Langmuir 1997, 13, 1931-1937
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Anisotropic Rotation of Salicylate Anions in Threadlike Micelles Toshiyuki Shikata* and Yotaro Morishima Department of Macromolecular Science, Osaka University, Toyonaka, Osaka 560, Japan Received October 22, 1996. In Final Form: December 30, 1996X Microscopic dynamics of salicylate (Sal-) anions in long rodlike or threadlike micelles formed by cetyltrimethylammonium bromide (CTAB) and sodium salicylate in aqueous solution was examined by use of magnetic nuclear resonance (NMR) spin-lattice relaxation time (T1) measurement. Molecular motions of Sal- anions are remarkably restricted in the threadlike micelle. The rotational correlation times for the Sal- anion estimated from the T1, by taking into account only intramolecular dipole-dipole interaction, are in good agreement with those previously estimated from fluorescence anisotropy. Rotational motions of free Sal- anions in aqueous solution are slightly anisotropic presumably because their molecular shape is not spherical. Within the threadlike micelle, however, tumbling motions of the Sal- anion are highly restricted due to the fact that the Sal- anion is electrostatically restrained by CAT+ cations. Molecular motions of the CTA+ cation in the micelle are also highly restricted. The rotational correlation time for the CTA+ cation in the micelle is not affected by the concentration of the free Sal- anion, although its concentration has a strong effect on rheological behavior. Thus, the microscopic motions and some related physical parameters, such as the persistence length of the micelle, are essentially independent of the concentration of the free Sal- anion once the threadlike micelle is formed.
Introduction Some types of detergent molecules form very long and stable rodlike or threadlike micelles with or without additives in aqueous solution.1-5 Cetyltrimethylammonium bromide (CTAB) is a typical cationic surfactant, forming threadlike micelles with additives; e.g., it can form threadlike micelles with sodium salicylate (NaSal) in aqueous solution even at low concentrations.4,5 This system (CTAB:NaSal/W) shows profound viscoelastic behavior due to entanglement between the micellar threads. When one pays attention to the physical behavior of the threadlike micellar systems on a time scale longer than 100 ms, viscoelastic properties of the systems, especially the longest relaxation processes,5-7 must be the most interesting behavior. However, the structure of the micelles is not immobile on a time scale shorter than 1 ms but is fluctuating very quickly, because the micelle is not constructed with permanent chemical bonding but only with intermolecular interactions such as hydrophobic bonding. Individual detergent and additive molecules are able to migrate very easily within the micelles. In the case of the CTAB:NaSal/W system, the threadlike micelle is constituted in the form of a 1:1 complex between the CTA+ cation and the Sal- anion, a type of salt. When one adds an excess amount of NaSal to CTAB, Sal- remains in the bulk aqueous phase. Then, Sal- anions are exchanged between states or sites in the micellar interior and in the bulk aqueous phase.5 NMR spectroscopy is a powerful technique to investigate microscopic behavior and dynamics of molecules that constitute the threadlike micelle, because one can focus on a chemical circumstance around individual functional groups or atoms as well as their motional information X
Abstract published in Advance ACS Abstracts, March 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) Lequeux, F. Europhys. Lett. 1992, 19, 675. (7) 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.
