The dielectric nature of polar liquids underpins much of their ability to act as useful solvents, but its description is complicated by the long-ranged nature of dipolar interactions. This is particularly pronounced under the periodic boundary conditions commonly used in molecular simulations. In this article, the dielectric properties of a water model whose intermolecular electrostatic interactions are entirely short-ranged are investigated. This is done within the framework of local molecular field theory (LMFT), which provides a well controlled mean-field treatment of long-ranged electrostatics. This short-ranged model gives a remarkably good performance on a number of counts, and its apparent shortcomings are readily accounted for. These results not only lend support to LMFT as an approach for understanding solvation behavior, but are relevant to those developing interaction potentials based on local descriptions of liquid structure.
The electrostatic interaction in ionic fluids is well-known to give rise to a characteristic phase behavior and structure. Sometimes its long range is proposed to single out the electrostatic potential over other interactions with shorter ranges. Here the importance of the range for the phase behavior and the structure of ionic fluids is investigated by means of grandcanonical Monte Carlo simulations of the lattice restricted primitive model (LRPM). The long-ranged electrostatic interaction is compared to various types of short-ranged potentials obtained by sharp and/or smooth cut-off schemes.…
We propose that the degree of sweeling of the 30nm chromatin fiber (a "measure" of its transcriptional activity) is mainly determined by the short-ranged electrostatical interaction between different sections of the "folded" DNA chain. These sections constitute only a small fraction of the chain and they are located close to the entry-exit points of the DNA chain at the nucleosome core particles. We present a model that allows to estimate the degree of swelling of chromatin fibers as a function of salt concentration, charge density of the strands etc. Different mechanisms by which the state of…
The nature of electrostatic interaction between like-charged particles at water-air interface is analyzed in this paper. We show that long-ranged electrostatic dipolar attraction between these objects generally exists. Our result provides a natural mechanism to explain the experimental observations of attraction between like-charge species trapped at water-air interface. We speculate that a similar (but presumably weaker) mechanism also exists for particles near water-solid interface.
We study the strong-coupling (SC) interaction between two like-charged membranes of finite thickness embedded in a medium of higher dielectric constant. A generalized SC theory is applied along with extensive Monte-Carlo simulations to study the image charge effects induced by multiple dielectric discontinuities in this system. These effects lead to strong counterion crowding in the central region of the inter-surface space upon increasing the solvent/membrane dielectric mismatch and change the membrane interactions from attractive to repulsive at small separations. These features agree quanti…
We examine the effective counterion-mediated electrostatic interaction between two like-charged dielectric cylinders immersed in a continuous dielectric medium containing neutralizing mobile counterions. We focus on the effects of image charges induced as a result of the dielectric mismatch between the cylindrical cores and the surrounding dielectric medium and investigate the counterion-mediated electrostatic interaction between the cylinders in both limits of weak and strong electrostatic couplings (corresponding, e.g., to systems with monovalent and multivalent counterions, respectively). T…
Spherical truncations of Coulomb interactions in standard models for water permit efficient molecular simulations and can give remarkably accurate results for the structure of the uniform liquid. However truncations are known to produce significant errors in nonuniform systems, particularly for electrostatic properties. Local molecular field (LMF) theory corrects such truncations by use of an effective or restructured electrostatic potential that accounts for effects of the remaining long-ranged interactions through a density-weighted mean field average and satisfies a modified Poisson's equat…
Charge-stabilized colloidal spheres dispersed in deionized water are supposed to repel each other. Instead, artifact-corrected video microscopy measurements reveal an anomalous long-ranged like-charge attraction in the interparticle pair potential when the spheres are confined to a layer by even a single charged glass surface. These attractions can be masked by electrostatic repulsions at low ionic strengths. Coating the bounding surfaces with a conducting gold layer suppresses the attraction. These observations suggest a possible mechanism for confinement-induced attractions.
