Ion hydration co-sphere interactions in the double-layer and ionic solutions

Two-dimensional concentrations of adsorbed ions in double-layers at charged interfaces, especially when appreciable specific adsorption obtains, are equivalent to quite substantial (1–4 M) three-dimensional concentrations in regular electrolyte solutions. Under such conditions, ion-specific Gurney co-sphere overlap interactions give an important contribution to the non-ideal free energy of electrolytes in solution. It is proposed that similar interaction effects arise two-dimensionally in double-layers, giving rise to a contribution to the lateral interaction energy in monolayer arrays of ions. Three types of calculations are described by which these interaction effects can be evaluated. One is applied to some recent data on tetrapropylammonium ion adsorption at Hg, where hydrophobic interactions arise.Related problems concerned with solvent dipole orientation in the inner layer, when appreciable surface concentrations of hydrated ions are present, are referred to. The probable role of field-gradient/quadrupole interactions is noted.     

Diffusiophoresis in a suspension of spherical particles with arbitrary double-layer thickness

The diffusiophoresis in a homogeneous suspension of identical dielectric spheres with an arbitrary thickness of the electric double layers in a solution of a symmetrically charged electrolyte with a constant imposed concentration gradient is analytically studied. The effects of particle interactions (or particle volume fraction) are taken into account by employing a unit cell model, and the overlap of the double layers of adjacent particles is allowed. The electrokinetic equations that govern the ionic concentration distributions, the electrostatic potential profile, and the fluid flow field in the electrolyte solution surrounding the charged sphere in a unit cell are linearized assuming that the system is only slightly distorted from equilibrium. Using a perturbation method, these linearized equations are solved with the surface charge density (or zeta potential) of the particle as the small perturbation parameter. Analytical expressions for the diffusiophoretic velocity of the dielectric sphere in closed form correct to the second order of its surface charge density or zeta potential are obtained from a balance between its electrostatic and hydrodynamic forces. Comparisons of the results of the cell model with different conditions at the outer boundary of the cell are made.     

Transient electrophoresis of spherical particles at low potential and arbitrary double-layer thickness

A theoretical study is presented for the dynamic electrophoretic response of a charged spherical particle in an unbounded electrolyte solution to a step change in the applied electric field. The electric double layer surrounding the particle may have an arbitrary thickness relative to the particle radius. The transient Stokes equations modified with the electrostatic effect which govern the fluid velocity field are linearized by assuming that the system is only slightly distorted from equilibrium. Semianalytical results for the transient electrophoretic mobility of the particle are obtained as a function of relevant parameters by using the Debye-Huckel approximation. The results demonstrate that the electrophoretic mobility of a particle with a constant relative mass density at a specified dimensionless time normalized by its steady-state quantity decreases monotonically with a decrease in the parameter kappaa, where kappa(-1) is the Debye screening length and a is the particle radius. For a given value of kappaa, a heavier particle lags behind a lighter one in the development of the electrophoretic mobility. In the limits of kappaa --> infinity and kappaa = 0, our results reduce to the corresponding analytical solutions available in the literature. The electrophoretic acceleration of the particle is a monotonic decreasing function of the time for any fixed value of kappaa. In practical applications, the effect of the relaxation time for the transient electrophoresis is negligible, regardless of the value of kappaa or the relative mass density of the particle.     

Magnetohydrodynamic effects on a charged colloidal sphere with arbitrary double-layer thickness

An analytical study is presented for the magnetohydrodynamic (MHD) effects on a translating and rotating colloidal sphere in an arbitrary electrolyte solution prescribed with a general flow field and a uniform magnetic field at a steady state. The electric double layer surrounding the charged particle may have an arbitrary thickness relative to the particle radius. Through the use of a simple perturbation method, the Stokes equations modified with an electric force term, including the Lorentz force contribution, are dealt by using a generalized reciprocal theorem. Using the equilibrium double-layer potential distribution from solving the linearized Poisson-Boltzmann equation, we obtain closed-form formulas for the translational and angular velocities of the spherical particle induced by the MHD effects to the leading order. It is found that the MHD effects on the particle movement associated with the translation and rotation of the particle and the ambient fluid are monotonically increasing functions of κa, where κ is the Debye screening parameter and a is the particle radius. Any pure rotational Stokes flow of the electrolyte solution in the presence of the magnetic field exerts no MHD effect on the particle directly in the case of a very thick double layer (κa→0). The MHD effect caused by the pure straining flow of the electrolyte solution can drive the particle to rotate, but it makes no contribution to the translation of the particle.     

