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At least 91 records · Page 5

Modeling Rate Dependent Volume Change in Porous Electrodes in Lithium-Ion Batteries

Automotive manufacturers are working to improve individual cell, module, and overall pack design by increasing the performance, range, and durability, while reducing cost. One key piece to consider during the design process is the active material volume change, its linkage to the particle, electrode, and cell level volume changes, and the interplay with structural components in the rechargeable energy storage system. As the time from initial design to manufacture of electric vehicles decreases, design work needs to move to the virtual domain; therefore, a need for coupled electrochemical-mechanical models that take into account the active material volume change and the rate dependence of this volume change need to be considered. In this study, we illustrated the applicability of a coupled electrochemical-mechanical battery model considering multiple representative particles to capture experimentally measured rate dependent reversible volume change at the cell level through the use of an electrochemical-mechanical battery model that couples the particle, electrode, and cell level volume changes. By employing this coupled approach, the importance of considering multiple active material particle sizes representative of the distribution is demonstrated. The non-uniformity in utilization between two different size particles as well as the significant spatial non-uniformity in the radial direction of the larger particles is the primary driver of the rate dependent characteristics of the volume change at the electrode and cell level.

Electrochemistry↗

Mathematical modeling of a primary zinc/air battery

The mathematical model developed by Sunu and Bennion has been extended to include the separator, precipitation of both solid ZnO and K2Zn(OH)4, and the air electrode, and has been used to investigate the behavior of a primary Zn-Air battery with respect to battery design features. Predictions obtained from the model indicate that anode material utilization is predominantly limited by depletion of the concentration of hydroxide ions. The effect of electrode thickness on anode material utilization is insignificant, whereas material loading per unit volume has a great effect on anode material utilization; a higher loading lowers both the anode material utilization and delivered capacity. Use of a thick separator will increase the anode material utilization, but may reduce the cell voltage.

Mao, Z.↗

Simulations of Cyclic Voltammetry for Electric Double Layers in Asymmetric Electrolytes: A Generalized Modified Poisson-Nernst-Planck Model

This paper presents a generalized modified Poisson–Nernst–Planck (MPNP) model derived from first principles based on excess chemical potential and Langmuir activity coefficient to simulate electric double-layer dynamics in asymmetric electrolytes. The model accounts simultaneously for (1) asymmetric electrolytes with (2) multiple ion species, (3) finite ion sizes, and (4) Stern and diffuse layers along with Ohmic potential drop in the electrode. It was used to simulate cyclic voltammetry (CV) measurements for binary asymmetric electrolytes. The results demonstrated that the current density increased significantly with decreasing ion diameter and/or increasing valency |z i | of either ion species. By contrast, the ion diffusion coefficients affected the CV curves and capacitance only at large scan rates. Dimensional analysis was also performed, and 11 dimensionless numbers were identified to govern the CV measurements of the electric double layer in binary asymmetric electrolytes between two identical planar electrodes of finite thickness. A self-similar behavior was identified for the electric double-layer integral capacitance estimated from CV measurement simulations. Two regimes were identified by comparing the half cycle period τ CV and the “RC time scale” τ RC corresponding to the characteristic time of ions’ electrodiffusion. For τ RC ← τ CV , quasi-equilibrium conditions prevailed and the capacitance was diffusion-independent while for τ RC → τ CV , the capacitance was diffusion-limited. The effect of the electrode was captured by the dimensionless electrode electrical conductivity representing the ratio of characteristic times associated with charge transport in the electrolyte and that in the electrode. The model developed here will be useful for simulating and designing various practical electrochemical, colloidal, and biological systems for a wide range of applications.

