J . Phys. Chem. 1987, 91, 6088-6089
6088
Fractal Modeling of Luminescence Quenching in Microemulsions P. Lianos* and S. Modes University of Patras, School of Engineering, 26000 Patras, Greece (Received: June 4, 1987)
Luminescence decay profiles of R~(bpy)~*’ in the presence of Fe(CN)63 were analyzed for a series of water-in-oil microemulsions. The applicability of various decay models has been tested with a least-squares fit. It has been found that fractal modeling can be applied to quenching in microemulsions when quencher exchange between droplets is allowed.
Micelles and microemulsions have been repeatedly studied with fluorescent probes. The most generally applied model to describe fluorescent quenching under pulsed excitation is given by
I = A l exp(-Azt
+ A3[exp(-A4t) - 11)
(1)
A2 = ko + kJQ1
and A3 = [ Q l / W l
(2)
where ko is the decay rate constant in the absence of quencher, k , is the rate constant for the exchange of quenchers between micelles (or microdroplets), [Q] is the quencher and [MI the micellar concentration, and A4 (or k,) is the quenching rate constant. These equations are explained in several publications since literature is very rich on this subject.’ When the exchange of quenchers is negligible, A2 = ko. On the contrary, improved but more complicated versions of eq 2 have been used in cases where the quencher exchanges also between the interface and the continuous phase.2 In all cases, A2 and A3 depend linearly on [Q], provided that [MI stays constant with changing [Q]. Equation 1 has been successfully employed to study a great variety of organized However, in extreme cases of multicomponent microemulsions and in particular water-in-oil microemulsions, departures from linearity between A2 or A3 and [Q] are ~ b s e r v e d . This ~ problem has been directly or indirectly treated by some recent works. Thus, it has been found that large solubilizates affect the micellar size,s while micellar polydispersity6 or fragmentation-coagulation’ complicates the kinetics of luminescence quenching in microemulsions. We have attempted to circumvent this question by studying fluorescence (luminescence) quenching in microemulsions from a different point of view. Thus, in the present work we test the applicability of the recently developed procedures of fractal modeling of disordered systems to microemulsions. An organized assembly could be considered as a three-dimensional space embedding two domains of fractal dimensions, one hydrophobic and one hydrophilic. Each microdroplet of a microemulsion is a solubilization site for lumophore (1) (a) Atik, S.S.; Thomas, J. K. J . Am. Chem. SOC.1981,103,4367.(b) Atik, S.S.; Nam, M.; Singer, L. A. Chem. Phys. Lett. 1979, 67,75. (c) Yekta, A.; Aikawa, M.; Turro, N. J. Chem. Phys. Lett. 1979,63,543. (d) Baxendale, J. H.; Rodgers, M. A. J . Am. Chem. SOC.1982,86,4906. (e) Lianos, P.; Dinh-cao, M.; Lang, J.; Zana, R. J . Chim. Phys. Phys.-Chim. Biol.
1981,78, 497. (2) (a) Tachiya, M. Chem. Phys. Lett. 1975,33,289. (b) Infelta, P. P.; Gratzel, M.; Thomas, J. K. J . Phys. Chem. 1974,78, 190. (c) Grieser, F. Chem. Phys. Lett. 1981,83,59. (d) Almgren, M.; Lofroth, J.-E.; van Stam, J. J . Phys. Chem. 1986,90,4431. ( e ) Gelade, E.; De Schryver, F. C. J . Photochem. 1982, 18,223. (0 Malliaris, A,; Lang, J.; Zana, R. J . Phys. Chem. 1986,90,655. (3)(a) Lianos, P.; Lang, J.; Strazielle, C.; Zana, R. J . Phys. Chem. 1982, 86,1019. (b) Zana, R.; Lianos, P.; Lang, J. J . Phys. Chem. 1985,89,41.(c) Almgren, M.; Swarup, S.; Lofroth, J.-E. J . Phys. Chem. 1985,89,4621. (d) Gelade, E.; Boens, N.; De Schryver, F. C. J. Am. Chem. SOC.1982,104,6288. (e) Hatlee, M.; Kozak, J. J.; Rothenberger, G.; Infelta, P. P.; Gratzel, M. J . Phys. Chem. 1980,84, 1508. (4). Lianos, P.; Zana, R.; Lang, J.; Cazabat, A.-M. In Surfactants in Solution; Mittal, K. L., Bothorel, P., Eds.; Plenum: New York, 1986; Vol. 6,p 1365. ( 5 ) Pileni, M. P.; Brochette, P.; Hickel, B.; Lerebours, B. J . Colloid I n terface Sci. 1984,98,549. (6)Almgren, M.; Lofroth, J.-E. J . Chem. Phys. 1982,76,2734. (7) (a) Malliaris, A.; Lang, J.; Sturm, J.; Zana, R. J . Phys. Chem. 1987, 91,1475. (b) Lang, J.; Zana, R. J . Phys. Chem. 1986,90, 5258.
