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Molecular Motions in Threadlike Micelles Toshiyuki Shikata,* Shin-ichiro Imai, and Yotaro Morishima Department of Macromolecular Science, Osaka University, Toyonaka, Osaka 560, Japan Received November 21, 1996. In Final Form: June 24, 1997X Molecular motions of a cetyltrimethylammonium cation (CTA+) and a salicylate anion (Sal-) in threadlike micelles formed by themselves in aqueous solution were examined by use of fluorescence probe techniques. Long and stable threadlike micelles are formed around the equimolar ratio of cetyltrimethylammonium bromide (CTAB) and sodium salicylate (NaSal), and the system shows a profound viscoelasticity. Cetylacridinium orange bromide (CAOB) and sodium 2-hydroxy-3-naphthoate (NaHNA) were employed as substitute fluorescence probes for the CTA+ cation and the Sal- anion, respectively. The fluorescence lifetime and the steady-state fluorescence anisotropy of these probes were measured with varying the NaSal concentration, while the concentrations of CTAB and the probes were kept constant. Since the probes had unimodal fluorescence lifetimes at any molar ratios of NaSal to CTAB, the conventional Perrin equation relating the fluorescence lifetime and rotational relaxation time (τφ) through fluorescence anisotropy was used to evaluate τφ of the probes. The τφ values for both the probes are essentially independent of the molar ratio of NaSal/CTAB, once the threadlike micelle has grown sufficiently above a ratio higher than unity. These imply that molecular motions of the probes, which may be identical to those of the CTA+ cation and the Sal- anion in the threadlike micelle, are essentially independent of macroscopic viscoelastic behavior of the micellar system such as the longest relaxation time or viscosities. Because the transition moment of the probe CAO+ cation is located within the 9-carbon to 10-nitrogen direction of an acridinium head group, the lateral diffusional coefficient of the CAO+ cation, which should be quite similar to that of CAT+, in the threadlike micelle is roughly evaluated to be ca. 1 × 10-5 cm2 s-1 with a simple equation of Dlat ∼ a2/τφ, where a is the radius of the micelle.
Introduction Some detergent molecules make very long and stable rodlike or threadlike micelles with or without additives in aqueous solution.1-5 A cationic surfactant, cetyltrimethylammonium bromide (CTAB), is one of the typical examples forming threadlike micelles with additives. CTAB forms a threadlike micelle with sodium salicylate (NaSal) in aqueous solution even at a low concentration on the order of 1 mM.4,5 The system (CTAB:NaSal/W) shows profound viscoelastic behavior due to entangling between the threadlike micelles formed.4,5 It is well-known that rheological behavior of the CTAB: NaSal/W system has a plateau modulus in a lower frequency range than 10 Hz and its magnitude is proportional to the square of the concentration of CTAB, like concentrated polymer systems.4,5 Thus, the entanglement between threadlike micelles is an essential reason for the elasticity as it is in the polymer system. However, the threadlike micellar system shows a single relaxation process in the slowest mode with a time constant which is strongly affected by the concentration of free salicylate (Sal-) anions not bound to the micelle.5 The single mode of the longest relaxation process in the threadlike micelle is quite in contrast to the distribution of relaxation modes in the slowest process in concentrated polymer system.6,7 Some other threadlike micellar systems also show a single relaxation mode in the longest relaxation.8,9 The X Abstract published in Advance ACS Abstracts, September 1, 1997.
(1) Gravsholt, S. J. Colloid Interface Sci. 1976, 57, 575. (2) Candau, S. J.; Hirsch, E.; Zana, R. J. Colloid Interface Sci. 1985, 105, 521. (3) Rehage, H.; Hoffmann, H. Mol. Phys. 1991, 74, 933. (4) Shikata, T.; Hirata, H.; Kotaka, T. Langmuir 1987, 3, 1081. (5) Shikata, T.; Hirata, H.; Kotaka, T. Langmuir 1988, 4, 354. (6) Ferry, J. D. Viscoelastic Properties of Polymers, 3rd ed.; John Wiley & Sons: New York, 1980. (7) Doi, M.; Edwards, S. F. The Theory of Polymer Dynamics; Oxford University Press: London, 1986. (8) Khatory, A.; Lequeur, F.; Kern, F.; Candau, S. J. Langmuir 1993, 9, 1456. (9) Candau, S. J.; Khatory, A.; Lequeur, F.; Kern, F. J. Phys. IV 1993, 3, 197.