Wang, Hainan↗

Exploring Electrode-Level State-of-Charge and State-of-Health Dynamics in Lithium-Ion Battery Cells: Modeling and Experimental Identification

A computationally efficient model serves as a critical prerequisite for battery performance analysis and advanced battery management algorithm design. Although battery models that capture cell-level behavior have been widely explored in existing literature, electrode-level battery models have received much lesser attention till to date. However, such electrode-level models can significantly increase battery performance and life by enabling electrode-level health-conscious control. Such electrode-level control can effectively expand usable energy and power limits of the battery cells by utilizing the knowledge of individual electrodes' charge and health. In this context, this paper presents a comprehensive battery model developed with a reference electrode insertion that captures (i) electrode-level charge/discharge dynamics, (ii) stoichiometric and temporal dependencies of electrode-level resistances, (iii) solid electrolyte interface (SEI) layer growth as key degradation phenomenon, and (iv) capacity fade and resistance rise in each electrode due to nominal battery aging. The proposed model is identified, and a preliminary validation is performed utilizing terminal voltage and negative electrode potential data collected from a pouch cell under one continuous cycling and accelerated aging conditions where the cell experienced 14% capacity loss.

aging↗

Towards Predictive Plasma Science and Engineering through Revolutionary Multi-Scale Algorithms and Models (Final Report)

This report describes the high-level accomplishments from the Plasma Science and Engineering Grand Challenge LDRD at Sandia National Laboratories. The Laboratory has a need to demonstrate predictive capabilities to model plasma phenomena in order to rapidly accelerate engineering development in several mission areas. The purpose of this Grand Challenge LDRD was to advance the fundamental models, methods, and algorithms along with supporting electrode science foundation to enable a revolutionary shift towards predictive plasma engineering design principles. This project integrated the SNL knowledge base in computer science, plasma physics, materials science, applied mathematics, and relevant application engineering to establish new cross-laboratory collaborations on these topics. As an initial exemplar, this project focused efforts on improving multi-scale modeling capabilities that are utilized to predict the electrical power delivery on large-scale pulsed power accelerators. Specifically, this LDRD was structured into three primary research thrusts that, when integrated, enable complex simulations of these devices: (1) the exploration of multi-scale models describing the desorption of contaminants from pulsed power electrodes, (2) the development of improved algorithms and code technologies to treat the multi-physics phenomena required to predict device performance, and (3) the creation of a rigorous verification and validation infrastructure to evaluate the codes and models across a range of challenge problems. These components were integrated into initial demonstrations of the largest simulations of multi-level vacuum power flow completed to-date, executed on the leading HPC computing machines available in the NNSA complex today. These preliminary studies indicate relevant pulsed power engineering design simulations can now be completed in (of order) several days, a significant improvement over pre-LDRD levels of performance.

42 ENGINEERING↗

First-principles Modeling and Design of Solid-State Interfaces for the Protection and Use of Lithium Metal Anodes

Li-ion batteries are one of the most advanced energy storage technologies in use today. Li-ion batteries are used in a multitude of applications ranging from consumer electronics, medical devices, sensors and grid storage. However, improving the capacity and energy density delivered by current Li-ion technology requires advanced materials research into novel chemical systems. In this project we have focused particularly in the use of solid-state electrolytes with lithium metal electrodes. Research into all solid-state batteries (ASSB) with Li metal electrodes has significantly expanded in recent years, however most studies reported experimental findings, which left substantial room for theoretical and modeling work as a tool to understand and determine design principles allowing reliable and safe use of ASSBs with Li metal. Among the remaining obstacles preventing reliable use of ASSBs with a Li metal electrode, the stability of the interface between the solid electrolyte and Li metal, and the propagation/dendrite formation of Li metal and resulting mechanical degradation of the electrolyte are key phenomenon that are yet to be fully understood. In the current project we have addressed these two coupled phenomena using first principles calculations and mesoscale continuum modeling. We have obtained chemical and electrochemical stability windows for several solid electrolyte materials. Additionally, from mathematical and numerical modeling of Li protrusion and dendrite initiation during plating and stripping we have determined design criteria in terms of chemical, electrochemical, and mechanical properties and operating conditions for which stable deposition can occur. We also considered the effects of mixed electronic-ionic conduction in solid electrolytes, which has more recently been suggested as another important mechanism involved in ASSB failure. Throughout our work we have successfully addressed important questions necessary for the use of ASSB’s. We have determined guiding principles for materials properties and operating conditions necessary to operate ASSB’s. And have proposed novel solid electrolyte materials with predicted chemical stability an ionic conductivity. Although this represents significant progress in our understanding, open questions remain in order to fully develop reliable and safely operate ASSBs with Li metal. Future work, building on this project will require further experimental, theoretical and simulation efforts to address remaining questions.