TABLE I: Data Obtained by Least-Squares Fit with Various Quenching Models and Various Water-in-Oil Micr~emulsions~~ microdecay fractal emulsion no. model k., s-] M-’ effective kOb expnt 0 2.6 X lo6 s-I 1.2 X lo9 6.6 X lo6 s-l 1.5 X lo7 (s-’)(M-] 0.69 5.1 x 109 2.5 x 107 s-I 1.5 X lo8 (s-’)fM-’ 0.77 1.7 X 10” (s-I,’ M-’ 0.93 -1.0
x
-
1010
1.5 x 107 s-1 2.0 x 109 ( S - I ~ M - I
0.98
OFit with the last 360 points. *fexponent introduced to take care of the units of time.
and quencher molecules, which are usually chosen to reside in only one of the two domains. In the time scale of the excited lumophore a microemulsion allows or does not allow exchange of solubilizates between sites, depending on the nature of the water41 interfa~e.4.~ A “rigid” microemulsion forces solubilizates to stay resident at sites, i.e., inside the micrcdroplets. On the contrary, in a “nonrigid microemulsion the solubilizates can exchange between sites in a way that for the present discussion will be considered equivalent to a random walk of the lumophore from site to site. In all cases the transient luminescence intensity is described by the following general equation8q9 k
I = lo exp(-kot)nexp(-k,(ri)t) i=1
(3)
where ri is the center-tecenter distance between interacting species. The main feature of this equation is the dependence of the quenching rate constant on space and consequently on time. If an average k, extending to all quenchers is considered instead of the time-dependent one, then k, is proportional to the number of quenchers at a site. Assuming Poisson statistics for the distribution of quenchers, one obtains eq 1 through 3.8 It is obvious then that eq 1 does not take into account the inhomogeneity of the interaction medium. The interaction between species diffusing in disordered media has been previously treated.’@I3 The inhomogeneity of space reflects into eq 3 on the dependence of k, on ri and subsequently on time. The interaction between an excited lumophore and a (8) Habti, A,; Keravis, D.; Levitz, P.; van Damme, H. J . Chem. Soc., Faraday Trans. 2 1984,80,67. (9) Blumen, A. Nuouo Cimento 1981,63,SO. (10)Blumen, A,; Klafter, J.; Zumofen, G. In Fractals in Physics; Pietronero, L., Tosatti, E., Eds.; Elsevier: Amsterdam, 1986; p 399 and references therein. (1 1) (a) Klymko, P. W.; Kopelman, R. J. Phys. Chem. 1982,86,3686.(b) Klymko, P. W.; Kopelman, R. Ibid. 1983,87,4565. (c) Newhouse, J. S.; Argyrakis, P.; Kopelman, R. Chem. Phys. Lett. 1984,107,48.(d) Kopelman, R.J . Stat. Phys. 1986,42,185. (e) Prasad, J.; Kopelman, R. J . Phys. Chem.
1987,91,265. (12) Djordjevic, Z. In Fractals in Physics; Pietronero, L., Tosatti, E., Eds.; Elsevier: Amsterdam, 1986; p 413. (13) (a) Evesque, P. J . Phys. (Les Ulis,Fr.) 1983,44,1217. (b) Alexander, S.; Orbach, R. J . Phys., Lett. 1982,43,L-625. (c) Rammal, R.; Toulouse, G. J . Phys., Lett. 1983,44, L-13.
0022-3654/87/209 1-6088$0 1 .SO10 0 1987 American Chemical Society
The Journal of Physical Chemistry, Vol. 91, No. 24, I987
Letters
k. -25' +8,4;
Residuals
-2s J
Bssidual I
6.
a 299 499 688 898 lDol nr Figure 1. Luminescence decay profiles obtained with microemulsion 1 (A) and microemulsion 3 (B).I4 quencher, of concentrations [L*] and [Q], respectively, obeys the differential equation -d[L*]/dt = k,[L*][Q] where k, is a time-dependent value. If we consider the excited lumophore as a random walker visiting sites occupied by quenchers (traps), then in analogy to E v e s q ~ ek,l ~=~ k ' N ( t ) / twhere N ( t ) is the total number of sites visited. N ( t ) ;ti/2, d being the so-called spectral dimension.l&I3 Substitution into eq 3 yields the following equation, which we propose in substitution of eq 1
-
I = 10 expi-kot - (k,'[Q1 /f)tq
(4)
wheref = d/2 and k,' is the effective quenching rate constant which is now time-independent. Equation 4 has been used to describe supertrapping processes in doped crystals13awhere the concentration nA of the excited donor is much smaller than the concentration of the unexcited acceptors (corresponding to [L*]
