High-Performance Lithium-Sulfur Batteries via Molecular Complexation.

Beyond lithium-ion technologies, lithium-sulfur batteries stand out because of their multielectron redox reactions and high theoretical specific energy (2500 Wh kg-1). However, the intrinsic irreversible transformation of soluble lithium polysulfides to solid short-chain sulfur species (Li2S2 and Li2S) and the associated large volume change of electrode materials significantly impair the long-term stability of the battery. Here we present a liquid sulfur electrode consisting of lithium thiophosphate complexes dissolved in organic solvents that enable the bonding and storage of discharge reaction products without precipitation. Insights garnered from coupled spectroscopic and density functional theory studies guide the complex molecular design, complexation mechanism, and associated electrochemical reaction mechanism. With the novel complexes as cathode materials, high specific capacity (1425 mAh g-1 at 0.2 C) and excellent cycling stability (80% retention after 400 cycles at 0.5 C) are achieved at room temperature. Moreover, the highly reversible all-liquid electrochemical conversion enables excellent low-temperature battery operability (>400 mAh g-1 at -40 °C and >200 mAh g-1 at -60 °C). This work opens new avenues to design and tailor the sulfur electrode for enhanced electrochemical performance across a wide operating temperature range.

Black-Scholes Theory and Diffusion Processes on the Cotangent Bundle of the Affine Group.

The Black-Scholes partial differential equation (PDE) from mathematical finance has been analysed extensively and it is well known that the equation can be reduced to a heat equation on Euclidean space by a logarithmic transformation of variables. However, an alternative interpretation is proposed in this paper by reframing the PDE as evolving on a Lie group. This equation can be transformed into a diffusion process and solved using mean and covariance propagation techniques developed previously in the context of solving Fokker-Planck equations on Lie groups. An extension of the Black-Scholes theory with coupled asset dynamics produces a diffusion equation on the affine group, which is not a unimodular group. In this paper, we show that the cotangent bundle of a Lie group endowed with a semidirect product group operation, constructed in this paper for the case of groups with trivial centers, is always unimodular and considering PDEs as diffusion processes on the unimodular cotangent bundle group allows a direct application of previously developed mean and covariance propagation techniques, thereby offering an alternative means of solution of the PDEs. Ultimately these results, provided here in the context of PDEs in mathematical finance may be applied to PDEs arising in a variety of different fields and inform new methods of solution.

The unusual fluid dynamics of particle electrophoresis.

The classical problem of the electrophoretic motion of a spherical particle has been treated theoretically by Overbeek in his 1941 PhD thesis and almost 40 years later by O'Brien & White. Although both approaches used identical assumptions, the details are quite different. Overbeek solved for the pressure, velocity fields as well as the electrostatic potential, whereas O'Brien & White obtained the electrophoretic mobility without the need to consider the pressure and velocity explicitly. In this paper, we establish the equivalence of these two approaches that allow us to show that the tangential component of the fluid velocity has a maximum near the surface of the particle and outside the double layer, the velocity decays as 1/r3, where r is the distance from the sphere, instead of 1/r in normal Stokes flow. Associated with this behavior is that of an irrotational outer flow field. This is consistent with the fact that a sphere moving with a constant electrophoretic velocity experiences zero net force. A study of the forces on the particle also provides a physical explanation of the independence of the electrophoretic mobility on the electrostatic boundary conditions or dielectric permittivity of the particle. These results are important in situations where inter-particle interaction is considered, for instance, in electrokinetic deposition.