J . Phys. Chem. 1993,97, 11242-1 1248
11242
Fluorescence Quenching in Micelles in the Presence of a Probe-Quencher Ground-State Charge-Transfer Complex Marcel0 H. Gehlen' Instituto de Fisica e Quimica de Sao Carlos, Universidade de Sao Paulo, 13560 Sao Carlos-SP, Brazil
Frans C. De Schryver' Chemistry Department, Katholieke Universiteit Leuven, Celestijnenlaan 200F, 3001 Leuven, Belgium Received: February 18, 1993; In Final Form: August 9, 1993'
Time-resolvedfluorescencequenching experiments combined with stationary measurements are used to investigate nonfluorescent ground-state charge-transfer-complex formation of pyrene with methylviologen in sodium dodecyl sulfate (SDS) micelles. The fluorescence-quenching decay surface and the experimental data from stationary measurements were interpreted by a model based on the statistical aspects of probe-quencher association in a micellar confinement. Data analysis allowed the determination of all model parameters related to the dynamic and static quenching process. In the region of 0.0354l.156 M surfactant concentration, the average aggregation number of the SDS micelles changed from 60 f 3 to 81 f 3, the value of the intramicellar quenching rate constant was in the range (5.33-4.22) X lo7 s-l, and the "apparent" complexation constant was nearly constant at 293 K.
1. Introduction Fluorescence-quenching methods have been widely used in the study of micelles and several other systems capable of forming microdomains in solution.14 The analysis of fluorescence decay surfaces allows one to determine parameters such as the average aggregation number, intramicellar quenching rate constant, and the rate constants related with the binding of probe and quencher to the micelle. The standard equation used to describe the fluorescence decay in micellar solutions was proposed by Infeltas and Tachiyaa6 Advanced treatments considering the effects of micelle polydispersity7J and intermicellar migration of the probee14 have been recently introduced as extensions of the basic model. The study of a ground-state charge-transfer complex of probe and quencher in micellar confinements and its influence on the fluorescence-quenching process has received little attention. Complexation in micellar aggregates may proceed efficiently due to the high local concentration of the reacting species and the properties of the microenvironment.l>l* Probe-quencher intramicellar complexation usually results in a more effective upward curvature of the Stern-Volmer plot of the relative fluorescence intensity when observed using continuous excitation than the calculated relative intensity based on the micellar quenching model parameters determined from time-resolved fluorescence-quenching measurements. Time-resolved decay profiles relate to the fraction of molecules engaged in dynamic quenching while the absolute fluorescence intensity, measured using continuous excitation, is a function of both dynamic and static quenching processes. Fluorescence-quenching experiments are not the only technique that could show evidence of complexation between probe and quencher. For instance, the formation of the ground-statecomplex between pyrene and methylviologen in the presence of sodium dodecyl sulfate micelles is characterized by a red shift of the absorption spectrum of pyrene and more importantly by the appearance, in the visible part of the spectrum, of a new band that has been attributed to the presence of a charge-transfer complexof the donor molecule, pyrene, with the acceptor molecule, methylviologen.1sJ6 In such circumstances, measuring the in-
.
Abstract published in Aduance ACS Abstracts, October 1, 1993.