S0743-7463(96)01026-8 CCC: $14.00
by use of NMR chemical shifts and NMR relaxation behavior.8-13 In fact, sites of additive molecules, for example Sal- anions, in the micelle were characterized on the basis of their chemical shift data.5,8 In the case of the CTAB: NaSal/W system, a resonance peak due to a proton in the Sal- anion in the threadlike micelle appears in significantly lower magnetic field than that of the free state in the bulk aqueous phase. Moreover, the exchange rate of the Sal- anions between the micellar state and the free state seems sufficiently faster than the difference between their chemical shifts (typically 70 Hz). Therefore, the observed resonance for a solution at an arbitrary composition shows only single peaks with a chemical shift proportional to the population of these states. The spinlattice and spin-spin relaxation times (T1 and T2, respectively) provide information about the dynamics of the molecules in the micelles, which can be quantified in terms of the correlation time, τc.9-13 In NMR relaxation studies of molecular motions of detergent molecules in micelles, a two-state model14-18 for the motion of the detergent was proposed. This model is based on two distinctive observed correlation times; one is short, on the order of 10 ps, relating to quick local motions, and the other is much longer and related to global motion (rotation of the micelle) of the micelle or the rate of migration (or, in other words, lateral diffusion) of the detergent in the micelle. To test the validity of the twostate model, temperature must be changed to alter τc, or (8) Bunton, C. A.; Minch, M.; Hidalgo, J.; Sepulveda, L. J. Am. Chem. Soc. 1973, 95, 3262. (9) Ulmius, J.; Wennerstro¨m, H.; Johansson, L. A. B.; Lindblom, G.; Gravsholt, S. J. Phys. Chem. 1979, 83, 2232. (10) Monduzzi, M.; Olsson, U.; So¨derman, O. Langmuir 1993, 9, 2914. (11) Anet, F. A. N. J. Am. Chem. Soc. 1986, 108, 7102. (12) Menger, F. M.; Jerkunica, J. M. J. Am. Chem. Soc. 1978, 100, 688. (13) Stark, R. E.; Storrs, R. W.; Kasakevich, M. L. J. Phys. Chem. 1985, 89, 272. (14) Wennerstro¨m, H.; Ulmius, J. J. Magn. Reson. 1976, 23, 431. (15) Ulmius, J.; Wennerstro¨m, H. J. Magn. Reson. 1977, 238, 309. (16) Henriksson, U.; O ¨ dberg, L.; Eriksson, J. C.; Westman, L. J. Phys. Chem. 1977, 81, 76. (17) Wennerstro¨m, H.; Lindman, B.; So¨derman, O.; Drakenberg, T.; Rosenholm, J. B. J. Am. Chem. Soc. 1979, 101, 6860. (18) Chachaty, C.; Warr, G. G.; Jansson, M.; Li, P. J. Phys. Chem. 1991, 95, 3830.
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more different resonance frequencies must be used to determine the precise shape of the frequency dependence of T1 and/or T2. Given that a raise of the temperature would frequently cause fatal damage to the structure and dynamics of the micelle, it should be much better to change the resonance frequency than to change the temperature. Fluorescence spectroscopy is also a powerful method for the investigation of microenvironments and molecular motions, provided an appropriate fluorescence probe can be introduced in micellar systems.19 Actually, the Salanion is strongly fluorescent in aqueous solution19 with an adequate fluorescence lifetime. Because the fluorescence intensity and lifetime of some fluorescence probes are dependent on the microenvironment or chemical circumstances about the fluorescence probe molecules, a change in the intensity and the lifetime can be a proof of alteration of the site occupied by the probe molecules. The fluorescence anisotropy and the rotational relaxation time (τφ) are a good measure of the molecular motions of probe molecules. As the Sal- anion is small in size and is quickly rotating in dilute aqueous solution, its fluorescence anisotropy is usually too small to accurately determine. However, as the motion of the Sal- anion localized in the micellar interior is highly restricted, significantly large fluorescence anisotropy and long τφ values are observed for the Sal- anion in the micelle. In the case of the fluorescence anisotropy measurement, the rotational motion of the transition moment in the probe molecule is only active to decay of the anisotropy, so that only one rotational mode could be detected and discussion about anisotropic rotation around multiple axes is impossible. However, rotational motions with different rotational axes can sometimes be detected separately because the dipole-dipole interaction between two proton (1H) nuclei is very important in the spin-lattice NMR relaxation. Then, discussion about anisotropic rotational motions of the molecule could be possible. In this study, we report some results of the spin-lattice proton NMR relaxation measurements at several resonance frequencies, which would be very important to get exact information about the NMR relaxation mechanisms and rotational motions of the monitored molecules. Then, we discuss anisotropic rotational motions of the Sal- anion confined to the localized site in the threadlike micelle in comparison with those of free Sal- anions in the aqueous phase. Molecular motions of detergent molecules are also discussed. Experimental Section Materials. CTAB, purchased from Wako Pure Chemical Industries LTD (Osaka, Japan), was purified by recrystallization from a solution in an ethanol/acetone mixture. Extrapure grade NaSal was purchased from the same company and used without further purification. Deuterium oxide (99.7 wt % D2O) was also purchased from the same company. Spectrometers and T1 Measurements. Five types of JEOL NMR spectrometers, FX90Q, FX200, EX270, GSX400, and GSX500, were operated to measure the spin-lattice NMR relaxation times (T1) of 1H in Sal- anions and CTA+ cations at 25 °C in the Fourier transform (FT) mode. An FX90 spectrometer has an ordinary electromagnet, and its resonance frequency for 1H is 90 MHz. The other spectrometers have superconducting electromagnets, and their resonance frequencies for 1H are 200, 270, 400, and 500 MHz, respectively. To achieve steady resonance conditions, an internal lock of D2O was used in all the spectrometers. A conventional inversion recovery (IR) pulse sequence (180°τ-90°) was employed to measure T1. D2O solutions of CTAB and NaSal are as viscoelastic as their aqueous solutions. There was no noticeable difference in the (19) Shikata, T.; Morishima, Y. Langmuir 1996, 12, 5307.
