Faraday law, oxidation numbers, and ionic conductivity: The role of topology

Abstract

Faraday's experiment measures -- within a modern view -- the charge adiabatically transported over a macroscopic distance by a given nuclear species in insulating liquids: the reason why it is integer is deeply rooted in topology. Whole numbers enter chemistry in a different form: atomic oxidation states. They are not directly measurable, and are determined instead from an agreed set of rules. Insulating liquids are a remarkable exception: Faraday's experiment indeed measures the oxidation numbers of each dissociated component in the liquid phase, whose topological values are unambiguous. Ionic conductivity in insulating liquids is expressed in terms of the autocorrelation function of the fluctuating charge current at a given temperature in zero electric field; topology plays a major role in this important observable as well. The existing literature deals with the above issues by adopting the independent-electron framework; here I provide the many-body generalization of all the above findings, which furthermore allows for compact and very transparent notations and formulas.

10 pages, one figure

References in corpus (4)

• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• Role of dipolar correlations in the IR spectra of water and ice
• Topological quantisation and gauge invariance of charge transport in liquid insulators
• Oxidation states, Thouless' pumps, and non-trivial ionic transport in non-stoichiometric electrolytes

Cited by in corpus (3)

• Self-interaction and transport of solvated electrons in molten salts
• Probing the semiconductor-to-dirac semimetal transition in Na-Sb-Bi alloys with x-ray Compton scattering
• Topology, oxidation states, and charge transport in ionic conductors