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 microions far away from the colloid. Both the mobility and polarizability exhibit a dependency on the frequency of the external fields, which can be attributed to the concentration polarization, the mobility of the microions, and the inertia of microions. The effects of the colloidal charge, the salt concentration, and the frequency of the external fields are investigated systematically.
We present a theory that enables us to calculate the effective surface charge of colloidal particles and to efficiently obtain titration curves for different salt concentrations. The theory accounts for the shift of pH of solution due to the presence of 1:1 electrolyte. It also accounts self-consistently for the electrostatic potential produced by the deprotonated surface groups. To examine the accuracy of the theory we have performed extensive reactive Monte Carlo simulations, which show excellent agreement between theory and simulations without any adjustable parameters.
We propose a novel actuation mechanism for colloids, which is based on the Seebeck effect of the electrolyte solution: Laser heating of a nonionic particle accumulates in its vicinity a net charge Q, which is proportional to the excess temperature at the particle surface. The corresponding long-range thermoelectric field provides a tool for controlled interactions with nearby beads or with additional molecular solutes. An external field Eext drags the thermocharged particle at a velocity that depends on its size and absorption properties; the latter point could be particularly relevant for sep…
The liquid-gas transition of an electroneutral mixture of oppositely charged colloids, studied by Monte Carlo simulations, is found in the low temperature -- low density region. The critical temperature shows a non-monotonous behavior as a function of the interaction range, $κ^{-1}$, with a maximum at $κσ\approx 10$, implying an island of coexistence in the $κ$-$ρ$ plane. The system is arranged in such a way that each particle is surrounded by shells of particles with alternating charge. In contrast with the electrolyte primitive model, both neutral and charged clusters are obtained in the vap…
Dynamic processes in dispersions of charged spherical particles are of importance both in fundamental science, and in technical and bio-medical applications. There exists a large variety of charged-particles systems, ranging from nanometer-sized electrolyte ions to micron-sized charge-stabilized colloids. We review recent advances in theoretical methods for the calculation of linear transport coefficients in concentrated particulate systems, with the focus on hydrodynamic interactions and electrokinetic effects. Considered transport properties are the dispersion viscosity, self- and collective…
We report on the low temperature behaviour of the colloidal electrolyte by means of Molecular Dynamics simulations, where the electrostatic interactions were modeled using effective screened interactions. As in previous works, we have found a region of gas-liquid coexistence located in the low $T$- low $ρ$ region. At temperatures much lower than the critical one, the system cannot reach equilibrium, that is, the gas-liquid transition is arrested. Two different mechanisms have been identified to cause arrest: gelation in the lowest $T$ and crowding at intermediate $T$ values, the latter associa…
We show that describing the screened electrostatic interactions in a periodic stack of rigid parallel identical charged plate-like colloids within a local density functional theory approach, generically leads to a swelling behaviour. Within the same framework, we find that the effective potential between a pair of such plates immersed in an electrolyte is repulsive at all distances. This general result is in contradiction with a theory put forward by Sogami, Shinohara and Smalley, that we criticize and thoroughly reconsider to show how the two approaches can be reconciled.
