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C. Goupil

Publications and source records attributed to C. Goupil.

At least 19 recordsLinked to original sources
arXiv2021

The thermoelectric conversion efficiency problem: Insights from the electron gas thermodynamics close to a phase transition

The bottleneck in modern thermoelectric power generation and cooling is the low energy conversion efficiency of thermoelectric materials. The detrimental effects of lattice phonons on performance can be mitigated, but achieving a high thermoelectric power factor remains a major problem because the Seebeck coefficient and electrical conductivity cannot be jointly increased. The conducting electron gas in thermoelectric materials is the actual working fluid that performs the energy conversion, so its properties determine the maximum efficiency that can theoretically be achieved. By relating the thermoelastic properties of the electronic working fluid to its transport properties (considering noninteracting electron systems), we show why the performance of conventional semiconductor materials is doomed to remain low. Analyzing the temperature dependence of the power factor theoretically in 2D systems and experimentally in a thin film, we find that in the fluctuation regimes of an electronic phase transition, the thermoelectric power factor can significantly increase owing to the increased compressibility of the electron gas. We also calculate the ideal thermoelectric conversion efficiency in noninteracting electron systems across a wide temperature range neglecting phonon effects and dissipative coupling to the heat source and sink. Our results show that driving the electronic system to the vicinity of a phase transition can indeed be an innovative route to strong efficiency enhancement, but at the cost of an extremely narrow temperature range for the use of such materials, which in turn precludes potential development for the desired wide range of thermoelectric energy conversion applications.

cond-mat.mtrl-sci↗
arXiv2021

Nernst and Ettingshausen effects in the Laughlin geometry

The ideal reversible thermodynamic cycle visualization of the Nernst effect in Laughlin geometry, excluding the kinetic contribution is proposed. The Ettingshausen effect is also treated in the fashion using the reverse cycle. The corresponding values of the off-diagonal thermoelectric coefficients are expressed through the ratio of the entropy budget per magnetic flux. Our approach enlightens the profound thermodynamic origin of the relation between the Nernst effect and magnetization currents.

cond-mat.mes-hall↗
arXiv2020

Thermodynamics of animal locomotion

Muscles are biological actuators extensively studied in the frame of Hill's classic empirical model as isolated biomechanical entities, which hardly applies to a living organism subjected to physiological and environmental constraints. Here we elucidate the overarching principle of a \emph{living} muscle action for locomotion, considering it from the thermodynamic viewpoint as an assembly of actuators (muscle units) connected in parallel, operating via chemical-to-mechanical energy conversion under mixed (potential and flux) boundary conditions. Introducing the energy cost of effort, $COE_-$, as the generalization of the well-known oxygen cost of transport, $COT$, in the frame of our compact locally linear non-equilibrium thermodynamics model, we analyze oxygen consumption measurement data from a documented experiment on energy cost management and optimization by horses moving at three different gaits. Horses adapt to a particular gait by mobilizing a nearly constant number of muscle units minimizing waste production per unit distance covered; this number significantly changes during transition between gaits. The mechanical function of the animal is therefore determined both by its own thermodynamic characteristics and by the metabolic operating point of the locomotor system.

physics.bio-ph↗
arXiv2019

Thermodynamics of metabolic energy conversion under muscle load

The metabolic processes complexity is at the heart of energy conversion in living organisms and forms a huge obstacle to develop tractable thermodynamic metabolism models. By raising our analysis to a higher level of abstraction, we develop a compact -- i.e. relying on a reduced set of parameters -- thermodynamic model of metabolism, in order to analyze the chemical-to-mechanical energy conversion under muscle load, and give a thermodynamic ground to Hill's seminal muscular operational response model. Living organisms are viewed as dynamical systems experiencing a feedback loop in the sense that they can be considered as thermodynamic systems subjected to mixed boundary conditions, coupling both potentials and fluxes. Starting from a rigorous derivation of generalized thermoelastic and transport coefficients, leading to the definition of a metabolic figure of merit, we establish the expression of the chemical-mechanical coupling, and specify the nature of the dissipative mechanism and the so called figure of merit. The particular nature of the boundary conditions of such a system reveals the presence of a feedback resistance, representing an active parameter, which is crucial for the proper interpretation of the muscle response under effort in the framework of Hill's model. We also develop an exergy analysis of the so-called maximum power principle, here understood as a particular configuration of an out-of-equilibrium system, with no supplemental extremal principle involved.

cond-mat.stat-mech↗
arXiv2018

Maximization of the thermoelectric cooling of graded Peltier by analytical heat equation resolution

