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Rotational Friction in AOT Microemulsions: Relevance of Hydrodynamic and Dielectric Contributions to Microviscosities Probed by Fluorescent Bis[4-(dimethylamino)phenyl] Squaraine Ce´sar A. T. Laia and Sı´lvia M. B. Costa* Centro de Quı´mica Estrutural, Complexo 1, Instituto Superior Te´ cnico, 1049-001 Lisboa, Portugal Received August 6, 2001. In Final Form: November 9, 2001 Fluorescence depolarization of a squaraine dye (HSq, bis[4-(dimethylamino)phenyl] squaraine) was studied in pure viscous solvents triacetin (glycerol triacetate) and ethylene glycol. In ethylene glycol, the hydrodynamic friction given by the Stokes-Einstein equation accounts for the observed results; in triacetin, the dielectric friction becomes important because of the slow dielectric response of the liquid. Average rotational relaxation times were calculated from fluorescence anisotropy measurements within reversed micelles with water, glycerol, and formamide as the entrapped polar solvents, and the variation in the trend with the amount of each polar solvent (wo, go, or fo) is quite different. The results are interpreted by comparison with those obtained in pure viscous solvents and show the contribution of the dielectric friction in aqueous reversed micelles. In glycerol reversed micelles, the importance of both the dielectric and hydrodynamic friction is shown. In formamide reversed micelles, the inner pool appears immobilized. The dye rotation dynamics is affected by the location of the inner pool, which in turn reflects the dielectric interactions with the media. The dye partition between different interfacial sites was assessed by steady and transient-state (picosecond time scale) fluorescence measurements.
Introduction The dynamics of confined liquids in biological environments has been a hot topic in current research.1 In these systems, the liquids have different physical properties that greatly affect the course of chemical reactions. Normally, the polarity is smaller and the local viscosity is higher than in the bulk liquid. Conversely, the liquid dynamics exhibits components on the nanosecond time scale that are not found in the bulk state. Reasons for such behavior are not yet completely clear, making mimetic models such as reversed micelles particularly important for the understanding of such features.1 Reversed micelles are spherical molecular aggregates dispersed in an oil phase that is coated by a surfactant layer, with the polar solvent inside the droplet.1-4 These structures are found on the L2 (oil-continuous) phase of the ternary diagram. A common system where reversed micelles are formed without the help of a fourth component is the isooctane/AOT/water system, in which AOT (aerosol OT or sodium bis(2-ethylhexyl)sulfosuccinate) is an anionic surfactant with a hydrophobic double chain.3,4 The structure of this system is now relatively well understood: spherical aggregates are formed, the hydrodynamic radius changes linearly with the amount of water in the solution (the parameter wo ) [H2O]/[AOT]), and both the temperature (T) and the dispersed-phase volume fraction (φ) * Corresponding author. E-mail:
[email protected]. Telephone: (351) 21 8419271. Fax: (351) 21 8464455. (1) Nandi, N.; Bhattacharyya, K.; Bagchi, B. Chem. Rev. 2000, 100, 2013. Bhattacharyya, K.; Bagchi, B. J. Phys. Chem. A 2000, 104, 10603. (2) Fendler, J. H. Acc. Chem. Res. 1976, 9, 153. Chem. Rev. 1987, 87, 877. (3) Luisi, P. L.; Giomini, M.; Pileni M. P.; Robinson, B. H. Biochim. Biophys. Acta 1988, 947, 209. (4) Meier, W.; Eicke, H.-F. Curr. Opin. Colloid Interface Sci. 1996, 1, 279.
within the solubilization phase boundary have a low impact on the aggregate structure.5,6 The substitution of water by other polar solvents such as glycerol and formamide has been recently attempted, and the aggregate’s structure7-18 was studied by dynamic light scattering.7,9,17,18 Some fundamental aspects of solvation dynamics in these restricted environments were investigated,19,20 and the application of these systems as media for polymerization reactions has been highlighted.21 Isooctane/AOT/glycerol reversed micelles resemble aqueous systems, namely, the aggregates remain spherical, (5) Zulauf, M.; Eicke, H.-F. J. Phys. Chem. 1979, 83, 480. (6) Ricka, J.; Borkovec, M.; Hoffmeier, U. J. Chem. Phys. 1991, 94, 8503. (7) Fletcher, P. D. I.; Galal, M.; Robinson, B. H. J. Chem. Soc., Faraday Trans. 1 1984, 80, 3307. (8) Fletcher, P. D. I.; Robinson, B. H.; Tabony, J. J. Chem. Soc., Faraday Trans. 1 1986, 82, 2311. (9) Laia, C. A. T.; Lo´pez-Cornejo, P.; Costa, S. M. B.; d’Oliveira, J.; Martinho, J. M. G. Langmuir 1998, 14, 3531. (10) Bergenståhl, B.; Jo¨nsson, A.; Sjo¨blom, J.; Stenius, P.; Wa¨rnheim, T. Prog. Colloid Polym. Sci. 1987, 74, 108. (11) Martino, A.; Kaler, E. W. J. Phys. Chem. 1990, 94, 1627. Langmuir 1995, 11, 779. (12) Schubert, K.-V.; Strey, R.; Kahlweit, M. Prog. Colloid Polym. Sci. 1992, 89, 263. (13) Schubert, K.-V.; Busse, G.; Strey, R.; Kahlweit, M. J. Phys. Chem. 1993, 97, 248. (14) Mathew, C.; Saidi, Z.; Peyrelasse, J.; Boned, C. Phys. Rev. A: At., Mol., Opt. Phys. 1991, 43, 873. (15) Boned, C.; Saidi, Z.; Xans, P.; Peyrelasse, J. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 1994, 49, 5295. (16) Arcoleo, V.; Aliotta, F.; Goffredi, M.; La Manna, G.; Liveri, V. T. Mater. Sci. Eng., C 1997, 5, 47. (17) Riter, R. E.; Kimmel, J. R.; Undiks, E. P.; Levinger, N. E. J. Phys. Chem. B 1997, 101, 8292. (18) Laia, C. A. T.; Brown, W.; Almgren, M.; Costa, S. M. B. Langmuir 2000, 16, 8763. (19) Riter, R. E.; Undiks, E. P.; Kimmel, J. R.; Levinger, N. E. J. Phys. Chem. B 1998, 102, 7931. (20) Shirota, H.; Horie, K. J. Phys. Chem. B 1999, 103, 1437. (21) Schubert, K.-V.; Lusvardi, K. M.; Kaler, E. W. Colloid Polym. Sci. 1996, 274, 875.
