Abstract. The dc response of an electrochemical thin film, such as the separator in a microbattery, is analyzed by solving the Poisson-Nernst-Planck equations, subject to boundary conditions appropriate for an electrolytic/galvanic cell. The model system consists of a binary electrolyte between parallel-plate electrodes, each possessing a compact Stern layer, which mediates Faradaic reactions with nonlinear Butler-Volmer kinetics. Analytical results are obtained by matched asymptotic expansions in the limit of thin double layers and compared with full numerical solutions. The analysis shows that (i) decreasing the system size relative to the Debye screening length decreases the voltage of the cell and allows currents higher than the classical diffusion-limited current; (ii) finite reaction rates lead to the important possibility of a reaction-limited current; (iii) the Stern-layer capacitance is critical for allowing the cell to achieve currents above the reaction-limited current; and (iv) all polarographic (current-voltage) curves tend to the same limit as reaction kinetics become fast. Dimensional analysis, however, shows that "fast" reactions tend to become "slow" with decreasing system size, so the nonlinear effects of surface polarization may dominate the dc response of thin films.Key words. Poisson-Nernst-Planck equations, electrochemical systems, thin films, polarographic curves, Butler-Volmer reaction kinetics, Stern layer, surface capacitance. AMS subject classifications. 34B08, 34B16, 34B60, 34E05, 80A30Introduction. Micro-electrochemical systems pose interesting problems for applied mathematics because traditional "macroscopic" approximations of electroneutrality and thermal equilibrium [1], which make the classical transport equations more tractable [2], break down at small scales, approaching the Debye screening length. Of course, the relative importance of surface phenomena also increases with miniaturization. Micro-electrochemical systems of current interest include ion channels in biological membranes [3,4,5] and thin-film batteries [6,7,8,9, 10], which could revolutionize the design of modern electronics with distributed on-chip power sources. In the latter context, the internal resistance of the battery is related to the nonlinear current-voltage characteristics of the separator, consisting of a thin-film electrolyte (solid, liquid, or gel) sandwiched between flat electrodes and interfacial layers where Faradaic electron-transfer reactions occur [11]. Under such conditions, the internal resistance is unlikely to be simply constant, as is usually assumed.Motivated by the application to thin-film batteries, here we revisit the classical problem of steady conduction between parallel, flat electrodes, studied by Nernst [12] and Brunner [13, 14] a century ago. As in subsequent studies of liquid [15,16] and solid [17,18] electrolytes, we do not make Nernst's assumption of bulk electroneutrality and work instead with the Poisson-Nernst-Planck (PNP) equations, allowing for diffuse charge in solution [1...

Abstract. We study a model electrochemical thin film at dc currents exceeding the classical diffusion-limited value. The mathematical problem involves the steady Poisson-Nernst-Planck equations for a binary electrolyte with nonlinear boundary conditions for reaction kinetics and Stern-layer capacitance, as well as an integral constraint on the number of anions. At the limiting current, we find a nested boundary layer structure at the cathode, which is required by the reaction boundary condition. Above the limiting current, a depletion of anions generally characterizes the cathode side of the cell. In this regime, we derive leading-order asymptotic approximations for the (i) classical bulk space-charge layer and (ii) another, nested highly charged boundary layer at the cathode. The former involves an exact solution to the Nernst-Planck equations for a single, unscreened ionic species, which may apply more generally to Faradaic conduction through very thin insulating films. By matching expansions, we derive current-voltage relations well into the space-charge regime. Throughout our analysis, we emphasize the strong influence of the Stern-layer capacitance on cell behavior.

We analyze the simplest problem of electrochemical relaxation in more than one dimension -the response of an uncharged, ideally polarizable metallic sphere (or cylinder) in a symmetric, binary electrolyte to a uniform electric field. In order to go beyond the circuit approximation for thin double layers, our analysis is based on the Poisson-Nernst-Planck (PNP) equations of dilute solution theory. Unlike most previous studies, however, we focus on the nonlinear regime, where the applied voltage across the conductor is larger than the thermal voltage. In such strong electric fields, the classical model predicts that the double layer adsorbs enough ions to produce bulk concentration gradients and surface conduction. Our analysis begins with a general derivation of surface conservation laws in the thin double-layer limit, which provide effective boundary conditions on the quasi-neutral bulk. We solve the resulting nonlinear partial differential equations numerically for strong fields and also perform a time-dependent asymptotic analysis for weaker fields, where bulk diffusion and surface conduction arise as first-order corrections. We also derive various dimensionless parameters comparing surface to bulk transport processes, which generalize the Bikerman-Dukhin number. Our results have basic relevance for double-layer charging dynamics and nonlinear electrokinetics in the ubiquitous PNP approximation.