25 ENERGY STORAGE↗

Quantifying Aging-Induced Irreversible Volume Change of Porous Electrodes

Automotive manufacturers are working to improve cell and pack design by increasing their performance, durability, and range. One of the critical factors to consider as the industry moves towards materials with higher energy density is the ability to consider the irreversible volume change characteristic of the accelerated SEI layer growth tied to the large volume change and particle cracking typically associated with active material strain. As the time from initial design to manufacture of electric vehicle is decreased in order to rapidly respond to consumer demands and widespread adoption of electric vehicles, the ability to link aging and volume change to end of life vehicle requirements using virtual tools is critical. In this study, apply a mechano-electrochemical model to determine the irreversible volume change at the electrode and cell level, allowing for virtual design iterations to predict the volume change at battery cell aged states.

Electrochemistry↗

Fully Coupled Simulation of Lithium Ion Battery Cell Performance

Lithium-ion battery particle-scale (non-porous electrode) simulations applied to resolved electrode geometries predict localized phenomena and can lead to better informed decisions on electrode design and manufacturing. This work develops and implements a fully-coupled finite volume methodology for the simulation of the electrochemical equations in a lithium-ion battery cell. The model implementation is used to investigate 3D battery electrode architectures that offer potential energy density and power density improvements over traditional layer-by-layer particle bed battery geometries. Advancement of micro-scale additive manufacturing techniques has made it possible to fabricate these 3D electrode microarchitectures. A variety of 3D battery electrode geometries are simulated and compared across various battery discharge rates and length scales in order to quantify performance trends and investigate geometrical factors that improve battery performance. The energy density and power density of the 3D battery microstructures are compared in several ways, including a uniform surface area to volume ratio comparison as well as a comparison requiring a minimum manufacturable feature size. Significant performance improvements over traditional particle bed electrode designs are observed, and electrode microarchitectures derived from minimal surfaces are shown to be superior. A reduced-order volume-averaged porous electrode theory formulation for these unique 3D batteries is also developed, allowing simulations on the full-battery scale. Electrode concentration gradients are modeled using the diffusion length method, and results for plate and cylinder electrode geometries are compared to particle-scale simulation results. Additionally, effective diffusion lengths that minimize error with respect to particle-scale results for gyroid and Schwarz P electrode microstructures are determined.

25 ENERGY STORAGE↗

Unraveling the Ion Adsorption Kinetics in Microporous Carbon Electrodes: A Multiscale Quantum-Continuum Simulation and Experimental Approach

With the understanding that sorption in porous carbon electrodes is crucial to many environmental and energy technologies, such as capacitive deionization (CDI), supercapacitor energy storage, and activated carbon filters. In each of these examples, a practical model that can describe ion electrosorption kinetics is highly desirable for accelerating material design. Here, we proposed a multiscale model to study the ion electrosorption kinetics in porous carbon electrodes by combining quantum mechanical simulations with continuum approaches. Our model integrates the Butler-Volmer (BV) equation for sorption kinetics and a continuously stirred tank reactor (CSTR) formulation with atomistic calculations of ion hydration and ion-pore interactions based on density functional theory (DFT). We validated our model experimentally by using ion mixtures in a flow-through electrode CDI device and developed an in-line UV absorption system to provide unprecedented resolution of individual ions in the separation process. We showed that the multiscale model captures unexpected experimental phenomena that cannot be explained by the traditional ion electrosorption theory. The proposed multiscale framework provides a viable approach for modeling separation processes in systems where pore sizes and ion hydration effects strongly influence the sorption kinetics, which can be leveraged to explore possible strategies for improving carbon-based and, more broadly, pore-based technologies

