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.

Electrolytes in regimes of strong confinement: surface charge modulations, osmotic equilibrium and electroneutrality.

In the present work, we study an electrolyte solution confined between planar surfaces with nanopatterned charged domains, which has been connected to a bulk ionic reservoir. The system is investigated through an improved Monte Carlo (MC) simulation method, suitable for simulation of electrolytes in the presence of modulated surface charge distributions. We also employ a linear approach in the spirit of the classical Debye-Hückel approximation, which allows one to obtain explicit expressions for the averaged potentials, ionic profiles, effective surface interactions and the net ionic charge confined between the walls. Emphasis is placed on the limit of strongly confined electrolytes, in which case local electroneutrality in the inter-surface space might not be fulfilled. In order to access the effects of such a lack of local charge neutrality on the ion-induced interactions between surfaces with modulated charge domains, we consider two distinct model systems for the confined electrolyte: one in which a salt reservoir is explicitly taken into account via the osmotic equilibrium with an electrolyte of fixed bulk concentration, and a second one in which the equilibrium with a charge neutral ionic reservoir is implicitly considered. While in the former case the osmotic ion exchange might lead to non-vanishing net charges, in the latter model charge neutrality is enforced through the appearance of an implicit Donnan potential across the charged interfaces. A strong dependence of the ion-induced surface interactions on the employed model system is observed at all surface separations. These findings strongly suggest that due care is to be taken while choosing among different scenarios to describe the ion exchange in electrolytes confined between charged surfaces, even in cases when the monopole (non zero net charge) surface contributions are absent.

Osmotic stress and pore nucleation in charged biological nanoshells and capsids.

A model system is proposed to investigate the chemical equilibrium and mechanical stability of biological spherical-like nanoshells in contact with an aqueous solution with added dissociated electrolyte of a given concentration. The ionic chemical equilibrium across the permeable shell is investigated in the framework of an accurate Density Functional Theory (DFT) that incorporates electrostatic and hardcore correlations beyond the traditional mean-field (e.g., Poisson-Boltzmann) limit. The accuracy of the theory is tested by a direct comparison with Monte Carlo (MC) simulations. A simple analytical expression is then deduced which clearly highlights the entropic, electrostatic, and self-energy contributions to the osmotic stress over the shell in terms of the calculated ionic profiles. By invoking a continuum mean-field elastic approach to account for the shell surface stress upon osmotic stretching, the mechanical equilibrium properties of the shell under a wide variety of ionic strengths and surface charges are investigated. The model is further coupled to a continuum mechanical approach similar in structure to a Classical Nucleation Theory (CNT) to address the question of mechanical stability of the shells against a pore nucleation. This allows us to construct a phase diagram which delimits the mechanical stability of capsids for different ionic strengths and shell surface charges.

Quenching of fully symmetric mixtures of oppositely charged microgels: the role of soft stiffness.

Using molecular dynamics simulations, we investigate the self-assembly of a coarse-grained binary system of oppositely charged microgels, symmetric in size and concentration. The microgel pair interactions are described by an effective pair potential which implicitly accounts for the averaged ionic contributions, in addition to a short-range elastic repulsion that accounts for the overlapping of the polymer chains, the latter being described by the Hertzian interaction. Particular emphasis is placed on the role played by the strength of the soft repulsive interaction on the resulting particle aggregation. It is found that the possibility of particle inter-penetration in oppositely charged soft particles results in a much wider variety of cluster morphologies in comparison with their hard-spheres counterparts. Specifically, the softness of the steric interactions enhances the competition between repulsive and attractive electrostatic interactions, leading to the formation of aggregates that are comprised of strongly bounded charged particles displaying a low degree of charge ordering.

Self-Assembly of Ionic Microgels Driven by an Alternating Electric Field: Theory, Simulations, and Experiments.

The structural properties of a system of ionic microgels under the influence of an alternating electric field are investigated both theoretically and experimentally. This combined investigation aims to shed light on the structural transitions that can be induced by changing either the driving frequency or the strength of the applied field, which range from string-like formation along the field to crystal-like structures across the orthogonal plane. In order to highlight the physical mechanisms responsible for the observed particle self-assembly, we develop a coarse-grained description, in which effective interactions among the charged microgels are induced by both equilibrium ionic distributions and their time-averaged hydrodynamic responses to the applied field. These contributions are modeled by the buildup of an effective dipole moment at the microgels backbones, which is partially screened by their ionic double layer. We show that this description is able to capture the structural properties of this system, allowing for very good agreement with the experimental results. The model coarse-graining parameters are indirectly obtained via the measured pair distribution functions and then further assigned with a clear physical interpretation, allowing us to highlight the main physical mechanisms accounting for the observed self-assembly behavior.

Ionic size effects on the Poisson-Boltzmann theory.

In this paper, we develop a simple theory to study the effects of ionic size on ionic distributions around a charged spherical particle. We include a correction to the regular Poisson-Boltzmann equation in order to take into account the size of ions in a mean-field regime. The results are compared with Monte Carlo simulations and a density functional theory based on the fundamental measure approach and a second-order bulk expansion which accounts for electrostatic correlations. The agreement is very good even for multivalent ions. Our results show that the theory can be applied with very good accuracy in the description of ions with highly effective ionic radii and low concentration, interacting with a colloid or a nanoparticle in an electrolyte solution.

Lattice Model of an Ionic Liquid at an Electrified Interface.

