Counterion and polyion dynamics in highly asymmetrical electrolyte solutions

Comparison of different coupling schemes between counterions and charged nanoparticles in multiparticle collision dynamics

We applied the multiparticle collision dynamics (MPC) simulation technique to highly asymmetric electrolytes in solution, i.e., charged nanoparticles and their counterions in a solvent. These systems belong to a domain of solute size which ranges between the electrolyte and the colloidal domains, where most analytical theories are expected to fail, and efficient simulation techniques are still missing. MPC is a mesoscopic simulation method which mimics hydrodynamics properties of a fluid, includes thermal fluctuations, and can be coupled to a molecular dynamics of solutes. We took advantage of the size asymmetry between nanoparticles and counterions to treat the coupling between solutes and the solvent bath within the MPC method. Counterions were coupled to the solvent bath during the collision step and nanoparticles either through a direct interaction force or with stochastic rotation rules which mimic stick boundary conditions. Moreover, we adapted the simulation procedure to address the issue of the strong electrostatic interactions between solutes of opposite charges. We show that the short-ranged repulsion between counterions and nanoparticles can be modeled by stochastic reflection rules. This simulation scheme is very efficient from a computational point of view. We have also computed the transport coefficients for various densities. The diffusion of counterions was found in one case to increase slightly with the volume fraction of nanoparticles. The deviation of the electric conductivity from the ideal behavior (solutes at infinite dilution without any direct interactions) is found to be strong.

Dynamics of solutes with hydrodynamic interactions: comparison between Brownian dynamics and stochastic rotation dynamics simulations

The dynamics of particles in solution or suspension is influenced by thermal fluctuations and hydrodynamic interactions. Several mesoscale methods exist to account for these solvent-induced effects such as Brownian dynamics with hydrodynamic interactions and hybrid molecular dynamics-stochastic rotation dynamics methods. Here we compare two ways of coupling solutes to the solvent with stochastic rotation dynamics (SRD) to Brownian dynamics with and without explicit hydrodynamic interactions. In the first SRD scheme [SRD with collisional coupling (CC)] the solutes participate in the collisional step with the solvent and in the second scheme [SRD with central force coupling (CFC)] the solutes interact through direct forces with the solvent, generating slip boundary conditions. We compare the transport coefficients of neutral and charged solutes in a model system obtained by these simulation schemes. Brownian dynamics without hydrodynamic interactions is used as a reference to quantify the influence of hydrodynamics on the transport coefficients as modeled by the different methods. We show that, in the dilute range, the SRD CFC method provides results similar to those of Brownian dynamics with hydrodynamic interactions for the diffusion coefficients and for the electrical conductivity. The SRD CC scheme predicts diffusion coefficients close to those obtained by Brownian dynamic simulations without hydrodynamic interactions, but accounts for part of the influence of hydrodynamics on the electrical conductivity.

Brownian Simulations Contribution to the Study of Ionic Dynamics in Aqueous Solutions

We review some results concerning the dynamics of ionic solutions that we have recently obtained by Brownian dynamics simulations; we also present new results concerning the dynamical behavior of asymmetrical electrolytes (1–10 and 2–20 electrolytes). The Brownian dynamics treats the solution in the framework of the continuous solvent model, with a ‘soft-core’ version of the primitive model. Both direct interactions and hydrodynamic interactions between solutes are taken into account in the calculations. The method allows one to obtain the self-diffusion coefficient of each ion and the electrical conductivity of the solution. The computed transport coefficients are in good agreement with experimental determinations in various cases (in aqueous solutions of 1–1 electrolytes as well as in aqueous solutions of micelles). We show that hydrodynamic interactions must be taken into account to obtain electrical conductivities in agreement with experiments. The effect of hydrodynamic interactions on the self-diffusion is also striking, especially in solutions of asymmetrical electrolytes. If this effect remains weak in simple electrolyte solutions and for small ions in 1–20 and 2–20 electrolyte solutions, it is great for macroions in latter solutions (increase of about 15 to 40%).

Coarse-graining in suspensions of charged nanoparticles

A coarse-grain description of nanocolloidal suspensions in the presence of an added salt is presented here. It enables us to simulate trajectories of the nanoparticles from effective functions that depend on average densities of salt ions. In practice, the ion-averaged effective potential is used as input of a Brownian dynamics (BD) simulation. This potential may be derived by various methods, ranging from purely analytical to fully numerical ones. For the description of dynamical properties, this simulation also requires an effective diffusion coefficient that must be calculated or experimentally determined, and that accounts for the effects of microions on the mobility of the nanoparticles. The different versions of our coarse-graining procedure are applied to the case of a maghemite suspension, for which an explicit description of all ions would be very time-consuming.