10.1021/la011238j CCC: $22.00 © 2002 American Chemical Society Published on Web 02/07/2002
Rotational Friction in AOT Microemulsions Scheme 1
Langmuir, Vol. 18, No. 5, 2002 1495 Table 1. HSq Photophysics in Triacetin and Ethylene Glycol T/K
and the size changes linearly with the parameter go ) [glycerol]/[AOT].7,9 A significant effect on the aggregation of these reversed micelles is due to strong attractive interactions between the droplets, and clusters of reversed micelles are formed at lower values of T and φ than those used in related aqueous systems.18 For the isooctane/AOT/ formamide reversed micelles, however, the situation is more complicated. The classical linear relation between the hydrodynamic radius and the amount of polar solvent (in this case, fo ) [formamide]/[AOT]) does not exist, and strong variations with both T and φ are found.18 Many aspects concerning the photophysics of organic molecules in nonaqueous microemulsions remain unknown because they are relatively new. Problems related to the diffusion and partition of molecules inside the droplets are to the best of our knowledge almost unexplored, with few known studies in existence.17,22 The photophysics of a squaraine dye (HSq, bis[4(dimethylamino)phenyl] squaraine, see Scheme 1) was studied earlier in aqueous reversed micelles of AOT to probe the interface polarity23 and dynamic features of the dye photophysics in the interfacial region.24 The solvatochromism of HSq is sensitive to the local polarity and proticity of the environment, and a partition of the dye between two different regions of the interface was observed. In this contribution, we report the photophysical features of HSq in nonaqueous reversed micelles and the results of steady-state fluorescence anisotropy studies whereby the probe rotation was used to gain insight into how the aggregate structural features affect the fluidity of the confined liquid. Furthermore, some important microscopic aspects of the glycerol and formamide reversed micelles, namely, solute diffusion, partition, and polar solvent penetration at the interface, are revealed and must be taken into account when both structural18 and dynamic aspects are discussed.19,20 It is shown that the low polarity of these systems, the slow dielectric relaxation, and the high concentration of salt in the inner pool have a great impact on solute diffusion because of the contribution of dielectric friction.25,26 It is concluded that the separation of dielectric and hydrodynamic friction is not possible, and it is suggested that in this complex media they are coupled. Experimental Section A. Materials. Squaraines were obtained from Xerox Inc. and used as received. AOT was purchased from Sigma and purified by solubilization with methanol in contact with active charcoal for 24 h and evaporation of the methanol under reduced pressure. After purification, the surfactant was kept in a desiccator with CaCl2. Spectroscopic grade isooctane and triacetin were purchased from Labscan; spectroscopic grade glycerol and formamide were purchased from Aldrich. All solvents were used as received. AOT concentration was kept constant at 0.1 M. Dye concentra(22) Lo´pez-Cornejo, P.; Costa, S. M. B. Langmuir 1998, 14, 2042. (23) Laia, C. A. T.; Costa, S. M. B. Phys. Chem. Chem. Phys. 1999, 1, 4449. (24) Laia, C. A. T.; Costa, S. M. B. J. Chem. Soc., Faraday Trans. 1998, 94, 2367. (25) Maroncelli, M. J. Chem. Phys. 1997, 106, 1545. (26) Balabai, N.; Sukharevsky, A.; Read, I.; Strazisar, B.; Kurnikova, M.; Hartman, R. S.; Coalson, R. D.; Waldeck, D. H. J. Mol. Liq. 1998, 77, 37.
279.3 284.7 293.8 302.9 311.8 320.9 329.8 339.0
φf
τ/ns
Triacetin 0.47 2.22 0.45 2.09 0.44 1.88 0.40 1.68 0.39 1.50 0.38 1.34 0.35 1.19 0.32 1.06
r 0.267 0.260 0.220 0.201 0.168 0.140 0.118 0.109
T/K 280.4 288.4 295.6 299.2 302.8 307.3 311.8 320.9 329.9 338.9
φf
τ/ns
Ethylene Glycola 0.22 0.85 0.18 0.68 0.13 0.52 0.12 0.46 0.11 0.09 0.08 0.06 0.05 0.03
r 0.291 0.297 0.295 0.288 0.279 0.277 0.277 0.281 0.275 0.263
a For ethylene glycol, only φ values were obtained above 300 K f because of the short τf value of the probe. Because kf does not change with temperature (kf ) 0.26 × 109 s-1), τf was estimated from τf ) φf/kf.
