Effective multipoles and Yukawa electrostatics in dressed molecule theory

In this paper we derive the multipolar expansion of the screened Coulomb potential in electrolyte solutions with molecular solvent. The solute and solvent molecules can have arbitrary sizes, shapes, and internal charge distributions. We use the exact statistical mechanical definition of renormalized charge distributions coming from "dressed molecule theory" to determine the effective multipoles of a molecule immersed in an electrolyte. The effects of many-body correlations are fully included in our formally exact theory. We restrict ourselves to sufficiently dilute solutions so the screened Coulomb potential decays for large distances like a Yukawa function, exp(-kappa r)/r, where r is the distance and 1/kappa is the decay length (it is normally different from the Debye length). The resulting "Yukawa electrostatics" differ in many respects from ordinary, unscreened electrostatics. The "Yukawa charge" of a molecule (the lowest order moment in the multipolar expansion) is in general not equal to its Coulombic charge and it is not the integral of the renormalized charge distribution of the molecule. Moreover, as shown in this paper, the multipolar expansion of the Yukawa potential does not correspond, contrary to the case of the Coulomb potential, to its asymptotic expansion for large r. As a consequence, the charge term in the multipolar expansion is not the leading term in the asymptotic expansion. Instead, for large r values, multipoles of all orders contribute to the leading asymptotic term. Thus, the electrostatic potential from, for example, an electroneutral solvent molecule in an electrolyte solution has generally the same range as that from an ion. The proper asymptotic expansion for electrostatic interactions in electrolytes is derived. It is briefly shown how the multipole expansion formalism can also be applied in the Poisson-Boltzmann approximation for primitive model electrolytes.     

Effect of surface hydrophobicity on the adhesion of S. cerevisiae onto modified surfaces by poly(styrene-ran-sulfonic acid) random copolymers

The hydrophobicity of solid surfaces has been regarded as a controlling factor in microbial adhesion phenomena. In this study, the surface hydrophobicity was modified by coating with a poly(styrene-ran-sulfonic acid) random copolymer (PS-x-SA, charge density (x): 0-15.3%), and the adhesion rate, J0, of S. cerevisiae performed with a direct observation technique. The results indicated that the degree of sulfonation of PS-x-SA greatly influenced the hydrophobicity of substrates and the adhesion of yeast cells. The J0 of PS-x-SA substrates were gradually decreased as increasing charge density. The interactions between cells and substrates explained by the XDLVO theory, predicted that the decrease of J0 as increasing charge density was not due to the increase of electric double layer repulsion, but mainly due to the hydrophobic acid-base interactions. Also, it predicted that microbial adhesions of PS-x-SA were mostly reversible, while some of PS and PS-5.1-SA adhered cells were hardly removed. Based on these results, XDLVO theory was effective for predicting adhesion phenomena of S. cerevisiae onto the PS-x-SA-coated substrates.     

Influence of atomistic physics on electro-osmotic flow: an analysis based on density functional theory

Molecular density profiles and charge distributions determined by density functional theory (DFT) are used in conjunction with the continuum Navier-Stokes equations to compute electro-osmotic flows in nanoscale channels. The ion species of the electrolyte are represented as centrally charged hard spheres, and the solvent is treated as a dense fluid of neutral hard spheres having a uniform dielectric constant. The model explicitly accounts for Lennard-Jones interactions among fluid and wall molecules, hard sphere repulsions, and short range electrical interactions, as well as long range Coulombic interactions. Only the last of these interactions is included in classical Poisson-Boltzmann (PB) modeling of the electric field. Although the proposed DFT approach is quite general, the sample calculations presented here are limited to symmetric monovalent electrolytes. For a prescribed surface charge, this DFT model predicts larger counterion concentrations near charged channel walls, relative to classical PB modeling, and hence smaller concentrations in the channel center. This shifting of counterions toward the walls reduces the effective thickness of the Debye layer and reduces electro-osmotic velocities as compared to classical PB modeling. Zeta potentials and fluid speeds computed by the DFT model are as much as two or three times smaller than corresponding PB results. This disparity generally increases with increasing electrolyte concentration, increasing surface charge density and decreasing channel width. The DFT results are found to be comparable to those obtained by molecular dynamics simulation, but require considerably less computing time.     

