Quenching of Excited State Pyrene by Halothane in Poly(oxyethylene

Oct 30, 1999 - It is shown that these parameters depend on the concentration of halothane in the system and the hydrophobic/hydrophilic balance of the...
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10092

J. Phys. Chem. B 1999, 103, 10092-10097

Quenching of Excited State Pyrene by Halothane in Poly(oxyethylene)-Poly(oxypropylene)-Poly(oxyethylene) Triblock Copolymers X. Wen,† M. Sikorski,‡,§ I. V. Khmelinskii,| and R. E. Verrall*,† Department of Chemistry, UniVersity of Saskatchewan, 110 Science Place, Saskatoon, Saskatchewan S7N 5C9, Department of Chemistry and Biochemistry, UniVersity of Notre Dame, Notre Dame, Indiana 46556, A. Mickiewicz UniVersity, Faculty of Chemistry, 60-780 Poznan, Poland, and AlgarVe UniVersity, Faculty of Sciences and Humanities, P-8000 Faro, Portugal ReceiVed: May 20, 1999; In Final Form: September 7, 1999

Time-resolved fluorescence quenching of excited state pyrene by halothane was investigated in aqueous solutions of poly(oxyethylene)-poly(oxypropylene)-poly(oxyethylene) triblock copolymers, P84, P104, and F38, at 25 °C. The occupancy number of halothane in the block copolymer micelles and the dispersive factor were obtained from nonlinear least-squares fitting of the immobile quencher-probe and dispersive kinetic models, respectively. It is shown that these parameters depend on the concentration of halothane in the system and the hydrophobic/hydrophilic balance of the block copolymers. The application of dispersive kinetics appears to be a suitable technique to investigate the self-aggregation behavior of self-assembly systems. Exponential series lifetime-distribution analysis was also carried out and the results support the presence of aggregates of triblock copolymers in these systems. The results of this study suggest that halothane molecules distribute primarily in the core of the micelles but, upon saturation of the core, begin to locate in the corona of the block copolymer aggregates.

Introduction There have been several studies reporting the use of micelles as model systems to gain a better understanding of the behavior of inhalation anesthetics in cellular membranes. For example, the cationic surfactants hexadecyltrimethylammonium bromide and chloride (HTAC and HTAB, respectively) were studied in the presence of halothane to determine whether the additive has any effect on the morphology of the micelle aggregates.1 As well, the widely studied anionic surfactant sodium dodecylsulfate (SDS) has been investigated in the presence of halothane to determine the location of anesthetic molecules in the SDS micelles.2-4 This paper describes the results of a study using nonionic, triblock copolymer surfactants as model systems. These specific copolymer systems, known under the trade name, Pluronics, consist of poly(oxyethylene)-poly(oxypropylene)poly(oxyethylene) (POE-POP-POE) blocks. They are used extensively in industry for a variety of applications, especially in cosmetic formulations, drug delivery,5-7 the extraction of proteins,8 and corrosion protection.9 Their physicochemical properties have been extensively reported.10,11 Techniques as diverse as light scattering,12,13 fluorescence spectroscopy,14,15 NMR,16 specific volume,17,18 and SANS19,20 have been used to gain new insight into the aggregation behavior of these systems. The results of these investigations clearly show that they have the propensity to self-aggregate and form micelles with a hydrophobic core composed of POP segments and a corona composed of the hydrophilic POE segments. Furthermore, they are convenient compounds to use when one wishes to study the effect of hydropobic/hydrophilic balance on a system property since a number of homologues are available †

University of Saskatchewan. University of Notre Dame. § A. Mickiewicz University. | Algarve University. ‡

having different block lengths. The results reported herein are part of a study initiated to determine whether the aggregates formed by these systems may serve as a useful model of the interface between hydrophilic and hydrophobic regions of physiological membranes. The chemical structures of the POEPOP-POE triblock copolymers and the inhalation anesthetic used in this study, halothane, are shown in Scheme 1. There have been a few studies reporting the effect of additives on the aggregation properties of these copolymer systems in aqueous medium. The additives used have been mainly inorganic salts and urea, and the concentrations used have been rather high, commonly at the molar level.21 The results reported herein will show that halothane affects the micellization of Pluronic copolymers at the millimol level, i.e., at concentrations near to those observed for the onset of anesthesia in physiological systems. Recently,22 a dispersive kinetic model has been used to analyze the fluorescence quenching of the excited states of 1-pyrenesulfonic and 2-pyrenebutanoic acids in aqueous solution containing cationic micelles of HTAC. It was shown that the fluorescence quenching process could be adequately described in terms of dispersive kinetics using a time-dependent rate coefficient for the intramicellar quenching process. The dispersive kinetic model has been successfully used to analyze a wide range of reaction mechanisms in different environments,23-25 especially at very low temperatures and/or very short time scales. This is consistent with the expectation that reactions are usually less dispersive at higher temperatures or longer time scales. However, very little attention has been paid to the application of dispersive kinetics in the study of photophysical processes in micelles at room temperature, especially the dynamics of fluorescence quenching of solubilized probe molecules. It will be shown that exponential series lifetime distribution analysis can be applied to this dynamic process. It has the

