Inhomogeneous Reaction Research Articles

Electrochemical Quartz Crystal Microbalance Measurements of Lithium-Aluminum Alloy in a Glyme-Lithium Salt Molten Complex

Lithium-aluminum alloying reaction was investigated in lithium bis(trifluoromethylsulfonyl)amide triglyme solvate ionic liquid as a model system for the negative electrode of lithium secondary batteries. The formation of β-phase LiAl was confirmed by X-ray diffraction. The potential of α+β coexisting region was approximately 0.35 V vs. Li/Li(I). The slow relaxation of open circuit voltage and scanning electron microscope images suggested the inhomogeneous alloying reaction along with the active sites. The mass changes with doping and undoping of Li were measured qualitatively by electrochemical quartz crystal microbalance technique.

X-ray absorption fine structure imaging of inhomogeneous electrode reaction in LiFePO4 lithium-ion battery cathode

To improve the performance of rechargeable lithium-ion batteries, a microscopic understanding of the electrochemical reaction at the cathode is necessary. The spatial distribution of the electrode redox reaction for the LiFePO4 cathode was analyzed by X-ray absorption fine structure (XAFS) imaging. Chemical state maps of the planar cathode electrode obtained by the in situ XAFS imaging revealed the inhomogeneity of the chemical state of Fe during the charge/discharge process. The chemical state maps for the reverse charge/discharge process demonstrated the reversibility of the inhomogeneous distribution. The in-plane radial progress of the reaction distribution strongly suggests that the inhomogeneous electrode reaction is caused by the difference in electrical conductivity; the charging and discharging reactions proceed through reaction channels with low electrical resistance in the cathode.

The Impact of Platinum Reduction on Oxygen Transport in Proton Exchange Membrane Fuel Cells

Key challenges to the acceptance of Proton Exchange Membrane Fuel Cells (PEMFCs) for Fuel Cell Electric Vehicles (FCEVs) are the cost reduction and improvements in power density for compactness.High current density operation is one of the most effective solutions for cost reduction and power density improvements. It contributes to size reduction of PEMFCs as well as lower amounts of Platinum (Pt). However, high current density operation causes an increase in concentration overpotential, resulting in lower cell performance. In addition, the oxygen transport resistance typically increases under lower Pt loadings.The effect of rib/channel widths and Pt loading on oxygen transport resistance and cell performance were investigated by coupled experimental and numerical analyses in this study. Oxygen transport resistance was obtained by measuring limiting current with various rib/channel widths and platinum loadings, and it significantly increased depending on the rib/channel widths as well as platinum loadings. A three-dimensional numerical model was developed by implementing the oxygen transport resistance from the pores in catalyst layer to the platinum surface. Numerical validations showed that the rib/channel widths caused inhomogeneous reaction distributions in both in-plane and through-plane directions. This resulted in an increase in the oxygen transport resistance. Also, the numerical model revealed that the oxygen flux per platinum surface area significantly increased when platinum loading is decreased, causing an increase in the oxygen transport resistance. Moreover, the model could reproduce the cell performances under high current density with different rib/channel widths and platinum loadings. These results suggested that a reduction of oxygen flux per platinum surface area was essential to achieve high current density operation with lower platinum loadings.

Ultrafast acquisition of localized two-dimensional magnetic resonance correlated spectra of inhomogeneous biological tissues with resolution improvements

Long acquisition time and strict requests of homogeneous magnetic fields restrain wide applications of localized 2D magnetic resonance spectroscopy. Here, a pulse sequence utilizing the spatial encoding technique and spin echo is proposed to obtain localized 2D correlated spectra with resolution improvements under inhomogeneous fields within greatly reduced times. The localized correlated spectrum of pig marrow obtained with the proposed scheme retained more information compared to the conventional spectrum. The method proposed herein offers important perspectives for fast in vivo analyses of metabolites in living inhomogeneous organisms and in situ characterization of intermediates of inhomogeneous chemical reaction systems.

