Alok Samanta

Mode coupling theory of self and cross diffusivity in a binary fluid mixture: Application to Lennard-Jones systems

A microscopic approach has been developed for the self as well as cross diffusivity of a binary fluid mixture based on the concepts of mode coupling theory. Illustrative numerical results calculated for a Lennard-Jones fluid mixture are presented and are shown to be in good agreement with the available computer simulation results. The effects of mass, composition, interaction strength, and sizes of the components on the diffusivities are studied in order to obtain insight into the role of different modes in the diffusion process. The mass dependence of diffusivity is found to be weak with a power law behavior in contrast to the Enskog theory prediction of strong mass dependence. Also the mass and concentration of one component are found to have significant and interesting effects on the diffusivity of the other component. The new expressions derived here are shown to predict positive values for the cross diffusion constant over the various parameter ranges considered, which is consistent with the simulati...

STUDY OF CORRELATION EFFECTS IN AN EXACTLY SOLVABLE MODEL TWO-ELECTRON SYSTEM

The correlation energies for a system of two electrons moving under mutual Coulomb repulsion augmented by a linear interparticle potential and bound to a central harmonic oscillator potential are studied through an exact analytical solution proposed recently by the authors. The same are also obtained for a related model with no linear term through numerical solution. Several plots of the local as well as averaged correlation holes for varying strengths of the binding potential for both the models provide insight into the shape and radius of the holes. The effect of correlation on the single particle density is manifested through reduction of the probability density near the center with a consequent increase in the outer region.

Universal scaling laws of diffusion: application to liquid metals.

This work focuses on the universal scaling laws, which relate scaled diffusivity to excess entropy in fluids and their mixtures. The derivation of the new scaling law for diffusivity proposed recently [A. Samanta, Sk. M. Ali, and S. K. Ghosh, Phys. Rev. Lett. 92, 145901 (2004)] is discussed in details highlighting the nature of approximations involved. Also the applicability of the scaling law is extended to a new class of liquids, viz., liquid metals. The results calculated based on the scaling laws are shown to be in very good agreement with the simulation results for liquid Rb and Cs metals along the liquid-vapor coexistence curve corresponding to a wide variation of temperature and density. The new universal scaling law discussed here is superior to the earlier empirically proposed scaling laws and provides a very simple route to calculate a dynamical quantity such as diffusivity from an equilibrium property such as the radial distribution function.

Density functional approach to the solvent effect on the dynamics of nonadiabatic electron transfer reactions

A density functional approach is proposed for calculating the activation free energy in a nonadiabatic electron transfer reaction where the molecular nature of the solvent is incorporated in a self‐consistent manner. The overall electron transfer rate constant is obtained by taking into account the static as well as dynamic aspects of solvent effects. Illustrative numerical results are presented for both the activation barrier and the electron transfer rate constant.

Theory of cross-diffusivity in a binary fluid mixture

A microscopic approach for the cross-diffusivity in a binary fluid mixture has been developed using the theoretical frameworks of density functional theory (DFT) as well as mode coupling theory (MCT). In MCT, we have identified a particular mode selection which leads to an expression for the cross-diffusivity identical to that obtained from the DFT. An alternative choice based on analogous physical considerations though leads to a different expression, on numerical evaluation shows that the calculated results are close to the predictions from DFT. Both the theories are applied to a Lennard-Jones fluid mixture and the calculated cross-diffusivities are found to be in good agreement with the available computer simulation results.

A microscopic theory of tracer diffusivity: crossover to the hydrodynamic limit

A microscopic approach is developed for the tracer diffusivity in fluids based on the concepts of mode coupling theory. The calculated numerical results for the tracer diffusivity in a Lennard-Jones (LJ) fluid are shown to be in good agreement with the corresponding simulation results. The hydrodynamic limit is found to be reached at higher mass and larger size of the solute particle which is consistent with the results of simulation studies.

A study of solvent dynamical effects on nonadiabatic electron transfer reaction rates

Abstract We have studied rates of nonadiabatic electron transfer reactions (charge separation as well as charge recombination) by considering a one dimensional reaction coordinate and obtaining its equilibrium distribution through basis set expansion, in the form of the Marcus result multiplied by a polynomial in the reaction coordinate. A Smoluchowski equation is proposed for motion along this reaction coordinate and the first and second order rate constants are obtained for charge recombination and charge separation reactions respectively, using model harmonic and anharmonic free energy curves. Although solvent fluctuations have a negligible effect on charge recombination reactions (unless the medium is highly viscous), they have a significant effect on charge separation reactions, except in the barrierless regime.

Velocity correlation function and frequency-dependent conductivity of electrolyte solutions in dipolar fluids

Abstract The velocity correlation function and frequency-dependent conductivity of a model electrolyte solution consisting of hard sphere ions in a Stockmayer fluid have been calculated by using a microscopic theoretical approach with self-consistent evaluation of diffusion constant and dielectric friction. The oscillating behaviour of the calculated quantities agrees quite well with available simulation results and through their dependence on various solvent and solute properties provide insight into the velocity correlation at intermediate time scale and ionic conductivity in the low frequency region.

Effect of confinement on the structure and energetics of Zundel cation present inside the hydrophobic carbon nanotubes: an ab initio study

Protonated water clusters confined to the carbon nanotube (CNT) channels of sub-nanometer diameter is beyond the realm of a continuum description. The steric compulsions offered by the narrow geometry can restrict the formation of hydrogen bond between the water molecules but enhance water and channel interactions. Herein, we have made an attempt to investigate the factors, which are strongly affecting the structure and energy barrier for proton transfer in Zundel cation under the confinement of CNT by employing dispersion-corrected density functional theory-based methods. Our results reveal that the diverse nature of water–water and water–wall interaction inside the nanotube for different size of CNT channels can have remarkable effects on the energetics of the proton transfer process, geometrical parameters, oscillatory shuttling motion of the proton and various energy components, viz. interaction energy, hydrogen bond energy, etc. Due to these factors, the proton oscillation in Zundel cation is shown to be nonmonotonic in nature with respect to the degree of confinement. Finally, we have demonstrated that the effect of confinement rendered by CNT(6,6) on Zundel cation can be the best suitable candidate among the series of CNTs considered in the present study, for assisting the proton transfer in the Zundel cation easily. These conclusions can have important implications and motivate further investigations to understand the fluidics under confined nanomaterials.

Exact results on diffusion from a piecewise linear potential well

We obtain an exact solution for the Laplace transformed distribution function P(x,s) for a Brownian particle trapped in a piecewise linear potential well with a finite barrier on one side. Explicit analytical expressions for the rate of diffusion over the barrier are thereby derived.