Increasing the maximum cooling effect of a Peltier cooler can be achieved through materials and device design. The use of inhomogeneous, FGM (functionally graded materials) may be adopted in order to increase maximum cooling without improvement of the zT (figure of merit), however these systems are usually based on the assumption that the local optimization of the zT is the suitable criterion to increase thermoelectric performances. In the present paper, we solved the heat equation in a graded material and performed both analytic and numerical analysis of a graded Peltier cooler. We find a local criterion that we used to assess the possible improvement of graded materials for thermoelectric cooling. A fair improvement of cooling effect is predicted for semiconductor materials (up to $36\%$) and the best graded system for cooling is described. The influence of the equation of state of the electronic gas of the material is discussed, and the difference in term of entropy production between the graded and the classical system is also described.

physics.app-ph↗
arXiv2016

Closed-loop approach to thermodynamics

We present the closed loop approach to linear nonequilibrium thermodynamics considering a generic heat engine dissipatively connected to two temperature baths. The system is usually quite generally characterized by two parameters: the output power $P$ and the conversion efficiency $η$, to which we add a third one, the working frequency $ω$. We establish that a detailed understanding of the effects of the dissipative coupling on the energy conversion process, necessitates the knowledge of only two quantities: the system's feedback factor $β$ and its open-loop gain $A_{0}$, the product of which, $A_{0}β$, characterizes the interplay between the efficiency, the output power and the operating rate of the system. By placing thermodynamics analysis on a higher level of abstraction, the feedback loop approach provides a versatile and economical, hence a very efficient, tool for the study of \emph{any} conversion engine operation for which a feedback factor may be defined.

cond-mat.stat-mech↗
arXiv2016

A note on the electrochemical nature of the thermoelectric power

While thermoelectric transport theory is well established and widely applied, there remains some degree of confusion on the proper thermodynamic definition of the Seebeck coefficient (or thermoelectric power) which is a measure of the strength of the mutual interaction between electric charge transport and heat transport. Indeed, as one considers a thermoelectric system, it is not always clear whether the Seebeck coefficient is to be related to the gradient of the system's chemical potential or to the gradient of its electrochemical potential. This pedagogical article aims to shed light on this confusion and clarify the thermodynamic definition of the thermoelectric coupling. First, we recall how the Seebeck coefficient is experimentally determined. We then turn to the analysis of the relationship between the thermoelectric power and the relevant potentials in the thermoelectric system: As the definitions of the chemical and electrochemical potentials are clarified, we show that, with a proper consideration of each potential, one may derive the Seebeck coefficient of a non-degenerate semiconductor without the need to introduce a contact potential as seen sometimes in the literature. Furthermore, we demonstrate that the phenomenological expression of the electrical current resulting from thermoelectric effects may be directly obtained from the drift-diffusion equation.

cond-mat.mtrl-sci↗
arXiv2016

The thermoelectric working fluid: thermodynamics and transport

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.

cond-mat.stat-mech↗
arXiv2016

On the fundamental aspect of the first Kelvin's relation in thermoelectricity

Kelvin's relations may be considered as cornerstones in the theory of thermoelectricity. Indeed, they gather together the three thermoelectric effects, associated respectively with Seebeck, Peltier and Thomson, to get a unique and consistent description of thermoelectric phenomena. However, their physical status in literature are quite different. On the one hand, the second Kelvin's relation is associated with the microscopic reversibility, considered as a fundamental thermodynamical property. On the other hand, the first Kelvin's relation is traditionally introduced only as a convenient mathematical relation between Seebeck and Thomson coefficients. In the present article, we stress that, contrary to common believes, this relation may demonstrates deeper insights than a bold mathematical expression between thermoelectric coefficients. It actually reflects the coexistence of two different mechanisms taking place inside thermoelectric systems: Energy conversion and reorganization of heat flow when Seebeck coefficient varies.

cond-mat.mtrl-sci↗
arXiv2015

Green thermoelectrics: Observation and analysis of plant thermoelectric response

Plants are sensitive to thermal and electrical effects; yet the coupling of both, known as thermoelectricity, and its quantitative measurement in vegetal systems never were reported. We recorded the thermoelectric response of bean sprouts under various thermal conditions and stress. The obtained experimental data unambiguously demonstrate that a temperature difference between the roots and the leaves of a bean sprout induces a thermoelectric voltage between these two points. Basing our analysis of the data on the force-flux formalism of linear response theory, we found that the strength of the vegetal equivalent to the thermoelectric coupling is one order of magnitude larger than that in the best thermoelectric materials. Experimental data also show the importance of the thermal stress variation rate in the plant's electrophysiological response. Therefore, thermoelectric effects are sufficiently important to partake in the complex and intertwined processes of energy and matter transport within plants.

physics.bio-ph↗
arXiv2015

Equivalent parameters for series thermoelectrics

We study the physical processes at work at the interface of two thermoelectric generators (TEGs) thermally and electrically connected in series. We show and explain how these processes impact on the system's performance: the derivation of the equivalent electrical series resistance yields a term whose physical meaning is thoroughly discussed. We demonstrate that this term must exist as a consequence of thermal continuity at the interface, since it is related to the variation of the junction temperature between the two TEGs associated in series as the electrical current varies. We then derive an expression for the equivalent series figure of merit. Finally we highlight the strong thermal/electrical symmetry between the parallel and series configurations and we compare our derivation with recent published results for the parallel configuration.

