Determination of kinetic parameters of probe migration in micelles

5592

J . Phys. Chem. 1992, 96, 5592-5601

(20) Tolman, R. C. J . Chem. Phys. 1948, 16, 758; 1949, 17, 333. (21) Ben-Shaul, A.; Szleifer, I.; Gelbart, W. M. J . Chem. Phys. 1985,83, 3597. Szleifer, I.; Ben-Shaul, A,; Gelbart, W. M. J . Chem. Phys. 1986, 85, 5345. (22) Flory, P. J. Statistical Mechanics of Chain Molecules; Wiley: New York, 1969. (23) Shing, K. S.; Gubbins, S. T. Mol. Phys. 1981, 43, 717. (24) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Oxford University Press; Oxford, 1989, Section 2.4 and references therein.

(25) Fujita, H.Polymer Solutions, Elsevier: Amsterdam, 1990; p 287. (26) Puwada, S.; Chung, D. S.;Thomas, H.G.;Blankschtein. D.; Benedek, G. B. To be published, (27) Missel, P. J.; Mazer, N. A.; Benedek, G. B.; Young, C. Y.; Carey, M. C. J . Phys. Chem. 1980, 84, 1044. (28) Ben-Shaul, A.; Rorman, D. H.; Hartland, G. V.; Gelbart, W. M. J . Phys. Chem. 1986, 90, 5277. (29) Kaler, E. W.; Murthy, A. K.; Rodriguez, B. E.; Zasadzinski, J. A. N. Science 1989, 245, 137 1 .

Determination of Kinetic Parameters of Probe Migration in Micelles Using Simultaneous Analysis of the Fluorescence Decay Surface M. H. Getden,*.+N. Boens, F. C. De Schryver,* M. Van der Auweraer, and S. Reekmans Chemistry Department, Katholieke Universiteit Leuven, Celestijnenlaan ZOOF, 3001 Leuven, Belgium (Received: December 19, 1991)

Global analysis with the reference convolution method is applied to study the effect of probe migration between micelles on the fluorescence quenching. Analysis of synthetic single-photon timing data based on a modified Infelta-Tachiya equation including probe migration is used to test the capability to discriminate between competing models and determine the accuracy of the recovered model parameters. The applicability of this simultaneous analysis is extended to real experimental data obtained for quenching of the probe sodium 1-pyrenesulfonate by the quencher N-tetradecylpyridinium chloride in aqueous hexadecyltrimethylammonium chloride (CTAC) micelles. Values of the rate constant of quenching and probe migration as well as the mean aggregation number ( v ) of CTAC are determined as a function of the surfactant concentration. In the range 0.02-0.07 M surfactant no appreciable variation in the mean aggregation number of CTAC micelles and also in the quenching rate constant (k,) was observed. The average values of v and k, were 82 f 7 and (8.4 0.5) X lo7 s-l, respectively. Within this range of surfactant concentration the probe migration rate constant ( k ) was a linear function of the micelle concentration ([MI) (k = k,[M] with k, = (3.0 0.4) X lo9 L mol-l s-l). Analysis of the system where the probe sodium l-pyrenesulfonate was replaced by 1-methylpyrene confirms that this more hydrophobic probe does not migrate between micelles during its excited-state lifetime.

*

*

1. Introduction Fluorescence quenching in micellar solution has been a topic of extensive study during the past two decades. Structural properties, such as the mean aggregation number, as well as kinetic parameters correlated with the dynamics of the probe-quencher-micelle system have been determined by this technique. In the early studies of micellar systems the probe migration among micelles has been neglected; Le., the probe has been considered as an immobile molecular species residing in the same micelle during its excited-state lifetime.'-5 Although the assumption of an immobile probe may be valid for a class of highly hydrophobic probes which do not exchange via the aqueous phase or by micelle collisions, it cannot be valid in general. At a higher concentrations of aqueous micelles and/or in the presence of small amounts of additives such as short-chain alkyl alcohols or electrolytes, a possible mechanism for probe migration is hopping of the probe between micellesU6This process becomes important when the probe is a singly or doubly charged species with opposite sign to that of the micelle surface.' In the case of inverted micelles and microemulsions the latter mechanism may still be valid, but an alternative mechanism for the exchange of solubilized species in the water droplets is the so-called fusionfission process.*-I0 Almgren et al.II pointed out that, in a general case including the exchange of quenchers via the bulk solution, probe migration by hopping, and the fusion-fission process, the fluorescence decay might still be described in a good approximation by an InfeltaTachiya but with a generalized interpretation of the parameters of the decay function. The Laplace transform and the matrix formulation (the eigenvalues and eigenvectors problem) 'Permanent address: IFQSC, Universidade de SZo Paulo, S I 0 Carlos, 13560, SP, Brazil.

0022-3654/92/2096-5592$03.00/0

methods have been applied by Tachiya in the numerical analysis of the probe migration and fusion-fission processes.12 Very recently, Gehlen et al.I3J4derived an exact solution based on the integral equation formalism for the problem of probe migration. The solution to the fluorescence decay, At),after 6 pulse excitation is found by solving an integral equation of the convolution type

At) = kAt)

@

g(t) + g(t)

(1)

with g ( t ) = exp[-yt

+ p(e-@'- I)]

(2) of the rate constants of probe migration, quenching, and quencher exchange. k is the probe migration rate constant, and 0 denotes the convolution operator. The derivation of eq 1 and the definition of all parameters are reported e1~ewhere.l~ The solution of this integral equation can be expressed by the following von Neumann type series. y, p, and j3 are functions

At) = g(t) + W )@ g ( t ) + k2g(t)@ g(t)@g(t) + ...

(3)

The solution to a particular case of an immobile quencher (quencher with a small probability of undergoing migration between micelles or exchange via the aqueous phase during the excited-state lifetime of the probe) can still be expressed by eq 3 , but with g(t) reduced to a more simple formI4 g(t) = exp[-(ko

+ k)t + ii(e%'

- l)]

(4)

where ko is the reciprocal of the probe's excited-state singlet lifetime in the absence of quenchers, k is the quenching rate constant, and ii is the average number o? quenchers per micelle assuming a Poisson distribution (ii = [Q]/[M], where [Q] and [MI denote the concentration of quencher and micelle, respectively). 0 1992 American Chemical Society

The Journal of Physical Chemistry, Vol. 96, No. 13, 1992 5593

Probe Migration in Micelles It has been shown that fitting of synthetic fluorescence sample decays (simulated data based on eqs 1 and 4) by an InfeltaTachiya type equation At) = A l exp[-Azt + A3(exp[-A4rl - 111 (5) usually yields acceptable statistical parameters.’, Based on this fact and using the Almgren approximation, the following approximate analytical expressions of the A parameters have been developed:I4 AI Az = ko

+ k(1 - exp[-iik,(k, + k)-’])

(6) (7)

- exp[-iik,(k, + k)-l])/k,n)z

(8)

- k(l - exp[-iik,(k, + k)-I])/k,ii)-l

(9)

A3 = A(l - k(1 A, = k,(l

=f(O)

In the present contribution, global analysis with the reference convolution is applied to a series of simulated data based on eqs 5-9 in order to investigate the recovery of the model parameters ko, [MI, k , and k. In a second part, this approach is used to analyze rea? single-photon timing data of the experimental micellar system hexadecyltrimethylammonium chloride/N-tetradecylpyridinium chloride/sodium 1-pyrenesulfonate. Analysis of the system where sodium 1-pyrenesulfonate is replaced by 1methylpyrene is also performed.