S0743-7463(96)02028-8 CCC: $14.00
mechanism for the longest single mode relaxation of threadlike micellar systems is still in controversy.5,10,11 The entanglement release in the threadlike micellar systems would not be controlled by a single process; however, it would depend on the types of detergents and additives in the threadlike micellar systems. From experimental results12 of a high-frequency viscoelastic measurement and a dynamic electric birefringence measurement, the fastest relaxation process in the CTAB:NaSal/W system has the shortest relaxation time on the order of 10 µs. Thus, the threadlike micelle having a long threadlike shape with a finite radius will obey Gaussian dynamics and statistics, as do flexible polymer chains, on a time scale longer than 10 µs. The threadlike micelle must possess microscopic dynamics of much shorter time scale than 1 µs and of a small spatial scale comparable to the dimension of micelle-forming species such as the CTA+ cation and the Sal- anion. Nuclear magnetic resonance (NMR) spectroscopy is one of the typical techniques to investigate microscopic behavior of molecules forming the threadlike micelle.5,13,14 Actually, sites of additive molecules bound in the threadlike micelle are assigned in detail based on their chemical shifts data.5,13 Furthermore, from NMR relaxation times, T1 and/or T2, information about microscopic dynamics of micelle-forming molecules is obtained.14,15 We previously reported rotational correlation times for the Sal- anion in the threadlike micelle determined by use of T1 data.15 Fluorescence spectroscopy is also a powerful method to investigate the microdynamics in the threadlike micelle if appropriate fluorescence probes for the system can be (10) Lequeux, F. Europhys. Lett. 1992, 19, 675. (11) Cates, M. E. Structure and Flow in Surfactant Solutions; ACS Symposium Series 578; Herb, C. A., Prud’homme, R. K., Eds.; American Chemical Society: Washington DC, 1994; Chapter 2, p 31. (12) Shikata, T.; Morishima, Y. To be submitted. (13) Bunton, C. A.; Minch, M.; Hidalgo, J.; Sepulveda, L. J. Am. Chem. Soc. 1973, 95, 3262. (14) Molecular motions of surfactant molecules in micelles are discussed in, for example: Monduzzi, M.; Olsson, U.; So¨derman, O. Langmuir 1993, 9, 2914. (15) Shikata, T.; Morishima, Y. Langmuir 1997, 13, 1931.
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employed.16-18 The additive Sal- anion is strongly fluorescent in aqueous solution12 with an adequate fluorescence lifetime to carry out experiments with an ordinary instrument with a nanosecond time resolution. Because fluorescence intensity and lifetime are good indicators about microenvironments around a fluorescence probe, a change in the intensity and the lifetime should be exact proof of alteration of the site occupied by the probe molecule.18 The rotational relaxation time (τφ) in fluorescence anisotropy is a good measure of a frequency of a molecular motion of the probe molecule. We carried out fluorescence anisotropy measurements with the Sal- anion and determined the rotational relaxation time in the threadlike micelle.18 Although the Sal- anion is quite tiny and quickly rotating in free aqueous solution, rotational motions of the Sal- anion incorporated in the micellar interior are highly restricted and the obtained τφ value agrees well with that obtained from T1 data.15 In this study, we employed two kinds of fluorescence molecules, sodium 2-hydroxy-3-naphthoate (NaHNA) and cetylacridinium orange bromide (CAOB), as substitute probe molecules for NaSal and CTAB, respectively, to investigate molecular motions of both the CTA+ cation and the Sal- anion in detail in the threadlike micelle. In