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Entanglements in a Threadlike Micellar System As Studied by Dielectric Relaxation Toshiyuki Shikata* and Shin-ichiro Imai Department of Macromolecular Science, Osaka University, Toyonaka, Osaka 560-0043, Japan Received October 6, 1999. In Final Form: March 7, 2000 The presence of contact (or entanglement) points in an aqueous threadlike micellar system consisting of equimolar cetyltrimethylammonium bromide (CTAB) and sodium salicylate (NaSal) was confirmed using a dielectric relaxation measurement covering the frequency (ω) range from 6.3 × 106 to 6.3 × 109 rad s-1. The rotational relaxation mode of an ionic pair formed by CTA+ and Sal- in a threadlike micelle was around ω ∼ 109 rad s-1. The magnitude of concentration-normalized relaxation strength for the rotational relaxation mode decreased, while that of a relaxation mode around ω ∼ 2 × 108 rad s-1 increased with the concentration (cD-S) of CTAB and NaSal at cD-S > 30 m mol kg-1. However, the concentrationnormalized relaxation strength for other relaxation modes did not change. These findings suggest that the rotational motion of the ionic pair is strictly interrupted and slowed at contact points between threadlike micelles owing to interaction between two portions constructed by ionic pairs on the micellar surface.
Introduction Some cationic surfactants, such as cetyltrimethylammonium bromide (CTAB), form long, stable threadlike micelles with additives such as sodium salicylate (NaSal) in aqueous solutions.1-3 Threadlike micellar systems show remarkable viscoelasticity like polymeric materials in solution and/or in the molten state. In polymeric systems, entanglement points between polymer chains work as temporally cross-linking points to generate rubber elasticity.4 The relationship between the magnitude of the rubbery plateau, GN, which is plateau modulus determined at the high-frequency side using a frequency sweep viscoelastic measurement, and the concentration (cp) of polymer molecules for concentrated polymer solutions is usually described as GN ∝ cp2∼2.2. In practice, the value of GN is used to estimate the molecular weight between entanglement points in polymeric systems.4 In aqueous threadlike micellar systems such as CTAB and NaSal, the relationship between GN and the concentration of surfactants is identical to that in the polymeric system.2 Therefore, the origin of the strong viscoelasticity is probably entanglement between threadlike micelles in the aqueous CTAB and NaSal system, as it is in polymeric materials. The relationship between GN and surfactant concentration is similar in many threadlike micellar systems.3 Detecting the presence of entanglement between two threadlike substances, except for viscoelastic measurements, is quite difficult. Type A polymers have electric dipole moments aligned parallel to polymer backbones. Dielectric relaxation measurements can detect the onset of entanglement by the lengthened global relaxation time of these polymers.5 A static scattering experiment on an entangling polymeric system provides information on correlation length between entanglement points.6,7 In threadlike micellar systems, a portion of the cylindrical * Corresponding author. Tel: +81-6-6850-5462. Fax: +81-66850-5461. E-mail:
[email protected]. (1) Gravsholt, S. J. Colloid Interface Sci. 1976, 57, 575. (2) Shikata, T.; Hirata, H.; Kotaka, T. Langmuir 1987, 3, 1081. (3) Rehage, H.; Hoffmann, H. Mol. Phys. 1991, 74, 933. (4) Ferry, J. D. Viscoelastic Properties of Polymers, 3rd ed.; Wiley: New York, 1980. (5) Adachi, K.; Kotaka, T. Macromolecules 1984, 17, 120.
