Turnovers and photocatalysis: A mathematical description

Abstract

In previous articles we dwelled on the usage of relative photonic efficiencies [N. Serpone, G. Suave, R. Koch, H. Tahiri, P. Pichat, P. Piccinini, E. Pelizzetti, H. Hidaka, J. Photochem. Photobiol. A: Chem. 94 (1996) 191; N. Serpone, J. Photochem. Photobiol. A: Chem. 104 (1997) 1] and quantum yields Φ [N. Serpone, R. Terziaw, D. Lawless, P. Kennepohl, G. Suave, J. Photochem. Photobiol. A: Chem. 73 (1993) 11]. Recently, we also provided an experimental protocol to measure Φ in heterogeneous media [N. Serpone, A. Salinaro, Pure Appl. Chem. 71 (1999) 303] to infer which of several photocatalyzed processes might be the more significant and efficient process. In this article we revisit photocatalysis and discuss how to describe mathematically (photo)catalytic activity and how to compare (photo)catalytic activities of various materials. Specifically, we address the usage and provide a kinetic description of the three turnover quantities: turnover number (TON), turnover rate (TOR) and turnover frequency (TOF) as they bear on the (photo)catalytic activity of a given material in heterogeneous solid/liquid or solid/gas (photo)catalysis. We argue that these turnover quantities are conceptually distinct. TON and TOR require knowledge of the number of active sites on the (photo)catalyst’s surface, contrary to the requirement to determine TOF. Most significant, these turnovers also depend on the nature of the active state of the catalyst, and hence on how the active centers are described. This goes back to the differences in the nature of photocatalysis and photoinduced catalysis.