We use appropriately defined short ranged reference models of liquid water to clarify the different roles local hydrogen bonding, van der Waals attractions, and long ranged electrostatic interactions play in the solvation and association of apolar solutes in water. While local hydrogen bonding in- teractions dominate hydrophobic effects involving small solutes, longer ranged electrostatic and dis- persion interactions are found to be increasingly important in the description of interfacial structure around large solutes. The hydrogen bond network sets the solute length scale at which a crossov…
An exact analytical solution based on the method of images has been obtained for the description of the electrostatic field in the system comrising of atomic force microscope (AFM)tip, dielectric, and conductor. The solution provides a step towards quantitative modelling of AFM-assisted electrostatic nanolithography in polymers.
We present a lattice Monte Carlo algorithm based on the one originally proposed by Maggs and Rossetto for simulating electrostatic interactions in inhomogeneous dielectric media. The original algorithm is known to produce attractive interactions between particles of the same dielectric constant in the medium of different dielectric constant. We demonstrate that such interactions are spurious, caused by incorrectly biased statistical weight arising from particle motion during the Monte Carlo moves. We propose a simple parallel tempering algorithm that corrects this unphysical bias. The efficacy…
Industrial as well as natural aggregation of fine particles is believed to be associated with electrostatics. Yet like charges repel, so it is unclear how similarly treated particles aggregate. To resolve this apparent contradiction, we analyze conditions necessary to hold aggregates together with electrostatic forces. We find that aggregates of particles charged with the same sign can be held together due to dielectric polarization, we evaluate the effect of aggregate size, and we briefly summarize consequences for practical aggregation.
The modification of the boundary condition for polyelectrolyte adsorption on charged surface with short-ranged interaction is investigated under two regimes. For weakly charged Gaussian polymer in which the short-ranged attraction dominates, the boundary condition is the same as that of the neutral polymer adsorption. For highly charged polymer (compressed state) in which the electrostatic interaction dominates, the linear relationship (electrostatic boundary condition) between the surface monomer density and the surface charge density needs to be modified.
We investigate the statistical mechanics of an inhomogeneous Coulomb fluid composed of charged particles with static polarizability. We derive the weak- and the strong-coupling approximations and evaluate the partition function in a planar dielectric slab geometry with charged boundaries. We investigate the density profiles and the disjoining pressure for both approximations. Comparison to the case of non-polarizable counterions shows that polarizability brings important differences in the counterion density distribution as well as the counterion mediated electrostatic interactions between cha…
We introduce a field-theoretic electrolyte model composed of structured solvent molecules and salt ions coupled by electrostatic and hard-core interactions. Within this explicit solvent theory, we characterize the salt-driven dielectric decrement beyond weak-coupling (WC) electrostatics. The WC approximation of prior formalisms is relaxed by treating the salt charges via a virial expansion. This virial approach enables the explicit inclusion of the many-body salt-solvent interactions, and directly leads to the experimentally observed linear decay of the electrolyte permittivity with added dilu…
We investigate the effect of quenched surface charge disorder on electrostatic interactions between two charged surfaces in the presence of dielectric inhomogeneities and added salt. We show that in the linear weak-coupling regime (i.e., by including mean-field and Gaussian-fluctuations contributions), the image-charge effects lead to a non-zero disorder-induced interaction free energy between two surfaces of equal mean charge that can be repulsive or attractive depending on the dielectric mismatch across the bounding surfaces and the exact location of the disordered charge distribution.
