Inhomogeneous Current Density Distribution Research Articles

Nanostructured Anode to Inhibit Dendrite Growth in Li Metal Batteries

Li metal is considered as the “Holy Grail” of energy storage systems due to its extremely high theoretical specific capacity (3860 mAh g−1), low gravimetric density (0.59 g cm−3), and lowest negative redox potential (−3.040 V vs. standard hydrogen electrode). The bright prospects give rise to worldwide interests in the metallic Li for the next generation energy storage systems, including highly considered rechargeable metallic Li batteries such as Li-O2 and Li-sulfur (Li–S) batteries. However, the formation of Li dendrites induced by inhomogeneous distribution of current density on the Li metal anode and the concentration gradient of Li ions at the electrolyte/electrode interface is a crucial issue that hinders the practical demonstration of high-energy-density metallic Li batteries. A unique nanostructured anode with Li metal distributed in fibrous Li7B6 matrix is proposed as a promising anode to prevent the dendrite growth. The nanostructured anode is with a large specific area, thus rendering a low current density on the Li metal anode. The dendrite growth is effectively inhibited via decreasing the growth velocity of Li deposits and then limiting the final size of deposited Li on the nanostructured matrix, thus leading to the dendrite-free morphology at macroscale. The concentration gradient of Li ions near the anode surface are sharply reduced, because the 3D Li7B6 fibrous structure provides quantities of free space to accommodate electrolyte. To improve the Coulombic efficiency of Li depositing/dissolution, a dual-phase Li metal anode containing polysulfide-induced SEI and nanostructured graphene framework was investigated for Li-S batteries. Free-standing graphene foam provides several promising features as underneath layer for Li anode, including (1) relative larger surface area than 2D substrates to lower the real specific surface current density and the possibility of dendrite growth, (2) interconnected framework to support and recycle dead Li, and (3) good flexibility to sustain the volume fluctuation during repeated incorporation/extraction of Li. The synergy between the LiNO3 and polysulfides provides the feasibility to the formation of robust SEI in an ether-based electrolyte. The efficient in-situ formed SEI-coated graphene structure allows stable Li metal anode with the cycling Coulombic efficiency of ∼97 % with high safety and efficiency performance, which is with a low resistance of 19.65 Ω (29.10 Ω for Cu foil based Li metal anode) and high ion conductivity of 5.42×10-2 mS cm-1 (2.33×10-2 mS cm-1 for Cu foil based Li metal anode). These results indicated that interfacial engineering of nanostructured electrode were a promising strategy to handle the intrinsic problems of Li metal anodes, thus shed a new light toward LMBs, such as Li-S and Li-O2 batteries with high energy density. Reference [1] X. B. Cheng, H. J. Peng, J. Q. Huang, F. Wei, Q. Zhang, Small 2014, 10, 4257 [2] X. B. Cheng, H. J. Peng, J. Q. Huang, R. Zhang, C. Z. Zhao, Q. Zhang, ACS Nano 2015, 9, 6373

Inhomogeneities in Large Format Lithium Ion Cells: A Study by Battery Modelling Approach