Shikata and Morishima viscoelastic behavior of CTAB:NaSal solutions between D2O and H2O. Hence, the structure and dynamic features of formed threadlike micelles in D2O would be practically the same as those in water.5 The NaSal concentration (CS) was 100 mM for the measurement of T1 in the free rotational state in the pure solvent. In solutions for the T1 measurement of the Sal- anion in the micellar interior site, the CTAB concentration (CD) was kept at 100 mM and CS was varied from 70 to 200 mM. According to the previous study,5 in a solution with CD ) 100 mM and CS ) 70 mM the threadlike micelles are fully grown to make a strong entanglement network, and all Sal- anions are bound in the micellar interior site; thus, no Sal- anion is there in the bulk aqueous phase. No particular care was taken to remove oxygen from the above solutions.
Results Free Sal Anions. In general, the effect of oxygen on T1 is very large if the examined nuclei have a long T1. To check if the dissolved oxygen gas affects the T1 of 1H in the Sal- anion in a pure NaSal/D2O solution which must have the longest T1, a solution with CS ) 20 mM was prepared and Ar gas was bubbled in the solution for several hours to remove the oxygen gas as much as possible. Then, the degassed solution was subjected to the T1 measurement. The T1 value obtained was not at all different from those for a nondegassed solution with the same CS. Thus, we concluded that the effect of dissolved oxygen gas on T1 was very small in all the solutions examined in this study. A typical time course of resonance signals of 1H in the Sal- anion in the process of the inversion recovery (IR) sequence obtained at 270 MHz is shown in Figure 1. Since the chemical shifts of 4-1H and 6-1H are different, the T1 for each 1H can be determined separately. Thus, we will discuss later rotational motions around the different axes 1 and 2 (see inset of Figure 1), the difference in which can be viewed as anisotropic rotation. The signal intensities (I(τ)) of all the 1H increase with time (τ), and they reach certain constant values (I(∞)) at a sufficiently long time. According to the standard method to evaluate T1, semilogarithmic plots of I(∞) - I(τ) against τ provide straight lines and their slopes represent (T1)-1 for each 1H individually (Figure 2). The obtained (T1)-1 values for 4-1H and 6-1H in Sal- at different resonance frequencies (in ω/rad s-1) are plotted in Figure 3. Because the (T1)-1 values for 4-1H and 6-1H are independent of the frequency, both the protons are under extremely narrowing conditions. Thus, the rotational molecular motion of the Sal- anion is fast under the free aqueous condition. The (T1)-1 values for 4-1H are very close to those of 6-1H at all the frequencies examined. If intramolecular dipole-dipole (D-D) interaction is the most essential mechanism for the NMR relaxation in Saland the resonance condition is the extremely narrowing one, the magnitude of (T1)-1 should be proportional to the number of interacting 1H in the molecules. 6-1H has only one interacting 1H (5-1H) while 4-1H has two (3-1H and 5-1H); thus, (T1)-1 for 4-1H should be twice as large as that for 6-1H, if the rotational motion of the Sal- anion is isotropic and the rotational correlation times of 6-1H and 4-1H are the same. Therefore, the results in Figure 3 suggest that the rotational correlation times of 6-1H and 4-1H are different and the rotational motion of Sal- is anisotropic with more than two rotational axes even in the free aqueous state. Behavior of Sal- Anions in a Threadlike Micellar System. As reported in the previous paper5 on NMR chemical shifts of Sal- in the threadlike micellar system, Sal- exists in two states. One is the free rotating state in the bulk aqueous phase, which shows a resonance peak in the higher local magnetic field, and the other is the site -
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Figure 1. Typical time course of NMR signals for 3,5-1H, 4-1H, and 6-1H in a Sal- anion in aqueous solution in the process of the inversion recovery pulse sequence at a resonance frequency of 270 MHz. The inset is a schematic representation of the Sal- anion and its rotational axes.
