Diffusion-controlled solid-state reactions of spherical particles, a general model for multiphase binary systems

The formal treatment of the diffusion-controlled growth of n binary compounds with narrow homogeneity range during the reaction of a sphere of reactant A immersed in reactant B is presented and discussed. Both constituents are assumed to be mobile. The reaction products are assumed to grow simultaneously as uniform and compact concentric layers with ideal contact at the interfaces as well as at the external surface of the sphere. The kinetic equations follow from the coupling between chemical reactions and partitioning of the diffusion flux at phase boundaries. The results for the formation of two and three compounds are presented. The influence of the initial radius of the sphere, of the relative magnitude of the kinetic constants, and of the volume variation is discussed in detail.     

Long-time self-diffusion of charged colloidal particles: electrokinetic and hydrodynamic interaction effects

The authors analyze the long-time self-diffusion of charge-stabilized colloidal macroions in nondilute suspensions using a mode-coupling scheme developed for multicomponent suspensions of interacting Brownian spheres. In this scheme, all ionic species, including counterions and electrolyte ions, are treated on an equal footing as charged hard spheres undergoing overdamped Brownian motion. Hydrodynamic interactions between all ions are accounted for on the far-field level. We show that the influence on the colloidal long-time self-diffusion coefficient arising from the relaxation of the microionic atmosphere surrounding the colloids, the so-called electrolyte friction effect, is usually insignificant in comparison with the friction contributions arising from direct and hydrodynamic interactions between the colloidal particles. This finding is true even for small colloid concentrations unless the mobility difference between colloidal particles and microions is not large. Furthermore, we observe an interesting nonmonotonic density dependence of the colloidal long-time self-diffusion coefficient in suspensions with low amount of added salt. We show that this unusual density dependence is due to colloid-colloid hydrodynamic interactions.     

Long-range interaction between heterogeneously charged membranes

Despite their neutrality, surfaces or membranes with equal amounts of positive and negative charge can exhibit long-range electrostatic interactions if the surface charge is heterogeneous; this can happen when the surface charges form finite-size domain structures. These domains can be formed in lipid membranes where the balance of the different ranges of strong but short-ranged hydrophobic interactions and longer-ranged electrostatic repulsion result in a finite, stable domain size. If the domain size is large enough, oppositely charged domains in two opposing surfaces or membranes can be strongly correlated by the electrostatic interactions; these correlations give rise to an attractive interaction of the two membranes or surfaces over separations on the order of the domain size. We use numerical simulations to demonstrate the existence of strong attractions at separations of tens of nanometers. Large line tensions result in larger domains but also increase the charge density within the domain. This promotes correlations and, as a result, increases the intermembrane attraction. On the other hand, increasing the salt concentration increases both the domain size and degree of domain anticorrelation, but the interactions are ultimately reduced due to increased screening. The result is a decrease in the net attraction as salt concentration is increased.     

Dynamic interaction between oppositely charged vesicles: aggregation, lipid mixing, and disaggregation

We investigated dynamic interactions between oppositely charged small unilamellar vesicles using positively charged vesicles containing 1,2-dioleoyl-3-trimethylammonium-propane or 3beta-[N-(N('),N(')-dimethylaminoethane)-carbamoyl] cholesterol and negatively charged vesicles containing L-alpha-phosphatidyl-DL-glycerol. Aggregation, lipid bilayer mixing, contents mixing and contents leakage were systematically examined using optical density measurements, fluorescence resonance energy transfer assays, fluorescence quenching assays, light-scattering analyses, and freeze-fracture transmission electron microscopy. The oppositely charged vesicles aggregated immediately. Lipid mixing was observed, but there was no mixing of the contents. The vesicle aggregates disaggregated spontaneously after several minutes. The surface potential of the disaggregated vesicles was neutralized. From these results, we infer that the lipids in the external monolayers were exchanged between the oppositely charged vesicles while the internal monolayers remained intact. The two types of cationic lipids used exhibited different speeds of disaggregation.     

Effective interaction between charged nanoparticles and DNA

We investigate the effective interaction mediated by salt ions between charged nanoparticles (NPs) and DNA. DNA is modeled as an infinite cylinder with a constant surface charge in an implicit solvent. Monte Carlo simulations are used to compute the free energy of the system described in the framework of the primitive model of electrolytes, which accounts for excluded volumes of salt ions. A mean-field Poisson-Boltzmann theory also allows us to compute the free energy and provides us with explicit formulae for its main characteristics (position and depth of the minimum). We intend here to identify the physical parameters that have a major impact on the NP-DNA interaction, in an attempt to evaluate physico-chemical properties which could play a role in genotoxicity or, which could be exploited for therapeutic use. Thus, we investigate the influence on the effective interaction of: the shape of the nanoparticle, the magnitude of the nanoparticle charge and its distribution, the value of the pH of the solution, the magnitude of Van der Waals interactions depending on the nature of the constitutive material of the NP (metal vs. dielectric). We show that for positively charged concave NPs the effective interaction is repulsive at short distance, so that it presents a minimum at distance from the DNA. This short-range repulsion is specific to indented particles and is a robust property that holds for a large range of materials and charge densities.     