2. Analysis of Simulated Data 2.1. Referewe Convolution Method. The reference convolution method is one of the best routes in single-photon timing experiments to correct for the wavelength variation of the instrument response function. Is-’’ The time-resolved fluorescence profile of the sample, ds(AeX&,,,r), obtained by excitation at wavelength hX and observed at emission wavelength A,, can be written as ds(Aex,AemJ) 1(AexJemJ) @ f(AcxrAem,f) (10) where l(Aex,Aem,r) is the instrument response function and f(&x,Aem,r) is the true sample response function. In the reference convolution method, eq 10 is replaced by ds(L,xJem,t) = dr(AexAem,t) 0 RAcx,Ae,,t) (1 1) In eq 11, d,(A,,,A,,,t) is the decay of a reference compound measjred at the same instrumental settings as used for the sample and f(ACX,ACm,r) is the modified sample response function. It has been shown that if the fluorescence 6 response function of the reference compound is m o n o e x p o r ~ e n t i a l ~ ~ J ~ J ~ f X t ) = or ex~[-t/rrl

(12) where ‘I,denotes the decay time of t_he reference compound and a, the corresponding scaling factor,f(t) satisfying eq 11 is given by At> = ~F’VTO) 6 ( t ) + ~ ( t )+ f i t ) / r r ~ (13) where 6 ( t ) is the Dirac delta function andf’(t) denotes the time derivative. Considering the 6 response function given by eq 5, the following modified sample response function can be written Rt) = al{6(t) + (1/‘1, - A -~ A3A4 exp[-A,t]) exp[-Azt + A3(exp[-A4r] - l)]) (14) with 01 =

A I/ a ,

2.2. Synthetic Data Generation and the Global Analysis. Synthetic sample decays with K data points were generated by convolution of f ( f ) (eq 5) with a nonsmoothed measured instrument response function I(r). Values of 125 ns, IO7 s-l, and M were assumed for l/ko, k,, and the micelle concentration [MI, respectively. The value of the average occupancy, ii, was changed from 0.5 to 3.0. The value of the probe migration rate constant, k, was kept constant within the same series of sample decays at different values of A. Different sets of decay traces were generated with k varying from the low limit of 0.05kqto 0.4kq.

The reason for this upper bound limit is the range of k in which the approximate solution remains valid’, (vide infra). Synthetic reference decays were simulated by convolution of monoexponential reference decaysf,(f) (eq 12) with the same instrument response function l ( t ) . The reference lifetime and the time increment per channel were 5.0 ns and 0.7 ns/channel, respectively. By adjusting the preexponential factors, the number of peak a u n t s of the sample decays was always within the range 8 X lo3to 104. Each generated ds,drpair had different and independent Poisson noise. More details about the synthetic data generation are given el~ewhere.”~~~ Estimates of the fitting parameters (ko, [MI, k,, k, and T J were computed by a global iteratively reweighted reconvolution program based on the Marquardt algorithmz1for nonlinear least squares. The entire decay profiles, including the rising edge, were analyzed. In this procedure, several (synthetic) fluorescenp decays were analyzed simultaneously according to eq 11 withflt) given by eq 14. Two procedures in the simultaneous analysis of synthetic fluorescence decay curves were followed. In the first one, the five model parameters k,,, [MI, k,, k, and rr were linked. In the second one, the micelle concentration ([MI) was not linked. Under this condition, a monoexponential decay with a rate constant ko (corresponding to a sample with no quencher) was included together with decays at different ii. This procedure was investigated because it is very close to what could be expected in real experiments. The monoexponential decay of the probe in the micelle can be always added to a series of decays. Experimental errors in the determination of the concentration of surfactant or quencher may be present in a real data set. Also, the intrinsic dependence of the average number of quencher per micelle with the quencher concentration has been observednZ2 The numerical statistical tests to judge the goodness of fit were the calculation of the global reduced chi-square statistic xz and its normal deviate ZxZgThe goodness of fit of the individual &cay curves was examined by the Durbin-Watson test statistics (DW),u the ordinary runs test (rt),24the local reduced chi-square value xzl, and its normal deviate ZxzI.Graphical methods such as the plot of the autocorrelation function values25and the plot of the weighted residuals were also used in the statistical analysis. Standard deviations of the optimized parameters were calculated from the diagonal elements of the covariance matrix in the last iteration of the least-squares minimization. All calculations in the global program were done on an IBM 6150 or System 6000 computer in single precision. 2.3. Simulated Results. In this section, synthetic fluorescence sample decays are analyzed individually (single-curve approach) and simultaneously (global approach) according to the methodology described in section 2.2. The main objective here is to recover the model parameters ko, [MI, k,, and k. The parameters recovered by single-curve analysis and global analysis (with all parameters linked) are plotted in Figure 1 as a function of [QJ. The true values of k,,, [MI, k,, and k are shown as horizontal lines. Judged by the statistical fitting criteria, all the fits were amptable. The results clearly show the lower accuracy of the single-curve analysis in recovering the model parameters ko, [MI, and k. Only parameter k, is recovered accurately by single-curve analysis, but it has a large standard deviation. On the other hand, simultanaus analyses with various combinations of experiments could recover the parameters accurately. (The relative percent errors are less than 1.5% on average.) Also, this analysis usually results in recovered parameters with high precision. When collecting decay traces, one either can measure a single decay curve with high signal-to-noise ratio and analyze it individually or, alternatively, during the allocated time can collect several decays with lower total number of counts and analyze the resulting curves simultaneously. In order to test which of the two strategies is the best, two sets of synthetic decay traces with 20 X IO3 and 5 X lo3 peak counts were generated and analyzed as follows. Simultaneous analysis of four samples with 5 X IO3peak counts each was then compared to the single-curve analysis of samples with 20 X lo3peak counts. The total numbers of counts in both analyses were practically the same. The results for the

5594 The Journal of Physical Chemistry, Vol. 96, No. 13, 1992

Gehlen et al. 8.5 -

kl. 80

A A

A .

-

8.0

-

-

A

A

A

A

o m o m o m O

A

A

0

0

Y

1

b l

,1

O9

'Im

L1

1

I ,

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1 6 --M

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2c

[a]

l4i 12

8i +

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.

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,

,

,

,

,

,

,

,

,

,

,

.

