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Langmuir 1997, 13, 3052-3054
Notes High-Frequency Dielectric Relaxation of Linear Micelles in Aqueous Solutions of Cetyltrimethylammonium Bromide with Sodium Salicylate Junichi Oizumi,* Hiroshi Furusawa, Yasuyuki Kimura, Kohzo Ito, and Reinosuke Hayakawa Department of Applied Physics, Graduate School of Engineering, The University of Tokyo, Bunkyo-ku, Tokyo 113, Japan Received July 30, 1996. In Final Form: January 2, 1997
It is well-known that ionic surfactants in aqueous solutions with added salts aggregate to form a linear (rodlike or wormlike) micelle with electric charges.1-3 This kind of linear micelle can be called a quasi-polyion because it has a charge distribution and linear conformation similar to the polyion. It is noted, however, that the linear micelle is different from the polyion in that the number of surfactant molecules (i.e., “monomers”) constituting the micelle is changeable with environmental conditions. For example, when salts of usual kinds are added to the ionic surfactant solutions, the aggregation of surfactants proceeds and the contour length L of a linear micelle becomes longer. An exceptional salt is sodium salicylate (NaSal)4-6 added to aqueous solutions of cetyltrimethylammonium bromide (CTAB): when the ratio of the NaSal concentration CS to the surfactant concentration CCTAB is less than unity, the viscoelastic measurement indicates that the relaxation time gets longer with increasing CS, which implies that the aggregation of surfactant proceeds. When the ratio of CS to the CCTAB is larger than unity, the relaxation time decreases with increasing CS, which is peculiar to NaSal. In a recent study we have investigated the influence of NaSal concentration CS on the dynamics of linear micelles in CTAB solutions by using the frequency-domain electric birefringence relaxation (FEB) spectroscopy.7 The FEB spectroscopy gives the information on the relaxation time for the micelle rotation as well as the relaxation time of the low-frequency (LF) dielectric relaxation due to the induced dipole moment produced by Sal- counterions which are tightly bound to the linear micelle and can fluctuate along the micelle contour. The dependence of the contour length L of linear micelles on the NaSal concentration CS has been obtained from the both relaxation times, which shows that Sal- ions play an decisive role in the surfactant aggregation. We have also found that the diffusion constant of tightly bound Sal- ions along the micelle contour is smaller than the diffusion constant of Sal- ions in a free state. This hindered diffusion of Salions along the micelle contour is consistent with an NMR * Corresponding author. (1) Shikata, T.; Sakaiguchi, Y.; Urakami, H.; Tamura, A.; Hirata, H. J. Colloid Interface Sci. 1986, 119, 291. (2) Candau, S. J.; Hirsch, E.; Zana, R. J. Colloid Interface Sci. 1985, 105, 521. (3) Porte, G.; Appell, J.; Poggi, Y. J. Chem. Phys. 1980, 84, 3105. (4) Rehage, H.; Hoffmann, H. J. Phys. Chem. 1988, 92, 4712. (5) Shikata, T.; Hirata, H.; Kotaka, T. Langmuir 1988, 4, 354. (6) Berret, J. B.; Appell, J.; Porte, G. Langmuir 1993, 9, 2851. (7) Oizumi, J.; Kimura, Y.; Ito, K.; Hayakawa, R. J. Chem. Phys. 1996, 104, 9137.
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result5 which suggests that Sal- ions put their aromatic rings half into the micelle. The fluctuation of Sal- ions along the micelle contour causes the fluctuation of charge density along the contour and produces positively and negatively charged local areas on the micelle, even if the micelle is neutral in the average. This situation can be treated by Oosawa’s theory8 for the polarizability of polyelectrolytes due to the fluctuation of counterions along the polyions. In the present case, the other counterions, Br- and Na+ ions, are expected to be loosely bound to the local areas with positive and negative charges, respectively, and fluctuate in the direction perpendicular to the micelle contour much faster than the charge fluctuation due to Sal- ions. This faster fluctuation of loosely bound counterions is expected to produce the high-frequency (HF) dielectric relaxation of linear micelles in a similar way to the HF relaxation of the polyelectrolyte solutions.9 In this paper, we investigate the dielectric relaxation of linear micelles in the CTAB solutions with NaSal in the high-frequency range in order to confirm the above picture or conjecture for the fluctuations of two kinds of counterions bound to the micelles loosely and tightly, respectively. Experimental Section CTAB and NaSal of special grade were purchased from Nacalai Tesque. CTAB was recrystallized twice, and NaSal was used without further purification. The solvent was distilled water. The CTAB solution with NaSal was equilibrated for at least 2 days before measurement. The measurement of dielectric relaxation in the high-frequency range (1 MHz to 1 GHz) was carried out by using an RF impedance analyzer (HP 4192A). The specimen cell was a coaxial type of cylindrical condenser with platinum-plated stainless steel electrodes.
Results and Discussion Figure 1 shows the complex dielectric constant * () ′ - i′′) for the solution of CTAB (60 mM)/NaSal (24 mM) as a typical example, where the contributions of the dc conductivity σ(0) and the dielectric constant of solvent have been subtracted. The solid line in Figure 1 represents the best fitted curve using the semi-empirical formula of Havriliak-Negami type.10
* )
σ(0) ∆ + + (∞) β iω 1 + (iωτ) 0
(1)
where ∆ is the dielectric increment and τ is the average relaxation time. The parameter β represents the broadness in the relaxation time distribution, 0 is the vacuum permittivity, and (∞) is the high-frequency (HF) limit of *. Figures 2 and 3 show the CCTAB dependences of ∆ and τ, respectively, obtained from the best fitting of the data by using eq 1, when the ratio CS/CCTAB is fixed. Each symbol corresponds to a different value of CS/CCTAB. The HF dielectric relaxation of polyelectrolytes is attributed to the fluctuation of loosely bound counterions in the direction perpendicular to the polyion axis.9 From the similarity between linear micelles and polyelectrolytes, (8) Oosawa, F. Biopolymers 1970, 9, 689. (9) Ito, K.; Yagi, A.; Ookubo, N.; Hayakawa, R. Macromolecules 1990, 23, 857. (10) Havriliak, S.; Negami, J. J. Polym. Sci. 1966, C14, 99.
