Thermodynamic aspects of energy conversion systems with focus on osmotic membrane and selectively permeable membrane (Donnan) systems including two applications of the Donnan potential

This article deals with the thermodynamics of energy conversion systems with a focus on osmotic membrane and selectively permeable membrane systems for beginners of research in membrane chemistry. Two applications of the concept of the reversible Donnan potential are presented: the irreversible steady-state membrane potential across a biological membrane and irreversible dialytic potential in the dialytic (mixing entropy) batteries. The osmotic pressure and Donnan (membrane) potential are developed as the diffusible species, water and ions of interest, pass through a selectively permeable membrane, followed by mixing with the non-permeating macromolecular ions present in another compartment to finally attain the osmotic equilibrium and the membrane equilibrium, respectively. The former osmotic equilibrium is characterized by the equality of the hydrostatic chemical potential of diffusible water, and the latter membrane equilibrium is characterized by the equality of the combined hydrostatic chemical potential and electrochemical potential of diffusible ions, respectively. The equilibrium Donnan potential is clearly distinguished from irreversible diffusion potential such as the steady-state membrane potential and dialytic potential. The Goldman–Hodgkin–Katz potential and Wagner–Schmalzried potential are briefly introduced and derived on the basis of an electrodiffusion model under the assumption of “the independence principle” for each ion and/or electron participating. Additionally it is justified from the Goldman–Hodgkin–Katz potential and Wagner–Schmalzried potential along with the Daniell potential that the Donnan (Nernst) potential is just the reversible potential across the ideal one single ion permeable membrane and the pure ion-conducting membrane in both directions. Future key issues about the role of the transference number of the ions of interest on a molecular basis in electrochemical kinetics of a variety of membranes should be clarified.