Figure 3. Dependence of T1-1 for 4-1H and 6-1H in the Salanion on the resonance frequency, ω, in free aqueous solution. Figure 2. Typical time course of NMR signal intensity, ln{I(∞) - I(τ)}, for 4-1H and 6-1H in the Sal- anion in aqueous solution in the process of the inversion recovery pulse sequence.
in the micelle. Because the exchange rate between the two sites is sufficiently fast, the chemical shift of the resonance for 4-1H is proportional to the population or fraction of both the sites. According to the previous data,5 the population (Pm) of the micellar interior site was able to be estimated for solutions examined at CD ) 100 mM. Actually, at CS ) 70 mM all the Sal- anions are located in the micellar interior site. The relationship between Pm and (T1)-1 for 4-1H and 6-1H in Sal- at a resonance frequency of 90 MHz is shown in Figure 4. With increasing Pm, the (T1)-1 values for both the 1H nuclei increase
gradually, with the rate of the increase around Pm ) 1 being quite steep. A much larger magnitude of (T1)-1 at Pm ) 1 than that at Pm ) 0 (free aqueous state) means slowing down of the molecular motion of Sal- localized in the site of the micellar interior. In the cases where the chemical exchange of the mentioned 1H between the two states with different (T1)-1 is an important process for NMR relaxation and the exchange rate between the sites is larger than the difference in the chemical shifts of the sites, as is the case for 4-1H and 6-1H in the Sal- anion in the threadlike micellar system, the observed (T1)-1 is proportional to the population of those sites.5 However, the (T1)-1 values of both 4-1H and 6-1H in the Sal- anion in the threadlike micellar system are not proportional to Pm, as seen in
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Shikata and Morishima
1
1
Figure 4. Relationship between T1 for 4- H and 6- H in the Sal- anion and its fraction, Pm, occupying the micellar interior site of the threadlike micelle in the CTAB:NaSal/W system. -1
Figure 5. ω dependence of T1-1 for 4-1H in the Sal- anion in the micellar interior site and in the free aqueous state. Solid and broken lines represent theoretical predictions by use of eqs 1 and 2.
Figure 4. The average residence time of a Sal- anion in the micellar interior site would alter depending on the Pm except for a condition at Pm ) 1. Moreover, the Sal- anion which gets into the micellar interior site would need a certain retardation time to reach steady state molecular motions there. At this stage, we think that these factors may be responsible for the deviation of (T1)-1 data from the proportionality. The magnitude of (T1)-1 at Pm ) 1 for 4-1H is remarkably larger than that for 6-1H. This suggests that the rotational motions of the Sal- anion in the threadlike micelle are not isotropic but that the Sal- anion has more than two anisotropic rotational axes with different rotational correlation times as it does in the free aqueous solution. The resonance frequency (ω) dependence of (T1)-1 for 4-1H and 6-1H in the Sal- anion at Pm ) 1 is exhibited in Figures 5 and 6. (T1)-1 data at Pm ) 0 are also plotted in the same figures. At Pm ) 1, both the (T1)-1 values show a significant ω dependence, as seen in the figures; therefore, the resonance condition for both 1H nuclei in the Sal- anion at Pm ) 1 is not the extremely narrowing one. The solid and broken lines in Figures 5 and 6 represent the theoretical prediction based on the D-D interaction between 1H nuclei which will be discussed later in detail. Behavior of CAT+ Cations in the Threadlike Micelles. T1 values for 1H nuclei in the CTA+ cation were also estimated with the IR pulse sequence. Resonance signals for methyl 1H in the ammonium head and in the alkyl tail group were clearly recognized. However, those for 1H nuclei in each methylene group in the alkyl tail
Figure 6. ω dependence of T1-1 for 6-1H in the Sal- anion in the micellar interior site and in the free aqueous state. Solid and broken lines represent theoretical predictions by use of eqs 1 and 2.