The performance of lithium ion battery cells is influenced by microscopic and macroscopic parameters. The microscopic parameters are generally responsible for the electrochemical, thermal, safety and lifetime performance of a battery. These parameters are cell chemistry, particle size, diffusion coefficient, equilibrium potential, reaction rate, thermodynamic parameters, thermal and electrical conductivity, heat capacity of active materials and different components of a cell etc. The macroscopic parameters are cell form, aspect ratio, thickness of active materials current collector and separator, tab size and its location. They are used in the cell design process and are optimized to enhance the performance and lifetime of a given cell. When considering upscaling the cell size, the macroscopic parameters attain significance in determining the overall performance of large format cells, which may be largely ignored in short format cells. Increase in the cell size has certain advantages such as, increased cell capacity, fewer connections to the battery pack (parallel connection), low assembly cost, high weight/volume ratio and high reliability of the components of a battery pack. But on the other hand it increases the cell cost, increased safety risk and difficult thermal management etc. But the main disadvantages in terms of performance and lifetime are related to the inhomogeneities occurring in the cell due to increase in cell size. The inhomogeneities can be listed as temperature, current density and state of the charge (SOC) distribution. The current distribution in the cell is affected by tab configuration, current collector thickness and cell aspect ratio. Recent studies show that increasing the cell size increases inhomogeneous current density distribution. Despite the optimized design, the current flow near the tabs is constricted and the location near cell tabs experience higher current density compared to surfaces far away from the tabs. The current distribution influences the local heat generation and introduces temperature inhomogeneity, especially near cell tabs. It also introduces SOC inhomogeneity as SOC in the integral of current over time. These inhomogeneities are related to one another and will have a cascading effect on the overall cell performance. A long term exposure to these inhomogeneities leads to localized aging of the cell. The localized aging creates stronger and weaker regions in cell and further accelerating the aging and leads to premature end of life (EOL) of the cell. With the existing methodologies it is difficult to evaluate cell inhomogeneity as it is completely a localized process. However, recently some experimental and modelling techniques are able to evaluate cell inhomogeneity. These methods can be classified into two as, direct measurement such as, spatial temperature measurements both inside and on the cell surface, multiple or segmented electrode measurements, in-situ and ex-situ diffraction or neutron imaging tools and the second classification is modelling and simulation techniques, which is the focus of this study. This paper shows two modelling techniques, first with spatially distributed battery model developed in Matlab/Simulink and second with Multiphysics based modelling in COMSOL. Both models are able to evaluate inhomogeneity in a large format cell. This work also compares these modelling techniques with respect to complexity, computation and accuracy of the simulation results. Figure 1

Structured Anode to Inhibit Dendrite Growth in Li Metal Batteries

Li metal is considered as the “Holy Grail” of energy storage systems due to its extremely high theoretical specific capacity (3860 mAh g−1), low gravimetric density (0.59 g cm−3), and lowest negative redox potential (−3.040 V vs. standard hydrogen electrode). The bright prospects give rise to worldwide interests in the metallic Li for the next generation energy storage systems, including highly considered rechargeable metallic Li batteries such as Li-O2 and Li-sulfur (Li–S) batteries. However, the formation of Li dendrites induced by inhomogeneous distribution of current density on the Li metal anode and the concentration gradient of Li ions at the electrolyte/electrode interface is a crucial issue that hinders the practical demonstration of high-energy-density metallic Li batteries. A unique nanostructured anode with Li metal distributed in fibrous Li7B6 matrix is proposed as a promising anode to prevent the dendrite growth. The nanostructured anode is with a large specific area, thus rendering a low current density on the Li metal anode. The dendrite growth is effectively inhibited via decreasing the growth velocity of Li deposits and then limiting the final size of deposited Li on the nanostructured matrix, thus leading to the dendrite-free morphology at macroscale. The concentration gradient of Li ions near the anode surface are sharply reduced, because the 3D Li7B6 fibrous structure provides quantities of free space to accommodate electrolyte. To improve the Coulombic efficiency of Li depositing/dissolution, a dual-phase Li metal anode containing polysulfide-induced SEI and nanostructured graphene framework was investigated for Li-S batteries. Free-standing graphene foam provides several promising features as underneath layer for Li anode, including (1) relative larger surface area than 2D substrates to lower the real specific surface current density and the possibility of dendrite growth, (2) interconnected framework to support and recycle dead Li, and (3) good flexibility to sustain the volume fluctuation during repeated incorporation/extraction of Li. The synergy between the LiNO3 and polysulfides provides the feasibility to the formation of robust SEI in an ether-based electrolyte. The efficient in-situ formed SEI-coated graphene structure allows stable Li metal anode with the cycling Coulombic efficiency of ∼97 % with high safety and efficiency performance, which is with a low resistance of 19.65 Ω (29.10 Ω for Cu foil based Li metal anode) and high ion conductivity of 5.42×10-2 mS cm-1 (2.33×10-2 mS cm-1 for Cu foil based Li metal anode). These results indicated that interfacial engineering of nanostructured electrode were a promising strategy to handle the intrinsic problems of Li metal anodes, thus shed a new light toward LMBs, such as Li-S and Li-O2 batteries with high energy density. Reference [1] X. B. Cheng, H. J. Peng, J. Q. Huang, F. Wei, Q. Zhang, Small 2014, 10, 4257 [2] X. B. Cheng, H. J. Peng, J. Q. Huang, R. Zhang, C. Z. Zhao, Q. Zhang, ACS Nano 2015, 9, 6373

