A thermodynamic study of the effect of small-scale electrolytes on equilibrium redox potentials

Expressions are derived to calculate the equilibrium oxidation–reduction potentials for the Al+3/Al, Cu+2/Cu, and Zn+2/Zn systems in small-scale electrolytes. The geometrical system consists of a droplet of electrolyte resting on a flat metal plate, and the metal is considered to be immersed in a solution of its own ions. When the radius of the drop is allowed to vary, both the size of the electrolyte and the size of the active metal beneath the droplet change simultaneously. The total free energy change for the system consists of both electrochemical and surface chemical contributions. The interfacial free energy for the solid/liquid interface has been estimated from the Girifalco–Good expression or from spreading pressure considerations. When the droplet becomes sufficiently small in radius, the surface chemical contributions become significant, and the calculated redox potential changes from its normal value to more negative values as the size of the system decreases. The magnitude of this effect depends on the particular system. For 2 M Cu+2, the calculated redox potential for a 0.8 nm radius droplet is 0.259 V more negative than for the bulk electrolyte. The effect is much smaller for aluminum and zinc. In all three systems, calculated redox potentials approach values for the bulk solution for droplet radii of about 10 nm.