Attractive double-layer forces and charge regulation upon interaction between electrografted amine layers and silica

Chitosan (CS) and poly(acrylic acid) (PAA) were crosslinked by an ionic gelation method to form super absorbent polymers (SAPs). CS and PAA form amide bonds between the amino and carboxyl groups. The CS-PAA copolymers were synthetically engineered by varying the feed ratios of the prepolymer units. The copolymer materials possess tunable sorption and mucoadhesive properties with a backbone structure resembling proteinaceous materials. The sorption properties of the copolymers toward methylene blue (MB) in aqueous solution were studied using UV-Vis spectrophotometry at ambient pH and 295 K. The copolymers showed markedly varied interactions with MB, from physisorption- to chemisorption-like behavior, in accordance with their composition, surface area, and pore structure characteristics. The sorption isotherms were evaluated with the Sips model to provide estimates of the sorption properties. The sorbent surface area (271 and 943 m²/g) and the sorption capacity (Q_m = 1.03 and 3.59 mmol/g) were estimated for the CS-PAA copolymer/MB systems in aqueous solution.     

Photoinduced relaxation of surface charge in a dye-polyvinylcarbazole layer

Single-layer and dual-layer xerographic photoreceptors based on polyvinylcarbazole, a novolac resin, and the pyrocatechol violet dye were studied. The single-layer photoreceptors exhibited an order of magnitude higher photosensitivity as compared with their dual-layer counterparts. It was found that the character of conductivity decay in a photoreceptor after positive or negative corona charging of its outer surface depended on the technological conditions of substrate pretreatment.     

Electrical double-layer interaction between oppositely charged dissimilar oxide surfaces with charge regulation and Stern-Grahame layers

The force of double-layer interaction between dissimilar flat oxide surfaces charged oppositely at infinite separation and with Stern-Grahame layers was calculated as a function of the surface separation under the conditions of charge regulation. The interaction force showed a monotonic attraction with respect to the surface separation, lying between constant surface potential and constant surface charge conditions. The variations of surface potentials and surface charge densities of respective double layers were also presented as functions of the surface separation. When the negative diffuse-layer potential at infinite separation changed its sign to positive as a result of specific adsorption of cations on the negatively changed surface, the double-layer interaction force showed a repulsive force barrier followed by an attraction at some particular separation.     

Effect of charged boundary on electrophoresis: Sphere in spherical cavity at arbitrary potential and double-layer thickness

The boundary effect on electrophoresis is investigated by considering a spherical particle at an arbitrary position in a spherical cavity. Our previous analysis is extended to the case where the effect of double-layer polarization can be significant. Also, the effect of a charged boundary, which yields an electroosmotic flow and a pressure gradient, thereby making the problem under consideration more complicated, is investigated. The influences of the level of the surface potential, the thickness of double layer, the relative size of a sphere, and its position in a cavity on the electrophoretic behavior of the sphere are discussed. Some results that are of practical significance are observed. For example, if a positively charged sphere is placed in an uncharged cavity, its mobility may have a local minimum as the thickness of the double layer varies. If an uncharged sphere is placed in a positively charged cavity, the mobility may have a local minimum as the position of the sphere varies. Also, if the size of a sphere is fixed, its mobility may have a local minimum as the size of a cavity varies. These provide useful information for the design of an electrophoresis apparatus.     

ESCA studies of charge transfer interactions in electroactive polymers

X-ray photoelectron spectroscopy (XPS) data suggest that proton modifications of nitrogens in polypyrrole (PPY) give rise to a number of intrinsic redox states analogous to those observed in polyaniline (PAN). The behavior of the corresponding oxidation states in both polymers towards oxidation/reduction, deprotonation/reprotonation or charge transfer (CT) interactions are grossly similar. For the thiophene polymers, such as the poly(2,2′-bithiophene) (PBT) complexes and poly(3-methylthiophene) (P3MT) complexes, XPS results reveals the simultaneous presence of neutral and polarized (or partially charged) species in both carbon and sulfur. The relative amounts of the neutral and polarized species vary in accordance with the oxidation level of the polymer. These results suggest that each dopant anion is associated with a thiophenium ion in the polymer chain. Substantially lower extent of CT is observed in the complexes involving photoconductive substituted polyacetylenes, such as polyphenylacetylene (PPA) and poly[[o-(trimethylsilyl)phenyl] acetylene] or poly(o-Me₃SiPA).     

