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.     

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.     

Donnan effects in the steady-state diffusion of metal ions through charged thin films

The steady-state diffusion of metals ions through thin films with fixed charged groups was investigated using diffusive gradients in thin films (DGT) measurements. Copolymers of acrylamide and sodium acrylate cross-linked with N,N'-methylenebisacrylamide were used as diffusive gels. The rate of diffusion of cadmium ions through the gels was measured by determining the mass of cadmium bound to a backing chelex resin after a known deployment time. Variation of the ionic strength as well as the fixed charge density and the thickness of the gel layer allowed evaluation of the impact of the Donnan partitioning and the diffusion layer in solution on the observed steady-state flux of ions through the layer. The results underscore that, as the Donnan partitioning increases, the impact of the diffusion layer in solution becomes more significant. At modest Donnan potentials, Donnan partitioning controls the net flux of metal ions, whereas at conditions of increasing Donnan potential, i.e., at decreasing ionic strength, the flux is increasingly limited by diffusion in solution. An analytical expression is developed to describe the influence of Donnan partitioning on the observed steady-state flux of metal ions.     

Protein diffusion in charged polyacrylamide gels. Visualization and analysis

Protein diffusion in anionic, cross-linked polyacrylamide-based gels supported in fused-silica capillaries was characterized by a direct visualization method. Microphotography was used to obtain transient protein concentration profiles in these gels using cytochrome c as a probe molecule. Gels based on acrylamido-methylpropane sulfonic acid with 2.5-10% N,N'-methylene-bisacrylamide as a cross-linker and with a total polymer concentration of 0.21 g/cm3 yielded diffuse protein concentration profiles which were quantitatively consistent with a Fickian diffusion model. An analytical method was developed to calculate the diffusivity as a function of protein concentration in the gel from the experimental profiles. The diffusivity was found to assume values in the range 2.5-5.5x10(-8) cm2/s and varied somewhat with the protein concentration in the gel. The effects of some of the polymer properties, such as cross-link density, polymer concentration and charge, were also investigated for a limited range of conditions to derive qualitative trends. Results showed that the transport rates increased with a decrease in the cross-link density, were extremely reduced when the polymer concentration was doubled, and were slightly increased when the charge density was decreased by half by polymerizing a 1:1 mixture of acrylamide and acrylamido-methylpropane sulfonic acid monomers.     

Molecular thermodynamics for swelling of a mesoscopic ionomer gel in 1 : 1 salt solutions

For a microphase-separated diblock copolymer ionic gel swollen in salt solution, a molecular-thermodynamic model is based on the self-consistent field theory in the limit of strongly segregated copolymer subchains. The geometry of microdomains is described using the Milner generic wedge construction neglecting the packing frustration. A geometry-dependent generalized analytical solution for the linearized Poisson-Boltzmann equation is obtained. This generalized solution not only reduces to those known previously for planar, cylindrical and spherical geometries, but is also applicable to saddle-like structures. Thermodynamic functions are expressed analytically for gels of lamellar, bicontinuous, cylindrical and spherical morphologies. Molecules are characterized by chain composition, length, rigidity, degree of ionization, and by effective polymer-polymer and polymer-solvent interaction parameters. The model predicts equilibrium solvent uptakes and the equilibrium microdomain spacing for gels swollen in salt solutions. Results are given for details of the gel structure: distribution of mobile ions and polymer segments, and the electric potential across microdomains. Apart from effects obtained by coupling the classical Flory-Rehner theory with Donnan equilibria, viz. increased swelling with polyelectrolyte charge and shrinking of gel upon addition of salt, the model predicts the effects of microphase morphology on swelling.     

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.     

