Fernando O. Raineri

Smoluchowski fluctuation theory of dielectric relaxation

A recently proposed theory for transport coefficients in ionic solutions can be reinterpreted so that it becomes applicable to calculating the dielectric relaxation processes in dipolar fluids and in ionic solutions in dipolar solvents. The resulting theory is the same as the Smoluchowski–Vlasov theory which has been derived in various other ways by Munakata, Calef and Wolynes, and Chandra and Bagchi. Here the theory is applied to calculate the time correlation function for the fluctuating polarization density field in simple dipolar fluid, and in an ionic solution in a dipolar solvent. The results are similar to those derived some time ago by Berne using a ‘‘forced diffusion equation’’ as the theory for calculating the response. Comparison is also made with the results of Chandra and Bagchi using the Smoluchowski–Vaslov theory.

Electrolyte solutions that unmix. Hydrophobic ions in water

Simple models for the solvent-averaged ion-ion pair potentials for aqueous solutions of tetraalkylammonium halides were previously treated under the HNC (hypernetted chain) approximation to find the parameters needed to fit osmotic coefficient data of the corresponding real solutions. Here the model Pr4NI is modified by changing the A+− Gurney parameter to give the ‘Pr4NX’ model which exhibits the unmixing (separation into two solution phases of different concentrations) that has been reported for several real aqueous tetraalkylammonim salt solutions. The models used here are established at the McMillan-Mayer (MM) or solvent-averaged level, so careful attention is given to the choice of the thermodynamic potential from which we may derive the condition of material stability (stability with respect to separation into two phases of slightly different composition), and calculate the required thermodynamic coefficients from the MM pair correlation functions. The emphasis is on the study of the hydrophobic unmixing in terms of thermodynamic coefficients derived from the pair correlation functions calculated for the Pr4NX model under HNC. In the temperature-concentration (T-cS) plane we can locate the ‘solvability line’ (which separates states for which the HNC equation can be solved from the rest) and portions of the coexistence line. To locate the coexistence line in regimes in which the double tangent method is not effective we use a method based on the osmotic pressure and the solute chemical potential isotherms. Our results suggest that for the Pr4NX model in the T-cS plane the spinodal line lies within the solvability line which, in turn, lies within the coexistence line for the states where the latter could be determined. The role of the thermodynamic inconsistency implicit in the HNC correlation functions is given special attention, as is the remarkable role of the 1/r4 cavity term in the model pair potential. Single-ion activity coefficients and DELα functions are calculated for some of the states studied.

The role of reference frames in the molecular theory of diffusive transport in solutions

Starting with the Green–Kubo formulas for the phenomenological coefficients of irreversible thermodynamics, the molecular expression for the distinct diffusion coefficient Dd[R],αβ in any internal reference frame R is derived. It follows that Dd[R],αβ is given by the time integral of a time correlation function (tcf) Λd[R],αβ(t) whose dynamical variables are the velocities of two different particles of species α and β, each relative to a microscopic reference velocity wR . These relative dynamic variables have the welcome feature of being orthogonal to the total momentum of the system so that Λd[R],αβ(t) vanishes at long times. Hence the divergence of the barycentric distinct diffusion coefficients, suggested by their usual interpretation in terms of a time correlation function that lacks an explicit dependence on the reference frame, is resolved. The influence of the reference frame on the behavior of the barycentric distinct tcf ’s is analyzed. In great measure this influence is exposed by considering ...

Velocity correlations in the molecular dynamics ensemble: Computation of the distinct diffusion coefficients

The theory of the correction for the difference in the fluctuations among the different ensembles is applied to derive the time correlation function formula required to compute the distinct diffusion coefficients in the barycentric reference frame by molecular dynamics. In the process it is found that the dynamical variables in the time correlation function of any mass transport coefficient of any reference frame are the same in the canonical as in the molecular dynamics ensemble. The result agrees with the accepted formulas for computing the kinetic part of the mutual diffusion coefficient in a binary mixture of nonelectrolytes and for computing the electrical conductivity in molten salts and electrolyte solutions. The static velocity correlations in the molecular dynamics ensemble are analyzed without recourse to the other ensembles. In sharp contrast with the ensembles which are not constrained with respect to the total momentum, the laboratory‐frame velocities of two different particles at the same ti...