Competitive interaction between two different spherical sinks

Competitive interactions within diverse mixed populations of chemically active sites are prevalent throughout nature, science, and engineering. Their effects are readily seen in the distribution of dead and surviving aerobic cells within a thick biofilm and particle shape changes during the growth and coarsening of crystals. Even in the most dilute case, competition for a reactant requires at least two spheres/cells, and the solution of the two-spherical sink problem is of interest for several reasons. The solution accurately describes lower cell concentration behavior (10(8) cells/l), and like the Smoluchowski diffusion-reaction treatment for a single sphere, the analysis is extremely helpful in understanding the fundamental phenomena of the effect on the first spherical sink of the presence of a second different spherical sink. In addition these exact solutions are required for the systematic extension to higher density behavior by rigorous expansions in the spherical sink densities. The method of the twin spherical expansion is used with a formal matrix elimination scheme to generate an exact solution for two distinct spherical sinks of differing sizes and kinetics. The two sinks exist in a medium, which supplies a reactant to the sinks via Fickian diffusion. The two sinks compete for the same reactant with different first-order reactions occurring at the surface of each sink. Earlier work focused on two spherical sinks of the same size with identical surface reaction kinetics. This work has been advanced to allow for diversity in the theory of cellular or reactive sink competition. A number of interesting higher order interactive phenomena are observed in this paper when the different reactive sinks are in close proximity. (c) 2004 American Institute of Physics.     

Electrostatic interaction between two spherical colloidal particles

Explicit exact analytic expressions are obtained in the form of infinite series for the potential distribution and the potential energy of the electrostatic interaction for the system of two dissimilar spheres in an electrolyte solution on the basis of the linearized Poisson—Boltzmann equation without recourse to Derjaguin's approximation. The leading term of the expression for the interaction energy (the zeroth order approximation) corresponds to the interaction energy that would be obtained if both spheres were ion-penetrable spheres (“soft” spheres). This term is a screened Coulomb interaction due to a simple linear superposition of the unperturbed potentials of the respective spheres, which is proportional to the product of their unperturbed surface potentials. The first-order approximation corresponds to the interaction energy that would be obtained if either sphere were a soft particle (the other being hard). The first-order correction term consists of two sub-terms, each of which is proportional to the square of the unperturbed surface potential of either sphere and does not depend on the unperturbed surface potential of the other sphere, can be interpreted as the interaction between the soft sphere and its image with respect to the hard sphere. This image interaction is attractive if the surface potential of the hard sphere is constant and repulsive if the surface charge density of the sphere is constant. It is shown that Derjaguin's method as well as its extension to the interaction of unequal spheres by Hogg, Healy and Fuerstenau (HHF) is quite a good approximation.     

Electro-osmosis at inhomogeneous charged surfaces: hydrodynamic versus electric friction

Electrokinetic methods are efficient in probing the electrostatic surface properties of charged systems. However, anomalies observed in experiments indicate that the classical electrokinetic theory should be reconsidered. Using Green's function methods and hydrodynamic simulations, we investigate electro-osmosis driven by electric-field-induced ion motion near a charged planar substrate with smooth or rough boundary. First, a reformulation of electro-osmotic theory for planar charged surfaces employing Green's functions shows that the Helmholtz-Smoluchowski (HS) relation between electrostatic potential and solvent velocity is exact for smooth surfaces, even in the presence of ion correlations. Deviations from HS theory are caused by combined hydrodynamic and electric surface friction, as our hydrodynamic simulations of ions at smooth and corrugated charged surfaces in lateral electric fields demonstrate. Within the simulations, hydrodynamic interactions are treated in the continuum limit and the presence of a no-slip boundary condition at the surface is taken into account. While electrofriction is relevant in highly charged system and/or for multivalent ions, hydrodynamic friction is dominant in systems with moderate surface charge density and/or low ionic valency. We also derive the effective electrokinetic surface charge from the electro-osmotic solvent profiles, which is substantially reduced when compared with the bare value and shows qualitative agreement with the experimental tendency.     

