Electric fields near undulating dielectric membranes.

Dielectric interfaces are crucial to the behavior of charged membranes, from graphene to synthetic and biological lipid bilayers. Understanding electrolyte behavior near these interfaces remains a challenge, especially in the case of rough dielectric surfaces. A lack of analytical solutions consigns this problem to numerical treatments. We report an analytic method for determining electrostatic potentials near curved dielectric membranes in a two-dimensional periodic "slab" geometry using a periodic summation of Green's functions. This method is amenable to simulating arbitrary groups of charges near surfaces with two-dimensional deformations. We concentrate on one-dimensional undulations. We show that increasing membrane undulation increases the asymmetry of interfacial charge distributions due to preferential ionic repulsion from troughs. In the limit of thick membranes, we recover results mimicking those for electrolytes near a single interface. Our work demonstrates that rough surfaces generate charge patterns in electrolytes of charged molecules or mixed-valence ions.

Spiers Memorial Lecture: Towards understanding of iontronic systems: electroosmotic flow of monovalent and divalent electrolyte through charged cylindrical nanopores.

In many practical applications, ions are the primary charge carrier and must move through either semipermeable membranes or through pores, which mimic ion channels in biological systems. In analogy to electronic devices, the "iontronic" ones use electric fields to induce the charge motion. However, unlike the electrons that move through a conductor, motion of ions is usually associated with simultaneous solvent flow. A study of electroosmotic flow through narrow pores is an outstanding challenge that lies at the interface of non-equilibrium statistical mechanics and fluid dynamics. In this paper, we will review recent works that use dissipative particle dynamics simulations to tackle this difficult problem. We will also present a classical density functional theory (DFT) based on the hypernetted-chain approximation (HNC), which allows us to calculate the velocity of electroosmotic flows inside nanopores containing 1 : 1 or 2 : 1 electrolyte solution. The theoretical results will be compared with simulations. In simulations, the electrostatic interactions are treated using the recently introduced pseudo-1D Ewald summation method. The zeta potentials calculated from the location of the shear plane of a pure solvent are found to agree reasonably well with the Smoluchowski equation. However, the quantitative structure of the fluid velocity profiles deviates significantly from the predictions of the Smoluchowski equation in the case of charged pores with 2 : 1 electrolyte. For low to moderate surface charge densities, the DFT allows us to accurately calculate the electrostatic potential profiles and the zeta potentials inside the nanopores. For pores with 1 : 1 electrolyte, the agreement between theory and simulation is particularly good for large ions, for which steric effects dominate over the ionic electrostatic correlations. The electroosmotic flow is found to depend very strongly on the ionic radii. In the case of pores containing 2 : 1 electrolyte, we observe a reentrant transition in which the electroosmotic flow first reverses and then returns to normal as the surface change density of the pore is increased.

Effects of electrostatic coupling and surface polarization on polyelectrolyte brush structure.

In this work, we perform molecular dynamics simulations to study a spherical polyelectrolyte brush. We explore the effects of surface polarization and electrostatic coupling on brush size and distribution of counterions. The method of image charges is considered to take into account surface polarization, considering a metallic, an unpolarizable, and a dielectric nano-core. It is observed that, for all cases, a moderate shrinking-swelling effect appears with an increase in the electrostatic coupling parameter. This effect occurs under high Manning ratios. The curves relating the average size of polyelectrolyte brush as a function of coupling show a minimum. The results show that the grafting density of polyelectrolytes on the nano-core surface plays an important role in the polarization effect. We consider a modified Poisson-Boltzmann theory to describe the counterion profiles around the brush in the case of unpolarizable nano-cores and weak electrostatic coupling.

Reversal of Electroosmotic Flow in Charged Nanopores with Multivalent Electrolyte.

We study the reversal of electroosmotic flow in charged cylindrical nanopores containing multivalent electrolyte. Dissipative particle dynamics is used to simulate the hydrodynamics of the electroosmotic flow. The electrostatic interactions are treated using 3D Ewald summation, corrected for a pseudo-one-dimensional geometry of the pore. We observe that, for sufficiently large surface charge density, condensation of multivalent counterions leads to the reversal of the pore's surface charge. This results in the reversal of electroosmotic flow. Our simulations show that the Smoluchowski equation is able to quantitatively account for the electroosmotic flow through the nanopore, if the shear plane is shifted from the position of the Stern contact surface.

