308 - Electrophoretic study of cell surface properties theory and experimental applicability

Polarization of a diffuse soft particle subjected to an alternating current field

The polarization of a diffuse soft particle submerged in an aqueous electrolyte and subjected to a uniform alternating electric field is theoretically analyzed with the standard electrokinetic model (the Poisson-Nernst-Planck equations). The particle consists of a rigid uncharged core and a charged diffuse polyelectrolytic shell (soft layer) permeable to ions and solvent. Our focus is on the impact of the characteristics of the soft layer including the Donnan potential, the soft layer thickness, and the friction coefficient of the soft layer on the dipole coefficient, characterizing the strength of the polarization. Under the limits of thin double layers and thin polyelectrolytic shells, approximate analytical expressions to evaluate the dipole moment coefficients are derived for high-frequency and low-frequency ranges, respectively. The analytical results are compared and agree favorably with those numerically computed by the standard model. Interestingly, we discover that when the double layer is comparable to the soft layer the dipole moment behaves qualitatively differently at different Donnan potentials. When the Donnan potential is small, the dipole moment decreases as the double layer increases. In contrast, at large Donnan potentials, the dipole moment increases with the increase in the double layer. The distinct responses to Donnan potentials are attributed to the impact of the associated double layer on the charge distribution of mobile ions inside the soft layer. The theoretical model provides a fundamental basis for interpreting the polarization of heterogeneous systems, including environmental or biological colloids or microgel particles.

Electrokinetics of a poly(N-isopropylacrylamid-co-carboxyacrylamid) soft thin film: evidence of diffuse segment distribution in the swollen state

Streaming current measurements were performed on poly(N-isopropylacrylamid-co-carboxyacrylamid) (PNiPAAM-co-carboxyAAM) soft thin films over a broad range of pH and salt concentration (pH 2.5-10, 0.1-10 mM KCl) at a constant temperature of 22 °C. The films are negatively charged because of the ionization of the carboxylic acid groups in the repeat unit of the copolymer. For a given salt concentration, the absolute value of the streaming current exhibits an unconventional, nonmonotonous dependence on pH with the presence of a maximum at pH ∼6.4. This maximum is most pronounced at low electrolyte concentration and gradually disappears with increasing salinity. Complementary ellipsometry data further reveal that the average film thickness increases by a factor of ∼2.2 with increasing pH over the whole range of salt concentration examined. The larger the solution salt concentration, the lower the pH value where expansion of the hydrogel layer starts to take place. The dependence of film thickness on pH and electrolyte concentration remarkably follows that obtained for surface conductivity. The streaming current and surface conductivity results could be consistently interpreted on a quantitative basis using the theory we previously derived for the electrokinetics of charged diffuse (heterogeneous) soft thin films complemented here by the derivation of a general expression for the surface conductivity of such systems. In particular, the maximum in streaming current versus pH is unambiguously attributed to the presence of an interphasial gradient in polymer segment density following the heterogeneous expansion of the chains within the film upon swelling with increasing pH. A quantitative inspection of the data further suggests that pK values of ionogenic groups in the film as derived from the streaming current and surface conductivity data differ by ∼0.9 pH unit. Such a difference is attributed to the impact of position-dependent hydrophobicity across the film on the degree of ionization of carboxylic sites.

Primary electroviscous effect in a dilute suspension of soft particles

A theory for the primary electroviscous effect in a dilute suspension of soft particles (i.e., particles coated with an ion-penetrable surface layer of polyelectrolytes) in an electrolyte solution is presented. The general expression for the effective viscosity eta s of the suspension and the primary electroviscous coefficient p, which is further expressed in terms of a function L, is given. On the basis of the general expressions, we derive approximate analytic expressions for eta s and p, which are applicable when the density of the fixed charges distributed within the surface layer is low. Further we obtain a simple approximate analytic expression (without involving numerical integrations) for p applicable for most practical cases. It is found that the function L exhibits a minimum when plotted as a function of kappa a (kappa is the Debye-Hückel parameter and a is the particle core radius), unlike the case of a suspension of hard particles, in which case L decreases as kappa a increases, exhibiting no minimum. The presence of a minimum for the case of a suspension of soft particles is due to the fact that L is proportional to 1/kappa 2 at small kappa a and to kappa 2 at large kappa a. Because of the presence of this minimum, the difference in L between soft and hard particles becomes very large for large kappa a.