our previous fluorescence studies on the CTAB:NaSal/W system,18 we focused on the fluorescence behavior of the Sal- anion. Therefore, we were unable to change the concentration of the Sal- anion in a wide range. However, in this study we can change the Sal- concentration freely, because we monitor fluorescence from the HNA- anion instead of the Sal- anion. Thus, molecular motions of micelle-forming species of both the CTA+ cation and the Sal- anion will be discussed under conditions where viscoelastic behavior is dramatically changed at high Salconcentrations.5 Experimental Section Materials. CTAB was purchased from Wako Pure Chemical Industries, Ltd. (Osaka, Japan), and was purified by recrystallization from a solution of a mixture of ethanol and acetone. Extra pure grade NaSal and NaHNA were also purchased from the same company and used without further purification. Water for solvent was deionized with a MilliQ SP system (Millipore) and had a specific resistance higher than 14 MΩ cm-1. CAOB was synthesized according to the method by Miethke and Zanker.19,20 Acridine orange hydrochloride was purchased from the same company, and HCl was removed by neutralization with equimolar sodium hydroxide in aqueous solution. Acridine orange was treated with cetyl bromide in toluene under reflux for several hours. The resulting precipitates (CAOB) were recrystallized from methanol. CAOB was identified by elementary analysis and NMR spectroscopy. CTAB concentration (CD) was kept at 10 mM, while NaSal concentration (CS) was varied from 0 to 410 mM. NaHNA concentration was changed from 0.05 to 1 mM for solutions with CS ) 50 mM and was kept at 1 mM in other solutions. The concentraiton of the other probe, CAOB, was kept constant at lower than 1 µM. Glycerine was used as a solvent to measure the instantaneous fluorescence anisotropy (r0) of both NHA- and CAO+ because they were slightly soluble in glycerine which had a high viscosity and is glassy below -10 °C; r0 is the fluorescence anisotropy at time zero. The concentrations of NaHNA and CAOB in glycerine for the r0 determination were lower than 0.1 µM. (16) Verman, B.; Valanlinkar, B. S.; Manohar, C. J. Sci. Technol. 1987, 3, 19. (17) For example, Grieser, F.; Drummond, C. J. J. Phys. Chem. 1988, 92, 5580. (18) Shikata, T.; Morishima, Y. Langmuir 1996, 12, 5307. (19) Miethke, E.; Zanker, V. Z. Phys. Chem. (Frankfurt am Main) 1958, 18, 375. (20) Yamazaki, A.; Masui, T.; Watanabe, F. J. Phys. Chem. 1981, 85, 281.
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Figure 1. Time dependent fluorescence intensity of the HNAanion in aqueous solution (a) and in the CTAB:NaSal/W system at CD ) 10 mM and CS ) 30 mM (b) at 25 °C. Excitation wavelength was 380 nm and fluorescence was monitored through a cutoff filter L48 (λ > 480 nm). One must be very careful about fluorescence quenching by oxygen molecules and heavy atoms existing in systems. Our systems including CTAB possess Br- anions which can be a strong quencher in some cases. We confirmed that Br- had no effect on the fluorescence intensity in aqueous solutions of NaHNA with varying NaBr concentrations up to 20 mM, concluding the Br- was not a quencher for HNA-. This is presumably because of electrostatic repulsion between Br- and HNA- anions. We did not take any special care to remove oxygen, because the fluorescence lifetimes of NHA- and CAO+ were short enough ( 480 nm, Toshiba) was placed in front of the photomultiplier for measurements with solutions containing NaHNA and Y50 (λ > 500 nm, Toshiba) for solutions containing CAOB. The same quartz cell as above was employed for the fluorescence lifetime measurements, and temperature was kept at 25 °C.