tions were always lower than 1 × 10-6 M because of their low solubilities and to keep the optical density below 0.1. Samples were made from stock solutions in chloroform by careful solvent evaporation. All measurements were made 1 day after sample preparation to ensure complete dye solubilization. B. Apparatus. Absorption spectra were recorded with a JASCO V-560 UV/vis spectrophotometer. Steady-state emission measurements were recorded with a Perkin-Elmer LS 50B spectrofluorimeter with the sample holder thermostatted at 22 °C and instrument corrected. Oxazin 1 was used as the fluorescent standard (φf ) 0.11).27 Steady-state fluorescence anisotropy measurements were also made in the same spectrofluorimeter by recording emission spectra using different combinations of horizontal or vertical polarization for excitation and emission. The values obtained were constant within the random noise. The r values shown in this work are the averages of these results. Fluorescence decays of HSq in triacetin were measured using the time-correlated single photon counting technique (S.P.C.) with a PTI LS-100 instrument from Photon Technology International.28,29 A hydrogen lamp (relative pressure ) 17 in. Hg) was used as the excitation source, with fwhm ≈ 2.1 ns. Excitation was at 600 nm, and emission was collected at 650 nm. All decays were well fitted by a single exponential. In triacetin and ethylene glycol, fluorescence quantum yields were determined in the temperature range 280-340 K. Fluorescence decays in triacetin were in the same range; in ethylene glycol, the range was 280-299.2 K. Experiments in reversed micelles were always performed at room temperature (298 K). Time-resolved fluorescence decays in reversed micelles were measured using a S.P.C. instrument with picosecond resolution. A rhodamine 6G dye laser (Spectra Physics model 375) was synchronously pumped by a mode-locked Nd:YAG laser (Spectra Physics model 3400). Excitation was at 595 nm, and the emission was collected at 650 and 675 nm. The fwhm of the instrument response function was typically about 130 ps. Further details may be found elsewhere.30
Results and Discussion A. HSq in Triacetin and Ethylene Glycol: SteadyState Fluorescence Anisotropy. In this work, we made use of fluorescence depolarization of HSq in viscous homogeneous media. Experiments in triacetin (glycerol triacetate) and ethylene glycol were performed to obtain the fundamental fluorescence anisotropy, r0, and the hydrodynamic radius of the molecule. These results are listed in Table 1, along with fluorescence quantum yield, φf, and fluorescence lifetime, τf, data. (27) Kringel, U. Ph.D. Thesis, 1988 Siegen. (28) Medeiros, G. M. M.; Le ita˜o, M. F.; Costa, S. M. B. J. Photochem. Photobiol. A 1993, 72, 255. (29) Ferreira, J. A. B.; Costa, S. M. B.; Ferreira, L. F. V. J. Phys. Chem. A 2000, 104, 11909. (30) Bogen, S.-T.; Karolin, J.; Molotkovsky, J.; Johansson, L. B.-Å. J. Chem. Soc., Faraday Trans. 1998, 94, 2435.
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D)
kBT ζhf + ζdf
(3)
The hydrodynamic friction is given by the Debye-StokesEinstein equation:33,34
ζhf ) 8πηfR3Cslip
Figure 1. HSq Perrin plot (eq 1) in ethylene glycol (O) and in triacetin (b). Insert: Expanded ethylene glycol data.
According to Perrin, the steady-state fluorescence anisotropy is related to the fluorescence lifetime through eq 1:31
r0 1 kBTτf -1) r Vh η
(1)
where r is the experimental steady-state anisotropy, Vh is the molecular hydrodynamic volume, kB is the Boltzmann constant, T is the temperature, and η is the solvent viscosity. Accordingly, a plot of 1/r versus Tτf/η should be a straight line for both solvent systems, and as long as we are in the stick limit, (see Figure 1) r0 and Vh values may be extracted. Different slopes obtained in triacetin and in ethylene glycol are the first indication that eq 1 does not hold for this system. Also, the value obtained for r0 (r0 ) 0.32) is lower than expected. Even in micellar environments where fluorescence depolarization occurs, r can reach the value of 0.32, and the maximum value of the fundamental anisotropy that a molecule can have (with parallel absorption- and emission-transition moments) is 0.4. The measured value of r0 should be higher and closer to this limiting value. Finally, Vh can be calculated by summing the van der Waals volumes according to the standard procedure.32 The van der Waals radius should be approximately 4.1 Å, but the value extracted from the Perrin plot is 5.96 Å. The reasons for this discrepancy may have several sources. On one hand, the molecule does not have a spherical shape;33 on the other hand, nonhydrodynamic contributions to the friction, such as dielectric friction,25,26 may appear, and these features are not taken into account in the Perrin plot. The concept of dielectric friction originates from the physical picture of a point dipole, µ, rotating inside a spherical cavity. As the dipole rotates, a polarization in the solvent is induced that acts on the dipole according to the reaction field of the medium. Because the medium does not respond instantaneously, the reaction field delays the rotation of the point dipole. This is the so-called dielectric friction, ζdf,26 that can be decoupled from the hydrodynamic (mechanical) friction, ζhf, that results from hard collisions with the repulsive wall of the intermolecular potential. Therefore, the total friction, ζf, is given by eq 2:26
(4)
Cslip is the slip factor (Cslip ) 1 in the stick limit), f accounts for the molecular nonspherical shape,33 and R is the spherical molecular radius. An expression for the dielectric friction of a Debye solvent (with exponential dielectric relaxation)35 was derived by Nee and Zwanzig; it has the following form in the zero frequency limit when the solvent high-frequency dielectric constant, ∞, is equal to 1:
ζdf )
6µ2 - 1 τD a3 (2 + 1)2
(5)
a is the cavity radius and τD is the Debye-solvent relaxation time. For HSq, µ ) 0, but it has a relatively strong quadrupole moment. It was shown by Balabai et al. and Hartman et al. that in such molecules the dielectric friction is also important and can be quantified if the distribution of charges is known.26,36 The expression may be found elsewhere, but the important result also depends on and τD in the same manner:
ζdf ∝
-1 τD (2 + 1)2
(6)
Considering the HSq molecular structure, the assumption that it may be treated as a spherical solute is unrealistic, and the shape factor, f, should be calculated. Perrin37 studied this problem and derived the following expression for the case of an oblate ellipsoid:33
f)
2 3
[
1 - F4
]
F2 (2 - F ) arctan(F2 - 1)1/2 - F2 2 1/2 (1 - F ) 2
(7)
F is the axial ratio of the ellipsoid and may be calculated using the results of Bigelow and Freund38 from semiempirical molecular orbital calculations on the structural and electronic properties of HSq. The axial dimensions are a ) 10 Å and b ) 2.4 Å, which gives F ) 4.2 and f ) 1.92. The rotational relaxation time, τR, can be experimentally determined using eq 8:
r τ τR ) 3 r0 - r f
(8)
The dependence of τR on the properties of the liquid is
τR )
4πf CslipR3 η 3µap2 1 - 1 τD + 3 kB T a okB (2 + 1)2 T
(9)
(2)
o is the vacuum permittivity. For the two solvents, we adjusted the results with eqs 8 and 9 in which the only
(31) Perrin, F. J. Phys. Radium 1926, 7, 390. (32) Edward, J. T. J. Chem. Educ. 1970, 47, 261. (33) Philips, L. A.; Webb, S. P.; Clark, J. H. J. Chem. Phys. 1985, 83, 5810.