10.1021/jp9916687 CCC: $18.00 © 1999 American Chemical Society Published on Web 10/30/1999

Quenching of Excited State Pyrene by Halothane

J. Phys. Chem. B, Vol. 103, No. 46, 1999 10093

SCHEME 1

TABLE 1: Triblock Copolymers Used in the Present Study pluronics

POE %

molar mass (amu)

POP (amu)

composition

POP/POE

F38 P84 P104

80 40 40

4700 3700 5410

950 2250 3250

E42P16E42 E19P39E19 E27P56E27

0.25 1.5 1.5

inherent advantage of not requiring, a priori, any specific kinetic model with a given set of adjustable parameters. The only limitation to this approach is that the respective processes should be unimolecular or pseudo-unimolecular, i.e., the quencher concentration must be much greater than that of the probe molecule, which was indeed the case in all experiments performed in this study. We report the results of studies of pyrene fluorescence in triblock POE-POP-POE micelles in the absence and presence of halothane with the view of obtaining information about the effect of the additive on the self-assembly of the copolymers. It will be shown that the application of dispersive kinetics can provide information about the dynamics of these heterogeneous systems. The triblock copolymers studied in this work were P84, P104, and F38. They were chosen since they show a wide variation in their degree of aggregation at room temperature. Experimental Section Materials. The Pluronic compounds F38, P84, and P104, cf. Table 1, were gifts from BASF. Their molecular weight distributions were checked by means of gel permeation chromatography, and their relative molar masses were estimated by acetylation and back-titration of the unreacted acetylation reagent, as previously described.18 The molar masses in Table 1 were taken from the manufacturer. Halothane was a gift from the Department of Anesthesiology, Royal University Hospital, at the University of Saskatchewan. Water and any stabilizer were removed from the halothane by passing it through an activated aluminum oxide column. Equipment and Methods. Pyrene was used as the fluorescence probe and was purified by recrystallization from acetone three times. It was subsequently dissolved in hexane, and the desired amount of this solution was put into a volumetric flask. The solvent was removed by passing a stream of nitrogen gas over the solution. The stock solution of block copolymer was then added to the flask so that the final concentration of pyrene in solution was always around 10-7 M. The preparation of solutions containing halothane was carried out as follows. The stock solution containing dissolved pyrene was transferred to ampules (5 or 10 mL). Liquid anesthetic was then quickly added into the ampules by using a microsyringe, which was weighed before and after the addition of the anesthetic. The emission

Figure 1. Residuals of fitting results, assuming monoexponential decay, of the fluorescence of pyrene in 5 wt % copolymer aqueous solutions of P84, P104, and F38 in the absence of halothane. The residuals demonstrate that the decay character is not strictly monoexponential. The values of the fitted fluorescence lifetimes of pyrene are given in Table 2.

from the solution without the probe, under the conditions of time-resolved fluorescence measurements, was insignificant. Fluorescence decay curves were obtained by using the single photon counting technique. The excitation source was a synchronously pumped, cavity-dumped, frequency-doubled DCM picosecond dye laser exciting at a wavelength of 340 nm with a pulse frequency of 800 kHz. The emission wavelength was 385 nm. The bandwidth of the emission monochromator was in the range 0.04-0.2 mm. All fluorescence decay curves were observed at the magic angle, 54.7 °, and data were collected with a 512-multichannel analyzer with a minimum of 104 counts in the peak channel. This measuring system has been previously described in detail.26,27 The measurements were carried out at 25 °C. The I/III vibronic intensity ratio of pyrene was obtained using a SPEX Fluorolog 1680 instrument. The slit width was set to 1 mm. The excitation wavelength was 310 nm. The increment was 0.5 nm with an increment time of 1 s. The exponential series lifetime distribution analysis was carried out using a nonlinear least-squares fitting algorithm. In all, 18 logarithmically spaced exponentials28,29 were required to cover the range of decay rate constants from the experimental data. This range was estimated from partial fitting of the initial and final sections of the decay traces to a single exponential. The results were verified from model numerical calculations by imposing a normally distributed noise on the theoretical decay trace, obtained from fitting an experimental decay, and then reanalyzing the convoluted trace. The reproducibility of the results was consistently better than 15%. Results and Discussion Time-Resolved Fluorescence Quenching of Pyrene by Halothane. The fluorescence decay of pyrene was measured in 5 wt % copolymer aqueous solutions of each of the three block copolymers. As seen from the residuals, Figure 1, the fluorescence decay is not exactly single exponential in any of these systems. However, it is the case that a single-exponential approximation is best represented by the data for P104, which shows well-defined micelles at 25 °C and, thus, is more representative of pyrene located in a uniform type of environ-