Fundamental aspects of electrostatic interactions and charge renormalization in electrolyte systems

The consistent inclusion of ion-ion correlations and molecular solvent effects in electrolyte theory can be expressed in a physical formalism, where the particles acquire a renormalized charge density and where they interact electrostatically via a generalized screened Coulomb potential. The latter usually decays for large distances r like a Yukawa function exp(-κr)/r, where 1/κ is the decay length (normally different from the Debye length), but, for smaller r, the screened Coulomb potential is a more complicated function. The resulting electrostatic theory, “Yukawa electrostatics”, differs in many important aspects from ordinary (unscreened) Coulomb electrostatics. In the present paper, we give illustrations and explanations of some important differences between Coulomb and Yukawa electrostatics. The effective “Yukawa charge” of a particle differs from the ordinary Coulombic charge. Furthermore, contributions from multipoles of all orders contribute, in general, to the leading asymptotic term in the potential for large r, which decays like exp(-κr)/r. Thus, the electrostatic potential from, for example, an electroneutral molecule with an internal charge distribution has generally the same range as the potential from an ion. Some implications of these facts are pointed out. The presentation is based on exact statistical mechanical analysis where all particles are treated on the same fundamental level, but the main focus lies on physical consequences and interpretations of the theory. The text was submitted by the author in English.     

Time-domain ab initio study of charge relaxation and recombination in dye-sensitized TiO2

In order to investigate the electron dynamics at the alizarin/I2-/TiO2 interface this study uses a novel state-of-the-art quantum-classical approach that combines time-dependent density functional theory with surface hopping in the Kohn-Sham basis. Representing the dye-sensitized semiconductor Gr?tzel cell with the I-/I3- mediator, the system addresses the problems of an organic/inorganic, molecule/bulk interface that are commonly encountered in molecular electronics, photovoltaics, and photoelectrochemistry. The processes studied include the relaxation of the injected electron inside the TiO2 conduction band (CB), the back electron transfer (ET) from TiO2 to alizarin, the ET from the surface to the electrolyte, and the regeneration of the neutral chromophore by ET from the electrolyte to alizarin. Developing a theoretical understanding of these processes is crucial for improving solar cell design and optimizing photovoltaic current and voltage. The simulations carried out for the entire system that contains many electronic states reproduce the experimental time scales and provide detailed insights into the ET dynamics. In particular, they demonstrate the differences between the optimized geometric and electronic structure of the system at 0 K and the experimentally relevant structure at ambient temperature. The relaxation of the injected electron inside the TiO2 CB, which affects the solar cell voltage, is shown to occur on a 100 fs time scale and occurs simultaneously with the electron delocalization into the semiconductor bulk. The transfer of the electron trapped at the surface to the ground state of alizarin proceeds on a 1 ps time scale and is facilitated by vibrational modes localized on alizarin. If the electrolyte mediator is capable of approaching the semiconductor surface, it can form a stable complex and short-circuit the cell by accepting the photoexcited electron on a subpicosecond time scale. The ET from TiO2 to both alizarin and the electrolyte diminishes the solar cell current. Finally, the simulations show that the electrolyte can efficiently regenerate the neutral chromophore. This is true even though the two species do not form a chemical bond and, therefore, the electronic coupling between them is weaker than in the TiO2-chromophore and TiO2-electrolyte donor-acceptor pairs. The chromophore-electrolyte coupling can occur both directly through space and indirectly through bonding to the semiconductor surface. The ET events involving the electrolyte are promoted primarily by the electrolyte vibrational modes.     

Electrophoresis of a colloidal sphere in a spherical cavity with arbitrary zeta potential distributions and arbitrary double-layer thickness

The electrophoretic motion of a dielectric sphere situated at the center of a spherical cavity with an arbitrary thickness of the electric double layers adjacent to the particle and cavity surfaces is analyzed at the quasisteady state when the zeta potentials associated with the solid surfaces are arbitrarily nonuniform. Through the use of the multipole expansions of the zeta potentials and the linearized Poisson-Boltzmann equation, the equilibrium double-layer potential distribution and its perturbation caused by the applied electric field are separately solved. The modified Stokes equations governing the fluid velocity field are dealt with using a generalized reciprocal theorem, and explicit formulas for the electrophoretic and angular velocities of the particle valid for all values of the particle-to-cavity size ratio are obtained. To apply these formulas, one only has to calculate the monopole, dipole, and quadrupole moments of the zeta potential distributions at the particle and cavity surfaces. In some limiting cases, our result reduces to the analytical solutions available in the literature. In general, the boundary effect on the electrophoretic motion of the particle is a qualitatively and quantitatively sensible function of the thickness of the electric double layers relative to the radius of the cavity.     

Electrostatic relaxation and hydrodynamic interactions for self-diffusion of ions in electrolyte solutions

The concentration dependence of self-diffusion of ions in solutions at large concentrations has remained an interesting yet unsolved problem. Here we develop a self-consistent microscopic approach based on the ideas of mode-coupling theory. It allows us to calculate both contributions which influence the friction of a moving ion: the ion atmosphere relaxation and hydrodynamic interactions. The resulting theory provides an excellent agreement with known experimental results over a wide concentration range. Interestingly, the mode-coupling self-consistent calculation of friction reveal a nonlinear coupling between the hydrodynamic interactions and the ion atmosphere relaxation which enhances ion diffusion by reducing friction, particularly at intermediate ion concentrations. This rather striking result has its origin in the similar time scales of the relaxation of the ion atmosphere relaxation and the hydrodynamic term, which are essentially given by the Debye relaxation time. The results are also in agreement with computer simulations, with and without hydrodynamic interactions.     

