<i>Non-Equilibrium Thermodynamics</i>

Groot, S.R. de; Mazur, P.; Choi, Sang‐Il

doi:10.1063/1.3050930

Cited by 402 publications

(769 citation statements)

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“…(18) is necessary for the positiveness of the entropy production and a consequence of fundamental principles of nature [20]. The physical meaning of the various transport coefficients α, κ, γ, β, ν, t + is getting more obvious after transforming equivalently the constitutive equations into the more traditional form…”

Section: Modelmentioning

confidence: 99%

“…The Onsager relations which guarantee the positivity of the entropy production and impose strict relations between the equations for densities, charges and temperature, play a central part in the derivation. Chemical reactions can easily be treated within this formalism [20]. The interface conditions can also be derived by necessary continuity constraints (as e.g conservation of charges, energy etc. )…”

Section: Introductionmentioning

confidence: 99%

“…The interface conditions can also be derived by necessary continuity constraints (as e.g conservation of charges, energy etc. ) and considering the physical and chemical processes within the interface [20]. Contrary to the phenomenological approaches the terms contributing to the heat production are systematically derived using nothing else but generally valid thermodynamic relations and total energy conservation, instead of just physical intuition and experimental experience.…”

Section: Introductionmentioning

confidence: 99%

“…A different approach to treat transport in electrochemical systems is the systematic approach of nonequilibrium thermodynamics [20] pioneered by Landau [21,22]. In this approach only conservation equations and general principles of statistical mechanics were used to derive the general form of the relevant transport equations.…”

Section: Introductionmentioning

confidence: 99%

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Thermodynamic consistent transport theory of Li-ion batteries

Latz

Zausch

2011

Journal of Power Sources

188

220

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Most Li ion insertion batteries consist of a porous cathode, a separator filled with electrolyte and an anode, which very often also has some porous structure. The solid part especially in the cathode is usually produced by mixing a powder of the actual active particles, in which Li ions will be intercalated, binder and carbon black to enhance the electronic conductivity of the electrode. As a result the porous structure of the electrodes is very complex, leading to complex potential, ion and temperature distributions within the electrodes. The intercalation and deintercalation of ions cannot be expected to be homogeneously distributed over the electrode due to the different transport properties of electrolyte and active particles in the electrode and the complex three-dimensional pore structure of the electrode. The influence of the final microstructure on the distribution of temperature, electric potential and ions within the electrodes is not known in detail, but may influence strongly the onset of degradation mechanisms. For being able to numerically simulate the transport phenomena, the equations and interface conditions for ion, charge and heat transport within the complex structure of the electrodes and through the electrolyte filled separator are needed. We will present a rigorous derivation of these equations based exclusively on general principles of nonequilibrium thermodynamics. The theory is thermodynamically consistent i.e. it guarantees strictly positive entropy production. The irreversible and reversible sources of heat are derived within the theory. Especially the various contribution to the Peltier heat due to the intercalation of ions are obtained as a result of the theory

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Section: Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Thermodynamic consistent transport theory of Li-ion batteries

Latz

Zausch

2011

Journal of Power Sources

188

220

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“…The basic hypotheses of this macroscopic theory of transport phenomena are the assumption that fluxes are proportional to thermodynamic forces and that the system evolves close to equilibrium [97]. For instance, when dealing with heat transport in a solid, one defines the thermal conductivity κ through the Fourier law J = −κ∇T , (2.10) where the heat flux J is the amount of heat transported through the unit surface in unit time and T (x, t) is the local temperature.…”

Section: Heat Transport In Lattice Modelsmentioning

confidence: 99%

Dynamics of Oscillator Chains

Lichtenberg

Livi

Pettini

et al.

The Fermi-Pasta-Ulam Problem

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Abstract. The Fermi-Pasta-Ulam (FPU) nonlinear oscillator chain has proved to be a seminal system for investigating problems in nonlinear dynamics. First proposed as a nonlinear system to elucidate the foundations of statistical mechanics, the initial lack of confirmation of the researchers expectations eventually led to a number of profound insights into the behavior of high-dimensional nonlinear systems. The initial numerical studies, proposed to demonstrate that energy placed in a single mode of the linearized chain would approach equipartition through nonlinear interactions, surprisingly showed recurrences. Although subsequent work showed that the origin of the recurrences is nonlinear resonance, the question of lack of equipartition remained. The attempt to understand the regularity bore fruit in a profound development in nonlinear dynamics: the birth of soliton theory. A parallel development, related to numerical observations that, at higher energies, equipartition among modes could be approached, was the understanding that the transition with increasing energy is due to resonance overlap. Further numerical investigations showed that time-scales were also important, with a transition between faster and slower evolution. This was explained in terms of mode overlap at higher energy and resonance overlap at lower energy. Numerical limitations to observing a very slow approach to equipartition and the problem of connecting high-dimensional Hamiltonian systems to lower dimensional studies of Arnold diffusion, which indicate transitions from exponentially slow diffusion along resonances to power-law diffusion across resonances, have been considered. Most of the work, both numerical and theoretical, started from low frequency (long wavelength) initial conditions. Coincident with developments to understand equipartition was another program to connect a statistical phenomenon to nonlinear dynamics, that of understanding classical heat conduction. The numerical studies were quite different, involving the excitation of a boundary oscillator with chaotic motion, rather than the excitation of

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Peltier Effect in Semiconductors

Gurevich

Pérez

2014

Wiley Encyclopedia of Electrical and Electronics Engineering

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In recent years, devices based on the Peltier effect, which is the basis for solid‐state thermoelectric cooling, have evolved rapidly to meet the fast‐growing electronic industry. The Peltier effect corresponds to the heat extraction or absorption occurring at the contact between two different conducting media when a direct current (DC) electric current flows through this contact. A comprehensive study of the mechanisms of heating and cooling originated by an electrical current in semiconductor devices is reported. The thermoelectric cooling in n ‐ n , p ‐ p , and p ‐ n junction contacts, as well as inhomogeneous bulk semiconductors, are analyzed. Both degenerate and nondegenerate electron and hole gases are considered. The role of recombination and nonequilibrium charge carriers in the contact cooling (heating) effect is discussed. Along with the above, special attention is paid to several aspects of nonequilibrium thermodynamics of thermoelectric phenomena involved in Peltier effect in semiconductors that demand a careful examination. The formulation of an adequate self‐consistent theoretical model describing the Peltier effect is also presented.

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Non-Equilibrium Thermodynamics

Cited by 402 publications

References 0 publications

Thermodynamic consistent transport theory of Li-ion batteries

Thermodynamic consistent transport theory of Li-ion batteries

Dynamics of Oscillator Chains

Peltier Effect in Semiconductors

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