(34) Dote, J. L.; Kivelson, D.; Schwartz, R. N. J. Phys. Chem. 1981, 85, 2169. (35) Nee, T.-W.; Zwanzig, R. J. Chem. Phys. 1970, 52, 6353. (36) Hartman, R. S.; Konitsky, W. M.; Waldeck, D. H.; Chang, Y. J.; Castner, E. W., Jr. J. Chem. Phys. 1997, 106, 7920. (37) Perrin, F. J. Phys. Radium 1934, 5, 497. (38) Bigelow, R. W.; Freund, H.-J. Chem. Phys. 1986, 107, 159.
ζf ) ζhf + ζdf The rotational diffusion coefficient is given by eq 3:
Rotational Friction in AOT Microemulsions
Langmuir, Vol. 18, No. 5, 2002 1497
Figure 2. HSq rotational relaxation times obtained in ethylene glycol (0) and in triacetin (O). The thick line represents the hydrodynamic prediction using the Stokes-Einstein equation (eqs 3 and 4), and the dashed lines include the dielectric friction contribution given by the Nee and Zwanzig (eqs 3 and 5). The overall fitting expression is eq 12.
adjustable parameters were r0 (still unknown) and 3µap2/ a3. The last parameter gives only a proportionality. No value of µ2 may be extracted because the dielectric friction comes from the HSq quadrupole moment. All other parameters are known or calculated, with the exception of τD. Ethylene glycol and triacetin are not Debye solvents; therefore, average values were calculated from the data in the literature.39-41 The triacetin case is, however, problematic. At room temperature, the relaxation is of the Cole-Davidson type, and only a value at 298 K is known.41 Therefore, we choose to use instead the solvation times, τS, obtained earlier in this solvent. The relation between this time and τD is given by eq 10:
τS )
2∞ + C τ 2 + C D
(10)
C is the cavity dielectric constant. As an approximation, we can set C ) 2, which gives25
τS )
∞ + 1 τ +1 D
(11)
Because only average τS values are known, only average τD values can be calculated with ∞ ) nD2. The fitting of eqs 8 and 9 to the experimental results was successful, enabling the calculation of realistic values for the adjustable parameters (Figure 2). The values obtained for HSq were r0 ) 0.352 and µap ) 5.1 D when we set a ) 4.1 Å. The most striking result is that the dielectric friction is very important in triacetin, whereas in ethylene glycol it is not. Reasons for this difference reside in the low value of triacetin and higher τD values, which result in a slow dielectric response to alterations in the charge distribution in the cavity. The effect of the solvent on the rotation of HSq is given by eq 12:
τR/ns ) 0.4039(η/cP) + 352.4
-1 (τD/ns) (12A) (2 + 1)2
r0 ) 0.352
(12B)
(39) Jordan, B. P.; Sheppard, R. J.; Szwarnowski, S. J. Phys. D: Appl. Phys. 1978, 11, 695. (40) Walker, G. C.; Åkesson, E.; Johnson, A. E.; Levinger, N. E.; Barbara, P. F. J. Phys. Chem. 1992, 96, 3728. (41) Castner, E. W., Jr.; Maroncelli, M. J. Mol. Liq. 1998, 77, 1.
B. HSq in Nonaqueous Microemulsions: Solvatochromism. In aqueous microemulsions, the HSq absorption and emission spectra shift to the red with increasing the water content because of an increase in the interfacial polarity.23 The substitution of water by glycerol and formamide in the inner core leads also to bathochromic shifts, as one can observe in Figure 3 (glycerol (a) and formamide (b) microemulsions). However, the wavelength maxima do not reach those in pure solvents (Figure 4). At high concentrations of glycerol and formamide, isosbestic points in the absorption spectra are observed. Also, isoemissive points are found in the emission spectra. Thus, as observed earlier in aqueous reversed micelles, the existence of two different species in the media is clearly shown spectroscopically. This effect is caused by the partition of the dye between different sites at the reversed micelle interface.24 The solvatochromic shifts are consistent with the existence of a nanophase that is rich in the polar solvent in the inner pool of the micellar aggregates. Similar shifts found in other microemulsions with polar solvents such as ethylene glycol22 show that the formation of pools is a common phenomenon in such systems and that the presence of water is not necessarily needed. C. HSq Nonradiative Processes in Nonaqueous Microemulsions. Fluorescence quantum yields, φf, were measured in glycerol and formamide AOT reversed micelles. A decrease in the value of φf with an increase in polar solvent content is observed, which is an expected result that is caused by the increase in polarity in the dye vicinity. Fluorescence decays (Figure 5) are biexponential, in accordance with previous results in aqueous AOT reversed micelles.24 As in previous work, the data were analyzed using the two-state excited-state model42,43 in which two different species are distinguished from each other: one resides in the hydrophobic part of the interface, and another is located in the polar part (in the borders of the pool).24 In such a scheme, partition equilibria for the HSq solubilization between these two areas in the interface must be considered. This type of analysis is presented for both nonaqueous systems in the following sections. Isooctane/AOT/glycerol microemulsions. For g0 ) 0 (the same as w0 ) 0), the fluorescence decay is monoexponential in accordance with previous results.24 As glycerol is added, the decays are increasingly biexponential with a small but steady decrease of the average fluorescence lifetime. In Table 2, the results of the decay analysis (λem ) 650 nm) are presented. In Figure 6, it is possible to observe that the decay time constants are independent of the emission wavelength, likewise in water systems.24 However, unlike those in aqueous reversed micelles, the lifetime variations for the long-lived components are small. Also, the existence of only two components in the fluorescence decays corroborates the assumption of a dye partition between two sites inside the reversed micelles, as was also assumed in water-in-oil microemulsions. In the present case, the situation is more clear because we have taken into account the isosbestic and isoemissive points in the spectroscopic measurements. In the application of the two-state excited-state scheme (see Appendix 1) to the HSq partition in aqueous reversed micelles, the fluorescence quenching by water needed to be considered and made the analysis more difficult.24 In glycerol reversed micelles, however, the decay time (42) Berberan-Santos, M. N.; Martinho, J. M. G. J. Chem. Educ. 1990, 67, 375. (43) Andriessen, R.; Boens, N.; Ameloot, M.; De Schryver, F. C. J. Phys. Chem. 1991, 95, 2047.
