Electrostatic interaction between soft particles

Electrostatic interaction between two soft particles (i.e., polyelectrolyte-coated particles) in an electrolyte solution is discussed. An approximate analytic expression for the interaction energy between two dissimilar soft spheres is derived by applying Derjaguin's approximation to the corresponding interaction energy between two parallel dissimilar soft plates for the case where the density of fixed charges within the polyelectrolyte layer is low. The obtained expression covers various limiting cases that include hard sphere/hard sphere interaction, spherical polyelectrolyte/spherical polyelectrolyte interaction, soft sphere/spherical polyelectrolyte interaction, soft sphere/hard sphere interaction, and spherical polyelectrolyte/hard sphere interaction.     

Calculation of electrostatic interaction forces between ellipsoidal particles

An analytical expression is presented for describing the electrostatic interaction forces between various shaped particles having mutual orientations. The expression is derived by applying the surface integration method, which is a generalization of the Derjaguin summation procedure. Based on previous theoretical considerations it is possible to calculate the electrostatic interaction force between regularly shaped bodies (both convex or concave in the vicinity of their contact point) by multiplying the interaction energy derived for paralled plates with the corresponding geometric factor. The forces acting between two equal shaped ellipsoids are described and discussed, considering three different limiting orientations, the parallel, the perpendicular, and the contact of the edges' orientation.     

Electric double layer and electrostatic interaction of hydrophobic particles

An hypothesis regarding the impact of water density near hydrophobic surfaces on the electrostatic component of their interaction was offered. A theoretical model of the electric double layer and the interparticle interaction under conditions of the variable density and, consequently, variable dielectric permittivity of water has been developed. It was shown that reduction of the dielectric permittivity near interfaces determined by their hydrophobicity resulted in compression of double electrical layers and weakening of their overlapping. This, in its turn, results in reduction of the electrostatic repulsion of hydrophobic disperse particles as compared with nonhydrophobic ones.     

The interaction energy between two parallel plates with constant surface charge density

On the basis of Langmuir's suggestion we simplify the Poisson-Boltzmann equation and derive the relation of surface potential, potential midway, and the plate distance. Thus we obtain the interaction force and energy equations between two dissimilar plates in the case of constant surface charge density. Agreement with the exact numerical values of the interaction of dissimilar plates is good. This method may not only apply to the cases of high constant potential but to the case of high constant charge density.     

The wall and multivalent counterion effects on the electrostatic force between like-charged spherical particles confined in a charged pore

The effect of wall confinement (wall charge and wall-sphere separation distance) on the electrostatic force between two charged spheres confined in a long charged pore in symmetric and asymmetric electrolytes have been quantified by solving the nonlinear Poisson-Boltzmann equation (PBE), using adaptive finite elements combined with error minimization techniques. The computed force indicated the strong effect of the wall potential on the reduction of the repulsive force for all type of electrolytes. The influence of the wall effect was reduced when the valence of the electrolyte was increased. A significant reduction in the repulsive force between the two spheres was also observed when the distance between the pore wall and the sphere surface was reduced. A smaller long-range repulsive interaction was observed between spheres when the solutions contained multivalent counterions as compared with a monovalent solution. However, at short ranges of separation distances multivalent counterions increase the electrostatic repulsive force between the spheres. The effect of the dimensionless radius of the spheres on the electrostatic force between them has been determined and a significant reduction observed as the dimensionless radius was reduced.     

An analysis of the electrostatic interaction between nucleic acid bases

Results from several commonly used approximate methods of evaluating electrostatic interactions have been compared to the rigorous, nonexpanded electrostatic energies at both uncorrelated and correlated levels of theory. We examined a number of energy profiles for both hydrogen bonded and stacked configurations of the nucleic acid base pairs. We found that the penetration effects play an extremely important role and the expanded electrostatic energies are significantly underestimated with respect to the ab initio values. Apart from the inability to reproduce the magnitudes of the ab initio electrostatic energy, there are other problems with the available approximate electrostatic models. For example, the distributed multipole analysis, one of the most advanced methods, is extremely sensitive to the basis set and level of theory used to evaluate the multipole moments. Detailed ab initio results are provided that other researchers could use to test their approximate models.     