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[QI mM Figure 1. Recovered model parameters ko,k,, k, and [MI from statistically acceptable single- and multiple-curve analyses according to eq 14 plotted versus [Q]: (0)single curve, lo4 peak counts; (0,0 , A, V, A) multiple curve, lo4 peak counts; (speckled 0)single curve, 2 X lo4 peak counts; (speckled A) multiple curves, 5 X lo3peak counts. The parameters ko. [MI, k,, k, and T , were linked in the simultaneous analysis. Values of the rate constant are in &, and concentrations are in mM. The standard deviations on the global fitting parameters are shown as vertical bars when they are not within the plot symbols, while those on the single-curve fitting parameters are not shown because they are larger than 100% of the true values.

recovered parameters are also shown in Figure 1 as speckled symbols. They indicate that no substantial improvement is obtained in the parameter recovery in single-curve analysis by increasing the number of peak counts of the decay traces from lo4 to 2 X lo4. On the other hand, simultaneous analysis is able to recover the model parameters with much higher accuracy than single-curve fitting. Considering those results and the fact that the number of peak counts is proportional to the data collection time, it is recommended to collect a series of decay traces and

Figure 2. Recovered model parameters ko,k,,, [MI, and k from statistically acceptable multiple-curve analyses according to eq 14 plotted versus [Q]. See text for details.

analyze them simultaneously rather than to collect a single decay trace with high signal-to-noise ratio and analyze it individually. Figure 2 shows the recovery of the model parameters using the m n d procedure. The open symbols represent the results obtained from simultaneous analyses of six curves at various nonzero quencher concentrations. The parameters k and k were linked while [MIwas not linked in the analyses. +he parameters ko, k,, and [MIwere the same in all global analysis while three different values for k were used. The closed symbols represent the results obtained from simultaneous analyses of four curves, three a t different nonzero quencher concentrations plus a monoexponential decay (with linked k,) corresponding to a sample with no added quencher. It can be seen that the reduction of the number of analyzed curves a t different quencher concentrations together with the inclusion of the monoexponential decay yields

The Journal of Physical Chemistry, Vol. 96, No. 13, 1992 5595

Probe Migration in Micelles

TABLE I: Recovered Model Parameters kO,[MI, k,, and k from Global Analysis of Synthetic Sample Decays Generated from Eqs 1 and 4 and A ~ l v z e dwith the Approximate Solution (&I 5)" DW' Zxzl rtb k x2, %d x2, Zx2, [QI, mM k0 [MI, mM kq 0.953 -0.733 0.61 1.93 96.4 0.998 -0.074 0 8.0 f 0.012 1.024 0.378 0.79 2.16 95.4 0.960f 0.012 0.5 9.50 f 0.15 0.92 f 0.12 0.983 -0.270 -0.11 1.86 95.6 0.971 f 0.010 1 .o 1.100 1.571 -0.31 1.86 95.0 0.967 f 0.009 1.5 0.958 -0.663 1.01 1.92 95.6 0.960 f 0.008 2.0 0.63 1.94 96.4 0.952 -1.688 0.953 -0.744 0 8.01 f 0.01 0.951 -0.766 -0.94 1.88 96.0 0.998 f 0.009 0.5 9.81 f 0.16 1.72 f 0.12 0.890 -1.723 0.38 1.90 96.0 0.983 f 0.010 1 .o 0.973 f 0.009 0.977 -0.360 -0.49 1.96 95.8 1.5 1.016 0.68 1.97 96.2 0.978 0.008 0.253 2.0 0.985 -0.655 0.96 1.92 96.4 0.996 -0.130 0 8.00 i 0.01 1.004 0.056 1.75 2.14 96.4 0.977 f 0.014 0.5 9.42 f 0.16 2.28 f 0.14 0.984 -0.253 0.962 f 0.010 0.73 1.98 95.6 1 .o 0.38 2.05 97.2 0.962 f 0.010 0.954 -0.720 1.5 0.951 f 0.010 1.110 1.729 -1.45 1.83 94.6 2.0 0 8.00 f 0.01 0.957 -0.679 0.78 1.93 96.4 1.023 0.820 0.824 0.965 f 0.016 1.053 1.71 2.04 94.4 0.5 1.92 96.4 0.929 f 0.013 8.94 f 0.18 3.26 f 0.16 0.924 -1.199 -0.85 1 .o 0.924f 0.012 1.136 2.104 -0.76 2.05 94.5 1.5 0.914f 0.011 1.082 1.267 -0.63 1.91 94.5 2.0 0 8.00 f 0.01 0.956 -0.696 0.96 1.93 96.4 0.954 -1.601 0.941 -0.918 -0.16 1.97 96.0 0.920 f 0.016 0.5 8.49 f 0.18 4.35 f 0.18 0.958 -0.656 -0.91 1.95 96.2 1 .o 0.900 f 0.014 0.886 f 0.013 0.59 1.95 97.1 1.5 0.906 -1.461 1.038 0.594 -1.99 1.95 94.5 0.850 f 0.012 2.0 0.96 1.93 96.4 1.035 1.233 0 8.00 f 0.01 0.953 -0.735 1.086 0.9430 f 0.019 1.355 0.29 2.06 94.6 0.5 8.79 f 0.22 5.98 f 0.21 1.066 1 .o 1.037 -1.78 1.86 95.2 0.922 f 0.016 0.904 f 0.015 0.982 -0.276 0.00 1.93 96.5 1.5 1.118 1.838 -0.18 2.00 94.1 0.891 f 0.014 2.0 "The true values of k,, [MI, and k, are 8.0,1.0 mM, and 10.0,respectively. The true values of k along the six series are 1.0,1.5, 2.0,3.0,4.0,and 5.0 (rate constant in ps-I). *Runs test. 'Durbin-Watson parameter. dPercentage of weighted residuals between -2 and 2. TABLE 11: Recovered Model Migration Process" [QL mM k0 0 8.007 f 0.01 0.2 0.4 0.6

Parameters ko,[MI, k,, and k from Global Analysis of Synthetic Sample Decays in the Absence of the Probe [MI, mM

0.398 f 0.005 0.397 f 0.004 0.395 f 0.003

kq

9.93 f 0.17

k

5.7 X

lo-' f 0.09

x2, Zx2, rtb 1.036 0.566 2.16 0.984 -0.248 1.51 1.077 1.207 0.01 0.999 -0.011 1.57

"The true values of ko, [MI, k,, and k are 8.0,0.4,10.0,and 0.0,respectively (rate constants in dPercentage of weighted residuals between -2 and 2.

a parameter recovery with the same precision as that in the case of a higher number of decay curves excluding the monoexponential decay. The two procedures have shown stability with respect to the recovery of the probe migration constant k within the range 0.05kq < k < 0.4kq. Considering the results obtained using global analysis, we are now in a condition to compare eq 1 (with g(t) given by eq 4) with the approximate solution expressed in eq 5 in order to determine the model parameter region where eq 5 remains experimentally valid. Simulated data were obtained by computing in double precision the von Neumann series (eq 3) up to 10 or more terms until the divergence from the m + 1 term and the m term of eq 3 over ail data points was smaller than Those 6 response functions were then used to generate synthetic decay traces using the same method as described above. Several decay trace sets with different values of k but with the same values of ko, [MI, and k were generated. They were globally analyzed using the second procedure, and the results are shown in Table I. For all analyzed decay trace sets, good fits were obtained. At a low k / k , ratio a good recovery of all model parameters was obtained. For values of k / k q > 0.3 the recovery of the model parameters [MI, k,, and k started to be less satisfactory. However, ko was still recovered with high precision probably due to the presence of the decay trace with no added quencher. Along the data sets the fitted model parameters deviate systematically from those used in the synthetic data generation. Within the same series where only the quencher concentration is changed, the nonlinked [MI parameter

ps").