surface of two distinct threadlike micelles will come into contact at an entanglement point. Some physicochemical properties on (or near) the surface of the threadlike micelle should be changed by physically contacting the surfaces of other threadlike micelles at an entanglement point. If interaction between the two surfaces of a threadlike micelle is enough strong, changes in physicochemical properties might be easily induced by the approaching of two threadlike micellar surfaces. The area on the micellar surface with changed physicochemical properties should be extended beyond the contact area at entanglement. Dielectric relaxation measurements (DR) can detect the electric dipole moments. DR is also powerful enough to detect the rate of rotational motion for groups with electric dipole moments. The dielectric relaxation features of some aqueous surfactant micellar solutions such as CTAB, tetradecyltrimethylammonium bromide (TTAB), and dodecyltrimethylammonium bromide (DTAB) have been extensively investigated.8-11 These studies confirmed the presence of dipole moments in spherical and threadlike micelles formed by CTAB and NaSal in aqueous solution. Ionic pairs composed of a cationic surfactant ion, such as CTA+, and a counteranion, Br-, have electric dipole moments with a rotational relaxation time around 10-9 s in spherical micellar systems. On the other hand, ionic pairs formed in threadlike micellar systems are complexes between CTA+ and the salicylate anion, Sal-. The rotational rate of the ionic pair in the threadlike micellar system is not so different from that of the spherical systems and is independent of the concentration of CTAB and NaSal below 10 m mol kg-1.11 However, the relaxation spectra are much broader for the threadlike than for the spherical micellar systems. The location of hydrophilic headgroups of ionic pairs in both spherical and threadlike micelles should be very close to the micellar surface. Thus, the values of rotational (6) de Gennes, P. G., Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca, NY, and London, 1979; Chapter 3. (7) Daoud, M.; Cotton, J. P.; Farnoux, B.; Jannik, G.; Sarma, G.; Benoit, H.; Duplessix, R.; Picot, C.; de Gennes, P. G. Macromolecules 1975, 8, 804. (8) Barchini, R.; Pottel, R. J. Phys. Chem. 1994, 98, 7899. (9) Shikata, T.; Imai, S. Langmuir 1998, 14, 6804. (10) Imai, S.; Shikata, T. Langmuir 1999, 15, 8388. (11) Shikata, T.; Imai, S. J. Phys. Chem. B 1999, 103, 8694.
10.1021/la9913248 CCC: $19.00 © 2000 American Chemical Society Published on Web 04/29/2000
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relaxation time for the ionic pair in threadlike micelles at moderately high concentration conditions should change, since the ionic pairs belonging to different threadlike micelles would interrupt rotational motion by contact with each other at entanglement points. In this report, changes in the shape of dielectric spectra with the concentration of a surfactant are discussed in conjunction with the number of entanglement points in an aqueous threadlike micellar system formed by CTAB and NaSal. We also discuss the number of hydrated water molecules in the threadlike micellar system measured using the magnitude of the dielectric relaxation strength of the system. Experimental Section Materials. CTAB from Wako Pure Chemicals Ltd. (Osaka) was purified twice by recrystallization with a mixed solvent of methanol and acetone. Special grade NaSal was purchased from the same company and used without further purification. Highly deionized water with a specific resistance above 16 MΩ cm-1 was obtained as the solvent with a Milli Q SP system (Millipore). Aqueous equimolar CTAB and NaSal solutions with concentrations (cD-S) ranging from 10 to 400 m mol kg-1 were kept standing for over 2 days prior to DR measurements to equilibrate. Methods. The electric conductance (G) and capacitance (C) of samples were measured using an RF impedance analyzer (Hewlett-Packard, HP4191A) equipped with a homemade electrode cell9 at room temperature (25 °C) in the ω range from 6.28 × 106 to 6.28 × 109 s-1. Data Processing. The dielectric constant (′) and loss (′′) were calculated as ′ ) CC0-1 and ′′ ) GC0-1ω-1,12 where C0 means capacitance of the vacant measuring electrode cell. To estimate the pure contribution (∆′) of micelles to the dielectric constant, the component ′m due to the medium (water) was subtracted from the ′ value. When the values of G for samples were rather high, the electrode polarization effect 10,13 brought ′ to much higher values than expected in the lower ω range examined. Under such conditions, the precise ′ values for the micellar system were evaluated using the correction procedure described below. According to the classical interpretation of the electrode polarization effect,13 we assumed that the surface of electrodes containing an aqueous sample has an electric double layer with a specific electric capacitance (Cel). The aqueous sample has an ω-independent (direct current) electric conductance (Gdc) as a high bias, and it also has an ω-dependent small component (Gs) related to the dielectric relaxation caused by the sample. Then, the system can be described as an equivalent electric circuit formed by the series connection of Cel and the resistance of Gdc-1 in the low-ω side because the contribution of Gs is negligibly small there. Consequently, the system has ω-dependent capacitance (C(ω)) in the real part as given by eq 1.
