Electrokinetic phenomena at grafted polyelectrolyte layers

During the last decades the electrokinetic theory of Smoluchowski (Z. Phys. Chem. 92 (1918) 129) was extended to be applicable for soft surfaces (grafted polyelectrolyte layers (PL), biological and artificial membranes, etc.) by either using the Debye approximation or numerical solutions. In the theory of Ohshima (Colloids Surf. A 103 (1995) 249) the nonlinearized Poisson-Boltzmann (PB) equation for thick and uniform PL is solved analytically and a general hydrodynamic equation is derived in an integral form. These advantages in the theory of Ohshima provided a base for the further development of a generalized electrokinetic theory for soft surfaces. In his theory the final equation for the electroosmotic (electrophoretic) velocity is specified for the case of the complete dissociation of ionic sites within PL. Accordingly, the equation may be used only if the difference between pK and pH is very large. However, it turned out that an analytical solution of the nonlinearized PB equation for thick PL is possible for any degree of dissociation. This was achieved using the approximation of excluded coions if the absolute value of the reduced Donnan potential is larger than 2 and due to the simplification in the case of weak dissociation, when the absolute value of the reduced Donnan potential is less than 2. Combining this generalized double layer (DL) theory for PL and the theory of Ohshima enables to obtain an analytical equation for electroosmosis for the general case of any degree of dissociation. This equation creates for the first time a theoretical base for the interpretation of electrokinetic fingerprinting (EF) for the characterization of soft surfaces.     

Bulk conductivity of soft surface layers: experimental measurement and electrokinetic implications

Conductivity measurements were carried out on a family of polyacrylamide-co-sodium acrylate gels cross-linked with N,N'-methylenebisacrylamide in a homemade electrokinetic cell. The conductivity data allowed the equilibrium Donnan potential difference between the bulk gel and the bulk electrolyte solution to be estimated at various ionic strengths. The data were fit to a simple model assuming full dissociation of functional groups as well as to a more complete model (Dukhin, S. S.; Zimmerman, R.; Werner, C. J. Colloid Interface Sci. 2004, 274, 309) that accounts for the weak electrolyte nature of the acrylate groups fixed within the gel structure. The conductivity of the gel layers was observed to be significantly larger than the conductivity of the bulk electrolyte solutions at low ionic strengths. The increased conductivity reflects the enhanced concentration of ions within the gel structure due to Donnan equilibrium and the mobility of ions within the high water content gel layers. The electrokinetic implications of the bulk conductivity of gel-like soft surface layers are discussed in terms of the influence of the gel conductance on the resulting streaming potential.     

Electrical double layer interactions between dissimilar oxide surfaces with charge regulation and Stern-Grahame layers

Models of surfaces with intrinsic ionisable amphoteric surface sites governed by the dissociation of acid-base potential determining ion species together with the capacity for the adsorption of anion and cations of the supporting electrolyte are required to describe both the results of electrokinetic and titration measurements of inorganic oxides. The Gouy-Chapman-Stern-Grahame (CGSG) model is one such model that has been widely used in the literature. The electrical double layer interaction between two dissimilar CGSG surfaces has been studied by Usui recently [S. Usui, J. Colloid Interface Sci. 280 (2004) 113] where erroneous discontinuities in the slope of the pressure-separation relation were observed. We revisit this calculation and provide a simple general methodology to analyse the electrical double layer interaction between dissimilar ionisable surfaces with ion adsorption.     

Surface potential and shear plane thickness for a treated concrete particulate

Concrete was treated for the removal of chlorides before the zeta potential (mV), zeta, was measured amphoterically to prepare the adsorbent for onward adsorption of silver on it. The Gouy-Chapman theory, which describes the relationship between the potential at any distance (X) from the surface, Psi(x), and the potential at the surface, Psi(0), was applied to determine the shear plane thickness X(S), and to calculate the surface potential Psi(0). The X(S), for a treated concrete particulate was calculated to be 7.0 A. The Psi(0) calculated was equivalent to the measured zeta potential (zeta), Psi(x) at high electrolyte concentrations, where in general the surface potential greatly deviates from the Nernstian response.     