Experimental and theoretical evidence of overcharging of calcium silicate hydrate

Electrokinetic measurements such as electrophoresis may show an inversion of the effective surface charge of colloidal particle called overcharging. This phenomenon has been studied by various theoretical approaches but up to now very few attempts of confrontation between theory and experiment have been conducted. In this work we report electrophoretic measurements as well as Monte Carlo simulations of the electrokinetic potential for the surface of calcium silicate hydrate (CSH), which is the major constituent of hydrated cement. In the simulations, the surface charge of CSH nanoparticles in equilibrium with the ionic solution is determined by a single site characteristic and electrostatic interactions between all explicit charges at the surface and in the electric double layer. We will show that ordinary electrostatic interactions are enough to describe all experimental observations. Actually, an excellent agreement is found between experimental and simulated results without any fitting parameter, both with respect to surface titration and electrokinetic behaviour. The agreement extends over a wide range of electrostatic coupling, from a weakly charged surface with mainly monovalent counter-ions to a highly charged one with divalent counter-ions.     

Interaction potentials, structural ordering and effective charges in dispersions of charged colloidal particles

As colloidal dispersions of charged particles exhibit a wide variety of commercial, technological and scientific applications, a considerable theoretical effort has been devoted to finding an effective interaction potential from primitive models. The forces derived from this potential should justify the spatial ordering experimentally observed under certain conditions. This paper reviews the advances in these theoretical studies as well as some experiments (based on the mentioned order) that try to corroborate them. Special attention has been paid to the Derjaguin-Landau-Verwey-Overbeek (DLVO) potential. Nowadays, many of these theoretical investigations suggest that it could be applied if some of its parameters are renormalized. Nevertheless, to achieve a renormalization procedure in a strict way (from a primitive model) is a difficult task as a result of the size and charge asymmetries between small ions and macroions. Thus, several procedures for computing renormalized charges in a simple way have been developed. However, the notion of effective charge has also been widely used (as a adjustable parameter) in order to justify results found for several kinds of colloids (like solid particle dispersions or micellar systems) by means of quite different experimental techniques. Renormalization (as well as ion condensation) approaches, experiments and the controversial relationship between theoretical and phenomenological effective charges are also reviewed in this work.     

The renormalized Jellium model of colloidal suspensions with multivalent counterions

An extension of the renormalized Jellium model which allows to study colloidal suspensions containing trivalent counterions is proposed. The theory is based on a modified Poisson-Boltzmann equation which incorporates the effects of counterion correlations near the colloidal surfaces using a new boundary condition. The renormalized charges, the counterion density profiles, and osmotic pressures can be easily calculated using the modified renormalized Jellium model. The results are compared with the ones obtained using the traditional Wigner-Seitz (WS) cell approximation also with a new boundary condition. We find that while the thermodynamic functions obtained within the renormalized Jellium model are in a good agreement with their WS counterpart, the effective charges predicted by the two theories can be significantly different.     

Study on osmotic pressure of non-ionic and ionic surfactant solutions in the micellar and microemulsion regions

To investigate the osmotic pressure of non-ionic and ionic surfactant solutions in the micellar and microemulsion regions, a potential of mean force including hard-core repulsion, van der Waals attraction and electric double layer repulsion is proposed to describe the interactions between micelles and between microemulsions. Both van der Waals attraction and electric double layer repulsion are represented using Yukawa tails. The explicit analytical expression of osmotic pressure derived from the first-order mean spherical approximation is implemented by accounting for the Donnan membrane effect. The proposed theory has been applied to micelle solutions of the non-ionic surfactant, n-dodecyl hexaoxyethylene monoether, the cationic surfactant, cetylpyridinium chloride, the anionic surfactant, sodium dodecyl sulfate, and spherical oil-in-water microemulsion system. Successful comparison is made between the proposed theory and the experimental osmotic pressure data for the studied surfactant solutions. Theoretical results show that the long-range electric double layer repulsion dramatically influences the osmotic pressure of both cationic and anionic surfactant solutions in the micellar region. The regressed model parameters such as effective micelle diameter, the mean aggregation number and effective micellar charge are in good agreement with those from static light scattering studies in the literature.     