Electrostatic self-assembly of neutral particles on a dielectric substrate: A theoretical study via a multiple-image method and an effective-dipole approach
We probe the electrostatic cost associated with the approach phase of DNA translocation events. Within an analytical theory at the Debye-Huckel level, we calculate the electrostatic free energy of a rigid DNA molecule interacting with a dielectric membrane. For carbon or silicon based low permittivity neutral membranes, the DNA molecule experiences a repulsive energy barrier between 10 kBT and 100 kBT. In the case of engineered membranes with high dielectric permittivity, the membrane surface attracts the DNA with an energy of the same magnitude. Both the repulsive and attractive interactions …
In biological and synthetic materials, many important processes involve charges that are present in a medium with spatially varying dielectric permittivity. To accurately understand the role of electrostatic interactions in such systems, it is important to take into account the spatial dependence of the permittivity of the medium. However, due to the ensuing theoretical and computational challenges, this inhomogeneous dielectric response of the medium is often ignored or excessively simplified. We develop a variational formulation of electrostatics to accurately investigate systems that exhibi…
We introduce a constrained energy functional to describe dielectric response. We demonstrate that the local functional is a generalization of the long ranged Marcus energy. Our re-formulation is used to implement a cluster Monte Carlo algorithm for the simulation of dielectric media. The algorithm avoids solving the Poisson equation and remains efficient in the presence of spatial heterogeneity, nonlinearity and scale dependent dielectric properties.
The standard Maxwell formulation of the problem of polarized dielectrics suffers from a number of difficulties, both conceptual and practical. These difficulties are particularly significant in the case of liquid interfaces, where the ability of the interfacial multipoles to change their orientations to minimize their free energies leads to interfacial polarization localized within a thin microscopic layer. A formalism to capture this physical reality of localized interfacial polarization is proposed and is based on the surface charge as the source of microscopic electric fields in dielectrics…
We develop of a field-theoretic approach for the treatment of both the non-local and the non-linear response of structured liquid dielectrics. Our systems of interest are composed of dipolar solvent molecules and simple salt cations and anions. We describe them by two independent order parameters, the polarization field for the solvent and the charge density field for the ions, including and treating the non-electrostatic part of the interactions explicitly and consistently. We show how to derive functionals for the polarization and the electrostatic field of increasingly finer scales and solv…
Electrostatic polarization is important in many nano-/micro-scale physical systems such as colloidal suspensions, biopolymers, and nanomaterials assembly. The calculation of polarization potential requires an efficient algorithm for solving 3D Poisson's equation. We have developed a useful image charge method to rapid evaluation of the Green's function of the Poisson's equation in the presence of spherical dielectric discontinuities. This paper presents an extensive study of this method by giving an convergence analysis and developing a coarse-graining algorithm. The use of the coarse graining…
Long-ranged electrostatic interactions in electrolytes modify their contact angles on charged substrates in a scale and geometry dependent manner. For angles measured at scales smaller than the typical Debye screening length, the wetting geometry near the contact line must be explicitly considered. Using variational and asymptotic methods, we derive new transcendental equations for the contact angle that depend on the electrostatic potential only at the three phase contact line. Analytic expressions are found in certain limits and compared with predictions for contact angles measured with lowe…
We present a detailed analysis of the effective force between two smooth spherical colloids floating at a fluid interface due to deformations of the interface. The results hold in general and are applicable independently of the source of the deformation provided the capillary deformations are small so that a superposition approximation for the deformations is valid. We conclude that an effective long--ranged attraction is possible if the net force on the system does not vanish. Otherwise, the interaction is short--ranged and cannot be computed reliably based on the superposition approximation.…
We have measured equilibrium sedimentation profiles in a colloidal model system with confocal microscopy. By tuning the interactions, we have determined the gravitational length in the limit of hard-sphere-like interactions, and using the same particles, tested a recent theory [R.van Roij, J. Phys. Cond. Mat. 15, S3569, (2003)], which predicts a significantly extended sedimentation profile in the case of charged colloids with long-ranged repulsions, due to a spontaneously formed macroscopic electric field. For the hard-sphere-like system we find that the gravitational length matches that expec…
