Pradeep R. Guduru

A finite strain model of stress, diffusion, plastic flow, and electrochemical reactions in a lithium-ion half-cell

We formulate the continuum field equations and constitutive equations that govern deformation, stress, and electric current flow in a Li-ion half-cell. The model considers mass transport through the system, deformation and stress in the anode and cathode, electrostatic fields, as well as the electrochemical reactions at the electrode/electrolyte interfaces. It extends existing analyses by accounting for the effects of finite strains and plastic flow in the electrodes, and by exploring in detail the role of stress in the electrochemical reactions at the electrode–electrolyte interfaces. In particular, we find that that stress directly influences the rest potential at the interface, so that a term involving stress must be added to the Nernst equation if the stress in the solid is significant. The model is used to predict the variation of stress and electric potential in a model 1-D half-cell, consisting of a thin film of Si on a rigid substrate, a fluid electrolyte layer, and a solid Li cathode. The predicted cycles of stress and potential are shown to be in good agreement with experimental observations.

In Situ Measurements of Stress-Potential Coupling in Lithiated Silicon

An analysis of the dependence of electric potential on the state of stress of a lithiated-silicon electrode is presented. Based on the Larche and Cahn chemical potential for a solid solution, a thermodynamic argument is made for the existence of the stresspotential coupling in lithiated silicon; based on the known properties of the material, the magnitude of the coupling is estimated to be 60 mV/GPa in thin-film geometry. An experimental investigation is carried out on silicon thin-film electrodes in which the stress is measured in situ during electrochemical lithiation and delithiation. By progressively varying the stress through incremental delithiation, the relation between stress change and electric-potential change is measured to be 100–120 mV/GPa, which is of the same order of magnitude as the prediction of the analysis. The importance of the coupling is discussed in interpreting the hysteresis observed in the potential vs state-of-charge plots and the role of stress in modifying the maximum charge capacity of a silicon electrode under stress.

Measurement and modeling of the mechanical and electrochemical response of amorphous Si thin film electrodes during cyclic lithiation

A combination of experimental measurements and numerical simulations are used to characterize the mechanical and electrochemical response of thin film amorphous Si electrodes during cyclic lithiation. Parameters extracted from the experiment include the variation of elastic modulus and the flow stress as functions of Li concentration; the strain rate sensitivity; the diffusion coefficient for Li transport in the electrode; the free energy of mixing as a function of Li concentration in the electrode; the exchange current density for the Lithium insertion reaction; as well as reaction rates and diffusion coefficients characterizing the rate of formation of solid-electrolyte interphase layer at the electrode surface. Model predictions are compared with experimental measurements; and the implications for practical Si based electrodes are discussed.

Shell buckling of individual multiwalled carbon nanotubes using nanoindentation

Although the mechanical behavior of carbon nanotubes has been studied extensively in recent years, very few experimental results exist on the shell buckling of nanotubes, despite its fundamental importance in nanotube mechanics and applications. Here we report an experimental technique in which individual multiwalled carbon nanotubes were axially compressed using a nanoindenter and the critical shell-buckling load was measured. The results are compared with predictions of existing continuum theories, which model multiwalled carbon nanotubes as a collection of single-walled shells, interacting through van der Waals forces. The theoretical models significantly underpredict the experimental buckling load.

A simple finite element model of diffusion, finite deformation, plasticity and fracture in lithium ion insertion electrode materials

We describe a finite element method for modeling deformation, diffusion, fracture and electrochemical reactions in materials used as lithium ion insertion electrodes. With a view to modeling high-capacity composite electrode materials such as silicon or tin, the model accounts for finite deformations and plastic flow, and models the evolving electrochemical boundary conditions resulting from the creation of new fracture surfaces using a cohesive zone. In addition, a simple mixed element is used to account for the driving force for diffusion arising from stress gradients. In this approach, the equations for diffusion and deformation are fully coupled, and can be integrated using a stable implicit time-stepping scheme. The method is illustrated by modeling plastic flow and fracture during cyclic lithiation of a thin-film Si electrode and a simple model of a battery microstructure.

Buckling instabilities in multiwalled carbon nanotubes under uniaxial compression

We report experimental observations of shell buckling instabilities in freestanding, vertically aligned multiwalled carbon nanotubes subjected to uniaxial compression. Highly ordered and uniform arrays of carbon nanotubes embedded in an alumina matrix were fabricated and subjected to uniaxial compression using a nanoindenter. The buckling load was found to be on the order of 2μN for nanotubes with 25nm outer radius, 13nm inner radius, and heights of 50 and 100nm. Good agreement was found between the experimental observations and the predictions of linear elastic shell buckling theory.

Adhesion and sliding response of a biologically inspired fibrillar surface: experimental observations.

