PAFC空气电极催化层相界面结构分析

提出一个考虑了催化层中电压不均匀分布,可以在任意气体压力p、输出电流密度I工作条件下,表征PAFC空气电极行为的数学模型.发现表征“气/液”相界面比表面的参数AB与I在不同的p下呈不同的线性关系.其中在较低的压力下AB对I有较深的依赖关系,而在较高的压力p下,AB趋向与I无关.表征“液/固”界面的参数AI在不同p、I下基本保持不变.利用所构建的数学模型对PAFC空气电极中催化反应层内O2电化学还原速率进行了定量分析.结果表明,大电流下运行的空气电极,其主要的电极反应发生在“扩散层/催化层”交界处的催化反应层中,意味着厚的催化反应层是不必要的.     

Analytical model of the anode side of DMFC: the effect of non-Tafel kinetics on cell performance

Analytical model of the anode side of a direct methanol fuel cell is developed. The model takes into account non-Tafel kinetics of electrochemical reaction of methanol oxidation, diffusion transport of methanol through the backing layer and methanol crossover. General expression for the polarization voltage of the anode side is derived and simplified in a limits of small and large currents. Total limiting current density appears to be a combination of reaction- and diffusion-limiting current densities. The effect of methanol crossover on performance of the anode side is rationalized.     

A mathematical description of redox sorption of molecular oxygen taking into account the degree of metal dispersity in an electron-ion exchanger

The paper presents a physicochemical model of the redox sorption of molecular oxygen from water by a metal-containing electron-ion exchanger. The model takes into account the dispersity of metal particles, the special features of their chemical oxidation, and interrelation between the total process rate and the properties of the ion-exchange matrix. This model was used to formulate the problem mathematically, obtain a numerical solution, and theoretically analyze it as depending on the main parameters of the sorption system. A criterion was introduced for estimating the contributions of the diffusion and kinetic stages taking into account the dispersity of metal particles.     

The voltage–current curve of a direct methanol fuel cell: “exact” and fitting equations

Based on exact solutions of the problem of catalyst layer performance, the fitting equation for voltage–current curve of a direct methanol fuel cell is derived. Voltage losses due to imperfect transport of reactants in the diffusion layers and due to methanol crossover are taken into account. The coefficients in fitting equation are expressed in terms of basic transport and kinetic parameters on both sides of the cell. Fitting of experimental voltage–current gives the estimate of these parameters. The formula for optimal methanol concentration is derived; with good accuracy it reproduces the experimental value.     

Crystallization impedance in the case of D.C. superposition

An expression for the impedance frequency dependence in the case of d.c. superposition has been derived and analyzed for the crystallization process of metals taking into account the two-dimensional diffusion of ions in solution and the surface diffusion of adatoms and using the simplest surface model with parallel step lines. It is shown that in the general case it is impossible to present the crystallization impedance as the sum of the surface diffusion impedance and the Warburg impedance. It has been found that in the case of anode polarization an unusual effect of the impedance increasing with agitation intensity takes place which is typical of this mechanism. Possible methods for determination of the model parameters from impedance measurements are discussed. The authors suggest an iteration procedure which permits to determine all the parameters of the model under consideration including the surface diffusion coefficient of adatoms and the spacing between the growth step lines.     

Number of Nuclei Formed during Electrocrystallization and Overall Time Dependence of Their Growth Current

A model for continuous (progressing) nucleation is developed. The model takes into account (1) the mixed kinetics of growth of every nucleus, (2) different degree of the diffusion influence on the growth rate of nuclei formed at different time instants after switching the current on, and (3) the presence of hemispherical diffusion simultaneously with the developing front of plane diffusion. Equations that are obtained for the time dependence of the current include, in addition to values of concentrations, diffusion coefficients, and individual parameters of metals, the exchange current density and the overvoltage. The nucleation in depleted-by-diffusion zones around the growing nuclei is considered. It is shown that the average nucleation retardation degree in such zones is time-independent. Therefore, at an arbitrary time instant, the entire surface may be represented as comprising areas with an ordinary nucleation rate (whose share diminishes) and areas with a lower (but constant) nucleation rate (whose share rises). At not-too-low overvoltages, the decrease in the nucleation rate is mainly due to the decrease in the surface concentration of ions-reactants. The overall number of clusters, calculated with the proposed model, is usually a few orders of magnitude than found by known models.     

Computer aided simulation of hydrogen–oxygen (air) fuel cell with regard to the degradation mechanism of platinum catalyst on the cathode

A mathematical model of a hydrogen–oxygen (air) fuel cell that takes into account the phenomena of degradation of the cathodic platinum catalyst is presented. For potential cycling from 0.6 to 1.1 V with a scan rate of 0.1 V/s, depending on the platinum loadings, the following factors are found to prevail in the mechanism of electroactive surface degradation: the coalescence of platinum nanoparticles at large loadings and the platinum dissolution/redeposition and diffusion to the membrane at medium and low loadings. Based on mathematical simulation, the data on the discharge curves are calculated. The observed decrease in the discharge characteristics is attributed to the degradation of the catalyst active surface and the increased transport losses during accelerated stress testing.     

