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 representations of surface charges. We demonstrate that while the model of uniform surface charges gives a rather simple picture, the model of discrete surface charges can exhibit different scenarios, depending on the respective values of ion-surface distance versus lattice spacing and a self-image interaction parameter.
We explore, using the recently developed efficient Monte Carlo simulation method, the interaction of an anionic polyelectrolyte solution with a like-charged dielectric surface. In addition to polyions, the solution also contains salt with either monovalent, divalent, or trivalent counterions. In agreement with recent experimental observations, we find that multivalent counterions can lead to strong adsorption of polyions onto the surface. On the other hand, addition of a 1:1 electrolyte diminishes the adsorption induced by the multivalent counterions. Dielectric discontinuity at the interface …
For charged systems in heterogeneous dielectric media, a key obstacle for molecular dynamics (MD) simulations is the need to solve the Poisson equation in the media. This obstacle can be bypassed using MD methods that treat the local polarization charge density as a dynamic variable, but such approaches require access to a true free energy functional; one that evaluates to the equilibrium electrostatic energy at its minimum. In this letter, we derive the needed functional. As an application, we develop a Car-Parrinello MD method for the simulation of free charges present near a spherical emuls…
We investigate the ion distribution and overcharging at charged interfaces with dielectric inhomogeneities in the presence of asymmetric electrolytes containing polyvalent and monovalent ions. We formulate an effective "dressed counterion" approach by integrating out the monovalent salt degrees of freedom and show that it agrees with results of explicit Monte-Carlo simulations. We then apply the dressed counterion approach within the framework of the strong-coupling theory, valid for polyvalent ions at low concentrations, which enables an analytical description for salt effects as well as diel…
In this work, the dielectric behavior of water inside charged nanoslit of graphene is studied to analized the water molecules under electrical confinement; through polarizing the nanoslit of graphene, creating an electric field inside the nanopore. How the water molecules are structured under this type of electrical confinement is studied with two force fields of water, the three-site water models here used are the SCP/$ε$ and the FAB/$ε$, the first is a rigid model that improves the SPC model and the second is a flexible model that improves all the force fields of three sites non-polarizables…
Aequous dielectrics are ubiquitous in soft- and bio-nano matter systems. The theoretical description of such systems in terms of continuum (`macroscopic') theory remains a serious challenge. In this perspective we first review the existing continuum phenomenological approaches that have been developed in the past decades. In order to describe a path to advance continuum theory beyond these approaches we then take recourse to the Onsager-Dupuis theory of the dielectric behaviour of ice, which, for the case of a solid dielectric, exemplified important conceptual issues we deem relevant for the d…
The basic continuum model for polar fluids is deceptively simple. The free energy integral consists of four terms: The coupling of polarization to an external field, the electrostatic energy of the induced electric field interacting with itself and the stored polarization energy quadratic in the polarization. A local function of density accounts for the mechanical state of the fluid. Viewed as a non-equilibrium free energy functional of number density and polarization, minimization in these two densities under constraints of the Maxwell field equations should lead the correct equilibrium state…
We present a simulation method to study electrolyte solutions in a dielectric slab geometry using a modified 3D Ewald summation. The method is fast and easy to implement, allowing us to rapidly resum an infinite series of image charges. In the weak coupling limit, we also develop a mean-field theory which allows us to predict the ionic distribution between the dielectric charged plates. The agreement between both approaches, theoretical and simulational, is very good, validating both methods. Examples of ionic density profiles in the strong electrostatic coupling limit are also presented. Fina…
We extend results developed by Chandler [J. Chem. Phys. 65, 2925 (1976)] for the dielectric constant of neutral site-site molecular models to mixtures of both charged and uncharged molecules. This provides a unified derivation connecting the Stillinger-Lovett moment conditions for ions to standard results for the dielectric constant for polar species and yields exact expressions for the small-k expansion of the two-point intermolecular charge-density function used to determine the total Coulomb energy. The latter is useful in determining corrections to the thermodynamics of uniform site-site m…
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. …
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…
Dipolar susceptibility of interfacial water and the corresponding interface dielectric constant were calculated from numerical molecular dynamics simulations for neutral and charged states of buckminsterfullerene C$_{60}$. Dielectric constants in the range 10--22, depending on temperature and solute charge, were found. The hydration water undergoes a structural crossover as a function of the solute charge. Its main signatures include the release of dangling O-H bonds pointing toward the solute and the change in the preferential orientations of hydration water from those characterizing hydropho…
Brownian Dynamics simulations are carried out to understand the effect of temperature and dielectric constant of the medium on microphase separation of charged-neutral diblock copolymer systems. For different dielectric media, we focus on the effect of temperature on the morphology and dynamics of model charged diblock copolymers. In this study we examine in detail a system of partially charged block copolymer consisting of 75% neutral blocks and 25% of charged blocks with 50% degree of ionization. Our investigations show that due to the presence of strong electrostatic interactions between th…
Using a variational field theory, we show that an electrolyte confined to a neutral cylindrical nanopore traversing a low dielectric membrane exhibits a first-order ionic liquid-vapor pseudo-phase-transition from an ionic-penetration "liquid" phase to an ionic-exclusion "vapor" phase, controlled by nanopore-modified ionic correlations and dielectric repulsion. For weakly charged nanopores, this pseudotransition survives and may shed light on the mechanism behind the rapid switching of nanopore conductivity observed in experiments.