Electrophoresis of diffuse soft particles

A theory is presented for the electrophoresis of diffuse soft particles in a steady dc electric field. The particles investigated consist of an uncharged impenetrable core and a charged diffuse polyelectrolytic shell, which is to some extent permeable to ions and solvent molecules. The diffuse character of the shell is defined by a gradual distribution of the density of polymer segments in the interspatial region separating the core from the bulk electrolyte solution. The hydrodynamic impact of the polymer chains on the electrophoretic motion of the particle is accounted for by a distribution of Stokes resistance centers. The numerical treatment of the electrostatics includes the possibility of partial dissociation of the hydrodynamically immobile ionogenic groups distributed throughout the shell as well as specific interaction between those sites with ions from the background electrolyte other than charge-determining ions. Electrophoretic mobilities are computed on the basis of an original numerical scheme allowing rigorous evaluation of the governing transport and electrostatic equations derived following the strategy reported by Ohshima, albeit within the restricted context of a discontinuous chain distribution. Attention is particularly paid to the influence of the type of distribution adopted on the electrophoretic mobility of the particle as a function of its size, charge, degree of permeability, and solution composition. The results are systematically compared with those obtained with a discontinuous representation of the interface. The theory constitutes a basis for interpreting electrophoretic mobilities of heterogeneous systems such as environmental or biological colloids or swollen/deswollen microgel particles.

Electrokinetics of diffuse soft interfaces. 2. Analysis based on the nonlinear Poisson-Boltzmann equation

In a previous study (Langmuir 2004, 20, 10324), the electrokinetic properties of diffuse soft layers were theoretically investigated within the framework of the Debye-Hückel approximation valid in the limit of sufficiently low values for the Donnan potential. In the current paper, the electrokinetics is tackled on the basis of the rigorous nonlinearized Poisson-Boltzmann equation, the numerical evaluation of the electroosmotic velocity profile, and the analytically derived hydrodynamic velocity profile. The results are illustrated and discussed for a diffuse soft interface characterized by a linear gradient for the friction coefficient and the density of hydrodynamically immobile ionogenic groups in the transition region separating the bulk soft layer and the bulk electrolyte solution. In particular, it is shown how the strong asymmetry for the potential distribution, as met for high values of the bulk fixed charge density and/or low electrolyte concentrations, is reflected in the electrokinetic features of the diffuse soft layer. The analysis clearly highlights the shortcomings of the discontinuous approximation by Ohshima and others for the modeling of the friction and electrostatic properties of soft layers exhibiting high Donnan potentials. This is in line with reported electrokinetic measurements of various soft particles and permeable gels at low electrolyte concentrations which fail to match predictions based on Ohshima's theory.

