By starting from fundamental principles, the heterogeneous nucleation and growth of electrodeposited anode materials is analyzed. Thermodynamically, we show that an overpotential-controlled critical radius has to be overcome in order for dendrite formation to become energetically favorable. Kinetically, surface tension and overpotential driving forces define a critical kinetic radius above which an isolated embryo will grow and below which it will shrink. As a result, five regimes of behavior are identified: nucleation suppression regime, long incubation time regime, short incubation time regime, early growth regime, and late growth regime. In the nucleation suppression regime, embryos are thermodynamically unstable and unable to persist. For small overpotentials, below a critical overpotential, 2η○, and between the thermodynamic and kinetic critical radius, a metastable regime exists where the local electrochemically enabled Gibbs-Thomson interactions control the coarsening of the embryos, thus defining the long incubation time regime. In addition, very broad nuclei size distributions are favored. For large overpotentials, above 2η○, a short incubation time regime develops as a result of the small energy barrier and large galvanostatic driving forces. In addition, very narrow size distributions of nuclei are favored. In the early growth regime, thermodynamically and kinetically favored nuclei grow to reach an asymptotic growth velocity. Finally, in the late growth regime, morphological instabilities and localized electric fields dominate the morphology and microstructural evolution of the deposit.

The ability to engineer electrode microstructures to increase power and energy densities is critical to the development of high-energy density lithium-ion batteries. Because high tortuosities in porous electrodes are linked to lower delivered energy and power densities, in this paper, we experimentally and computationally study tortuosity and consider possible approaches to decrease it. We investigate the effect of electrode processing on the tortuosity of in-house fabricated porous electrodes, using three-dimensionally reconstructed microstructures obtained by synchrotron x-ray tomography. Computer-generated electrodes are used to understand the experimental findings and assess the impact of particle size distribution and particle packing on tortuosity and reactive area density. We highlight the limitations and tradeoffs of reducing tortuosity and develop a practical set of guidelines for active material manufacture and electrode preparation.

In high energy density, low porosity, lithium-ion battery electrodes, the underlying microstructural tortuosity controls the macroscopic charge capacity, average lithium-ion diffusivity, and macroscopic resistivity of the cell, particularly at high discharge rates and power densities. In this paper, an analytical framework is presented to extend widely used empirical tortuosity relations such as the Bruggemann relation to incorporate the effects of the mesoscale tortuosity through analytical integration along the width of the electrode (in the limit of high porosities), and integration along a statistically representative tortuous path (in the limit of low porosities). The framework presented herein enables to establish analytical tortuosity-porosity relations that combine the constitutive properties of the individual components. As an example application, the macroscopic tortuosity-porosity relation of a mixture of two porous particle systems of widely different length scales and well-known individual tortuosity constitutive equations, one displaying mesoscale porosity (the carbon black-electrolyte mixture) and a second one displaying microporosity (the electrochemically active phase), are combined into a self-consistent macroscopic tortuosity expression that is in agreement with recently reported empirical measures of tortuosity.

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