Effects of Nanoparticle Geometry and Size Distribution on Diffusion Impedance of Battery Electrodes

The short diffusion lengths in insertion battery nanoparticles render the capacitive behavior of bounded diffusion, which is rarely observable with conventional larger particles, now accessible to impedance measurements. Coupled with improved geometrical characterization, this presents an opportunity to measure solid diffusion more accurately than the traditional approach of fitting Warburg circuit elements, by properly taking into account the particle geometry and size distribution. We revisit bounded diffusion impedance models and incorporate them into an overall impedance model for different electrode configurations. The theoretical models are then applied to experimental data of a silicon nanowire electrode to show the effects of including the actual nanowire geometry and radius distribution in interpreting the impedance data. From these results, we show that it is essential to account for the particle shape and size distribution to correctly interpret impedance data for battery electrodes. Conversely, it is also possible to solve the inverse problem and use the theoretical "impedance image" to infer the nanoparticle shape and/or size distribution, in some cases, more accurately than by direct image analysis. This capability could be useful, for example, in detecting battery degradation in situ by simple electrical measurements, without the need for any imaging.Comment: 30 page

Velocity profile of granular flows inside silos and hoppers

We measure the flow of granular materials inside a quasi-two dimensional silo as it drains and compare the data with some existing models. The particles inside the silo are imaged and tracked with unprecedented resolution in both space and time to obtain their velocity and diffusion properties. The data obtained by varying the orifice width and the hopper angle allows us to thoroughly test models of gravity driven flows inside these geometries. All of our measured velocity profiles are smooth and free of the shock-like discontinuities ("rupture zones") predicted by critical state soil mechanics. On the other hand, we find that the simple Kinematic Model accurately captures the mean velocity profile near the orifice, although it fails to describe the rapid transition to plug flow far away from the orifice. The measured diffusion length $b$, the only free parameter in the model, is not constant as usually assumed, but increases with both the height above the orifice and the angle of the hopper. We discuss improvements to the model to account for the differences. From our data, we also directly measure the diffusion of the particles and find it to be significantly less than predicted by the Void Model, which provides the classical microscopic derivation of the Kinematic Model in terms of diffusing voids in the packing. However, the experimental data is consistent with the recently proposed Spot Model, based on a simple mechanism for cooperative diffusion. Finally, we discuss the flow rate as a function of the orifice width and hopper angles. We find that the flow rate scales with the orifice size to the power of 1.5, consistent with dimensional analysis. Interestingly, the flow rate increases when the funnel angle is increased.Comment: 17 pages, 8 figure

Freezing point depression and freeze-thaw damage by nano-fuidic salt trapping

A remarkable variety of organisms and wet materials are able to endure temperatures far below the freezing point of bulk water. Cryo-tolerance in biology is usually attributed to "anti-freeze" proteins, and yet massive supercooling ($< -40^\circ$C) is also possible in porous media containing only simple aqueous electrolytes. For concrete pavements, the common wisdom is that freeze-thaw damage results from the expansion of water upon freezing, but this cannot explain the large pressures ($> 10$~MPa) required to damage concrete, the observed correlation between pavement damage and de-icing salts, or the damage of cement paste loaded with benzene (which contracts upon freezing). In this Letter, we propose a different mechanism -- nanofluidic salt trapping -- which can explain the observations, using simple mathematical models of dissolved ions confined to thin liquid films between growing ice and charged surfaces. Although trapped salt lowers the freezing point, ice nucleation in charged pores causes enormous disjoining pressures via the rejected ions, until their removal by precipitation or surface adsorption at a lower temperatures releases the pressure and allows complete freezing. The theory is able to predict the non-monotonic salt-concentration dependence of freeze-thaw damage in concreter and provides a general framework to understand the origins of cryo-tolerance.Comment: 5 figure

Size scaling of strength in thin film delamination

We investigate by numerical simulation the system size dependence of the shear delamination strength of thin elastic films. The films are connected to a rigid substrate by a disordered interface containing a pre-existing crack. The size dependence of the strength of this system is found to depend crucially on the crack shape. For circular cracks, we observe a crossover between a size-independent regime at large crack radii which is controlled by propagation of the pre-existing crack, and a size-dependent regime at small radii which is dominated by nucleation of new cracks in other locations. For cracks of finite width that span the system transversally, we observe for all values of the crack length a logarithmic system size dependence of the failure stress. The results are interpreted in terms of extreme value statistics.Comment: 10 pages, 4 figure

