Statistical Thermodynamics of Supercapacitors and Blue Engines

Abstract

The scarcity of fresh water, the depletion of fossil fuels, and theever-increasing demand for electric power are important issuesthat receive increasing attention in a variety of branches ofscience and technology. In all three cases, nanoporous carbonelectrodes, immersed in a liquid medium with charge carriers,are being considered as device elements. For instance, in carbide-derived carbon electrodes with nanometer-sized pores filled withan ionic liquid, electric energy can be stored/released throughthe adsorption/desorption of ionic charges on/from the surface ofthe charging/discharging electrodes [Chmiola et al. (2006); Miller and Simon (2008); Merlet et al. (2012)]. Carbon electrodes are also being explored in capacitive devices to harvest sustainableenergy from mixing fresh river water with salty sea water [Brogioli(2009); Brogioli et al. (2011); Rica et al. (2012); Sales et al. (2010)]. This salinity-gradient energy, or “blue” energy, is obtained fromcharging up a pair of electrodes immersed in sea water (wherebyions adsorb onto the electrodes at a low potential) and dischargingthem again immersed in fresh water (whereby ions desorb fromthe electrodes at a higher potential). This capacitive mixing process,with brackish water as a waste product, intercepts the spontaneousdiffusion of ions from high to low salinity in much the same wayas heat engines intercept the heat flow from hot to cold heatbaths; for typical salt concentrations in river and sea water, these“blue engines” can produce of the order of 2 kJ of energy perliter of river water, in principle even completely reversibly [Boonand van Roij (2011)]. The reverse process, which can be seen asa “blue fridge,” is a desalination process in which two volumes ofinitially brackish water are converted into a volume of fresh waterand a volume of brine by charging up the electrodes in one ofthe volumes (which then desalinates due to ion adsorption ontothe electrodes, at a high potential) and discharging them in theother volume (which then becomes more salty due to the releaseof the ions from the electrodes, at a low potential) [Biesheuvel(2009)]. Of course, the “blue fridge” requires a net energy input, andongoing research questions involve the efficiency and speed of suchprocesses.