0022-365419312097- 11242$04.00/0
crease in absorbance of the charge-transfer band upon addition of thequencher allows one to determinethecomplexation constant. The present paper introducesa model which takes into account the dynamic and the static quenching processes in micelles due to probe-quencher complexation. It is shown that analysis of time-resolved and stationary fluorescence quenching data allows one to determine an apparent complexation constant of probe and quencher in the micellar phase. Its relationship with the thermodynamic constantof complexation for a macroscopic phase is discussed on the basis of a stochastic treatment of the complexation process in micellar confinements. As an example, the method is applied to the ground-state complexation between pyrene and methylviologen in sodium dodecyl sulfate micelles. Global analysisof the decay surface with the referenceconvolution method19J0 is used to extract the parameters of the dynamic quenching process. The value of the complexation constant is compared with that reported by Martens and Verhoevenls and that reported by Fornasiero and Grieserl6 using absorption measurements. 2. Theory
If thequenchingin homogeneoussolution occurs as well through a collision process as by ground-state complexation between fluorophore (probe) and quencher leading to a nonfluorescent complex, the stationary relative fluorescence intensity is2'
where IO and Z are the fluorescence intensity in the absence and presence of quencher, respectively, and [Qlt denotes the total quencher concentration. K ~ vand KC are the Stern-Volmer constant and the complexation constant, respectively. KSV = k h where ~ k b is the bimolecular quenching rate constant and TO is the decay time of the fluorophore in the absence of added quencher. The efficiency of the quenching process in a microheterogeneous system is controlled by the local concentrationof quencher in the micelles rather than the analytical concentrationof the quencher, as in the case of the process in homogeneous solution. A key aspect of the fluorescence quenching when the reactants are 0 1993 American Chemical Society
The Journal of Physical Chemistry, Vo1.97, No. 43, 1993 11243
Fluorescence Quenching in Micelles compartmentalized in aqueous micelles, inverted micelles, or microemulsions is the statistical distribution of the quencher and probe. In the absence of a probe-quencher ground-state complex and assuming that both species are Poisson distributed over the micelles, the relative fluorescence intensity in the limit of a low average number of probe per micelle is414 Zo/Z
= 70(4-’ - k )
(2)
where
YJ
XY,Z
d = exP[-Plq
PX
+XB)
(3)
+ (4)ke,, k,/B
(4)
x-
x!(y
We now define an apparent equilibrium constant of complexation,24 Kapp,as a function of the average number of species per micelle
and Y = 701+k
(14)
(5)
Assuming that the probe is almost exclusively solubilized in the micellar phase, then
(6) B = kq + kexq In the equationsabove, k, is defined as the intramicellar quenching rate constant. k and kuq are the rate constants related to the intermicellar migration of the probe and of the quencher, respectively. ( 4 )is the average number of quencher molecules per micelle. Very often, highly hydrophobic probe and quencher pairs are used in experimentsof fluorescencequenching in aqueous micelles. If the probe-quencher pair is completely bound to the micellar phase and no intermicellar migration occurs during the excited-state lifetime of the probe, then eq 2 is simplified to the limiting case of immobile probe and quencher22.23
where [PI, is the analytical concentration of the probe. To derive expressions for observables in time-resolved experiments as well as in measurements using continuous excitation, a simplification of the model, in agreement with experimental conditions, is made. It is considered that due to the low intensity of the excitation light not more than one uncomplexed probe molecule per micelle is promoted to its singlet excited state. The excitation process is represented by
P
= (4)k,2/B2
(7) To derive an expression for the relative fluorescence intensity of a system where probe and quencher, solubilized in a micelle, may form a nonfluorescentcomplex, an approximatekineticmodel based on the particle distribution in a micellar confinement is introduced. Let x, y , and z be the discrete number of quencher, probe, and complex molecules in a given micelle, respectively. The probability of finding a micelle with x quenchers, y probes, and z complexes is defined as the micelle concentration in this configuration, [ M x y J ]divided , by the total micelle concentration, [MI
(9) XYJ
In fluorescence-quenchingexperiments, the probe concentration is usually much lower than the quencher concentration. Typical experimental conditions consist in a variation of the quencher concentration correspondingto changes in the average occupancy per micelle from 0 to 2.0 keeping the probe occupancy constant and below 0.1. An ideal distribution of the quencher over the micellesis therefore a good approximation since the complexation process can be considered as a weak perturbation and PxyJ may be expressed as
This allows one to express the averages as
-
- .
kl+Xk.
