Frequency dependence of ionic conductivity of electrolyte solutions

A theory for the frequency dependence of ionic conductivity of an electrolyte solution is presented. In this theory contributions to the conductivity from both the ion atmosphere relaxation and the electrophoretic effects are included in a self-consistent fashion. Mode coupling theory, combined with time-dependent density functional theory of ion atmosphere fluctuations, leads to expressions for these two contributions at finite frequencies. These expressions need to be solved self-consistently for the frequency dependence of the electrolyte friction and the ion conductivity at varying ion concentrations. In the limit of low concentration, the present theory reduces exactly to the well-known Debye-Falkenhagen (DF) expression of the frequency-dependent electrolyte friction when the non-Markovian effects in the ion atmosphere relaxation are ignored and in addition the ions are considered to be pointlike. The present theory also reproduces the expressions of the frequency-dependent conductivity derived by Chandra, Wei, and Patey when appropriate limiting situations are considered. We have carried out detailed numerical solutions of the self-consistent equations for concentrated solutions of a 1:1 electrolyte by using the expressions of pair correlation functions given by Attard. Numerical results reveal that the frequency dependence of the electrolyte friction at finite concentration can be quite different from that given by the DF expression. With the increase of ion concentration, the dispersion of the friction is found to occur at a higher frequency because of faster relaxation of the ion atmosphere. At low frequency, the real part of the conductivity shows a small increase with frequency which can be attributed to the well-known Debye-Falkenhagen effect. At high frequency, the conductivity decreases as expected. The extensions of the present theory to treat frequency-dependent diffusivities of charged colloid suspensions and conductivity of a dilute polyelectrolyte solution are discussed

Molecular theory of solvation and solvation dynamics of a classical ion in a dipolar liquid

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Polarization relaxation, dielectric dispersion, and solvation dynamics in dense dipolar liquid

A unified treatment of polarization relaxation, dielectric dispersion and solvation dynamics in a dense, dipolar liquid is presented. It is shown that the information of solvent polarization relaxation that is obtained by macroscopic dielectric dispersion experiments is not sufficient to understand dynamics of solvation of a newly created ion or dipole. In solvation, a significant contribution comes from intermediate wave vector processes which depend critically on the short range (nearest-neighbor) spatial and orientational order that are present in a dense, dipolar liquid. An analytic expression is obtained for the time dependent solvation energy that depends, in addition to the translational and rotational diffusion coefficients of the liquid, on the ratio of solute-solvent molecular sizes and on the microscopic structure of the polar liquid. Mean spherical approximation (MSA) theory is used to obtain numerical results for polarization relaxation, for wave vector and frequency dependent dielectric function and for time dependent solvation energy. We find that in the absence of translational contribution, the solvation of an ion is, in general, nonexponential. In this case, the short time decay is dominated by the longitudinal relaxation time but the long time decay is dominated by much slower large wave vector processes involving nearest-neighbor molecules. The presence of a significant translational contribution drastically alters the decay behavior. Now, the long-time behavior is given by the longitudinal relaxation time constant and the short time dynamics is controlled by the large wave vector processes. Thus, although the continuum model itself is conceptually wrong, a continuum model like result is recovered in the presence of a sizeable translational contribution. The continuum model result is also recovered in the limit of large solute to solvent size ratio. In the opposite limit of small solute size, the decay is markedly nonexponential (if the translational contribution is not very large) and a complete breakdown of the continuum model takes place. The significance of these results is discussed

Ionic contribution to the viscosity of dilute electrolyte solutions: towards a microscopic theory

The concentration dependence of viscosity of an electrolyte solution has remained largely an ill-understood problem of solution chemistry. Here we present a microscopic study of the problem aimed at removing this lacuna. A new microscopic expression for the ionic contribution to the viscosity of an electrolyte solution has been derived which expresses it in terms of the static and dynamic structure factors of the charge and the number densities of the electrolyte solution. This ionic contribution becomes the excess viscosity for extremely dilute solutions. The celebrated expression of Falkenhagen follows exactly from the microscopic expression in the limit of very low ion concentration. The present theory is a self-consistent theory which also includes the concentration dependence of the electrolyte friction on the ions. Numerical results reveal that the viscosity of a solution at finite concentration can be very different from that given by the Falkenhagen expression. The present theory predicts a stronger increase of viscosity with increase of ion concentration, especially for ions of higher valence which is in qualitative agreement with experimental results. The theory suggests that, for viscosity, the molecular nature of the ion-solvent interactions could be important even at very low ion concentration