Electrokinetics of diffuse soft interfaces. 1. Limit of low Donnan potentials

The current theoretical approaches to electrokinetics of gels or polyelectrolyte layers are based on the assumption that the position of the very interface between the aqueous medium and the gel phase is well defined. Within this assumption, spatial profiles for the volume fraction of polymer segments (phi), the density of fixed charges in the porous layer (rho fix), and the coefficient modeling the friction to hydrodynamic flow (k) follow a step-function. In reality, the "fuzzy" nature of the charged soft layer is intrinsically incompatible with the concept of a sharp interface and therefore necessarily calls for more detailed spatial representations for phi, rho fix, and k. In this paper, the notion of diffuse interface is introduced. For the sake of illustration, linear spatial distributions for phi and rho fix are considered in the interfacial zone between the bulk of the porous charged layer and the bulk electrolyte solution. The corresponding distribution for k is inferred from the Brinkman equation, which for low phi reduces to Stokes' equation. Linear electrostatics, hydrodynamics, and electroosmosis issues are analytically solved within the context of streaming current and streaming potential of charged surface layers in a thin-layer cell. The hydrodynamic analysis clearly demonstrates the physical incorrectness of the concept of a discrete slip plane for diffuse interfaces. For moderate to low electrolyte concentrations and nanoscale spatial transition of phi from zero (bulk electrolyte) to phi o (bulk gel), the electrokinetic properties of the soft layer as predicted by the theory considerably deviate from those calculated on the basis of the discontinuous approximation by Ohshima.

Membrane electrostatics

In conclusion, charged membrane together with their adjacent electrolyte solution form a thermodynamic and physico-chemical entity. Their surfaces represent an exceptionally complicated interfacial system owing to intrinsic membrane complexity, as well as to the polarity and often large thickness of the interfacial region. Despite this, charged membranes can be described reasonably accurately within the framework of available theoretical models, provided that the latter are chosen on the basis of suitable criteria, which are briefly discussed in Section A. Interion correlations are likely to be important for the regular and/or rigid, thin membrane-solution interfaces. Lateral distribution of the structural membrane charge is seldom and charge distribution perpendicular to the membranes is nearly always electrostatically important. So is the interfacial hydration, which to a large extent determines the properties of the innermost part of the interfacial region, with a thickness of 2-3 nm. Fine structure of the ion double-layer and the interfacial smearing of the structural membrane charge decrease whilst the surface hydration increases the calculated value of the electrostatic membrane potential relative to the result of common Gouy-Chapman approximation. In some cases these effects partly cancel-out; simple electrostatic models are then fairly accurate. Notwithstanding this, it is at present difficult to draw detailed molecular conclusions from a large part of the published data, mainly owing to the lack of really stringent controls or calibrations. Ion binding to the membrane surface is a complicated process which involves charge-charge as well as charge-solvent interactions. Its efficiency normally increases with the ion valency and with the membrane charge density, but it is also strongly dependent on the physico-chemical and thermodynamic state of the membrane. Except in the case of the stereospecific ion binding to a membrane, the relatively easily accessible phosphate and carboxylic groups on lipids and integral membrane proteins are the main cation binding sites. Anions bind preferentially to the amine groups, even on zwitterionic molecules. Membrane structure is apt to change upon ion binding but not always in the same direction: membranes with bound ions can either expand or become more condensed, depending on the final hydrophilicity (polarity) of the membrane surface. The more polar membranes, as a rule, are less tightly packed and more fluid. Diffusive ion flow across a membrane depends on the transmembrane potential and concentration gradients, but also on the coulombic and hydration potentials at the membrane surface.(ABSTRACT TRUNCATED AT 400 WORDS)

Conformation of surface bound polyelectrolytes: I. Implications for cell electrophoresis

We present a self-consistent calculation for a layer of short-chain polyelectrolytes grafted to a planar interface. Individual self-avoiding chain configurations are generated on a tetrahedral lattice. By evaluating the complete ensemble of configurations in the presence of a self-consistent field we determine averages for the equilibrium layer height, segment and charge density profiles. These describe the response of the layer to changes in the surrounding medium, in particular to electrolyte concentration. This self-consistent model of a biological cell, which is known to have an extended layer of charge exterior to the membrane bilayer surface, is applied to the problem of cell electrophoretic mobility. We compare the electrophoretic mobility deduced from the application of this model with that for a constant profile of charge and segments and with the case of a constant segment profile with a plane of charge, usually assumed in the literature. We find that, within the region of concentrations studied here and with the chain lengths used, there is general agreement between the different descriptions.