1890
J. Phys. Chem. 1991, 95, 1890-1895
mean that either FTMor J is larger than reasonably assumed which, on the other hand, is not in accord with the size of effects observed in the high-field region where the Ag RPM is effective. Another possibility that the low-field HFC-RPM effect is theoretically overestimated in our MB'/p-I-An'+ system could be sought in the nonapplicability of the semiem irical factor of 1.7 relating AFSM (Eo= 0) and AFSM ( E , >> B,,2 RFC). Whereas this may be a good estimate if no direct recombination of triplet RPs can occur (Le., if AFSM = FTJ, it may not be so if spinmotion-induced recombination and direct triplet RP recombination interfere. In this paper only the To-S spin motion has been explicitly taken into account; a full treatment of the Th,o S process might be necessary to clarify the problem of the low-field effect for RPs with appreciable SOC.
-
7. Conclusion The quantitative study up to high fields of the heavy-atominduced magnetic field effect on the yield of free radicals has allowed us to differentiate the contributions of the triplet exciplex and the geminate radical pair to fast electron back-transfer in triplet electron-transfer reactions producing radicals devoid of Coulombic attraction. The magnetic field dependence exhibited +t high fields where the contributions due to the triplet mechanism are expected to be close to saturation is well accounted for by the radical pair mechanism employing Ag-induced To/S mixing. A refined version of Pedersen's analytical result for the radical pair mechanism taking also into account reaction-induced S/T dephasing and reversible exciplex formation has been derived. In effect these modifications correspond to an enhancement of exchange interaction. The influence of these modifications, which increases with
the reaction diameter, can be compensated by assuming a larger Ag value. At present the accuracy of our knowledge of the g factors of the radicals studied in this work limits the information on the effects related to exchange interaction that can be gained from an analysis of the experimental results. In zero field 90% of the triplets quenched by electron transfer do not reach the stage of free radicals because they follow the heavy-atom-enhanced ISC path in the triplet exciplex. The contribution of back electron transfer in geminate radical pairs originating through dissociation of the exciplex is very low at zero field. In a field as high as 3.3 T where the rate of Ag-induced magnetic To/S mixing in the radical pair corresponds to an effective field difference of about 200 G between both radicals, fractions of 7% (MeOH) to 11% (40% EGLY mixture) of the geminate radical pairs undergo recombination after ISC by the Ag mechanism. From the magnetic field effect contribution due to the triplet mechanism, the decay constants of the extremely short-lived exciplexes that should actually be conceived as contact radical pairs have been obtained as a function of solvent viscosity 7. The dissociation rate constant has been found to be inversely proportional to 9 with the same slope as previously determined for fluorescing singlet exciplexes.60 The effective rate constant of rotational diffusion also varies as 1/7, however, with an 7-independent contribution pointing to some participation of spin relaxation mechanisms other than rotation of the exciplex as a whole. Acknowledgment. Financial support by the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Industrie is gratefully acknowledged.
Diffusion-Limited Reactions at Solid-Liquid Interfaces: Effects of Surface Geometry Joshua Samuel, Michael Ottolenghi,* and David Avnir* Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel (Received: April 23, 1990; I n Final Form: September 4, 1990)
The diffusion-controlled reaction between a molecule (excited Ru(bpy)32+)adsorbed at the irregular surface of porous silicas and a reactant (anthracene) diffusing from an intrapore liquid phase was studied by nanosecond laser excitation. I t was found that the reaction is controlled by the short-range irregularity of the surface but not by the average pore diameter (in the 40-100O-Arange). It is suggested that the chemical reactivity correlates with the fractal dimension of the surface accessible for adsorption.
Introduction A large variety of natural and man-made chemical processes take place at solid interfaces. A quantitative assessment of the reaction kinetics of such systems requires understanding of the effects imposed by the complex geometrical features associated with most porous and amorphous solids. These are described by empirical parameters such as pore size, particle size, and formalisms involving fractal' or spectral2 dimensions. Recent work, both theoretical and experimental, has demonstrated the applicability of the fractal formalism to a variety of problems in heterogeneous chemistry and in surface ~ c i e n c e . ~The effects of ( I ) Mandelbrot, B. B. The Fractal Geometry of Nature; Freeman: San Francisco, 1982. (2) (a) Alexander, S.;Orbach, R. J . Phys. Lett. 1 9 8 2 , 4 6 2 6 . (b) Rammal, R.; Toulouse. G. J . Phys. Lett. 1983, 44, L13.
