J . Phys. Chem. 1984, 88, 669-671
669
Cage Displacement Model for Inefficient Fluorescence Quenching. Effect of Preferential Fluor Solvation Brian Stevens,* Kenneth L. Marsh, and Margarite A. Sylvia Department of C h e m i s t r y , University of S o u t h Florida, Tampa, Florida 33620 (Received: N o v e m b e r 28, 1983)
A cage displacement model developed to describe the mixed solvent quenching of O2(]Ag) luminescence is applied to the
fluorescence quenching of aromatic hydrocarbons by inefficient liquid quenchers up to the limiting concentration of pure quenching solvent. The nonlinear dependence of fluorescence decay constant (7-I) on quencher mole fraction is quantitatively described by the displacement model if the effects of fluor solvation are accommodated by the introduction of an index of preferential solvation as an empirical parameter.
Introduction The Stern-Volmer' eq I describe the reduction in fluorescence quantum yield rF(nQ) and lifetime 7 ( n Q ) of an emitting state in the gas phase, in the presence of a quenching species Q a t concentration nQ:
= 1+k
YF'/YP
1/ 7 = 1/TO
~ 7 0 n ~
kQnQ
(Ia) (Ib)
kQ is a quenching rate constant. In solution the correlation of fluor-quencher pairs imposes a nonrandom distribution of quenching molecules in the vicinity of a potentially fluorescent species A* with the result that nQ(r) exhibits a fluor-quencher separation ( r ) dependence in this region described by nQ(')
=
nQ(mO)gA*Q(r)
where gA.Q(r)is the radial distribution function for Q molecules around A*. In the presence of a significant concentration of efficient quenching species this leads to a nonexponential decay of A* and a nonlinear dependence of yFo/yFon nQ which have been variously treated in terms of transient (time-dependent) effectsZand/or "static" q u e n ~ h i n garising ~ ? ~ from ground-state A complexation. Recently Keizer4 has given a nonequilibrium statistical thermodynamic description of positive deviations from eq Ia using an analytical expression for gA.Q(r),which requires that the (efficient) quenching is essentially diffusional in nature. The corollary that inefficient quenching is not subject to significant correlation effects is supported by the observation of exponential 02( 'Ag) luminescence decay in pure quenching solvent^.^-^ This contribution reports the measurement of 7 ( n ~for ) several aromatic compounds in the presence of weak quenching liquids up to the limiting concentration of nQ = VQ-lin pure quenching solvent ( V here is the molar volume). It is not expected that these data will be described by eq I b since, a t relatively high quencher concentrations, kQ should vary with solventquencher composition which determines the fluor-quencher encounter rate; moreover a t mole fractions XQ 2 C' where C molecules constitute a solvent cage, there will be on average a t least one quenching molecule Stern, 0.;Volmer, M. Phys. Z . 1919, 20, 183. (2) E.g. Nemzek, T. L.; Ware, W. R. J . Chem. Phys. 1975,62,477. Viriot, M. L.; Andre, J. C.; Ware, W. R. J . Photochem. 1980, 14, 133. (3) Bowen, E. J.; Metcalf, W. S. Proc. R. SOC.London, Ser. A 1951, 206, (1)
937. (4) Keizer, J. J . A m . Chem. SOC.1983, 105, 1494. ( 5 ) Salokhiddinov, K. I.; Byteva, I. M; Dzhagarov, B. M. Opr. Spearosc. 1979, 47, 487. (6) Hurst, J. R.; McDonald, J. R.; Schuster, G . B. J . Am. Chem. SOC. 1982, 104, 2065. (7) Parker, J. G.; Stanbro, W. D. J . Am. Chem. SOC.1982, 104, 2067. (8) Ogilby, P. R.; Foote, C. S. J . Am. Chem. SOC.1982, 104, 2069. (9) Rodgers, M. A. J. J . Am. Chem. SOC.1983, 105, 6201.
0022-3654/84/2088-0669$01.50/0
in the cage and diffusion should not be a quenching prerequisite. Under these conditions a cage displacement model, developed for the nonlinear dependence of 02(lh,)relaxation constant on mixed solvent compositionlo and outlined below, may be appropriate. In the presence of nonquenching and quenching solvents at mole fractions X s , XQ the probability that the excited species A* escapes cage quenching is
Ps = 1 - CXQCYQ where aQis an encounter quenching probability. If v denotes a relative displacement frequency of A * from one solvent cage to the next, the probability that A * survives an interval t after excitation is given by PE(t) = PSYrexp(-t/TO) = exp(-t/r) The lifetime T'(XQ = 0) is reduced to the observed value 7 ( X Q ) expressed as 1/7 = 1,'~~ - u In (1 - CXQaQ)
(IIa)
which in the limit XQ = 1 becomes l/rq
1/70 - up In (1 - CCYQ)
(IIb)
where ui denotes the displacement frequency in pure solvent i. The elimination of CaQ from eq I1 with
+
I / v = X , / V ~ XQ/VQ
provides the relationship
for inefficient quenching (aQ 1 1 ns) exceeded the excitation pulse half-width by a factor of -3, fluorescence response curves were analyzed over two or more half-lives beginning at least 7 ns after the peak signal. Over these ranges convolution of excitation and fluorescence response functions was negligible, and (IO) Stevens, B.; Marsh, K. L. J . Phys. Chem. 1982, 86, 4473.