GDL and MPL Characterization and Their Relevance to Fuel Cell Modelling

PEM fuel cells (PEMFC) are a promising technology for electrochemical energy conversion. However, especially for applications requiring high current density, the gas diffusion layer (GDL) deserves further attention and efforts. Liquid water saturation of pores in the GDL limits the flow of reactants to the catalyst and creates starvation areas with inhomogeneous current density distribution. This leads to accelerated material degradation in these areas and to poor overall performance. Traditional fuel cell models, e.g. CFD simulation modules, make simplifying assumptions, i.e. by modelling the GDL fibre structure as homogeneous porous material, which may cause current density distributions to appear more uniform than they really are. This presentation will give a survey on relevant parameters for GDL characterization, useful methods for investigations and on implications of these results to GDL modelling. The GDL structure inside of an assembled fuel cell can be characterized using X-ray based methods, especially synchrotron or µ-CT based radiography and tomography [1, 2]. Radiographic methods allow for a relatively quick investigation on the integral water distribution within the different MEA layers, especially the GDL substrate and - to some extent - also for the membrane, depending on the selection of material and operating parameters. On the other hand, tomographic methods allow for 3D resolved water distribution analysis, especially for the water distribution within the GDL substrate. Moreover, the different GDL structures due to flow field compression under-land and under-channel are subject of these investigations. Such measurements are performed with sub-μm pixel size at ZSW/HZB to account for the effects of fine pores and fiber structures in detail. The structural information obtained can be used for advanced modelling techniques determining reactant concentrations in the gaseous media employing single-phase approaches. Liquid water effects caused by pore volume reduction may be directly used as model input at this stage. To perform a reasonable modelling of the water distribution itself, not only structural, but also surface parameters must be known. These have to be additionally determined by ex situ techniques. Ideally, the surface properties inside the porous structure would be known down to a sub µm scale. Unfortunately, no generally applicable methods are known until today. First approaches are e.g. the STXM method [3]. But at least integral surface property data can be determined requiring significantly less effort. Different approaches to characterize the wettability of porous media will be discussed. As a very efficient method to determine the inner contact angle of the GDL, inverse gas chromatography techniques may be used. This inner contact angle has been successfully used for a modelling technique (Monte Carlo (MC) modelling) describing the behavior of liquid water inside the porous fibre structure [4]. Thus, using both structural and surface properties, water distribution and GDL transport parameters may be modelled (MC, CFD at µm to mm level) and introduced into models on the macro-scale (e.g. CFD at cell level with segmented GDL areas over rib and over channel). Furthermore, GDL material characteristics regarding transport properties require special attention. As relevant parameters for ex-situ characterization, rating of GDL materials and as important modelling input, structure and material related physical parameters as Leverett function, electrical and heat conductivity, mechanical parameters as E module and shear modulus G can be determined by both modelling on the basis of accurate structure data, e.g. from µ-CT imaging, and – on the macro scale – by direct measurement. Specially, the compression force cycle behavior is mainly obtained from direct measurements. Also, permeability data (in and through plane) may be measured directly. Besides permeation, gas-phase diffusion of the relevant species in the substrate and – on a much smaller scale involving different diffusion mechanisms – in the MPL pores is not trivial to characterize. First results obtained by recently designed setups employing a special low turbulence cell in combination with molar flow analysis for determination of diffusion coefficients and a method to determine the Leverett function will be presented. The ex situ methods recommended will be listed and described in the presentation.