Relationship between energy gap time correlation and fluorescence stokes shift correlation functions in solvation dynamics

The relationship between the energy gap time correlation function (EGTCF), measured in optical lineshape experiments, for a charged particle in a polar liquid, and the time correlation function obtained from time-dependent fluorescence Stokes shift measurements is explored. We show that if the distortion of the host solvent by the polar solute molecule is neglected, then both provide the same dynamical information. In the presence of a sizeable solvent distortion, emission and absorption lineshapes and Stokes shift measurements are all influenced differently by the solvent dynamics

Solvation of an ion and of a dipole in a dipolar liquid: How different are the dynamics

Theoretical expressions for the time-dependent solvation energy of an ion and of a dipole in a dense dipolar liquid are derived from microscopic considerations. We show that in contradiction to the prediction of the continuum models, the dynamics of these two species are significantly different from each other. Especially, the zero wavevector contribution, which is significant for ions, is totally absent for dipoles. Dipolar solvation may be profoundly influenced by the translational modes of the host solvent

Beyond the classical transport laws of electrochemistry: new microscopic approach to ionic conductance and viscosity

The concentration dependence of the transport properties (i.e., the conductivity and the viscosity) of an electrolyte solution has been a subject of lively debate for a very long time. The foundation for understanding the transport properties of electrolyte solutions was laid down by Debye, Huckel, Onsager, and Falkenhagen who derived several limiting laws valid at low ion concentration. These classical laws have been rederived several times, although their extension to concentrated solutions has proven to be very difficult. We discuss a new microscopic approach toward understanding the transport laws of electrochemistry. This new approach is based on the general ideas of the mode coupling theory. We show that the mode coupling theory approach is appropriate in the present case because concentration effects arise from collective variables (like charge density and current) which are treated correctly by the mode coupling theory. The new theory can describe the crossover from the low to high concentration seamlessly. Our study yields microscopic expressions of both conductivity and viscosity in terms of static and dynamic structure factors of the charge and number densities of the electrolyte solution. The celebrated expressions of Debye, Huckel, and Onsager for static conductance, of Debye and Falkenhagen for frequency dependent electrolyte friction, and of Falkenhagen for the viscosity follow exactly from the present microscopic theory in the limit of very low ion concentration. Recently derived microscopic expressions of Chandra, Wei, and Patey for the frequency dependent conductivity can also be derived from the present scheme. The present theory is a self-consistent theory. For conductance, the agreement of the present theory with experimental results is satisfactory even up to one molar concentration. For viscosity, the theory seems to give the right trend and suggests directions for further improvement to explain the myriad of unexplained behavior known for a long time

Ion conductance in electrolyte solutions

We develop a new theoretical formulation to study ion conductance in electrolyte solutions, based on a mode coupling theory treatment of the electrolyte friction. The new theory provides expressions for both the ion atmosphere relaxation and electrophoretic contributions to the total electrolyte friction that acts on a moving ion. While the ion atmosphere relaxation term arises from the time-dependent microscopic interaction of the moving ion with the surrounding ions in the solution, the electrophoretic term originates from the coupling of the ion's velocity to the collective current mode of the ion atmosphere. Mode coupling theory, combined with time-dependent density functional theory of ion atmosphere fluctuations, leads to self-consistent expressions for these two terms which also include the effects of self-motion of the ion under consideration. These expressions have been solved for the concentration dependence of electrolyte friction and ion conductance. It is shown that in the limit of very low ion concentration, the present theory correctly reduces to the well-known Debye-Huckel-Onsager limiting law which predicts a linear dependence of conductance on √c. At moderate and high concentrations, the present theory predicts a significant nonlinear and weaker dependence on which is in very good agreement with experimental results. The present theory is self-contained and does not involve any adjustable parameter