In this methods article, we describe application of Prandtl-Tomlinson models and their extensions to interpret dry atomic-scale friction. The goal is to provide a practical overview of how to use these models to study frictional phenomena. We begin with the fundamental equations and build on them step-by-step-from the simple quasistatic one-spring, one-mass model for predicting transitions between friction regimes to the two-dimensional and multi-atom models for describing the effect of contact area. The intention is to bridge the gap between theoretical analysis, numerical implementation, and predicted physical phenomena. In the process, we provide an introductory manual with example computer programs for newcomers to the field, and an illustration of the significant potential for this approach to yield new fundamental understanding of atomic-scale friction.

Simulations of lithium-ion battery cells are usually performed with volume averaging methods that employ effective transport properties. Bruggeman's model, which is widely used to determine these effective properties, is primarily based on the volume fraction of porous electrodes. It does not consider actual particle shape, size or the topology of constituent phases; these play a crucial role in determining effective transport. In this paper, a general derivation of the effective thermal conductivity of multiphase materials, which can be correlated with these factors, is derived using the volume averaging technique. Three-dimensional finite volume meshes of fully-resolved lithium-ion battery cathode microstructures are reconstructed from scanned images. Effective volume averaged thermal conductivity is then determined from numerical analysis of thermal transport on these meshes. It is shown that the Bruggeman model for effective thermal conductivity must be recalibrated to fit the effective thermal conductivity computed from these detailed simulations. The relevance of these results to effective transport properties typically employed in electrochemical simulations is presented. Commonly used theories for effective thermal transport in composites are evaluated for comparison. Furthermore, it is shown that Bruggeman's exponents yield an important quantitative measure, the connectivity, to characterize the physical path for transport through the underlying phases. The importance of lithium-ion batteries is now well recognized in light of the global energy crisis, global warming and the need for efficient and inexpensive energy storage options.1,2 Battery physics encompass thermodynamics, electrochemistry, material science, transport phenomena and solid mechanics, and span multiple length and time scales.3 Realistic modeling of batteries across these disparate physics and scales is critical for their effective and safe commercialization. 4 Research in lithium-ion batteries has been primarily driven by the need to develop cathode, anode and electrolyte materials that deliver high potential and capacity. 5,6 On the cell level, the battery consists of a porous composite anode and cathode filled with an electrolyte and separated by a separator. Typically, the thickness of such a sandwich is hundreds of microns, while lateral dimensions are of the order of centimeters. Lithium ions shuttle between cathode and anode during charge and discharge. Active cathode particles (for e.g. LiCoO 2 , LiMn 2 O 4 , LiFePO 4 ), which form the key constituent of batteries, are lithium insertion compounds and have high lithium ion conductivity. These active particles are spatially dispersed and held together by binder (such as polyvinylidene fluoride [PVDF]), while the electrolyte resides in the pores, wetting the active particles, and facilitating transport of lithium ions. The electronic conductivity of these active materials is generally low compared to lithium ion conductivity. Therefore additives like carbon particles are dispersed ...

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Slip behavior of three liquids with distinct molecular shapes--linear (hexadecane), branched (pentaerythritol tetra), and a chain of rings (polyphenylether)--is studied using molecular dynamics simulation and reduced-order modeling. Slip at a liquid-solid interface is shown to be affected by the molecular structure of the liquid. A two-dimensional Frenkel-Kontorova model captures the fundamental structural features of the liquid molecules and gives insight into how molecules flex and slip along the surface. We formulate an approximation to the Peierls-Nabarro energy which incorporates both the position of liquid atoms relative to substrate atoms and molecular flexibility. We find that increased molecular flexibility can lead to reduced slip by allowing the liquid to conform epitaxially to the substrate with only a small energetic penalty. Liquid molecules which are less flexible can conform to the substrate only with greater expense of conformational energy, and so exhibit larger slip.

Compressibility of thin lubricating films remains incompletely understood. Molecular dynamics simulations of a polymeric fluid confined in a nanoscale channel are used to investigate the effects of pressure and temperature on a thin film's response to compression. The observed trends are analyzed and compared to predictions of traditional, bulk fluid compressibility models. At ambient temperatures and pressures, molecular dynamics and bulk fluid models predict consistent trends for both the volume ratio and the bulk modulus. However, small deviations between the models suggest that molecular-scale confinement may, under some conditions, affect a fluid's compressibility such that it is not necessarily predictable using bulk fluid theories.