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Wen et al.

TABLE 2: Values of Parameters Obtained from Immobile and Dispersive Modelsa polymers P84

P104

F38

halothane (mM) 0 0.4 0.79 1.98 7.9 15.8 0 0.4 0.79 1.19 1.98 7.9 15.8 0 7.9

n0

% halothane associated with POP

τ/µs

Infelta-Tachiya model n kqm (s-1)

0.181 0.24 0.34 2.0 5.5 8.3

9.5 × 106 11 × 106 6.6 × 106 5.2 × 106 4.6 × 106

0.2 × 106 0.4 × 106 9.9 × 106 26 × 106 35 × 106

0.42 0.43 0.69 0.87 0.91

0.6 1.0 2.2 3.7 7.8 9.6

1.4 × 106 1.3 × 106 0.9 × 106 1.0 × 106 1.5 × 106 2.2 × 106

0.48 × 106 0.87 × 106 1.5 × 106 3.1 × 106 11 × 106 20 × 106

0.79 0.82 0.89 0.88 0.92 0.94

1.7

25 × 106

31 × 106

0.41

0.229 1.4 2.7 4.1 6.9 27.4 54.7

43 37 54 54 28 18

dispersive kinetic k0 ) 1/τ0 (s-1) R

0.200

a

n0, theoretical occupancy number; n, experimental occupancy number from immobile kinetic analysis; kqm, quenching rate constant from immobile kinetic analysis; k0, apparent quenching rate constant from dispersive kinetic analysis.

ment. The other systems adhere, less, to single-exponential decay behavior due to the more diverse nature of the environments in which the pyrene is located. This gives rise to a distribution of pyrene lifetimes. Nevertheless, the single-exponential approximation was used as a reasonable starting point for the modeling of these data. The measured fluorescence lifetime of pyrene in the absence of halothane was 181 ns in P84, 229 ns in P104, and 200 ns in F38, respectively, cf. Table 2. The value for P104 is in reasonable agreement with the previously reported lifetime of 215 ns.30 An important aspect of the interaction between anesthetics and triblock copolymers is to know where the anesthetic is located in the block copolymer aggregates. Fluorescence spectroscopy provides a means to determine this. In a previous study of these binary aqueous block copolymer systems, the magnitude of the I/III vibronic intensity ratio of pyrene indicated that, when micelles are present, the pyrene molecules locate in the core of the micelle consisting of the POP segments.31 As well, timeresolved fluorescence quenching can provide information concerning the dynamics of the interaction between probe and quencher.32 In the present work, it was found that halothane quenches the pyrene fluorescence emission, and this provided an opportunity to interpret these data in terms of the location of halothane (quencher). There are two possible mechanisms of fluorescence quenching, i.e., collisional (short range) and Coulombic (long range). In long-range quenching, the absorbance spectrum of the quencher must overlap the emission spectrum of the probe. Since halothane does not absorb light in the 300-500 nm region, the quenching mechanism in these systems must be short range and, hence, the quenching of pyrene by halothane is evidence that halothane must be located near to pyrene, for example, at the periphery of the core of the micelle. This is consistent with a previous study that showed halothane quenched the fluorescence emission of a protein component located in a hydrophobic environment and, therefore, the halothane must have been located in this same environment.33 Extent of Aggregation in Aqueous Solutions of P104, P84 and F38. The micellar properties of block copolymers P104 and P84, in the presence and absence of halothane, have been reported in a recent paper.31 It was determined for binary aqueous solutions of 5 wt % P104 that both the I/III intensity ratio of pyrene and the scattered light intensity showed the presence of micelles above the critical micelle temperature (CMT) of ca. 17 °C. Dynamic light-scattering studies further

