Semiconductors' photoelectrochemistry: A kinetic and thermodynamic analysis in the light of equilibrium and nonequilibrium models

Kinetic and energetic aspects of the photoinduced transfer of charge at the semiconductor-electrolyte interface are analyzed in the Light of the equil ibrium, conventional photoelectrochemical model (A) attributable to Gerisch er, the irreversible, stochastic model (B) proposed by Williams and Nozik, and the nonequilibrium, irreversible model presented here. On the basis of detailed balance and local microscopic reversibility principles, Gerischer' s model presents a complete theoretical framework able to describe the kine tic behavior of a photoelectrochemical cell and adopt the quasi-Fermi Level formalism as an approach to nonequilibrium. illumination conditions Althou gh model A considers entropy loss as unavoidable (the entropy increases to a maximum near equilibrium), it is not able to predict the time dependent e ntropy term which characterizes any irreversible process (nonequilibrium co nditions). By contrast, model B considers detailed balance and microscopic reversibility principles to be incompatible with the existence of irreversi bility, which constitutes a handicap for describing interfacial charge-tran sfer rate constants under illumination. Moreover, the stochastic model does not take into account the entropy that must be lost in any photoelectroche mical reaction. To overcome the limitations of models A and B, a new irreve rsible approach, model C, built up-on the basis of nonequilibrium thermodyn amics and able to reconcile the irreversible character of:photoelectrochemi cal reactions with the production of entropy, is presented here. Identical kinetic behavior is predicted by equilibrium model A and nonequilibrium mod el C, since both-models compute interfacial charge-transfer rate constant r atios in accord with detailed balance and microscopic reversibility princip les. The physical meaning of the nonequilibrium quasi-Fermi energy as well as its thermodynamic implications in concepts Like photogenerated free ener gy and entropy loss in a photoelectrochemical reaction are reexamined in th e light of the Gibbs expression. A new energy balance formalism based upon the concepts of photoelectrochemical affinity and entropy production introd uced.