Two-component Gaussian core model: strong-coupling limit, Bjerrum pairs, and gas-liquid phase transition

In the present work we investigate a gas-liquid transition in a two-component Gaussian core model, where particles of the same species repel and those of different species attract. Unlike a similar transition in a one-component system with particles having attractive interactions at long separations, and repulsive interactions at short separations, a transition in the two-component system is not driven solely by interactions, but by a specific feature of the interactions, the correlations. This leads to extremely low critical temperature, as correlations are dominant in the strong-coupling limit. By carrying out various approximations based on standard liquid-state methods, we show that a gas-liquid transition of the two-component system posses a challenging theoretical problem

Electroviscous effects of simple electrolytes under shear

On the basis of a hydrodynamical model analogous to that in critical fluids, we investigate the influences of shear flow upon the electrostatic contribution to the viscosity of binary electrolyte solutions in the Debye-H\"{u}ckel approximation. Within the linear-response theory, we reproduce the classical limiting law that the excess viscosity is proportional to the square root of the concentration of the electrolyte. We also extend this result for finite shear. An analytic expression of the anisotropic structure factor of the charge density under shear is obtained, and its deformation at large shear rates is discussed. A non-Newtonian effect caused by deformations of the ionic atmosphere is also elucidated for $\tau_D\dot{\gamma}>1$. This finding concludes that the maximum shear stress that the ionic atmosphere can support is proportional to $\lambda_D^{-3}$, where $\dot{\gamma}$, $\lambda_D$ and $\tau_D=\lambda_D^2/D$ are, respectively, the shear rate, the Debye screening length and the Debye relaxation time with $D$ being the relative diffusivity at the infinite dilution limit of the electrolyte.Comment: 13pages, 2figure

Finite size melting of spherical solid-liquid aluminium interfaces

We have investigated the melting of nano-sized cone shaped aluminium needles coated with amorphous carbon using transmission electron microscopy. The interface between solid and liquid aluminium was found to have spherical topology. For needles with fixed apex angle, the depressed melting temperature of this spherical interface, with radius $R$, was found to scale linearly with the inverse radius $1/R$. However, by varying the apex angle of the needles we show that the proportionality constant between the depressed melting temperature and the inverse radius changes significantly. This lead us to the conclusion that the depressed melting temperature is not controlled solely by the inverse radius $1/R$. Instead we found a direct relation between the depressed melting temperature and the ratio between the solid-liquid interface area and the molten volume.Comment: to appear in Philosophical Magazine (2009

Asymmetric Bethe-Salpeter equation for pairing and condensation

The Martin-Schwinger hierarchy of correlations are reexamined and the three-particle correlations are investigated under various partial summations. Besides the known approximations of screened, ladder and maximally crossed diagrams the pair-pair correlations are considered. It is shown that the recently proposed asymmetric Bethe-Salpeter equation to avoid unphysical repeated collisions is derived as a result of the hierarchical dependencies of correlations. Exceeding the parquet approximation we show that an asymmetry appears in the selfconsistent propagators. This form is superior over the symmetric selfconsistent one since it provides the Nambu-Gorkov equations and gap equation for fermions and the Beliaev equations for bosons while from the symmetric form no gap equation results. The selfenergy diagrams which account for the subtraction of unphysical repeated collisions are derived from the pair-pair correlation in the three-particle Greenfunction. It is suggested to distinguish between two types of selfconsistency, the channel-dressed propagators and the completely dressed propagators, with the help of which the asymmetric expansion completes the Ward identity and is $\Phi$-derivable.Comment: 12 pages. 26 figure

Analysis of linear and nonlinear conductivity of plasma-like systems on the basis of the Fokker-Planck equation