Inscribing wettability gradients onto polymer substrates with different stiffness using corona discharge in point-to-plane geometry

We use direct current (DC) corona discharge to create wettability gradients on polymer surfaces. The inhomogeneous current density distribution due to a point-to-plane arrangement induces local changes of the wettability of polymer surfaces, resulting in macroscopic wettability gradients. We found that condensation of water vapor on the surface allows a more precise characterization of the wettability gradient than macroscopic contact angle measurements. Condensation experiments allow characterizing different zones with different wettability. The wettability pattern depends on the stiffness of the substrate. We conjecture that Coulomb interactions influence the spatial distribution of wettability. Indirect measurements of the electrostatic surface potential after exposure support this assumption.

The avalanche process in gold covered MgB2 films

Below a certain threshold temperature, the critical state of superconducting thin films can become unstable, which results in large magnetic flux jumps, called flux avalanches. The phenomenon of magnetic flux avalanches is strongly connected to the thermal and electrical conductivity in the material. Enhancing both by metallic cover layers on the superconducting film can suppress the magnetic avalanches. It was found that it is feasible to subdivide the avalanche process into a formation and a propagation step. In this work we want to address the question regarding the stage at which the metallic cover layer influences the avalanche mechanism. The investigations are carried out on thin MgB2 films with an inhomogeneous current density distribution, where both the formation and propagation of magnetic flux avalanches are highly supported. Evaporating a gold cover layer on top of the inhomogeneous MgB2 films leads to a suppression of the instabilities in this case. Magnetization measurements and magneto-optical imaging are used to observe the instabilities in pure MgB2 films and MgB2 films covered with gold layers. We investigate how the two steps of the avalanche process, nucleation and propagation, are influenced by the additional gold layer. We find a particular influence on the initial phase of the avalanche formation.

Spatial Distribution of Electrochemical Performance in a Segmented SOFC: A Combined Modeling and Experimental Study

AbstractSpatially inhomogeneous distribution of current density and temperature in solid oxide fuel cells (SOFC) contributes to accelerated electrode degradation, thermomechanical stresses, and reduced efficiency. This paper presents a combined experimental and modeling study of the distributed electrochemical performance of a planar SOFC. Experimental data were obtained using a segmented cell setup that allows the measurement of local current‐voltage characteristics, gas composition and temperature in 4 × 4 segments. Simulations were performed using a two‐dimensional elementary kinetic model that represents the experimental setup in a detailed way. Excellent agreement between model and experiment was obtained for both global and local performance over all investigated operating conditions under varying H2/H2O/N2 compositions at the anode, O2/N2 compositions at the cathode, temperature, and fuel utilization. A strong variation of the electrochemical performance along the flow path was observed when the cell was operated at high fuel utilization. The simulations predict a considerable gradient of gas‐phase concentrations along the fuel channel and through the thickness of the porous anode, while the gradients are lower at the cathode side. The anode dominates polarization losses. The cell may operate locally in critical operating conditions (low H2/H2O ratios, low local segment voltage) without notably affecting globally observed electrochemical behavior.

Investigation of Locally Resolved Current Density Distribution of Segmented PEM Fuel Cells to Detect Malfunctions

With the aid of PCB technology, current density distribution could be achieved by measuring the local current density inside the fuel cell, which would be more precisely reflecting the local electrochemical reaction. An important application of segmented cell technology was used for in-situ error detection of the evolution of membrane leakage. From the evolution of current density distributions, starting locations of membrane leakages and their spreading could be detected. The effect of operation conditions could be found: the steeply decreased pressure and the fast cooling of the local membrane was the main reason for the degradation of the membrane. It caused large temperature gradient in different local membranes, which resulted in inhomogeneous current density distribution and mechanical strain and stress. With the aid of segmented cell, malfunction could be detected at an early stage and thereby catastrophic failure of the whole stack may be avoided.