DW' 2.22 2.08 1.94 2.10

%d

x2,

Zx,

95.8 96.4 94.4 96.0

1.019

0.5983

*Runs test. CDurbin-Watson parameter.

decreases systematically when the quencher concentration is increased. This same situation is also observed when one compares a series with different k values. Along those series the recovered kq values were smaller whereas the k values were larger than their true values. This comparative test between the exact and the approximate model suggests that the use of the approximate solution should be restricted to a model parameter region where k / k , I 0.3 for occupancy (E) up to 2. However, when working with experimental data there is no way to know a priori the ratio of k / k , while the occupancy can be experimentally controlled. Moreover, considering that the optimized k / k , values are slightly larger than those which could be ideally obtained by using the exact solution, it seems that this aspect plays in favor of the cited model parameter region for the use of the approximate solution. In order to investigate the situation where the probe migration process is absent (i.e. k = 0), synthetic samples at different values of ii were generated and analyzed according to the second procedure (with inclusion of the monoexponential decay of a sample with no added quencher). The results of the global analysis are summarized in Table 11. The model parameters were recovered with high precision. The recovered value of the probe migration rate constant was approximately zero. However, for the inverted situation, Le., simulated data based on the probe migration model are analyzed with the model of Infelta-Tachiya where both probe and quencher are considered t o be immobile, statistically acceptable fits could be obtained especially a t a low ratio of k/k,. These results are summarized

5596 The Journal of Physical Chemistry, Vol. 96, No. 13, 1992

Gehlen et al.

TABLE 111: Global Analysis of the Decay Surface of the Probe Migration Model with the Infeltn-Tachiya Equation in the Case of Immobile Species“

[QI,

mM 0 0.5 1.o 1.5 2.0 0 0.5 1.o 1.5 2.0 0 0.5 1.o 1.5 2.0 0 0.5 1.o 1.5 2.0 0 0.5 1.o 1.5 2.0 0 0.5 1 .o 1.5 2.0

TO

ti

k,

X21

ZXZl

ZX2g

96.2 95.2 96.0 94.2 95.4

1.022

0.762

8.64 f 0.06

DWC 1.93 2.12 1.78 1.79 1.90

x2p

-0.709 0.637 0.408 2.204 -0.608

rtb 0.52 1.66 -0.49 -0.52 -0.20

%d

0.955 1.041 1.026 1.40 0.961

-0.599 0.458 -0.725 1.116 2.179

-0.05 -2.01 -0.48 -2.81 -1.21

1.91 1.73 1.77 1.80 1.75

95.9 94.8 96.6 94.0 94.0

1.028

0.985

8.18 f 0.05

0.962 1.029 0.954 1.071 1.139

-0.100 1.424 0.784 1.526 4.044

-0.03 0.83 -1.70 -0.31 -1.21

1.85 1.98 1.87 1.79 1.61

95.8 94.8 95.4 94.6 94.2

1.093

3.267

7.342 f 0.06

0.994 1.09 1 1.050 1.097 1.258

0.018 3.649 1.984 4.452 3.092

0.00 -0.87 -3.24 -1.99 -2.25

1.84 1.75 1.58 1.81 1.71

95.8 92.4 93.6 90.6 94.3

1.163

5.718

6.37 f 0.06

1.001 1.232 1.126 1.286 1.199

0.070 1.562 3.075 1.443 4.828

-0.1 1 -2.00 -4.36 -2.80 -4.90

1.83 1.70 1.57 1.61 1.54

95.8 95.6 93.0 95.1 93.8

1.135

4.730

5.54 f 0.05

1.004 1.099 1.196 1.093 1.311

0.134 4.876 5.029 3.811 9.523

-0.31 -2.24 -2.78 -3.72 -4.27

1.83 1.72 1.51 1.53 1.43

95.8 92.0 92.8 93.2 89.0

1.292

10.270

4.90 f 0.05

1.009 1.310 1.320 1.243 1.607

124.7 f 0.15 0.560 f 0.005 1.099 f 0.005 1.645 f 0.007 2.201 f 0.008 124.5 f 0.15 0.576 f 0.005 1.152 f 0.006 1.725 f 0.007 2.272 f 0.009 124.8 f 0.16 0.617 f 0.005 1.231 f 0.007 1.821 f 0.008 2.435 f 0.009 124.7 f 0.16 0.677 f 0.008 1.369 2.027 2.706 124.8 f 0.16 0.770 f 0.007 1.526 2.271 f 0.013 3.007 124.8 f 0.17 0.859 f 0.008 1.686 2.511 f 0.017 3.338

“The true values of r 0 and k9 are 125 ns and 10.0 ps-’,respectively. The micelle concentration is 1.0 mM. The true values of the occupancies are 0.5, 1.0, 1.5, and 2.0 in all series. *Runs test. ‘Durbin-Watson parameters. dPercentage of weighted residues beween -2 and 2.

in Table 111. The analyzed traces are the same as those of Table I. A systematic error in the recovery of fi and kq is detected when increasing the ratio k/k Increasing the ratio k/k, results in values of fi that are too xigh whereas values of k are too low compared to the true values. It should be noted t i a t those deviations are much higher than those observed when one uses the approximate solution. For example, in the series where k/k, is 0.3, the errors in the recovery of fi and kq were approximately 35% and 36%, respectively. Using the approximate solution, those model parameters deviate 7% and 10% from the true values, respectively. The results from this section show that presence or absence of the probe migration process in the fluorescence quenching can be investigated by the proposed method. On the other hand, a system with a slow migration rate of the probe compared to ko and kq will probably be in the situation where its decay surface could be fitted (with linked ko and k and fi as a local parameter) by the model of immobile species. however, in such a case, inaccurate model parameters will be obtained compromising the reliability of the method.

3. Analysis of Experimentally Measured Decays 3.1. Experimental Procedures. The fluorescent probe sodium 1-pyrenesulfonate (PSA) was purchased from Molecular Probes. The punty of the probe was checked by thin-layer chromatography on silica gel with methanol and by measuring its fluorescence lifetime in different solvents. A monoexponential decay was obtained in all cases. The fluorescence lifetimes are reported in Table IV. 1-Methylpyrene was synthesized and purified as described by Roelants et al.35 The quencher N-tetradecylpyridinium chloride (Henkel) was purified by recrystallization from a 1: 1 (v/v) methanol/acetone mixture. The surfactant hexadecyltrimethylammonium chloride (CTAC) (Kodak) was purified by Soxhlet extraction with diethyl ether followed by recrystallization from a 1:1 (v/v) acetondiethyl ether mixture. A micellar solution containing only surfactant did not show any fluorescence when excited under the same experimental conditions

TABLE I V Fluorescence Lifetime of Sodium 1-Pyrenesulfonate in Different Solvents at Room Temperature solventf T , ns 63.4 f 0.1; 63.W.* H20 126.3 f 0.2 methanol 135.9 f 0.2 ethanol 159.6 f 0.2 2-propanol 140.0 f 0.2 1-butanol 140.3 f 0.2 1-pentanol 140.8b 1-hexanol 126.4 f l.Oc CTAC 50.W CTAB 70.W CTAB microemulsion 114.8d DAP “dValues from refs 27, 28,29, and 30, respectively. CAveragevalue in different CTAC concentrations in aqueous phase (see Table V for more details). fCTAB = hexadccyltrimethylammonium bromide and DAP = dodecylammonium propionate reversed micelle.

as the probe. N-Isopropylcarbazole in butyronitrile ( T ~= 14.6 ns) and anthracene in methanol (7, = 5.5 ns) were used as reference compounds. The fluorescence decays obtained by excitation at 320 nm and observed under magic angle (54.7O) a t 378 nm were measured with the single-photon timing technique using a cavity-dumped, frequency-doubled D C M (4-(dicyanomethylene)-2-methyl-6-@-(dimethylamino)st~l)-4~-p~n) dye laser synchronously pumped by an argon ion laser. The number of peak counts in samples and reference was about 104. The details of the picosecond time-resolved fluorimeter used for the fluorescence decay measurements reported here were described previously.26 All the fluorescence decays were recorded at 20 OC using K data points of the multichannel analyzer. The probe concentration was kept low enough to avoid multiple occupancy over the micelles. Milli-Q water was used to prepare the solutions. All samples were degassed by repeated freeze-pumpthaw cycles before the measurement.