Figure 7. Relationship between T1-1 for 1H in N-CH3, CH2, and CH3 groups in a CTA+ cation forming the threadlike micelle and Pm of the Sal- anion occupying the micellar interior site of the threadlike micelle in the CATB:NaSal/W system.
were not clearly isolated; they show only a broad single peak. Then, T1 for the methylene 1H was estimated from the broad single signal as the average for all the methylene groups. T1 values estimated at 90 MHz for each 1H are shown in Figure 7 as a function of Pm. Obviously, the T1 values for all the protons are very weakly dependent on Pm. The cmc of CTAB in pure aqueous solution is 8 × 10-4 M, and that in a solution containing NaSal would be a little lower than this value. Thus, essentially all the CTA+ cations are located in the threadlike micelle in all the solutions examined here. Therefore, molecular motions of the CTA+ cation, for example the rotation of the methyl group in the ammonium head and that of methylene groups around the long alkyl tail of the CTA+ cation, are not affected by the amount of free Sal- anion outside the micelle. Since the frequency of the molecular motion of the CTA+ cation in the micelle would be related to the flexibility and the persistence length of the threadlike micelle, Figure 7 means that the persistence length of the threadlike micelle is not affected by the amount of the free Sal- or Pm. The dependence of T1 for 1H nuclei in the CTA+ cation on the resonance frequency (ω) was investigated at only 90 and 500 MHz. As seen in Figure 8, the T1 value for 1H in the CTA+ cation is strongly dependent on ω; therefore, 1H nuclei in the CTA+ cation are not in the extremely narrowing condition but are in a condition where molecular motions are strongly restricted. Discussion Anisotropic Rotation of Free Sal- Anions. Anet11 reported that both 4-1H and 6-1H had a positive nuclear
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Figure 8. ω dependence of T1-1 for 1H in N-CH3, CH2, and CH3 groups in the CTA+ cation forming the threadlike micelle. Solid, broken, and dot-dash lines represent theoretical predictions by use of eqs 1 and 4 with the parameters summarized in Table 1.
Overhauser effect (NOE) in the condition of 3-1H and 5-1H saturation in free aqueous solution. This means that the D-D interaction is an essential mechanism for the relaxation and τc satisfies the condition of extreme narrowing of τcω , 1. According to Bloembergen, Purcell, and Pound theory,20 if a molecule is in isotropic rotational motion and the essential relaxation mechanism of longitudinal relaxation in NMR is the D-D interaction between two nuclei which are the same nuclear species of 1H in the molecule, relaxation time (T1) can be expressed as
(
)
τc 4τc γh2I(I + 1) 1 ) + 2 2 6 2 T1 10π r 1 + ω τc 1 + 4ω2τc2
(1)
where γ, h, I, τc, r, and ω are the gyromagnetic ratio, Planck’s constant, a spin quantum number ) 1/2 for 1H nuclei, the correlation time, the distance between two interacting 1H nuclei, and the resonance frequency, respectively. In the condition of extreme narrowing at ω , τc-1 eq 1 can be simplified as
γh2I(I + 1)τc 1 ) T1 2π2r6
(2)
In this condition, (T1)-1 is independent of ω, as can be seen in Figure 3 for the free Sal- anion in aqueous solution. In the case of 6-1H, 5-1H is the only proton that interacts with 6-1H by the D-D interaction, because the distance between 6-1H and 5-1H is 2.4 Å, the nearest in the phenyl ring. Then, the τc value can be obtained as 32 ps with the use of eq 2. A solid line in Figure 6 represents the ω dependence of eq 1 with τc ) 32 ps. It is obvious that the resonance condition of 6-1H in free aqueous solution belongs to the extremely narrowing one. On the other hand, 4-1H has two interacting 1H nuclei with the same distance of 2.4 Å, 3-1H and 5-1H, through the D-D interaction. Therefore, one must double eq 2 to evaluate the τc value for 4-1H, and thus, 15 ps was obtained. The solid line in Figure 5 shows the ω dependence of eq 1 for 4-1H with τc ) 15 ps. The significant difference between the τc values for 4-1H and 6-1H suggests that the rotational molecular motions (20) Bloembergen, N.; Purcell, P. E. M.; Pound, R. V. Phys. Rev. 1948, 73, 679. (21) Woessner, D. E. J. Chem. Phys. 1962, 37, 647. (22) Levy, G. C.; Gargioli, J. D.; Anet, F. A. J. Am. Chem. Soc. 1973, 95, 1527.
