Low-temperature anomalous specific heat without tunneling modes: a simulation for a-Si with voids

Using empirical potential molecular dynamics we compute dynamical matrix eigenvalues and eigenvectors for a 4096 atom model of amorphous silicon and a set of models with voids of different size based on it. This information is then employed to study the localization properties of the low-energy vibrational states, calculate the specific heat C(T) and examine the low-temperature properties of our models usually attributed to the presence of tunneling states in amorphous silicon. The results of our calculations for C(T) and "excess specific heat bulge" in the C(T)/T^3 vs. T graph for voidless a-Si appear to be in good agreement with experiment; moreover our investigation shows that the presence of localized low-energy excitations in the vibrational spectrum of our models with voids strongly manifests itself as a sharp peak in C(T)/T^3 dependence at T < 3K. To our knowledge this is the first numerical simulation that provides adequate agreement with experiment for the very low-temperature properties of specific heat in disordered systems within the limits of harmonic approximation.Comment: 5 pages with 2 ps figures, submitted to PR

Electrostatic and electrokinetic contributions to the elastic moduli of a driven membrane

We discuss the electrostatic contribution to the elastic moduli of a cell or artificial membrane placed in an electrolyte and driven by a DC electric field. The field drives ion currents across the membrane, through specific channels, pumps or natural pores. In steady state, charges accumulate in the Debye layers close to the membrane, modifying the membrane elastic moduli. We first study a model of a membrane of zero thickness, later generalizing this treatment to allow for a finite thickness and finite dielectric constant. Our results clarify and extend the results presented in [D. Lacoste, M. Cosentino Lagomarsino, and J. F. Joanny, Europhys. Lett., {\bf 77}, 18006 (2007)], by providing a physical explanation for a destabilizing term proportional to \kps^3 in the fluctuation spectrum, which we relate to a nonlinear ($E^2$) electro-kinetic effect called induced-charge electro-osmosis (ICEO). Recent studies of ICEO have focused on electrodes and polarizable particles, where an applied bulk field is perturbed by capacitive charging of the double layer and drives flow along the field axis toward surface protrusions; in contrast, we predict "reverse" ICEO flows around driven membranes, due to curvature-induced tangential fields within a non-equilibrium double layer, which hydrodynamically enhance protrusions. We also consider the effect of incorporating the dynamics of a spatially dependent concentration field for the ion channels.Comment: 22 pages, 10 figures. Under review for EPJ

Time-dependent ion selectivity in capacitive charging of porous electrodes

In a combined experimental and theoretical study, we show that capacitive charging of porous electrodes in multicomponent electrolytes may lead to the phenomenon of time-dependent ion selectivity of the electrical double layers (EDLs) in the electrodes. This effect is found in experiments on capacitive deionization of water containing NaCl/CaCl2 mixtures, when the concentration of Na+ ions in the water is five times the Ca2+-ion concentration. In this experiment, after applying a voltage difference between two porous carbon electrodes, first the majority monovalent Na+ cations are preferentially adsorbed in the EDLs, and later, they are gradually replaced by the minority, divalent Ca2+ cations. In a process where this ion adsorption step is followed by washing the electrode with freshwater under open-circuit conditions, and subsequent release of the ions while the cell is short-circuited, a product stream is obtained which is significantly enriched in divalent ions. Repeating this process three times by taking the product concentrations of one run as the feed concentrations for the next, a final increase in the Ca2+/Na+-ratio of a factor of 300 is achieved. The phenomenon of time-dependent ion selectivity of EDLs cannot be explained by linear response theory. Therefore, a nonlinear time-dependent analysis of capacitive charging is performed for both porous and flat electrodes. Both models attribute time-dependent ion selectivity to the interplay between the transport resistance for the ions in the aqueous solution outside the EDL, and the voltage-dependent ion adsorption capacity of the EDLs. Exact analytical expressions are presented for the excess ion adsorption in planar EDLs (Gouy-Chapman theory) for mixtures containing both monovalent and divalent cations

Imposed currents in galvanic cells

We analyze the steady-state behavior of a general mathematical model for reversible galvanic cells, such as redox flow cells, reversible solid oxide fuel cells, and rechargeable batteries. We consider not only operation in the galvanic discharging mode, spontaneously generating a positive current against an external load, but also operation in two modes which require a net input of electrical energy: (i) the electrolytic charging mode, where a negative current is imposed to generate a voltage exceeding the open-circuit voltage, and (ii) the “super-galvanic” discharging mode, where a positive current exceeding the short-circuit current is imposed to generate a negative voltage. Analysis of the various (dis-)charging modes of galvanic cells is important to predict the efficiency of electrical to chemical energy conversion and to provide sensitive tests for experimental validation of fuel cell models. In the model, we consider effects of diffuse charge on electrochemical charge-transfer rates by combining a generalized Frumkin-Butler-Volmer equation for reaction kinetics across the compact Stern layer with the full Poisson-Nernst-Planck transport theory, without assuming local electroneutrality. Since this approach is rare in the literature, we provide a brief historical review. To illustrate the general theory, we present results for a monovalent binary electrolyte, consisting of cations, which react at the electrodes, and non-reactive anions, which are either fixed in space (as in a solid electrolyte) or are mobile (as in a liquid electrolyte). The full model is solved numerically and compared to analytical results in the limit of thin diffuse layers, relative to the membrane thickness. The spatial profiles of the ion concentrations and electrostatic potential reveal a complex dependence on the kinetic parameters and the imposed current, in which the diffuse charge at each electrode and the total membrane charge can have either sign, contrary perhaps to intuition. For thin diffuse layers, simple analytical expressions are presented for galvanic cells valid in all three (dis-)charging modes in the two subsequent limits of the ratio δ of the effective thicknesses of the compact and diffuse layers: (i) the “Helmholtz limit” (δ → ∞) where the compact layer carries the double layer voltage as in standard Butler-Volmer models, and (ii) the opposite “Gouy-Chapman limit” (δ → 0) where the diffuse layer fully determines the charge-transfer kinetics. In these limits, the model predicts both reaction-limited and diffusion-limited currents, which can be surpassed for finite positive values of the compact layer, diffuse layer and membrane thickness