pore ~ i z eand ~ , of ~ surface fractality6-I2 on photoprocesses have been studied in several laboratories. In spite of the wide interest (3) The Fractal Approach to Heterogeneous Chemistry: Polymers. Colloids, Surfaces; Avnir, D..Ed.; Wiley: Chichester 1989. (4) (a) Turro, N . J.; Zimmt, M.; Gould, 1.; Mahler, W. J . Am. Chem. Soc. 1985, 107, 5826. (b) Turro, N . J. Teirahedron 1987, 43, 7 , 1589. (5) (a) Avnir, D.; Busse, R.; Ottolenghi, M.; Wellner, E.; Zacchariasse, K. J . Phys. Chem. 1985, 89, 3521. (b) Wellner, E.; Ottolenghi, M.; Avnir, D.;Huppert, D. Langmuir 1986,2,616-619. (c) Birenbaum, H.; Avnir, D.; Ottolenghi, M. Langmuir 1989, 5, 48-54. (6) (a) Gritzel, M. In Photochemical Energy Conuersion; Norris, J., Meisel, D., Eds.; Elsevier: Amsterdam, 1989; p 284. (b) Vlachopoulus, N.; Liska, P.; Augustinski, J.; Gratzel, M. J . Am. Chem. Soc. 1988, 110, 1216. (7) Yang, C.-L.; El-Sayed, M. A.; Squib, S . L. J . Phys. Chem. 1987,91, 4440. (8) Pines, D.; Huppert, D. Chem. Phys. Lett. 1989, 156, 223. (9) Takami, A.; Mataga, M. J . Phys. Chem. 1987, 91, 618. (IO) Even, U.; Redeman, K.; Jortner, J.; Maor, N.; Reisfeld, R. Phys. Reu. Lett. 1984, 52, 2164.
0022-3654/91/2095- 1890$02.50/0 0 199 1 American Chemical Society
Reactions at Solid-Liquid Interfaces
The Journal of Physical Chemistry, Vol. 95, No. 5, 1991 1891
in this area, experimental data in well-defined systems are still scarce. A basic problem that has generated considerable interest is the effect of surface geometry on the rate at which a "marked" (e.g., excited) molecule diffuses from a solution to a reactive (e.g., quenching) surface. This problem was analyzed theoretically13J4 and tested experimentally by Pajkossi et aI.l5 in electrochemical experiments involving electrodes fabricated with a specific fractal dimension. In the present work we analyze a related but different system: One in which the "marked" (e.g., excited) molecule is situated at the solid-liquid interface and reacts with a molecule (quencher) diffusing from the intrapore liquid phase, in an Eley-Rideal type process.I6 A related problem has been previously approached by Drake et al.," who studied a reaction of this type where the rate-determining step is the arrival of a gaseous (quencher) reactant from the intrapore volume of a porous solid to an excited adsorbate at the solid surface. Work with a series of homologous porous silicas with different average pore sizes (aps) revealed that, within the "Knudsen regime", i.$, when A, the mean free path of gaseous diffusion, is larger than the aps, reaction rates increase with the average pore size. Kopelman and co-workers approached the problem, in a h > A*. (b) A* and Q are well separated spatially (i.e., the amounts of A* present in the liquid and of Q adsorbed on the surface are negligible). (c) The geometry of the solid support is well defined in terms of its average pore size and of the fractal dimension (D)of the surface available for molecular interactions, as determined from adsorption experiments26-2sand from energy-transfer experiments between adsorbates.20 Our experiments indicate that the quenching rate does not correlate with the aps values of the silicas. Instead, it depends on the irregularity of the surface, as represented by the fractal dimension of the surface accessible to molecular interactions. We have qualitatively confirmed this general trend by Monte Carlo random walk simulations of an analo:ous reaction whose rate is controlled by the diffusion of a reactant from a two-dimensional ( I I ) (a) Avnir, D. J. Am. Chem. SOC.1987, 109, 2931-8. (b) Pines, D.; Huppert, D.; Avnir, D. J . Chem. Phys. 1988.89, 1177-1 180. (c) Seri-Levy, A.; Samuel, J.; Farin, D.; Avnir, D. Stud. Sur/. Sci. Catal. 1989.47, 353-374. (d) Avnir, D.; Citri, 0.;Farin, D.; Ottolenghi, M.; Samuel, J.; Seri-Levy, A. In Optimal Structures in Heterogeneous Chemistry; Plath, P., Ed.; Springer Verlag: Berlin, 1989; pp 65-81, (e) Farin, D.; Kiwi, J.; Avnir, D. J . Phys. Chem. 1989, 93, 5851-5854. (12) (a) Kopelman, R. In The Fractal Approach to Heterogeneous Chemistry; Polymers, Colloids, Surfaces; Avnir, D., Ed.; Wiley: Chichester, 1989; Chapter 4.1.3. (b) Kopelman, R. J . Stat. Phys. 1986, 42, 185. (13) de Gennes, P . 4 . C. R. Acad. Sci. Ser. 2 1983, 296, 881. (14) Pfeifer, P.; Avnir, D.; Farin, D. J . Stat. Phys. 1984, 36, 699; 1985, 39, 262. (15) Pajkossy, T.; Niykos, L. Electrochim. Acta 1989, 34, 2171. ( I 6) Rideal, E. K. Proc. Cambridge Philos. SOC.1939, 35, 130. (17) Drake, J. M.;Levitz, P.; Turro, N. J.; Nitsche, K. S.;Cassidy, K. F. J . Phys. Chem. 1988, 92, 4680. (18) Prasad, J.; Kopelman, R. J . Phys. Chem. 1987, 91, 265. (19) Kalyanasundaram, K. Coord. Chem. Reu. 1982, 46, 159. (20) (a) Pines, D.; Huppert, D. Isr. J . Chem. 1989, 29, 473. (b) Pines, D.;Huppert, D. J. Chem. Phys. 1989, 91,1298.