Modeling of electrocatalytic processes at conducting polymer modified electrodes

A mathematical model of electrocatalytic processes taking place at conducting polymer modified electrodes has been developed. The model takes into account the diffusion of solution species into a polymer film, diffusion of charge carriers within the film, and a chemical redox reaction within the film. The space- and time-resolved profiles for reactant and charge carrier concentration within the film, as well as dependencies of electric current on the concentration of solute species, reaction rate constant and thickness of a polymer layer have been obtained and discussed. It has been shown that, even at a relatively fast diffusion of charge carriers within the conducting polymer film, exceeding the diffusion rate of reactant by two orders of magnitude, electrocatalysis of solute species at conducting polymer modified electrodes proceeds within the polymer film rather than at the outer polymer/solution interface, i.e., electrocatalytic conversion follows a redox-mechanism rather than metal-like one. Based on the results obtained, optimization of reaction system parameters could be made for any particular case to get an optimum efficiency or reactant to product conversion.      

STOCHASTIC MODEL OF PERIODIC OPERATION PERFORMANCE FOR THE CONTINUOUS COUNTER－CURRENT ADSORPTION PROCESS

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Engineered 3D tissue models for cell-laden microfluidic channels

Delivery of nutrients and oxygen within three-dimensional (3D) tissue constructs is important to maintain cell viability. We built 3D cell-laden hydrogels to validate a new tissue perfusion model that takes into account nutrition consumption. The model system was analyzed by simulating theoretical nutrient diffusion into cell-laden hydrogels. We carried out a parametric study considering different microchannel sizes and inter-channel separation in the hydrogel. We hypothesized that nutrient consumption needs to be taken into account when optimizing the perfusion channel size and separation. We validated the hypothesis by experiments. We fabricated circular microchannels (r = 400 μm) in 3D cell-laden hydrogel constructs (R = 7.5 mm, volume = 5 ml). These channels were positioned either individually or in parallel within hydrogels to increase nutrient and oxygen transport as a way to improve cell viability. We quantified the spatial distribution of viable cells within 3D hydrogel scaffolds without channels and with single- and dual-perfusion microfluidic channels. We investigated quantitatively the cell viability as a function of radial distance from the channels using experimental data and mathematical modeling of diffusion profiles. Our simulations show that a large-channel radius as well as a large channel to channel distance diffuse nutrients farther through a 3D hydrogel. This is important since our results reveal that there is a close correlation between nutrient profiles and cell viability across the hydrogel. Young Seok Song and Richard L. Lin have contributed equally to this contribution     

A comparison of the pseudo-steady-state and shrinking-core model for the reduction of titanium dioxide to titanium

A multistage shrinking-core model is proposed for the electrodeoxidation of titanium dioxide to titanium. This takes place through a series of steps from TiO₂ to Ti₃O₅ to Ti₂O₃ to TiO to Ti. Ideally, the model would incorporate a number of shells of the above lower oxide phases with the shrinking core of TiO₂ in the center but this would be mathematically intractable. A simpler method would be to use the shrinking-core model for each of the individual reductions. Taking the experimental parameters and diffusion coefficient of oxygen in the different phases into account, an analytical solution is developed for the transient differential equation. The first ten eigenvalues are taken into account for the computation of the series solution. This is then compared with a solution based on a pseudo-steady-state approximation to the transient equations. Based on the results, for higher values (>0.01) of dimensionless applied current density, I _d , both the solutions disagree in terms of the time it takes for the core to shrink completely. The difference appears to be decreasing with lower values of I _d but for larger values of I _d the pseudo-steady-state approximation fails to yield results close to the analytical solution.     

Generalization of the Nernst layer model to take into account the difference in diffusivity between the components of the system in bromate reduction in steady-state one-dimensional mode: Current limiting by proton transport

The reduction of nonelectroactive bromate anion BrO ₃ ^- from acidic solutions while limiting the maximum current by diffusion transport of protons was studied by methods of numerical integration of transport equations. The calculation was performed based on a generalization of the Nernst steady diffusion layer model, in which the choice of the layer thickness for each component of the system is made using the Levich formula and takes into account the difference in diffusivity between the components. This difference in layer thickness was shown to have a significant effect on the main characteristics of the system, such as the maximum possible discharge current, and also the concentration profiles of the components.     

银在质子交换膜燃料电池空气阴极内促进氧传递研究

利用离子交换及随后的氢还原,将单质银负载在质子交换膜(Nafion)孔道内.TEM、XRD表征载银Nafion膜的结构,电化学极限电流法测定氧在载银Nafion膜内的扩散系数.结果表明,因银晶颗粒大于Nafion孔道直径,致使Nafion孔道有所扩张;氧在载银Nafion膜内的扩散系数是无银Nafion膜的4倍.据此,把银引入质子交换膜燃料电池空气阴极催化剂表面的Nafion薄层,则电池的性能在高电流密度下有明显的提高,显示了银对该电极内氧传递的促进作用.     

