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Dielectric Relaxation of Cationic Micellar Solutions Shin-ichiro Imai and Toshiyuki Shikata* Department of Macromolecular Science, Osaka University Toyonaka, Osaka 560-0043, Japan Received April 2, 1999. In Final Form: July 20, 1999 Dielectric relaxation behavior for aqueous cetyltrimethylammonium bromide (CTAB) solutions with sodium bromide (NaBr) were examined in the frequency (ω) range from 6 × 106 to 6 × 109 rad s-1. Two modes with relaxation times, ca. 0.7 and 10 ns, were detected. A fast relaxation mode was attributed to the orientational relaxation of ionic pairs formed between a cationic headgroup of CTA+ and Br-. On the other hand, a slow relaxation mode which increased its strength due to the addition of NaBr was caused by the fluctuation of electrically bound Br- in the ionic cloud around the spherical micelle. Transition in micellar shape from spherical to threadlike shape caused by the addition of NaBr was related to a change in the ω dependence of dielectric relaxation spectra from fairly sharp spectra to broad ones with the fastest relaxation time of ca. 0.3 ns.
Introduction Surfactant or detergent molecules form molecular aggregations called micelles in aqueous solution above their critical micelle concentrations (cmc). The shape of the micelle depends on the species of the detergent and the presence of additives. For example, a cationic detergent, cetyltrimethylammonium bromide (CTAB), forms spherical micelles in pure water. However, it forms long rodlike or threadlike micelles in aqueous solution with simple salts such as NaBr at high concentration.1 CTAB also forms a long threadlike micelle in aqueous solution when aromatic compounds such as sodium salicylate are added at molar concentrations equal to or higher than CTAB.2 Dielectric relaxation analysis (DRA) is a well-known classical technique, however, is very sensitive to the presence of dipole moments. DRA is also useful to detect information about the rate of molecular motions of dipole moments existing in systems.3,4 The micelle formed with ionic surfactant molecules in aqueous solution possesses several kinds of dipole moments, which can be investigated with DRA. For example, in the spherical micelle formed with CTAB, ionic pairs consisting of a cetyltrimethylammonium cation (CTA+) and a bromide anion (Br-) are generated and they behave as relaxing dipole moments. The relaxation of these dipole moments can be detected by DRA around 2 × 109 rad s-1, and the relaxation strength is proportional to the concentration (CD) of CTAB.3,4 Another distinct dielectric relaxation mode is observed in the aqueous CTAB solution at lower frequency, around 108 rad s-1. The relaxation strength of this mode decreases with increasing CD, and disappears above 100 mM. The fluctuation of dissociated Br- anion distribution around the spherical micelle could be a possible cause for this slow relaxation. The other possible mechanism for slow relaxation is the fluctuation of the distribution of dissociated CTA+ cations in the spherical micelle. Adding a small amount of a simple salt, NaBr, to aqueous CTAB with CD equal to or higher than 100 mM will determine which mechanism is essential to the slow dielectric (1) Imae, T.; Kamiya, R.; Ikeda, S. J. Colloid Interface Sci. 1985, 108, 215. (2) Shikata, T.; Hirata, H.; Kotaka, T. Langmuir 1987, 3, 1081. (3) Shikata, T.; Imai, S. Langmuir 1998, 14, 6804-6810. (4) Barchini, R.; Pottel, R. J. Phys. Chem. 1994, 98, 7899.