Self-diffusion coefficients of ions in electrolyte solutions by nonequilibrium Brownian dynamics

The self‐diffusion coefficients of the ions in a model electrolyte solution are calculated with a novel implementation of the nonequilibrium Brownian dynamics technique. The ions are coupled to an external color field E by color charges in such a way that each ionic species as a whole is electrically neutral to E. The ion–ion forces are not directly affected by the color charges or E. The method is tested on a model of a 1 M NaCl aqueous solution without hydrodynamic interactions and the results are compared with those of a previous equilibrium simulation for the same model system. The self‐diffusion coefficients of Na+ and Cl− are determined with 2%–3% accuracy and, within this margin, agree with the results of the equilibrium simulation obtained with more than twice the computational effort. Furthermore, within the range of field strengths studied, the average color flows depend linearly on E.

Velocity correlation functions in different reference frames. Their relation with phenomenological and empirical transport coefficients

In base of a baricentric expression given by H. Mori and with the introduction of a new set of collective dynamical variables, the ‘mean molecular velocities’ of the components, new Green–Kubo type expressions for the mass-transport phenomenological coefficients of irreversible thermodynamics in any reference frame are obtained. The dynamical variables involved in the time correlation functions are the mean molecular velocities of the components relative to the corresponding ‘microscopic reference velocity’, which is defined by analogy with the usual macroscopic one. The linear dependence of the relative mean molecular velocities determines that the sets of time correlation functions, their time integrals and the phenomenological coefficients are also linearly dependent. Nevertheless, the Onsager reciprocal relations are valid for each set. As the reference velocity appears explicitly, general transformation formulae among different frames for all these quantities are readily obtained at a microscopic level. As an application the expression by time correlation functions of some empirical transport coefficients such as the electric conductivity, transport numbers and ionic conductivities in mixed electrolyte solutions, and the interdiffusion coefficients in non-electrolyte mixtures, are deduced. The new expressions show explicitly the microscopic interpretation of these transport coefficients and their dependence on the reference frame.

Charge and electrical potential distributions in a nonequilibrium inhomogeneous electrolyte solution. A statistical mechanical approach. I. Single binary electrolyte. Theory

A molecular theory of the liquid junction between two different solutions of the same single binary electrolyte is derived from the statistical mechanical theory of linear response to thermal perturbations. The new theory employs a certain salt representation of the electrolyte solution that involves the transport numbers of the ion constituents. In this representation the solution is formally treated as a binary mixture of nonelectrolytes. The theory leads to expressions for the profiles (distributions through the junction) of charge, electrical potential, and number densities of the ion constituents in terms of the transport numbers and static equilibrium correlation functions formulated at the Born–Oppenheimer level. The implications of the new theory for the liquid junction potential (LJP) at this level remain to be developed. A simple approximation reduces the calculation of these profiles to the McMillan–Mayer level where only the ion–ion equilibrium correlation functions are required. The LJP deriv...

Determination of the mutual-diffusion coefficient of a binary mixture by non-equilibrium molecular dynamics viewed as a sedimentation experiment

We show that the computer simulation ‘colour-conductivity’ experiment that is used in non-equilibrium molecular dynamics to determine the kinetic part d of the mutual-diffusion coefficient of a binary mixture of non-electrolytes may be interpreted as a sedimentation experiment. Correspondingly, the expression that relates the colour conductivity to d is a special case of the Svedberg relation.

Salt velocity correlation functions: a microscopic interpretation. Part 2.—Solution of two or more binary electrolytes with a common ion

The new variational principle recently introduced is applied to extend the concept of the mean molecular velocity of a salt presented earlier for solutions of several electrolytes with a common ion constituent. All the isothermal vectorial transport coefficients of these systems are described in terms of the dissipative motions of the ion constituents, which are built up by two linear fully decoupled contributions. These are (1) a migrational part, associated with the movement of the ion constituent relative to its corresponding salt and (2) a diffusional part, associated to the movement of its salt relative to the solvent. Each salt velocity is dynamically orthogonal to the electric current; this guarantees that diffusion and electrical transport superpose but do not interact. The new formalism is entirely consistent with the formulations of irreversible thermodynamics and of velocity correlation integrals. By means of projection operators it is easily shown that the ionic phenomenological conductance coefficients as well as the ionic velocity correlation coefficients consist of two linear fully decoupled components which correspond to the migrational and the diffusional contributions.

The microscopic velocity of a salt in an electrolyte solution. An alternative characterization by a new variational principle

A new variational principle is described which leads to an expression for the microscopic salt velocity in a binary electrolyte solution which is identical with that introduced earlier, and shows this velocity to be that which which makes the dissipation function a minimum for a fixed thermodynamic state of the binary system.