Electroosmotic Flow in Polarizable Charged Cylindrical Nanopores.

We present a simulation method to study electroosmotic flow in charged nanopores with dielectric contrast between their interior and the surrounding medium. To perform simulations, we separate the electrostatic energy into the direct Coulomb and the polarization contributions. The polarization part is obtained using periodic Green functions and can be expressed as a sum of fast converging modified Bessel functions. On the other hand, the direct Coulomb part of the electrostatic energy is calculated using fast converging three-dimensional (3D) Ewald summation method, corrected for a pseudo one-dimensional (1D) geometry. The effects of polarization are found to be particularly important for systems with multivalent counterions and narrow nanopores. Depending on the surface charge density, polarization can increase the volumetric flow rate by 200%. For systems with 3:1 electrolyte, we observe that there is a saturation of the volumetric flow rate. In this case, for polarizable pores, the flow rate is 100% higher than for nonpolarizable pores.

Correction: Electroosmosis as a probe for electrostatic correlations.

Correction for 'Electroosmosis as a probe for electrostatic correlations' by Ivan Palaia et al., Soft Matter, 2020, 16, 10688-10696, DOI: 10.1039/D0SM01523G.

Electroosmotic Flow Grows with Electrostatic Coupling in Confining Charged Dielectric Surfaces.

In this work, the effects of polarization of confining charged planar dielectric surfaces on induced electroosmotic flow are investigated. To this end, we use dissipative particle dynamics to model solvent and ionic particles together with a modified Ewald sum method to model electrostatic interactions and surfaces polarization. A relevant difference between counterions number density profiles, velocity profiles, and volumetric flow rates obtained with and without surface polarization for moderate and high electrostatic coupling parameters is observed. For low coupling parameters, the effect is negligible. An increase of almost 500% in volumetric flow rate for moderate/high electrostatic coupling and surface separation is found when polarizable surfaces are considered. The most important result is that the increase in electrostatic coupling substantially increases the electroosmotic flow in all studied range of separations when the dielectric constant of electrolytes is much higher than the dielectric constant of confining walls. For the higher separation simulated, an increase of around 340% in volumetric flow rate when the electrostatic coupling is increased by a factor of two orders of magnitude is obtained.

Interaction between Charge-Regulated Metal Nanoparticles in an Electrolyte Solution.

We present a theory which allows us to calculate the interaction potential between charge-regulated metal nanoparticles inside an acid-electrolyte solution. The approach is based on the recently introduced model of charge regulation which permits us to explicitly-within a specific microscopic model-relate the bulk association constant of a weak acid to the surface association constant for the same weak acid adsorption sites. When considering metal nanoparticles we explicitly account for the effect of the induced surface charge in the conducting core. To explore the accuracy of the approximations, we compare the ionic density profiles of an isolated charge-regulated metal nanoparticle with explicit Monte Carlo simulations of the same model. Once the accuracy of the theoretical approach is established, we proceed to calculate the interaction force between two charge-regulated metal nanoparticles by numerically solving the Poisson-Boltzmann equation with charge regulation boundary condition. The force is then calculated by integrating the electroosmotic stress tensor. We find that for metal nanoparticles the charge regulation boundary condition can be well approximated by the constant surface charge boundary condition, for which a very accurate Derjaguin-like approximation was recently introduced. On the other hand, a constant surface potential boundary condition often used in colloidal literature, shows a significant deviation from the charge regulation boundary condition for particles with large charge asymmetry.

Electroosmosis as a probe for electrostatic correlations.

We study the role of ionic correlations on the electroosmotic flow in planar double-slit channels, without salt. We propose an analytical theory, based on recent advances in the understanding of correlated systems. We compare the theory with mean-field results and validate it by means of dissipative particle dynamics simulations. Interestingly, for some surface separations, correlated systems exhibit a larger flow than predicted by mean-field. We conclude that the electroosmotic properties of a charged system can be used, in general, to infer and weight the importance of electrostatic correlations therein.