relaxation in the aqueous CTAB micellar system. If the vanishing slow relaxation mode at CD ) 100 mM revives by adding NaBr, the mechanism is caused by the fluctuation of Br- distribution in the ionic cloud around the spherical micelle. Here, we report results of DRA for aqueous CTAB micellar solutions with several amounts of NaBr in the frequency range from 1 MHz to 1 GHz (6 × 106 to 6 × 109 rad s-1). We consider not only which mechanism is essential to the slow relaxation mode, but also a pronounced change in dielectric spectra due to the transition in the shape of micelles from spherical to long and threadlike caused by adding a salt. Experimental Section Materials. CTAB was purchased from Wako Pure Chemicals Ltd. (Osaka) and was purified by recrystallization from a mixture of methanol and acetone. Specific grade NaBr was also purchased from the same company and was used without further purification. Highly deionized water with specific resistance higher than 14 MΩ cm-1 was obtained with Milli Q system (Milli Pore). Sodium 2-hydroxy-3-naphthoate (NaHNA) used as a fluorescence probe molecule incorporated in the micelles was also purchased from the same company and used without further purification. The concentration (CD) of CTAB was kept constant at 100 mM, while the concentration (CS) of NaBr was ranged from 0 to 100 mM. The concentration of NaHNA was on the order of µM and was much lower than CD. Methods. An RF impedance analyzer (4191A, Hewlet Packard) equipped with a homemade electrode cell3 was operated to determine dielectric relaxation spectra for the aqueous solutions with CTAB and NaBr. Dielectric measurements were carried out at room temperature, ca. 25 °C. Dielectric data were collected in the parallel mode of capacitance, C, and conductance, G, as functions of frequency, ω. The dielectric constant, ′, and the loss, ′′, were calculated in this way of ′ ) CC0-1 and ′′ ) GC0-1ω-1, C0; the capacitance of the vacant measuring electrode cell. To estimate the pure contribution, ∆′, of the presence of micelles to the dielectric constant, a component, m′, due to a solvent or a medium was subtracted from the ′ value. When the conductance of samples was rather high, the electrode polarization effect5,6 affected the ′ value in the lower ω range examined in this study. In this case, to evaluate precise ′ values for the micellar system, we conducted the correction procedure below. (5) Mandel, M.; Odijk, T. Annu. Rev. Phys. Chem. 1984, 35, 75-108. (6) Cirkel, P. A.; van der Ploeg, J. P. M.; Koper, G. J. M. Physica A 1997, 235, 269-278.
10.1021/la990387n CCC: $18.00 © 1999 American Chemical Society Published on Web 09/30/1999
Dielectric Relaxation of Cationic Micellar Solutions
Langmuir, Vol. 15, No. 24, 1999 8389 described above. Debye type theoretical model functions, ∆′cal and ∆′′cal, were employed to determined the ω dependence of ∆′ and ∆′′ quantitatively with up to four Debye type elements as given in eq 2, if necessary. 4
∆′cal )
∆i
∑1+ω τ i)1
2 2 i
4
∆′′cal )
∆iωτi
∑1+ω τ i)1
2 2 i
(2)
Fluorescence anisotropy relaxation analysis was carried out at 25 °C with a conventional method described elsewhere.7 We conducted a steady-state fluorescence depolarization measurement and also a fluorescence lifetime measurement for the probe molecule, NaHNA, incorporated in the micelle, to estimate the rotational relaxation time of NaHNA.
Results and Discussion
Figure 1. Relationship between (CelC0)-1Gdc2 and Gdc for aqueous CTAB and NaBr system with CD ) 100 mM, and for the aqueous NaBr system at 25 °C. According to the classical interpretation of the electrode polarization effect,5,6 the electrode surface has an electric double layer with a certain electric capacitance (Cel). On the other hand, the sample solution has an ω independent (direct current) electric conductance (Gdc) in the low ω side. The entire system can be described electrically as a circuit made with the series connection of the capacitance and the resistance (Gdc-1). Consequently, the system should have ω dependent capacitance (C(ω)) as given by eq 1.