0 1984 American Chemical Society
670
The Journal of Physical Chemistry, Vol. 88, No. 4, 1984
Letters
1
TABLE I: Solvent Parameters' and Indices of Preferential Quencher Solvation YQ
Q
fluor
pyrene
1 0 3 ~ ~L vP ~ ,
1.05
C,H,Br
pyrene naphthalene chrysene pyrene
S
CH OH C,H,OH n-C,H,OH n-C g H ,,OH n-C,H 1 4 n-C*H,, n-c,OH*, C,- HA -
1 0 3 ~ s v sL, P 0.22 0.64 2.40 11 0.38 0.88 1.8 0.55
o-C,H,Cl,
3.2
CH,OH
0.22
C,H&
1.05
o-C,H,Cl,
3.2
YO
0 0.67 1.2 2.2 -1.1 -0.5
0.06 -0.3 -1.2 -1.2 -0.7 1.0
* Values of
Vi are computed as molecular weiglit/density quotients from data cited in ref 19. Viscosity data a t 25 "C are obtained from the same source by using interpolation where necessary. Viscosities ofo-C,H,Cl, (2.8 CP) and 1-octanol (7 CP) were measured at 25 "C
with a n Ostwald viscometer.
2.0
fir)
1.0
/
"0
/
X
05
10
"
,' Q 0
05
10
Figure 1. Fluorescence decay constant ( l / r ) for pyrene ( 5 X M) as a function of mole fraction X, of bromobenzene. (a) In methanol ( 0 ) and 1-butanol (0). Curves are drawn according to eq V for methanol (solid line) and 1-butanol (dashed line) with tabulated values of WV. (b) In n-hexane (A)and n-decane (A). Curves drawn according to eq V for n-hexane (dashed line) and n-decane (solid line).
f /
a random distribution of weighted residuals from an exponential best fit curve was obtained in each case. Pyrene (zone-refined), chrysene, n-hexane (99+%), n-octane (99+%), n-decane (99+%), and 1-octanol (99+%) were used as supplied by Aldrich; methanol (MCB 99% glass distilled), ethanol (Florida distillers reagent quality), bromobenzene (Baker reagent grade), and o-dichlorobenzene (MCB reagent grade) were not subjected to further purification. Naphthalene (MCB) was recyrstallized from ethanol, and 1-butanol (Mallinckrodt) was dried over calcium hydride and distilled.
Results and Discussion Figure 1 illustrates representative data 1/7(xQ) for pyrene (A*) in the presence of brornobenzene (Q) with alcohols and n-alkanes as cosolvents. According to the absolute rate theory of viscous flow, the displacement frequency vir viscosity vl, and molar volume for solvent i are related by'OJ1 v,q,V, = RT
(IV)
The elimination of v1 from eq 111 and IV leads to eq V which, with
the tabulated values of (vV)~,is used to draw the curves in Figure 1. Although eq V provides a satisfactory description of the experimental data 1/7(XQ) for methanol and n-decane as cosolvents S, it is clearly not appropriate for pyrene-bromobenzene systems with 1-butanol and n-hexane as cosolvents. (11) Glasstone, S.; Laidler, K. J.; Eyring, H. "The Theory of Rate Processes"; McGraw-Hill: New York, 1941.
Figure 2. Data 1/r(Xq) for pyrene quenched by bromobenzene displayed in accordance with eq VII: (a) Cosolvents are methanol ( 0 ) ;ethanol (A); 1-butanol (+); 1-octanol (v);(b) in cosolvents n-hexane (+); n-octane ( 0 ) ;n-decane (A).
It has been recognized12that the cosolvent composition in the solvent cage reflects solute-solvent interactions and may differ from that in the bulk solvent. Preferential solute solvation in mixed solvents has been invoked to account for the nonlinear dependence of solute infrared band widths,12 exciplex emission frequencie~'~ and solvatochromic shifts14on solvent composition. Specifically Yoshino'* has proposed that the mole fractions YA,YB of solvents A and B in the solvent cage are related by
YA/YB = (XA/XB) ~ X
Y PA
where the index Y~ of preferential solute solvation by component (12) Yoshino, T. J . Chem. Phys. 1956, 24, 7 6 . (13) Van, S.-P.; Hammond, G. S. J . Am. Chem. SOC.1978, 100, 3895. (14) Nitsche, K.-S.; Suppan, P. Chimia 1982, 36, 346.
Letters
The Journal of Physical Chemistry, Vol. 88, No. 4, 1984 671
A is determined by the energies of infinite solution E, and EB of the solute in each solvent according to the relationship YA
=
(EA
-
(VI)
The replacement of Xi by Y, in eq V and rearrangement provides the useful relationship VII, used, with tabulated values of ( v V ) ~ ,
position-independent parameter in the development outlined above is probably unrealistic, although the concomitant linear dependence off(7) onf(X) (eq VII) is apparent from Figure 2. The displacement model is based on the premise that diffusion along concentration gradients is not a quenching prerequisite at higher quencher concentrations. It is of interest therefore to compare the limiting form of eq IIa at low quencher concentrations with the Stern-Volmer eq Ib, where the rate constant has the reencounter amplified diffusional kQsv(oQ