A simulation study of electrostatic effects on mixed ionic micelles confined between two parallel charged plates

Confined colloidal systems have been the subject of extensive theoretical and experimental research, and the recent observation of long-range like-charge attraction in such systems has only highlighted their peculiar behavior. On the other hand, surfactant solutions are often used in small confined space, yet their behavior in confinement has received relatively little attention. A distinct feature of confined self-assembling systems is that the aggregates are capable of adjusting their composition, size, and shape in response to their external environment, which may lead to very different phase characteristics compared to bulk solutions. The primary objective of this study is to explore the effects of varying micelle composition on the structural behavior of a confined mixed ionic micellar solution. Mesoscale canonical Monte Carlo simulations were used to probe the structure of the confined solution, while a molecular-thermodynamic model was used to systematically account for the change in micelle size as we varied its composition. Significant micelle ordering was found under certain conditions, which implies that large deviations from the minimum-energy micelle configuration may not be entropically favorable. Accumulation of micelles along the midplane was observed when the confining walls are weakly charged, suggesting that micelle shape transformation should be considered in more detail. On the other hand, with high wall charge density, apparent attraction was found between like-charged micelles and wall. These findings point to the need for a more quantitative theoretical treatment in describing surfactant self-assembly in confined geometries.     

The interaction energy between identical particles

The improved Derjaguin’s method is used to derive the approximate expressions for the electrostatic interaction energy between spherical colloidal particles. The approximate results are in good agreement with the exact numerical solutions. The results from the product of the original Derjaguin approximation with curvature correction 2a/R can be used satisfactorily at different αa and κh, no matter high or low the potential of spherical particle is. The text was submitted by the authors in English.     

Discrete charge effects on the Donnan potential and surface potential of a soft particle

The Donnan potential and surface potential of soft particles (i.e., polyelectrolyte-coated hard particles) in an electrolyte solution play an essential role in their electric behaviors. These potentials are usually derived via a continuum model in which fixed charges inside the surface layer are distributed with a continuous charge density. In this paper, for a plate-like soft particle consisting of a cubic lattice of fixed point charges, on the basis of the linearized Poisson–Boltzmann equation, we derive expressions for the electric potential distribution in the regions inside and outside the surface layer. This expression is given in terms of a sum of the screened Coulomb potentials produced by the point charges within the surface layer. We show that the deviation of the results of the discrete charge model from those of the continuous charge model becomes significant as the ratio of the lattice spacing to the Debye length becomes large.     

Nematic ordering of rigid rod polyelectrolytes induced by electrostatic interactions: effect of discrete charge distribution along the chain

Similar to the Debye-Hu?ckel plasma, charged groups in solutions of rigid rod polyelectrolytes attract each other. We derive expression for the correlation free energy of electrostatic attraction of the rods within the random phase approximation. In this theory, we explicitly take into account positions of charged groups on the chains and examine both charge and polymer concentration fluctuations. The correlation free energies and the osmotic pressures are calculated for isotropic and completely ordered nematic phase. The results of the discrete model are compared with results of a continuous model. The discrete model gives rise to a stronger attraction between the charged groups both in the isotropic and nematic phases and to a stronger orienting action of the electrostatic forces.     

Direct measurements of the effects of salt and surfactant on interaction forces between colloidal particles at water-oil interfaces

The forces between colloidal particles at a decane-water interface, in the presence of low concentrations of a monovalent salt (NaCl) and the surfactant sodium dodecyl sulfate (SDS) in the aqueous subphase, have been studied using laser tweezers. In the absence of electrolyte and surfactant, particle interactions exhibit a long-range repulsion, yet the variation of the interaction for different particle pairs is found to be considerable. Averaging over several particle pairs was hence found to be necessary to obtain a reliable assessment of the effects of salt and surfactant. It has previously been suggested that the repulsion is consistent with electrostatic interactions between a small number of dissociated charges in the oil phase, leading to a decay with distance to the power -4 and an absence of any effect of electrolyte concentration. However, the present work demonstrates that increasing the electrolyte concentration does yield, on average, a reduction of the magnitude of the interaction force with electrolyte concentration. This implies that charges on the water side also contribute significantly to the electrostatic interactions. An increase in the concentration of SDS leads to a similar decrease of the interaction force. Moreover, the repulsion at fixed SDS concentrations decreases over longer times. Finally, measurements of three-body interactions provide insight into the anisotropic nature of the interactions. The unique time-dependent and anisotropic interactions between particles at the oil-water interface allow tailoring of the aggregation kinetics and structure of the suspension structure.     