The Journal of Physical Chemistry, Vol. 96, No. 13, 1992 5597

Probe Migration in Micelles

TABLE V Rate Constants and Associated Parameters of the Fluorescence Quenching of Sodium 1-F'yrenesulfonateby Tetradecylpyridinium Chloride in Aqueous CTAC Micelles" series [SI, mM [Q], mM ko [MI, mM k, k xZ1 Zx21 rtb DW' %d xZg Zxs v I 20.9 0 7.98 f 0.01 1.045 0.708 -1.39 1.82 95.1 1.054 1.684 85 f 4 1.001 0.022 -2.55 1.92 95.6 0.124 0.219 f 0.003 0.238 f 0.003 7.96 f 0.16 0.73 f 0.10 1.127 1.971 0.73 2.03 93.9 0.248 0.243 f 0.003 1.062 0.913 -0.41 1.95 95.9 0.372 7.96 f 0.01 1.103 1.613 -1.49 1.73 94.1 1.056 1.699 74 f 3 I1 26.3 0 0.913 -1.362 -1.82 1.77 96.7 0.447 0.359 f 0.004 0.337 f 0.003 8.97 f 0.13 1.31 f 0.15 0.986 -0,219 1.40 2.12 96.6 0.745 0.333 f 0.003 1.285 3.993 -2.35 1.65 92.5 1.193 1.082 1.293 0.15 2.02 95.6 1.055 1.935 80 f 2 111 38.8 0 7.85 f 0.01 0.487 f 0.007 0.993 -0,108 -0.76 1.95 95.0 0.218 0.469 f 0.005 8.71 f 0.12 1.46 f 0.14 1.050 0.791 -0.54 1.88 95.4 0.436 0.475 f 0.004 0.941 -0.928 -1.74 1.83 95.6 0.873 1.230 3.604 -1.88 1.49 93.6 1.309 0.465 f 0.004

IV

64.7

0 0.688 1.217 1.826

7.87 f 0.01

1.080 0.692 f 0.019 1.093 0.707 f 0.017 8.13 f 0.25 2.42 f 0.23 1.063 0.719 f 0.016 1.007

1.259 0.06 2.02 1.446 -1.31 1.70 0.982 -0.92 1.87 0.105 -3.13 1.65

95.0 1.057 1.780 90 f 2 94.0 94.0 95.3

[SI, [Q], and [MI are the surfactant, quencher, and micelle concentration, respectively. The average aggregation number ( u ) is calculated by u = ([SI- cmc)/[M] where cmc is the critical micelle concentration. ko, k,, and k are the decay rate constant of the probe in the absence of quencher, the intramicellar quenching rate constant, and the probe migration rate constant, respectively (values in jd). Runs test. Durbin-Watson parameter. dPercentage of weighted residuals between -2 and 2. TABLE VI: Results from the Global Analysis of Decay Traces Series of the Fluorescence Quenching of PSA by N-Tetradeeylpyridinium Chloride in Aqueous CTAC Micelles Considering the Case of an Immobile Probe (Data Set the Same as That in Table V)

series I

r0, ns 125.0 f 0.2

fi

0.616 f 0.007 1.122 f 0.008 1.644 f 0.010

I1

7.01 f 0.08

8.18 f 0.09

127.0 f 0.2 0.502 f 0.005 1.029 f 0.006 1.998 f 0.009 3.042 f 0.010

IV

PS-'

125.5 f 0.2 1.345 f 0.006 2.356 f 0.009 3.799 f 0.010

I11

k,,

7.65 f 0.05

127.1 f 0.2 0.963 f 0.007 1.878 f 0.012 2.738 f 0.017

7.36 i 0.07

X21

zx21

rt"

DWb

1.058 1.011 1.172 1.143

0.816 0.178 2.685 2.031

-0.56 -1.51 0.37 -1.16

1.81 1.92 1.97 1.88

%' 94.9 95.2 93.3 94.9

1.092 0.920 1.087 1.360

1.448 -1.257 1.359 5.079

-1.48 -1.88 0.11 -2.50

1.74 1.76 1.93 1.54

1.086 1.018 1.044 1.032 1.334 1.080 1.103 1.047 1.037

1.352 0.276 0.685 0.507 5.252 1.261 1.598 0.727 0.576

-0.04 -0.22 -0.22 -2.99 -3.52 0.06 -1.48 -1.30 -2.77

2.01 1.91 1.90 1.67 1.36 2.02 1.68 1.90 1.60

x2g 1.089

ZX28 2.732

94.5 96.6 95.5 92.3

1.100

3.054

95.2 94.8 93.4 95.2 92.4 95.4 93.4 94.6 95.5

1.100

3.505

1.064

2.000

"Runs test. Durbin-Watson parameter. CPercentageof weighted residuals between -2 and 2.

3.2. Experhntal Results and Discussion. Table V summarizes the experimentally determined rate constants and parameters associated with the kinetics of the fluorescence quenching of the probe sodium 1-pyrenesulfonate by the quencher N-tetradecylpyridinium chloride in CTAC micelles as a function of the total surfactant concentration. The model parameters ko,[MI, k and k were obtained by simultaneous analysis of four or five Xecay traces including the monoexponential decay corresponding to a sample with no added quencher. ko,k,, and k were linked within the same experimental series whereas [MI was a local fitting parameter. The fitting procedure in the reference convolution method was identical to that applied in the simulated data analysis. Figure 3 shows the autocorrelation function values and the weighted residuals of the decay traces shown in Figure 4 corresponding to the third set of decay traces of Table V. Judged by the statistical goodness-of-fit criteria, each global analysis could be considered acceptable. The parameters of the goodness of fit of the individual decay curves were also indicative of a good fit. The least satisfactory individual fits were obtained for the last sample of the second and third series corresponding to the highest average number of quenchers per micelle. The reasons for this small deviation may be ascribed to a perturbation of the micellar structure at a higher average number of quencher per micelle which could lead to changes in the values of the kinetic parameters or to the fact that the approximate solution starts to break down

a t high quencher concentration. To compare the kinetics with probe migration with the kinetics where both probe and quencher have less probability of undergoing migration to another micelle during the probe's excited-state lifetime (leading to the Infelta-Tachiya equation with A2 = ko. A , = ii, A4 = k,), the same decay traces as those of Table V were simultaneously fitted in the condition of ko and kq as linked parameters and ii as a nonlinked parameter. The results are shown in Table VI. All of the series could be fitted by the InfeltaTachiya model. The slightly higher values of x2gand Zx2gwhen compared to those from Table V do not allow one to distinguish between the two models. However, application of the TachiyaInfelta model resulted in larger ii and smaller kq values than those obtained with the probe migration model. Note that this relation was already apparent when comparing the models using simulated data based on the probe migration model. This fact together with the linear dependence of the probe migration rate constant with the micelle concentration (vide infra) suggests the presence of intermicellar mobility of PSA in CTAC solution during its excited-state lifetime. The small ratio k/k, and also the shorter lifetime of PSA when compared to the average time of the probe exchange process (=l/k) are probably the factors which make a clearer model distinction more difficult. The possibility of a condition opposite to migration of the probe (Le., an immobile probe and a mobile quencher) was also in-

Gehlen et al.