Simulations of electrolyte between charged metal surfaces.

We present a new method for simulating ungrounded charged metal slabs inside an electrolyte solution. The ions are free to move between the interior and exterior regions of the slab-electrolyte system. This leads to polarization of both sides of each slab, with a distinct surface charge induced on each surface. Our simulation method is based on the exact solution of the Poisson equation using periodic Green functions. To efficiently perform the calculations, we decouple the electrostatic energy due to surface polarization from that of purely Coulomb interaction between the ions. This allows us to combine a fast 3D Ewald summation technique with an equally fast calculation of polarization. As a demonstration of the method, we calculate ionic density profiles inside an electrolyte solution and explore charge neutrality violation in between charged metal slabs.

Consistent description of ion-specificity in bulk and at interfaces by solvent implicit simulations and mean-field theory.

Solvent-implicit Monte Carlo (MC) simulations and mean-field theory are used to predict activity coefficients and excess interfacial tensions for NaF, NaCl, NaI, KF, KCl, and KI solutions in good agreement with experimental data over the entire experimentally available concentration range. The effective ionic diameters of the solvent-implicit simulation model are obtained by fits to experimental activity coefficient data. The experimental activity coefficients at high salt concentrations are only reproduced if the ion-specific concentration-dependent decrement of the dielectric constant is included. The dielectric-constant dependent contribution of the single-ion solvation free energy to the activity coefficient is significant and is included. To account for the ion-specific excess interfacial tension of salt solutions, in addition to non-ideal solution effects and the salt-concentration-dependent dielectric decrement, an ion-specific ion-interface interaction must be included. This ion-interface interaction, which acts in addition to the dielectric image-charge repulsion, is modeled as a box potential, is considerably more long-ranged than the ion radius, and is repulsive for all ions considered except iodide, in agreement with previous findings and arguments. By comparing different models that include or exclude bulk non-ideal solution behavior, dielectric decrement effects, and ion-interface interaction potentials, we demonstrate how bulk and interfacial ion-specific effects couple and partially compensate each other. Our MC simulations, which correctly include ionic correlations and interfacial dielectric image-charge repulsion, are used to determine effective ion-surface interaction potentials that can be used in a modified Poisson-Boltzmann theory.

Isothermal adsorption of polyampholytes on charged nanopatterned surfaces.

We investigate the adsorption of neutral polyampholytes on charged nanopatterned surfaces. The surfaces have charged domains but are overall neutral. To perform efficient simulations, we use an approach which combines the explicit form of the interaction potential between the polyampholyte monomers and the surface with a 3d Ewald summation method. We observe that the amount of adsorption and the structure of the adsorbed polyampholytes depend strongly on the surface pattern, the relative size of the surface domains, and the charge distribution along the polyampholyte backbone.

Like-Charge Attraction between Metal Nanoparticles in a 1∶1 Electrolyte Solution.

We calculate the force between two spherical metal nanoparticles of charge Q_{1} and Q_{2} in a dilute 1∶1 electrolyte solution. Numerically solving the nonlinear Poisson-Boltzmann equation, we find that metal nanoparticles with the same sign of charge can attract one another. This is fundamentally different from what is found for like-charged, nonpolarizable, colloidal particles, the two-body interaction potential for which is always repulsive inside a dilute 1∶1 electrolyte. Furthermore, the existence of like-charge attraction between spherical metal nanoparticles is even more surprising in view of the result that such attraction is impossible between parallel metal slabs, showing the fundamental importance of curvature. To overcome a slow convergence of the numerical solution of the full nonlinear Poisson-Boltzmann equation, we developed a modified Derjaguin approximation which allows us to accurately and rapidly calculate the interaction potential between two metal nanoparticles or between a metal nanoparticle and a phospholipid membrane.

Simulations of Nanoseparated Charged Surfaces Reveal Charge-Induced Water Reorientation and Nonadditivity of Hydration and Mean-Field Electrostatic Repulsion.

