Cycle life is critically important in applications of rechargeable batteries, but lifetime prediction is mostly based on empirical trends, rather than mathematical models. In practical lithium-ion batteries, capacity fade occurs over thousands of cycles, limited by slow electrochemical processes, such as the formation of a solid-electrolyte interphase (SEI) in the negative electrode, which compete with reversible lithium intercalation. Focusing on SEI growth as the canonical degradation mechanism, we show that a simple single-particle model can accurately explain experimentally observed capacity fade in commercial cells with graphite anodes, and predict future fade based on limited accelerated aging data for short times and elevated temperatures.The theory is extended to porous electrodes, predicting that SEI growth is essentially homogeneous throughout the electrode, even at high rates. The lifetime distribution for a sample of batteries is found to be consistent with Gaussian statistics, as predicted by the single-particle model. We also extend the theory to rapidly degrading anodes, such as nanostructured silicon, which exhibit large expansion on ion intercalation. In such cases, large area changes during cycling promote SEI loss and faster SEI growth. Our simple models are able to accurately fit a variety of published experimental data for graphite and silicon anodes.

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Cement paste has a complex distribution of pores and molecular-scale spaces. This distribution controls the hysteresis of water sorption isotherms and associated bulk dimensional changes (shrinkage). We focus on two locations of evaporable water within the fine structure of pastes, each having unique properties, and we present applied physics models that capture the hysteresis by dividing drying and rewetting into two related regimes based on relative humidity (RH). We show that a continuum model, incorporating a poreblocking mechanism for desorption and equilibrium thermodynamics for adsorption, explains well the sorption hysteresis for a paste that remains above approximately 20% RH. In addition, we show with molecular models and experiments that water in spaces of ≲1 nm width evaporates below approximately 20% RH but reenters throughout the entire RH range. This water is responsible for a drying shrinkage hysteresis similar to that of clays but opposite in direction to typical mesoporous glass. Combining the models of these two regimes allows the entire drying and rewetting hysteresis to be reproduced accurately and provides parameters to predict the corresponding dimensional changes. The resulting model can improve the engineering predictions of long-term drying shrinkage accounting also for the history dependence of strain induced by hysteresis. Alternative strategies for quantitative analyses of the * Corresponding author. hmj@mit.edu PHYSICAL REVIEW APPLIED 3, 064009 (2015) 2331-7019=15=3(6)=064009 (17) 064009-1

Why is it difficult to refold a previously folded sheet of paper? We show that even crease patterns with only one designed folding motion inevitably contain an exponential number of 'distractor' folding branches accessible from a bifurcation at the flat state. Consequently, refolding a sheet requires finding the ground state in a glassy energy landscape with an exponential number of other attractors of higher energy, much like in models of protein folding (Levinthal's paradox) and other NP-hard satisfiability (SAT) problems. As in these problems, we find that refolding a sheet requires actuation at multiple carefully chosen creases. We show that seeding successful folding in this way can be understood in terms of sub-patterns that fold when cut out ('folding islands'). Besides providing guidelines for the placement of active hinges in origami applications, our results point to fundamental limits on the programmability of energy landscapes in sheets. arXiv:1703.04161v1 [cond-mat.soft]

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Our formula is able to fit and interpret both primary and scanning sorption/desorption isotherms for a variety of adsorbates (noble gases, water, and organics) and porous materials (cement pastes, dental enamels, porous glasses, carbon black and nanotubes), including cases with broad pore-size distributions and large hysteresis. It allows quantification of the prevalence of percolating macropores in the material, even though these pores are never filled during the sorption experiments. A distinct bump in sorption isotherms is explained as a lowering of the barrier to nucleation of the vapor phase with a universal temperature scaling.

We examine the role of mobile rings on the stretching profile of a single polyrotaxane molecule that is tethered in space by fixing one of the rings, the "control ring". We show that the translational entropy of the mobile rings can lead to dramatic changes in the response of the chain at small applied forces. In particular, if the mobile rings are placed asymmetrically about the control ring, the chain can be very stiff at low force, displaying a yield force below which chain extension is minimal. However, at large forces, the entropy of the chain dominates the response of the polyrotaxane, and the effect of the mobile rings is negligible. These predictions of a stiffer polyrotaxane chain with added mobile rings might have implications in the design of polyrotaxane gels.

Programmable stiff sheets with a single low-energy folding motion have been sought in fields ranging from the ancient art of origami to modern meta-materials research. Despite such attention, only two extreme classes of crease patterns are usually studied; special Miura-Ori-based zero-energy patterns, in which crease folding requires no sheet bending, and random patterns with high-energy folding, in which the sheet bends as much as creases fold. We present a physical approach that allows systematic exploration of the entire space of crease patterns as a function of the folding energy. Consequently, we uncover statistical results in origami, finding the entropy of crease patterns of given folding energy. Notably, we identify three classes of Mountain-Valley choices that have widely varying ‘typical' folding energies. Our work opens up a wealth of experimentally relevant self-folding origami designs not reliant on Miura-Ori, the Kawasaki condition or any special symmetry in space.