Evaluating First-Order Molecular Properties of Delocalized Ionic or Excited States in Molecular Aggregates by Renormalized Excitonic Method

In the past few years, the renormalized excitonic model (REM) approach was developed as an efficient low-scaling ab initio excited state method, which assumes the low-lying excited states of the whole system are a linear combination of various single monomer excitations and utilizes the effective Hamiltonian theory to derive their couplings. In this work, we further extend the REM calculations for the evaluations of first-order molecular properties (e.g. charge population and transition dipole moment) of delocalized ionic or excited states in molecular aggregates, through generalizing the effective Hamiltonian theory to effective operator representation. Results from the test calculations for four different kinds of one dimensional (1D) molecular aggregates (ammonia, formaldehyde, ethylene and pyrrole) indicate that our new scheme can efficiently describe not only the energies but also wavefunction properties of the low-lying delocalized electronic states in large systems.     

A macroion correlation effect on the structure of charged stabilized colloidal suspensions: a self-consistent integral equation study

Using the mean field Poisson–Boltzmann (PB) and the Ornstein–Zernike (OZ) integral equation theories, we have determined the macroions effective interactions and the structure of charged stabilized colloidal suspension for a large charge range of macroion and screening parameter values. The renormalized parameters are calculated by solving the PB equation written in the framework of the modified Jellium model. The structures have been determined by solving the OZ equation coupled with a self-consistent integral equation, which is related to the Verlet’s modified closure. Our results of the effective parameters are in good agreement with the experimental data, also the structure presents acceptable improvement compared to the Monte Carlo simulation data, against the HNC structure results, PACS: 61.20 Gy, 82.70 Dd, and 82.70 Kj.     

Deposition of latex particles on alumina fibers

The deposition of sub-micron latex particles during flow through beds of fine alumina fibers has been studied as a function of pH and ionic strength in the vicinity of the fiber isoelectric point (i.e.p.). Conditions were chosen so that the predominant capture mechanism was diffusion. Results have been compared with the “classical” theory of convective diffusion to cylinders and with modern theory, which takes into account colloidal and hydrodynamic interactions between particles and collector.Initial fiber collection efficiencies, determined at the i.e.p. where the fibers bear no surface charge, are considerably lower than those predicted by classical theory and are insensitive to ionic strength. This lack of dependence on ionic strength suggests that neither constant potential nor constant charge conditions are maintained during particle-fiber encounters and that some intermediate condition is more appropriate. Particle capture results obtained at pH values above and below the fiber i.e.p. agree qualitatively with the predictions of the Spielman and Friedlander “surface reaction” model, although this is not strictly valid below the i.e.p. where the fibers are positively charged and there is no repulsion barrier. Under these conditions a significant enhancement of capture efficiency is observed at low ionic strength, as a result of double layer attraction. Above the i.e.p., where the fibers and particles are both negatively charged, double layer repulsion causes a large reduction in capture efficiency, although the predicted is even larger.The saturation coverage of the fibers by deposited particles was found to decrease strongly as the ionic strength was decreased, indicating the importance of lateral interactions between particles.     

Application of the method of images on electrostatic phenomena in aqueous Al2O3 and ZrO2 suspensions

A new solution for the Poisson equation for the diffuse part of the double layer around spherical particles will be presented. The numerical results are compared with the solution of the well-known DLVO theory. The range of the diffuse layer differs considerably in the two theories. Also, the inconsistent representation of the surface and diffuse layer charge in the DLVO theory do not occur in the new theory. Experimental zeta potential measurements were used to determine the charge of colloidal Al2O3 and ZrO2 particles. It is shown that the calculated charge can be interpreted as a superposition of independent H+ and OH- adsorption isotherms. The corresponding Langmuir adsorption isotherms are taken to model the zeta potential dependence on pH. In the vicinity of the isoelectric point the model fits well with the experimental data, but at higher ion concentrations considerable deviations occur. The deviations are discussed. Furthermore, the numerical results for the run of the potential in the diffuse part of the double layer were used to determine the electrostatic interaction potential between the particles in correlation with the zeta potential measurements. The corresponding total interaction potentials, including the van der Waals attraction, were taken to calculate the coagulation half-life for a suspension with a particle loading of 2 vol%. It is shown that stability against coagulation is maintained for Al2O3 particles in the pH region between 3.3 and 7 and for ZrO2 only around pH 5. Stability against flocculation can be achieved in the pH regime between 4.5 and 7 for Al2O3, while the examined ZrO2 particles are not stable against flocculation in aqueous suspensions.     

