Beyond Poisson-Boltzmann: Numerical sampling of charge density fluctuations

We present a method aimed at sampling charge density fluctuations in Coulomb systems. The derivation follows from a functional integral representation of the partition function in terms of charge density fluctuations. Starting from the mean-field solution given by the Poisson-Boltzmann equation, an original approach is proposed to numerically sample fluctuations around it, through the propagation of a Langevin like stochastic partial differential equation (SPDE). The diffusion tensor of the SPDE can be chosen so as to avoid the numerical complexity linked to long-range Coulomb interactions, effectively rendering the theory completely local. A finite-volume implementation of the SPDE is described, and the approach is illustrated with preliminary results on the study of a system made of two like-charge ions immersed in a bath of counter-ions

Simulating (electro)hydrodynamic effects in colloidal dispersions: smoothed profile method

Previously, we have proposed a direct simulation scheme for colloidal dispersions in a Newtonian solvent [Phys.Rev.E 71,036707 (2005)]. An improved formulation called the ``Smoothed Profile (SP) method'' is presented here in which simultaneous time-marching is used for the host fluid and colloids. The SP method is a direct numerical simulation of particulate flows and provides a coupling scheme between the continuum fluid dynamics and rigid-body dynamics through utilization of a smoothed profile for the colloidal particles. Moreover, the improved formulation includes an extension to incorporate multi-component fluids, allowing systems such as charged colloids in electrolyte solutions to be studied. The dynamics of the colloidal dispersions are solved with the same computational cost as required for solving non-particulate flows. Numerical results which assess the hydrodynamic interactions of colloidal dispersions are presented to validate the SP method. The SP method is not restricted to particular constitutive models of the host fluids and can hence be applied to colloidal dispersions in complex fluids

Beyond Poisson-Boltzmann: Fluctuations and Correlations

We formulate the non-linear field theory for a fluctuating counter-ion distribution in the presence of a fixed, arbitrary charge distribution. The Poisson-Boltzmann equation is obtained as the saddle-point, and the effects of fluctuations and correlations are included by a loop-wise expansion around this saddle point. We show that the Poisson equation is obeyed at each order in the loop expansion and explicitly give the expansion of the Gibbs potential up to two loops. We then apply our formalism to the case of an impenetrable, charged wall, and obtain the fluctuation corrections to the electrostatic potential and counter-ion density to one-loop order without further approximations. The relative importance of fluctuation corrections is controlled by a single parameter, which is proportional to the cube of the counter-ion valency and to the surface charge density. We also calculate effective interactions between charged particles, which reflect counter-ion correlation effects.Comment: 12 pages, 8 postscript figure

Suppression of non-Poissonian shot noise by Coulomb correlations in ballistic conductors

We investigate the current injection into a ballistic conductor under the space-charge limited regime, when the distribution function of injected carriers is an arbitrary function of energy F_c(epsilon). The analysis of the coupled kinetic and Poisson equations shows that the injected current fluctuations may be essentially suppressed by Coulomb correlations, and the suppression level is determined by the shape of F_c(epsilon). This is in contrast to the time-averaged quantities: the mean current and the spatial profiles are shown to be insensitive to F_c(epsilon) in the leading-order terms at high biases. The asymptotic high-bias behavior for the energy resolved shot-noise suppression has been found for an arbitrary (non-Poissonian) injection, which may suggest a new field of investigation on the optimization of the injected energy profile to achieve the desired noise-suppression level.Comment: extended version 4 -> 8 pages, examples and figure adde

Suppression of non-Poissonian shot noise by Coulomb correlations in ballistic conductors

We investigate the current injection into a ballistic conductor under the space-charge limited regime, when the distribution function of injected carriers is an arbitrary function of energy F_c(epsilon). The analysis of the coupled kinetic and Poisson equations shows that the injected current fluctuations may be essentially suppressed by Coulomb correlations, and the suppression level is determined by the shape of F_c(epsilon). This is in contrast to the time-averaged quantities: the mean current and the spatial profiles are shown to be insensitive to F_c(epsilon) in the leading-order terms at high biases. The asymptotic high-bias behavior for the energy resolved shot-noise suppression has been found for an arbitrary (non-Poissonian) injection, which may suggest a new field of investigation on the optimization of the injected energy profile to achieve the desired noise-suppression level.Comment: extended version 4 -> 8 pages, examples and figure adde

Symmetry breaking and electrostatic attraction between two identical surfaces

This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.By allowing the surface charge of one surface to affect the adsorption equilibrium of the other, we establish the existence of a long-range attractive interaction between two identical surfaces in an electrolyte containing polyvalent counter ions with a mean-field Poisson-Boltzmann approach. A Stern electrostatic condition from linearization of the mass-action adsorption isotherm is used to capture how polyvalent ion condensation affects and reverses the surface charge. We furthermore establish a direct mapping between this Stern layer conditions and previously derived modified Mean-field formulations associated with correlated fluctuations theory. For a sufficiently potential-sensitive isotherm, antisymmetric charge inversion can occur to produce an attractive force that increases with decreasing ionic strengths. Analyses of a mass-action isotherm produce force-separation relations, including an exponential far-field force decay distinct but consistent with previously proposed correlated fluctuation theories, and in quantitative agreement with experimental data

Increase in the random dopant induced threshold fluctuations and lowering in sub-100 nm MOSFETs due to quantum effects: a 3-D density-gradient simulation study

In this paper, we present a detailed simulation study of the influence of quantum mechanical effects in the inversion layer on random dopant induced threshold voltage fluctuations and lowering in sub-100 mn MOSFETs. The simulations have been performed using a three-dimensional (3-D) implementation of the density gradient (DG) formalism incorporated in our established 3-D atomistic simulation approach. This results in a self-consistent 3-D quantum mechanical picture, which implies not only the vertical inversion layer quantization but also the lateral confinement effects related to current filamentation in the “valleys” of the random potential fluctuations. We have shown that the net result of including quantum mechanical effects, while considering statistical dopant fluctuations, is an increase in both threshold voltage fluctuations and lowering. At the same time, the random dopant induced threshold voltage lowering partially compensates for the quantum mechanical threshold voltage shift in aggressively scaled MOSFETs with ultrathin gate oxides

Fluctuation-enhanced electric conductivity in electrolyte solutions

In this letter we analyze the effects of an externally applied electric field on thermal fluctuations for a fluid containing charged species. We show in particular that the fluctuating Poisson-Nernst-Planck equations for charged multispecies diffusion coupled with the fluctuating fluid momentum equation, result in enhanced charge transport. Although this transport is advective in nature, it can macroscopically be represented as electrodiffusion with renormalized electric conductivity. We calculate the renormalized electric conductivity by deriving and integrating the structure factor coefficients of the fluctuating quantities and show that the renormalized electric conductivity and diffusion coefficients are consistent although they originate from different noise terms. In addition, the fluctuating hydrodynamics approach recovers the electrophoretic and relaxation corrections obtained by Debye-Huckel-Onsager theory, and provides a quantitative theory that predicts a non-zero cross-diffusion Maxwell-Stefan coefficient that agrees well with experimental measurements. Finally, we show that strong applied electric fields result in anisotropically enhanced velocity fluctuations and reduced fluctuations of salt concentrations.Comment: 12 pages, 1 figur