of the Sal- anion consist of more than two kinds of rotational axes with distinctive rotational relaxation times. Because a hydrogen bond is formed between the OH group and the COO- group in the Sal- anion, the size of Sal- would be somehow larger in the direction from COOto 4-1H than that from 3-1H to 6-1H. Thus, rotational speed around axis 2 would be faster than that around axis 1 even in free aqueous solution because the hydrodynamic resistance for the rotation experienced by the molecule should depend on the molecular size from the rotating axes. Correlation Times of Sal- Anions in the Threadlike Micelles. The most important mechanism in the spin-lattice NMR relaxation process for 1H in the Salanion in the threadlike micelle as well as in free aqueous solution should be the D-D interaction. Anet11 reported that the NOE enhancement of both 4-1H and 6-1H in the Sal- anion in the micellar interior in a condition of NMR saturation of a merging signal for 3-1H and 5-1H by radiation of radio frequency exhibited negative values. This means the D-D intramolecular interaction in Salis still effective even in the site in the micelle. However, the local concentration of both the CTA+ cation and the Sal- anion is so high that other mechanisms for the spinlattice NMR relaxation such as an intermolecular D-D interaction might also be very important. The broken line in Figure 5 represents the dependence of (T1)-1 on ω calculated from eq 1, which has an extra factor of two because of two interacting 1H nuclei and has τc ) 0.35 ns for the best fit to the data. Since we used various resonance frequencies, τc can be estimated quite precisely by seeking the best fit curve to the experimental data. The τc value for 4-1H in the micellar interior site is longer than that in the free aqueous phase by a factor of ca. 25. This means the rotational motion of the Sal- anion in the micellar site is highly restricted due to a high local concentration. Recently, we carried out a fluorescence anisotropy analysis of Sal- anions located in the micellar interior site.19 From the fluorescence anisotropy analysis the rotational relaxation time (τφ), which corresponds to 3τc by definition, was estimated to be 1.6 ns in solutions at various CD/CS ratios. Because the τc value for 4-1H almost satisfies the relationship of τφ ) 3τc, a rotational motion around axis 1 estimated from the 4-1H NMR relaxation would be identical to that detected by the fluorescence anisotropy. As a Sal- anion has two hydrophilic groups, OH and COO-, a tumbling motion inserting the hydrophilic groups into the hydrophobic micellar interior should be quite unlikely. Moreover, considering the transient moment of the Sal- anion, an effective rotation for the fluorescence anisotropy relaxation must be that around axis 1.19 These considerations imply that the rate of the rotational motion of the Sal- anion around axis 1 in the micellar interior can be detected by both NMR and fluorescence methods. In the case of 6-1H, (T1)-1 data were not satisfied with eq 1 with only one τc. The broken line in Figure 6 is a composed curve consisting of two curves with different correlation times. We assumed two kinds of motions with the same amplitude, which must be a front factor in eq 1, but different correlation times, 0.5 and 1.2 ns. This procedure is essentially identical to using eq 4, which appears later. A mode effective for the 6-1H relaxation in the micellar interior site as well as in the free aqueous phase should be the intramolecular D-D interaction between 5-1H. Although a motion of the Sal- anion for the intramolecular D-D interaction is tumbling, the tumbling is highly restricted in the micellar interior site. Another motion effective to relax the intramolecular D-D
