Onsager's reciprocal relations in electrolyte solutions. I. Sedimentation and electroacoustics.

In the framework of irreversible thermodynamics, we show that the sedimentation current in electrolyte solutions is mathematically equivalent to the low frequency limit of the ionic vibration current, appearing in the presence of an acoustic wave. This non-trivial result is obtained thanks to a careful choice of the reference frame used to express the mass fluxes in the context of electroacoustics. Coupled transport phenomena in electrolyte solutions can also be investigated in a mechanical framework, with a set of Newtonian equations for the dynamics of charged solutes. Both in the context of sedimentation and of electroacoustics, we show that the results obtained in the mechanical framework, in the ideal case (i.e., without interactions between ions), do satisfy the Onsager's reciprocal relations. We also derive the general relation between corrective forces accounting for ionic interactions which must be fulfilled so that the Onsager's reciprocal relations are verified. Finally, we show that no additional diffusion term needs to be taken into account in the flux of solutes (far from the walls), even if local concentration gradients exist, contrarily to what was done previously in the literature.

Onsager's reciprocal relations in electrolyte solutions. II. Effect of ionic interactions on electroacoustics.

In electrolyte solutions, an electric potential difference, called the Ionic Vibration Potential (IVP), related to the ionic vibration intensity, is generated by the application of an acoustic wave. Several theories based on a mechanical framework have been proposed over the years to predict the IVP for high ionic strengths, in the case where interactions between ions have to be accounted for. In this paper, it is demonstrated that most of these theories are not consistent with Onsager's reciprocal relations. A new expression for the IVP will be presented that does fulfill the Onsager's reciprocal relations. We obtained this expression by deriving general expressions of the corrective forces describing non-ideal effects in electrolyte solutions.

Nonideal effects in electroacoustics of solutions of charged particles: combined experimental and theoretical analysis from simple electrolytes to small nanoparticles.

The electric signal induced by an ultrasonic wave in aqueous solutions of charged species is measured and analyzed. A device is developed which measures the raw induced electric signal for small sample volumes (few milliliters) and without any preceding calibration. The potential difference generated between two identical electrodes, called the ionic vibration potential (IVP), is thus easily deduced. In parallel, a theory for the IVP is built based on a robust analytical theory already used successfully to account for other transport coefficients in electrolyte solutions. From the analysis of the IVP measured for several aqueous electrolyte solutions, which are well-defined model systems for this technique, we explain and validate the different contributions to the signal. In particular, the non-ideal effects at high concentrations are thoroughly understood. A first step towards colloidal systems is presented by the analysis of the signal in solutions of a polyoxometallate salt, opening the possibility of determinations of reliable electrophoretic mobilities in dispersions of nanoobjects.

Critical effect of pore characteristics on capillary infiltration in mesoporous films.

Capillary phenomena governing the mass-transport (capillary filling, condensation/evaporation) has been experimentally investigated in around 20 different silica thin films exhibiting various porosities with pores dimension ranging from 2 to 200 nm. Films have been prepared by sol-gel chemistry combined with soft-templating approaches and controlled dip coating process. Environmental ellipsometric porosimetry combined with electronic microscopy were used to assess the porosity characteristics. Investigation of lateral capillary filling was performed by following the natural infiltration of water and ionic liquids at the edge of a sessile drop in open air or underneath a PDMS cover. The Washburn model was applied to the displacement of the liquid front within the films to deduce the kinetic constants. The role of the different capillary phenomena were discussed with respect to the porosity characteristics (porosity vol%, pore dimensions and constrictions). We show that correlation between capillary filling rate and pore dimensions is not straightforward. Generally, with a minimum of constrictions, faster filling is observed for larger pores. In the case of mesopores (<50 nm in diameter), the presence of bottle necks considerably slows down the infiltration rate. At such a small dimension, evaporation/capillary condensation dynamics, taking place at the meniscus inside the porosity, has to be considered to explain the transport mode. This fundamental study is of interest for applications involving liquids at the interface of mesoporous networks such as nanofluidics, purification, separation, water harvesting or heat transfer.

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.

Two-scale Brownian dynamics of suspensions of charged nanoparticles including electrostatic and hydrodynamic interactions.

We propose here a multiscale strategy based on continuous solvent Brownian dynamics (BD) simulations to study the dynamical properties of aqueous suspensions of charged nanoparticles. We extend our previous coarse-graining strategy [V. Dahirel et al., J. Chem. Phys. 126, 114108 (2007)] to account for hydrodynamic interactions between solute particles. Within this new procedure, two BD simulations are performed: (1) The first one investigates the time scales of the counterions and coions (the microions) with only one nanoparticle in the simulation box but explicit microions, (ii) the second one investigates the larger time scale of the nanoparticles with numerous nanoparticles in the simulation box but implicit microions. We show how individual and collective transport coefficients can be computed from this two-scale procedure. To ensure the validity of our procedure, we compute the transport coefficients of a 10-1 model electrolyte in aqueous solution with a 1-1 added salt. We do a systematic comparison between the results obtained within the new procedure and those obtained with explicit BD simulations of the complete system containing several nanoparticles and explicit microions. The agreement between the two methods is found to be excellent: Even if the new procedure is much faster than explicit simulations, it allows us to compute transport coefficients with a good precision. Moreover, one step of our procedure also allows us to compute the individual transport coefficients relative to the microions (self-diffusion coefficients and electrophoretic mobility).

Ion-mediated interactions between charged and neutral nanoparticles.