M*Xy-lJ MXYJ The time-dependent probability of finding a micelle with one excited probe at time t is governed by the following differential equation:
-dp*xY-lJ - -(ko + xkq)P*xy-lJ dt
The total micelle concentration is
From eqs 8-10, one obtains
where y, the uncomplexed probe occupancy, is larger than or equal to one. A number of different situations concerning the probe and quencher intermicellar mobility can, in principle, be analyzed. However, the most simple case, where both probe and quencher are assumed to remain in the same micelle during the quenching event, is considered here. The fluorescence decay is represented by
(18)
In the presence of a complex between the probe and a nonabsorbing quencher, the absorption spectra of the probe may change upon addition of the quencher, and isosbestic points may be observed (vide infra). Excitation of the system at a given isosbestic point leads to a particular situation where the light intensity of the excitation pulse profile in time-resolved experiments or the light intensity in continuousexcitation of the sample at a given volume element in solution is constant in a series of samples with different quencher concentration. Thus, it follows that the probabilityof finding at t = 0 a micellein the configuration M*,,,,+ due to a &pulse excitation may be represented by where Zand e(P) are the photon intensity amplitude of the delta excitation pulse and the extinction coefficient of the probe at a given isosbestic point respectively. It is implicit in eq 19 that the absorption of the exciting light follows the Lambert-Beer law, which simply indicates that a photon interacting with a micelle containing y probes is y times more likely to be absorbed than a photon which interacts with a micelle containing only one probe.
11244 The Journal of Physical Chemistry, Vol. 97, No. 43, 1993 Direct integration of eq 18 results in eq 20.
P*xy-l,(t) = ImYpxY,exp[-(ko + xk,)tl (20) The fluorescencedecay for &pulse excitation,f(t), is proportional to the following summation over the occupancy configurations:
Gehlen and De Schryver
‘ I
wheref(0) is the amplitude of the decay at time zero. Making use of eqs 10 and 12, eq 2 1 can be expressed as
At) =AO)(v)exp[-kot-
(q)(exp[-k,tI - 111 (22) The relative fluorescence intensity in the absence and presence of added quencher including the static quenching process, observed using continuous excitation, is related to
310
330
350
370
wavelength (11171) Figure 1. Absorption spectra of pyrene (lk5M)in 0.05 M of SDS at several concentrations of methylviologen: (1) 0, (2) 0.27, (3) 0.40, (4) 0.54, (5) 0.80, and (6) 1.07 X lk3M.
The final value theorem in Laplace transform theoryz’ allows direct evaluation of the improper integral in eq 24. Using eq 15, the resulting expression of the relative fluorescence intensity is
The relative fluorescence intensity is then a product of a static quenching factor, 1 K,,(q), and a dynamic quenching factor represented by the Poisson weighted series of (1 xk,ro)-*. Note that a product of two separated terms for each type of quenching process also appears in the expression of the relative fluorescence intensity in homogeneous solution, eq 1. In an investigation of the exciplex formation between stilbene derivativesand methylviologen in SDS micelles using fluorescence quenching method, Whitten and co-workers2*observed that, for all cases investigated, the plots of Io/I versus quencher concentration were nearly linear. Any dynamic quenching component would be expected to be minimal due to the extremely short fluorescencelifetime of the stilbene derivatives. In this situation, where kq70 is very small, the dynamic quenching factor in eq 25 is practically 1 for ( q ) less than 2. As a result, eq 25 may turn into a linear relationship of Io/Z with ( q ) , explaining the experimental findings. The rate constants, ko and k,, and ( q ) can be determined from time-resolved experiments and used to evaluate the dynamic quenching factor. The ratio of the observed relative fluorescence intensity and the calculated dynamic quenching factor is the static quenching factor. This static quenching factor is a result of the presence of a nonfluorescent complex. Note that plotting this ratio versus the quencher occupancy should yield a linear relation with a slope equal to Kwp.