Length-scale dependent relaxation shear modulus and viscoelastic hydrodynamic interactions in polymer liquids

A quantitative theory of hydrodynamic interactions in unentangled polymer melts and concentrated solutions is presented. The study is focussed on the pre-Rouse transient time regimes (t < τ(R), the Rouse relaxation time) where the hydrodynamic response is governed mainly by the viscoelastic effects. It is shown that transient viscoelastic hydrodynamic interactions are not suppressed (screened) at large distances and are virtually independent of polymer molecular mass. A number of transient regimes of unusual and qualitatively different behavior of isotropic and anisotropic hydrodynamic response functions are elucidated. The regimes are characterized in terms of two main length-scale dependent characteristic times: momentum spreading time τ(i) ∝ r(4∕3) and viscoelastic time τ(?) ∝ r(4). It is shown that for t > τ(i) the viscoelastic hydrodynamic interactions can be described in terms of the time or length scale dependent effective viscosity which, for t < τ(R) and/or for r < R(coil), turns out to be much lower than the macroscopic "polymer" viscosity η(m). The theory also involves a quantitative analysis of the length-scale dependent stress relaxation in polymer melts. The general predictions for hydrodynamic interactions in thermostated systems with Langevin friction are obtained as well.     

Electron-phonon interactions and intra- and intermolecular charge mobility in the monocations of annulenes

Possible electron pairing in pi-conjugated positively charged annulenes such as (CH)(18) (18an) and (CH)(30) (30an) is studied and compared with that in the positively charged acenes. The total electron-phonon coupling constants in the monocations (l(HOMO)) for 18an and 30an are estimated. The E(2g) modes of 1611 and 1201 cm(-1) most strongly couple to the highest occupied molecular orbitals (HOMO) in 18an and 30an, respectively. The l(HOMO) values for annulenes are larger than those for acenes. The phase pattern difference between the HOMO of acenes localized on the edge part of carbon atoms and the delocalized HOMO of annulenes is the main reason for the calculated results. In view of the calculated results of the l(HOMO) values, intramolecular electron mobility (sigma(intra,HOMO)), and the reorganization energies (RE(HOMO)) in the positively charged molecules, the monocations of annulenes cannot easily become good conductors compared with the monocations of acenes, but the condition of the attractive electron-electron interactions is realized more easily in the monocations of annulenes than in the monocations of acenes. The hypothetical intramolecular supercurrent originating from both intramolecular and intermolecular vibrations in the monocations of annulenes and acenes in a case where the distance between two adjacent molecules is too large for the molecular crystal to become normal metallic state, is also discussed.     

Nonmonotoic fluctuation-induced interactions between dielectric slabs carrying charge disorder

We investigate the effect of monopolar charge disorder on the classical fluctuation-induced interactions between randomly charged net-neutral dielectric slabs and discuss various generalizations of recent results [A. Naji et al., Phys. Rev. Lett. 104, 060601 (2010)] to highly inhomogeneous dielectric systems with and without statistical disorder correlations. We shall focus on the specific case of two generally dissimilar plane-parallel slabs, which interact across vacuum or an arbitrary intervening dielectric medium. Monopolar charge disorder is considered to be present on the bounding surfaces and/or in the bulk of the slabs, may be in general quenched or annealed and may possess a finite lateral correlation length reflecting possible "patchiness" of the random charge distribution. In the case of quenched disorder, the bulk disorder is shown to give rise to an additive long-range contribution to the total force, which decays as the inverse distance between the slabs and may be attractive or repulsive depending on the dielectric constants of the slabs. By contrast, the force induced by annealed disorder in general combines with the underlying van der Waals forces in a nonadditive fashion, and the net force decays as an inverse cube law at large separations. We show, however, that in the case of two dissimilar slabs, the net effect due to the interplay between the disorder-induced and the pure van der Waals interactions can lead to a variety of unusual nonmonotonic interaction profiles between the dielectric slabs. In particular, when the intervening medium has a larger dielectric constant than the two slabs, we find that the net interaction can become repulsive and exhibit a potential barrier, while the underlying van der Waals force is attractive. On the contrary, when the intervening medium has a dielectric constant between that of the two slabs, the net interaction can become attractive and exhibit a free energy minimum, while the pure van der Waals force is repulsive. Therefore, the charge disorder, if present, can drastically alter the effective interaction between net-neutral objects.