On the origin of horizontal counter-rotating electrolyte flow during copper magnetoelectrolysis

The understanding of electrolyte flow (convection) during metal magnetoelectrolysis can help towards a better quantitative understanding of the magnetohydrodynamic (MHD) effect. This paper summarizes numerical simulations of copper electrolysis in cuboid cells with vertical wall electrodes under the influence of homogeneous external magnetic fields. Horizontal counter-rotation in the top and bottom region is found in cuboid cells exposed to vertical magnetic fields as well as in tall cells exposed to electrode-normal magnetic fields. The main reason for this characteristic convection type induced by the Lorentz force is the vertical thickness variation of the concentration boundary layer along anode and cathode due to natural convection which results in an inhomogeneous current density distribution. Then, in both cases, the magnetic field and the corresponding normal component of the current density create a rotational Lorentz force which drives the horizontal counter-rotating flow.

Electric-field control of electron interference effects in 2D semiconductor nanostructures with parabolic quantum wells

The possibility of the influence of a constant electric field on spatial reproduction effects for quantum-mechanical current density, which arise during interference of electron waves in 2D semiconductor nanostructures, is studied theoretically. It is found that, in structures comprising a narrow rectangular quantum well and a wide parabolic quantum well placed successively in the direction of propagation of an electron wave, the transverse current density distribution existing at the input of the wide quantum well is reproduced in this well with a certain accuracy in periodically repeated cross sections. The inhomogeneous current density distribution arises because of the interference of electron waves propagating in the wide quantum well simultaneously in different quantum-dimensional subbands. It is shown that it is possible to control these effects via the use of a constant electric field perpendicular to the axis of the structure in the region of the wide quantum well.

Magnetization, Magnetotransport and Ferromagnetic Resonance in A Permalloy Antidot Array with Square Holes

ABSTRACTA Permalloy antidot array with square hole size 800?800 nm2 has been fabricated by the means of electron-beam lithography and lift-off techniques. An out-of-plane anisotropy was found in both the reference film of Permalloy and the antidot array with the thickness of 100 nm. Inhomogeneous current-density distribution and complex domain structures in the antidot nanostructure result in unique behavior of the magnetoresistance. Quantized standing spin-wave modes originating from the lateral confinement of the antidot nanostructure were clearly observed for the magnetic field applied normal to the array plane. Two uniform precession resonance modes occurred when the field deviated more than 30 degrees from the normal to the plane. These two resonances originate from different regions of the array having distinct dipolar field patterns with different orientation and magnitude of magnetostatic field. The easy axes of the anisotropy in these regions are in-plane and orthogonal to each other.

Plasma localization in an extended hollow cathode of the plasma source of a ribbon electron beam

The plasma density distributions in the slit aperture of the extended rectangular hollow cathode of the source of a ribbon electron beam are investigated experimentally. It is found that a local maximum whose parameters are determined by the discharge current appears in the density distribution when the slot width is less than a certain threshold value. This maximum results in an inhomogeneous current density distribution in the beam. It is shown that the appearance of the local maximum in the plasma density is related to the overlapping of the ion sheaths in the slit aperture of the hollow cathode.

Calculated E-I characteristics of HTS pancakes and coils exposed to inhomogeneous magnetic fields

The upper limit of the operating current of LTS solenoids can be estimated as the coordinate of the crossing point of its load line with IC (B) line of the superconductor. For HTS coils this approach seems to underestimate the allowable operating current of the coil. A better approach is to obtain a full electric field distribution over the coil and to use it as the base for a more sophisticated coil design criteria. We developed an algorithm and a Matlab program for calculating distributions of the current density, magnetic field and electric field in HTS solenoids made of pancakes, considering the inhomogeneous current density distribution inside the anisotropic tape. I-V curves of several Bi-2223 coils are calculated and good agreeement of the calculated and measured critical currents, IC, and indexes, n, are attained. One can utilize the program in the coil design choosing his own criteria of coil's critical current, e.g., 1) The average electric field 10−4 V/m over the coil, 2) The electric field 10−4 V/m at the weak point of the coil, 3) The energy dissipation in the entire coil, 4) Distribution of local energy dissipation.