C(ω) )
Cel 1 + ω (CelGdc-1)2 2
(1)
In the ω range much higher than Cel-1Gdc, eq 1 leads to C(ω) ) Cel-1Gdc2ω-2. Then, the contribution of the electrode polarization to ′ can be estimated to be ′el ) (CelC0)-1Gdc2ω-2. If one knows Cel as a function of Gdc (or CS), the pure contribution of the micelle presence to the dielectric constant is evaluated to be ∆′ ) ′ ′m - ′el. When ∆′ is constant in the low ω side, (CelC0)-1Gdc2 can be estimated as a slope of a plot between ′ - ′m - ∆′ () ′el) and ω-2. In the case of a system with CD ) 100 mM and CS lower than 30 mM, the values of ∆′ were judged to be constant in the low ω side, and the values of (CelC0)-1Gdc2 was determined as a function of Gdc as shown in Figure 1as a log-log plot. The slope equal to two in this plot means Cel is independent of Gdc. A similar argument was possible for an aqueous NaBr system possessing ∆′ ) 0. In this case, the proportionality in the relationship between ′ - ′m () ′el) and ω-2 was easily obtained. The estimated values of (CelC0)-1Gdc2 are also plotted in Figure 1. The slope of two is again obtained with a different proportional constant. The reason for a different Cel should be related to the presence or absence of the adsorption layer of CTAB on the surface of the electrodes used. Consequently, the fact that Cel was independent of Gdc allowed us to estimate precise ∆′ values for the aqueous CTAB and NaBr system with CD ) 30 mM with the solid thick line in Figure 1. In the case of dielectric loss, the pure contribution, ∆′′, due to the presence of micelles was estimated in this manner of ∆′′ ) ′′ - m′′-GdcC0-1ω-1: m′′ is the dielectric loss component due to the medium (water). The Gdc values were determined adequately as calculated ∆′′ curves exhibited ω dependencies consistent with those of ∆′ curves determined in the procedure
Two Relaxation Modes. The frequency dependencies of ∆′ and ∆′′ for aqueous CTAB solutions with several CD values from 10 to 100 mM were reported in our previous paper.3 The fast relaxation mode with strength proportional to CD has been attributed to the rotational relaxation mode of ionic pairs consisting of CTA+ and Br-.3 No one knows a suitable theoretical method to evaluate the value of the dipole moment (µ) of the ionic pair in the micelle from the experimental dielectric relaxation strength such as observed in the fast relaxation mode shown in Figures 3-5 of ref 3. However, one is able to estimate µ very roughly through the ionic head portion size of the ionic pair. Because the number of the CTA+ cations in a spherical micelle of CTAB was reported to be 90,1,8 the size (radius, l) of the ionic head portion can be estimated to be ∼0.5 nm with the mean radius (r ∼ 3 nm)1 of the CTAB spherical micelle. Thus, the value of µ is evaluated to be ∼8 × 10-29 Cm through the product of the elementary electric charge and the estimated separation, l, between the center of an ammonium headgroup of CTA+ and Br-. The ionic pair might include a number of hydrating water molecules, which provides an additive increment or decrement to the total dipole moment of the ionic pair. The slow relaxation mode with relaxation time, ca. 10 ns, independent of CD, has been attributed to the fluctuation of a distribution of an electrically bound ionic cloud made with dissociated Br- anion around the spherical micelle.3 Because the translational diffusional constant for the Br- anion in aqueous solution is estimated to be 2.1 × 10-5 cm2 s-1, a time constant necessary for Br- anions to produce a localized distribution around the spherical micelle as seen schematically in Figure 2a can be roughly evaluated as r2/D ∼ 10 ns.3 This time constant can be a good measure of the dielectric relaxation time for the slow mode. The other possibility for the slow relaxation mode is the fluctuation of a distribution for dissociated CTA+ cations in the spherical micelle. According to the roughly estimated lateral diffusional constant, Dlat ∼ 2 × 10-5 cm2 s-1, of the CTA+ cation in the spherical micelle with a fluorescence probing technique,3,7 a time constant necessary to produce a localized distribution of the CTA+ cation on the micellar surface as shown in Figure 2b can be roughly estimated to be r2/Dlat ∼ 10 ns. This time constant also approximates the dielectric relaxation time and is incidentally very similar to the value estimated above. Thus, both mechanisms can be the essential cause for the dielectric relaxation around 108 rad s-1. (7) Shikata, T.; Imai, S.; Morishima, Y. Langmuir 1997, 13, 5229. (8) Barry, B. W.; Russell, G. F. J. J. Colloid Interface Sci. 1972, 40, 174.
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Figure 2. Schematic illustration for the induced electric dipole moment caused by (a) the fluctuation of an electrically bound Br- distribution in the ionic cloud around a spherical micelle, and by (b) the fluctuation of a distribution of CTA+ in the spherical micelle.
Figure 4. Dependencies of ∆′ and ∆′′ on ω for the aqueous CTAB and NaBr system with CD ) 100 mM and CS from 0 to 100 mM at 25 °C.
Figure 3. Relationship between Gdc and CS for the aqueous CTAB and NaBr system with CD ) 100 mM, and for the aqueous NaBr system at 25 °C.