confirmed the presence of micelles and that their hydrodynamic radius was ca. 8.5 nm at 25 °C. Furthermore, their size remained approximately constant with increasing temperature. In this same study, it was shown that aqueous solutions of 5 wt % P84 are in the premicelle state at 25 °C. This was evident from the large magnitude of the I/III intensity ratio of pyrene at 25 °C. However, estimates of the hydrodynamic radius from dynamic light scattering measurements as a function of temperature showed that well-defined micelles began to form at ca. 35 °C. It was concluded that an increase in temperature depletes the hydration water from around the POP segments and enhances hydrophobic interactions, thus inducing the formation of micelles of P84. Micelle formation in aqueous solutions of P84 and of P104 was also investigated in the presence of halothane,31 and the latter was found to induce micelle formation in both of these copolymers in a manner similar to that of an increase in temperature. It was proposed that halothane molecules replace hydration water around the POP segments. The addition of halothane was found not to change the size of P104 aggregates until a concentration of ca. 80 mM of halothane was reached. However, at these conditions, halothane was also found to affect the hydration water around the POE segments. In the case of 5 wt % P84, the formation of micelles was also supported by a sharp drop in the I/III intensity ratio of pyrene and the fact that dynamic light-scattering results showed the presence of aggregates having a hydrodynamic radius of ca. 8.5 nm. In contrast to the P104 and P84 systems, the I/III intensity ratio of pyrene and light-scattering data did not show the existence of any micelles in aqueous 5% F38 copolymer systems, either at temperatures up to 60 °C or at concentrations of halothane up to 20 mM. Immobile Quenching of Pyrene by Halothane. In a quantitative description of the fluorescence quenching processes in a micelle, it is usual to introduce the fluorescence decay in the form32

I(t) ) A1 exp(-A2t + A3(exp(-A4t) - 1))

(1)

where, A1, A2, A3, and A4 are fitting coefficients. In the application of this expression, it is assumed that the occupation of micelles by probe and quencher follows Poisson statistics and that the probe and the quencher are associated almost exclusively with the micelle phase. The general kinetic description, taking into account such assumptions, can be reduced to the Infelta-Tachiya model,34,35 with eq 1 rewritten as

Quenching of Excited State Pyrene by Halothane

t I(t) ) A1 exp - + n(exp(-kqmt) - 1) τ

[

J. Phys. Chem. B, Vol. 103, No. 46, 1999 10095

]

(2)

where A1 is the fluorescence intensity at zero time, τ is the lifetime of the fluorescence probe in the absence of quencher, n is the mean occupancy number of quencher in the micelles, and kqm is the intramicellar quenching rate constant. For a detailed discussion of the model, and its limitations, readers are referred to a comprehensive monograph32 and original papers.34,35 The application of eq 2 to the analysis of the fluorescence decay of pyrene in the absence and presence of different halothane concentrations in P104 micelles is illustrated in Figure 2. The results of the best fit of the experimental data to eq 2 are shown in Table 2. Changes in kqm are observed for P104, for which self-organization occurs even in the absence of halothane. It is believed that these changes in kqm reflect changes associated with the removal and replacement of water by halothane at the core-corona interface of the micelles.31 It is to be noted that the kqm values in P104 are the smallest of all the systems reported here. The theoretical occupancy number, n0, of the quencher in P104 micelles (Table 2) was estimated from the nominal molar mass (5410 amu) and the aggregation number (32) of P104 at 25 °C,36 the number of moles of halothane added to the solution and the weight percent of the block copolymer present in solution. The fact that the experimental occupancy number, n, is smaller than the theoretical value suggests that some of the halothane is not associated with the core. The remaining halothane may be in the corona of the micelle or in the bulk water phase. It is also possible that some of the halothane may be adsorbed at the glass walls. An estimate of the percent of halothane associated with the core of the P104 aggregates (Table 2) was obtained from the ratio of the experimental to the theoretical occupancy number, assuming that the experimental occupancy number represents the halothane that is associated with the core of the micelle. These results depend on the validity of the assumptions made in the Infelta-Tachiya model, especially that the probe and the quencher are associated almost exclusively within the micelle phase. In a previous study of these systems at 25 °C,31 it was shown that halothane is only partially micellized in P84 micelles, i.e., it is partitioned between the micelle and aqueous phases, and that micelles of F38 are not formed. In the case when the quencher is partially micellized, the appropriate analysis should be done using eq 1, reformulating the parameters A1, A2, A3, and A4.32 Under these circumstances, one must know the distribution coefficient, the exit and entry rate constants of a quencher molecule from the micelle, and the quenching rate constant of an excited probe by a quencher molecule in the micelle. However, one should note that the functional form of eq 1 is similar to eq 2 and that the quality of the fit of eq 2 to the experimental data was good in all the cases studied. In the absence of additional information, the more general case, eq 1, was not applied. The results of the analysis of the experimental data using eq 2 are summarized in Table 2. Dispersive Kinetic Analysis. For a more detailed discussion of the basis of the theory of dispersive kinetics, the reader is referred to refs 22, 24, and 25. Traditionally, it has been used to describe monoexponential decay in a variety of relaxation phenomena. The decay is regarded as a superposition of exponential decays each having a different probability of occurrence or, in effect, it represents a distribution of rates. It has been shown that fluorescence decay can be expressed in terms of dispersive kinetics22,24,25 by the expression

