Diffusion constants are typically considered to be independent of particle size with the benefit of nanosizing materials arising solely from shortened transport paths. We show that for materials with one-dimensional atomic migration channels, the diffusion constant depends on particle size with diffusion in bulk being much slower than in nanoparticles. This model accounts for conflicting data on LiFePO(4), an important material for rechargeable lithium batteries, specifically explaining why it functions exclusively on the nanoscale.

Using a recently proposed mathematical model for intercalation dynamics in phase-separating materials ( Singh , G. K. , Ceder , G. and Bazant , M. Z. Electrochimica Acta 2008 , 53 , 7599. ), we show that the spinodal and miscibility gaps generally shrink as the host particle size decreases to the nanoscale. Our work is motivated by recent experiments on the high-rate Li-ion battery material LiFePO(4); this serves as the basis for our examples, but our analysis and conclusions apply to any intercalation material. We describe two general mechanisms for the suppression of phase separation in nanoparticles, (i) a classical bulk effect, predicted by the Cahn-Hilliard equation in which the diffuse phase boundary becomes confined by the particle geometry; and (ii) a novel surface effect, predicted by chemical-potential-dependent reaction kinetics, in which insertion/extraction reactions stabilize composition gradients near surfaces in equilibrium with the local environment. Composition-dependent surface energy and (especially) elastic strain can contribute to these effects but are not required to predict decreased spinodal and miscibility gaps at the nanoscale.

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A general continuum model has recently been proposed for the dynamics of ion intercalation in a single crystal of rechargeable-battery electrode materials [1]. When applied to strongly phase-separating, highly anisotropic materials such as LiFePO4, phase-transformation waves are predicted between the lithiated and unlithiated portions of a crystal. In this paper, we extend the analysis of the wave dynamics, and we describe a new mechanism for current capacity fade through the interactions of these waves with defects in the material.

Three-dimensional (3D) ac electro-osmotic (ACEO) pumps have recently been developed that are much faster and more robust than previous planar designs. The basic idea is to create a "fluid conveyor belt" by placing opposing ACEO slip velocities at different heights. Current designs involve electrodes with electroplated steps, whose heights have been optimized in simulations and experiments. Here, we consider changing the boundary conditions-rather than the geometry-and predict that flow rates can be further doubled by fabricating 3D features with nonpolarizable materials. This amplifies the fluid conveyor belt by removing opposing flows on the vertical surfaces, and it increases the slip velocities that drive the flow.