1936 Langmuir, Vol. 13, No. 7, 1997
interaction should be the translation or migration of the Sal- anion along the curved micellar surface. In a migration process along the surface of the threadlike micelle, which is not flat but circular in cross section, the angle between the direction from 5-1H to 6-1H and the magnetic field will be altered with time and spin-lattice relaxation will occur. This migration mode would need a longer time to lose the correlation of the angle between the 5-1H to 6-1H direction and the magnetic field than τc for the rotation around axis 1. Therefore, the evaluated longer τc, 1.5 ns, would be the correlation time for the migration mode. On the other hand, the rotation of the Sal- anion around axis 1 is unable to alter the angle between the 5-1H to 6-1H direction and the magnetic field effectively, so that this mode is not essential for the intramolecular D-D interaction. However, the evaluated shorter τc, 0.5 ns, is not much different from the τc for 4-1H. The rotational mode around axis 1 would still be effective for 6-1H relaxation via the intermolecular D-D interaction, because there are a number of 1H nuclei belonging to different Sal- anions and also to CTA+ cations. Since the depths of 6-1H from the surface of the micelle for different Salspecies should be close to one another, the angle between the direction from 6-1H to the next 6-1H and the magnetic field must alter with time due to the rotational mode around axis 1 for each Sal- anion. This undulation of the angle should be the origin of the spin-lattice NMR relaxation, and a correlation time for this undulation should not be much different from the τc for 4-1H due to the rotation around axis 1. The same discussion can be made for the intermolecular D-D interaction between 6-1H in the Sal- anion and 1H in the CTA+ cation. To apply curve-fitting analysis to the (T1)-1 data, we simply assumed that the average distance (r) between interacting 1H nuclei in eq 1 is the same as the distance ()2.4 Å) between 6-1H and 5-1H, as in the case of intramolecular D-D interaction. For a quantitative discussion of the intermolecular D-D interaction, one must develop a method to estimate the average distance between interacting 1H nuclei. Molecular Motions of CTA+ in the Threadlike Micelles. Because CTA+ cations have a number of chemical bonds which can freely rotate, the motional freedom of each 1H is much greater than those of the Salanion itself, having a rigid phenyl ring. Motions of 1H in the methylene groups in CTA+ have less freedom than those of the methyl groups at the end of the alkyl tail and in the trimethylammonium group. Assuming that an essential mechanism for the spin-lattice NMR relaxation for the CTA+ cation is the intramolecular D-D interaction, eq 1 can be applied to the data in Figure 8. The (T1)-1 data only for 1H in the methylene groups are fitted with a τc of 0.2 ns, as shown in Figure 8 with a solid line. The value of r is assumed to be 1.8 Å on the basis of the chemical structure. Therefore, the fast local motion of the methylene groups in the CTA+ cation does not contribute much to the spin-lattice NMR relaxation. The τc ()0.2 ns) essentially reflects the rotational rate of the CTA+ cation around the long molecular axis, because the lateral diffusional motion of CTA+ in the micelle is not so fast as can be detected by other experiments.23 On the other hand, the (T1)-1 data for both 1H nuclei in the methyl groups could not be expressed with one τc assuming contribution from two of the 1H nuclei in the groups. Because the (T1)-1 curves calculated from eq 1 for both the methyl groups are always larger than experiment, the reason for this disagreement is not only (23) Shikata, T.; Morishima, Y. Submitted to Langmuir.