36 MATERIALS SCIENCE↗

Predictive Modeling of Electrodeposition in a Single Pore Flow-Through Electrode: From Electronucleation to Coating Thickness Uniformity

The emergence of advanced manufacturing methods capable of producing porous three-dimensional structures has expanded the design space for next-generation functional components. The ability to fabricate ordered 3D foams for use in electrocatalysis reactors has increased the need for controlled deposition of catalytic metals onto porous support materials, such as carbon. However, there is a lack of clear design guidelines for electrodeposition onto 3D substrates, due to the geometric complexity and multi-scale nature of the problem. Furthermore, electro-nucleation phenomena are often overlooked in macro-scale models of current distribution during deposition. Here, a graphite flow-through electrode (FTE) is used as a model system for copper deposition within a single pore. Potential distributions and electro-nucleation phenomena are coupled in a continuum level model by incorporating nucleation size and density as a function of overpotential, determined experimentally using in situ atomic force microscopy (AFM). The model predictions are validated by measuring the coating uniformity in the pore using micro-computed X-ray tomography (μCT). A scaling analysis comprising dimensionless parameters such as the Wagner number is presented. The simplified scaling relationship framework can guide the electrodeposition process and electrode design to optimize plating of porous substrates under fluid flow conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Modeling Co-Extruded Cathodes for High Energy Lithium-Ion Batteries

Utilizing an existing macro-homogeneous porous electrode model developed by John Newman, this talk presents the potential energy density gains that can be realized in lithium-ion battery electrodes fabricated with co-extrusion (CoEx) technology. CoEx uses carefully engineered fluidic channels to cause multiple streams of dissimilar fluids to impart shape to one another. The result is a high-speed, continuous deposition process that can create fine linear structures much smaller than the smallest physical feature within the printhead. By eliminating the small channels necessary for conventional extrusion and injection processes, CoEx is able to deposit highly loaded and viscous pastes at high line speeds under reasonable operating pressures. The CoEx process is capable of direct deposition of features as small as 10 μm with aspect ratios of 5 or greater, and print speeds > 80 ft/min. We conduct an analysis on two-dimensional cathode cross-sections in COMSOL and present the electrochemical performance results, including calculated volumetric energy capacity for Lithium Nickel Manganese Cobalt Oxide (NMC) co-extruded cathodes, in the presence of a lithium metal anode, polymer separator and ethylene carbonate–diethyl carbonate (EC:DEC) liquid electrolyte. The impact of structured electrodes on cell performance is investigated by varying the physical distribution of a fixed amount of cathode mass over a space of dimensions which can be fabricated by CoEx. By systematically varying the thickness and aspect ratio of the electrode structures, we present an optimal subset of geometries and design rules for co-extruded geometries. Modeling results demonstrate that NMC CoEx cathodes, on the order of 125-200 µm thick, can garner an improvement in material utilization and in turn capacity through the addition of fine width electrolyte channels or highly conductive electrode regions. We also present initial experimental results on CoEx NMC cathode structures.

25 ENERGY STORAGE↗

Highly-Active and Contaminant-Tolerant Cathodes for Durable Solid Oxide Fuel Cells (Final Report)