A systematic ab initio study of the optical as well as structural and electronic properties of the carbon nanotubes within density-functional theory in the local-density approximation has been performed. Highly accurate full-potential projected augmented wave method was used. Specifically, the optical dielectric function and second-order optical susceptibility (2) as well as the band structure of a number of the armchair ͓͑3,

pressures (10-30 MPa), but also demands a large deal of H 2 mainly from natural gas reforming which causes abundant consumption of fossil fuels and huge CO 2 emissions. [3-6] As a result, for energy conservation and environmental protection, it is of crucial importance to explore a clean and sustainable route for NH 3 production. Electrocatalytic N 2 reduction reaction (NRR) under ambient conditions has been emerged recently as an attractive strategy for the green synthesis of NH 3 through utilizing inexhaustible N 2 and H 2 O. [7-12] However, due to the competition with H 2 evolution reaction (HER) and ultra-stable NN covalent triple bond, NRR suffers from unsatisfactory Faradaic efficiency (FE) and sluggish reaction kinetics. [13] It is of eager desire, but very challenging to develop selective and efficient electrocatalysts toward NRR that can inhibit the competitive HER and activate the N 2 molecule. Among various developed electrocatalysts, perovskite oxides have proven their great potential toward NRR because of their low cost, good adjustability in intriguing physicochemical properties, as well as economic and environmental friendliness. Typical examples include a few simple perovskite oxides, such as LaCoO 3 , LaCrO 3 , LaFeO 3 , La 2 Ti 2 O 7 , and Ce 1/3 NbO 3. [14-19] Although significant progress has been made, their NRR performance is still far from the requirements of commercial NH 3 synthesis. Most recently, several studies have shown that the electrocatalytic The electrocatalytic N 2 reduction reaction (NRR) under ambient conditions is an attractive strategy for green synthesis of NH 3. Due to the ultra-stable NN covalent triple bond, it is very challenging to develop highly selective and efficient electrocatalysts toward NRR. Here a general strategy to enhance the NRR activity through modulating A-site-deficiency-induced oxygen vacancies of perovskite oxides is reported. One successful example is La x FeO 3−δ (L x F, x = 1, 0.95, and 0.9) perovskite oxides with tunable oxygen vacancies that are directly proportional to the La-site deficiencies. As compared to the pristine LF, the L 0.95 F and L 0.9 F exhibit significantly improved NRR activities, which are positively correlated with the La-site deficiency and the amount of oxygen vacancies. Among them, the L 0.9 F delivers the best activity, with an NH 3 yield rate of 22.1 µg•h −1 •mg −1 cat. at −0.5 V and a Faradaic efficiency of 25.6% at −0.3 V, which are 2.2 and 1.6 times those of the pristine LF, respectively. Both experimental characterizations and theoretical calculations suggest that the enhanced NRR activity can be mainly attributed to the favorable merits produced by the oxygen vacancies: the promoted adsorption/activation of reaction species, and thus optimized reaction pathways. Application of this strategy to other perovskite oxides generates similarly successful results.

In studies of interfaces with dynamic chemical composition, bulk and interfacial quantities are often coupled via surface conservation laws of excess surface quantities. While this approach is easily justified for microscopically sharp interfaces, its applicability in the context of microscopically diffuse interfaces is less theoretically well-established. Furthermore, surface conservation laws (and interfacial models in general) are often derived phenomenologically rather than systematically. In this article, we first provide a mathematically rigorous justification for surface conservation laws at diffuse interfaces based on an asymptotic analysis of transport processes in the boundary layer and derive general formulae for the surface and normal fluxes that appear in surface conservation laws. Next, we use nonequilibrium thermodynamics to formulate surface conservation laws in terms of chemical potentials and provide a method for systematically deriving the structure of the interfacial layer. Finally, we derive surface conservation laws for a few examples from diffusive and electrochemical transport.

In this paper, we study triply periodic surfaces with minimal surface area under a constraint in the volume fraction of the regions (phases) that the surface separates. Using a variational level set method formulation, we present a theoretical characterization of and a numerical algorithm for computing these surfaces. We use our theoretical and computational formulation to study the optimality of the Schwartz P, Schwartz D, and Schoen G surfaces when the volume fractions of the two phases are equal and explore the properties of optimal structures when the volume fractions of the two phases not equal. Due to the computational cost of the fully, threedimensional shape optimization problem, we implement our numerical simulations using a parallel level set method software package.

Developing a self-adapting photocatalytic system that efficiently captures light all-day is not only a dream but also a challenge. Here, we report a ‘bionic sunflower’ based on a light-responsive smart...