Coulometry and Calorimetry of Electric Double Layer Formation in Porous Electrodes

Abstract

Coulometric measurements on salt-water-immersed nanoporous carbon electrodes reveal, at a fixed voltage, a charge decrease with increasing temperature. During far-out-of-equilibrium charging of these electrodes, calorimetry indicates the production of both irreversible Joule heat and reversible heat, the latter being associated with entropy changes during electric double layer (EDL) formation in the nanopores. These measurements grant experimental access-for the first time-to the entropic contribution of the grand potential; for our electrodes, this amounts to roughly 25% of the total grand potential energy cost of EDL formation at large applied potentials, in contrast with point-charge model calculations that predict 100%. The coulometric and calorimetric experiments show a consistent picture of the role of heat and temperature in EDL formation and provide hitherto unused information to test against EDL models. DOI: 10.1103/PhysRevLett.119.166002 Where surfaces of charged electrodes meet fluids that contain mobile ions, so-called electric double layers (EDLs) form that screen the electric surface charge by a diffuse cloud of counterionic charge. This EDL has been intensively studied for over a century and is of paramount importance to many processes in physical chemistry and soft matter physics. With the ongoing development of nanomaterials, nowadays electrodes can be made from porous carbon with internal surface areas exceeding 1000 m 2 g −1 . These porous electrodes can be immersed in a variety of electrolyte solutions or ionic liquids. A socalled electric double layer capacitor (EDLC) is then formed, whose high capacitance makes it a prime candidate for capacitive energy storage, energy conversion [1,2], and water desalination [3][4][5]. In these porous electrodes, solvated ions have a size similar to that of their confining geometry; hence, a realistic theory must at least address both the electrostatics and the packing of the ions. Simulations and in situ analytical techniques [6] have revealed a wealth of phenomena in EDLCs [7], including overscreening [8], ion desolvation [9,10], in-plane structural transitions [11], layered packings of counterionic charge at high surface potentials [12], and, relatedly, oscillations in the EDL capacitance with decreasing pore width [13][14][15]. Unfortunately, the gap between (computationally demanding) first-principles models and experimental measurements on the charging behavior of porous electrodes is far from closed, with many questions remaining regarding the precise screening mechanisms at play [16]. While our understanding of the EDL is based mainly on isothermal numerical and experimental methods, recent work has revealed an interplay between temperature, heat, and entropy in the EDL. In particular, both model calculations [17] and experiments [2] indicate that the surface potential of an electrode with a fixed high surface charge should rise by about 1 mV K −1 with increasing temperature. Conversely, EDL formation under adiabatic settings induces a thermal r...

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