Electrochemical energy storage device for securing future renewable energy

An electrochemical cell comprising molten sodium and molten sulphur as the anode and cathode, respectively, with beta alumina electrolyte has never found extensive use. An approach to develop large energy storage device based on aqueous sodium electrolyte at low temperature is described. An electrochemical cell with low cost, safe and utilizing sustainable manganese dioxide (MnO2) cathode coupled with zinc (Zn) anode in aqueous sodium hydroxide (NaOH) electrolyte is reported. The cyclic voltammetric (CV) profiles are found to be quite different in terms of peak position and current response depending on concentration of NaOH electrolyte. Among the concentrations of NaOH studied (2, 5, 7 and 10M) the best performance was found to be between 5 and 7M. The CV curves exhibits a pair of reversible redox peaks (within 1e− region) corresponding to sodium ion insertion and extraction but while extending the potential window to second electron reduction resulted in irreversible nature. This is explained to the formation of inhomogeneous reduction reaction due to slow electron diffusion. CV experiments at various scan rates revealed that the MnO2 material may not be suitable enough for higher scan rates indicating a sluggish kinetics occurring in the bulk material. Our study highlights the MnO2 cathode in NaOH electrolyte features a flat discharge voltage of 1.3V vs. Zn with discharge capacity of 220mAh/g.

Generalized Traveling Waves in Disordered Media: Existence, Uniqueness, and Stability

We prove existence, uniqueness, and stability of transition fronts (generalized traveling waves) for reaction-diffusion equations in cylindrical domains with general inhomogeneous ignition reactions. We also show uniform convergence of solutions with exponentially decaying initial data to time translations of the front. In the case of stationary ergodic reactions, the fronts are proved to propagate with a deterministic positive speed. Our results extend to reaction-advection-diffusion equations with periodic advection and diffusion.

Mapping spatially inhomogeneous electrochemical reactions in battery electrodes using high energy X-rays

The spatial distribution of a reaction through a lithium-ion battery electrode has been resolved using micro-beam high-energy X-ray scattering measurements coupled with Pair Distribution Function (PDF) analysis. The electrochemical reaction was most advanced at the interface between the electrode and electrolyte-soaked separator, with linear variation in reaction progress with distance from this interface.

Interfacial characterization of silicon nitride/silicon nitride joints brazed using Cu-base active metal interlayers

Silicon nitride/silicon nitride joints were vacuum brazed at 1317K for 5min and 30min using ductile Cu-base active metal interlayers. The joints were characterized using scanning electron microscopy (SEM), energy dispersive spectroscopy (EDS), electron back scattered diffraction (EBSD), and transmission electron microscopy (TEM). An inhomogeneous Ti-rich reaction layer (∼2–3μm thick) formed in 5min at the Si3N4/braze interface. The inhomogeneity disappeared after brazing for 30min and was replaced with a compact and featureless reaction zone. TEM studies revealed fine grains in the reaction layer, and larger grains in the inner part of the joint interfaces. The joints were crack-free and presented features associated with plastic deformation, which indicated accommodation of strain associated with CTE mismatch. Electron Backscatter diffraction (EBSD) revealed a highly textured braze alloy interlayer and its crystallographic orientation was determined. The formation of additional phases at the joint interface during brazing is discussed.

Anode and cathode overpotentials and temperature profiles in a PEMFC

The separate anodic and cathodic overpotentials in a proton exchange membrane fuel cell (activation, ohmic, concentration and mass transport) were measured in conventional and segmented hardware via reference electrodes, and multi-component gas analysis. The results show that the anodic overpotentials cannot be ignored, even when the operating conditions are changed at the cathode only. Under drying conditions the difference in the current density across the active area creates in-plane thermal gradients due to inhomogeneous reaction rates, and water phase changes. The resulting inhomogeneous temperature distributions can result in membrane and electrode degradation. The combination of reference electrodes and multi-component gas analysis enables the measurement and calculation of kinetic and diffusion parameters that can be used for modeling, and improved fuel cell design, efficiency, and durability.