Results Fluorescence Lifetimes. Fluorescence decays for all the solutions examined were well reproduced by fitting with a single-exponential function with lifetime τlife. Typical decay profiles for HNA- are shown in Figure 1. An aqueous solution of free NaHNA without CTAB and NaSal shows a very short τlife of 1.6 ns, but a solution with both CTAB and NaSal at CD ) 10 mM and CS ) 30 mM shows a much longer τlife of 5.0 ns. It is well-known that the fluorescence lifetime is sensitive to chemical environments around a fluorescence probe and can be a measure of micropolarity. In a previous paper,18 we reported that fluorescent Salanions had two distinctive lifetimes in the CTAB:NaSal/W system: a short τlife of 4 ns in the free aqueous phase, and a longer τlife of 8 ns in the micellar interior phase. When CS is higher than CD, the Sal- anion has fluorescence decay curves which can be decomposed into long and short lifetime components proportional to the population of both
Molecular Motions in Threadlike Micelles
Figure 2. Dependence of fluorescence lifetime (τlife) on CS for the HNA- anion in the CTAB:NaSal/W system with CD ) 10 mM at 25 °C. A closed symbol means data in NaSal aqueous solution.
the states. In the case of the HNA- anion, fluorescence decay curves for solutions at CD < CS can be well expressed with only one τlife, and the τlife values are weakly dependent on CS as seen in Figure 2. This implies that all HNAanions are incorporated in a micellar interior phase under the conditions CD < CS, and no HNA- anion can exist in the bulk aqueous phase any more. Because the τlife values for the HNA- anion are independent of its concentrations in the range 0.05-1.0 mM in the solutions with CD ) 10 and CS ) 50 mM, the HNA- anion well works as a substitute fluorescence probe of the Sal- anion in the concentration up to 1.0 mM to reflect chemical environments of the threadlike micellar interior of the CTAB: NaSal/W system. The pH values for the solutions at CS ) 10 and 300 mM were 6.9 and 7.5, respectively. Because the pKa value of 2-hydroxy-3-naphthoic acid is not far from the pKa value ()2.8) of salicylic acid, most NaHNA molecules are dissociated into HNA- form in all the conditions examined. Thus, the fraction of the HNA- form was very close to 1.0 and was not altered in the solutions. Presumably, the pH change from 6.9 to 7.5 in the solutions results in slight reduction in the τlife values as seen in Figure 2. Since CAOB is hardly soluble in water, the τlife of CAO+ in free aqueous solution is not available. However, CAOB is slightly soluble in a less viscous aqueous solution of CTAB at CD ) 10 mM. In this solution, CAOB is dissociated and incorporated or dissolved in spherical micelles formed by CTA+. In Figure 3, the dependence of the τlife values on CS is shown at CD ) 10 mM. The τlife value at CS ) 0 mM reflects the state in the spherical micelle and the others in the threadlike micelle. Since CAO+ can hardly exist in the bulk aqueous phase, all CAO+ cations are in the micellar interior. When CD < CS, the τlife values are essentially independent of CS as observed in the case of HNA-. The longer τlife value (ca. 1 ns) at CD < CS than that (ca. 0.3 ns) at CS ) 0 mM indicates that the microenvironment around the CAO+ in the threadlike micelle is less polar than in the spherical micelle. Fluorescence Anisotropy. Fluorescence anisotropy (r) is defined by eq 1 below. If one carries out fluorescence anisotropy measurements with a spectrometer which can sample out fluorescence data as a function of time, r should be defined as a function of elapse time after excitation by spikelike light. In this case, the rotational correlation time of a fluorescence probe can be estimated directly from time dependence of r. Since the time-correlated single-photon counting system used in this study does
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Figure 3. Dependence of τlife on CS for the CAO+ cation in the CTAB:NaSal/W system with CD ) 10 mM at 25 °C.