Figure 2. Typical fitting results of the fluorescence decay of pyrene in the absence and presence of different concentrations of halothane in P104 solutions. The experimental data (dots) and best-fit curve (solid lines) to eq 2 are shown. The values of the fitted parameters are shown in Table 2.

[ ( )]

t t I(t) ) A1 exp - τ τ0

R

(3)

where A1 and τ have the meaning defined previously, τ0 is the “effective lifetime”, and R is the width of the distribution of reaction lifetimes and has values in the range 0 < R e 1. In this kinetic model it is assumed that the time-dependent rate coefficient for the pseudo-first-order process of intramicellar quenching has the form

kqm(t) ) BtR-1

(4)

where B is a constant. As a result, the “effective lifetime” can be expressed in the form

τ0 )

(RB)

1/R

(5)

The meaning of the parameter R should be emphasized. If R ) 1, then the rate coefficient expressed by eq 4 is no longer time dependent, i.e., it is a classical kinetic process. The fit to eq 3 of the experimental fluorescence decay data of pyrene in the absence and presence of different concentrations of halothane in P104 micelles is shown in Figure 3 and it is seen that it is as good as in Figure 2. The values of the fitting parameters are summarized in Table 2. It is clear from previous studies31 that the propensity of each of the triblock copolymer systems to aggregate in water at 25 °C differs considerably. For example, in P104 self-aggregation is essentially complete at 25 °C, in P84 self-aggregation becomes apparent at 28 °C or in the presence of ca. 2 mM halothane at 25 °C, and in F38 self-aggregation is not apparent, even in the presence of 7.9 mM halothane. Since copolymer F38 does not form aggregates at the concentrations used in the current study, the dispersive factor obtained for F38 is low and the mobility of the probe/quencher system is expected to be the greatest, as shown by the value of kqm ) 25 × 106 s-1 (Table 2). On the other hand, P104 exists in the form of micelles at 25 °C and, hence, one should expect to see a greater dispersive factor. In this case, the changes in the magnitude of the parameter kqm are less significant as halothane concentration is increased.

10096 J. Phys. Chem. B, Vol. 103, No. 46, 1999

Figure 3. Typical fitting results of the fluorescence decay of pyrene in the absence and presence of different concentrations of halothane in P104 solutions. The experimental data (dots) and best-fit curve (solid lines) to eq 3 are shown. The values of the fitted parameters are shown in Table 2.

Wen et al.

Figure 5. Exponential series lifetime distribution of pyrene in 5% P104 aqueous solution as a function of halothane concentration (mM). Logarithmically spaced decay rate constants were used, and the amplitudes presented were fitted using a nonlinear least-squares technique.

Figure 4. Dispersive factor of halothane in 5% P84 and P104 aqueous solutions as a function of halothane concentration.