Homogenization of the current density in polymer electrolyte fuel cells by in-plane cathode catalyst gradients

Polymer electrolyte fuel cells (PE fuel cells) working with air at low stoichiometries (<2.0) and standard electrochemical components show a high degree of inhomogeneity in the current density distribution over the active area. An inhomogeneous current density distribution leads to a non-uniform utilization of the active area, which could negatively affect the time of life of the cells. Furthermore, it is also believed to lower cell performance. In this work, the homogenization of the current density, realized by means of tailored cathodes with along-the-air-channel redistributed catalyst loadings, is investigated. The air stoichiometry range for which a homogenization of the current density is achieved depends upon the gradient with which the catalyst is redistributed along the air channel. A gentle increasing catalyst loading profile homogenizes the current density at relatively higher air stoichiometries, while a steeper profile is suited better for lower air stoichiometries. The results show that a homogenization of the current density by means of redistributed catalyst loading has negative effects on cell performance. Model calculations corroborate the experimental findings on homogenization of the current density and deliver an explanation for the decrease in cell performance.

Current inhomogeneity effect in single-layer ferromagnetic antirectangular structures

The magnetotransport properties of antirectangular arrays (2×10μm2) embedded into 200-Å-thick continuous Ni80Fe20 films with the interhole spacing equal to 2μm have been investigated. We observed that the inhomogeneous current-density distribution, due to the placement of electrical contacts, caused an unusual positive magnetoresistance (MR) behavior for the in-plane longitudinal measurements. Finite element simulations on current-density distribution are in agreement with experimental data on small area antirectangular structures. For the continuous film, however, the current-density distribution does not play a significant role in determining the shape of the MR curve.

Microstructure‐Property Relations of Solid Oxide Fuel Cell Cathodes and Current Collectors: Cathodic Polarization and Ohmic Resistance

Microstructure, cathodic polarization, and ohmic resistance on the cathode side of ‐based solid oxide fuel cells have been studied for the intermediate temperature operation range between 700 and 900°C. Starting powder characteristics, powder calcination temperature, and sintering temperature strongly influence the final microstructure of cathodes. Electrochemical performance depends on these processing parameters as well as on the cathode thickness and the contact spacing of current collectors. A decrease in effective electrode area occurs both on the microscopic level with coarse and inhomogeneous cathode microstructure and on the macroscopic level with a wide contact spacing of the current collectors. The smaller effective electrode area causes inhomogeneous current density distribution and results consequently in higher ohmic losses originating from the electrolyte and higher cathodic polarization. These losses are evaluated using cathodes with different microstructures and on the mole percent electrolyte. The influence of current path constrictions on the ohmic and nonohmic losses is demonstrated using Pt current collectors of different geometric spacings.

Magnetic- and stress-fields of cylindrical non-uniform current density superconducting coils

Superconducting coils with an inhomogeneous current density distribution yield more field for less volume of superconductor. The advantages of these systems are lower costs and an improved cooling. The latter is important for high field magnets. Mechanical stresses induced by the electromagnetic forces are the limiting factor in designing such coils. The inhomogeneous current field is produced by a set of concentric subcoils. The radial and tensile stresses and the radial displacements in the subcoils are calculated. This calculation requires the field-shape in the coils. An exact calculation shows a linear decrease of the field with the radius in each subcoil. Thus the stress-calculations are very simple and one does not need a computer. As an example this method is applied to a 10 T-magnet with three subcoils. In this case the results of our exact calculation differ from the approximation of Kilbet al., Steklyet al. and from the magnetic pressure estimateB 2/2μ 0 up to a factor of three.