Figure 4. Dependence of fluorescence anisotropy (r) on CS for the HNA- anion in the CTAB:NaSal/W system with CD ) 10 mM at 25 °C. A closed symbol means data in NaSal aqueous solution.
not have enough time resolution to estimate the rotational correlation times of the probes precisely, r was measured under the steady state excitation conditions with a steadystate spectrometer. In eq 1, Ivv denotes fluorescence intensity when the system is excited by vertically polarized light and emission is monitored through a vertical polarizer, and Ivh denotes the intensity excited by vertical light and monitored through a horizontal polarizer.
r)
Ivv - gIvh Ivv + 2gIvh
(1)
The g factor in eq 1 is defined as Ihv/Ihh, which is a polarization characteristic of the spectrometer used. The g factor is a function of monitored emission wavelength, and the g factor is 1.37 and 1.38 at 520 and 530 nm, respectively, for our spectrometer. The r values of HNA- are plotted as a function of CS in Figure 4. A closed symbol in the same figure implies the r value for free HNA- in aqueous solution and in aqueous NaSal solution. In the free and NaSal aqueous solution rotational motion of HNA- is so fast that the r is very small close to 0.001. However, the r values for solutions of the threadlike micelles fully grown at CS larger than CD are almost independent of CS and very much larger than that for the free aqueous solution. This means that
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Figure 5. Dependence of r on CS for the CAO+ cation in the CTAB:NaSal/W system with CD ) 10 mM at 25 °C.
the rotational motion of HNA- is highly restricted in the micellar solutions. As described in the previous section, the difference in the fluorescence lifetimes of HNA- anions in the free aqueous solution and in the CTAB:NaSal/W system strongly suggests that most HNA- anions are incorporated in the threadlike micelle. Thus, the increase in the r value for the probe in the CTAB:NaSal/W system reflects depression of the rate of rotational motions in the threadlike micelle. Because molecular size and structure of the HNA- anion are not so different from those of a salicylate (Sal-) anion, HNA- can be regarded as a substitute molecular probe for Sal- in the micelle. In Figure 5, the r values of CAO+ cations in the CTAB: NaSal/W system are also plotted as a function of CS. Since CAOB was insoluble in water, the r of the CAO+ cation in free aqueous solution was not obtained. The r values in the CTAB:NaSal/W system are essentially independent of CS under conditions in which the threadlike micelle has grown as seen in those of the HNA- anion. The CAO+ cation must be incorporated in the threadlike micelles because of its insolubility in the bulk water phase. The CS independent r values of the CAO+ cation in the micelle imply that a rotational motion of the CAO+ cation is not affected by CS under conditions where the threadlike micelle has sufficiently grown. The r value at CS ) 0 mM is not different from those at higher CS. This does not mean that the rate of the rotational motion of the CAO+ cation at CS ) 0 mM in the spherical micelle is the same as in the threadlike micelle. Because the τlife of the CAO+ cation in the spherical micellar interior is much shorter than those in the threadlike micellar one, the rate of rotational motion of the CAO+ cation in the spherical micelle is much faster than that in the threadlike micellar interior (see below). Rotational Relaxation Times. The fluorescence anisotropy (r) measured under the steady excitation conditions can be related to the rotational relaxation time (τφ) of a fluorescence molecular probe with the Perrin equation (eq 2),18 if free rotation of the probe can be assumed.
(
)
3τlife 1 1 ) 1+ r r0 τφ
(2)
Here r0 is the instantaneous fluorescence anisotropy of an examined fluorescence probe. Generally, r0 can be determined from time-dependent fluorescence decay. However, the instrument we operated for the fluorescence
Figure 6. Dependence of the rotational relaxation time (τφ) on CS for the HNA- anion in the CTAB:NaSal/W system with CD ) 10 mM at 25 °C. A closed symbol means data in NaSal aqueous solution.