© 1997 American Chemical Society
Notes
Langmuir, Vol. 13, No. 11, 1997 3053
Figure 1. Complex dielectric constant * () ′ - i′′) for the solution of CTAB (60 mM)/NaSal(24 mM) plotted against the logarithmic frequency. The solid lines are the best fitted curves.
Figure 2. Dielectric increment ∆ plotted against CCTAB for fixed values of CS/CCTAB ) 0.6 (b), 0.8 ([), 1.0 (2), 1.2 (O), 1.6 (]), and 2.0 (4).
Figure 3. Relaxation time τ plotted against CCTAB for fixed values of CS/CCTAB (symbols in the figure as in Figure 2).
the HF dielectric relaxation of linear micelles is expected to be explainable by the same kind of molecular mechanism due to loosely bound counterions. In addition to the counterion fluctuation, the rotation of micelles around the micelle axis and the fluctuation of surfactants on the micelle surface are possible mechanisms to produce the HF relaxation. The relaxation times for the both mechanisms, however, are commonly determined by the radius of linear micelles and would be almost unaffected by the surfactant concentration CCTAB or the salt concentration CS. The strong dependence of τ on CCTAB and CS shown in Figure 3 is in favor of the counterion fluctuation mechanism for the HF relaxation. This mechanism gives the expressions for ∆ and τ as
∆ ∝ Nl2
(2)
τ ∝ l2
(3)
where N and l are the number concentration and the fluctuation distance of loosely bound counterions, respectively. From eqs 2 and 3, we have
∆/τ ∝ N
(4)
In order to decide what kinds of counterions contribute
Figure 4. ∆/τ plotted against CCTAB + CS for fixed values of CS/CCTAB (symbols in the figure as in Figure 2).
Figure 5. τ1/2 plotted against κ-1 for fixed values of CS/CCTAB (symbols in the figure as in Figure 2).
to the HF relaxation, ∆/τ is plotted against CCTAB + CS in Figure 4 by using the experimental values of ∆ and τ in Figures 2 and 3. Figure 4 shows that ∆/τ is proportional to CCTAB + CS irrespective of the values of CS/CCTAB. This result compared with eq 4 indicates the proportionality between N and CCTAB + CS, which implies that both of Br- and Na+ ions contribute to the HF relaxation as loosely bound counterions. Sal- ions also increase in number concentration with increasing CCTAB + CS, but they would contribute to the LF relaxation as tightly bound counterions and not to the HF relaxation, as described in the introduction. Further, it is noted that the proportionality between N (i.e., ∆/τ) and CCTAB + CS holds also in the case of CS/ CCTAB equal to unity. This indicates that, even if the linear micelle is electrically neutral in the average, there is an electric potential around the linear micelle in which loosely bound counterions (Br- and Na+) are confined, and the electric potential is produced by a non-uniform distribution of Sal- ions which are tightly bound to the linear micelle and fluctuate along the micelle contour much more slowly than the fluctuation of loosely bound counterions. Thus, we can confirm the picture that the fluctuation of Salions produces the fluctuating local areas with positive and negative charges. In order to estimate the fluctuation distance l, we have to consider the electric potential profile around the micelle, because the fluctuation of loosely bound counterions is spatially restricted within the electric potential trough produced by charges on the linear micelle. Then, the distance l is estimated as the width of the potential trough, which is, in turn, roughly equated with Debye length κ-1 in the present case with added salts. In Figure 5, τ1/2 which is proportional to l as seen from eq 3 is plotted against κ-1. Here, the values of κ have been calculated from the concentrations of loosely bound counterions (Br-, Na+, and Sal- ions in excess of CCTAB). Figure 5 shows that l is nearly proportional to κ-1 irrespective of the values of CCTAB and CS, as expected above. We have not considered in the above discussion the
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break/recombination model11 or the quasi-network model5 with transient junctions which temporally break and reform. The relaxation frequencies related to these models may compete with the viscoelastic relaxation frequency of kHz order but would be much smaller than the HF relaxation frequency which ranges between 1 MHz and 1 GHz. This means that the break/recombination mechanism or transient junctions have little influence on the HF dielectric relaxation. In conclusion, the HF dielectric relaxation measurement of linear micelles has confirmed the picture for bound counterions which was suggested by the FEB measurement: The Sal- ions tightly bound to the linear micelle fluctuate slowly along the micelle contour and cause the (11) Cates, M. E. J. Phys. 1988, 49, 1593.
Notes
LF dielectric relaxation. A non-uniform charge distribution on the micelle, which is produced by the fluctuation of Sal- ions, generates the troughs of electric potential around positively or negatively charged local areas on the micelle. The other small ions, Br- and Na+, in the solution are bound to the troughs and can fluctuate in the troughs perpendicularly to the micelle contour. This fluctuation, much faster than the fluctuation of the electric potential, causes the HF dielectric relaxation. Acknowledgment. This work was partly supported by a grant from Research Fellowships of Japan Society for the Promotion of Science for Young Scientists. LA960753S
