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We discuss thermal rectification and thermoelectric energy conversion from the perspective of nonequilibrium statistical mechanics and dynamical systems theory. After preliminary considerations on the dynamical foundations of the phenomenological Fourier law in classical and quantum mechanics, we illustrate ways to control the phononic heat flow and design thermal diodes. Finally, we consider the coupled transport of heat and charge and discuss several general mechanisms for optimizing the figure of merit of thermoelectric efficiency.
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We derive the efficiency at maximal power of a scale-invariant (critical) quantum junction in exact form. Both Fermi and Bose statistics are considered. We show that time-reversal invariance is spontaneously broken. For fermions we implement a new mechanism for efficiency enhancement above the Curzon-Ahlborn bound, based on a shift of the particle energy in each heat reservoir, proportional to its temperature. In this setting fermionic junctions can even reach at maximal power the Carnot efficiency. The bosonic junctions at maximal power turn out to be less efficient then the fermionic ones.
The electronic Seebeck response in a conductor involves the energy-dependent mean free path of the charge carriers and is affected by crystal structure, scattering from boundaries and defects, and strain. Previous photothermoelectric (PTE) studies have suggested that the thermoelectric properties of polycrystalline metal nanowires are related to grain structure, though direct evidence linking crystal microstructure to the PTE response is difficult to elucidate. Here, we show that room temperature scanning PTE measurements are sensitive probes that can detect subtle changes in the local Seebeck coefficient of gold tied to the underlying defects and strain that mediate crystal deformation. This connection is revealed through a combination of scanning PTE and electron microscopy measurements of single crystal and bicrystal gold microscale devices. Unexpectedly, the photovoltage maps strongly correlate with gradually varying crystallographic misorientations detected by electron backscatter diffraction. The effects of individual grain boundaries and differing grain orientations on the PTE signal are minimal. This scanning PTE technique shows promise for identifying minor structural distortions in nanoscale materials and devices.
Thermoelectric devices are heat engines, which operate as generators or refrigerators using the conduction electrons as a working fluid. The thermoelectric heat-to-work conversion efficiency has always been typically quite low, but much effort continues to be devoted to the design of new materials boasting improved transport properties that would make them of the electron crystal-phonon glass type of systems. On the other hand, there are comparatively few studies where a proper thermodynamic treatment of the electronic working fluid is proposed. The present article aims to contribute to bridge this gap by addressing both the thermodynamic and transport properties of the thermoelectric working fluid covering a variety of models, including interacting systems.
The theory of small-system thermodynamics was originally developed to extend the laws of thermodynamics to length scales of nanometers. Here we review this nanothermodynamics, and stress how it also applies to large systems that subdivide into a heterogeneous distribution of internal subsystems that we call regions. We emphasize that the true thermal equilibrium of most systems often requires that these regions are in the fully-open generalized ensemble, with a distribution of region sizes that is not externally constrained, which we call the nanocanonical ensemble. We focus on how nanothermodynamics impacts the statistical mechanics of specific models. One example is an ideal gas of indistinguishable atoms in a large volume that subdivides into an ensemble of small regions of variable volume, with separate regions containing atoms that are distinguishable from those in other regions. Combining such subdivided regions yields the correct entropy of mixing, avoiding Gibbs paradox without resorting to macroscopic quantum symmetry for semi-classical particles. Other models are based on Ising-like spins (binary degrees of freedom), which are solved analytically in one-dimension, making them suitable examples for introductory courses in statistical physics. A key result is to quantify the net increase in entropy when large systems subdivide into small regions of variable size. Another result is to show similarity in the equilibrium properties of a two-state model in the nanocanonical ensemble and a three-state model in the canonical ensemble. Thus, emergent phenomena may alter the thermal behavior of microscopic models, and the correct ensemble is necessary for accurate predictions.
Electrochemical ion insertion involves coupled ion-electron transfer reactions, transport of guest species, and redox of the host. The hosts are typically anisotropic solids with two-dimensional conduction planes, but can also be materials with one-dimensional or isotropic transport pathways. These insertion compounds have traditionally been studied in the context of energy storage, but also find extensive applications in electrocatalysis, optoelectronics, and computing. Recent developments in operando, ultrafast, and high-resolution characterization methods, as well as accurate theoretical simulation methods, have led to a renaissance in the understanding of ion-insertion compounds. In this Review, we present a unified framework for understanding insertion compounds across time and length scales ranging from atomic to device levels. Using graphite, transition metal dichalcogenides, layered oxides, oxyhydroxides, and olivines as examples, we explore commonalities in these materials in terms of point defects, interfacial reactions, and phase transformations. We illustrate similarities in the operating principles of various ion-insertion devices ranging from batteries and electrocatalysts to electrochromics and thermal transistors, with the goal of unifying research across disciplinary boundaries.
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