TABLE I: Surface Areas (BET) and Representative Coverage (Adsorption) Values for Ru(bpy)32+,for the Various Commercial Porous Adsorbates Employed surf. area Ru(bpy),2+ silica system and its aps, 8, Si-40 Si-60 Si- 100 Si- 1000 CPG-75 CPG- 1000 Vycor (60)
N2BET, m2/g 700 500 250 20 182 26 98
coverage, pmol/g 13.6 17.2 12.7 1.5 15 2.3 3.3
% coverage 6 9 10 12 9 10
"liquid" phase to a fractal line. Although formally representing a strictly photophysical process, our results are relevant to any diffusion-controlled reaction at complex solid-liquid interfaces. They also bear on the rates of diffusion of nonadsorbing solutes in the liquid phase trapped in the complex pore network of irregular solids.2' Experimental Section
Silica Samples and Chemicals. The following silicas, in which the numbers refer to the average pore diameter, were used: Si-40, Si-60, and Si-I00 (Merk lichroprep), Si-1000 (Merk fractosil). Controlled porous glasses (cpg-75 and cpg-1OOO) were from C.P.G. Inc. Porous Vycor was a 7930 Corning sample. The effective surface of the glasses (BET) is given in Table I. Ruthenium tris(bipyridy1) chloride and anthracene (Gold Label) were from Aldrich. Methylene chloride (Fluka) was dried over molecular sieves. Sample Preparation. R ~ ( b p y ) , ~was + adsorbed by overnight equilibration with an aqueous solution, followed by sample filtration and drying. The amount of R ~ ( b p y ) , ~adsorbed + was determined by spectrophotometric analysis of the filtrate. In all cases a large percentage of the R ~ ( b p y ) , ~in+ the solution was adsorbed so that the residual amount left in the pore volume after filtration was minimal. Adsorption by equilibration, rather than by solvent evaporation, was employed so as to avoid nonhomogeneous (aggregation) phenomena. The surface area available for R ~ ( b p y ) , ~adsorption + and thus the percent coverage was estimated using the D (energy transfer) valuesZoand the crosssectional areas of R ~ ( b p y ) , ~(172 + AZZ2)and of nitrogen (16.2 A*23). The N2 BET values of the surface area were those supplied by the producer (Table I). The sample was transferred to the sidearm of a I-mL cuvette and dried under low pressure (IO-* Torr) at 100 OC. A solution of anthracene in methylene chloride was then added to the sidearm and the sample degassed by several freeze-thaw cycles to remove oxygen. Fluorescence Lifetime Measurements. At low anthracene concentrations R ~ ( b p y ) , ~was + excited with the 337. I-nm line of a pulsed P.R.A. LN-1000 (0.5 ns, 1.5 mJ) nitrogen laser. Fluorescence was collected through a monochromator onto a multichannel plate (Hamamatsu R 15644). The signal was amplified and digitized by a Tektronix 791 2 AD oscilloscope followed by averaging and storing using an Olivetti PC. The fwhm of the system was 1 ns. To avoid absorption of the exciting light by anthracene at relatively high concentrations, the 337. I-nm N2 line was replaced by the visible lines (-450 nm) of a dye laser (Molectron DL-200, pumped by a UV-14 nitrogen laser). The fwhm of this system was -10 ns. Adsorption Measurements. The degree of anthracene adsorption on the silica surfaces employed was measured by overnight equilibration of the adsorbant with a minimum amount of an anthracene solution. The change in anthracene concentration in the supernatant was measured spectrophotometrically on a Cary 219 instrument. On Si-60 these experiments set an upper limit
-
(2!) Spiro, M. In Comprehenriue Chemical Kinetics; Compton, R. G.. Ed.; Elsevier: Amsterdam, 1989; Vol. 28. (22) Wolfgang, S.; Gaffney, H. J . Phys. Chem. 1987, 57, 5395. (23) Gregg, S . J.; Sing, K. S. W. Adsorption, Surface Ara and Porosity; Academic Press: London, 1982.
Samuel et al.
1892 The Journal of Physical Chemistry, Vol. 95, No. 5, 1991 5'>.
%, , '
