Supercapacitors have an asymmetric electrode potential and charge due to nonelectrostatic electrolyte interactions

In recent years we have built up a theoretical framework which aims to explain ion specific effects observed in colloids at high salt concentrations. Our approach adds nonelectrostatic ion interactions (ion dispersion energies) alongside the usual electrostatic interactions of the ions. Using these techniques we have explored the impact that ion specificity may have on supercapacitors. Our model uses graphite electrodes at constant potential difference in 1.2 M Li salt dissolved in propylene carbonate. For the counterion we used the common battery anions, PF6-, BF4- and ClO4- along with BrO4-, IO4- and Cl-. When nonelectrostatic ionic interactions are included, a potential difference V will not be split symmetrically between the two electrodes. We address two alternative mechanisms for partitioning the potential difference. If the circuit is isolated, then the charge at each electrode must be equal. This defines a potential psi(eq) not equal V/2 at the positive electrode and therefore psi(eq) - V at the negative. Alternatively, if the circuit is connected to an external environment (ground, defining zero potential), then the state of the system is determined by minimisation of the total free energy, resulting in asymmetric electrode charges as well as potentials. The potentials determined by the two mechanisms are different, psi(min) not equal psi(eq), with both the difference (averaging about 10%) and the direction of the difference between them depending on the ions. The free energy of the system with equalised charge exceeds the minimised free energy by less than 10%. Total free energies follow the Hofmeister series Cl- > PF6- > BF4- > ClO4- > BrO4- > lO(4)(-). Despite the differences in electrode potential and charge under the two potential partitioning mechanisms, the capacitances under both mechanisms are similar. Local electrode capacitances C-1 = d sigma/d psi relative to the positive electrode potential follow the same Hofmeister series as the energy. The energy-capacitance slope is nonlinear, becoming smaller as C-1 increases. The Hofmeister series in the differential capacitance C-2 = d sigma/dV relative to the potential difference V swaps BF4- > PF6-. The asymmetry in capacitance between positive and negative electrodes indicates that the capacitance of a two-electrode supercapacitor or battery ought be treated as a two-value quantity rather than as a single value, similar to the matrix of mutual capacitances used in multielectrode devices.