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

Micellar formation of cationic surfactants

The micellar structure of six alkyl trimethylammonium halides was studied via conductivity. It was found that the aggregation number increased with the decreasing carbon chain length. Furthermore, Br⁻ significantly enhanced the micellar formation over Cl⁻. However, the aggregation number and ionization degree remain similar for both anions. The modelling results validate that the counter-anions affect micellar formation via equilibrium constants, instead of their hydration size. In particular, the association constants between surfactant (both monomer and micelle) and Br⁻ are significantly higher than Cl⁻. This is consistent with the qualitative description of hydrated Br⁻ in the literature. The experimental and modelling results confirm that micelles are formed via “ion-paring/hydration” structure, instead of the conventional “packing” concept.

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.

Electrical conductivity of mixed electrolytes: Modeling within the mean spherical approximation

The purpose of this study is to predict the electrical conductivity of an electrolyte solution containing several simple ionic species. Explicit equations of the MSA-transport theory for the electrical conductivity in this complex solution are given. The theoretical conductivity of simple salts is first compared to experimental results of the literature to deduce the sizes of the ions. These sizes allow us to calculate the conductivity for a mixture of several ionic species without any additional parameter. We have also measured the electrical conductivity of solutions of LiCl, NaCl, and KCl and of KBr and MgCl(2) at 25 degrees C. A very good agreement between theoretical calculations and experimental values is obtained for each studied system.

Interpretation of conductivity results from 5 to 45 degrees C on three micellar systems below and above the CMC

Electrical conductivity has been used at different temperatures to study three micellar systems: tetradecyltrimethylammonium chloride (TTACl), dodecyltrimethylammonium chloride (DTACl), and decyltrimethylammonium chloride (DeTACl). A phenomenon of premicellization is observed for DeTACl and DTACl below the critical micellar concentration (CMC). Association constants are introduced in the MSA-transport theory to correctly reproduce experimental conductivity and also calculate the effective charge of the micelles and their degree of dissociation. Various mechanisms are considered to explain premicellization. The formation of a neutral pair followed by an association involving two monomers and a counterion appears to be the most probable first step in the premicellization process.

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.

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.

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.