New coarse-graining procedure for the dynamics of charged spherical nanoparticles in solution

A multiscale strategy based on the Brownian dynamics (BD) simulation method is presented here. It leads to an approximate but realistic reproduction of the dynamics of charged nanoparticles in suspension. This method is particularly suited to systems containing highly dissymmetric electrolytes with added salts, such as micellar suspensions or protein solutions. The coarse-graining procedure leads to a description where only the translational degrees of freedom of the nanoparticles are left, all the degrees of freedom related to the smallest solutes being rigorously averaged out. The authors' contribution aims at quantitatively evaluating the influence of the eliminated forces on the dynamics of the nanoparticles. For this purpose, an effective diffusion coefficient has to be calculated. In practice, this effective diffusion coefficient is taken as an input of a coarse-grained simulation that uses the potential of mean force between nanoparticles. The procedure has been validated by the quantitative comparison between the coarse-grained calculations and BD simulations at the "microscopic" level of description (which explicitly include microions). For a model of aqueous solutions of 10-1 electrolyte with a 1-1 added salt, the agreement is found to be excellent. This new method allows us to compute the diffusion coefficients of nanoparticles with a computation time at least one order of magnitude lower than with explicit BD.

Field theory for size- and charge-asymmetric primitive model of ionic systems: mean-field stability analysis and pretransitional effects

The primitive model of ionic systems is investigated within a field-theoretic description for the whole range of diameter-, lambda , and charge, Z ratios of the two ionic species. Two order parameters (OP) are identified. The relation of the OP's to physically relevant quantities is nontrivial. Each OP is a linear combination of the charge density and the number-density waves. Instabilities of the disordered phase associated with the two OP's are determined in the mean-field approximation (MF). In MF a gas-liquid separation occurs for any Z and lambda is not equal to 1 . In addition, an instability with respect to various types of periodic ordering of the two kinds of ions is found. Depending on lambda and Z , one or the other transition is metastable in different thermodynamic states. For sufficiently large size disparity we find a sequence of fluid-crystal-fluid transitions for the increasing volume fraction of ions, in agreement with experimental observations. The instabilities found in MF represent weak ordering of the most probable instantaneous states, and are identified with structural loci associated with pretransitional effects.

Structural properties of charge-stabilized ferrofluids under a magnetic field: A Brownian dynamics study

We present Brownian dynamics simulations of real charge-stabilized ferrofluids, which are stable colloidal dispersions of magnetic nanoparticles, with and without the presence of an external magnetic field. The colloidal suspensions are treated as collections of monodisperse spherical particles, bearing point dipoles at their centers and undergoing translational and rotational Brownian motions. The overall repulsive isotropic interactions between particles, governed by electrostatic repulsions, are taken into account by a one-component effective pair interaction potential. The potential parameters are fitted in order that computed structure factors are close to the experimental ones. Two samples of ferrofluid differing by the particle diameter and consequently by the intensity of the magnetic interaction are considered here. The magnetization and birefringence curves are computed: a deviation from the ideal Langevin behaviors is observed if the dipolar moment of particles is sufficiently large. Structure factors are also computed from simulations with and without an applied magnetic field H: the microstructure of the repulsive ferrofluid becomes anisotropic under H. Even our simple modeling of the suspension allows us to account for the main experimental features: an increase of the peak intensity is observed in the direction perpendicular to the field whereas the peak intensity decreases in the direction parallel to the field.

Transport coefficients of aqueous dodecyltrimethylammonium bromide solutions: Comparison between experiments, analytical calculations and numerical simulations

We study dynamical properties of ionic species in aqueous solutions of dodecyltrimethylammonium bromide, for several concentrations below and above the critical micellar concentration (cmc). New experimental determinations of the electrical conductivity are given which are compared to results obtained from an analytical transport theory; transport coefficients of ions in these solutions above the cmc are also computed from Brownian dynamics simulations. Analytical calculations as well as the simulation treat the solution within the framework of the continuous solvent model. Above the cmc, three ionic species are considered: the monomer surfactant, the micelle and the counterion. The analytical transport theory describes the structural properties of the electrolyte solution within the mean spherical approximation and assumes that the dominant forces which determine the deviations of transport processes from the ideal behavior (i.e., without any interactions between ions) are hydrodynamic interactions and electrostatic relaxation forces. In the simulations, both direct interactions and hydrodynamic interactions between solutes are taken into account. The interaction potential is modeled by pairwise repulsive 1/r(12) interactions and Coulomb interactions. The input parameters of the simulation (radii and self-diffusion coefficients of ions at infinite dilution) are partially obtained from the analytical transport theory which fits the experimental determinations of the electrical conductivity. Both the electrical conductivity of the solution and the self-diffusion coefficients of each species computed from Brownian dynamics are compared to available experimental data. In every case, the influence of hydrodynamic interactions (HIs) on the transport coefficients is investigated. It is shown that HIs are crucial to obtain agreement with experiments. In particular, the self-diffusion coefficient of the micelle, which is the largest and most charged species in the present system, is enhanced when HIs are included whereas the diffusion coefficients of the monomer and the counterion are roughly not influenced by HIs.