In the present work, we have extended a weak coupling theory [A. Bakhshandeh, A. P. dos Santos and Y. Levin Phys. Rev. Lett 107, 107801 (2011)] for systems with added 1:1 electrolyte. To study the accuracy of the developed theory, we compare its numerical predictions with Monte Carlo simulation data and a recent theory which accounts for the surface polarization. A very good agreement is found for the case of monovalent electrolytes, up to very high salt concentrations and different colloidal charges
We use a reactive Monte Carlo simulation method and primitive model of electrolyte to study acid-base equilibrium that controls charge regulation in colloidal systems. The simulations are performed in a semi-grand canonical ensemble in which colloidal suspension is in contact with a reservoir of salt and strong acid. The interior of colloidal particles is modeled as a low dielectric medium, different from the surrounding water. The effective colloidal charge is calculated for different number of surface acidic groups, pH, salt concentrations, and types of electrolyte. In the case of potassium …
From a multiple scale analysis, we find an analytic solution of spherical and cylindrical Poisson-Boltzmann theory for both a 1:2 (monovalent co-ions, divalent counter-ions) and a 2:1 (reversed situation) electrolyte. Our approach consists in an expansion in powers of rescaled curvature $1/(κa)$, where $a$ is the colloidal radius and $1/κ$ the Debye length of the electrolytic solution. A systematic comparison with the full numerical solution of the problem shows that for cylinders and spheres, our results are accurate as soon as $κa>1$. We also report an unusual overshooting effect where the c…
We consider the non-linear Poisson-Boltzmann theory for a single cylindrical or spherical macro-ion in symmetric 1:1, together with asymmetric 1:2 and 2:1 electrolytes. We focus on the regime where $κa $, the ratio of the macro-ion radius $a$ over the inverse Debye length in the bulk electrolyte, is large. Analyzing the structure of the analytical expansion emerging from a multiple scale analysis, we uncover a hidden structure for the electrostatic potential. This structure, which appears after a heuristic resummation, suggests a new and convenient expansion scheme that we present and work out…
We discuss the peculiarities of the Seebeck effect in stabilized electrolytes containing the colloidal particles. Its unusual feature is the two-stage character, with the linear increase of differential thermopower as the function of colloidal particles concentration $n_{\odot}$ during the first stage and dramatic drop of it at small $n_{\odot}$ during the second one (steady state). We show that the properties of the initial state are governed by the thermo-diffusion flows of the mobile ions of the stabilizing electrolyte medium itself and how the colloidal particles participate in formation o…
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)…
Electrode polarization error is the biggest problem when measuring the low frequency dielectric properties of electrolytes or suspensions of particles, including cells, in electrolytes. We present a simple and robust method to remove the polarization error, which we demonstrate to work on weak and strong ionic electrolytes as well as on cell suspensions. The method assumes no particular behavior of the electrode polarization impedance; it makes use of the fact that the effect dies out with frequency. The method allows for direct measurement of the polarization impedance, whose behavior with th…
Anisotropic colloidal particles constitute an important class of building blocks for self-assembly directed by electrical fields. The aggregation of these building blocks is driven by induced dipole moments, which arise from an interplay between dielectric effects and the electric double layer. For particles that are anisotropic in shape, charge distribution, and dielectric properties, calculation of the electric double layer requires coupling of the ionic dynamics to a Poisson solver. We apply recently proposed methods to solve this problem for experimentally employed colloids in static and t…
Using a field-theoretic approach, we derive the first few coefficients of the exact low-density (``virial'') expansion of a binary mixture of positively and negatively charged hard spheres (two-component hard-core plasma, TCPHC). Our calculations are nonperturbative with respect to the diameters $d_+$ and $d_-$ and charge valences $q_+$ and $q_-$ of positive and negative ions. Consequently, our closed-form expressions for the coefficients of the free energy and activity can be used to treat dilute salt solutions, where typically $d_+ \sim d_-$ and $q_+ \sim q_-$, as well as colloidal suspensio…
The effective electrostatic interaction between a pair of colloids, both of them located close to each other at an electrolyte interface, is studied by employing the full, nonlinear Poisson-Boltzmann (PB) theory within classical density functional theory. Using a simplified yet appropriate model, all contributions to the effective interaction are obtained exactly, albeit numerically. The comparison between our results and those obtained within linearized PB theory reveals that the latter overestimates these contributions significantly at short inter-particle separations. Whereas the surface co…