5598 The Journal of Physical Chemistry, Vol. 96, No. 13, 1992 1

-1 3.34

c

I

1

I

R i

-3.34 1

AC

-1 2.94

R i

-2.94 1

AC

-1 3.3s

I

t

R i

-3.3s 1

AC

c

-1 3.46 F

I

1

1-3.46

1

R i

-3.46

1 nC

-1

5.91

R i

- S a 91

I

I

I

Figure 3. Autocorrelation function values (AC) and weighted residual plots (Ri) for the global analysis of the third series of the Table V. The quencher concentration increases from top to bottom according to the values in Table V.

The Journal of Physical Chemistry, Vol. 96, No. 13, 1992 5599

Probe Migration in Micelles 5

, 0

a

100

0

200

300

d

400

Channel numbir

500

DECAN

Figure 4. Time-resolved fluorescence quenching of sodium 1-pyrenesulfonate by the quencher N-tetradecylpyridinium chloride in CTAC micella at several quencher concentrations. The monoexponential decay of a sample in the absence of quencher is also shown. The decay curves correspond to the samples of the third series of the Table V. TABLE VII: Simultaneous Analysis Considering Mobile Quenchers" s2, 106 series kn,ps-' S,,mM-I Ad, ps-l ps-l mM-I x2. Zx2. 1.139 4.297 8.269 1.478 I 8.04 3.793 2.643 1.127 3.892 2.251 11.220 I1 7.94 2.210 1.058 2.055 11.209 111 7.88 1.541 1.130 4.339 8.396 0.873 IV 7.91 1.236 "The series are the same as those of Table V.

vestigated. In such a situation the extended version of the Infelta-Tachiya model taking into account the exchange of quenchers via the aqueous phase and also during micelle collisions results in a four-parameter decay function with the A parameters given by1-3*sv31 Az = ko + SdQ1 A3 = S3[Q1 A4 = k, + k- + k,[M]

(15) (16) (17)

with k, k+ + k A M 1 1 K[M]

s2 = A4

+

where K = k+/k- (the binding constant of the quencher to the micellar surface), k+ is the entrance rate constant for a quencher into a micelle, k- is the exit rate constant for a quencher from a micelle, and k, is the second-order rate constant for exchange of quencher during micelle collision. The same experimental decay traces of the system PSAINtetradecylpyridinium chloride/CTAC were then globally analyzed with ko, S3,A4, and S2 linked. The results are summarized in Table VII. The irregular changes in S2 and also the fluctuations

of A4 along the different series indicate that the exchange of the quencher is probably an improper assumption. Also,experimental results obtained for the fluorescence quenching of 1-methylpyrene by N-tetradecylpyridinium chloride in the presence of alkyltrimethylammonium chloride surfactants have demonstrated that the quencher remains in the same micelle during the excited-state lifetime of the probe.32 Since the single excited-state lifetime of 1-methylpyrene is larger than that of sodium 1-pyrenesulfonate, the condition of immobility of the quencher should be even better fulfilled in the present system. Fluorescence decay measurements with 1-methylpyrene/Ntetradecylpyridinium chloride/CTAC system were also performed. They were globally analyzed using the Infelta-Tachiya model with immobile probe and quencher and the model of this study. The results are shown in Table VIII. The fluorescence decays could be well described by the Infelta-Tachiya model and also by the model including the probe migration process. However, the very low value obtained for the probe migration rate constant (almost 3 orders of magnitude less than the quenching rate constant) indicates that this process is practically absent in the case of 1-methylpyrene. These results partly confirm the results of the analysis of the synthetic sample decays, namely, that the presence or absence of the probe migration process can be detected by global analysis with the present model. The decay rate constant of the probe in the micellar phase in the absence of quencher (bin Table V) is shown to be independent of the total surfactant concentration within the experimental error, and its value is close to that in methanol (see Table IV). This is an indication that the probe is located in the Stern layer where the micelle has a dielectric constant similar to that of methanol. The intramicellar quenching rate constant (k,) shows small changes with the variation of surfactant concentration. The average value of the quenching rate constant ((8.4 f 0.5) X lo6 s-l) is within the range expected for rate constants of diffusion-controlled reactions taking place at the surface of a spherical miThe value of the quenching rate constant in methanol solution was obtained independently by measurements of stationary fluorescence intensities and monoexponential fluorescence decays as a function of the quencher concentration. The value of the Stern-Volmer constant from stationary measurements was (2.0 f 0.18) X lo3 L mol-', yielding a value of (1.57 f 0.14) X 1Olo L mol-' s-l for the second-order rate constant of the quenching process in methanol solution. The value of k, obtained from time-resolved measurements was (1.70 f 0.01) X 1OIo L mol-I s-l. These values of k in methanol are close to the diffusional limit in this solvent. T\is gives support to a possible diffusional limit to the quenching process in micelles. The larger quenching rate constant observed for 1-methylpyrene as a probe compared to PSA suggests that, if both processes are considered as diffusion controlled, the location of the probes is slightly different with 1-methylpyrene being located more toward the micelle interior and PSA located on the surface. Quenching involving diffusion on the surface is a slower process than that which involves a certain degree of compartmentalization of reactants.33

TABLE VIII: Rate Constants and Associated Parameters of the Fluorescence Quenching of 1-Methylpyrene by N-Tetradecylpyridinium Chloride in Aqueous CTAC Micelles" Global Analysis with the Infelta-Tachiya Model

ns 180.5 f 0.4

k0

5.546

k,

X21

14.55 f 0.23

1.011 1.156 1.041

A

70,

1.275 f 0.008 0.818 f 0.007 0.364 f 0.007

* 0.027 (180.3 ns)

[MI, mM 0.157 f 0.001 0.245 f 0.003 0.553 & 0.002

ZX2l 0.164 2.423 0.628

rt

DW

2.36 0.21 -0.48

2.05 1.98 1.77

Global Analysis with the Probe Migration Model k, k x21 ZxZ1 14.48 f 0.29

0.019 f 0.067

1.026 1.168 1.045

0.408 2.603 0.699

% 95.9 95.5 95.5

rt

DW

1.66 0.17 -0.39

2.01 1.95 1.76

x2g

zx2g

Y

1.065

1.741

56 76 89

% 95.7 95.7 95.5

X2, 1.074

ZxZg Y 1.987 55 76 88

"The results refer to three samples with the same concentration of quencher (0.20 mM) but at different surfactant concentrations (0.01,0.02, and 0.5 M). Values of the rate constants in ps-'. All statistical parameters have the same meaning as those in Table V.

