Predictions of the maximum energy extracted from salinity exchange inside porous electrodes

Abstract

Capacitive energy extraction based on double layer expansion (CDLE) is the name of a new method devised for extracting energy from the exchange of fresh and salty water in porous electrodes. It is based on the change of the capacitance of electrical double layers (EDLs) at the electrode/solution interface when the concentration of the bulk electrolyte solution is modified. The use of porous electrodes provides huge amounts of surface area, but given the typically small pore size, the curvature of the interface and EDL overlap should affect the final result. This is the first aspect dealt with in this contribution: we envisage the electrode as a swarm of spherical particles, and from the knowledge of their EDL structure, we evaluate the stored charge, the differential capacitance and the extracted energy per CDLE cycle. In all cases, different pore radii and particle sizes and possible EDL overlap are taken into account. The second aspect is the consideration of finite ion size instead of the usual point-like ion model: given the size of the pores and the relatively high potentials that can be applied to the electrode, excluded volume effects can have a significant role. We find an extremely strong effect: the double layer capacitance is maximum for a certain value of the surface potential. This is a consequence of the limited ionic concentration at the particle-solution interface imposed by the finite size of ions, and leads to the presence of two potential ranges: for low electric potentials the capacitance increases with the ionic strength, while for large potentials we find the opposite trend. The consequences of these facts on the possibility of net energy extraction from porous electrodes, upon changing the solution in contact with them, are evaluated.

Materials selection for optimum energy production by double layer expansion methods

“…Table 3 shows some preliminary results, obtained with layers of the indicated carbon particles. Although the theoretical predictions [20] indicate that the effect of the average pore size on the voltage rise should be negligible, our data show that this is true for samples SR- In addition, there is a very noticeable difference between the three samples: the rate of elevation of the voltage when the solutions are exchanged is much faster for SR-03 (i.e., the sample with smallest average pore size) than for the others (Fig. 10).…”

“…Models on the phenomenon and its kinetics 4 have been developed by Rica et al [17][18][19], and Jiménez et al [20]. A pair of electrodes are connected to an external power source while wetted with a salt solution of high concentration (sea water); then, the solution is exchanged for a low-concentration one (fresh or river water) in open circuit (constant charge).…”

“…At very low voltages, calculations of the chargepotential in a swarm of spherical particles considering ion size [20] indicate that the potential drop in salt water is smaller than its rise in fresh water, if double layers are equilibrated with the corresponding solutions. At larger potential, the model predicts identical voltage differences, as in fact observed experimentally; this is the optimal working range.…”

“…In addition, the difficulty for complete exchange of salty water by fresh one will always be present, contributing to increasing the salinity of the pores above the nominal equilibrium value, this in turn leading to a lower potential rise. Overall, this goes against the charge transfer in the CDLE cycle and hence against energy production [20].…”

“…This is because the measured quantities (in brief, potential difference between the electrodes in the cell and current from one to the other as a function of time) are a macroscopic average of values which can change from one position to another in the electrode in distances smaller than the electrode thickness [21]. In fact, although the walls of the pores can be considered equipotential in open circuit throughout the whole electrode, the surface charge may behave differently, considering that a concentration profile will be established along the electrode, and that the EDLs can be quite different in macro-and micropores [17][18][19][20][22][23][24].…”