Dynamic scaling of polymer gels comprising nanoparticles

We present dynamic light scattering (DLS) measurements of soft poly(methyl-methacrylate) (PMMA) and polyacrylamide (PA) polymer gels prepared with trapped bodies (latex spheres or magnetic nanoparticles). We show that the anomalous diffusivity of the trapped particles can be analyzed in terms of a fractal Gaussian network gel model for the entire time range probed by DLS technique. This model is a generalization of the Rouse model for linear chains extended for structures with power law network connectivity scaling, which includes both percolating and uniform bulk gel limits. For a dilute dispersion of strongly scattering particles trapped in a gel, the scattered electric field correlation function at small wavevector ideally probes self-diffusion of gel portions imprisoning the particles. Our results show that the time-dependent diffusion coefficients calculated from the correlation functions change from a free diffusion regime at short times to an anomalous subdiffusive regime at long times (increasingly arrested displacement). The characteristic time of transition between these regimes depends on scattering vector as approximately q(-2), while the time decay power exponent tends to the value expected for a bulk network at small q. The diffusion curves for all scattering vectors and all samples were scaled to a single master curve.     

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.     

The pH inside a swollen polyelectrolyte gel: poly(N-vinylimidazole)

The pH inside a dissolved polyelectrolyte coil or a swollen ionic polymer network is not accessible to direct measurement. It is here calculated through a simple model, based on Donnan equilibrium, counterion condensation (for charge density exceeding the critical value), and balance of mobile ions, without any assumption on the pKa of the ionizable groups. The data needed for the calculation with this model are polymer concentration, pH value in the initial solution, and pH value in the bath at equilibrium. All three can be determined experimentally by a batch method where the polymer is immersed in a different pot for each starting pH. The model is applied to a sample system, namely, chemically cross-linked poly(N-vinylimidazole) immersed in acidic baths of different pH values. The imidazole units are basic and become protonated by the acid, thus changing the pH of the initial bath. The model shows how the pH developed inside the swollen gel is several units higher than the pH of the bath at equilibrium, both with or without the correction for counterion condensation. Consequently, when the pKa of the polyelectrolyte is determined in the usual way (with the pH measured in the external bath), it gives an apparent value that is several units below the pKa determined from the actual pH inside the swollen gel at equilibrium. The inclusion of the counterion condensation decreases very slightly the polymer basicity. Surface effects and intramolecular association between protonated and unprotonated imidazole rings are discussed to explain the pKa behavior in the limit of low degree of ionization.     

Free isotropic-nematic interfaces in fluids of charged platelike colloids

Bulk properties and free interfaces of mixtures of charged platelike colloids and salt are studied within the density-functional theory. The particles are modeled by hard cuboids with their edges constrained to be parallel to the Cartesian axes corresponding to the Zwanzig model. The charges of the particles are concentrated in their center. The density functional is derived by functional integration of an extension of the Debye-Hückel pair distribution function with respect to the interaction potential. For sufficiently small macroion charges, the bulk phase diagrams exhibit one isotropic and one nematic phase separated by a first-order phase transition. With increasing platelet charge, the isotropic and nematic binodals are shifted to higher densities. The Donnan potential between the coexisting isotropic and nematic phases is inferred from bulk structure calculations. Nonmonotonic density and nematic order parameter profiles are found at a free interface interpolating between the coexisting isotropic and nematic bulk phases. Moreover, electrically charged layers form at the free interface leading to monotonically varying electrostatic potential profiles. Both the widths of the free interfaces and the bulk correlation lengths are approximately given by the Debye length. For fixed salt density, the interfacial tension decreases upon increasing the macroion charge.     