C(ω) )
Cel 1 + ω2(CelGdc-1)2
Figure 1. Relationship between (CelC0)-1Gdc2 and Gdc for aqueous CTAB and NaSal, CTAB and NaBr, and CTAB systems obtained using a homemade electrode cell.10
(1)
At ω ranges much higher than Cel-1Gdc, eq 1 leads to C(ω) ) Cel-1Gdc2ω-2. In standard aqueous samples, the value Cel-1Gdc is always much less than 1 Hz. Thus, the contribution of the electrode polarization to ′ can be estimated as ′el ) (CelC0)-1Gdc2ω-2 in the ω range examined. If Cel is a known function of Gdc, the pure contribution of the micelle to the dielectric constant is ∆′ ) ′ - ′m - ′el. When ∆′ is constant at low ω, (CelC0)-1Gdc2 can be estimated as the slope of a plot between ′ - ′m - ∆′ ()′el) and ω-2. In an aqueous NaBr system when ∆′ ) 0, proportionality in the relationship between ′ - ′m ()′el) and ω-2 is easily obtained.10 Thus, the estimated values of (CelC0)-1Gdc2 for the NaBr system are plotted as a function of Gdc in Figure 1. The slope of 2 is (12) Daniel, V. V. Dielectric Relaxation; Academic Press: London and New York, 1967. (13) Cirkel, P. A.; van der Ploeg, J. P.; Koper, G. J. M. Physica A 1997, 235, 269.
Figure 2. Typical ω dependence of ∆′ and ∆′′ for an aqueous CTAB and NaSal system obtained at cD-S ) 10 m mol kg-1. Thick and thin solid lines represent calculated fitting curves, ∆′cal and ∆′′cal, by eq 2 for ∆′ and ∆′′, respectively. obtained with a proportional constant. This means that Cel has no Gdc dependence in the aqueous NaBr system. A previous study11 revealed that an equimolar aqueous CTAB and NaSal system with cD-S e 10 m mol kg-1 had ∆′ and ∆′′ values that were close and proportional to ω-0.5 in the ω range round 107 rad s-1. Figure 2 shows the ω dependence of ∆′ and ∆′′ for an aqueous solution of CTAB and NaSal at cD-S ) 10 m mol kg-1. The ∆′ data without correction for ∆′ deviates upwardly from the reported ∆′ curve (a solid line) because of the electrode polarization. When the adequate (CelC0)-1Gdc2 value was subtracted from ∆′ data, a corrected ∆′ curve was obtained. Because the anticipated ω dependence of ∆′ for aqueous CTAB and NaSal solutions with cD-S higher than 10 m mol kg-1 is proportional to ω-0.5 in the low-ω range close to 107 rad s-1, the values of (CelC0)-1Gdc2 were estimated for each solution. The
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Shikata and Imai Table 1. Summary of Values for ∆Ei and τi for Equimolar Aqueous CTAB, NaSal Solutions
Figure 3. Dependence of ∆′ and ∆′′ on ω for an aqueous CTAB and NaSal system with several concentrations, cD-S. Thick and thin solid lines imply fitting curves, ∆′cal and ∆′′cal, for each solution. relationship between the estimated values of (CelC0)-1Gdc2 and Gdc is plotted in Figure 1. The estimated (CelC0)-1Gdc2 values for the previously studied aqueous CTAB and NaBr system10 are also plotted in Figure 1. The Gdc dependence of the (CelC0)-1Gdc2 values for the aqueous CTAB and NaSal and the CTAB and NaBr systems are in reasonable agreement. The slope of 2 (for solid lines) in this plot means Cel is independent of Gdc. The reason for different Cel values for aqueous NaBr and for aqueous CTAB and NaSal (or NaBr) systems should be related to the presence or absence of the adsorption layer of CTAB on the surface of the electrodes. Consequently, the fact that Cel was independent of Gdc allowed the precise ∆′ for the aqueous CTAB and NaSal system with cD-S above 10 m mol kg-1 to be calculated. In the case of dielectric loss, the pure contribution, ∆′′, due to the presence of micelles was estimated as ∆′′ ) ′′ - ′′m GdcC0-1ω-1; where ′′m is a dielectric loss component due to the medium (water). In standard aqueous systems with CelGdc-1 > 1 s, the contribution of the electrode polarization