Inspired by the adhesion mechanisms of several animal species such as geckos, beetles and flies, several efforts in designing and fabricating surface engineering strategies have been made recently to mimic the adhesive and frictional behaviour of biological foot pads. An important feature of such biological adhesion systems is the ability to switch between strong attachment and easy detachment, which is crucial for animal locomotion. Recent investigations have suggested that such a ‘switching’ mechanism can be achieved by the elastic anisotropy of the attachment pad, which renders the magnitude of the detachment force to be direction dependent. This suggestion is supported by the observations that the fibres of the foot pads in geckos and insects are oriented at an angle to the base and that geckos curl their toes backwards (digital hyperextension) while detaching from a surface. One of the promising bio-inspired architectures developed recently is a film-terminated fibrillar PDMS surface; this structure was demonstrated to result in superior detachment force and energy dissipation compared with a bulk PDMS surface. In this investigation, the film-terminated fibrillar architecture is modified by tilting the fibres to make the surface vertically more compliant and elastically anisotropic. The directional detachment and the sliding resistance between the tilted fibrillar surfaces and a spherical glass lens are measured: both show significant directional anisotropy. It is argued that the anisotropy introduced by the tilted fibres and the deformation-induced change in the compliance of the fibre layer are responsible for the observed anisotropy in the detachment force.

The dynamics of multiple neck formation and fragmentation in high rate extension of ductile materials

Abstract Dynamic necking bifurcation in rapidly extending cylindrical rods is investigated. It has been found that both short wavelength and long wavelength perturbations are suppressed by inertia and an intermediate wavelength is favored. The analysis predicts an increase in the number of necks and an increase in the bifurcation strain with increasing extension rate, in agreement with experimental observations. In terms of the number of necks formed as a function of extension rate, good agreement has been found between the experiments and the analysis. At any given aspect ratio, the model also predicts that beyond a critical extension rate, the mode number of the dominant perturbation increases rapidly and the perturbation begins to look more like a surface instability. This could lead to a fragmentation mechanism at high extension speeds which is different from multiple necking. Currently no experimental results are available to test this prediction. Numerical simulations have been conducted to simulate the fragmentation results, using Gurson’s constitutive law along with a porous failure criterion. Good agreement between the experimental observations and the numerical results has been obtained for the fragmentation statistics. However, the numerical results consistently overestimate the number of necks and the fracture strain, possibly due to uncertainty in the constitutive data used, especially at large strains.

Tutorial: Understanding residual stress in polycrystalline thin films through real-time measurements and physical models

Residual stress is a long-standing issue in thin film growth. Better understanding and control of film stress would lead to enhanced performance and reduced failures. In this work, we review how thin film stress is measured and interpreted. The results are used to describe a comprehensive picture that is emerging of what controls stress evolution. Examples from multiple studies are discussed to illustrate how the stress depends on key parameters (e.g., growth rate, material type, temperature, grain size, morphology, etc.). The corresponding stress-generating mechanisms that have been proposed to explain the data are also described. To develop a fuller understanding, we consider the kinetic factors that determine how much each of these processes contributes to the overall stress under different conditions. This leads to a kinetic model that can predict the dependence of the stress on multiple parameters. The model results are compared with the experiments to show how this approach can explain many features of stress evolution.

Systematic Investigation of Binders for Silicon Anodes: Interactions of Binder with Silicon Particles and Electrolytes and Effects of Binders on Solid Electrolyte Interphase Formation

The effects of different binders, polyvinylidene difluoride (PVdF), poly(acrylic acid) (PAA), sodium carboxymethyl cellulose (CMC), and cross-linked PAA-CMC (c-PAA-CMC), on the cycling performance and solid electrolyte interphase (SEI) formation on silicon nanoparticle electrodes have been investigated. Electrodes composed of Si-PAA, Si-CMC, and Si-PAA-CMC exhibit a specific capacity ≥3000 mAh/g after 20 cycles while Si-PVdF electrodes have a rapid capacity fade to 1000 mAh/g after just 10 cycles. Infrared spectroscopy (IR) and X-ray photoelectron spectroscopy (XPS) reveal that PAA and CMC react with the surface of the Si nanoparticles during electrode fabrication. The fresh Si-CMC electrode has a thicker surface coating of SiOx than Si-PAA and Si-PAA-CMC electrodes, due to the formation of thicker SiOx during electrode preparation, which leads to lower cyclability. The carboxylic acid functional groups of the PAA binder are reactive toward the electrolyte, causing the decomposition of LiPF6 and dissolution of SiOx during the electrode wetting process. The PAA and CMC binder surface films are then electrochemically reduced during the first cycle to form a protective layer on Si. This layer effectively suppresses the decomposition of carbonate solvents during cycling resulting in a thin SEI. On the contrary, the Si-PVDF electrode has poor cycling performance and continuous reduction of carbonate solvents is observed resulting in the generation of a thicker SEI. Interestingly, the Lewis basic -CO2Na of CMC was found to scavenge HF in electrolyte.