We study ionic liquids interacting with electrified interfaces. The ionic fluid is modeled as a Coulomb lattice gas. We compare the ionic density profiles calculated using a popular modified Poisson-Boltzmann equation with the explicit Monte Carlo simulations. The modified Poisson-Boltzmann theory fails to capture the structural features of the double layer and is also unable to correctly predict the ionic density at the electrified interface. The lattice Monte Carlo simulations qualitatively capture the coarse-grained structure of the double layer in the continuum. We propose a convolution relation that semiquantitatively relates the ionic density profiles of a continuum ionic liquid and its lattice counterpart near an electrified interface.

Charge neutrality breakdown in confined aqueous electrolytes: Theory and simulation.

We study, using Density Functional theory (DFT) and Monte Carlo simulations, aqueous electrolyte solutions between charged infinite planar surfaces, in contact with a bulk salt reservoir. In agreement with recent experimental observations [Z. Luo et al., Nat. Commun. 6, 6358 (2015)], we find that the confined electrolyte lacks local charge neutrality. We show that a DFT based on a bulk-HNC expansion properly accounts for strong electrostatic correlations and allows us to accurately calculate the ionic density profiles between the charged surfaces, even for electrolytes containing trivalent counterions. The DFT allows us to explore the degree of local charge neutrality violation, as a function of plate separation and bulk electrolyte concentration, and to accurately calculate the interaction force between the charged surfaces.

Equilibrium properties of charged microgels: a Poisson-Boltzmann-Flory approach.

The equilibrium properties of ionic microgels are investigated using a combination of the Poisson-Boltzmann and Flory theories. Swelling behavior, density profiles, and effective charges are all calculated in a self-consistent way. Special attention is given to the effects of salinity on these quantities. In accordance with the traditional ideal Donnan equilibrium theory, it is found that the equilibrium microgel size is strongly influenced by the amount of added salt. Increasing the salt concentration leads to a considerable reduction of the microgel volume, which therefore releases its internal material - solvent molecules and dissociated ions - into the solution. Finally, the question of charge renormalization of ionic microgels in the context of the cell model is briefly addressed.

Yukawa particles in a confining potential.

We study the density distribution of repulsive Yukawa particles confined by an external potential. In the weak coupling limit, we show that the mean-field theory is able to accurately account for the particle distribution. In the strong coupling limit, the correlations between the particles become important and the mean-field theory fails. For strongly correlated systems, we construct a density functional theory which provides an excellent description of the particle distribution, without any adjustable parameters.

Equation of state of charged colloidal suspensions and its dependence on the thermodynamic route.

The thermodynamic properties of highly charged colloidal suspensions in contact with a salt reservoir are investigated in the framework of the renormalized Jellium model (RJM). It is found that the equation of state is very sensitive to the particular thermodynamic route used to obtain it. Specifically, the osmotic pressure calculated within the RJM using the contact value theorem can be very different from the pressure calculated using the Kirkwood-Buff fluctuation relations. On the other hand, Monte Carlo simulations show that both the effective pair potentials and the correlation functions are accurately predicted by the RJM. It is suggested that the lack of self-consistency in the thermodynamics of the RJM is a result of neglected electrostatic correlations between the counterions and coions.

The renormalized Jellium model of colloidal suspensions with multivalent counterions.

An extension of the renormalized Jellium model which allows to study colloidal suspensions containing trivalent counterions is proposed. The theory is based on a modified Poisson-Boltzmann equation which incorporates the effects of counterion correlations near the colloidal surfaces using a new boundary condition. The renormalized charges, the counterion density profiles, and osmotic pressures can be easily calculated using the modified renormalized Jellium model. The results are compared with the ones obtained using the traditional Wigner-Seitz (WS) cell approximation also with a new boundary condition. We find that while the thermodynamic functions obtained within the renormalized Jellium model are in a good agreement with their WS counterpart, the effective charges predicted by the two theories can be significantly different.

A self-consistent renormalized jellium approach for calculating structural and thermodynamic properties of charge stabilized colloidal suspensions.

An approach is proposed which allows to self-consistently calculate the structural and the thermodynamic properties of highly charged aqueous colloidal suspensions. The method is based on the renormalized jellium model with the background charge distribution related to the colloid-colloid correlation function. The theory is used to calculate the correlation functions and the effective colloidal charges for suspensions containing additional monovalent electrolyte. The predictions of the theory are in excellent agreement with Monte Carlo simulations.

Structural anomalies for a three dimensional isotropic core-softened potential.

Using molecular dynamics simulations we investigate the structure of a system of particles interacting through a continuous core-softened interparticle potential. We found for the translational order parameter t a local maximum at a density rho(t-max) and a local minimum at rho(t-min)>rho(t-max). Between rho(t-max) and rho(t-min), the t parameter anomalously decreases upon increasing pressure. For the orientational order parameter Q(6) a maximum was observed at a density rho(t-max)

Thermodynamic and dynamic anomalies for a three-dimensional isotropic core-softened potential.

Using molecular-dynamics simulations and integral equations (Rogers-Young, Percus-Yevick, and hypernetted chain closures) we investigate the thermodynamics of particles interacting with continuous core-softened intermolecular potential. Dynamic properties are also analyzed by the simulations. We show that, for a chosen shape of the potential, the density, at constant pressure, has a maximum for a certain temperature. The line of temperatures of maximum density (TMD) was determined in the pressure-temperature phase diagram. Similarly the diffusion constant at a constant temperature, D, has a maximum at a density rho(max) and a minimum at a density rho(min) < rho(max). In the pressure-temperature phase diagram the line of extrema in diffusivity is outside of the TMD line. Although this interparticle potential lacks directionality, this is the same behavior observed in simple point charge/extended water.