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Figure 3. HSq absorption and emission spectra in (a,b) glycerol AOT microemulsions and in (c,d) formamide AOT microemulsions for different polar solvent concentrations given by go ) [glycerol]/[AOT] and fo ) [formamide]/[AOT].
Figure 4. HSq solvatochromic shifts in (a) glycerol and (b) formamide AOT microemulsions ((0) absorption, (9) emission, (4) absorption maxima, and (2) emission maxima in the pure glycerol and formamide.
constants change little with increases in g0. This behavior is an indication of a small quenching effect by glycerol and little change of the polarity of sites where HSq is solubilized; therefore, there is a small amount of penetration of glycerol into the interface, which is in contrast to the behavior observed in water. Nevertheless, a small amount of quenching of the long-time decay constant is observed.
Figure 5. HSq fluorescence decays in both (a) glycerol-in-oil and (b) formamide-in-oil AOT microemulsions (λex ) 590 nm, λem ) 650 nm).
In the two-state excited-state scheme, the decay constants are given by eq 13 (see Appendix 1 for details): λ1,2 ) [- (γi + γp + k1 + k2) ( x(γi + γp + k1 + k2)2 - 4(γiγp + k1γp + k2γi)] 2
(13)
Rotational Friction in AOT Microemulsions
Langmuir, Vol. 18, No. 5, 2002 1499 Table 3. Fitting Results with the Two-State Excited-State Model in Glycerol Reversed Micelles 0.015 ( 0.001 0.13 ( 0.01 0.45 ( 0.05 0.26 ( 0.01 0.26 ( 0.01 0 ( 0.01 0.086 ( 0.009 20 ( 30
KiSV kinr, ns-1 kpnr, ns-1 kif, ns-1 kpf , ns-1 k1, ns-1 k2, ns-1 Kp × p/I
Figure 6. HSq fluorescence decay times in glycerol reversed micelles (A) and formamide reversed micelles (B) obtained from biexponential analysis in eq 14 (λex ) 590 nm) ((0) λem ) 650 nm, (4) λem ) 675 nm). Table 2. HSq Fluorescence Quantum Yields, Steady-State Fluorescence Anisotropy (λex ) 600 nm), and Decay Times (λex ) 595 nm, λem ) 650 nm) in Glycerol and Formamide Reversed Micelles ([AOT] ) 0.1 M) Isooctane/AOT/Glycerol Reversed Micelles g0
φf
a1
τ1/ns
0 0.57 1.15 1.43 1.72 2.12 2.42 2.95 3.41 3.79
0.56 0.49 0.45 0.44 0.44 0.43 0.43 0.43 0.42 0.42
1.00 0.82 0.81 0.77 0.76 0.77 0.75 0.77 0.78 0.75
2.63 2.55 2.44 2.41 2.37 2.35 2.32 2.31 2.26 2.28
a2 0.18 0.19 0.23 0.24 0.23 0.25 0.23 0.22 0.25
τ2/ns
χ2
DW
r
1.35 1.23 1.24 1.18 1.27 1.19 1.23 1.34 1.22
1.336 1.210 1.157 1.160 1.108 1.192 1.113 1.158 1.254 1.147
1.795 2.066 2.033 2.020 2.044 2.032 2.055 2.014 2.020 2.006
0.15 0.21 0.27 0.29 0.30 0.30 0.31 0.32 0.32 0.32
Isooctane/AOT/Formamide Reversed Micelles f0
φf
a1
τ1/ns
a2
τ2/ns
χ2
DW
r
0.3 0.6 0.9 1.2 1.5 1.65 1.8
0.56 0.48 0.40 0.37 0.35 0.35 0.34
0.70 0.68 0.75 0.70 0.68 0.69 0.69
2.57 2.49 2.37 2.33 2.23 2.19 2.15
0.30 0.32 0.25 0.30 0.32 0.31 0.31
1.75 1.61 1.33 1.33 1.18 1.17 1.12
1.241 1.262 1.167 1.128 1.126 1.054 1.100
1.945 1.822 2.004 2.000 2.068 1.993 1.960
0.17 0.21 0.23 0.26 0.28 0.29 0.30
depends on the probe location at the reversed micelle. In the case of these microemulsions, the quenching is relatively weak; it is undetectable for the decay constant that corresponds mostly to the decay at the glycerol pool. Therefore, this approximation is acceptable and is preferred to the case of aqueous reversed micelles where the quenching was so strong that the approximation could not be made.24,44 Besides the transient data, information can also be obtained from steady-state results.24 The fluorescence quantum yields are related to the kinetic constants, thus enabling the quantification of φ from experimental results. The variation of φ with g0 comes from the change in the value of the volume ratio, Vp/Vi , between the pool and the interface:
( )( ) ( )( )
φi + φpKp φ) 1 + Kp
p i
p i
Vp Vi Vp Vi
(16)
φi is the fluorescence quantum yield in the hydrophobic domain equal to kif/(kif + kinr +kiSV× g0 + k1 - k2), and φp is the fluorescence quantum yield in the hydrophilic domain equal to kpf /(kpf + kpnr + kpSV× g0 - k1 + k2). p/i is the molar absorption coefficient ratio between the two domains. The volumes are calculated using the linear correlation between the reversed micelle hydrodynamic radius, rh, (in Å) and g0, which is fairly independent of both temperature and φ:9
The fluorescence decay is given by the following expression:
rh/Å ) 15 + 9g0
I(t,λex,λem) ) a1(λex,λem) exp(λ1t) + a2(λex,λem) exp(λ2t) (14)
(17)
kiSVg0 ) kiq[glycerol]i
(15a)
kpSVg0 ) kpq[glycerol]p
(15b)
The results of the fitting (Table 3) using these equations are similar to those obtained in the aqueous system for the radiative and nonradiative rate constants of the reversed micelle, that is, k1 is again negligible and k2 is slightly smaller than the value observed in the aqueous system.24 The major difference lies with the value of the partition coefficient, which is much larger in this system even though the error is large. This result was expected because the squaraine is much more soluble in glycerol than in water. Because of the large errors, however, we cannot reach a definite conclusion on this point. Isooctane/AOT/formamide microemulsions. The fluorescence quantum yields also decrease as the amount of polar solvent present in the system increases. This behavior is similar to that found in water and glycerol microemulsions. The fluorescence decays are also biexponential, and the decay constants are independent of the emission wavelengths. However, the lifetime τ2 is not constant, as observed in the glycerol microemulsions. This feature is observed in Figure 6 (see also Table 2);