Equilibrium distribution of permeants in polyelectrolyte microcapsules filled with negatively charged polyelectrolyte: the influence of ionic strength and solvent polarity

The effects of ionic strength and solvent polarity on the equilibrium distribution of fluorescein (FL) and FITC-dextran between the interior of polyelectrolyte multilayer microcapsules filled with negatively charged strong polyelectrolyte and the bulk solution were systematically investigated. A negatively charged strong polyelectrolyte, poly(styrene sulfonate) (PSS), used for CaCO3 core fabrication, was entrapped inside the capsules. Due to the semipermeability of the capsule wall, a Donnan equilibrium between the inner solution within the capsules and the bulk solution was created. The equilibrium distribution of the negatively charged permeants was investigated by means of confocal laser scanning microscopy as a function of ionic strength and solvent polarity. The equilibrium distribution of the negatively charged permeants could be tuned by increasing the bulk ionic strength to decrease the Donnan potential. Decreasing the solvent polarity also could enhance the permeation of FL, which induces a sudden increase of permeation when the ethanol volume fraction was higher than 0.7. This is mainly attributed to the precipitation of PSS. A theoretical model combining the Donnan equilibrium and Manning counterion condensation was employed to discuss the results.     

染料敏化太阳电池用聚合物电解质

综述了本研究小组近年来用于染料敏化太阳电池中聚合物电解质的研究概况.设计合成了几类性能优良的聚合物电解质,较好地改进了液体电解质染料敏化太阳电池(DSSC)的使用稳定性,研究结果具有实际应用的价值,并提出了此领域研究今后的发展方向.     

Phase behaviors of partially ionized hydrogels in aqueous salt solutions: Applicability of the modified double‐lattice model

We investigated the effect of charge densities of the gel network and ionic strength of solution on swelling behaviors of ionized gels. We used the modified double‐lattice model, Flory–Erman's elastic model, and the ideal Donnan theory to describe swelling behaviors of the electrolyte bounded hydrogels. Energy parameters (?/k, δ?/k) were obtained from fitting liquid–liquid equilibria data of the linear poly‐N‐isopropylacrylamide/water system and two adjustable model parameters obtained from a nonelectrolyte hydrogel system. Calculated values agreed with experimental data for the given systems. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2333–2338, 2002     

Consequences of the nanoporosity of cellulosic fibers on their streaming potential and their interactions with cationic polyelectrolytes

Electrokinetic tests, based on the streaming potential method, were used to elucidate interactions between cationic polyelectrolytes and cellulosic fibers and to reveal aspects of fibers’ nanoporosity. The fibrillated and nanoporous nature of bleached kraft fibers gave rise to time-dependent changes in streaming potential, following treatment of the wetted fibers with poly-diallyldimethylammonium chloride. Electrokinetic test results were consistent with an expected longer time required for higher-mass polyelectrolytes to diffuse into pore spaces, compared to lower-mass polyelectrolytes. Further evidence of the relative inability of polyelectrolyte molecules to diffuse into the pores of cellulose was obtained by switching back and forth between high and low ionic strength conditions during repeated measurement of streaming potential, after the fibers had been treated with a moderate amount of cationic polymer. By changing the concentration of sodium sulfate it was possible to switch the sign of streaming potential repeatedly from positive to negative and back again. Such results imply that a continuous path for liquid flow exists either in a fibrillar layer or within the cell walls. The same concepts also helped to explain the dosages of high-charge cationic polymer needed to achieve maximum dewatering rates, as well as the results of retention experiments using positively and negatively charged microcrystalline cellulose particles.     

Determination of amino acids, vitamins, and drug substances in aqueous solutions using new potentiometric sensors with Donnan potential as analytical signal