Electrostatic correlations and variable permittivity of electrolytes are essential for exploring many chemical and physical properties of interfaces in aqueous solutions. We propose a continuum electrostatic model for the treatment of these effects in the framework of the self-consistent field theory. The model incorporates a space-or field-dependent dielectric permittivity and an excluded ion-size effect for the correlation energy. This results in a self-energy modified Poisson-Nernst-Planck or Poisson-Boltzmann equation together with state equations for the self energy and the dielectric fun…
Sensitive sequencing of biopolymers by nanopore-based translocation techniques requires extension of the time spent by the molecule in the pore. We develop an electrostatic theory of polymer translocation to show that the translocation time can be extended via the dielectric trapping of the polymer. In dilute salt conditions, the dielectric contrast between the low permittivity membrane and large permittivity solvent gives rise to attractive interactions between the cis and trans portions of the polymer. This self-attraction acts as a dielectric trap that can enhance the translocation time by …
We study the effect of dielectric inhomogeneities on the interaction between two planparallel charged surfaces with oppositely charged mobile charges in between. The dielectric constant between the surfaces is assumed to be different from the dielectric constant of the two semiinfinite regions bounded by the surfaces, giving rise to electrostatic image interactions. We show that on the weak coupling level the image charge effects are generally small, making their mark only in the second order fluctuation term. However, in the strong coupling limit, the image effects are large and fundamental. …
We study the problem of charge regulation and its effects on electrostatic interactions between dissociable charge groups immersed in a univalent electrolyte, within a family of one dimensional exactly solvable models. We consider the case of both charge regulated plates, but also the interaction of pairs of finite size dielectric "particles". Using the transfer matrix formalism we are able to determine the disjoining pressure as well as the correlations between the charge and the dipole moments of the objects as a function of their separation and electrolyte concentration
The goal of this work is to propose a simple continuous model that captures the dielectric properties of water at the nanometric scale. We write an electrostatic energy as a functional of the polarisation field containing a term in $P^4$ and non-local Gaussian terms. Such an hamiltonian can reproduce two key properties of water: the saturation of the polarisation response of water in the presence of a strong electrostatic field and the nanometric dipolar correlations of the solvent molecules modifying the long range van der waals interaction. This model explores thus two fundamental aspects th…
We present an approximate method for calculating the electrostatic free energy of concentrated protein solutions. Our method uses a cell model and accounts for both the coulomb energy and the entropic cost of Donnan salt partitioning. The former term is calculated by linearizing the Poisson-Boltzmann equation around a nonzero average potential, while the second term is calculated using a jellium approximation that is empirically modified to reproduce the dilute solution limit. When combined with a short-ranged binding interaction, calculated using the mean spherical approximation, our model re…
In this work, we analyzed an isotropic colloidal model incorporating both short-range sticky attractions and long-range electrostatic repulsions. We computed the zero-shear viscosity and second virial coefficient for a dilute colloidal suspension (i.e., pair interactions only) as a function of the strength of attractions and repulsions. We also developed an analytical approximation that allows us to better understand the coupling of the two types of interactions. The attractions and repulsions contribute to the zero-shear viscosity and second virial coefficient in different ways, leading to ca…
We consider dynamically constrained Monte-Carlo dynamics and show that this leads to the generation of long ranged effective interactions. This allows us to construct a local algorithm for the simulation of charged systems without ever having to evaluate pair potentials or solve the Poisson equation. We discuss a simple implementation of a charged lattice gas as well as more elaborate off-lattice versions of the algorithm. There are analogies between our formulation of electrostatics and the bosonic Hubbard model in the phase approximation. Cluster methods developed for this model further impr…
We study metastable clusters in a colloidal system with competing interactions. A short-ranged polymer-induced attraction drives clustering, while a weak, long-ranged electrostatic repulsion prevents extensive aggregation. We compare experimental yields of cluster structures expected from theory, which assumes simple addition of the competing isotropic interactions. For clusters of size $4\leq m\leq6$, the yield is significantly less than that expected. We attribute this to an anisotropic self-organized surface charge distribution linked to the cluster symmetry: non-additivity of electrostatic…