The reason the relaxation strength of the slow relaxation mode decreases has been conjectured to be the degree of dissociation of CTAB as it decreases with CD.3 Both the number of electrically bound Br- in the ionic cloud to the spherical micelle and of dissociated CTA+ in the micelle decrease with reduction of the degree of dissociation. Addition of NaBr. The dependencies of the Gdc values on CS for the aqueous CTAB and NaBr system with CD ) 100 mM, and for the aqueous NaBr solutions are plotted in Figure 3. If the degree of dissociation of Br- is independent of CS for the aqueous CTAB and NaBr system, Gdc should increase in proportion to CS with the same slope as the NaBr system. However, as seen in Figure 3, the slope for the CTAB and NaBr system alters with CS. Since in the region of CS less than 20 mM, the slope of Gdc
is essentially the same as that of the NaBr system, the degree of dissociation of CTAB does not change. However, the slope decreases slightly in the CS region more than 20 mM, and is followed by an increase to the same value as that of the NaBr system above CS ) 70 mM. These mean that the degree of dissociation of CTAB starts to decrease with the addition of NaBr around CS ) 20 mM and levels off around CS ) 70 mM. Adding a small amount of NaBr less than 20 mM to an aqueous CTAB solution at CD ) 100 mM increases the number of electrically bound Br- anions in the ionic cloud around the spherical micelle, whereas it does not increase the number of the CTA+ cation in the spherical micelle. Therefore, the addition of NaBr to the solution will revive the slow electric relaxation mode around 108 rad s-1, if the fluctuation of the electrically bound Br- anion distribution of the ionic cloud around the spherical micelle is the essential cause of the slow relaxation model in the aqueous CTAB solution. On the other hand, if the fluctuation of the CTA+ distribution in the micelle is the essential cause, the addition of a small amount of NaBr will not have any influence in the slow relaxation mode. Effects of the addition of NaBr on the dielectric relaxation behavior for an aqueous CTAB solution at CD ) 100 mM are exhibited in Figure 4. In the range of CS ) 2-20 mM, the addition of NaBr makes shoulders in ∆′′ curves around 108 rad s-1, of which magnitudes increase with CS. In the ω range 108 rad s-1, no slow relaxation mode has been observed in NaBr free solutions.3 Essentially, no influence of the addition of NaBr to dielectric spectra in the high ω range is observed in this CS range. This strongly supports the explanation that the cause of the slow relaxation is the fluctuation of the electrically
Dielectric Relaxation of Cationic Micellar Solutions
Figure 5. Relationship between the rotational relaxation time, τφ, of the fluorescence probe molecule, NaHNA, and CS for the aqueous CTAB and NaBr system with CD ) 100 mM at 25 °C. The relationship between the fastest dielectric relaxation time, τf, and CS is also plotted.
bound Br- anion distribution in the ionic cloud around the spherical micelle. The addition of NaBr more than 70 mM strongly influences the dielectric relaxation spectra in the entire ω range as seen in Figure 4. Because we cannot find a complete plateau in ∆′ data in the low ω side, there is a possibility that a fitted ∆′cal curve (a solid thick line) is wrong in the low ω side. In the case that the chosen Gdc value to estimate ∆′′ is slightly overestimated, then the ω dependence of true ∆′′ becomes more similar to that of ∆′ in the low ω side. Nevertheless, the ω dependence of ∆′ and ∆′′ in the ω region higher than 108 rad s-1 is not affected by the procedure to determine the Gdc value. The ω dependencies of ∆′ and ∆′′ for solutions with CS ) 70 mM, the condition in which the existence of threadlike micelles was reported,1 are very similar to the ω dependencies for threadlike micellar solutions formed with CTAB and sodium salicylate in aqueous solution.9 Actually, the steep increase in the viscosity suggesting the formation of the threadlike micelle was observed in the solution with CD ) 100 mM and CS ) 70 mM. This implies that the broad ∆′ and ∆′′ spectra for solutions with CS ) 70 mM seen in this figure show typical spectra for the threadlike micelle formed with cationic detergents such as CTAB. In the threadlike micellar system with CS ) 70 mM, the fastest relaxation is estimated to be ca. 0.3 ns by curve fitting with eq 2, which is slightly shorter than the fastest relaxation time, ca. 0.7 ns, for spherical micelles and its relaxation strength is roughly one-fourth of that for spherical micelles without the addition of NaBr. Because the origin of the fastest dielectric relaxation is the rotation of the ionic pair between CTA+ and Br-, the physical meaning of the relaxation time obtained by use of DRA in this study is not so different from that obtained by the fluorescence technique with a probe molecule such as sodium 2-hydroxy-3-naphthoate (NaHNA) substituting for Br- .3,7 Figure 5 shows the CS dependence of the rotational relaxation time (τφ) for NaHNA in the aqueous CTAB and NaBr micellar system with CD ) 100 mM. The τφ value seems constant or very slightly decreasing with CS, as the fastest dielectric relaxation time (τf) slightly decreases and reaches a constant value above CS ) 70 (9) Shikata, T.; Imai, S. J. Phys. Chem. 1999, in press.