effect to the electric conductance, G, appears as decreasing G in the ω side lower than 104 rad s-1, because the ω dependence of the value of G due to the electric polarization effect is much weaker than that of the capacitance, C. Therefore, the contribution of the electrode polarization effect does not need to be considered when estimating the dielectric loss in this ω range. The Gdc values were determined as calculated ∆′′ curves exhibiting ω dependence consistent with that of the ∆′ curves determined in the procedure described above. Debye-type model functions,12 ∆′cal and ∆′′cal, with up to the four elements given in eq 2 were used to determine the ω dependence of ∆′ and ∆′′. 4
∆′cal )
∆i
∑1 + ω τ i)1
2 2 i
4
∆′′cal )
∆iωτi
∑1 + ω τ i)1
2 2 i
(2)
Results and Discussion Dielectric Spectra. The ω dependences of ∆′ and ∆′′ for aqueous CTAB and NaSal solutions with cD-S values higher than 10 m mol kg-1 are plotted in Figure 3. The ω dependences of ∆′ and ∆′′ for the solutions with cD-S values below 10 m mol kg-1 were identical to those of a solution at cD-S ) 10 m mol kg-1, whereas the magnitude of ∆′ and ∆′′ was proportional to cD-S. When cD-S e 10 m mol kg-1, the number of contacts or entanglements
cD-S/ m mol kg-1
∆1, τ1 ) 1.2 × 10-9 s
∆2, τ2 ) 0.6 × 10-8 s
∆3, τ3 ) 0.6 × 10-7 s
∆4, τ4 ) 0.7 × 10-6 s
10 30 50 70 100 200 400
0.9 2.1 2.5 2.8 2.0 3.0 2.0
1.0 3.3 7.5 11 20 48 92
3.0 9.0 15 21 30 60 120
17 48 80 120 160 320 640
Figure 4. Dependence of the magnitude of concentrationnormalized relaxation strength, ∆icD-S-1 (i ) 1-3), on cD-S for an aqueous CTAB and NaSal system.
between two threadlike micelles is so small that the contribution of the entanglement to dielectric behavior that will be discussed later is negligible. This is the reason the ω dependences of dielectric spectra for the samples with cD-S e 10 m mol kg-1 are identical to each other and the magnitudes of those are perfectly proportional to cD-S. The shape of the spectra changes around ω ) 109 rad -1 in Figure 3, becoming more obvious with increasing s cD-S values. However, both ∆′ and ∆′′ are proportional to ω-0.5 at low ω, and the magnitude of the spectra is essentially proportional to cD-S. To define the changes in the ω dependence of dielectric spectra, model functions given by eq 2 are fit with four sets of relaxation time (τi) and strength (∆i) values. All the spectra shown in Figure 3 are reasonably expressed with four constant τi and the cD-S-dependent ∆i summarized in Table 1. The values of ∆3 and ∆4 for the relaxation strength of the two longer relaxation times, τ3 and τ4, are proportional to cD-S. However, the values of ∆1 and ∆2 for the two shorter relaxation times are not proportional to cD-S. The values of concentration-normalized relaxation strength, ∆icD-S-1, are plotted in Figure 4 as functions of cD-S. The magnitude of ∆1cD-S-1 and ∆2cD-S-1 are incidentally identical at the cD-S region below 10 m mol kg-1. With increasing cD-S, the value of ∆1cD-S-1 decreases in proportion to the value of cD-S and diminishes around cD-S ) 120 m mol kg-1, while the ∆2cD-S-1 value increases linearly with the value of cD-S and finally reaches a constant value above cD-S ) 120 m mol kg-1. This means that the total relaxation strength, ∆1 + ∆2 + ∆3 + ∆4, is perfectly proportional to cD-S, whereas the ∆1cD-S-1 value for the fastest relaxation mode with the τ1 transfers gradually to the value of ∆2cD-S-1 for the second relaxation mode with increasing cD-S. Above cD-S ) 120 m mol kg-1 most of the ∆1 component moves to the second relaxation mode. The fastest relaxation mode with a relaxation time of τ1 is assigned to a rotational relaxation mode of an ionic pair formed by CTA+ and Sal- in threadlike micelles.