Basic principles of a new potentiometric sensor are considered. Its analytical signal is the Donnan potential at the ion-exchange polymer/studied solution of electrolyte interface. Assessments of potential drops at individual interfaces are presented, same as estimates of diffusion potentials in the electrochemical circuit for measurement of the sensor response. It is shown that the overall contribution of the values of all potentials to EMF of the electrochemical circuit, except for the Donnan potential, at the ion-exchange polymer/studied solution interface are negligibly low as compared to the experimental values of the circuit EMF in the studied systems. Certain regularities of the Donnan potential formation are studied in the systems with the polymers of different structure and solutions containing inorganic ions and organic electrolytes in different ionic forms. The possibility is shown of using a sensor with such an analytical signal as the Donnan potential for assay of amino acids, vitamins, and drug substances in aqueous solutions. The sensor was used as a selective electrode for determination of lysine in aqueous solutions with neutral amino acids in the range of pH 5.0–7.0 and glycine in aqueous alkali solutions in the range of pH 9.00–11.00. The developed sensor is introduced as a cross-sensitive electrode into the array of multisensor systems for multicomponent quantitative analysis of the lysine monohydrochloride, thiamine chloride, novocaine hydrochloride, lidocaine hydrochloride solutions containing potassium and sodium chlorides. The measurement error of electrolytes in aqueous solutions did not exceed 10%.     

A simplified molecular-thermodynamic model of a microphase-separated ionic gel swollen in salt solution

A molecular-thermodynamic model [A.I. Victorov, C.J. Radke, J.M. Prausnitz, Mol. Phys., 2004, submitted for publication] of diblock copolymer ionic gels swollen in brine is simplified by deriving asymptotic expressions for electrostatic terms. This model derived recently from the self-consistent field theory in the limit of strong segregation gives thermodynamic functions for gels of lamellar, bicontinuous, cylindrical and spherical morphologies and details the gel structure including equilibrium microdomain spacing, distribution of mobile ions, polymer segments, and the electric potential across the microdomains. The model reflects the copolymer chain composition, length, rigidity, ionization degree and the effective polymer–polymer and polymer–solvent interactions. Several asymptotic regimes are considered that lead to simple formulae for the solvent chemical potential. Applicability of asymptotic relations is tested. Equilibrium uptakes of salt are calculated for gels of varying ionic charge over a wide range of solution salinity.     

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.     

Aqueous dispersions of colloidal poly(3-hexylthiophene) gel particles with high internal porosity

This work outlines the development of nano-porous, sub-micron poly(3-hexylthiophene) (P3HT) gel particles as solution-processable inks for applications in polymer solar cells. These dispersions are produced by emulsifying bulk P3HT organogels into water containing surfactant. The optical characteristics and stability of the resulting gel particles are assessed and their structure characterized. The P3HT within the gel particles is shown to retain its crystallinity with no evidence of doping. The gel particles are shown to be stable against aggregation due to the presence of surfactant at the oil/water interface. The fracture of the gel network during emulsification produces a bimodal distribution of particles that increase in size with increasing P3HT concentration in the 'parent' organogel. Small Angle Neutron Scattering measurements show that the particles maintain the structure of the bulk gels with high specific surface area. Spray-coating the gel particle dispersions produces uniform thin-films, which have been used to fabricate polymer/fullerene solar cells with a fully spray-coated active layer.     

一种四臂聚苯乙烯凝胶的激光光散射研究

采用原子转移自由基方法(ATRP)合成窄分布的末端基为巯基的四臂星型聚苯乙烯(4-PS-SH).巯基容易被空气中的氧气氧化生成二硫键,会引起四臂星型聚苯乙烯分子间交联.利用激光光散射研究了四臂聚苯乙烯在亚浓溶液中氧化交联生成大的胶束进而生成宏观化学凝胶的过程.静态激光光散射测量结果表明四臂聚苯乙烯亚浓溶液以及凝胶样品的时间平均散射光强不随测量位置的变化而涨落,说明此凝胶是结构均一的化学凝胶.动态光散射结果表明在四臂聚苯乙烯亚浓溶液氧化生成凝胶的过程中,动态强度-强度时间相关函数的慢运动衰减的贡献最初随着氧化时间的增加逐渐增强,当氧化反应进行到一定程度时慢运动的贡献又逐渐减弱,最终慢运动消失.生成的化学凝胶的相关函数与最初亚浓溶液的相关函数几乎重合.静态和动态激光光散射结果表明生成的四臂聚苯乙烯凝胶是结构均匀的化学凝胶.