lifetime measurement had only a sub-nanosecond time resolution, which was not short enough to get r0 for both HNA- and CAO+ even in the micellar interior site. The other method to determine r0 is that the r value of a probe dissolved in an extremely high viscosity media can be regarded as the r0 value with high accuracy. Both NaHNA and CAOB are slightly soluble in glycerine, which is a sufficiently viscous glass around -10 °C to estimate r0. Thus, the r0 values of HNA- and CAO+ were determined to be 0.34 and 0.37, respectively, because the r values of both HNA- and CAO+ in glycerine remained constant in a temperature range from -10 to -15 °C. In general, r0 depends on the angle between the axes of the transition moment and of the emission of fluorescence. The r value becomes the maximum of 0.4 when the two axes are parallel. In the case of HNA- and CAO+, the obtained r0 values are close to 0.4; therefore, the angles between their axes are close to 0°. The rotational relaxation times (τφ) estimated from eq 2 are plotted as a function of CS for the HNA- anion in Figure 6. When the HNA- anion is in free and NaSal aqueous solution, the τφ is quite short (ca. 0.01 ns), indicating the HNA- anion can rotate very quickly. On the other hand, the HNA- anion has a much longer τφ value (ca. 1.5 ns) almost independent of CS, when it is incorporated in the threadlike micellar interior. This means that the rotation motion of the HNA- anion is highly restricted by surrounding detergent and additive molecules in the threadlike micellar interior. It is interesting to note that the τφ of the Sal- anion in the same threadlike micelle reported in the previous paper18 is identical to that of the NHA- anion. As we pointed out previously, the HNA- anion can be considered as a substitute molecular probe for the Sal- anion. The molecular motions of the HNA- anion might be quite similar to those of the Sal- in the threadlike micellar interior. In Figure 7, the τφ values for the CAO+ cation are shown as a function of CS. Although the τφ value in the spherical micellar interior at CS ) 0 mM is 1.5 ns, the τφ values become longer to be ca. 4 ns and independent of CS, just as the HNA- anion behaves in the fully grown threadlike micellar interior. This implies that the rotational motion of the CAO+ cation in the threadlike micellar interior is highly restricted due to the high local concentration of detergents and additives which depress the rate of rotation. Since the CAO+ cation can be regarded as a substitute fluorescence probe for the CTA+ cation, the dependence of the τφ values on CS of the CTA+ cation in
Molecular Motions in Threadlike Micelles
Figure 7. Dependence of τφ on CS for the CAO+ cation in the CTAB:NaSal/W system with CD ) 10 mM at 25 °C.
the threadlike micellar interior should be similar to those of the CAO+ cation. Macroscopic features such as viscosities and the longest relaxation times for the CTAB:NaSal/W system are strongly affected by the amount of excess Sal- anions which exist in the bulk aqueous phase. The concentration of the excess Sal- anion can be estimated in this manner as CS* ) CS - CD, because the threadlike micelle consists of a 1:1 complex between CTA+ and Sal-, like a salt. In the system at CD ) 10 mM, the values of the longest relaxation time of the system steeply decrease with CS typically from the order of 10 s to 10 ms.12 Thus, the time scale for entanglement release between threadlike micelles which must be the longest relaxation mechanism in the threadlike micellar system is strongly affected by CS. However, the molecular rotational motions of the micelle forming CTA+ and Sal- are essentially independent of CS when the threadlike micelle has sufficiently grown at CS > CD. These findings strongly suggest that the molecular motions of the micelle forming species are independent of macroscopic rheological behavior of the threadlike micellar system. Discussion Rotation of HNA and CAO+ in the Threadlike Micelle. The transition moment in the HNA) anion is illustrated in Figure 8. The direction of emission of fluorescence should be very close to that of the transition moment, because the obtained r0 of the HNA- anion is 0.34, not far from 0.4. Thus, for the HNA- anion a rotational molecular motion around the axis 1 can be most effective for fluorescence anisotropy relaxation. The HNAanion has two hydrophilic groups which must stick out radially from the surface of the micelle into the bulk aqueous phase as the Sal- anion does in the micelle (Figure 8). Thus, a naphthalene ring is stuck into the micellar interior. Indeed, the HNA- anion can migrate easily along the surface of the micelle, therefore, its rotational motion around the axis 1 occurs simultaneously during the translational migration along the surface of the threadlike micelle. Of course, the migrational motion along the surface can relax the time correlation of the direction of the transition moment of the HNA- anion because the surface of the threadlike micelle is a cylindrical shape. However, the rate of the rotation around the axis 1 is much faster than that of a rotation of the transition moment induced by the migrational motion. The τφ values for the HNA- anion in the fully grown threadlike micelle is quite close to those of the Sal- anion. -
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Figure 8. Schematic representation of the direction of transition moments and typical rotational axes for both the HNAanion and the CAO+ cation. The surface of the micelle formed in the CTAB:NaSal/W system is also described schematically.