Entanglements in a Threadlike Micellar System
However, other slower relaxation modes with τ2-τ4 are not clearly assigned to distinct molecular motions that occur in threadlike micelles. In our previous paper,11 a model was proposed to explain slow dielectric relaxation modes (with τ3 and τ4) in the equimolar aqueous CTAB and NaSal system with cD-S e 10 m mol kg-1. In the model, we assumed that exchange of Sal- by CTA+ occurred frequently in threadlike micelles, and the rate of Salexchange between two CTA+ cations determined slow dielectric relaxation times.11 Kinetics of Entanglement Formation. The average number density of contact (or entanglement) points (Nc) between threads should be proportional to the square of their concentration: Nc ∝ cD-S2, because the rate of contact formation is proportional to the square of the number density of unit elements (Nu) for the thread substance: Nu ∝ cD-S. Thus, the estimated number density of free unit elements (Nf) that do not form contacts or entanglements between other unit elements is to be Nf ) Nu - Nc ∝ cD-S (1 - RcD-S ), where R is a proportional constant. The rotational motion of ionic pairs formed in the threadlike micelles in an aqueous CTAB and NaSal system is assigned to the fastest relaxation time of τ1 when cD-S is less than 10 m mol kg-1 because the rotational relaxation time of Sal- in threadlike micelles estimated using a fluorescence anisotropy relaxation measurement agreed with τ1 from the DR measurement.11,14 The rotational motion should occur on the surface or at places close to that of the threadlike micelle. Therefore, making contact or entanglements between two threadlike micelles at moderately high cD-S will interrupt the free rotation of the ionic pairs. The relaxation time of the rotation should be slowed more or less due to physical contact between two ionic pairs belonging to different threadlike micelles near entanglement points. According to this conjecture, the decrease in the magnitude of the τ1 mode and corresponding increase in the τ2 mode shown in Figure 4 is comprehensive. It is likely that the relaxation time of interrupted rotational motion of ionic pairs near the entanglement points is incidentally identical to the τ2 value. Since the number of ionic pairs in the unit element of the threadlike micelle remains constant, the number of ionic pairs that can influence entanglement is proportional to Nc. On the other hand, the number of ionic pairs that cannot influence contact is proportional to Nf. Moreover, the magnitudes of relaxation strength for the free and interrupted rotation of ionic pairs in a threadlike micelle are proportional to Nf and Nc, respectively. Thus, the concentration-normalized relaxation strength, ∆1cD-S-1, corresponding to the number of free rotational motions for ionic pairs decreases with cD-S as seen in Figure 4 in the manner NfcD-S-1 ∝ (1 - RcD-S). On the other hand, the value of ∆2cD-S-1 relevant to two distinct contributions from the interrupted rotational motion of ionic pairs and from another relaxation mode independent of making contact or entanglements increases in the manner (N2 + Nc)cD-S-1 ∝ (1 + RcD-S), where N2 is the number density of elements contributing to the relaxation mode of τ2 without contact or entanglements in the threadlike micelle. Light and Topological Entanglements. The cD-S dependence of ∆1cD-S-1 and ∆2cD-S-1 in Figure 4 qualitatively agrees with the prediction based on entanglement formation discussed above, which implies that all ionic pairs can influence contact or entanglements and the free rotational motion of the ionic pairs diminishes above 120 m mol kg-1. However, in the cD-S dependence of a (14) Imai, S.; Shikata, T. Langmuir 1999, 15, 7993.