The magnitude of the I/III vibronic intensity ratio of pyrene in P84 showed that ca. 2 mM of halothane is required to induce formation of well-defined micelles.31 The results presented for P84 in Table 2 clearly show a sharp increase in the value of the dispersive factor and an increase in the experimental occupancy number, cf. Figure 4, at concentrations of halothane greater than 2 mM. It is interesting to note that there is a corresponding decrease in the value of kqm for the case of P84, and this may reflect changes in the morphology of the micelles of this system induced by addition of halothane. Increasing amounts of the latter would favor a more compact selforganization of the aggregates. As it is seen from Figure 3, a good fit of the experimental results is obtained when eq 3 is used to analyze the data for P104. As expected, the “effective lifetime” (τ0) of pyrene becomes shorter as the concentration of halothane is increased (Table 2). The lowest values of R (Table 2) occur for copolymer F38 in the presence 7.9 mM of halothane and for copolymer P84 in the presence of ca. 0.4-0.8 mM of halothane. These results indicate that under these conditions both copolymer systems show little evidence of self-assembly. On the other hand, copolymer P104, both in the absence and presence of halothane at all concentrations investigated, and copolymer P84, at

Figure 6. Exponential series lifetime distribution of pyrene in 5% P84 aqueous solution as a function of halothane concentration (mM). Data treatment was the same as for Figure 5.

concentrations of halothane exceeding 7.9 mM, show values of R in the range 0.79-0.94. These high values of R indicate a lower degree of dispersion in these systems and a higher degree of self- aggregation. In this context, the value of the dispersion coefficient obtained from dispersive kinetics appears to be a good probe of the degree of self-assembly in systems that are capable of undergoing such reorganization through intermolecular interactions. The dispersive kinetic model has been applied to the study of micelle systems of aqueous HTAC (hexadecyltrimethylammonium chloride).22 However, it is difficult to compare results as both the probe-quencher pair and the micelle systems are different. Exponential Series Lifetime Distribution Analysis. The results of this analysis are presented in Figures 5, 6, and 7, for copolymer systems P104, P84, and F38, respectively. Figure 5 illustrates essentially a single distribution of rate constants at all concentrations and suggests that the degree of order in the P104 system does not change much as a function of increasing halothane concentration. This is consistent with the fact that micelles are already present, even in the absence of halothane.

Quenching of Excited State Pyrene by Halothane

J. Phys. Chem. B, Vol. 103, No. 46, 1999 10097 systems that show a change in morphological structure as a function of their concentration. As well, it has been shown that exponential series lifetime distribution analysis can provide useful complementary information about the presence of aggregates and the onset of aggregation in systems where selfassembly can occur. Acknowledgment. M.S. is grateful to Professor A. Plonka for stimulating discussions concerning dispersive kinetics and to the British Council and State Committee for Scientific Research in Poland for their financial support. Funding of this work by the Natural Sciences and Engineering Research Council of Canada is appreciated. References and Notes

Figure 7. Exponential series lifetime distribution of pyrene in 5% F38 aqueous solution as a function of halothane concentration. Data treatment was the same as for Figure 5.

The only noticeable change is the shift of the entire distribution of rate constants to higher values at higher concentrations of additive. The increase in the magnitude of the rate constant with concentration is nonlinear, cf. Table 2, and is consistent with the decrease in the fraction of halothane in the micelle core. The case of P84 (Figure 6) is more complicated. Up to 0.4 mM of halothane, there exists a wide distribution of rate constants. At 0.79 mM of halothane, the distribution becomes bimodal. These changes may be interpreted as arising from initiation of the micelle formation process, noticeable even at 0.4 mM of halothane, which leads to creation of distinct environments for the pyrene molecules, with different quencher concentrations and/or diffusion coefficients. At 1.98 mM, it appears that most of the pyrene molecules are incorporated in well-defined micelles containing halothane. However, a small but distinct fraction of pyrene has longer lifetimes and is probably the pyrene associated within the more hydrophilic micelle corona and, thus, subject to lower concentrations of hydrophobic quencher. The amount of this longer-lived pyrene decreases as the halothane concentration is further increased since the pyrene environment becomes more hydrophobic due to micelle core dehydration, as discussed in our previous paper.31 F38 did not appear to form well-defined micelles even at higher concentrations of halothane.31 However, in Figure 7 it appears that there is definitely a bimodal distribution of rate constants in the presence of 7.9 mM of halothane, in some way similar to that observed with intermediate halothane concentrations for P84. This may be interpreted as showing the onset of micelle formation, which allows halothane to concentrate in the more hydrophobic environment of the micelle cores, jointly with a large fraction of the probe. This still leaves a significant fraction of pyrene located in the more hydrophilic corona where it is exposed to less quencher. This study has shown that dispersive kinetics can provide an alternative description of the degree of self-assembly in micelle systems. While it is not clear which of the two alternative kinetic models, immobile or dispersive, is more valid for the systems studied, the dispersive model does provide an opportunity to analyze the dynamics of aggregate systems under less restrictive conditions than are specified for the application of eq 1. This would be particularly useful for self-assembly in

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