7 April 2000 Ž . Chemical Physics Letters 320 2000 262–268 www.elsevier.nlrlocatercplett Dual asymptotic behavior in geminate diffusion-influenced reaction Kyril M. Solntsev 1 , Noam Agmon ) The Fritz Haber Research Center, Department of Physical Chemistry, The Hebrew UniÕersity, Jerusalem 91904, Israel Received 6 December 1999; in final form 4 February 2000 Abstract The kinetics of excited-state proton transfer to solvent from the strong photoacid 5-cyano-2-naphthol exhibits two different power-law asymptotic tails for acid and base, arising from competition between reversible and irreversible geminate reprotonation. We show that the data are in quantitative agreement with a recently developed theory for this diffusion-in- fluenced reaction. q 2000 Elsevier Science B.V. All rights reserved. 1. Introduction The study of diffusion-influenced reactions in so- lution was initiated by Smoluchowski longer than 80 wx years ago 1 . The simplest case is geminate recom- Ž . bination GR of isolated pairs. In spite of intensive work in the field of GR, there is scarcity of convinc- ing quantitative experimental evidence for diffu- sional effects even in the most comprehensive chem- ical kinetics accounts of diffusion-influenced reac- wx tions 2 . Indeed, diffusional effects are often masked by complicating factors: iodine GR – by vibrational wx relaxation 3 , GR of large organic radicals – by wx wx rotational diffusion 4 or transient solvation 5 . The kinetics of solvated electrons following photoioniza- w x tion of liquid water 6–8 is essentially a three body ) Corresponding author. Fax: q 972-2-6513742; e-mail: agmon@fh.huji.ac.il 1 Also at the School of Chemistry, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel Aviv 69978, Israel. process, since e y may recombine with either H q or aq the OH Ø radical. An unambiguous example of irre- versible GR, in which the ubiquitous power-law behavior characterizing diffusion processes has been w x observed 9,10 , required adjusting unknown diffu- sion coefficients to fit the data. Reversible GR occurs in excited-state proton Ž . w x transfer to solvent PTTS 11–13 , where the kinet- ics obey the transient Smoluchowski equation for diffusion in the proton–anion Coulomb potential with w x ‘back-reaction’ boundary conditions 14,15 . When Ž ) . the excited state lifetime, t , of the acid R OH is 0 Ž ) y . identical to that of the base RO , the ‘corrected’ w ) x Ž . acid fluorescence signal, R OH exp trt , exhibits 0 Ž y3 r2 . a long-time power-law t decay reflecting the probability of the randomly moving proton to re- turn to the excited anion. Under these con- ditions, the corresponding signal from the anion, w ) y x Ž . RO exp trt , does not convey additional inde- 0 pendent information. The situation changes for different lifetimes or in the presence of a competing contact quenching reac- 0009-2614r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. Ž . PII: S0009-2614 00 00190-1