Reversible heat production during electric double layer buildup depends sensitively on the electrolyte and its reservoir

Abstract

Several modern technologies for energy storage and conversion are based on the screening of electric charge on the surface of porous electrodes by ions in an adjacent electrolyte. This so-called electric double layer (EDL) exhibits an intricate interplay with the electrolyte's temperature that was the focus of several recent studies. In one of them, Janssen et al. [Phys. Rev. Lett. 119, 166002 (2017)] experimentally determined the ratio Qrev/W el of reversible heat flowing into a supercapacitor during an isothermal charging process and the electric work applied therein. To rationalize that data, here, we determine Qrev/W el within different models of the EDL using theoretical approaches like density functional theory (DFT) as well as molecular dynamics simulations. Applying mainly the restricted primitive model, we find quantitative support for a speculation of Janssen et al. that steric ion interactions are key to the ratio Qrev/W el . Here, we identified the entropic contribution of certain DFT functionals, which grants direct access to the reversible heat. We further demonstrate how Qrev/W el changes when calculated in different thermodynamic ensembles and processes. We show that the experiments of Janssen et al. are explained best by a charging process at fixed bulk density, or in a "semi-canonical" system. Finally, we find that Qrev/W el significantly depends on parameters as pore and ion size, salt concentration, and valencies of the cat-and anions of the electrolyte. Our findings can guide further heat production measurements and can be applied in studies on, for instance, nervous conduction, where reversible heat is a key element.

Extension of the primitive model by hydration shells and its impact on the reversible heat production during the buildup of the electric double layer

“…We describe one nanopore in a nanoporous electrode as two equally charged planar hard walls with distance L = 10 nm as done in ref. [10], if not mentioned otherwise. The setup is sketched in Fig.…”

“…As described in ref. [10], the electric work ∆W el for isothermal charging of one electrode from surface charge Q 1 to surface charge Q 2 is given by…”

“…The reversible heat involved in the build-up of electric double layers (EDLs) has been studied in recent works experimentally [1,2] and theoretically [3][4][5][6][7][8][9][10]. In one of these studies it has been claimed that heat effects in EDLs are described theoretically by simply modeling the Stern layer separation correct [10]. As a consequence, first, rather simple models would be sufficient to describe heat effects in capacitors or biological systems.…”

“…The RPM and, in particular, its structural properties are well described in the theoretical framework of classical density functional theory (DFT) [22], because the framework remarkably well handles hard-sphere interactions within fundamental measure theory [23][24][25][26]. In consequence, DFT is able to describe the structure of the first layers of ions in the vicinity of an electrode [27][28][29], a property that recently has been discussed to be key for properties like the heat production during charging [10] and the differential capacitance in EDLs [30].…”

“…In this work, our observable of choice is the reversible heat, because it was found to depend strongly on the Stern layer [10] and, therefore, on the crystallized instead of the hydrated diameter. We first briefly recapitulate the experiment in which the reversible heat production during EDL buildup has been measured (in sum over both electrodes) [2] and its theoretical description in DFT [10]. Second, we extend the RPM to describe hydration shell evasion within DFT.…”