Existence and Non-Existence of Fisher-KPP Transition Fronts

We consider Fisher-KPP-type reaction-diffusion equations with spatially inhomogeneous reaction rates. We show that a sufficiently strong localized inhomogeneity may prevent existence of transition-front-type global in time solutions while creating a global in time bump-like solution. This is the first example of a medium in which no reaction-diffusion transition front exists. A weaker localized inhomogeneity leads to existence of transition fronts but only in a finite range of speeds. These results are in contrast with both Fisher-KPP reactions in homogeneous media as well as ignition-type reactions in inhomogeneous media.

Templated growth of platinum nanowheels using the inhomogeneous reaction environment of bicelles

Novel platinum nanowheels were synthesized by the reduction of aqueous platinum complex with ascorbic acid in the presence of disk-like bicelles. The platinum nanowheels possess thickened centers and flared edges that are connected by dendritic platinum nanosheets. This structural complexity can be attributed to the inhomogeneous micro-environment of the templating bicelles consisting of a central bi-layer region and a high curvature rim. The formation mechanism of the nanowheels was investigated by imaging nanostructures at different stages of the reaction. The templating bicelles were also imaged by TEM with the aid of negative staining. The variation of reaction parameters including platinum concentration, temperature, and total concentration of surfactants (CTAB + FC7) led to other types of platinum nanostructures, such as circular dendritic nanosheets with a tunable diameter and rectangular dendritic nanosheets. Interestingly, under irradiation by a TEM electron beam, the dendritic nanosheet portion of the nanowheels transforms into a metastable holey sheet. In addition, the platinum nanowheels have an electrochemical active surface area comparable to that of ETEK platinum black and thus are expected to have potential applications in catalysis.

Exact analytical solutions for nonlinear waves in the inhomogeneous Fisher-Kolmogorov equation

Exact analytical solutions of the reaction-diffusion equations with spatial inhomogeneous reaction and diffusion coefficients are found. It is shown that the space-oscillating approximate solution of a traveling wave type [P.K. Brazhnik, J.J. Tyson, SIAM J. Appl. Math. 60, 371 (1999)] is the exact one for the inhomogeneous Fisher-Kolmogorov equation in two dimensions.

Spatial rock-paper-scissors models with inhomogeneous reaction rates

We study several variants of the stochastic four-state rock-paper-scissors game or, equivalently, cyclic three-species predator-prey models with conserved total particle density, by means of Monte Carlo simulations on one- and two-dimensional lattices. Specifically, we investigate the influence of spatial variability of the reaction rates and site occupancy restrictions on the transient oscillations of the species densities and on spatial correlation functions in the quasistationary coexistence state. For small systems, we also numerically determine the dependence of typical extinction times on the number of lattice sites. In stark contrast with two-species stochastic Lotka-Volterra systems, we find that for our three-species models with cyclic competition quenched disorder in the reaction rates has very little effect on the dynamics and the long-time properties of the coexistence state. Similarly, we observe that site restriction only has a minor influence on the system's dynamical properties. Our results therefore demonstrate that the features of the spatial rock-paper-scissors system are remarkably robust with respect to model variations, and stochastic fluctuations as well as spatial correlations play a comparatively minor role.

Front Propagation in a Heterogeneous Fisher Equation: The Homogeneous Case is Non-Generic

The large-time behaviour of an inhomogeneous reaction–diffusion equation is studied, it being shown that the mechanisms by which the wave speed of a front connecting an unstable state to a stable one is determined differ significantly according to whether the inhomogeneity is an increasing or a decreasing function of the spatial variable. Within this broader framework, the conventional (homogeneous) case represents an exceptional borderline case.