5600 The Journal of Physical Chemistry, Vol. 96, No. 13, 1992

coefficient is much higher than that of the CTAC micelle, it will have a certain probability to hit the opposite micelle during the whole process. In such mechanism, the values of l / k should be understood as the mean first passage times of the probe from one micelle surface to the other during the micellar interaction averaged Over the distribution of intermicellar distances. The absence of probe migration in the case of 1-MePy suggests that the driving force for migration of the ionic pyrene derivative, PSA, is probably its higher hydrophilic character.

k

I

Figure 5. Plot of the experimentally determined probe migration rate constant (k in MS-') as a function of surfactant concentration.

The values obtained for the mean aggregation number of CTAC micelles as a function of the surfactant concentration (see Table V) are slightly smaller than the previously reported values of Roelants et al.35(0.007 M, 80; 0.016 M, 81; 0.031 MI 89; 0.05 M, 116), Malliaris et (0.015 M, 90; 0.03 M, 99; 0.06 M, 106; 0.12 M, 118), and Almgren et aL3' (0.04 M, 90). The present values indicate a mean aggregation number of 82 f 7 in the range 0.02-0.07M surfactant. The theoretical value based on a surfactant packing model3*for CTAC forming spherical micelles is 87. In order to test the probe migration model, an extended region of the average number of quencher per micelle was investigated with values of R going from 0.4 to 3.0. Considering that any micellar system is subject to polydispersity effects, the lower values observed can in part be ascribed to the presence of polydispersity. Unfortunately, no model considering exchange of reactants and polydispersity is available. However, in the case of no exchange of reactants, the current theory predicts a dependence of the measured aggregation number v (referred to as apparent average aggregation number) on the quencher concentration given by the following Y

=

Y,

- ypJwq + y&q* - ...

Gehlen et al.

(20)

where Y, is the weight-average aggregation number and awand [ are the second and third cumulants of the weight distribution. q is the ratio of quencher to surfactant molecules in the aggregates. Equation 20 clearly predicts that lower values of Y are obtained when the quencher concentration is increased. If the objective is to measure the aggregation number, then it seems to be better to choose the system as simple as possible (where no exchange processes are present) and to investigate the quenching process within a quencher concentration range resulting in an occupancy lower than unity in order to avoid the effect of polydispersity. Figure 5 shows the values of the probe migration rate constant as a function of the micelle concentration. The transport of an excited probe located on the surface of a micelle to another micelle can involve a hopping of the probe or its diffusion through the bulk during micelle interaction. Both mechanisms are expected to be dependent on the micelle concentration because the increase of the micelle concentration leads to a reduction of the intermicellar free space and a corresponding increase of the migration rate of the probe. The values in Figure 5 support this assumption, and a linear relation between the probe migration rate constant and the micelle concentration is found. From the slope a value of (3.0 f 0.4) X lo9 L mol-I s-I is obtained for the second-order rate constant. A similar behavior has been found for the migration of ionic quenchers in aqueous sodium dodecyl sulfate micelles, and values of 5.5 X lo9, 6.0 X lo9,and 8.0 X lo9 L mol-I s-I have been determined for Tl', Cs+, and Ag' ions, respecti~ely.~~~ The experimental results do not allow one to discriminate between hopping and diffusion through the bulk. However, the mechanism by which the probe migrates probably involves the approach of two micelles through diffusion against the electrical potential. During the micellar approach, the overlap between the micelle charge distribution densities leads to a reduction of the micelle surface potential which increases the jump probability of the probe through the aqueous phase. Considering that the PSA's diffusion

4. Conclusions The approximate solution to the fluorescence quenching including the probe migration process among micelles occupied by Poisson distribution quenchers is tested within the framework of the global analysis with the reference convolution method. The results from the analysis of synthetic single-photon timing data based on the Infelta-Tachiya type equation clearly show that an accurate model parameter recovery can only be obtained by simultaneous analysis of several decay curves. The quenching process of sodium 1-pyrenesulfonate by N-tetradecylpyridinium chloride in CTAC micelles by this analysis procedure can be adequately described by the present model. The importance of the migration process of ionic p r o b located at the micellar surface in the overall quenching mechanism was demonstrated. Acknowledgment. M.H.G. thanks CNPq (Brazil) for a fellowship. N.B. is a Bevoegdverklaard Navorser of the Belgian Fonds voor Geneeskundig Wetenschappelijk Onderzoek (F.G. WO.). M.V.D.A. is an Onderzoeksleider of the Belgian Fonds voor Wetenschappelijk Onderzoek (N.F.WO.) S.R.is an aspirant of the N.F.W.O. The support of the K.U. Leuven, FKFO (Belgium), and the Ministry of Scientific Programming of Belgium (through UIAP- 16) is gratefully acknowledged. Registry No. CTAC, 112-02-7; sodium 1-pyrenesulfonate, 5932354-5; N-tetradecylpyridinium chloride, 2785-54-8; 1-methylpyrene, 238 1-21-7.

References and Notes (1) Infelta, P. P.; Gratzel, M.; Thomas, J. K. J . Phys. Chem. 1974, 78,190. (2) Tachiya, M. Chem. Phys. Lert. 1975, 69, 289. (3) Dederen, J. C.; Van der Auweraer, M.; De Schryver, F. C. Chem. Phys. Lett. 1979, 68, 451. (4) Grieser, F. C.; Tausch-Treml, R. J . Am. Chem. Soc. 1980, 102, 7258. (5) Dederen, J. C.; Van der Auweraer, M.; De Schryver, F. C. J . Phys. Chem. 1981,85, 1198. (6) Henglein, A.; Praske, Th. Ber. Bumen-Ges. Phys. Chem. 1978,82,471. (7) Almgren, M.;Linse, P.; Van der Auweraer, M.; De Schryver, F. C.; GeladE, E.; Croonen, Y. J. Phys. Chem. 1984,88,289. (8) Eicke, H. F.; Shepherd, J. C. W.; Steinemann, A. J. Colloid Interface Sei. 1976, 56, 168. (9) Fletcher, P. D. I.; Robinson, B. H. Ber. Bunsen-Ges. Phys. Chem. 1981, 85, 863. (10) Kahlweit, M. J. Colloid Interface Sei. 1982, 90, 92. (1 1) Almgren, M.; Lofroth, J. E.; Van Stam, J. J. Phys. Chem. 1986,90, 443 1. (12) Tachiya, M. Can. J . Phys. 1990, 68, 979. (13) Gehlen, M.H.; Van der Auweraer, M.;De Schryver, F. C. Photochem. Photobiol. 1991, 54, 613. (14) Gehlen, M. H.; Van der Auweraer, M.; Reekmans, S.;Neumann, M. G.; De Schryver, F. C. J. Phys. Chem. 1991, 95, 5684. (15) Gauduchon, P.; Wahl, Ph. Biophys. Chem. 1978,8, 87. (16) Zaker, M.; Szabo, A. G.; Bramall, L.; Krajcarsk, D. T.; Salinger, B. Rev. Sci. Instrum. 1985, 56, 14. (17) Van den &gel, M.; Boens, N.; Daems, D.; De Schryver, F.C. Chem. Phys. 1986, 101, 311. (18) Ameloot, M.; Beechem, J. M.; Brand, L. Biophys. Chem. 1986,23, 155.