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mM. This suggests that the rotational relaxation rate of the ionic pair becomes faster or stays constant in the threadlike micelle of CTAB caused by the addition of NaBr. On the other hand, it was reported that the rotational relaxation time for NaHNA substituting for sodium p-toluenesulfonate (NapTS) in the threadlike micelle formed with CTAB and NapTS is roughly twice as long as in the spherical micelle.10 Moreover, both values of τφ for sodium salicylate (NaSal) and of τf in the threadlike micelle formed with CTAB and NaSal were longer than those in the spherical micelle.7,9,11 This implies that the rotational relaxation rate of the ionic pair between CTA+ and aromatic additive anions is made slower in the threadlike micelle formed with CTAB caused by the addition of aromatic additives such as NapTS and NaSal. Therefore, the fact that the threadlike micelle formed with CTAB and NaBr has a shorter τf value than in the spherical micelle case, contrary to the behavior in the threadlike micellar system formed by the addition of aromatic additives, is a significant characteristic of the threadlike micellar system formed with CTAB by adding NaBr. A decrease in the relaxation strength for the fastest relaxation mode of the threadlike micellar system formed by adding NaBr should be related to the reduction of the separation between the ammonium headgroup and the Br- anion in the ionic pair formed in the threadlike micelle. In other words, the effective size of the ionic head portion of the ionic pair reduces to a smaller size in the threadlike micelle. This corresponds well to the argument developed by Israelachvili, in which the criterion between the spherical and threadlike micelle is based on a change in the packing parameter of the detergent.12 The ratio of head portion size to the length of the detergent tail should be another important parameter similar to Israelachvili’s to determine the shape of the micelle. In fact, the ratio reduces significantly when the shape of the micelle alters from sphere to threadlike. The ∆′ and ∆′′ spectra for a solution with CS ) 30 mM in Figure 4 reflects the intermediate state for the transition of the micellar shape from spherical to threadlike with increasing CS. Presumably, the solution at CS ) 30 mM contains mixtures of threadlike micelles possessing different lengths. The fraction of threadlike micelles long enough to exhibit the asymptotic dielectric spectra of the sufficiently long threadlike micelle, such as shown in the data for the solution with CS ) 70 mM in Figure 4, increases gradually with CS. Conclusions A dielectric relaxation mode with the relaxation time, ca. 10 ns, in aqueous CTAB solutions is assigned to the fluctuation of electrically bound Br- in the ionic cloud around the spherical micelle. The transition in micellar shape from spherical to threadlike in the aqueous CTAB solution caused by adding NaBr is related to a change in dielectric relaxation spectra from fairly sharp with only one relaxation time, ca. 0.7 ns, to very broad with the fastest relaxation time of ca. 0.3 ns in the system with the CTAB concentration of 100 mM. The rotational relaxation mode of the ionic pair formed between CTA+ and Br- is slightly faster in the threadlike micelle formed by the addition of NaBr than in the spherical micelle of CTAB. LA990387N (10) Imai, S.; Shikata, T. Langmuir 1999, in press. (11) Shikata, T.; Morishima, Y. Langmuir 1996, 12, 5307. (12) Israelachvili, J. N. Intermolecular and Surface Forces 2nd ed.; Academic Press: New York, 1991.
