Nernst Equations and Concentration Chemical Reaction Overpotentials for VRFB Operation
Clifford M. Krowne
Abstract
The vanadium redox flow battery (VRFB) has been intensively examined since the 1970s, with researchers looking at its electrochemical time varying electrolyte concentration time variation equations (both tank and cells, for negative and positive half cells), its thermal time variation equations, and fluid flow equations. Chemistry behavior of the electrolyte ions have also been intensively examined too. Our focus in this treatment is a new approach to understanding the physics, chemistry, and electronics of the VRFB by looking at the equilibrium and non-equilibrium aspects of the battery. Detailed examination of the behavior inside the porous electrodes of the electrolyte concentration is done by distinguishing between the concentrations near the pore surface wall and volume elements away from the solid surface-electrolyte boundary. Relationship to the battery charging or discharging current and current density is performed allowing macroscopic overpotentials to be determined for each electrode. These are concentration overpotentials and their exact relationship to the battery potentials is developed carefully so that a rigorous basis is established. It is found that there are two overpotentials making up the negative electrode overpotential, due to the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">V</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>+</mml:mo> </mml:mrow> </mml:msup> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">V</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> <mml:mo>+</mml:mo> </mml:mrow> </mml:msup> </mml:math> ions. Similarly, there are two overpotentials making up the positive electrode overpotential, due to the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">V</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>4</mml:mn> <mml:mo>+</mml:mo> </mml:mrow> </mml:msup> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">V</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>5</mml:mn> <mml:mo>+</mml:mo> </mml:mrow> </mml:msup> </mml:math> ions.