(19) Boens, N.; Amelmt, M.; Yamazaki, I.; De Schryver, F. C. Chem. Phys. 1988, 121, 73. (20) Boens, N.; Malliaris, A.; Van der Auweraer, M.; Luo, H.; De Schryver, F. C. Chem. Phys. 1988, 121, 199. (21) Marquardt, D. W. J. SOC.Ind. Appl. Math. 1963, 1 1 , 431. (22) Almgren, M.; LBfroth, J. E. J . Chem. Phys. 1982, 76, 2734. (23) Durbin, J.; Watson, G.S. Biometrika 1950, 37, 409; 1951, 38, 159; 1971, 58, 1. (24) Draper, N. R.; Smith, H. Applied Regression Analysis, 2nd ed.; Wiley: New York, 1981. (25) Grinvald, A.; Steinberg, 1. Z . Anal. Eiochem. 1974, 59, 583. (26) Boens, N.; Van den Zegel, M.; De Schryver, F. C.; Desie, G. In From Photophysics to Photobiology; Favre, A., Tyrrell, R., Cadet, J., Eds.;Elswier: Amsterdam, 1987; p 93.

5601

J . Phys. Chem. 1992,96, 5601-5604 (27) Klein, U. K.; Miller, D. J.; Hauser, M. Spectrmhim. Acta 1976,32A, 379. (28)Chu, D. Y.;Thomas, J. K. Macromolecules 1987, 20, 2133. (29)Atik, S. S.;Thomas, J. K. J . Am. Chem. SOC. 1981, 103, 4367. (30)Gelad& E.;Boens, N.; De Schryver, F. C. J . Am. Chem. SOC.1982, 104, 6288. (31) Reekmans, S.;Boens, N.; Van der Auweraer, M.; Luo, H.; De Schryver, F. C. Lungmuir 1989, 5 , 948. (32)Roelants, E.;De Schryver, F. C. Lungmuir 1987, 3, 209. (33) Hatlee, M. D.; Kozak, J.; Rothenberger, G.; Infelta, P. P.; Gritzel, M. J . Phys. Chem. 1980,84, 1508. (34)Sano, H.; Tachiya, M. J . Chem. Phys. 1981, 75, 2870.

(35) Roelants, E.;Geladi, E.; Van der Auweraer, M.; Croonen, Y.; De Schryver, F. C. J. Colloid Interface Sci. 1983, 96, 288. (36) Malliaris, A.; Lang, J.; a n a , R. J. Colloid Inrerface Sci. 1986,110,

237. (37) Almgren, M.; A M s , J.; Mukhtar, E.; Van Stam, J. J . Phys. Chem. 1988,92, 4479. (38)(a) Roelants, E.; De Schryver, F. C. Lungmuir 1987, 3, 209. (b) Nagarajan, R.; Ruckenstein, E. J . Colloid Interface Sci. 1979, 71, 580. (39)Almgren, M.;Lofroth, J. E.J . Chem. Phys. 1982, 76, 2734. (40)Warr, G.G.;Grieser, F. J . Chem. SOC.,Faraday Trans. 1 1986,82, 1813.

Quenching Mechanism of Exciplex Fluorescence by Inverted Micelles Chika Sat0 and Koichi Kikuchi* Department of Chemistry, Faculty of Science, Tohoku University, Aoba, Aramaki, Aoba- ku, Sendai 980, Japan (Received: January 2, 1992; In Final Form: March 12, 1992)

Fluorescence quenching of the pyreneN,N-dimethylaniline exciplex with water pools of various size constructed in inverted micelles is studied by an emissionabsorptionlaser photolysis method. Only the triplet state of pyrene is observed as a transient species. The rate of enhanced intersystem crossing due to exciplex quenching depends on the size of the water pools and is reduced by external magnetic fields. The quenching dynamics of exciplexes in inverted micellar solutions are discussed.

Introduction In previous work’ Kikuchi and Thomas investigated the rate k, of fluorescence quenching of the pyreneNJV-dimethylaniline exciplex with water pools of various size constructed in inverted micelles. Although the k, has been compared with the rate calculated by simple diffusion theory and some information about the nature of the micelle surfactant interface has been obtained, the quenching mechanism has not been elucidated yet. In this quenching system no ionic species are detected, but the triplet state of pyrene is observed. In the present work, the quenching mechanism was studied by measuring the triplet yield of pyrene at various quencher concentrations for various sizes of water pools. To determine the triplet yield of the exciplex quenching, the emissionabsorption laser photolysis method was used. The effect of micellar size and external magnetic field on the rate kqlr of enhanced intersystem crossing of the exciplex quenching by inverted micelles are shown to be useful in understanding the quenching dynamics in the micellar system. Experimental Section Materials. Pyrene (Py, Aldrich) was zone refined and sublimated under vacuum. N,N-Dimethylaniline (DMA, Wako, 99+%) was purified by sublimation under vacuum. 2-Ethylhexyl sulfosuccinate sodium salt (AOT, Nakarai, SP grade), benzyldimethylhexadecylammoniumchloride (BHDC, Kodak), methyl viologen dichloride hydrate (MV2+Clc, Aldrich, 98%), and nheptane (Nakarai, SP grade) were used as received. Benzene was distilled on sodium wire after standard pretreatments. Water was distilled twice. Apparatus and Procedure. The second harmonic of a Qswitched ruby laser (0.05 J, fwhm 30 ns) was used as an exciting light source for the emissionabsorption laser photolysis method. This method measures the transient absorption and the time profile of fluorescence intensity simultaneously.2 The former is used to determine the initial concentration of transient species, while the latter is used to evaluate the amount of light absorbed by a sample solution. The experimental error of this method is within 10%. The time resolution of fluorescence and transient-absorption measurement was 30 ns and 1 ps, respectively. The block diagram of the apparatus is shown in Figure 1. 0022-3654/92/2096-5601$03.00/0

The principle of the emissionabsorption laser photolysis method is briefly described below. The initial absorbance DT(A’) of triplet-triplet (T-T) absorption is related to the amount of light SIa, dt absorbed by a sample solution as follows: DT(A’)

cT(A’)

d#,JI,,

dt

(1)

Here cT(X’) is the molar extinction of T-T absorption, d = 1 cm is the optical path length of sample cell, and 4iscis the apparent triplet yield. The time-integrated fluorescence intensity SIF(h) dt during the rise and decay of fluorescence is described by

Here a is a constant depending on the experimental conditions.

4f is the apparent fluorescence yield. 4f and 4, may depend on the quencher concentration. From eqs 1 and 2 we obtain

-

E T ( X ’ ) ~ kisc’ kf

DT(X’) ---=-d X ’ ) d 4isc ]IF(X) dt 4r

(3)

ff

ff

Here k f is the radiative rate constant. kiK’is the apparent rate constant of intersystem crossing, and it may depend on the quencher concentration. When no quencher is involved in the solution, eq 3 is reduced to eT(A’)d 4is: =--=--

&‘(A’) JIFo(A)

dt

ff

CT(A’)d ki, kf

4?

(4)

ff

Here ki, is the intrinsic rate of intersystem crossing for the fluorescer. Superscript 0 stands for the solution without quencher. From eqs 3 and 4 we obtain y’

DT(A’)/JIF(A) dt &‘(A’)

/ JIFo(A)

dt

ki,‘ =-

kist

(5)

If kiscis known, therefore, we can determine kist'. The sample cell is located in the center of the Helmholtz coil which can generate magnetic fields up to 65 mT. Sample solutions containing 10-15 pM pyrene, 10-20 mM DMA, and 0-1.7 mM 0 1992 American Chemical Society