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…
A variational theory is developed to study electrolyte solutions, composed of interacting point-like ions in a solvent, in the presence of dielectric discontinuities and charges at the boundaries. Three important and non-linear electrostatic effects induced by these interfaces are taken into account: surface charge induced electrostatic field, solvation energies due to the ionic cloud, and image charge repulsion. Our variational equations thus go beyond the mean-field theory. The influence of salt concentration, ion valency, dielectric jumps, and surface charge is studied in two geometries. i)…
Plasma treatment of polymer films results in their electrical charging, which in turn gives rise to an increase in their surface energy. The process results in pronounced hydrophilization of the polymer surfaces. A phenomenological theory relating the change in the apparent contact angle of charged solids to the surface density of the electrical charge is introduced. Partial wetting, inherent for polymer films, becomes possible until the threshold surface density of the electrical charge is gained. The predictions of the theory are illustrated by plasma-treated polymer films and inflatable lat…
The ion distribution around charged colloids in solution has been investigated intensely during the last decade. However, few theoretical approaches have included the influence of variation in the dielectric permittivity within the system, let alone in the surrounding solvent. In this article, we introduce two relatively new methods that can solve the Poisson equation for systems with varying permittivity. The harmonic interpolation method (HIM) approximately solves the Green's function in terms of a spherical harmonics series, and thus provides analytical ion-ion potentials for the Hamiltonia…
We study the low-frequency dielectric response of highly charged spheres arranged in a cubic lattice and immersed in an electrolyte solution. We focus on the influence of the out-of-phase current in the regime where the ionic charge is neutral. We consider the case where the charged spheres have no surface conductance and no frequency-dependent surface capacitance. Hence, the frequency dispersion of the dielectric constant is dominated by the effect of neutral currents outside the electric double layer. In the thin double-layer limit, we use Fixman's boundary condition at the outer surface of …
We present a general theory of liquid crystals under inhomogeneous electric field in a Ginzburg-Landau scheme. The molecular orientation can be deformed by electric field when the dielectric tensor is orientation-dependent. We then investigate the influence of a charged particle on the orientation order in a nematic state. The director is aligned either along or perpendicular to the local electric field around the charge, depending on the sign of the dielectric anisotropy. The deformation becomes stronger with increasing the ratio $Ze/R$, where $Ze$ is the charge and $R$ is the radius of the p…
The behavior of a polyelectrolyte adsorbed on a charged surface of high-dielectric constant is studied by both Monte-Carlo simulation and analytical methods. It is found that in a low ionic strength medium, the transition is first-order with the repulsive charged surface. The order parameter which characterize the polyelectrolyte adsorption, the surface monomer density, follows a linear relation with surface charge density. It indicates the polyelectrolyte is always compressed on the substrate. No conformation change exists before the de-sorption. Finally, a new scaling law for the layer thick…
We present the results of an analytical theory and simulations of the field inside a cavity created in a dipolar liquid placed in a uniform external electric field. The analytical theory shows that the limit of continuum electrostatics is reached through a singularity in the microscopic response function responsible for a non-decaying longitudinal polarization wave. Fields in microscopic cavities are much different from macroscopic predictions, and low-polarity dielectrics are predicted to have a continuum limit distinct from the solution of Maxwell's equations. Computer Monte Carlo simulation…
Dielectric permittivity of water confined in stacks of charged lipid layers: extracting profiles from molecular dynamics simulations using a modified Poisson-Boltzmann equation
Université Claude Bernard Lyon 1, CNRS, Institut Lumière Matière（里昂第一大学，法国国家科学研究中心，光物质研究所）；UPR 22/CNRS, Institut Charles Sadron, Université de Strasbourg（斯特拉斯堡大学，法国国家科学研究中心查尔斯·萨德龙研究所）
There is a large body of literature investigating the static and dynamic properties of polyelectrolytes due both to their widespread application in industrial processes and their ubiquitous presence in biology. Because of their highly charged nature, polyelectrolytes tend to alter the local dielectric permittivity of the solution within a few nanometers of their backbone. This effect has, however, been almost entirely ignored in both simulations and theoretical work. In this article we apply our recently developed electrostatic solver based on Maxwell's equations to examine the effects of the …
A classical dielectric moving in a charged capacitor can create a magnetic field (Roentgen effect). A quantum dielectric, however, will not produce a magnetization, except at vortices. The magnetic field outside the quantum dielectric appears as the field of quantized monopoles.