where kSV is a pseudo-Stern-Volmer constant whose value
(44) Laia, C. A. T.; Costa, S. M. B. Chem. Phys. Lett. 1998, 285, 385.
These equations describe the two-state model generally. The definition of the kinetic constants will render the model specific to the systems studied in this work. k1 and k2 are the rate constants for the HSq* diffusion from the interface into the pool and for the reverse process, respectively. γi and γp are intrinsic rate constants of each species and are given by γi ) kif + kinr + kiq[glycerol]i and γp ) kpf + kpnr + kpq[glycerol]p. In the definition of γ, a bimolecular quenching term is included. Because the concentration of glycerol at each site is unknown, we make the approximation that glycerol quenching is proportional to g0. Therefore,
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Table 4. Fitting Results with the Two-State Excited-State Model in Formamide Reversed Micelles i KSV p KSV i knr, ns-1 kpnr, ns-1 kif, ns-1 kpf , ns-1 Kp × p/I
0.048 ( 0.003 0.21 ( 0.01 0.16 ( 0.01 0.22 ( 0.05 0.22 ( 0.01 0.29 ( 0.01 535 ( 500
therefore, a quenching effect at each site must be considered because of the formamide penetration at the interface. The radii of reversed micelles depend on f0 and the dispersed-phase volume fraction.18 Therefore, for a fixed concentration of AOT, the relationship between the radii of the reversed micelles and f0 is not linear.9 Also, it was found that the superficial area of each AOT molecule in formamide systems (0.75 nm2)10 is higher than those in water (0.6 nm2)6 and glycerol (0.4 nm2)7,9,18 microemulsions. Again, this result is an indication that formamide is present at the interface. These structural differences are reflected in our experimental results. While the micellar size is reflected in the partition of the dye between the different nanophases, the presence of formamide at the interface influences the HSq fluorescence intensity. The reversed micelle hydrodynamic radius (Å) is given by eq 18 for [AOT] ) 0.1 M and T ) 25 °C 9:
rh/Å ) 15 + 0.815 exp(2.60f0)
(18)
This information is fundamental to the analyses of both the steady-state anisotropy (because of the rotational diffusion of the reversed micelle discussed below) and the fluorescence kinetics (because of the dye partition). The fitting of the fluorescence quantum yields and time decay constants to the two-state scheme leads to interesting features (Table 4). The partition coefficient in formamide is much larger than it is in water and glycerolin-oil microemulsions, which is reasonable because HSq is more soluble in formamide than it is in water or glycerolin-oil. One interesting fact is that both k2 and k1 are negligible in this analysis, meaning that the diffusion of the solute in the subnanophases cannot be observed on this time scale. Another aspect is the fluorescence quenching by the polar solvent. Because the HSq fluorescence quantum yield depends on the solvent polarity, the fluorescence intensity decreases with both decreasing g0 and f0. Besides this aspect, which is linked to the dye partition coefficient, bimolecular fluorescence quenching caused by hydrogen bonding between the protic solvent and HSq is also possible. This phenomenon is very important in dioxane/ water mixtures and aqueous reversed micelles.24,44 In glycerol reversed micelles, this specific interaction occurs only at the hydrophobic interface, and it is only a small effect. In formamide reversed micelles, the quenching occurs on both sides, but it is also relatively weak. In both cases, it is not possible to establish a true bimolecular mechanism for the fluorescence quenching, although this mechanism has been elucidated in aqueous reversed micelle systems.24 Nevertheless, the existence of isosbestic points (when the amounts of polar solvents are changed) and small variations in the time decay constants (small quenching effect) indicate a small amount of penetration of the polar solvent at the interface. The partition coefficient is solvent-dependent; it is larger in formamide and smaller in aqueous systems. The general trend is a decrease in the value of the partition coefficient