Conformal mapping methods for interfacial dynamics

The article provides a pedagogical review aimed at graduate students in materials science, physics, and applied mathematics, focusing on recent developments in the subject. Following a brief summary of concepts from complex analysis, the article begins with an overview of continuous conformal-map dynamics. This includes problems of interfacial motion driven by harmonic fields (such as viscous fingering and void electromigration), bi-harmonic fields (such as viscous sintering and elastic pore evolution), and non-harmonic, conformally invariant fields (such as growth by advection-diffusion and electro-deposition). The second part of the article is devoted to iterated conformal maps for analogous problems in stochastic interfacial dynamics (such as diffusion-limited aggregation, dielectric breakdown, brittle fracture, and advection-diffusion-limited aggregation). The third part notes that all of these models can be extended to curved surfaces by an auxilliary conformal mapping from the complex plane, such as stereographic projection to a sphere. The article concludes with an outlook for further research.Comment: 37 pages, 12 (mostly color) figure

Electrode Polarization Effects in Broadband Dielectric Spectroscopy

In the present work, we provide broadband dielectric spectra showing strong electrode polarization effects for various materials, belonging to very different material classes. This includes both ionic and electronic conductors as, e.g., salt solutions, ionic liquids, human blood, and colossal-dielectric-constant materials. These data are intended to provide a broad data base enabling a critical test of the validity of phenomenological and microscopic models for electrode polarization. In the present work, the results are analyzed using a simple phenomenological equivalent-circuit description, involving a distributed parallel RC circuit element for the modeling of the weakly conducting regions close to the electrodes. Excellent fits of the experimental data are achieved in this way, demonstrating the universal applicability of this approach. In the investigated ionically conducting materials, we find the universal appearance of a second dispersion region due to electrode polarization, which is only revealed if measuring down to sufficiently low frequencies. This indicates the presence of a second charge-transport process in ionic conductors with blocking electrodes.Comment: 9 pages, 6 figures, experimental data are provided in electronic form (see "Data Conservancy"

Wide shear zones and the spot model: Implications from the split-bottom geometry

The spot model has been developed by Bazant and co-workers to describe quasistatic granular flows. It assumes that granular flow is caused by the opposing flow of so-called spots of excess free volume, with spots moving along the slip lines of Mohr-Coulomb plasticity. The model is two-dimensional and has been successfully applied to a number of different geometries. In this paper we investigate whether the spot model in its simplest form can describe the wide shear zones observed in experiments and simulations of a Couette cell with split bottom. We give a general argument that is independent of the particular description of the stresses, but which shows that the present formulation of the spot model in which diffusion and drift terms are postulated to balance on length scales of order of the spot diameter, i.e. of order 3-5 grain diameters, is difficult to reconcile with the observed wide shear zones. We also discuss the implications for the spot model of co-axiality of the stress and strain rate tensors found in these wide shear flows, and point to possible extensions of the model that might allow one to account for the existence of wide shear zones.Comment: 6 pages, 6 figures, to be published in EPJ

Electroosmotic flow of biorheological micropolar fluids through microfluidic channels

An analysis is presented in this work to assess the influence of micropolar nature of fluids in fully developed flow induced by electrokinetically driven peristaltic pumping through a parallel plate microchannel. The walls of the channel are assumed as sinusoidal wavy to analyze the peristaltic flow nature. We consider that the wavelength of the wall motion is much larger as compared to the channel width to validate the lubrication theory. To simplify the Poisson Boltzmann equation, we also use the Debye-Hückel linearization (i.e. wall zeta potential ≤ 25mV). We consider governing equation for micropolar fluid in absence of body force and couple effects however external electric field is employed. The solutions for axial velocity, spin velocity, flow rate, pressure rise and stream functions subjected to given physical boundary conditions are computed. The effects of pertinent parameters like Debye length and Helmholtz-Smoluchowski velocity which characterize the EDL phenomenon and external electric field, coupling number and micropolar parameter which characterize the micropolar fluid behavior, on peristaltic pumping are discussed through the illustrations. The results show that peristaltic pumping may alter by applying external electric fields. This model can be used to design and engineer the peristalsis-lab-on-chip and micro peristaltic syringe pumps for biomedical applications