The standard model for diffuse charge phenomena in colloid science, electrokinetics and biology is the Poisson-Boltzmann mean-field theory, which breaks down for multivalent ions and large surface charge densities due to electrostatic correlations. In this paper, we formulate a predictive continuum theory of correlated electrolytes based on two extensions of the Bazant-Storey-Kornyshev (BSK) framework: (i) a physical boundary condition enforcing continuity of the Maxwell stress at a charged interface, which upholds the Contact Theorem for dilute primitive-model electrolytes, and (ii) scaling r…
The forces between charged macromolecules, usually given in terms of osmotic pressure, are highly affected by the intervening ionic solution. While in most theoretical studies the solution is treated as a homogeneous structureless dielectric medium, recent experimental studies concluded that, for a bathing solution composed of two solvents (binary mixture), the osmotic pressure between charged macromolecules is affected by the binary solvent composition. By adding local solvent composition terms to the free energy, we obtain a general expression for the osmotic pressure, in planar geometry and…
Monopolar charge disorder effects are studied in the context of fluctuation-induced interactions between neutral dielectric slabs. It is shown that quenched bulk charge disorder gives rise to an additive contribution to the net interaction force which decays as the inverse distance between the slabs and may thus completely mask the standard Casimir--van der Waals force at large separations. By contrast, annealed (bulk or surface) charge disorder leads to a net interaction force whose large-distance behavior coincides with the universal Casimir force between perfect conductors, which scales as …
We study the low-frequency polarization response of a surface-charged oblate spheroidal particle immersed in an electrolyte solution. Because the charged spheroid attracts counter-ions which form the electric double layer around the particle, using usual boundary conditions at the interface between the particle and electrolyte can be quite complicated and challenging. Hence, we generalize Fixman's boundary conditions, originally derived for spherical particles, to the case of the charged oblate spheroid. Given two different counter-ion distributions in the thin electric double layer limit, we …
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 investigate the impact of dielectric boundary forces on the translocation process of charged rigid DNA segments through solid neutral nanopores. We assess the electrostatic contribution to the translocation free energy barrier of a model DNA segment by evaluating the potential of mean force in absence and presence of polarization effects by means of coarse-grained molecular dynamics simulations. The effect of induced polarization charges has been taken into account by employing ICC*, a recently developed algorithm that can efficiently compute induced polarization charges induced on suitably…
We analytically calculate the correlation potential of a test ion near a \emph{strongly} charged plate inside a dilute $m:-n$ electrolyte. We do this by calculating the electrostatic Green's function in the presence of a nonlinear background potential, the latter having been obtained using the nonlinear Poisson-Boltzmann theory. We consider the general case where the dielectric constants of the plate and the electrolyte are distinct. The following generic results emerge from our analyses: (1) If the distance to the plate $Δz$ is much larger than a Gouy-Chapman length, the plate surface will be…
Polarizable randomly charged dielectric objects have been recently shown to exhibit long-range lateral and normal interaction forces even when they are effectively net neutral. These forces stem from an interplay between the quenched statistics of random charges and the induced dielectric image charges. This type of interaction has recently been evoked to interpret measurements of Casimir forces in vacuo, where a precise analysis of such disorder-induced effects appears to be necessary. Here we consider the torque acting on a randomly charged dielectric surface (or a sphere) mounted on a centr…
Many theoretical studies were devoted in the past to ion-specific effects, trying to interpret a large body of experimental evidence, such as surface tension at air/water interfaces and force measurements between charged objects. Although several mechanisms were suggested to explain the results, such as dispersion forces and specific surface-ion interactions, we would like to suggest another source of ion-specificity, originating from the local variations of the dielectric constant due to the presence of ions in the solution. We present a mean-field model to account for the heterogeneity of th…