with an increase in the solvent proticity. HSq solubility is large in formamide and very small in glycerol, and it is insoluble in water. There are similar trends in the partition coefficient and the solvent proticity. This solubility effect of probes in micellar aggregates was studied through linear solvation energy relations,45 specifically the multiparametric empirical polarity scale from Kamlet and Taft.46 The solute basicity is always an important parameter to the solubility of solutes in water;45 the HSq basicity is relatively low in the ground state. In the excited state, the diffusion of the dye from the hydrophilic part of the interface to the hydrophobic part was detected; it is larger in water (k2 ) 1.7 × 108 s-1)24 than in glycerol (k2 ) 8.6 × 107 s-1) and negligible within our time scale in formamide microemulsions. The diffusion from the hydrophobic part into the pool (given by k1) is negligible in all systems. The preference for a more apolar medium in the excited state is understandable because the strength of the HSq quadrupole moment decreases upon electronic excitation to the singlet state.38 This phenomenon is polarity-dependent but relatively viscosityindependent; therefore, there is an energy barrier for this diffusion.47,48 The time scale for the diffusion is between 6 (water) and 11 ns (glycerol), which is similar to long solvation time scales observed in reversed micelles and found with other solutes.1,19,20,49-52 We believe that the diffusion of solutes within the interfacial region48,52 is a very important aspect that has to be taken into account in the interpretation of such experimental data. The presence of a viscous solvent (glycerol) does not affect the time scale because the profile for the solute distribution in the heterogeneous interface is mainly polarity-dependent. D. Rotational Dynamics of HSq in AOT Reversed Micelles. Steady-state fluorescence anisotropy values were obtained at room temperature in AOT reversed micelles with water, glycerol, and formamide as polar solvents. In Tables 5-7, these values are listed. The values of r increase with increasing polar solvent concentration, which directly reflects the size increase of micellar aggregates. For these values, two major mechanisms of fluorescence depolarization may be distinguished from each other: one comes from the rotation of the reversed micelles and the other comes from the rotation of the solute in the reversed micelles.53 A qualitative analysis of the anisotropy measurements may be carried out if the 〈τf〉 values are known (see Tables 5-7). The fluorescence anisotropy decays are not simple in reversed micelles because of the different mechanisms of fluorescence depolarization and the partition of the dye between different sites in the reversed micelles. However, a qualitative analysis may still be carried out as long as one bears in mind that the values of the friction that may be extracted from such an analysis are averages taken from different solute depolarization mechanisms. (45) Quina, F. H.; Alonso, E. O.; Farah, J. P. S. J. Phys. Chem. 1995, 99, 11708. (46) Kamlet, M. J.; Doherty, R. M.; Abraham, M. H.; Marcus, Y.; Taft, R. W. J. Phys. Chem. 1988, 92, 5244. (47) Pansu, R. B.; Yoshihara, K. J. Phys. Chem. 1991, 95, 10123. (48) Laguitton-Pasquier, H.; Pansu, R.; Chauvet, J.-P.; Pernot, P.; Collet, A.; Faure, J. Langmuir 1997, 13, 1907. (49) Zhang, J.; Bright, F. V. J. Phys. Chem. 1991, 95, 7900. (50) Sarkar, N.; Das, K.; Datta, A.; Das, S.; Bhattacharyya, K. J. Phys. Chem. 1996, 100, 10523. (51) Riter, R. E.; Willard, D. M.; Levinger, N. E. J. Phys. Chem. B 1998, 102, 2705. (52) Bangar Raju, R.; Costa, S. M. B. Phys. Chem. Chem. Phys. 1999, 1, 5029. (53) Keh, E.; Valeur, B. J. Colloid Interface Sci. 1981, 79, 465.
Rotational Friction in AOT Microemulsions
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Table 5. Determination of Average HSq Rotational Times 〈τR〉 or Friction 〈ζf〉 and Estimation of Microviscosity Valuesa 〈η〉ap or Average Debye Relaxation Timesb 〈τD〉ap in AOT Aqueous Reversed Micelles Using Equation 12 (Eeff ) 20) w0
rh /Å
〈τf〉 /ns
r
〈τR〉 /ns
〈ζf〉 × 1027 /kg m2 s-1
〈η〉ap /cP
〈τD〉ap /ns
0 3 6 9 12 18 25 30 40 50 60
15.3 20.3 25.5 30.8 36.0 46.5 58.8 67.5 85.0 102.5 120.0
2.691 1.522 0.825 0.634 0.565 0.475 0.415 0.398 0.396 0.362 0.376
0.145 0.210 0.230 0.247 0.256 0.264 0.268 0.273 0.273 0.273 0.273
65.3 12.7 5.6 4.9 4.7 4.4 4.0 4.1 4.1 3.7 3.9
0.537 0.105 0.046 0.040 0.039 0.036 0.033 0.034 0.033 0.030 0.032
31.5 13.8 12.1 11.7 10.8 9.9 10.2 10.1 9.2 9.5
3.20 1.40 1.23 1.19 1.09 1.01 1.03 1.02 0.93 0.97
a Assuming negligible dielectric friction. b Assuming negligible hydrodynamic friction.
Table 6. Determination of Average HSq Rotational Times 〈τR〉 or Friction 〈ζf〉 and Estimation of Microviscosity Valuesa 〈η〉ap or Average Debye Relaxation Timesb 〈τD〉ap in AOT/Glycerol Reversed Micelles Using Equation 12 (Eeff ) 20) g0
rh /Å
〈τf〉 /ns
r
0.0 0.6 1.2 1.8 2.4 3.0 3.6 3.9
15.0 20.4 25.8 31.2 36.6 42.0 47.4 50.1
2.691 2.579 2.337 2.388 2.210 2.238 2.235 2.207
0.145 0.213 0.272 0.296 0.310 0.318 0.322 0.320
〈τR〉 /ns
〈ζf〉 × 1027 /kg m2 s-1
〈η〉ap /cP
〈τD〉ap /ns
46.1 83.1 98.8 92.7 101.6 101.0 84.5
0.379 0.684 0.812 0.762 0.835 0.831 0.695
114 206 245 229 251 250 209
12 21 25 23 25 25 21
a Assuming negligible dielectric friction. b Assuming negligible hydrodynamic friction.