Electrocapillary at contact: potential-dependent adhesion between a gold electrode and a mica surface

Using the electrochemical surface forces apparatus, we investigated adhesion (from pull-off measurements) between gold and mica as the potential of the gold surface was changed externally. Measurements were performed at different concentrations of KClO(4) in a potential window where the gold electrode is ideally polarizable. At applied potentials where the gold-mica interactions are repulsive, we obtain double layer forces that are predictable by the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory of colloid stability but deviate from the theory at short range. At applied potentials where the gold-mica interactions are attractive, we observed a very strong dependence of adhesion on the applied potential, a result that cannot be directly related to DLVO theory. We show, however, that an approach based on electrocapillary thermodynamics can be employed to model the potential dependence of adhesion seen in our measurements. This electrocapillary approach presents evidence of charging at the gold-mica interface and stresses the relation between the charge within and outside of the contact area.     

A singlet reference interation site model theory for solid/liquid interfaces Part II: Electrical double layers

The previously established singlet reference interaction site model (SRISM) theory for the calculation of the fluid structure in the vicinity of a plane impenetrable interface is renormalized for the application to electrical double layers. In combination with the HNC and KH closures, the equations are solved numerically for a 1 M electrolyte solution adjacent to a charged wall with varying surface charge densities. The wall-solvent and wall-ion density distributions as well as the profiles of the electrical field and the electrical potential are compared to computer simulation results. Reasonable agreement is obtained.     

Ionic conduction and electrode polarization in a doped nonpolar liquid

Electrical current versus potential relationships were measured for solutions of dodecane containing the charge control agent poly(isobutylene succinimide) (PIBS) at various concentrations. Both one-dimensional (parallel planar electrodes) and two-dimensional (strip electrodes) fields were studied. The initial current was proportional to the applied voltage for both electrode configurations. Using the initial decay rate of the current (t < 0.5 s) in the planar electrode cell and the Gouy-Chapman model for electrode polarization, we determined the diffusion coefficient of the charge carriers (micelles) in the solution, from which we calculated their effective radius to be 10 nm. The constancy of the carrier radius over a 7-fold change in PIBS concentration, along with the proportionality between conductivity and concentration, supports the hypothesis that the charged species result from the interactions between two micelles. The experimentally determined geometric factor (cell constant) relating current to applied potential at time zero for the strip electrode cell agrees with the value predicted from the solution of Laplace's equation for the electrical potential in this system. The intermediate-time (0.5-3.0 s) decay rate of current was faster than predicted from the classical Gouy-Chapman theory of the double layer, possibly because of volume fraction effects in the double layer. The very long-time (minutes to hours) residual current that we observed is not explained, but we suspect that some charge transfer across the electrode must have occurred because there was insufficient ion capacity (i.e., amount of PIBS) in the solution to account for the total charge transferred through the cell.     

First Principles Study on FeAs Single Layers

FeAs^- single layer is tested as a simple model for LaFeAsO and BaFe2As2 based on firstprinciples calculations using generalized gradient approximation （GGA） and GGA＋U. The calculated single-layer geometric and electronic structures are inconsistent with that of bulk materials. The bulk collinear antiferromagnetic ground state failed to be obtained in the FeAs^- single layer. The monotonous behavior of the Fe-As distance in z direction upon electron or hole doping is also in contrast with bulk materials. The results indicate that, in LaFeAsO and BaFe2As2, interactions between FeAs layer and other layers beyond simple charge doping are important, and a single FeAs layer may not represent a good model for Fe based superconducting materials.     