This paper builds on two previous works, Lindgren et al. J. Comp. Phys. 371, 712-731 (2018) and Quan et al. arXiv:1807.05384 (2018), to devise a new method to solve the problem of calculating electrostatic interactions in a system composed by many dielectric particles, embedded in a homogeneous dielectric medium, which in turn can also be permeated by charge carriers. The system is defined by the charge, size, position and dielectric constant of each particle, as well as the dielectric constant and Debye length of the medium. The effects of taking into account the dielectric nature of the part…
Systems in which a short-ranged attraction and long-ranged repulsion compete are intrinsically frustrated, leading their structure and dynamics to be dominated either by mesoscopic order or by metastable disorder. Here we report the latter case in a colloidal system with long-ranged electrostatic repulsions and short-ranged depletion attractions. We find a variety of states exhibiting slow non-diffusive dynamics: a gel, a glassy state of clusters, and a state reminiscent of a Wigner glass. Varying the interactions, we find a continuous crossover between the Wigner and cluster glassy states, an…
Electrostatic interactions play an important role in numerous self-assembly phenomena, including colloidal aggregation. Although colloids typically have a dielectric constant that differs from the surrounding solvent, the effective interactions that arise from inhomogeneous polarization charge distributions are generally neglected in theoretical and computational studies. We introduce an efficient technique to resolve polarization charges in dynamical dielectric geometries, and demonstrate that dielectric effects \emph{qualitatively} alter the predicted self-assembled structures, with surprisi…
Two main approaches in particle-based simulations for modeling a charged surface are using explicit, discrete charges and continuum, uniform charges. It is well-known that these two approaches could lead to substantially distinct ionic distributions, whereas a systematic exploration of the origin is still absent. In this short communication, we calculate the electrostatic force of a single point charge above a planar substrate characterized by a surface charge density and dielectric mismatch and compare the differences in the electrostatic forces produced by discrete and continuum representati…
Non-local electrostatic interactions associated with the finite solvent size and ion polarizability are investigated within the mean-field linear response theory. To this end, we introduce a field theoretic model of a polar liquid composed of linear multipole solvent molecules and embedding polarizable ions modeled as Drude oscillators. Unlike previous dipolar Poisson-Boltzmann formulations treating the solvent molecules as point dipoles, our model is able to qualitatively reproduce the non-local dielectric response behavior of polar liquids observed in Molecular Dynamics simulations and Atomi…
In this paper, we formulate a field-theoretical model of dilute salt solutions of electrically neutral spherical colloid particles. Each colloid particle consists of a 'central' charge that is situated at the center and compensating peripheral charges (grafted to it) that are fixed or fluctuating relative to the central charge. In the framework of the random phase approximation, we obtain a general expression for electrostatic free energy of solution and analyze it for different limiting cases. In the limit of infinite number of peripheral charges, when they can be modelled as a continual char…
We present the results of numerical simulations of the electrostatics and dynamics of water hydration shells surrounding Kihara cavities given by a Lennard-Jones (LJ) layer at the surface of a hard-sphere cavity. The local dielectric response of the hydration layer substantially exceeds that of bulk water, with the magnitude of the dielectric constant peak in the shell increasing with the growing cavity size. The polar shell propagates into bulk water to approximately the cavity radius. The statistics of the electrostatic field produced by water inside the cavity follow linear response and app…
We report a computational strategy to obtain the charges of individual dielectric particles from experimental observation of their interactions as a function of time. This strategy uses evolutionary optimization to minimize the difference between trajectories extracted from experiment and simulated trajectories based on many-particle force fields. The force fields include both Coulombic interactions and dielectric polarization effects that arise due to particle-particle charge mismatch and particle-environment dielectric contrast. The strategy was applied to systems of free falling charged gra…
We present a comment to a recent paper by Dominguez et. al. They claimed that the electrostatic interaction between charged colloids trapped at an interface formed by a dielectric and a screening phase is always isotropic to order $d^-3$. Base on this result, they claimed that in-plane dipolar attraction of order $d^-3$ between colloids cannot exist, in contrast to previous proposals. We point out that their analysis is not completed and anisotropic (dipolar) interaction between colloids can exist up to order $d^-3$.
