viscosity of the solution, and epsilon0 is the permittivity of a vacuum. That is, the particle behaves as if its zeta potential were zetaco-ion(infinity), independent of zeta. For the case of a positively charged particle in an aqueous electrolyte solution at 25 degrees C, the value of zetaco-ion(infinity) is 35.6 mV for 1-1 electrolytes, 46.0 mV for 2-1 electrolytes, and 12.2 mV for 1-2 electrolytes. It is also found that the magnitude of mu(infinity) increases as the valence of co-ions increases, whereas the magnitude of mu(infinity) decreases as the valence of counterions increases.     

Cationic temperature-responsive poly(N-isopropyl acrylamide) graft copolymers: from triggered association to gelation

In this work temperature-triggered association and gel formation within aqueous solutions of a new family of cationic poly( N-isopropyl acrylamide) (PNIPAm) graft copolymers have been investigated. Five copolymers were synthesized using aqueous atom transfer radical polymerization (ATRP) involving a macroinitiator based on quaternarized N, N-dimethylaminoethyl methacrylate units (DMA+). The PDMA+) x - g-(PNIPAmn)y copolymers have x and y values that originate from the macroinitiator; values for n correspond to the PNIPAm arm length. The copolymer solutions exhibited temperature-triggered formation of nanometer-sized aggregates at the cloud point temperature, which was 33-34 degrees C. The aggregates were investigated using variable-temperature turbidity, hydrodynamic diameter, and electrophoretic mobility measurements. The aggregates were clearly evident using SEM and flowerlike or spherical morphologies were observed. Variable-temperature electrophoretic mobility measurements revealed that the zeta potentials of the aggregates increased with DMA+ content. A study of the effect of added NaNO3 showed that electrostatic interactions controlled the size of the aggregates. The concentrated graft copolymer solutions showed temperature-triggered gelation when the copolymer concentrations exceeded 5 wt %, Fluid-to-gel phase diagrams were constructed. It was found that electrostatic interactions also controlled the gelation temperature. A correlation was found between aggregate size and the minimum copolymer concentration needed to form a gel. A mechanism for the temperature-triggered structural changes leading to the formation of aggregates (in dilute solution) or gels (in concentrated solutions) is proposed.     

Modeling the electrophoresis of peptides and proteins: improvements in the "bead method" to include ion relaxation and "finite size effects"

A bead model methodology developed in our lab (Xin et al. J. Phys. Chem. B 2006, 110, 1038) and applicable to modeling the free solution electrophoretic mobility of peptides and proteins is generalized in two significant ways. First, an approximate account is taken of the relaxation effect, which makes the methodology applicable to more highly charged peptides and proteins than was previously possible. Second, a more accurate account is taken of the finite size of the beads making up the model structure. This improvement makes the method applicable at higher salt concentrations and/or to models consisting of larger sized subunits. The relaxation effect is accounted for by correcting "unrelaxed" mobilities on the basis of model size and average electrostatic surface, or zeta potential. Correction factors are estimated using those of spheres with the same hydrodynamic radius and zeta potential as the model structure. The correction factors of spheres are readily determined. The more general methodology is first applied to two sets of peptides (74 different peptides total) varying in size from 2 to 42 amino acids. The sets also cover a wide range of net charges. It is shown that accounting for finite bead size results in a small change in model mobilities under the conditions of the experiments (35 mM monovalent salt). The correction for ion relaxation, however, can be significant for highly charged peptides and improves agreement between model and experimental mobilities. Our correction procedure is also tested by examining the electrophoretic mobility of a particular protein "charge ladder" (Carbeck et al. J. Am. Chem. Soc. 1999, 121, 10,671), where the protein charge is varied over a wide range yet the conformation remains essentially constant. In summary, the effects of ion relaxation can be significant if the absolute electrophoretic mobility of a peptide exceeds approximately 0.20 cm2/(kV s).     

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.     

Transient electrophoresis in a suspension of charged particles with arbitrary electric double layers

The startup of electrophoretic motion in a suspension of spherical colloidal particles, which may be charged with constant zeta potential or constant surface charge density, due to the sudden application of an electric field is analytically examined. The unsteady modified Stokes equation governing the fluid velocity field is solved with unit cell models. Explicit formulas for the transient electrophoretic velocity of the particle in a cell in the Laplace transforms are obtained as functions of relevant parameters. The transient electrophoretic mobility is a monotonic decreasing function of the particle-to-fluid density ratio and in general a decreasing function of the particle volume fraction, but it increases and decreases with a raise in the ratio of the particle radius to the Debye length for the particles with constant zeta potential and constant surface charge density, respectively. On the other hand, the relaxation time in the growth of the electrophoretic mobility increases substantially with an increase in the particle-to-fluid density ratio and with a decrease in the particle volume fraction but is not a sensitive function of the ratio of the particle radius to the Debye length. For specified values of the particle volume fraction and particle-to-fluid density ratio in a suspension, the relaxation times in the growth of the particle mobility in transient electrophoresis and transient sedimentation are equivalent.