Liquid friction on charged surfaces: from hydrodynamic slippage to electrokinetics

Hydrodynamic behavior at the vicinity of a confining wall is closely related to the friction properties of the liquid/solid interface. Here we consider, using molecular dynamics simulations, the electric contribution to friction for charged surfaces, and the induced modification of the hydrodynamic boundary condition at the confining boundary. The consequences of liquid slippage for electrokinetic phenomena, through the coupling between hydrodynamics and electrostatics within the electric double layer, are explored. Strong amplification of electro-osmotic effects is revealed, and the nontrivial effect of surface charge is discussed. This work allows us to reconsider existing experimental data, concerning zeta potentials of hydrophobic surfaces and suggests the possibility to generate "giant" electro-osmotic and electrophoretic effects, with direct applications in microfluidics.     

Dispersion interaction between helium pair from hydrodynamic analogy to quantum mechanics

Frequency-dependent multipole polarizabilities of the He sequence have been calculated from a hydrodynamic model of quantum mechanics and using an independent-particle model Hamiltonian. Our present scheme is parallel to the uncoupled Hartree–Fock approximation so our values of polarizabilities, multipole transition energies and dispersion force coefficients between the He? He pair are comparable with earlier works using the uncoupled Hartree–Fock approximation.     

Electrostatic double-layer interaction between spherical particles inside a rough capillary

Predictions of electrostatic double-layer interaction forces between two similarly charged spherical colloidal particles inside an infinitely long "rough" capillary are presented. A simple model of a rough cylindrical surface is proposed, which assumes the capillary wall to be a periodic function of axial position. The periodic roughness of the wall is characterized by the wavelength and amplitude of the undulations. The electrostatic double-layer interaction force between two spherical particles located axially inside this rough capillary is determined by solving the nonlinear Poisson-Boltzmann equation employing finite element analysis. The effect of surface roughness of the cylindrical enclosure on the interaction force between two particles is extensively studied on the basis of this model. The simulations are carried out for dimensionless amplitudes (amplitude/particle radii) ranging from 0.05 to 0.15 and scaled wavelengths (wavelength/particle radii) ranging from 0.4 to 4.0. The interaction force between the particles is significantly modified by the proximity of the rough capillary wall. Generally, the interaction force for rough capillaries oscillates around the corresponding interaction force in a smooth capillary depending on the magnitudes of the scaled amplitude and wavelength of the roughness. The influence of roughness on the electrostatic interactions becomes more pronounced when the surface potential of the cylinder wall is different from the sphere surface potentials. When the cylinder and the particle surfaces have large potential differences, the axial force experienced by a particle is dominated by the capillary roughness. There are dramatic oscillations of the force, which alternately becomes repulsive and attractive as the particle moves from the crest to the trough of the rough capillary wall. These results suggest that manipulation of colloidal particles in narrow microchannels may be subject to significant force variations owing to the roughness inherent in microfabricated channels etched on metal films.     

Collision efficiencies of diffusing spherical particles: hydrodynamic,van der waals and electrostatic forces

A practical limitation of the application of Smoluchowski's classical estimate for the collisions probability of two diffusing spherical particles in Brownian motion is the non-consideration of interparticle forcves. For suspended particles in water such forces can arise from the disturbance the particle causes in the fluid (hydrodynamic forces), from the cloud of ions which surround an electrically charged particle (double layer forces) or they can be of molecular origin (van der Waals forces). In this paper corrections to Smoluckhowski's collision probability are computed when such forces operate Scoluchowski's collision probability are computed when such forces operate between two approaching particles of various sizes. Results for several values of the van der Waals energy of attraction and the ionic strength of the electrolyte are presented in a way convenient for particle collision modeling.     

Phase coexistence in polydisperse charged hard-sphere fluids: mean spherical approximation

Taking advantage of the availability of the analytic solution of the mean spherical approximation for a mixture of charged hard spheres with an arbitrary number of components we show that the polydisperse fluid mixture of charged hard spheres belongs to the class of truncatable free energy models, i.e., to those systems where the thermodynamic properties can be represented by a finite number of (generalized) moments of the distribution function that characterizes the mixture. Thus, the formally infinitely many equations that determine the parameters of the two coexisting phases can be mapped onto a system of coupled nonlinear equations in these moments. We present the formalism and demonstrate the power of this approach for two systems; we calculate the full phase diagram in terms of cloud and shadow curves as well as binodals and discuss the distribution functions of the coexisting daughter phases and their charge distributions.     