The hypernetted chain/mean spherical approximation (HNC/MSA) integral equation is obtained and solved numerically for a totally asymmetric primitive model electrolyte around a spherical macroparticle. The ensuing radial distribution functions show a very good agreement when compared to our Monte Carlo and molecular dynamics simulations for spherical geometry and with respect to previous anisotropic reference HNC calculations in the planar limit. We report an analysis of the potential vs charge relationship, radial distribution functions, mean electrostatic potential and cumulative reduced char…
We study the effective interaction between differently charged polyelectrolyte-colloid complexes in electrolyte solutions via Monte Carlo simulations. These complexes are formed when short and flexible polyelectrolyte chains adsorb onto oppositely charged colloidal spheres, dispersed in an electrolyte solution. In our simulations the bending energy between adjacent monomers is small compared to the electrostatic energy, and the chains, once adsorbed, do not exchange with the solution, although they rearrange on the particles surface to accomodate further adsorbing chains or due to the electros…
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…
Understanding dielectric spectra can reveal important information about the dynamics of solvents and solutes from the dipolar relaxation times down to electronic ones. In the late 1970s, Hubbard and Onsager predicted that adding salt ions to a polar solution would result in a reduced dielectric permittivity that arises from the unexpected tendency of solvent dipoles to align opposite to the applied field. So far, this effect has escaped an experimental verification, mainly because of the concomitant appearance of dielectric saturation from which the Hubbard-Onsager decrement cannot be easily s…
We study the Soret effect of charged polystyrene particles as a function of temperature and electrolyte composition. As a main result we find that the Soret coefficient is determined by charge effects, and that non-ionic contributions are small. In view of the well-kown electric-double layer interactions, our thermal field-flow fractionation data lead us to the conclusion that the Soret effect originates to a large extent from diffusiophoresis in the salt gradient and from the electrolyte Seebeck effect, both of which show strong specific-ion effects. Moreover, we find that thermophoresis of p…
Because micro-ions accumulate around highly charged colloidal particles in electrolyte solutions, the relevant parameter to compute their interactions is not the bare charge, but an effective (or renormalized) quantity, whose value is sensitive to the geometry of the colloid, the temperature or the presence of added-salt. This non-linear screening effect is a central feature in the field of colloidal suspensions or polyelectrolyte solutions. We propose a simple method to predict effective charges of highly charged macro-ions, that is reliable for mono-valent electrolytes (and counter-ions) in …
A numerical method is presented for first-principle simulations of charged colloidal dispersions in electrolyte solutions. Utilizing a smoothed profile for colloid-solvent boundaries, efficient mesoscopic simulations are enabled for modeling dispersions of many colloidal particles exhibiting many-body electrostatic interactions. The validity of the method was examined for simple colloid geometries, and the efficiency was demonstrated by calculating stable structures of two-dimensional dispersions, which resulted in the formation of colloidal crystals.
We study the response of single nanosized spherical colloids in electrolyte solution to an alternating electric field (AC field) by computer simulations. We use a coarse-grained mesoscopic simulation approach that accounts in full for hydrodynamic and electrostatic interactions as well as for thermal fluctuations. The solvent is modeled as a fluid of single Dissipative Particle Dynamics (DPD) beads, and the colloidal particle is modeled as a rigid body made of DPD beads. We compute the mobility and the polarizability of a single colloid and investigate systematically the effect of amplitude an…
The energy functional, the governing partial differential equation(s) (PDE), and the boundary conditions need to be consistent with each other in a modeling system. In electrolyte solution study, people usually use a free energy form of an infinite domain system (with vanishing potential boundary condition) and the derived PDE(s) for analysis and computing. However, in many real systems and/or numerical computing, the objective domain is finite, and people still use the similar energy form, PDE(s) but with different boundary conditions, which may cause inconsistency. In this work, (1) we prese…
We carry out the calculation of the surface tension for a model electrolyte to first order in a cumulant expansion about a free field theory equivalent to the Debye-Hückel approximation. In contrast with previous calculations, the surface tension is calculated directly without recourse to integrating thermodynamic relations. The system considered is a monovalent electrolyte with a region at the interface, of width h, from which the ionic species are excluded. In the case where the external dielectric constant epsilon_0 is smaller than the electrolyte solution's dielectric constant epsilon we s…