Diastereoselectivity controlled by electrostatic repulsion between the negative charge on a trifluoromethyl group and that on aromatic rings

Intramolecular electrostatic repulsions between the local negative charge on a trifluoromethyl group and that on the ortho position of an aryl moiety of a nucleophile was found to be a controlling factor of the diastereoselectivity in a cyclopropanation reaction, in which the electrostatic repulsion was evaluated quantitatively.     

Long-range interactions between soft colloidal particles in slit-pore geometries

Combining theoretical and experimental techniques, we investigate the structure formation of charged colloidal suspensions of silica particles in bulk and in spatial confinement (slit-pore geometry). Our focus is to identify characteristic length scales determining typical quantities, such as the position of the main peak of the bulk structure factor and the period of the oscillatory force profile in the slitpore. We obtain these quantities from integral equations/SANS experiments (bulk) and Monte Carlo simulations/colloidal probe-AFM measurements (confinement), in which the theoretical calculations are based on the Derjaguin-Landau-Verwey-Overbeck (DLVO) potential. Both in bulk and in the slitpore, we find excellent qualitative and quantitative agreement between theory and experiment as long as the ionic strength chosen in the DLVO potential is sufficiently low (implying a relatively long-ranged interaction). In particular, the bulk properties of these systems obey the widely accepted density scaling of xi proportional to phi(-1/3). On the other hand, systems with larger ionic strengths and, consequently, more short-ranged interactions do not obey such power law behavior and rather resemble an uncharged hard-sphere fluid, in which the relevant length scale is the particle diameter.     

Numerical computation of the electrostatic interaction energy between methanol and the dyad water-imidazole

Summary The electrostatic interaction energy between methanol and the dyad water-imidazole has been computed numerically at three levels of approximation from 3D grids of the charge density of one partner and the electrostatic potential of the other. The minimum positions and energy values thus obtained compare well with those calculated analytically. The numerical procedure is especially interesting for the prediction of the stable conformers.     

Effect of ions on the hydrophobic interaction between two plates

We use molecular dynamics simulations to investigate the solvent mediated attraction and drying between two nanoscale hydrophobic surfaces in aqueous salt solutions. We study these effects as a function of the ionic charge density, that is, the ionic charge per unit ionic volume, while keeping the ionic diameter fixed. The attraction is expressed by a negative change in the free energy as the plates are brought together, with enthalpy and entropy changes that both promote aggregation. We find a strong correlation between the strength of the hydrophobic interaction and the degree of preferential binding/exclusion of the ions relative to the surfaces. The results show that amplification of the hydrophobic interaction, a phenomenon analogous to salting-out, is a purely entropic effect and is induced by high-charge-density ions that exhibit preferential exclusion. In contrast, a reduction of the hydrophobic interaction, analogous to salting-in, is induced by low-charge-density ions that exhibit preferential binding, the effect being either entropic or enthalpic. Our findings are relevant to phenomena long studied in solution chemistry, as we demonstrate the significant, yet subtle, effects of electrolytes on hydrophobic aggregation and collapse.     

Diffuse double layer interaction between two parallel plates with constant surface charge density in an electrolyte solution

Summary The double layer interaction between two parallel metallic plates with adsorbed surface charge of constant density in a symmetrical electrolyte solution is considered. Numerical calculations using the nonlinearPoisson-Boltzmann equation are made. Analytic expressions for the interaction are also obtained by using theDebye-Hückel approximation. The double layer interaction is found to be influenced by true charges induced on the plate surface due to electrostatic induction. This influence becomes important at small plate separations. It is also shown that the force and potential energy of interaction between metallic plates are small compared with those between insulating plates.

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Zusammenfassung Die Wechselwirkung der Doppelschichten zwischen zwei parallelen metallischen Platten mit der konstanten Dichte der adsorbierten Oberflächenladung in einer symmetrischen Elektrolytlösung wird betrachtet. Numerische Berechnungen werden mittels der nichtlinearenPoisson-Boltzmannschen Gleichung ausgeführt. Durch Benutzung der Debye-Hückel-Näherung werden auch analytische Ausdrücke für die Wechselwirkung gewonnen. Es zeigt sich, daß die Wechselwirkung der Doppelschichten von reellen Ladungen, die an der metallischen Oberfläche durch elektrostatische Induktion induziert werden, beeinflußt wird. Dieser Einfluß wird besonders wichtig für kleine Plattenabstände. Die Kraft und die potentielle Energie der Wechselwirkung zwischen metallischen Platten sind kleiner als die zwischen Isolierplatten.

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With 4 figures and 3 tables