+
+
320 nm and observed at magic angle (54.79 at 390 nm were measured with a single-photon timing technique using a cavitydumped, frequency-doubled DCM (4-(dicyanomethylene)-2methyl-6-(p-(dimethylamino)styryl)-4H-pyran)dye laser synchronously pumped by a CW mode-locked argon ion laser. The number of peak counts in sample and reference was about lo4. All the fluorescence decays were recorded at 20 “C using 1/2 K data points of a Canberra multichannel analyzer. The details of the picosecond timeresolved fluorimeter used for the fluorescence decay measurements reported here were described previously.29 Corrected steady-state fluorescence spectra were recorded on a SLM 8000spectrofluorimeter. Absorption measurements were performed on a Perkin Elmer Lambda 6 UV-vis spectrophotometer. Figure 1 shows the changes in the pyrene absorption spectra upon addition of methylviologen. To have constant optical density along a series of different quencher concentrations and to allow absolute comparison of the total fluorescence intensity obtained using continuous excitation, excitation was performed at the isosbestic point corresponding to 329 nm. 3.2. Global Analysis of the Fluorescence Decay Surface.1gJo Considering the &response function of the micellar quenching kinetics given by eq 22, a feasible model-linking scheme in global analysiswith the reference convolutionmethod can be represented as
3. Experimental Section 3.1. Sample Preparation and Experimental Procedures. Pyrene was purified by twofold low-pressure sublimation. The quencher, methylviologen, was purchased from Fluka and purified by recrystallization from methanol. The surfactant, sodium dodecyl sulfate (Janssen), was purified by recrystallization from a 1:l (v/v) methanol/acetone mixture with carbon black. Milli-Q water was used to prepare thesolutions. All sampleswere degassed by repeated freeze-pumpthaw cycles before the measurements. No fluorescent impurities could be detected from the blank SDS solutions under the experimental conditions used in this work. N-Isopropylcarbazole in butyronitrile (rr= 14.6 ns) or l-cyanopyrene in cyclohexane ( T ~= 20.6 ns) was used as a reference compound. The fluorescence decays obtained by excitation at
It has been demonstratedthat such a procedure results in a superior recovery of model parameters than single-curveanalysis.30 Also, the inclusion of a sample decay with no added quencher (corresponding to sample 1 in the scheme above) and the linking of the probe’s decay time are a pertinent test of the assumed single-exponential decay of the sample in the absence of added quencher. The correctness of the single-exponential decay of pyrene in SDS micelles has been discussed by Siemiarczuk and Ware on the basis of experimental evidences of pyrene lifetime broadening.3‘ Lifetime distribution analysis with the maximum entropy method indicated that the distribution gets broader at surfactant concentrations close to the cmc as well as in the region of high
The Journal of Physical Chemistry, Vol. 97, No. 43, 1993 11245
Fluorescence Quenching in Micelles
TABLE I: Rate Constants and Parameters Associated with the Kinetics of Fluorescence Quenching by Methylviologen in Sodium Dodecyl Sulfate Micelles’ series
I
I1
I11
IV
[SI 35
51
105
156
[Q] (mM) 0 0.1144 0.1716 0.2288 0.3432 0.4576 0.5720 0 0.3020 0.4530 0.6040 0.9060 0 0.3952 0.5928 0.7904 1.1856 2.0946 0 0.6105 0.9157 1.2210 1.8320 2.4420
so(ns)
kq (ccs-l)
(4)
351.8 i 0
53.29 i 0.6
0.258 0.350 0.482 0.813 1.038 1.302
-
361 & 0.4
49.37i 0.46
0.485 0.696 0.899 1.391
-
363.1 i 0.6
45.20i 0.60
0.283 0.430 0.574 0.881 1.564
346 i 0.6
42.23 i 0.47
0.327 0.492 0.655 1.028 1.408
x21
Zx21
rtb
DWc
1.059 0.946 1.021 0.935 1.136 0.938 1.172 1.163 1.054 1.071 1.046 1.128 1.173 0.938 0.893 1.141 1.015 1.193 0.967 1.104 0.973 1.071 1.213 1.178
0.605 -0.551 0.211 -0.672 1.396 -0.633 1.763 2.541 0.845 1.112 0.708 1.939 1.733 -0.627 -1.074 1.421 0.146 1.941 -0.350 1.086 -0.278 0.473 2.172 1.862
