Wiedemann-Franz Law for Molecular Hopping Transport

Abstract

The Wiedemann-Franz (WF) law is a fundamental result in solid-state physics that relates the thermal and electrical conductivity of a metal. It is derived from the predominant origin of energy conversion in metals: the motion of quasi-free charge-carrying particles. Here, an equivalent WF relationship is developed for molecular systems in which charge carriers are moving not as free particles but instead hop between redox sites. We derive a concise analytical relationship between the electrical and thermal conductivity generated by electron hopping in molecular systems and find that the linear temperature dependence of their ratio as expressed in the standard WF law is replaced by a linear dependence on the nuclear reorganization energy associated with the electron hopping process. The robustness of the molecular WF relation is confirmed by examining the conductance properties of a paradigmatic molecular junction. This result opens a new way to analyze conductivity in molecular systems, with possible applications advancing the design of molecular technologies that derive their function from electrical and/or thermal conductance.

References in corpus (17)

• Molecular Transport Junctions: Vibrational Effects
• Observation of the Dirac fluid and the breakdown of the Wiedemann-Franz law in graphene
• A spin-boson thermal rectifier
• Heat dissipation in atomic-scale junctions
• A relationship between electron transfer rates and molecular conduction
• Fourier's Law for a Harmonic Crystal with Self-consistent Stochastic Reservoirs
• Inelastic effects in molecular junction transport: Scattering and self-consistent calculations for the Seebeck coefficient
• Electron transfer across a thermal gradient
• Electron-Transfer-Induced Thermal and Thermoelectric Rectification
• Thermal balance and quantum heat transport in nanostructures thermalized by local Langevin heat baths
• Electron transfer at thermally heterogeneous molecule-metal interfaces
• Designing $\pi$-stacked molecular structures to control heat transport through molecular junctions
• Thermal conductance of metallic atomic-size contacts: Phonon transport and Wiedemann-Franz law
• Validity of the Wiedemann-Franz law in small molecular wires
• Electrothermal Transistor Effect and Cyclic Electronic Currents in Multithermal Charge Transfer Networks
• Mean Field Theory of Thermal Energy Transport in Molecular Junctions
• Length-dependent Seebeck effect in single-molecule junctions beyond linear response regime

Cited by in corpus (8)

• Charge transport in doped conjugated polymers for organic thermoelectrics
• Thermal conductivity of benzothieno-benzothiophene derivatives at the nanoscale
• Energy transport between heat baths with oscillating temperatures
• Thermal and electrical cross-plane conductivity at the nanoscale in poly(3,4-ethylenedioxythiophene):trifuoromethanesulfonate thin films
• Electron hopping heat transport in molecules
• Thermoelectric Properties of Benzothieno-Benzothiophene Self-Assembled Monolayers in Molecular Junctions
• Transport in Single Quantum Dots: A Review from Linear Response to Nonlinear Regimes
• Neuromorphic heat transport effects in a molecular junction