The objective of this project is to investigate the fundamental degradation methods occurring in solid oxide fuel cell (SOFC) cathodes when exposed to chromium and carbon dioxide contamination and to rationally design alkaline earth-based catalysts to increase stability and tolerance to contaminate poisoning. With a mechanistic and fundamental understanding of the degradation methods, advanced catalytic surface modifications can be applied to reduce degradation. The specific technical objectives are: (1) To identify/develop new catalysts (alkaline-earth based-) that are compatible chemically with the state-of-the-art cathode materials at high temperatures required for fabrication and with contaminates commonly encountered under operating conditions; (2) To improve the infiltration process for optimal control of the thickness, composition, and uniformity of the catalyst coatings; (3) To evaluate the electro-catalytic activity toward ORR of the chemically-stable materials when exposed to different types of contaminants using electrical conductivity relaxation measurements on bar samples and performance evaluation of catalyst-infiltrated cathodes; (4) To unravel the contamination-tolerant mechanisms of the new catalyst coatings under realistic environmental conditions (with different types of contaminants) using powerful in situ and in operando characterization techniques performed on model cells with thin-film/pattern electrodes, as guided by modeling and simulation; (5) To establish scientific basis for rational design of new catalysts of high tolerance to contaminants; (6) To validate the long term stability of modified LSCF cathodes in commercially available cells/stacks under ROC. Alkaline earth-based catalysts have been systematically explored and tested under various contamination conditions. BaCoO 3-δ (BCO) was shown to produce the best catalytic activity enhancement as well as stability in a variety of contaminating conditions, including CO 2 and chromium. The microstructural evolution was investigated with SEM, EDS, and Raman spectroscopy, showing the BCO catalyst prevents the formation of insulating SrCrO 4 by forming electrically conductive BaCrO 4 . Electrochemical relaxation measurements determined the BCO catalyst coatings increased the surface diffusion coefficient but did not significantly affect the diffusion coefficient and determined an optimum surface modification layer of 100 nm. A novel Ba 0.9 Co 0.7 Fe 0.2 Nb 0.1 O x (BCFN) catalyst was also shown to have excellent stability in chromium containing atmospheres. A novel surface sol-gel (SSG) surface modification, which offers superior thickness and compositional control, was applied to SOFCs to produce BaO catalyst coatings. SSG BaO coatings were shown to produce conformal coatings on the electrode surface, greatly increasing stability in chromium containing atmospheres. An atomic level mechanistic approach was applied to investigate the stability of PrBa 0.8 Ca 0.2 Co2O 5+δ (PBCC) with respect to a variety of common contaminants, demonstrating thermodynamically its superior stability in CO2 containing atmospheres. Finally, the best catalyst coatings demonstrated in this project, BCO and PBCC, were applied to full cells which demonstrated superior stability for over 300 hours in CO 2 and Cr atmospheres.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Highly-Active and Contaminant-Tolerant Cathodes for Durable Solid Oxide Fuel Cells

The objective of this project is to investigate the fundamental degradation methods occurring in solid oxide fuel cell (SOFC) cathodes when exposed to chromium and carbon dioxide contamination and to rationally design alkaline earth-based catalysts to increase stability and tolerance to contaminate poisoning. With a mechanistic and fundamental understanding of the degradation methods, advanced catalytic surface modifications can be applied to reduce degradation. The specific technical objectives are: (1) To identify/develop new catalysts (alkaline-earth based-) that are compatible chemically with the state-of-the-art cathode materials at high temperatures required for fabrication and with contaminates commonly encountered under operating conditions; (2) To improve the infiltration process for optimal control of the thickness, composition, and uniformity of the catalyst coatings; (3) To evaluate the electro-catalytic activity toward ORR of the chemically-stable materials when exposed to different types of contaminants using electrical conductivity relaxation measurements on bar samples and performance evaluation of catalyst-infiltrated cathodes; (4) To unravel the contamination-tolerant mechanisms of the new catalyst coatings under realistic environmental conditions (with different types of contaminants) using powerful in situ and in operando characterization techniques performed on model cells with thin-film/pattern electrodes, as guided by modeling and simulation; (5) To establish scientific basis for rational design of new catalysts of high tolerance to contaminants; (6) To validate the long term stability of modified LSCF cathodes in commercially available cells/stacks under ROC. Alkaline earth-based catalysts have been systematically explored and tested under various contamination conditions. BaCoO 3-δ (BCO) was shown to produce the best catalytic activity enhancement as well as stability in a variety of contaminating conditions, including CO 2 and chromium. The microstructural evolution was investigated with SEM, EDS, and Raman spectroscopy, showing the BCO catalyst prevents the formation of insulating SrCrO 4 by forming electrically conductive BaCrO 4 . Electrochemical relaxation measurements determined the BCO catalyst coatings increased the surface diffusion coefficient but did not significantly affect the diffusion coefficient and determined an optimum surface modification layer of 100 nm. A novel Ba 0.9 Co 0.7 Fe 0.2 Nb 0.1 O x (BCFN) catalyst was also shown to have excellent stability in chromium containing atmospheres. A novel surface sol-gel (SSG) surface modification, which offers superior thickness and compositional control, was applied to SOFCs to produce BaO catalyst coatings. SSG BaO coatings were shown to produce conformal coatings on the electrode surface, greatly4 increasing stability in chromium containing atmospheres. An atomic level mechanistic approach was applied to investigate the stability of PrBa 0.8 Ca 0.2 Co 2 O 5+δ (PBCC) with respect to a variety of common contaminants, demonstrating thermodynamically its superior stability in CO 2 containing atmospheres. Finally, the best catalyst coatings demonstrated in this project, BCO and PBCC, were applied to full cells which demonstrated superior stability for over 300 hours in CO 2 and Cr atmospheres.