Surface conductivity reveals counterion condensation within grafted polyelectrolyte layers

Surface conductivity (SC) has been demonstrated to be a valuable parameter for the characterization of surface-bound polyelectrolyte layers (PLs). The measurement of the SC in dependence of the pH and solution concentration yields information about the Donnan potential, PsiD, the intrinsic charge, the potential of the PL electrolyte interface, Psi0, the pK of the ionizable groups within the PLs, and the concentration of segments, n. We discuss herein that SC measurements may additionally provide information about counterion condensation. The mobility of the counterions within grafted poly(acrylic acid) (PAA) layers was estimated from the density of COOH groups and SC data to be only 14% of that of free ions (Zimmermann, et al. Langmuir 2005, 21, 5108). In view of this large deviation and the limited sterical constraints within the brushes, we conclude that the number of freely moving counterions is decreased due to counterion condensation. This interpretation agrees well with the measurement of the osmotic pressure for PAA solution (Boisvert, et al. Polymer 2002, 43, 141), which can be exclusively attributed to the remaining mobile counterions of the polyelectrolyte.     

Charging and swelling of cellulose films

Charging and swelling of cellulose in aqueous environments are of highest interest with respect to the performance of cellulose based products and applications. To unravel the interplay between ionization and structural features of the biopolymer hydrogel we compared non-crosslinked and crosslinked cellulose thin films based on a determination of the Donnan potential [S.S. Dukhin, R. Zimmermann, C. Werner, J. Colloid Interface Sci. 274 (2004) 309] from microslit electrokinetic (streaming potential/streaming current) experiments and layer thicknesses from ellipsometry in aqueous electrolyte solutions. The pH dependence of the Donnan potential, reflecting the ionization of carboxylic acid groups within the cellulose films, was found to be significantly different from the related trend of the streaming current which reflects the characteristics of the topmost surface of the layers: While carboxylic acid groups on the surface of the films dissociate as isolated functionalities, the electrostatic interactions of ionized groups within the cellulose layers cause an incomplete dissociation (pK shift) of the carboxylic acid and a layer expansion (swelling) in the alkaline pH range. The system was found to restrict its volume charge density even after structural restrictions (crosslinking) of the layer and at lower ionic strength of the solutions through a further decrease of the degree of dissociation of the carboxylic acid functions. These findings were attributed to the local accumulation of the carboxylic acid groups caused by preferential oxidation of the amorphous regions of the cellulose and to the ordered water structure within the layer.     

Polyelectrolyte adsorption layers studied by streaming potential and particle deposition

Adsorption of a cationic polyelectrolyte, polyallylamine hydrochloride (PAH), having a molecular weight of 70,000 on mica was characterized by the streaming potential method and by deposition of negative polystyrene latex particles. Formation of PAH layers was followed by determining the apparent zeta potential of surface zeta as function of bulk PAH concentration. The zeta potential was calculated from the streaming potential measured in the parallel-plate channel formed by two mica plates precovered by the polyelectrolyte. The experimental data were expressed as the dependence of the reduced zeta potential zeta/zeta0 on the PAH coverage Theta(PAH), calculated using the convective diffusion theory. It was found that for the ionic strength of 10(-2) M, the dependence of zeta/zeta0 on Theta(PAH) can be reflected by the theoretical model formulated previously for surfaces covered by colloid particles. The electrokinetic measurements were complemented by particle deposition experiments on PAH-covered mica surfaces. A direct correlation between the polymer coverage and the initial deposition rate of particles, as well as the jamming coverage, was found. For ThetaPAH > 0.3 the initial deposition rate attained the value predicted from the convective diffusion theory for homogeneous surfaces. The initial deposition rates for surfaces modified by PAH were compared with previous experimental and theoretical results obtained for heterogeneous surfaces formed by preadsorption of colloid particles. It was revealed that negative latex deposition occurred at surfaces exhibiting negative apparent zeta potential, which explained the anomalous deposition of particles observed in previous works. It was suggested that the combined electrokinetic and particle deposition methods can be used for detecting adsorbed polyelectrolytes at surfaces for coverage range of a percent. This enables one to measure bulk polyelectrolyte concentrations at the level of 0.05 ppm.     

Electroosmotic Velocity in Fibrous Porous Media

A theory of electroosmosis in an array of parallel cylindrical fibers of Kozak and Davis (J. Colloid Interface Sci.,112, 403 (1986)), in which the liquid flow is normal to the axes of the cylinders, is developed to derive a simple approximate expression for the electroosmotic velocity for low zeta potentials without involving numerical integration. The relative error is less than 6%.     