We perform atomistic simulations of nanometer-separated charged surfaces in the presence of monovalent counterions at fixed water chemical potential. The counterion density profiles are well described by a modified Poisson-Boltzmann (MPB) approach that accounts for nonelectrostatic ion-surface interactions, while the effects of smeared-out surface-charge distributions and dielectric profiles are found to be relatively unimportant. The simulated surface interactions are for weakly charged surfaces well described by the additive contributions of hydration and MPB repulsions, but already for a moderate surface charge density of σ = -0.77 e/nm2 this additivity breaks down. This we rationalize by a combination of different effects, namely, counterion correlations as well as the surface charge-induced reorientation of hydration water, which modifies the effective water dielectric constant as well as the hydration repulsion.

Lattice model of ionic liquid confined by metal electrodes.

We study, using Monte Carlo simulations, the density profiles and differential capacitance of ionic liquids confined by metal electrodes. To compute the electrostatic energy, we use the recently developed approach based on periodic Green's functions. The method also allows us to easily calculate the induced charge on the electrodes permitting an efficient implementation of simulations in a constant electrostatic potential ensemble. To speed up the simulations further, we model the ionic liquid as a lattice Coulomb gas and precalculate the interaction potential between the ions. We show that the lattice model captures the transition between camel-shaped and bell-shaped capacitance curves-the latter characteristic of ionic liquids (strong coupling limit) and the former of electrolytes (weak coupling). We observe the appearance of a second peak in the differential capacitance at ≈0.5 V for 2:1 ionic liquids, as the packing fraction is increased. Finally, we show that ionic size asymmetry decreases substantially the capacitance maximum, when all other parameters are kept fixed.

Effective charges and zeta potentials of oil in water microemulsions in the presence of Hofmeister salts.

We present a theory which allows us to calculate the effective charge and zeta potential of oil droplets in microemulsions containing Hofmeister salts. A modified Poisson-Boltzmann equation is used to account for the surface and ion polarizations and hydrophobic and dispersion interactions. The ions are classified as kosmotropes and chaotropes according to their Jones-Dole viscosity B coefficient. Kosmotropes stay hydrated and do not enter into the oil phase, while chaotropes can adsorb to the oil-water interface. The effective interaction potentials between ions and oil-water interface are parametrized so as to accurately account for the excess interfacial tension.

Dielectric boundary effects on the interaction between planar charged surfaces with counterions only.

Using Monte Carlo simulations in conjunction with periodic Green's function methods, we study the interaction between planar charged surfaces with point-like counterions only in the presence of dielectric boundaries. Based on the calculated pressure profiles, we derive phase diagrams featuring correlation-induced negative pressure and thus attraction between the plates for large coupling parameters, i.e., low temperature or high surface charge and high ion valency. The counterion density profiles for low-dielectric and high-dielectric (metallic) surfaces are very different from the idealized case of a homogeneous dielectric constant. By contrast, the phase diagrams including the critical point and the two-phase coexistence region are rather insensitive to the presence of dielectric boundary effects. The single-image approximation that has been used in simulations before is by comparison with the exact formalism shown to be very accurate for low-dielectric surfaces but not for metallic surfaces.

Efficient simulation method for nano-patterned charged surfaces in an electrolyte solution.

We present a method to efficiently simulate nano-patterned charged surfaces inside an electrolyte solution. Simulations are performed in the grand canonical ensemble and are used to calculate the force between surfaces with various charge patterns. The electric field produced by the surfaces is calculated analytically and is used as an external potential. To treat the long range Coulomb interaction between the ions we use a modified 3d Ewald summation method. The force between the surfaces is found to depend strongly on the specific charge pattern, on the surface alignment and separation.

Simulations of Coulomb systems confined by polarizable surfaces using periodic Green functions.

We present an efficient approach for simulating Coulomb systems confined by planar polarizable surfaces. The method is based on the solution of the Poisson equation using periodic Green functions. It is shown that the electrostatic energy arising from the surface polarization can be decoupled from the energy due to the direct Coulomb interaction between the ions. This allows us to combine an efficient Ewald summation method, or any other fast method for summing over the replicas, with the polarization contribution calculated using Green function techniques. We apply the method to calculate density profiles of ions confined between the charged dielectric and metal surfaces.