Table 7. Determination of Average HSq Rotational Times 〈τR〉 or Friction 〈ζf〉 and Estimation of Microviscosity Valuesa 〈η〉ap or Average Debye Relaxation b Times 〈τD〉ap in AOT/Formamide Reversed Micelles Using Equation 12 (Eeff ) 6.3) f0
rh /Å
〈τf〉 /ns
r
0.00 0.30 0.60 0.90 1.20 1.50 1.65 1.80
15.3 16.2 18.3 22.9 32.9 54.6 73.7 102.0
2.698 2.600 2.500 2.340 2.260 2.200 2.100 2.049
0.145 0.174 0.211 0.233 0.263 0.280 0.288 0.295
〈τR〉 /ns
〈ζf〉 × 1027 /kg m2 s-1
〈η〉ap /cP
〈τD〉ap /ns
43.0 29.9 28.0 29.3 32.0
0.353 0.246 0.231 0.241 0.263
106 74 69 72 79
4.3 3.0 2.8 2.9 3.2
a Assuming negligible dielectric friction. b Assuming negligible hydrodynamic friction.
The simplest expression to describe steady-state anisotropy measurements is53
1 1 ) [1 + 6(DM + DI) 〈τf〉] r r0
(19)
where r is the measured steady-state fluorescence anisotropy , r0 is the fundamental anisotropy of the dye, DM is the rotational diffusion coefficient of the micelle, and DI is the internal rotational diffusion coefficient of the dye. This model implies that the anisotropy decay should be exponential and that the rotation of the reversed micelle plus the rotation of the dye inside the reversed micelle cause the overall depolarization. This is a very simple
model that ignores many features of the reversed micelle. In this work, the model does not take into account the partition of the dye inside the reversed micelle. Interfacial and geometrical effects are also neglected because the model is idealized to a homogeneous micelle situation. Nevertheless, it gives good insight into fluidity changes inside the reversed micelle with increasing concentrations of polar solvents, and it is very simple to use.54 The rotational diffusion coefficient is given by the wellknown Stokes-Einstein equation:
D)
kBT 6Vhη
(20)
Vh is the hydrodynamic volume of the rotating particle. To calculate DI from experimental values of r, several parameters are required. DM is easily calculated because the hydrodynamic radius of the reversed micelles was determined earlier for the three systems studied.3,9 For AOT aqueous microemulsions, the relation between rh with w0 is given by eq 21:
rh/Å ) 15 + 1.75w0
(21)
Values of DI were calculated afterwards for the three systems, which enabled us to determine average HSq rotational relaxation times inside the reversed micelles from eq 22:
〈τR〉 )
1 2DI
(22)
Alternatively, the average friction, 〈ζf〉, is
〈ζf〉 )
kBT DI
(23)
In Tables 5-7, all the calculations are shown to allow for easy comparison among the three systems. As expected, the values obtained are considerably higher than those in bulk solvents, with the exception of glycerol, which is very viscous (see also Table 8). The main problem that emerges concerns the origin of 〈ζf〉. Generally, the increase in friction is interpreted as an increase of the so-called “microviscosity”.53,54,57,58 This parameter enables the scaling of reactions in microheterogeneous systems that are diffusion-controlled with results obtained in pure solvents. However, specific effects in such data analysis are neglected not only for the dielectric but also for the ionic friction that comes out from the ionic atmosphere.26,33,59,60 In Tables 5-7, microviscosity values ,〈η〉ap, were calculated in the three systems neglecting all nonhydrodynamic contributions to the friction (i.e., setting ζdf ) 0, which implies that 〈ζf〉 ≈ 〈ζhf〉). In this way, 〈η〉ap values are readily calculated using the Stokes-Einstein equation. The values obtained in aqueous reversed micelles are qualitatively similar to those previously obtained in the same system with other solutes.54,57 At low water con(54) Hasegawa, M.; Sugimura, T.; Shindo, Y.; Kitahara, A. Colloids Surf. A 1996, 109, 305. (55) Rønne, C.; Thrane, L.; Åstrand, P.-O.; Wallqvist, A.; Mikkelsen, K. V.; Keiding, S. R. J. Chem. Phys. 1997, 107, 5319. (56) Rizk, H. A.; Elanwar, I. M. Z. Phys. Chem. (Leipzig) 1971, 245, 289. (57) Andrade, S. M.; Costa, S. M. B. Prog. Colloid Polym. Sci. 1996, 100, 195. (58) Drake, J. M.; Klafter, Phys. Today 1990, 46. (59) van der Zwan, G.; Hynes, J. T. Chem. Phys. 1991, 152, 169. (60) Hartman, R. S.; Konitsky, W. M.; Waldeck, D. H. J. Am. Chem. Soc. 1993, 115, 9692.
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Table 8. Calculated Values of Hydrodynamic Friction (ζhf), Dielectric Friction (ζdf), and Ionic-Atmosphere Friction (ζif) in Pure Solvents and in Reversed Micelles Using Equations 4, 5, and A6 Pure Solvents η cp
τD/ ps
ζhf × 1027/ ζdf × 1027/ ζif × 1027/ kg m2 s-1 kg m2 s-1 kg m2 s-1 a
water 0.98 8.2b 80.2 0.0033 glycerol 1490 8350c 42.5 4.9500 formamide 3.57 42d 111 0.0119
0.00007 0.13580 0.00027
0.00007
