The electric double layer put to work: thermal physics at electrochemical interfaces

Abstract

Where charged electrode surfaces meet fluids that contain mobile ions, so-called electric double layers (EDLs) form to screen the electric surface charge by a diffuse cloud of counterionic charge in the fluid phase. This double layer has been studied for over a century and is of paramount importance to many processes in physical chemistry and soft matter physics, as well as in electric double layer capacitors (EDLCs) used for energy storage. With the ongoing development of nanomaterials, electrodes can nowadays be built from porous carbon with internal surface areas up to 2000 m2/g, leading to very high capacitances. However, in EDLCs made from this material, the size of hydrated ions is on the same length scale as their confining geometry. This poses a substantial theoretical challenge, since EDL models must address both the electrostatics and the packing of the ions. To address this challenge, model calculations of different levels of sophistication are presented throughout this thesis. These calculations give access to the capacitance, the relation between the electrostatic potential and the charge on the electrodes’ surface. Particularly, we focus on the interplay between the capacitance and the temperature the electrolyte solution. First, we show that the electrostatic potential at fixed electrode charge rises with electrolyte temperature. This thermal voltage rise is predicted by calculations and observed in experiments, both in the case of an aqueous and an organic solvent. This finding opens the door to thermal energy harvesting with EDLCs. To this end, we propose to convert thermal into electric energy via a charging-heating-discharging-cooling cycle of an EDLC in alternating contact with heat reservoirs at either high or low temperature. The essence of this cycle is the surplus of energy harvested during discharging at high temperature (and associated high potentials) compared to the energy invested during charging at lower temperature (hence lower potentials). As another possible application of the thermal voltage rise, we show that harvesting “blue” energy from the spontaneous mixing process of fresh and salt water can be boosted by varying the water temperature during a capacitive mixing cycle. We show that the energy output of blue engines can be increased by a factor of order two if warm fresh water is mixed with cold seawater. Note that we do not advocate to consume fossil fuels to generate warm water, but rather to use (industrial) waste heat, which is abundantly available. While electrolyte temperature affects EDLC capacitance, the reverse is also true. As a second example of the interplay between temperature and EDLC capacitance, we consider how the charging of an EDLC affects the electrolyte temperature. For a thermally insulated capacitor that is charged quasi-statically, thermodynamics demands via the second law (dS = 0) that the ionic configuration entropy decrease upon EDL formation is counterbalanced by an electrolyte entropy increase: the EDLC heats up. Upon quasi-static adiabatic discharging, the opposite happens: the electrolyte cools while the EDL breaks down. We discuss various earlier models, and propose a new thermodynamic identity that fixes some of their shortcomings.