Heat and charge transport characteristics of nanocolloids have been bridged from fundamental analysis. The relationship between the two transport phenomena in dielectric nanostructure based polar colloids has been quantitatively presented. An extensional intuitive analogy to the Wiedemann Franz law has been drawn. Derived from the fact that mobile electrons transport both heat and charge within metallic crystal structure, the analogy can be extended to nanocolloids, wherein the dispersed population act as the major transporter. The analogy allows modeling the relationship between the two pheno…
We revisit the role of the local solvent structure on the activity coefficient of electrolytes with a general non-local dielectric function approach. We treat the concentrated electrolyte as a dielectric medium and suggest an interpolated formula for the dielectric response. The pure water limit is calibrated based on MD simulations and experimental data. Solving our model around a central ion, we find strong over-screening and oscillations in the potential, which are absent in the standard "primitive model" predictions. We obtain mathematically tractable closed-form expressions for the activi…
We study the thermal diffusion coefficient DT of a charged colloid in a temperature gradient, and find that it is to a large extent determined by the thermoelectric response of the electrolyte solution. The thermally induced salinity gradient leads in general to a strong increase with temperature. The difference of the heat of transport of coions and counterions gives rise to a thermoelectric field that drives the colloid to the cold or to the warm, depending on the sign of its charge. Our results provide an explanation for recent experimental findings on thermophoresis in colloidal suspension…
We consider a one-dimensional model allowing analytical derivation of the effective interactions between two charged colloids. We evaluate exactly the partition function for an electroneutral salt-free suspension with dielectric jumps at the colloids' position. We derive a contact relation with the pressure that shows there is like-charge attraction, whether or not the counterions are confined between the colloids. In contrast to the homogeneous dielectric case, there is the possibility for the colloids to attract despite the number of counter-ions ($N$) being even. The results are shown to re…
The ion distribution of electrolytes near interfaces with dielectric contrast has important consequences for electrochemical processes and many other applications. To date, most studies of such systems have focused on geometrically simple interfaces, for which dielectric effects are analytically solvable or computationally tractable. However, all real surfaces display nontrivial structure at the nanoscale and have, in particular, nonuniform local curvature. Using a recently developed, highly efficient computational method, we investigate the effect of surface geometry on ion distribution and i…
We theoretically study the electrolyte Seebeck effect in the vicinity of a heated metal nanostructure, such as the cap of an active Janus colloid in an electrolyte, or gold- coated interfaces in optofluidic devices. The thermocharge accumulated at the surface varies with the local temperature, thus modulating the diffuse part of the electric double layer. On a conducting surface with non-uniform temperature, the isopotential condition imposes a significant polarization charge within the metal. Surprisingly, this does not affect the slip velocity, which takes the same value on insulating and co…
We present the analysis of the impedance spectra for a binary electrolyte confined between blocking electrodes with dielectric layers. An expression for the impedance is derived from Poisson-Nernst-Planck equations in the linear approximation taking into account the voltage drop on the dielectric layer. The analysis shows, that characteristic features of the frequency dependence of the impedance are determined by the ratio of the Debay length and the effective thickness of the dielectric layer. The impact of the dielectric layer is especially strong in the case of high concentrated electrolyte…
When an electric field is applied to an electrolyte-saturated polymer gel embedded with charged colloidal particles, the force that must be exerted by the hydrogel on each particle reflects a delicate balance of electrical, hydrodynamic and elastic stresses. This paper examines the displacement of a single charged spherical inclusion embedded in an uncharged hydrogel. We present numerically exact solutions of coupled electrokinetic transport and elastic-deformation equations, where the gel is treated as an incompressible, elastic Brinkman medium. This model problem demonstrates how the displac…
Dielectric particles in weakly conducting fluids rotate spontaneously when subject to strong electric fields. Such Quincke rotation near a plane electrode leads to particle translation that enables physical models of active matter. Here, we show that Quincke rollers can also exhibit oscillatory dynamics, whereby particles move back and forth about a fixed location. We explain how oscillations arise for micron-scale particles commensurate with the thickness of a field-induced boundary layer in the nonpolar electrolyte. This work enables the design of colloidal oscillators.