Motion by anisotropic mean curvature as sharp interface limit of an inhomogeneous and anisotropic Allen–Cahn equation

We consider the spatially inhomogeneous and anisotropic reaction–diffusion equation ut = m(x)−1 div[m(x)ap(x,∇u)] + ε−2f(u), involving a small parameter ε > 0 and a bistable nonlinear term whose stable equilibria are 0 and 1. We use a Finsler metric related to the anisotropic diffusion term and work in relative geometry. We prove a weak comparison principle and perform an analysis of both the generation and the motion of interfaces. More precisely, we show that, within the time-scale of order ε2|ln ε|, the unique weak solution uε develops a steep transition layer that separates the regions {uε ≈ 0} and {uε | 1}. Then, on a much slower time-scale, the layer starts to propagate. Consequently, as ε → 0, the solution uε converges almost everywhere (a.e.) to 0 in Ω−t and 1 in Ω+t , where Ω−t and Ω+t are sub-domains of Ω separated by an interface Гt, whose motion is driven by its anisotropic mean curvature. We also prove that the thickness of the transition layer is of order ε.

The entropy dissipation method for spatially inhomogeneous reaction–diffusion-type systems

We study the long-time asymptotics of reaction–diffusion-type systems that feature a monotone decaying entropy (Lyapunov, free energy) functional. We consider both bounded domains and confining potentials on the whole space for arbitrary space dimensions. Our aim is to derive quantitative expressions for (or estimates of) the rates of convergence towards an (entropy minimizing) equilibrium state in terms of the constants of diffusion and reaction and with respect to conserved quantities. Our method, the so-called entropy approach, seeks to quantify convergence to equilibrium by using functional inequalities, which relate quantitatively the entropy and its dissipation in time. The entropy approach is well suited to nonlinear problems and known to be quite robust with respect to model variations. It has already been widely applied to scalar diffusion–convection equations, and the main goal of this paper is to study its generalization to systems of partial differential equations that contain diffusion and reaction terms and admit fewer conservation laws than the size of the system. In particular, we successfully apply the entropy approach to general linear systems and to a nonlinear example of a reaction–diffusion–convection system arising in solid-state physics as a paradigm for general nonlinear systems.

Erratum on “Singular Limit of a p-Laplacian Reaction-Diffusion Equation with a Spatially Inhomogeneous Reaction Term”

Erratum on “Singular Limit of a p-Laplacian Reaction-Diffusion Equation with a Spatially Inhomogeneous Reaction Term”

Two-dimensional arrays of DNA oligomers with n-octylamine ligands

Two-dimensional arrays of AAATTT (A = adenine, T = thymine) deoxyribonucleic acid hexamer stretched with n-octylamine ligands have been formed on a graphite surface. These structures were prepared with the inhomogeneous reaction at the interface between water and organic solvent of 1-phenyloctane and then transferred to the surface of graphite. Through STM observation it is demonstrated that the array is composed of stripes that are 4.6 nm long and are oriented along 〈18, 1, 0, 0〉 and 〈18, 0, 1, 0〉 directions of graphite. A surface structure model based on a hexamer–octylamine complex dimer has been proposed.

EFFECT OF NOISE AND STRUCTURAL INHOMOGENEITIES IN REACTION–DIFFUSION MEDIA

We investigate the pinning and depinning condition of a kink in both homogeneous and inhomogeneous reaction–diffusion media. We show that structural inhomogeneities hinder information propagation whereas noise enhances propagation.

Generalized reaction–diffusion textures

We present a method of synthesizing textures based on a modified reaction–diffusion equation. A non-Gaussian model of diffusion is employed to make a new class of textures possible. Whereas the Gaussian diffusion model is characterized by its covariance matrix (a rank-2 tensor), the generalized model of diffusion is characterized by a sequence of tensors of increasing rank which represent higher-order moments of the diffusion displacement probability. A numerical method of solving the new reaction–diffusion equation is described, as well as representative textures generated by this technique. The resulting patterns are inorganic in nature, often featuring sharp corners. The generalized reaction–diffusion textures display spatial inhomogeneity, even when the diffusion process is homogeneous, making it possible to generate complex textures from few parameters when compared with previous techniques employing inhomogeneous reaction–diffusion. The preferred orientations depend on the tensor sequence, and can be inspected prior to texture generation by plotting the non-Gaussian diffusion propagator.