Electrochemical Impedance of a Battery Electrode with Anisotropic Active Particles

Electrochemical impedance spectra for battery electrodes are usually interpreted using models that assume isotropic active particles, having uniform current density and symmetric diffusivities. While this can be reasonable for amorphous or polycrystalline materials with randomly oriented grains, modern electrode materials increasingly consist of highly anisotropic, single-crystalline, nanoparticles, with different impedance characteristics. In this paper, analytical expressions are derived for the impedance of anisotropic particles with tensorial diffusivities and orientation-dependent surface reaction rates and capacitances. The resulting impedance spectrum contains clear signatures of the anisotropic material properties and aspect ratio, as well as statistical variations in any of these parameters

Diffusion-Limited Aggregation on Curved Surfaces

We develop a general theory of transport-limited aggregation phenomena occurring on curved surfaces, based on stochastic iterated conformal maps and conformal projections to the complex plane. To illustrate the theory, we use stereographic projections to simulate diffusion-limited-aggregation (DLA) on surfaces of constant Gaussian curvature, including the sphere ($K>0$) and pseudo-sphere ($K<0$), which approximate "bumps" and "saddles" in smooth surfaces, respectively. Although curvature affects the global morphology of the aggregates, the fractal dimension (in the curved metric) is remarkably insensitive to curvature, as long as the particle size is much smaller than the radius of curvature. We conjecture that all aggregates grown by conformally invariant transport on curved surfaces have the same fractal dimension as DLA in the plane. Our simulations suggest, however, that the multifractal dimensions increase from hyperbolic ($K0$) geometry, which we attribute to curvature-dependent screening of tip branching.Comment: 4 pages, 3 fig

Multiscale Poromechanics of Wet Cement Paste

Capillary effects such as imbibition-drying cycles impact the mechanics of granular systems over time. A multiscale poromechanics framework was applied to cement paste, that is the most common building material, experiencing broad humidity variations over the lifetime of infrastructure. First, the liquid density distribution at intermediate to high relative humidities is obtained using a lattice gas density functional method together with a realistic nano-granular model of cement hydrates. The calculated adsorption/desorption isotherms and pore size distributions are discussed and compare well to nitrogen and water experiments. The standard method for pore size distribution determination from desorption data is evaluated. Then, the integration of the Korteweg liquid stress field around each cement hydrate particle provided the capillary forces at the nanoscale. The cement mesoscale structure was relaxed under the action of the capillary forces. Local irreversible deformations of the cement nano-grains assembly were identified due to liquid-solid interactions. The spatial correlations of the nonaffine displacements extend to a few tens of nm. Finally, the Love-Weber method provided the homogenized liquid stress at the micronscale. The homogenization length coincided with the spatial correlation length nonaffine displacements. Our results on the solid response to capillary stress field suggest that the micronscale texture is not affected by mild drying, while local irreversible deformations still occur. These results pave the way towards understanding capillary phenomena induced stresses in heterogeneous porous media ranging from construction materials, hydrogels to living systems.Comment: 6 figures in main text, 4 figures in the SI appendi

Crackling noise in three-point bending of heterogeneous materials

We study the crackling noise emerging during single crack propagation in a specimen under three-point bending conditions. Computer simulations are carried out in the framework of a discrete element model where the specimen is discretized in terms of convex polygons and cohesive elements are represented by beams. Computer simulations revealed that fracture proceeds in bursts whose size and waiting time distributions have a power law functional form with an exponential cutoff. Controlling the degree of brittleness of the sample by the amount of disorder, we obtain a scaling form for the characteristic quantities of crackling noise of quasi-brittle materials. Analyzing the spatial structure of damage we show that ahead of the crack tip a process zone is formed as a random sequence of broken and intact mesoscopic elements. We characterize the statistics of the shrinking and expanding steps of the process zone and determine the damage profile in the vicinity of the crack tip.Comment: 11 pages, 15 figure