Dynamic Light Scattering Based Microelectrophoresis: Main Prospects and Limitations

Microelectrophoresis based on the dynamic light scattering (DLS) effect has been a major tool for assessing and controlling the conditions for stability of colloidal systems. However, both the DLS methods for characterization of the hydrodynamic size of dispersed submicron particles and the theory behind the electrokinetic phenomena are associated with fundamental and practical approximations that limit their sensitivity and information output. Some of these fundamental limitations, including the spherical approximation of DLS measurements and an inability of microelectrophoretic analyses of colloidal systems to detect discrete charges and differ between differently charged particle surfaces due to rotational diffusion and particle orientation averaging, are revisited in this work. Along with that, the main prospects of these two analytical methods are mentioned. A detailed review of the role of zeta potential in processes of biochemical nature is given too. It is argued that although zeta potential has been used as one of the main parameters in controlling the stability of colloidal dispersions, its application potentials are much broader. Manipulating surface charges of interacting species in designing complex soft matter morphologies using the concept of zeta potential, intensively investigated recently, is given as one of the examples. Branching out from the field of colloid chemistry, DLS and zeta potential analyses are now increasingly finding application in drug delivery, biotechnologies, physical chemistry of nanoscale phenomena and other research fields that stand on the frontier of the contemporary science. Coupling the DLS-based microelectrophoretic systems with complementary characterization methods is mentioned as one of the prosperous paths for increasing the information output of these two analytical techniques.     

Influence of the Dukhin and Reynolds numbers on the apparent zeta potential of granular porous media

The Helmholtz-Smoluchowski (HS) equation is widely used to determine the apparent zeta potential of porous materials using the streaming potential method. We present a model able to correct this apparent zeta potential of granular media of the influence of the Dukhin and Reynolds numbers. The Dukhin number represents the ratio between the surface conductivity (mainly occurring in the Stern layer) and the pore water conductivity. The Reynolds number represents the ratio between inertial and viscous forces in the Navier-Stokes equation. We show here that the HS equation can lead to serious errors if it is used to predict the dependence of zeta potential on flow in the inertial laminar flow regime without taking into account these corrections. For indifferent 1:1 electrolytes (such as sodium chloride), we derived two simple scaling laws for the dependence of the streaming potential coupling coefficient (or the apparent zeta potential) on the Dukhin and Reynolds numbers. Our model is compared with a new set of experimental data obtained on glass bead packs saturated with NaCl solutions at different salinities and pH. We find fairly good agreement between the model and these experimental data.     

On the General Expression for the Electrophoretic Mobility of a Soft Particle

Electrokinetic equations for electrophoresis of a soft particle (that is, a hard particle covered with a layer of polyelectrolytes) have been solved previously under the conditions that the net force acting on the soft particle as a whole (the particle core plus the polyelectrolyte layer) must be zero and that the electrical force acting on the polymer segment is balanced with a frictional force exerted by the liquid flow (J. Colloid Interface Sci. 163, 474 (1994)). In the present work we replaced the latter condition by the alternative and more appropriate condition that pressure is continuous at the boundary between the surface layer and the surrounding electrolyte solution to solve the electrokinetic equations and obtained the general mobility expression for the electrophoretic mobility of a spherical soft particle. It is found that the general mobility expression thus obtained reproduces all of the approximate mobility expressions derived previously and, in addition, that the continuous pressure condition leads to the correct limiting behavior of the electrophoretic mobility in the case where the frictional coefficient tends to zero (this behavior cannot be derived from the force balance condition for the polyelectrolyte layer). Copyright 2000 Academic Press.     

Analytical expressions for the electrical potential near planar, cylindrical, and spherical surfaces for symmetric electrolytes

The conjecture of Tuinier (J. Colloid Interface Sci. 258 (2003) 45) for the electrical potentials near a cylindrical surface and near a spherical surface under the conditions of symmetric electrolyte and large scaled radius are derived by solving the corresponding Poisson-Boltzmann equation. The surface charge density-surface potential relations for these surfaces are also derived under the conditions of constant surface potential. We show that the level of surface charge density for planar, cylindrical, and spherical surfaces follows the order spherical surface > cylindrical surface > planar surface.     

Surfactant stabilised colloidal cholesterol

Cholesterol colloids stabilised by Tween 20 (Colloid I), SDS-Et₄ NBr (Colloid II), and CTAB-Nac (Colloid III) were prepared. Moving boundary electrophoresis established Colloid III to be positively charged with a zeta potential of 12.2 mV. Addition of 5 mmol dm^–3 Na₂SO₄ and 0.1 mmol dm^–3 bilirubin dye (Na-salt) decreased the zeta potential to 9.7 mV and 9.5 mV, respectively, by screening the surface charge of the colloidal particles. Higher concentrations of Na₂SO₄ and bilirubin (Na-salt) made making electrophoretic measurements difficult, and such a situation was also faced in the case of Colloid II even without external addition of an electrolyte. Addition of several electrolytes revealed that Colloids II and II were coagulated by the neutralisation of their positive charge, but Colloid I was destabilised by salting-out effect. Measured intrinsic viscosity values and electron microscopic measurements supported overall spherical shape of the colloid particles. Colloid II exibited structural viscosity; higher concentration of NaSO₄ decreased the viscosities of Colloid II and II by electroviscous effect which helped indirect determination of the electrokinetic potential (23.7 mV) of Colloid II.     