Can we avoid molecular dynamics simulations to estimate the electrostatic interaction between charged objects separated by a nanometric distance in water? To answer this question, we develop a continuous model for the dielectric properties of water based on a functional of the polarization. A phenomenological Landau-Ginzburg Hamiltonian for the electrostatic energy of water is parameterized to capture the dipolar correlations in the fluid at the nanometric scale. We show that in this framework, the effective interactions of simple objects such as point charges are analytically tractable. In pa…
We theoretically investigate electrostatic properties between two charged surfaces with a grafted polyelectrolyte layer in an aqueous electrolyte solution by using the Poisson-Boltzmann approach accounting for ion partitioning. In order to consider the ion partitioning effect, we focus on changes of electrostatic properties due to the difference in dielectric permittivity of the polyelectrolyte layer and the aqueous electrolyte solution. We find that ion partitioning enhances electrostatic potential in the region between two charged soft surfaces and hence increases the electrostatic interacti…
A theoretical approach is proposed to calculate an effective dielectric constant of a matrix disperse system (MDS) of metallic particles (spheres) randomly distributed and embedded in a uniform dielectric medium. Deviations from the well-known Maxwell Garnett formula have been observed. The effective dielectric constant for different volume fractions of the embedded particles is considered as well as the dependence on pair interaction between particles, and the relation between sizes of each pair of particles. The problem is solved in the electrostatic approximation.
Computer simulations are used to investigate the response of a charged colloid and its surrounding microion cloud to an external electric field. Both static fields (DC) and alternating fields (AC) are considered. A mesoscopic simulation method is implemented to account in full for hydrodynamic and electrostatic interactions. The response of the system can be characterized by two quantities: the mobility and the polarizability. Due to the interplay of the electrostatic attraction and hydrodynamic drag, the response of the microions close to the colloid surface is different from that of the micr…
The general form of the electrostatic potential around an arbitrarily charged colloid at an interface between a dielectric and a screening phase (such as air and water, respectively) is analyzed in terms of a multipole expansion. The leading term is isotropic in the interfacial plane and varies with $d^{-3}$ where $d$ is the in--plane distance from the colloid. The electrostatic interaction potential between two arbitrarily charged colloids is likewise isotropic and $\propto d^{-3}$, corresponding to the dipole--dipole interaction first found for point charges at water interfaces. Anisotropic …
While the important role of electrostatic interactions in aqueous colloidal suspensions is widely known and reasonably well-understood, the relevance of charge in nonpolar suspensions remains mysterious. We demonstrate that particles can have surprisingly strong electrostatic interactions in low dielectric constant environments when ions are solubilized by reverse micelles. A simple thermodynamic model, relating the structure of the micelles to the equilibrium ionic strength, is in good agreement with both conductivity and interaction measurements. Since dissociated ions are solubilized by rev…
We study the effective interaction mediated by strongly coupled Coulomb fluids between dielectric surfaces carrying quenched, random monopolar charges with equal mean and variance, both when the Coulomb fluid consists only of mobile multivalent counterions and when it consists of an asymmetric ionic mixture containing multivalent and monovalent (salt) ions in equilibrium with an aqueous bulk reservoir. We analyze the consequences that follow from the interplay between surface charge disorder, dielectric and salt image effects, and the strong electrostatic coupling that results from multivalent…
We investigate the modification of gas phase ion polarizabilities upon solvation in polar solvents and ionic liquids. To this aim, we develop a classical electrostatic theory of charged liquids composed of solvent molecules modeled as finite size dipoles, and embedding polarizable ions that consist of Drude oscillators. In qualitative agreement with ab-initio calculations of polar solvents and ionic liquids, the hydration energy of a polarizable ion in both type of dielectric liquid is shown to favor the expansion of its electronic cloud. Namely, the ion carrying no dipole moment in the gas ph…