30 DIRECT ENERGY CONVERSION↗

Highly-Active and Contaminant-Tolerant Cathodes for Durable Solid Oxide Fuel Cells

The objective of this project is to investigate the fundamental degradation methods occurring in solid oxide fuel cell (SOFC) cathodes when exposed to chromium and carbon dioxide contamination and to rationally design alkaline earth-based catalysts to increase stability and tolerance to contaminate poisoning. With a mechanistic and fundamental understanding of the degradation methods, advanced catalytic surface modifications can be applied to reduce degradation. The specific technical objectives are: (1) To identify/develop new catalysts (alkaline-earth based-) that are compatible chemically with the state-of-the-art cathode materials at high temperatures required for fabrication and with contaminates commonly encountered under operating conditions; (2) To improve the infiltration process for optimal control of the thickness, composition, and uniformity of the catalyst coatings; (3) To evaluate the electro-catalytic activity toward ORR of the chemically-stable materials when exposed to different types of contaminants using electrical conductivity relaxation measurements on bar samples and performance evaluation of catalyst-infiltrated cathodes; (4) To unravel the contamination-tolerant mechanisms of the new catalyst coatings under realistic environmental conditions (with different types of contaminants) using powerful in situ and in operando characterization techniques performed on model cells with thin-film/pattern electrodes, as guided by modeling and simulation; (5) To establish scientific basis for rational design of new catalysts of high tolerance to contaminants; (6) To validate the long term stability of modified LSCF cathodes in commercially available cells/stacks under ROC. Alkaline earth-based catalysts have been systematically explored and tested under various contamination conditions. BaCoO 3-δ (BCO) was shown to produce the best catalytic activity enhancement as well as stability in a variety of contaminating conditions, including CO 2 and chromium. The microstructural evolution was investigated with SEM, EDS, and Raman spectroscopy, showing the BCO catalyst prevents the formation of insulating SrCrO 4 by forming electrically conductive BaCrO 4 . Electrochemical relaxation measurements determined the BCO catalyst coatings increased the surface diffusion coefficient but did not significantly affect the diffusion coefficient and determined an optimum surface modification layer of 100 nm. A novel Ba 0.9 Co 0.7 Fe 0.2 Nb 0.1 O x (BCFN) catalyst was also shown to have excellent stability in chromium containing atmospheres. A novel surface sol-gel (SSG) surface modification, which offers superior thickness and compositional control, was applied to SOFCs to produce BaO catalyst coatings. SSG BaO coatings were shown to produce conformal coatings on the electrode surface, greatly 4 increasing stability in chromium containing atmospheres. An atomic level mechanistic approach was applied to investigate the stability of PrBa 0.8 Ca 0.2 Co 2 O 5+δ (PBCC) with respect to a variety of common contaminants, demonstrating thermodynamically its superior stability in CO 2 containing atmospheres. Finally, the best catalyst coatings demonstrated in this project, BCO and PBCC, were applied to full cells which demonstrated superior stability for over 300 hours in CO 2 and Cr atmospheres