The problems of high linear conductivity in an electric field, as well as nonlinear conductivity, are considered for plasma-like systems. First, we recall several observations of nonlinear fast charge transport in dusty plasma, molecular chains, lattices, conducting polymers and semiconductor layers. Exploring the role of noise we introduce the generalized Fokker-Planck equation. Second, one-dimensional models are considered on the basis of the Fokker-Planck equation with active and passive velocity-dependent friction including an external electrical field. On this basis it is possible to find the linear and nonlinear conductivities for electrons and other charged particles in a homogeneous external field. It is shown that the velocity dependence of the friction coefficient can lead to an essential increase of the electron average velocity and the corresponding conductivity in comparison with the usual model of constant friction, which is described by the Drude-type conductivity. Applications including novel forms of controlled charge transfer and non-Ohmic conductance are discussed.Comment: 14 pages with 6 figure

Asymmetric Primitive-Model Electrolytes: Debye-Huckel Theory, Criticality and Energy Bounds

Debye-Huckel (DH) theory is extended to treat two-component size- and charge-asymmetric primitive models, focussing primarily on the 1:1 additive hard-sphere electrolyte with, say, negative ion diameters, a--, larger than the positive ion diameters, a++. The treatment highlights the crucial importance of the charge-unbalanced ``border zones'' around each ion into which other ions of only one species may penetrate. Extensions of the DH approach which describe the border zones in a physically reasonable way are exact at high $T$ and low density, $\rho$, and, furthermore, are also in substantial agreement with recent simulation predictions for \emph{trends} in the critical parameters, $T_c$ and $\rho_c$, with increasing size asymmetry. Conversely, the simplest linear asymmetric DH description, which fails to account for physically expected behavior in the border zones at low $T$, can violate a new lower bound on the energy (which applies generally to models asymmetric in both charge and size). Other recent theories, including those based on the mean spherical approximation, have predicted trends in the critical parameters quite opposite to those established by the simulations.Comment: to appear in Physical Review

Nonlinear relaxation field in charged systems under high electric fields

The influence of an external electric field on the current in charged systems is investigated. The results from the classical hierarchy of density matrices are compared with the results from the quantum kinetic theory. The kinetic theory yields a systematic treatment of the nonlinear current beyond linear response. To this end the dynamically screened and field-dependent Lenard-Balescu equation is integrated analytically and the nonlinear relaxation field is calculated. The classical linear response result known as Debye - Onsager relaxation effect is only obtained if asymmetric screening is assumed. Considering the kinetic equation of one specie the other species have to be screened dynamically while the screening with the same specie itself has to be performed statically. Different other approximations are discussed and compared.Comment: language correction

Diffuse-Charge Dynamics in Electrochemical Systems

The response of a model micro-electrochemical system to a time-dependent applied voltage is analyzed. The article begins with a fresh historical review including electrochemistry, colloidal science, and microfluidics. The model problem consists of a symmetric binary electrolyte between parallel-plate, blocking electrodes which suddenly apply a voltage. Compact Stern layers on the electrodes are also taken into account. The Nernst-Planck-Poisson equations are first linearized and solved by Laplace transforms for small voltages, and numerical solutions are obtained for large voltages. The ``weakly nonlinear'' limit of thin double layers is then analyzed by matched asymptotic expansions in the small parameter $\epsilon = \lambda_D/L$, where $\lambda_D$ is the screening length and $L$ the electrode separation. At leading order, the system initially behaves like an RC circuit with a response time of $\lambda_D L / D$ (not $\lambda_D^2/D$), where $D$ is the ionic diffusivity, but nonlinearity violates this common picture and introduce multiple time scales. The charging process slows down, and neutral-salt adsorption by the diffuse part of the double layer couples to bulk diffusion at the time scale, $L^2/D$. In the ``strongly nonlinear'' regime (controlled by a dimensionless parameter resembling the Dukhin number), this effect produces bulk concentration gradients, and, at very large voltages, transient space charge. The article concludes with an overview of more general situations involving surface conduction, multi-component electrolytes, and Faradaic processes.Comment: 10 figs, 26 pages (double-column), 141 reference