This implies that the HNA- anion can rotate around the axis 1 at the same rate as the Sal- anion does in the micelle18 and the HNA- is a pefect substitute molecular probe for the Sal- anion. The transition moment of the CAO+ is placed in a direction from the 9-carbon to the 10-nitrogen. And the axis of fluorescence emission is essentially identical to the transient moment. A rotational motion around the axis 1 defined in Figure 8 is ineffective for the fluorescence anisotropy relaxation since the rotation can not alter the direction of the transition moment. However, a rotational motion around the axis 2 should be effective for the relaxation. The CAO+ cation should be incorporated in the threadlike micelle in the way that an acridinium head group is placed on the surface of the micelle and a long alkyl tail is deeply inserted in the hydrophobic core of the micelle as schematically depicted in Figure 8. Thus, the allowed molecular motion of the CAO+ cation in the micelle to relax the fluorescence anisotropy is a migrational motion along the cylindrically curved micellar surface. The Lateral Diffusion Coefficient of CTA+ in the Threadlike Micelle. Translational or migrational molecular motions of the CTA+ cation along the surface of the threadlike micelle are directly related to its lateral diffusion coefficient in the micelle. With the relaxation behavior of fluorescence anisotropy of the substitute molecular probe CAO+ in the threadlike micelle, one can discuss the lateral diffusion coefficient of the CTA+ cation in the threadlike micelle as follows. The migrational motion of the acridinium head group along the cylindrical surface of the threadlike micelle is schematically described in the Figure 9. Then, the migrational motion can be split into two modes; a mode in which the CAO+ cation translates on the surface in the direction of the long axis of the threadlike micelle, and the other mode in which the CAO+ cation has circular motions along the cross section of the threadlike micelle. The mode along the long axis should be effective for a self-diffusional motion of a tracer molecular probe detected by a fluorescence photobleaching recovery technique (FPR)22 or a forced Rayleigh scattering (FRS)23 but is not effective for the fluorescence anisotropy relaxation. How(21) Perrin, F. J. Phys. Radium. 1926, 7, 39. (22) Peter, R.; Cherry, R. J. Proc. Natl. Acad. Sci. U.S.A. 1982, 79, 4317. (23) Nemoto, N.; Yamamoto, T.; Osakai, K.; Shikata, T. Langmuir 1991, 7, 2607.
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anisotropy relaxation techniques.17 The rotational diffusion coefficient (Dr) of a spherical micelle with the radius of a can be expressed with the Stokes-Einstein law as21
Dr ) kBT/6Vη
Figure 9. Schematic representation of migrational motions of the CAO+ cation along the surface of the threadlike micelle. The random migrational motions of the probe can be separated into two motions: (a) linear translation motions along the long axis of the threadlike micelle; (b) circular motions along the cross section of the threadlike micelle.