Parameter identifiability in application of soft particle electrokinetic theory to determine polymer and polyelectrolyte coating thicknesses on colloids

Soft particle electrokinetic models have been used to determine adsorbed nonionic polymer and polyelectrolyte layer properties on nanoparticles or colloids by fitting electrophoretic mobility data. Ohshima first established the formalism for these models and provided analytical approximations ( Ohshima, H. Adv. Colloid Interface Sci.1995, 62, 189 ). More recently, exact numerical solutions have been developed, which account for polarization and relaxation effects and require fewer assumptions on the particle and soft layer properties. This paper characterizes statistical uncertainty in the polyelectrolyte layer charge density, layer thickness, and permeability (Brinkman screening length) obtained from fitting data to either the analytical or numerical electrokinetic models. Various combinations of particle core and polymer layer properties are investigated to determine the range of systems for which this analysis can provide a solution with reasonably small uncertainty bounds, particularly for layer thickness. Identifiability of layer thickness in the analytical model ranges from poor confidence for cases with thick, highly charged coatings, to good confidence for cases with thin, low-charged coatings. Identifiability is similar for the numerical model, except that sensitivity is improved at very high charge and permeability, where polarization and relaxation effects are significant. For some poorly identifiable cases, parameter reduction can reduce collinearity to improve identifiability. Analysis of experimental data yielded results consistent with expectations from the simulated theoretical cases. Identifiability of layer charge density and permeability is also evaluated. Guidelines are suggested for evaluation of statistical confidence in polymer and polyelectrolyte layer parameters determined by application of the soft particle electrokinetic theory.     

Ionic strength-dependent pK shift in the helix-coil transition of grafted poly(L-glutamic acid) layers analyzed by electrokinetic and ellipsometric measurements

Surface-bound layers of poly(L-glutamic acid) prepared by a recently described "grafting-from" method were analyzed with respect to electrical charging and structural alterations upon variation of pH and concentration of the background electrolyte in aqueous solutions. The microslit electrokinetic setup (MES) was utilized for the combined determination of zeta potential and surface conductivity on the basis of streaming potential and streaming current measurements at polypeptide layers in contact with aqueous electrolyte solutions of varied composition. In situ ellipsometry was applied at similar samples immersed in identical aqueous solutions to investigate the influence of the solution pH on the structure of the polypeptide layers. Zeta potential and Dukhin number versus pH plots revealed the dissociation behavior of the surface-bound polypeptides indicating a significant shift of the pK of their acidic side chains correlating with the concentration of the background electrolyte potassium chloride and the related variation of the Debye screening length. Surface conductivity data pointed at a more expanded structure of the polypeptide layer in the fully dissociated state as an increased ion conductance in this part of the interface was determined. The occurrence of a strong increase of the thickness and a corresponding decrease of the refractive index for the coil state of the layer strongly supports the findings of the electrokinetic measurements. This fully reversible "switching" of the layer structure was attributed to helix-coil transitions within the grafted polypeptides induced by the dissociation of carboxylic acid functions of the polypeptide side chains. The shift of the "switching pH" of the surface-bound poly(L-glutamic acid) layers at varied concentrations of the background electrolyte was interpreted as a result of the pK shift of the carboxylic acid groups of the polypeptide side chains. The observed patterns prove that the electrostatic interactions causing this shift occur within but not between the grafted chains.     

Deposition of colloid particles on protein layers: fibrinogen on mica

Colloid particle deposition was applied to characterize fibrinogen (Fb) monolayers on mica, which were produced by controlled adsorption under diffusion transport. By adjusting the time of adsorption and the bulk Fb concentration, monolayers of desired surface concentration were obtained. The surface concentration of Fb was determined directly by AFM enumeration of single molecules adsorbed over the substrate surface. It was proven that Fb adsorbed irreversibly on mica both at pH 3.5 and at pH 7.4 with the rate governed by bulk transport. The electrokinetic properties of Fb monolayers produced in this way were studied using the streaming potential method. The dependence of the apparent zeta potential of Fb monolayers was determined as a function of the coverage. It was shown that for pH 3.5 the initial negative zeta potential of the mica substrate was converted to positive for Fb coverage exceeding 0.16. On the other hand, for pH 7.4, the zeta potential of a Fb-covered mica remained negative for the entire coverage range. The charge distribution in Fb monolayers was additionally studied using the colloid deposition method, in which negatively and positively charged polystyrene latex particles (ca. 800 nm in diameter) were used. An anomalous deposition of negative latex particles on substrates exhibiting a negative zeta potential was observed. Results of these experiments were quantitatively interpreted in terms of the fluctuation theory assuming that adsorption sites consisted of two and three Fb molecules, for pH 3.5 and 7.4, respectively. These results suggested that for pH 7.4, the distribution of charge on Fb molecules was heterogeneous, characterized by the presence of positive patches, whereas the average zeta potential was negative, equal to -19 mV. The utility of the colloid deposition method for studying Fb monolayers was further demonstrated in deposition experiments involving positive latex particles. It was shown that for a rather broad range of fibrinogen coverage, both the positive and the negative latex particles can adsorb on surfaces covered by Fb, which behaved, therefore, as superadsorbing surfaces. It was also concluded that the colloid deposition method can be used to determine the Fb bulk concentration for the range inaccessible for other methods.     