cond-mat.mtrl-sci↗
arXiv2014

Influence of thermal environment on optimal working conditions of thermoelectric generators

Optimization analyses of thermoelectric generators operation is of importance both for practical applications and theoretical considerations. Depending on the desired goal, two different strategies are possible to achieve high performance: through optimization one may seek either power output maximization or conversion efficiency maximization. Recent literature reveals the persistent flawed notion that these two optimal working conditions may be achieved simultaneously. In this article, we lift all source of confusion by correctly posing the problem and solving it. We assume and discuss two possibilities for the environment of the generator to govern its operation: constant incoming heat flux, and constant temperature difference between the heat reservoirs. We demonstrate that, while power and efficiency are maximized simultaneously if the first assumption is considered, this is not possible with the second assumption. This latter corresponds to the seminal analyses of Ioffe who put forth and stressed the importance of the thermoelectric figure of merit $ZT$. We also provide a simple procedure to determine the different optimal design parameters of a thermoelectric generator connected to heat reservoirs through thermal contacts with a finite and fixed thermal conductance.

cond-mat.other↗
arXiv2014

Comment on "Effective thermal conductivity in thermoelectric materials"

In a recent article, Baranowski et al. [J. Appl. Phys. 113, 204904 (2013)] proposed a model that allegedly facilitates optimization of thermoelectric generators operation as these latter are in contact with hot and cold temperature baths through finite conductance heat exchangers. In this Comment, we argue that the results and analyses presented by these authors are misleading since their model is incomplete and rests on an inappropriate assumption derived from thermoelectric compatibility theory.

cond-mat.other↗
arXiv2014

Revisiting Feynman's ratchet with thermoelectric transport theory

We show how the formalism used for thermoelectric transport may be adapted to Smoluchowski's seminal thought experiment also known as Feynman's ratchet and pawl system. Our analysis rests on the notion of useful flux, which for a thermoelectric system is the electrical current and for Feynman's ratchet is the effective jump frequency. Our approach yields original insight into the derivation and analysis of the system's properties. In particular we define an entropy per tooth in analogy with the entropy per carrier or Seebeck coefficient, and we derive the analogue to Kelvin's second relation for Feynman's ratchet. Owing to the formal similarity between the heat fluxes balance equations for a thermoelectric generator (TEG) and those for Feynman's ratchet, we introduce a distribution parameter that quantifies the amount of heat that flows through the cold and hot sides of both heat engines. While it is well established that $γ$ = 1/2 for a TEG, it is equal to 1 for Feynman's ratchet. This implies that no heat may be rejected in the cold reservoir for the latter case. Further, the analysis of the efficiency at maximum power shows that the so-called Feynman efficiency corresponds to that of an exoreversible engine, with $γ$ = 1. Then, turning to the nonlinear regime, we generalize the approach based on the convection picture and introduce two different types of resistance to distinguish the dynamical behavior of the considered system from its ability to dissipate energy. We finally put forth the strong similarity between the original Feynman ratchet and a mesoscopic thermoelectric generator with a single conducting channel.

cond-mat.stat-mech↗
arXiv2014

Comment on "Heat dissipation in atomic-scale junctions"

We discuss the recent results of Lee et al. [Nature 498, 209 (2013)] using the notion of thermoelectric convection. In particular, we highlight the fact that this contribution to the thermal flux is not a dissipative process.

cond-mat.mes-hall↗
arXiv2013

A linear nonequilibrium thermodynamics approach to optimization of thermoelectric devices

Improvement of thermoelectric systems in terms of performance and range of applications relies on progress in materials science and optimization of device operation. In this chapter, we focuse on optimization by taking into account the interaction of the system with its environment. For this purpose, we consider the illustrative case of a thermoelectric generator coupled to two temperature baths via heat exchangers characterized by a thermal resistance, and we analyze its working conditions. Our main message is that both electrical and thermal impedance matching conditions must be met for optimal device performance. Our analysis is fundamentally based on linear nonequilibrium thermodynamics using the force-flux formalism. An outlook on mesoscopic systems is also given.

physics.class-ph↗
arXiv2012

Internal convection in thermoelectric generator models

Coupling between heat and electrical currents is at the heart of thermoelectric processes. From a thermal viewpoint this may be seen as an additional thermal flux linked to the appearance of electrical current in a given thermoelectric system. Since this additional flux is associated to the global displacement of charge carriers in the system, it can be qualified as convective in opposition to the conductive part associated with both phonons transport and heat transport by electrons under open circuit condition, as, e.g., in the Wiedemann-Franz relation. In this article we demonstrate that considering the convective part of the thermal flux allows both new insight into the thermoelectric energy conversion and the derivation of the maximum power condition for generators with realistic thermal coupling.

cond-mat.mtrl-sci↗