ever, the other mode along the cross section of the micelle is much more effective for the fluorescence anisotropy relaxation, because the direction of the transition moment can be randomized easily by this mode. Of course, values of the lateral diffusion coefficient for both the modes should be identical to each other. When one pays attention to the translational mode along the cross section, the time required for the acridine head group to randomize the direction of the transition moment by the diffusional translation should be τφ, and the mean square of curvilinear distance (〈l2〉) to randomize the direction would be proportional to the square of a radius (a2) of the threadlike micelle. τφ can be related to a2 through the lateral diffusional coefficient (Dlat) of the CAO+ in this manner as
τφ ∝ a2/Dlat
(3)
The proportionality constant is not obvious, but we estimate it to be the order of unity. Now one can roughly estimate the Dlat to be on the order of 10-5 cm2 s-1 with the values of τφ ) 4 ns and a ) 2.5 nm which is well-known from images of electromicrographs24 and light25 and neutron26 scattering data. Reported Dlat values22 for phospholipid molecules in vesicles measured by use of FPR range between 10-6 and 10-9 cm2 s-1. The Dlat values obtained in the threadlike micellar system is larger than those in the vesicle. Because this difference in the Dlat might imply difference in efficiency of molecular motions between those systems, it is likely that the migrational motion of the CTA+ cation in the threadlike micelle is much faster than that of the phospholipid molecule possessing two long tails in the vesicle. In the case of surfactant micellar systems, very few Dlat values have been reported. Most reported data27 were determined by use of NMR relaxation measurements in surfactant liquid crystalline phase systems, and the data range around 10-7 cm2 s-1. However, in micellar systems including spherical micelles with a small radius (ca. 2-3 nm), the rotational diffusion of the spherical micelle contributes seriously to the fluorescence anisotropy relaxation. Thus, one must be very careful about estimation of the Dlat for spherical micellar systems with fluorescence (24) Vinson, P. K.; Talmon, Y. J. Colloid Interface Sci. 1989, 133, 288. (25) Imae, T.; Ikeda, S. J. Phys. Chem. 1986, 90, 10030. (26) Herbst, L.; Kalus, J.; Schmelzer, U. J. Phys. Chem. 1993, 97, 7774. (27) Charvolin, J.; Rigny, P. J. Chem. Phys. 1973, 58, 3999.
(4)
where kB, T, V, and η, respectively, mean Boltzmann’s constant, the absolute temperature, the volume of a spherical micelle, and viscosity of a medium used. On the other hand, τφ ) 1/2Dr. Thus, when a2/Dlat is smaller than 1/2Dr, Dlat cannot be determined precisely with eq 3. In the CTAB:NaSal/W system at CD ) 10 mM and CS ) 0 mM only spherical micelles are formed. The τφ can be estimated based on the rotational diffusion of the spherical micelle by use of eq 4 with a of 2.5 nm, and τφ ) 48 ns is obtained. This τφ value is larger than that obtained in this study. Therefore, the τφ value at this condition essentially corresponds to the τφ value assigned to the migrational motion of the CTA+ cation in the spherical micelle. In the case of the spherical micelle, the τφ value can reflect the migrational motion of the CTA+ related to Dlat only when the τφ value is much shorter than 48 ns as this case. Nevertheless, in the case of the fully grown threadlike micellar system, motions of micellar portions should be highly restricted by existence of a long threadlike sequence connected to both sides. Therefore, the τφ values obtained reflect the migrational motion of the CTA+ cation along the surface of the threadlike micelle quite precisely. It is likely that the Dlat value in the spherical micelle is not so different from that in the threadlike micelle. The threadlike micelle in the CTAB:NaSal/W system has other microdynamic motions such as a bending motion. The bending motion should be an elementary one for generation of rubber-like elasticity on a long time scale due to conformational entropy of the long threadlike micelle. The frequencies of the bending motion of the threadlike micelle range between 101 and 105 Hz.12 Although the bending motion indeed can be effective for fluorescence anisotropy relaxation, the time scale for the bending is too long to be a major factor for the relaxation. Most parts of the relaxation are governed by the migrational motion along the surface of the micelle, especially along a circular cross section of the micelle in a time scale of 1 ns. Conclusions Molecular motions of the CTA+ cation and the Sal- anion in the threadlike micelle formed by themselves were investigated with fluorescence substitute probes, the CAO+ cation and the HNA- anion, by use of a fluorescence anisotropy analysis. Although the rheologically determined longest relaxation times are strongly affected by the Sal- concentration at a constant CTA+ concentration, the rotational relaxation times of both the probes are essentially independent of the Sal- concentration. This implies that the molecular motions of micelle forming species do not alter once the threadlike micelle is formed, and the rheological relaxation modes are completely independent of the molecular motions in the micelle. Moreover, the lateral diffusional coefficient of the CTA+ cation in the threadlike micelle is estimated to be on the order of 10-5 cm2 s-1 through the rotational relaxation time of the CAO+ cation. This value is larger than those of phospholipids in vesicles by a factor of ca. 10 or more. LA962028N