01 COAL, LIGNITE, AND PEAT↗

Unraveling membrane electrode assembly design for electrochemical conversion of carbon dioxide to formate/formic acid

This work presents a one-dimensional continuum modeling approach to investigate various cell architectures used for electrochemical conversion of CO 2 to formate/formic acid. Ion transport is simulated by a system of generalized modified Poisson–Nernst–Planck (GMPNP) equations that reflect the reactive transport phenomena including steric effects as the electrolyte solutions become concentrated. In the cathode catalyst layer, ionic current contributions from both the supporting electrolyte and solid-state ionomer are considered. Voltage and CO 2 utilization breakdowns are utilized to deconvolute the impacts of the cell architecture. The origins of (bi)carbonate formation in the cathode are explored, as the subsequent decrease in CO 2 availability is a key reason for low faradaic efficiencies to formate/formic acid. In addition, the role of a supporting electrolyte (KOH) is investigated to understand its tradeoffs: while the K + ions can improve both conductivity and electrochemically active surface area in the cathode, the presence of OH − ions raises the pH and leads to deleterious formation of (bi)carbonates. To this end, we also present parametric studies on the concentration and flow rate of supplied KOH to the cell, to establish a path towards eliminating the need for a supporting electrolyte.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A multi-agent quantum Monte Carlo model for charge transport: Application to organic field-effect transistors

We have developed a multi-agent quantum Monte Carlo model to describe the spatial dynamics of multiple majority charge carriers during conduction of electric current in the channel of organic field-effect transistors. The charge carriers are treated by a neglect of diatomic differential overlap Hamiltonian using a lattice of hydrogen-like basis functions. The local ionization energy and local electron affinity defined previously map the bulk structure of the transistor channel to external potentials for the simulations of electron- and hole-conduction, respectively. The model is designed without a specific charge-transport mechanism like hopping- or band-transport in mind and does not arbitrarily localize charge. An electrode model allows dynamic injection and depletion of charge carriers according to source-drain voltage. The field-effect is modeled by using the source-gate voltage in a Metropolis-like acceptance criterion. Although the current cannot be calculated because the simulations have no time axis, using the number of Monte Carlo moves as pseudo-time gives results that resemble experimental I/V curves.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

In Situ Raman Mapping of Si Island Electrodes and Stress Modeling as a Function of Lithiation and Size

Si is known for cracking and delamination during electrochemical cycling of a battery due to the large volume change associated with Li insertion and extraction. However, it has been found experimentally that patterned Si island electrodes that are 200 nm thick and less than 7 μm wide can deform in a purely elastic manner. Inspired by this, we performed in situ Raman stress characterization of model poly-crystalline Si island electrodes using an electrochemical cell coupled with an immersion objective lens and designed for a short working distance. A 5 μm wide Si island electrode showed a parabolic stress profile during lithiation, while for a 15 μm Si island electrode, a stress plateau in the center of the electrode was observed. A continuum model with coupled electro-chemo-mechanical (ECM) physics was established to understand the stress measurement. A qualitative agreement was reached between modeling and experimental data, and the critical size effect could be explained by the Li diffusive flux as governed by competition between the Li concentration and hydrostatic stress gradients. Below the critical size, the stress gradient drives Li toward the edges, where the electrode volume is free to expand, while above the critical size, the stress plateau inhibits Li diffusion to the edge and forces destructive stress relief by cracking. Furthermore, this work represents a promising methodology for in situ characterization of ECM coupling in battery electrodes, with suggestions provided for further improvement.

25 ENERGY STORAGE↗