Numerical calculation of the electrophoretic mobility of a spherical particle in a salt-free medium

By extending an approximate theory of the electrophoretic mobility of dilute spherical colloidal particles in a salt-free medium containing only counterions (H. Ohshima, J. Colloid Interface Sci. 248 (2002) 499--503), a systematic numerical method is given for the calculation of the electrophoretic mobility, which is based on an iteration method. We assume that each sphere is surrounded by a spherical free volume, within which counterions are distributed so that electro-neutrality is satisfied. The electrophoretic mobility is found to be determined mainly by the pressure due to the counterions at the outer surface of the free volume. It is shown how the mobility values deviate from those expected from Hückel's formula for high particle charges or zeta potentials because of the counterion condensation effect.     

Do bacteria have an electric permanent dipole moment?

In the scientific literature in the last 40 years, some data for the permanent dipole moment and the electric polarizability of Escherichia coli can be found [S.P. Stoylov, Colloid Electro-Optics - Theory, Techniques and Application, Academic Press, London, 1991]. In this paper the data based mainly on electro-optic investigation is considered as much as some dipolophoretic (most often called dielectrophoretic) studies. Serious grounds are found to doubt the conclusions made for the electric dipole moments of bacteria by one of the authors of this paper (SPS) and by some other researchers. This concerns both the permanent dipole moment and the electric charge dependent polarizabilities of E. coli. Here, along with the discussion of the old experimental data, new experimental data are shown for a strain of E. coli HB101. The conclusions from the analysis of the old and the new experimental data is that they do not provide correct evidence for the presence of a permanent dipole moment. It seems that all statements for the existence of electric permanent dipole moment in bacteria [S.P. Stoylov, Colloid Electro-Optics - Theory, Techniques and Application, Academic Press, London, 1991; S.P. Stoylov, S. Sokerov, I. Petkanchin, N. Ibroshev, Dokl. AN URSS 180 (1968) 1165; N.A. Tolstoy, A.A. Spartakov, A.A. Trusov, S.A. Schelkunova, Biofizika 11 (1966) 453; V. Morris, B. Jennings, J. Chem. Soc. Faraday Trans. II 71 (1975) 1948; V. Morris, B. Jennings, J. Colloid Interface Sci. 55 (1978) 313; S.P. Stoylov, V.N. Shilov, S.S. Dukhin, S. Sokerov, I. Petkanchin, in: S.S. Dukhin (Ed.), Electro-optics of Colloids, Naukova Dumka, Kiev, 1977 (in Russian).] based on electro-optic studies are result of incorrect interpretation. Therefore, they should be further ignored.     

A method for simultaneously determining the zeta potentials of the channel surface and the tracer particles using microparticle image velocimetry technique

The zeta potentials of channel surfaces and tracer particles are of importance to the design of electrokinetic microfluidic devices, the characterization of channel materials, and the quantification of the microparticle image velocimetry (microPIV) measurement of EOFs. A method is proposed to simultaneously measure the zeta potentials of the channel surface and the tracer particles in aqueous solutions using the microPIV technique. Through the measurement of the steady velocity distributions of the tracer particles in both open- and closed-end rectangular microchannels under the same water chemistry condition, the electrophoretic velocity of the tracer particles and the EOF field of the microchannel are determined using the expressions derived in this study for the velocity distributions of charged tracer particles in the open- and closed-end rectangular microchannels. Thus, the zeta potentials of the tracer particles and the channel surfaces are simultaneously obtained using the least-square method to fit the microPIV measured velocity distribution of the tracer particles. Measurements were carried out with a microPIV system to determine the zeta potentials of the channel wall and the fluorescent tracer particles in deionized water and sodium chloride and boric acid solutions of various concentrations.