The electromagnetic response of a nanoparticle of an ion-doped polymeric elastic insulator, commonly called as an electret, is considered in the continuum model of a uniformly charged elastic sphere. The spectral formulae for the frequency of optically induced spheroidal and torsional shear oscillations driven by bulk force of elastic and dielectric stresses are obtained in analytic form. Particular attention is given to relaxation dielectric mode of the electrostriction response and its stability in the lowest quadrupole mode. The practical usefulness of ultrafine particles of electrets as a …
We study the distribution of multivalent counterions next to a dielectric slab, bearing a quenched, random distribution of charges on one of its solution interfaces, with a given mean and variance, both in the absence and in the presence of a bathing monovalent salt solution. We use the previously derived approach based on the dressed multivalent-ion theory that combines aspects of the strong and weak coupling of multivalent and monovalent ions in a single framework. The presence of quenched charge disorder on the charged surface of the dielectric slab is shown to substantially increase the de…
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…
The structure of polar liquids and electrolytic solutions, such as water and aqueous electrolytes, at interfaces underlies numerous phenomena in physics, chemistry, biology, and engineering. In this work, we develop a continuum theory that captures the essential features of dielectric screening by polar liquids at charged interfaces, including oscillations in charge and mass, starting from the molecular properties of the solvent. The theory predicts an anisotropic dielectric tensor of interfacial polar liquids previously studied in molecular dynamics simulations. We explore the effect of the i…
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 Monte-Carlo algorithm for the simulation of charged particles moving in the continuum. Electrostatic interactions are not instantaneous as in conventional approaches, but are mediated by a constrained, diffusing electric field on an interpolating lattice. We discuss the theoretical justifications of the algorithm and show that it efficiently equilibrates model polyelectrolytes and polar fluids. In order to reduce lattice artifacts that arise from the interpolation of charges to the grid we implement a local, dynamic subtraction algorithm. This dynamic scheme is completely genera…
A strong-coupling theory for polarizable symmetrically charged walls with counterions only
Institute of Physics, Slovak Academy of Sciences（斯洛伐克科学院物理研究所）；Universidade Federal do Rio Grande do Sul（南里奥格兰德联邦大学）；Université Paris-Saclay（巴黎萨克雷大学）；École Normale Supérieure de Lyon（里昂高等师范学院）
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.
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.
Polyelectrolytes under confinement are crucial for energy storage and for understanding biomolecular functions. Using molecular dynamics simulations, we analyze a polyelectrolyte solution confined between two oppositely charged planar dielectric surfaces and include surface polarization effects due to dielectric mismatch at the two electrodes. Although the effect of polarization on the charge distribution seems minor, we find that surface polarization enhances energy storage and also leads to the emergence of negative differential capacitance in confined polyelectrolyte solutions.
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…
A simple field theory approach is developed to model the properties of charged, dielectric bodies and their associated counterions. This predictive theory is able to accurately describe the properties of systems (as compared to computer simulation data) from the weak coupling limit, where the Poisson-Boltzmann theory works well, through to the strong coupling limit. In particular, it is able to quantitatively describe the attraction between like-charged plates and the influence of image charge interactions.
Randomly charged net-neutral dielectric slabs are shown to interact across a featureless dielectric continuum with long-range electrostatic forces that scale with the statistical variance of their quenched random charge distribution and inversely with the distance between their bounding surfaces. By accounting for the whole spectrum of electromagnetic field fluctuations, we show that this long-range disorder-generated interaction extends well into the retarded regime where higher-order Matsubara frequencies contribute significantly. This occurs even for highly clean samples with only a trace a…
Screening is one of the most important concepts in the study of charged systems. Near a dielectric interface, the ion distribution in a salt solution can be highly nonuniform. Here, we develop a theory that self-consistently treats the inhomogeneous screening effects. At higher concentrations when the bulk Debye screening length is comparable to the Bjerrum length, the double layer structure and interfacial properties are significantly affected by the inhomogeneous screening. In particular, the depletion zone is considerably wider than that predicted by the bulk screening approximation or the …
