Calorimetry of Capacitive Porous Carbon Electrodes in Aqueous Media
Authors:   , Vos Joren Ezra 
Published: March 2023

Chapter 1 contains an overview of the background of this thesis. Porous carbon electrodes and their applications are introduced, followed by a discussion of the Electric Double Layer (EDL) in porous carbon electrodes. Then, experimental work on the thermodynamics of the EDL in porous electrodes is presented. This Chapter ends with a brief description of the electrochemical calorimetry setup.

In Chapter 2, the electrochemical calorimetry setup is examined in more detail. The cell contained an aqueous electrolyte solution and three electrodes. The potential of the working electrode (WE) was applied with respect to the reference electrode (RE), and the current was measured between WE and counter electrode (CE). Behind the WE, a heat flux sensor (HFS) measured the heat flow coming from the WE during the (dis)charging of the EDL. The heat was calibrated on the Joule heat produced in a full charge-discharge cycle. We us the setup to measure the heat of (dis)charging the WE as a function of the potential applied to the electrode.

Chapter 3 describes how the setup was used to determine the potential-dependent internal energy of porous carbon electrodes in aqueous solutions of different salts. Changes were calculated from the (electrical) work performed on the system and the heat released or absorbed by the system. The energy changes consist of two contributions, which respectively scaled linearly and quadratically with applied potential. The linear contribution was ascribed to the attraction of ions to the surface of the pores, given by the number of adsorbed ions times a fixed attraction energy per ion. The quadratic contribution was slightly smaller than expected for a parallel plate capacitor of the same capacitance, which we interpreted in terms of the average electric potential experienced by ions inside the pores.

Chapter 4 demonstrated that the formula found in Chapter 3 can also explain the time-dependent heat production. The charging rate was varied by changing the amount of time taken to build up the applied potential linearly until the final potential was reached. Using four constant parameters, both the reversible and irreversible heat production rates could be explained. We verified that the reversible heat was the same regardless of the charging rate. Agreement between model and experiment was only semi-quantitative, which we attributed to a time dependence of the electric current more complicated than mono-exponential decay.

In Chapter 5 we analyzed the time dependence of the current for the (dis)charging of porous carbon electrodes in 1M solutions. The rate of exponential decay of the current was initially determined by the RC time and later by a distribution of time constants, which we attributed
to polydispersity of the pores. The late-time current decay was slower at cathodic than at anodic potentials, but we argued that this was not because of the different diffusion coefficients of the cations and anions, which were nearly identical for KCl. Instead, the potential-dependent dynamics were discussed in terms of the different capacitance of the electrode in the cathodic and anodic ranges, resulting from specific ion adsorption.