A Mathematical Model for Intercalation Electrode Behavior: I. Effect of Particle‐Size Distribution on Discharge Capacity

706

718

This paper develops a mathematical model for lithium intercalation and phase change in an iron phosphate-based lithium-ion cell in order to understand the cause for the low power capability of the material. The juxtaposition of the two phases is assumed to be in the form of a shrinking core, where a shell of one phase covers a core of the second phase. Diffusion of lithium through the shell and the movement of the phase interface are described and incorporated into a porous electrode model consisting of two different particle sizes. Open-circuit measurements are used to estimate the composition ranges of the single-phase region. Model-experimental comparisons under constant current show that ohmic drops in the matrix phase, contact resistances between the current collector and the porous matrix, and transport limitations in the iron phosphate particle limit the power capability of the cells. Various design options, consisting of decreasing the ohmic drops, using smaller particles, and substituting the liquid electrolyte by a gel are explored, and their relative importance discussed. The model developed in this paper can be used as a means of optimizing the cell design to suit a particular application.

Section: Resultsmentioning

confidence: 99%

Discharge Model for the Lithium Iron-Phosphate Electrode

Srinivasan

Newman

2004

706

718

“…7 show that the external surface areas of activated carbons vary widely. In 14 to maximize the specific surface area and minimize electrode porosity. Figure 3 presents the galvanostatic discharge curves for capacitors with composite electrodes made from various activated carbons.…”

Section: Resultsmentioning

confidence: 99%

Modeling the Effects of Electrode Composition and Pore Structure on the Performance of Electrochemical Capacitors

Cheng

Popov

Ploehn

2002

This work presents a mathematical model for charge/discharge of electrochemical capacitors that explicitly accounts for particlepacking effects in a composite electrochemical capacitor consisting of hydrous RuO 2 nanoparticles dispersed within porous activated carbon. The model is also used to investigate the effect of nonuniform distributions of salt in the electrolyte phase of the electrode in the context of dilute solution theory. We use the model to compare the performance of capacitors with electrodes made from different activated carbons and to investigate the effects of varying carbon content and discharge current density. Even at low discharge current density, concentration polarization in the electrodes results in underutilization of the electrodes' charge-storage capability, and thus decreased performance. Among various types of activated carbons, those with large micropore surface areas and low meso-and macropore surface areas are preferred because they give high double-layer capacitance and favor efficient packing of RuO 2 nanoparticles, thus maximizing faradaic pseudocapacitance. Increasing the electrode carbon content decreases the delivered charge and energy density, but the reductions are not severe at moderate carbon content and high discharge current. This suggests the possibility of optimizing the carbon content to minimize cost while achieving acceptable discharge performance. Electrochemical capacitors are urgently needed as components in many advanced power systems requiring high power density, high energy density, and high cycleability.1-6 Energy storage mechanisms in an electrochemical capacitor include separation of charge at the interface between a solid electrode and a liquid electrolyte, leading to double-layer ͑DL͒ capacitance, and faradaic redox reactions occurring at or near a solid electrode surface, known as pseudocapacitance. Charge storage in DL capacitance is essentially electrostatic in nature, and so DL charge/discharge processes are usually highly reversible. Pseudocapacitance, originating from faradaic redox reactions of oxides like RuO 2 , IrO 2 , or Co 3 O 4 at or near the electrode surface, involves interfacial reaction as well as mass transfer of ionic charge across the double layer. 6 Capacitors employing both DL and pseudocapacitance generally perform better than those featuring just one kind of capacitance. Activated carbon has been frequently used because its porous structure and large internal surface area result in electrodes with high specific energy and specific power densities. 6 The pore structure of activated carbon is a significant element in determining electrochemical capacitor performance. Shi 7 argued that pores of different sizes ͑micro-, meso-, and macropores͒ play different roles in contributing to DL capacitance. Macropores make a small contribution to the total specific surface area and thus contribute little to the DL capacitance. At the other extreme, micropores are responsible for most of the specific surface area, but the smallest pores may not...

“…An opposite distribution discharges the SG even faster due to the larger surface. 32 In addition to the previously introduced SG and LG samples, we modeled a made-up medium sized graphite (MG) for the variation studies that has a D10 value of 3.9 μm, a D50 value of 10.7 μm and a D90 value of 26.4 μm. Also, the effective thickness of the electrode layer varies in order to keep a constant area specific capacity per electrode layer with changing porosities.…”

Section: Resultsmentioning

confidence: 99%

“…[32][33][34][35] We used the given D values for the two graphites as the three representative sizes. To not change the overall active volume V s of the cell, the volumetric share k m of each particle size needs to be considered.…”

Section: Modelmentioning

confidence: 99%

Reducing Inhomogeneous Current Density Distribution in Graphite Electrodes by Design Variation

Kindermann

Oßwald

Ehlert

et al. 2017

Inhomogeneous utilization of electrodes and consequent limitations in the operating conditions are a severe problem, reducing lifetime and safety. By using a previously developed laboratory cell setup, we are able to show an inhomogeneous retrieval of lithium-ions from a graphite electrode throughout the layer with spatial resolution for two different graphites. After provoking inhomogeneities via constant current operations, equilibration processes are recorded and are assigned to two different effects. One effect is an equilibration inside the particles (intra-particle) from surface to bulk whereas the second effect is an equalization between the particles (inter-particle) to reach a homogeneous degree of lithiation in each particle throughout the electrode layer. With the recorded data, we implemented a P2D model with multiple particle sizes and considered the electrode thickness in several separate domains. Using the relaxation data of intra-and inter-particle relaxation for parametrizing the model, we investigated the influence of different solid and liquid phase parameters. As the liquid phase parameters scaled via porosity and tortuosity showed the biggest impact, we performed a design variation study to achieve a more homogeneous utilization of the electrode. Structuring the electrode to lower tortuosity is identified as the most promising design variation for homogeneous utilization. Lithium-ion cells are the electrochemical power source of choice, not only for portable electronic devices but also for plug-in hybrid electric vehicles (PHEVs) and electric vehicles (EVs). Despite significant improvements regarding energy density and cycle stability, drawbacks remain, preventing the acceptance of EVs as a coequal alternative to internal combustion engine vehicles.Resulting from advancements in the quality of manufacturing processes, the ratio between active and inactive components could be improved by realizing thicker electrode coatings and thinner current collector foils.1 This increase in the energy density of the cells, however, comes with longer charging times due to a reduced rate capability. While concepts such as intelligent charging strategies require a comprehensive framework to be implemented, 2 the most obvious approach is to increase the charging power. As presented by Tesla's Supercharger concept, the battery is charged up to 80% state of charge (SOC) within 40 min using a charging power of up to 120 kW. 3 The high charging power requires high charging currents due to current limitations for 400 V high voltage on-board power systems.Various publications address the variations in current density distribution and the resulting SOC inhomogeneities. The impact of the cell design and the resulting equalization processes along the electrodes are presented using experimental cells [4][5][6][7][8][9][10][11] or by a modeling approach.12,13 The resulting inhomogeneous utilization of the active material leads to undesired side reactions and accelerated degradation, especially lithium plating 14,15 and ...