A chemical route to control molecular mobility on graphene

Controlling the motion of nanoscale building blocks on chemically contaminated or modified substrates is a bottleneck in bottom-up approaches to develop high performance Nanoscale Electro-Mechanical Systems (NEMS). Nevertheless, how such modification of a substrate surface affects the mobility of an admolecule has not been well understood. Here, we employ molecular dynamics (MD) simulations to study the surface diffusion of a C(60) admolecule on both pure and hydrogenated graphene. By changing temperature and hydrogen coverage, we obtain a diagram which shows evidently the existence of three distinct regimes of the surface diffusion of a C(60) admolecule, that is, superdiffusion, normal diffusion, and subdiffusion. Surprisingly, our simulations also show that minute hydrogenation on graphene leads to a giant reduction in molecular mobility. A theoretical model which takes into account the effects of both random traps and barriers is developed to predict the relation between the diffusion coefficient and the temperature and hydrogen coverage. The model predictions are in good agreement with our molecular dynamics simulation results.     

Grain Growth Kinetics of BaTiO3 Nanocrystals During Calcining Process

BaTiO3 nanocrystals were synthesized by sol-gel method using barium acetate (Ba(CH3COO)2) and tetrabutyl titanate (Ti(OC4H9)4) as raw materials. Xerogel precursors and products were characterized by means of thermogravimetric/differential scanning calorimetry (TG/DSC), X-ray diffraction (XRD) and transmission electron microscope (TEM). The influence of the calcination temperature and duration on the lattice constant, the lattice distortion, and the grain size of BaTiO3 nanocrystals was discussed based on the XRD results. The grain growth kinetics of BaTiO3 nanocrystals during the calcination process were simulated with a conventional grain growth model which only takes into account diffusion, and an isothermal model proposed by Qu and Song, which takes into account both diffusion and surface reactions. Using these models, the pre-exponential factor and the activation energy of the rate constant were estimated. The simulation results indicate that the isothermal model is superior to the conventional one in describing the grain growth process, implying that both diffusion and surface reactions play important roles in the grain growth process.     

The effect of mass transfer on electrochemical impedance of a solid oxide fuel cell anode

This paper presents electrochemical impedance simulation of a solid oxide fuel cell (SOFC) anode in order to investigate the effect of mass transport processes on the impedance spectra. The current model takes in to account the gas-phase transport processes both in the gas channel and within the porous electrode and couples the gas transport processes with the electrochemical kinetics. The impedance simulation is carried out in time domain, and the correlation between the anode harmonic responses to the sinusoidal excitation and the impedance spectra is analyzed. In order to solve the system of non-linear equations, an in-house code based on the finite difference method is developed and utilized. Results show a depressed semicircle in the Nyquist plot, which originates from gas transport processes in the gas channel, in addition to a Warburg diffusion impedance originates from gas transport in the thick porous anode. The influence of parameters such as electrode thickness, inlet gas composition, and temperature is also investigated and the results are discussed. The simulation results are in good agreement with published data.     

Diffusion effects in the oxidative degradation of vulcanized rubbers. II. Transient rate of chain scission

The effect of diffusion in the oxidative degradation of cis-1,4-polyisoprene vulcanizates was estimated by the analysis of the transient state of diffusion and oxidative degradation. An expression for the number of network chain scissions was obtained by solving the diffusion equation, which takes into account first-order oxygen consumption as well as constant scission efficiency. A practical method was proposed to analyze the transient process, which makes it possible to estimate diffusion coefficient and first-order rate constant independently. It was shown that the same analytical procedure would be applicable to the concentration jump method. The diffusion coefficient thus obtained was somewhat lower than the extrapolated value from the low-temperature data which was obtained in the absence of oxidation. Possible reasons responsible for this discrepancy were discussed.     

The current voltage plot of PEM fuel cell with long feed channels

The formula for voltage loss on the cathode side of the polymer electrolyte membrane fuel cell (PEMFC) is derived, taking into account oxygen consumption in the feed channel. Limiting current density due to the oxygen exhaustion along the channel is obtained. Theory predictions are in line with experiments that were performed to test the theory. The results reveal new reserves for the optimization of the cell performance. They also show new in situ electroanalytical options: the study of electrochemical reaction in the catalyst layer via the cell voltage–current plots and via detecting of the feed gas consumption or local current distribution along channel.     

Model for the multicomponent gas diffusion in a fuel cell porous electrode

A simple analytically solvable model for the diffusion of a multicomponent vapor-air mixture is proposed. The model, which accurately accounts for the oxygen and water balance on the gas diffusion cathode of a fuel cell, is used for computing polarization characteristics of a fuel cell with a polymer electrolyte. An analytical solution for the cathodic overvoltage in the extreme cases of high and low current densities is derived. The results are compared with the available theoretical and experimental data. It is shown that the solutions of the proposed model coincide with the solutions provided by the Bernardi-Verbrugge model, which is far more involved.