Interactions between chlorinated dioxins and a positively charged molecular probe: New molecular interaction potential

Interaction with the ligand binding domain of receptors for natural chemicals present one potential mechanism for the biological effects of environmental chemicals. Evidence suggests that the electrostatic interaction between the ligand and the receptor is an important component for binding to some of the relevant receptors. The presence of charged residues near the binding site suggests that the charge distribution of the free ligand may be different from the charge distribution of the ligand as it approaches the binding domain of the protein. In this study a new type of potential is computed for a series of dibenzo-p-dioxin (dioxin) ligands. This quantum mechanically computed potential results from interaction between the ligand and a trimethyl ammonium probe at a set of grid points. This interaction potential is compared with the molecular electrostatic potential computed from the wave function of the isolated ligands. Three types of local minima are found: (1) above the oxygen; (2) above the conjugated ring; and (3) above the chlorine(s). The molecular electrostatic potential emphasizes the minima associated with the chlorine atoms and, in that potential, the minima associated with the oxygen atoms disappear with chlorination. In the new potential, the minima over the oxygen atoms are maintained even in tetrachlorodioxin. As chlorination is increased the differences between the two potentials increases. The new potential shows the influence of the π-cation interaction, which is largest when there is little substitution on the ring. The presence of the probe induces a dipole component of 1 debye perpendicular to the plane of the ligand. Local minima in the interaction potential are then used as starting structures for the determination of the most stable ligand–probe complexes. The most stable structures are obtained from the minima associated with the oxygen atoms. These structures are stabilized by a hydrogen bond formation between the probe and the oxygen and the molecule is bent by 30° about the O(SINGLE BOND)O axis. For this series of molecules, the new potential retains some of the features that determine the hydrogen bond whereas the molecular electrostatic potential does not. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 673–684, 1998     

Friction and normal interaction forces between irreversibly attached weakly charged polymer brushes

Polyelectrolyte brushes were built on mica by anchoring polystyrene-poly(acrylic acid) (PS-b-PAA) diblock copolymers at a controlled surface density in a polystyrene monolayer covalently attached to OH-activated mica surfaces. Compared to physisorbed polymer brushes, these irreversibly attached charged brushes allow the polymer grafting density to remain constant upon changes in environmental conditions (e.g., pH, salt concentration, compression, and shear). The normal interaction and friction forces as a function of surface separation distance and at different concentrations of added salt (NaCl) were investigated using a surface forces apparatus. The interaction force profiles were completely reversible both on loading and receding and were purely repulsive. For a constant polymer grafting density, the influence of the polyelectrolyte charges and the Debye screening effect on the overall interaction forces was investigated. The experimental interaction force profiles agree very well with scaling models developed for neutral and charged polymer brushes. The variation of the friction force between two PAA brushes in motion with respect to each other as a function of surface separation distance appeared to be similar to that observed with neutral brushes. This similarity suggests that the increase in friction is associated with an increase in mutual interpenetration upon compression as observed with neutral polymers. The effect of the PAA charges and added ions was more significant on the repulsive normal forces than on the friction forces. The reversible characteristics of the normal force profiles and friction measurements confirmed the strong attachment of the PAA brushes to the mica substrate. High friction coefficients (ca 0.3) were measured at relatively high pressures (40 atm) with no surface damage or polymer removal.     

The electrostatic interaction between a charged sphere and an oppositely charged planar surface and its application to protein adsorption

To calculate the electrostatic interaction between a charged sphere and a charged surface under the condition of constant charge density on the two surfaces is difficult. The theory presented in this paper provides an approximate solution to this problem when the charge of the two bodies is of opposite sign. The proposed calculation model is based on a solution of the Poisson–Boltzmann (P–B) equation for two oppositely charged planar surfaces to which the approximate integration procedure developed by Deryaguin is applied. The obtained expression is rather simple and is in good agreement with retention data for a protein in ion exchange chromatography. The developed model is physically more sound than the previously developed ‘slab’ model for protein retention. Under the experimental conditions of ion exchange chromatography of proteins, the two models give comparable numerical values for the ionic strength dependence of retention.     

Diffusion-controlled reactions in two-dimensional fluids: discussion of measurements of lateral diffusion of lipids in biological membranes

Differences between the reaction kinetics of diffusion-controlled reactions in two and three dimensions are examined, and expressions for the rate of a diffusion-controlled reaction in a two-dimensional fluid are derived. A method of analysing the results of some recent investigations of lateral diffusion of lipids in biological membranes is presented.     

Viscoelasticity of dilute chain-molecule solutions: Evaluation of hydrodynamic interaction

The viscoelastic properties of chain molecules varying in flexibility and length have been calculated by use of the bead-spring model theory of Zimm. In the evaluation of the hydrodynamic interaction parameter, the number of springs in the bead-spring model, N, has been selected from the range in which the properties predicted by the theory are insensitive to the value of N. The results for limiting viscosity number agree with those predicted by the Yamakawa–Fujii theory of the limiting viscosity number of wormlike chains. The theory also fits the experimental data of Johnson on a sample of polystyrene of molecular weight 860,000 in theta solvents at infinite dilution. The viscoelastic properties of some moderate molecular weight deoxyribonucleic acid solutions are predicted to deviate from the non-free-draining behavior toward the free-draining behavior.