Shikata and Morishima Table 1. Fitting Parameters for Three Kinds of Protons in a CTA+ Cation Forming the Threadlike Micelle τc/ns CH2a N-CH3 CH3
τs/ns
fs
τf/ps
0.25 0.3
0.35 0.2
5.0 10
0.2
a A much better-fit curve can be obtained with τ ) 0.25 ns, f s s ) 0.7, and τf ) 10 ps.
an oversight of the contribution of other relaxation mechanisms such as the intermolecular D-D interaction, chemical shift anisotropy, and so on. To obtain best fit curves to the data based on the intramolecular D-D interaction, one must introduce more than two relaxation modes for two 1H nuclei in the methyl groups. According to the two-step model17 proposed for spinlattice 13C NMR relaxation in detergent micellar systems, the reduced spectral density (J(ω)), for an overall isotropic motion of 13C nuclei in the detergent, is expressed as
J(ω) )
SCH2τs
(1 - SCH2)τf + 2
1 + ω2τs
1 + ω2τf2
≈
SCH2τs 2
1 + ω τs
2
+ (1 - SCH2)τf (3)
where τs, τf, and SCH represent respectively the correlation times for slow and fast local modes and an order parameter for a 13C-1H bond of the fast mode. In 13C NMR relaxation, the intramolecular D-D interaction is the essential mechanism. In the 1H spin-lattice NMR relaxation, basically eq 3 holds by replacing SCH with an order parameter for a 1H-1H vector. Consequently, we can get eq 4 describing (T1)-1 on the basis of the two-step model for the 1H NMR relaxation
{
fsτs 4fsτs γh2I(I + 1) 1 ) + + 2 2 6 2 T1 10π r 1 + ω τs 1 + 4ω2τs2 (1 - fs)τf 4(1 - fs)τf + 1 + ω2τf2 1 + 4ω2τf2
}
(4)
where fs is the fraction of contribution of the slow mode. The broken line and the dot-dash line in Figure 8 represent the best fit curve for 1H nuclei in the methyl groups in the ammonium group and at the chain end in the CTA+ cation, respectively. The parameters used for the fitting are summarized in Table 1. Since the number of data for each 1H is only two, the accuracy of these fittings is not so good. The τf values listed in Table 1 are the longest ones which can make well-fitting curves. Thus, well-fitting curves for the data can be obtained with shorter τf values less than 1 ps. Therefore, it is likely that the real τf values are shorter than the values in Table 1. The τs values for the 1H nuclei both in the methyl groups in the ammonium group and at the chain end are very close to the τc ones for the 1H in the methylene groups in the alkyl tail. This means that the slow mode of CTA+ cations in the threadlike micelle is essentially the rotational motion around the long molecular axis, and the rotational motions of both the methylene groups around the C-N and C-C bonds are much faster than the slow mode. As shown in Table 1, when we apply the two-step model to the 1H in the methylene group, a much better-fit curve is obtained with the τs very close to that of 1H in the methyl group and with the fs much higher than that in the case of a methyl group. This sustains
Anisotropic Rotation of Salicylate Anions
that the contribution of the rotational motion around the long molecular axis to the 1H NMR relaxation is essential. In the procedure of the evaluation of the correlation times and their fractions for 1H in the CTA+ cation, only two resonance frequencies were used. However, more resonance frequencies should be used to improve the accuracy of the estimated values of the correlation times and the fractions. The local concentration of the CTA+ cation in the threadlike micelle is very high, so that the intermolecular D-D interaction is important in the 1H NMR relaxation. Thus, the measurement of T1 with 13C NMR, at various resonance frequencies, is a much better method to evaluate the correlation times of detergent and additive molecules in micelles except for consuming time, because the intramolecular D-D interaction is the only mechanism for the 13C NMR relaxation in most cases.
Langmuir, Vol. 13, No. 7, 1997 1937
Conclusions Even in free aqueous solution the Sal- anion possesses anisotropic rotational modes, because its structure is deviated from a spherical shape. The Sal- anion also exhibits a significant anisotropic rotation in a threadlike micelle consisting of CAT+ cations and Sal- anions. The correlation time of the Sal- anion for molecular rotation in the micelle is much longer than that in the free aqueous solution and well corresponds to the rotational relaxation time estimated by a fluorescence anisotropy analysis. Molecular motions of the CAT+ cation in the micelle are restricted but are not affected by the concentration of the Sal- anion, although rheological features are strongly affected by the concentration of the Sal- anion. LA9610260