Monte-Carlo simulations are used to study the ion-mediated effective interaction between weakly charged and highly charged nanoparticles in an implicit solvent. Three models of nanoparticles are successively studied, from crude charged hard spheres to dipolar and non-spherical nanoparticles. The analysis of the effective potential revealed that in an electrolyte solution, even a neutral nanoparticle feels an important repulsive force in the presence of a charged nanoparticle, with a typical range similar to the Debye length. When the two nanoparticles carry charges of opposite sign, we have shown that this repulsion can reverse the effect of the direct attractive electrostatic potential at short distances. This also yields the change of sign of the effective potential as a function of the relative orientations of two anisotropic nanoparticles. Moreover, we found that the 3-body terms of the effective potentials can overcome the 2-body terms, which is not observed in the case of symmetrically charged nanoparticles.

Electrostatic relaxation and hydrodynamic interactions for self-diffusion of ions in electrolyte solutions.

The concentration dependence of self-diffusion of ions in solutions at large concentrations has remained an interesting yet unsolved problem. Here we develop a self-consistent microscopic approach based on the ideas of mode-coupling theory. It allows us to calculate both contributions which influence the friction of a moving ion: the ion atmosphere relaxation and hydrodynamic interactions. The resulting theory provides an excellent agreement with known experimental results over a wide concentration range. Interestingly, the mode-coupling self-consistent calculation of friction reveal a nonlinear coupling between the hydrodynamic interactions and the ion atmosphere relaxation which enhances ion diffusion by reducing friction, particularly at intermediate ion concentrations. This rather striking result has its origin in the similar time scales of the relaxation of the ion atmosphere relaxation and the hydrodynamic term, which are essentially given by the Debye relaxation time. The results are also in agreement with computer simulations, with and without hydrodynamic interactions.

How the excluded volume architecture influences ion-mediated forces between proteins.

The effective interactions between model proteins of various shapes are computed by means of Monte Carlo simulations. In particular, we determine how the modification of the excluded volume architecture influences both entropic and purely electrostatic ion-mediated forces between proteins. We find that interprotein interactions are strongly affected by protein shape, which results in a high decrease of electrostatic screening for typical active site geometries. Effective interactions are then closer to the direct Coulombic interactions, and both affinity and selectivity are enhanced by several orders of magnitude.

Determining the radius and the apparent charge of a micelle from electrical conductivity measurements by using a transport theory: explicit equations for practical use.

We propose here a procedure which combines experiments and simple analytical formulas that allows us to determine good estimations of the size and charge of ionic micelles above the critical micellar concentration (cmc). First, the conductivity of n-tetradecyltrimethylammonium bromide and chloride (TTABr and TTACl, respectively) aqueous solutions was measured at 25 degrees C, before and above their cmc. Then, an analytical expression for the concentration dependence of the conductance of an ionic mixture with three species (monomers, micelles, and counterions) was developed and applied to the analysis of the experiments. The theoretical calculations use the mean spherical approximation (MSA) to describe equilibrium properties. Here, we propose new expressions for the electrical conductivity, adapted to the case of electrolytes that are dissymmetric in size, and applicable up to a total surfactant concentration of 0.1 mol L(-1). Moreover, we show that they are good approximations of the corresponding numerical results obtained from Brownian dynamics simulations. Since the analytical formulas given in the present paper involve a small number of unknown parameters, they allow one to derive the size and charge of macroions in solution from conductivity measurements.

Brownian dynamics investigation of magnetization and birefringence relaxations in ferrofluids.

Brownian dynamics simulations are used to investigate the dynamics of orientational properties of real charge-stabilized ferrofluids, i.e. stable colloidal dispersions of magnetic nanoparticles. The relaxation times of the magnetization and of the birefringence, data accessible by experimental techniques, have been computed at several volume fractions. Besides, the effect of hydrodynamic interactions has been investigated. Equilibrium simulations without field are found to be inadequate to determine the aforementioned relaxation times for the systems under study, the dipolar interaction being too weak. Thus a nonequilibrium simulation procedure that mimics the experimental operating mode has been developed. After equilibrium simulations under a magnetic field, both birefringence and magnetization decays are recorded once the field is suppressed. Birefringence and magnetization decays are markedly impeded as the volume fraction increases, whereas they are barely enhanced when the intensity of the initial magnetic field is increased at a fixed volume fraction. Eventually, hydrodynamic interactions exhibit a slight but systematic lengthening of the relaxation times.

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.

Relaxation of the electrical double layer after an electron transfer approached by Brownian dynamics simulation.

In this paper, the dynamical properties of the electrochemical double layer following an electron transfer are investigated by using Brownian dynamics simulations. This work is motivated by recent developments in ultrafast cyclic voltammetry which allow nanosecond time scales to be reached. A simple model of an electrochemical cell is developed by considering a 1:1 supporting electrolyte between two parallel walls carrying opposite surface charges, representing the electrodes; the solution also contains two neutral solutes representing the electroactive species. Equilibrium Brownian dynamics simulations of this system are performed. To mimic electron transfer processes at the electrode, the charge of the electroactive species are suddenly changed, and the subsequent relaxation of the surrounding ionic atmosphere are followed, using nonequilibrium Brownian dynamics. The electrostatic potential created in the center of the electroactive species by other ions is found to have an exponential decay which allows the evaluation of a characteristic relaxation time. The influence of the surface charge and of the electrolyte concentration on this time is discussed, for several conditions that mirror the ones of classical electrochemical experiments. The computed relaxation time of the double layer in aqueous solutions is found in the range 0.1 to 0.4 ns for electrolyte concentrations between 0.1 and 1 mol L(-1) and surface charges between 0.032 and 0.128 C m(-2).