We perform computational investigations of electrolyte-mediated interactions of charged colloidal particles confined within nanochannels. We investigate the role of discrete ion effects, valence, and electrolyte strength on colloid-wall interactions. We find for some of the multivalent charge regimes that the like-charged colloids and walls can have attractive interactions. We study in detail these interactions and the free energy profile for the colloid-wall separation. We find there are energy barriers and energy minima giving preferred colloid locations in the channel near the center and at…
We study the combined effects of electrostatic and hydrodynamic interactions (HI) on the short-time dynamics of charge-stabilized colloidal spheres. For this purpose, we calculate the translational and the rotational self-diffusion coefficients, $D^t_s$ and $D^r_s$, as function of volume fraction $ϕ$ for various values of the effective particle charge $Z$ and various concentrations $n_s$ of added 1--1 electrolyte. Our results show that the self-diffusion coefficients in deionized suspensions are less affected by HI than in suspensions with added electrolyte. For very large $n_s$, we recover th…
We use a hydrodynamic reciprocal approach to phoretic motion to derive general expressions for the electrophoretic and thermophoretic mobility of weakly charged colloids in aqueous electrolyte solutions. Our approach shows that phoretic motion can be understood in terms of the interfacial transport of thermodynamic excess quantities that arises when a colloid is kept stationary inside a bulk fluid flow. The obtained expressions for the mobilities are extensions of previously known results as they can account for different hydrodynamic boundary conditions at the colloidal surface, irrespective …
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 …
Since the early observation of nematic phases of disc-like clay colloids by Langmuir in 1938, the phase behaviour of such systems has resisted theoretical understanding. The main reason is that there is no satisfactory generalization for charged discs of the isotropic DLVO potential describing the effective interactions between a pair of spherical colloids in an electrolyte. In this contribution, we show how to construct such a pair potential, incorporating approximately both the non-linear effects of counter-ion condensation (charge renormalization) and the anisotropy of the charged platelets…
In the present article, we have studied the effect of the salt concentration (LiPF6) on transport properties and ion dynamics of blend solid polymer electrolyte (PEO PAN) prepared by solution cast technique. Fourier transform infrared (FTIR) spectroscopy confirms the presence of microscopic interactions such as polymer ion and ion ion interaction evidenced by a change in peak area of anion stretching mode. The fraction of free anions and ion pairs obtained from the analysis of FTIR implies that both influence the ionic conductivity with different salt concentration. The complex dielectric perm…
In spite of a large number of papers published in the last twenty years in the literature, the basic model of liquid water is still controversial. We have measured the dielectric permittivity of pure water and aqueous chlorides solutions in the range 0.2 to 1.5 THz and we have found that the overall dielectric behavior can be satisfactorily described with the weighted average of two single time constant Debye functions. The weights of the two components have been obtained by infrared spectra analysis and are related to two populations of water molecules having a different long range organizati…
We explore the force generation and surface interactions arising when electric fields are applied across fluid films. Using a surface force balance (SFB) we measure directly the force between two electrodes in crossed-cylinder geometry across dielectric and electrolytic fluids. In the case of dielectric films the field between the electrodes exerts a force which can be well explained using classic expressions and with no fitting parameters. However when the electrodes are separated by a film of electrolyte, an alternating electric field induces a force which diverges substantially from the cal…
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 …
Previously, we have proposed a direct simulation scheme for colloidal dispersions in a Newtonian solvent [Phys.Rev.E 71,036707 (2005)]. An improved formulation called the ``Smoothed Profile (SP) method'' is presented here in which simultaneous time-marching is used for the host fluid and colloids. The SP method is a direct numerical simulation of particulate flows and provides a coupling scheme between the continuum fluid dynamics and rigid-body dynamics through utilization of a smoothed profile for the colloidal particles. Moreover, the improved formulation includes an extension to incorporat…
The physical behaviour of anisotropic charged colloids is determined by their material dielectric anisotropy, affecting colloidal self-assembly, biological function and even out-of-equilibrium behaviour. However, little is known about anisotropic electrostatic screening, which underlies all electrostatic effective interactions in such soft or biological materials. In this work, we demonstrate anisotropic electrostatic screening for charged colloidal particles in a nematic electrolyte. We show that material anisotropy behaves markedly different from particle anisotropy: The electrostatic potent…
We use a variational principle to derive a mathematical model for a nematic electrolyte in which the liquid crystalline component is described in terms of a second-rank order tensor. The model extends the previously developed director-based theory and accounts for presence of disclinations and possible biaxiality. We verify the model by considering a simple but illustrative example of liquid crystal-enabled electro-osmotic flow (LCEO) around a stationary dielectric spherical particle placed at the center of a large cylindrical container filled with a nematic electrolyte. Assuming homeotropic a…
