Seebeck, Peltier, and Soret effects: On different formalisms for transport equations in thermogalvanic cells

Abstract

Thermogalvanic cells convert waste heat directly to electric work. There is an abundance of waste heat in the world and the opportunity represented by thermogalvanic cells may be underused. We discuss theoretical tools that can help us understand and therefore improve the cell performance. One theory is able to describe all aspects of the conversion, nonequilibrium thermodynamics. We recommend to use the theory with operationally defined, independent variables, as others have done before. These describe well-defined experiments. Three invariance criteria can be used as a basis: of local electroneutrality, of entropy production invariance, and of emf's independence of the frame of reference. Alternative formalisms are using different sets of variables, ionic or neutral components. We show that the heat flux is not the same in the two formalisms and derive a new relationship between the heat fluxes. The heat flux enters the definition of the Peltier coefficient and is essential for the understanding of the Peltier heat at the electrode interfaces and of the Seebeck coefficient of the cell. The Soret effect can occur independent of any Seebeck-effect, but the Seebeck effect will be affected by the presence of a Soret effect. Common misunderstandings are pointed out. Peltier coefficients are needed for interpretation and design of measurements.

Effect of the Ion, Solvent, and Thermal Interaction Coefficients on Battery Voltage

“…At isothermal conditions, molecular simulations naturally produce transport coefficients in the mixed component scenario. But operationally defined, experimentally obtained properties are usually related to neutral components. , The Rules for Coupling of Fluxes provide links between the two scenarios and thus between simulations and experiments. The set of transport coefficients of the neutral component scenario is our target, to be used for thermodynamic modeling of the battery electrolyte.…”

Coupled ion transport in concentrated PEO–LiTFSI polymer electrolytes

“…The magnitude of the coupling coefficient L +À is considerable relative to the main coefficients, L ++ and L ÀÀ , when compared to common carbonate-based battery electrolytes. 33 However, the relation L ii L jj Z L ij 2 holds for all systems. 27 The trend of the ionic conductivity is a consequence of the balance between the number of free charge carriers and their mobility, which is tightly coupled to the polymer segmental motion, as shown in several studies.…”

Ionic Peltier effect in Li-ion electrolytes

“…The NET of coupled mass, heat, and charge transport in electrochemical cells subjected to a temperature gradient, socalled thermogalvanic cells, has been thoroughly described in a book chapter by Agar. 17 Kjelstrup and co-workers recently provided a modern perspective on the NET of thermogalvanic cells, 18 building on their prior work. [19][20][21][22][23] Our Fig.…”

“…Choosing neutral components and one of the solvent components as the frame of reference is the most natural and facilitates comparisons between experiment and theory. 18 The Peltier coefficient is expected to depend on the time after the start of an electrical current. On short time scales, short compared to the characteristic time scale for diffusion of mass in the electrolyte t D = h 2 /(p 2 D) where h is the electrolyte thickness, the composition of the electrolyte is uniform and the chemical potential of the components is constant.…”