Mean field theory of charged dendrimer molecules

Using self-consistent field theory (SCFT), we study the conformational properties of polyelectrolyte dendrimers. We compare results for three different models of charge distributions on the polyelectrolytes: (1) a smeared, quenched charge distribution characteristic of strong polyelectrolytes; (2) a smeared, annealed charge distribution characteristic of weak polyelectrolytes; and (3) an implicit counterion model with Debye-Huckel interactions between the charged groups. Our results indicate that an explicit treatment of counterions is crucial for the accurate characterization of the conformations of polyelectrolyte dendrimers. In comparing the quenched and annealed models of charge distributions, annealed dendrimers were observed to modulate their charges in response to the density of polymer monomers, counterions, and salt ions. Such phenomena is not accommodated within the quenched model of dendrimers and is shown to lead to significant differences between the predictions of quenched and annealed model of dendrimers. In this regard, our results indicate that the average dissociated charge α inside the dendrimer serves as a useful parameter to map the effects of different parametric conditions and models onto each other. We also present comparisons to the scaling results proposed to explain the behavior of polyelectrolyte dendrimers. Inspired by the trends indicated by our results, we develop a strong segregation theory model whose predictions are shown to be in very good agreement with the numerical SCFT calculations.     

Surface properties of fluids of charged platelike colloids

Surface properties of mixtures of charged platelike colloids and salt in contact with a charged planar wall are studied within 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 [J. Chem. Phys. 39, 1714 (1963)] and the charges of the particles are concentrated at their centers. The density functional applied is an extension of a recently introduced functional for charged platelike colloids. It provides a qualitative approach because it does not determine the relation between the actual and the effective charges entering into the model. Technically motivated approximations, such as using the Zwanzig model, are expected not to influence the results qualitatively. Analytically and numerically calculated bulk and surface phase diagrams exhibit first-order wetting for sufficiently small macroion charges and isotropic bulk order as well as first-order drying for sufficiently large macroion charges and nematic bulk order. The asymptotic wetting and drying behaviors are investigated by means of effective interface potentials which turn out to be asymptotically the same as for a suitable neutral system governed by isotropic nonretarded dispersion forces. Wetting and drying points as well as predrying lines and the corresponding critical points have been located numerically. A crossover from monotonic to nonmonotonic electrostatic potential profiles upon varying the surface charge density has been observed. Nonmonotonic electrostatic potential profiles are equivalent to the occurrence of charge inversion. Due to the presence of both the Coulomb interactions and the hard-core repulsions, the surface potential and the surface charge do not vanish simultaneously, i.e., the point of zero charge and the isoelectric point of the surface do not coincide.     

Charge heterogeneity of surfaces: mapping and effects on surface forces

The DLVO theory treats the total interaction force between two surfaces in a liquid medium as an arithmetic sum of two components: Lifshitz–van der Waals and electric double layer forces. Despite the success of the DLVO model developed for homogeneous surfaces, a vast majority of surfaces of particles and materials in technological systems are of a heterogeneous nature with a mosaic structure composed of microscopic and sub-microscopic domains of different surface characteristics. In such systems, the heterogeneity of the surface can be more important than the average surface character. Attractions can be stronger, by orders of magnitude, than would be expected from the classical mean-field DLVO model when area-averaged surface charge or potential is employed. Heterogeneity also introduces anisotropy of interactions into colloidal systems, vastly ignored in the past. To detect surface heterogeneities, analytical tools which provide accurate and spatially resolved information about material surface chemistry and potential — particularly at microscopic and sub-microscopic resolutions — are needed.Atomic force microscopy (AFM) offers the opportunity to locally probe not only changes in material surface characteristic but also charges of heterogeneous surfaces through measurements of force–distance curves in electrolyte solutions. Both diffuse-layer charge densities and potentials can be calculated by fitting the experimental data with a DLVO theoretical model. The surface charge characteristics of the heterogeneous substrate as recorded by AFM allow the charge variation to be mapped. Based on the obtained information, computer modeling and simulation can be performed to study the interactions among an ensemble of heterogeneous particles and their collective motions. In this paper, the diffuse-layer charge mapping by the AFM technique is briefly reviewed, and a new Diffuse Interface Field Approach to colloid modeling and simulation is briefly discussed.