0.54 0.25 0.20 0.66 -1.84 0.21 -0.99 -2.44 -2.18 -1.48 -1.33 1.59 0.44 0.98 -0.06 0.88 1.27 0.02 0.54 0.14 0.69 1.11 0.90 -1.66
2.08 2.15 1.99 1.94 1.77 1.98 1.77 1.73 1.73 1.80 1.90 1.95 1.98 2.03 1.93 1.89 2.14 1.89 1.94 2.06 2.20 1.20 1.89 1.60
%d 93.5 97.2 94.4 96.8 93.5 96.3 95.4 93.7 93.7 93.9 95.4 94.6 93.2 95.1 97.1 93.2 96.1 92.3 95.1 94.2 96.4 94.6 92.5 96.0
xZg
ZxZn
NaU
1.018
0.486
61 55 57 64 61 61
1.071
2.194
69 66 64 66
1.047
1.157
1.072
1.841
69 70 I1 72 72 79 80 79
83 85 a [SIand [Q] are the surfactant and quencher concentration, respectively. N- is the calculated average aggregation number (see text for details). 70, pyrene decay time in the absence of quencher; k,, intramicellar quenching rate constant, ( q ) , average number of quenchers per micelle. Runs test. c Durbin-Watson parameter. Percentage of weighted residuals between -2 and 2.
surfactant concentration, where sphere to rod transitions occur. In the experiments reported here, the surfactant concentrations were in between but sufficiently far away from those critical regions. In all cases, the fitting using a single-exponentialdecay function was successful. Increase of the pyrene decay time with the surfactant concentration was observed (vide infra), in agreement with the shift of the maximum of the lifetime distribution reported by Siemiarczuk and Ware.” The amplitudes Aiare not linked. Once the decays arecollected up to a fixed number of peak counts, no relationship between the A, and the factor (1 + KaPp(q))-lmay be detected. From the analysis of the decay surface, it is possible to determine all parameters strictly related to the dynamic quenching. The timeresolved fluorescenceprofiles of the samples, d*(?),were analyzed using the reference convolution method”
where dr(r) and A t ) are the decay of a reference compound measured at the same instrumental settings as used for the sample and the modified sample 6-response function, respect5ely. For a monoexponential decay of the reference compound,f(t) of the micelle quenching kinetics discussed here30 is given by eq 28.
Estimates of the fitting parameters ( T O , k,, (4). and T ~ were ) computed by a global iteratively reweighted reconvolution program based on the Marquardt algorithm for nonlinear least squares. The numerical statistical test to judge the goodness of fit was the calculation of the global reduced chi-square x: and its normal deviate Zxg2.The goodness of fit of individual curves was examined by the Durbin-Watson test statistics, the ordinary runs test, thelocal reduced chi-squarevalue,anditsnormaldeviate. Graphical methods such as the plot of the weighted residuals and the plot of the autocorrelation function were also used in the statistical a n a l y s i ~ . ~ ~Standard .*~ deviations of the optimized parameters were calculated from the diagonal elements of the covariancematrix in the last iteration of the least-squares method.
All calculations in the global program were done on an IBM 6000 computer in single precision. 4. Experimental Results and Discussion 4.1. Time-Resolved Experiments. Table I summarizes the experimentally determined rate constants and parameters associated with the kinetics of the fluorescence quenching of pyrene by methylviologen in SDS micelles as a function of the total surfactant concentration. The model parameters TO,k,, and ( q ) were obtained by simultaneous analysis of five to seven decay traces including the monoexponential decay corresponding to a sample with no added quencher. TO and k, were linked within the same experimental series, while (4) was a local fitting parameter. Judged by the statistical goodness-of-fitcriteria, each global analysis could be considered acceptable. The parameters of goodness of fit of the individual decay traces were also indicative of a good fit. In the present experimental system, Ka&)
