An effective model for sodium insertion in hard carbons.

Sodium ion batteries (NIBs) are a potential alternative to Lithium ion batteries (LIBs) because of their lower cost and greater availability. As anodes, hard carbons (HCs) seem to be the most promising candidates for NIBs. Previous numerical theoretical research studies have focussed on the general conditions for Na insertion in HCs, while experiments have shown that the properties of Na insertion in HCs depend strongly on specific material properties of HCs.

Many-body effects in a binary nano-particle mixture dispersed in ideal polymer solutions.

A new mean-field theory is developed to treat a binary mixture of nanoparticles imbedded in a polydisperse polymer solution. The theory is based on a many-body polymer-mediated potential of mean force (PMF) between the particles and remains accurate even in the protein regime, where the particles' diameters cannot necessarily be considered large compared to the polymer radius of gyration. As implemented here, the theory is strictly valid for dilute to semi-dilute polymer solutions near the theta temperature (the so-called theta regime) or when the range of the PMF is strongly affected by the polymer size.

Many-body depletion forces of colloids in a polydisperse polymer dispersant in the long-chain limit.

We study a system of spherical non-adsorbing particles immersed in a polydisperse polymer fluid. We derive an analytic expression for the many-body depletion interactions between the colloidal particles in the limit of very long chains. We argue that this expression is essentially exact for long chains and justify this using explicit simulations.