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Figure 5. (a) Schematic representation of two types of contact (or entanglements). T means topological contact contributing to both mechanical and dielectric properties. L implies light contact contributing only to dielectric properties. (b) Schematic representation of two regions influenced dielectrically by light contact. The actual contact region between two threadlike substances is directly affected. Moreover, many ionic pairs in the vicinity of the real contact region would have dielectric effects due to the highly interrupted rotation of ionic pairs in the actual contact region. (c) Schematic representation of a 3-arm branch on a threadlike micelle. The curvature of the micellar surface in the vicinity of a branching point, shown by hatching, has the opposite sign to that of portions far from the branching point.
mechanical plateau modulus, GN, for the aqueous CTAB and NaSal system, the cD-S range satisfying the relationship of GN ∝ cD-S2 was extended up to 300 m mol kg-1.15 These findings mean that fewer entanglement points work as mechanical cross-link points than was estimated by the DR method at the same cD-S. A schematic representation for two types of contact (or entanglements) in a threadlike micellar system is presented in Figure 5a. In threadlike micelles, an entanglement point consists of an area on the cylindrical micellar surface that includes a great number of ionic pairs. Light contact represented by L in the figure will provide dielectric influence on a threadlike micelle if ionic pairs are located on the surface of the threadlike micelles. On the other hand, topological contact T provides both dielectric and mechanical effects in a threadlike substance system. In general, the number of light contacts is much greater than that of topological contacts. Therefore, the significant difference in the range of cD-S showing the regular entanglement relationship, Nc ∝ cD-S2, determined by the dielectric and mechanical method can be explained. Because dipole-dipole interaction between two ionic pairs is not such a long-range interaction, short separation between two micellar surfaces, namely, physical contact, (15) Shikata, T.; Pearson, D. S. Langmuir 1994, 10, 4027.
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would be necessary to generate dielectric effects. Many ionic pairs in the vicinity of an entanglement point (or area) would be also dielectrically affected owing to the highly interrupted motion of ionic pairs in the entanglement point as shown schematically in Figure 5b. Therefore, above cD-S ) 120 m mol kg-1 the surface of a threadlike micelle is essentially covered by another threadlike micellar surface caused by a large number of light contacts, and the free rotation of most ionic pairs on the micellar surface that are not within the contact area is also interrupted. The discussion above is based on an idea that threadlike micelles do not form branches. In practice, no branching points on threadlike micelles were found in electron micrographs for aqueous equimolar CTAB and NaSal solution.2,16 Even though there exist branching points on threadlike micelles in this system, the number of branching points should be very few. Therefore, we do not think the contribution of the branch to the dielectric behavior is important. We previously proposed a model to explain the unique single relaxation type rheological behavior for the aqueous CTAB and NaSal system. In the model,2 it was assumed that at an entanglement point two threadlike micelles fused to form a tentative 4-arm branch and then crossed each other like a ghost to release a high-energy state owing to the structure of the branch. The time necessary for the entanglement point to disappear by the crossing of two threadlike micelles corresponds to a rheological relaxation time. We think that the tentative 4-arm branch is unstable and its lifetime is not long. Thus, the average number fraction of the tentative 4-arm branch in the total entanglement points working to sustain mechanical energy should be low. Recently, many reports17-20 claiming the importance of branching points to mechanical properties of threadlike micellar systems were published. Some authors17,18 have suggested that branching points are steady and their number is not small in some viscoelastic threadlike micellar systems. The curvature of micellar surface in the vicinity of a branching point should be altered into the opposite sign as seen schematically in Figure 5c. The rate of molecular motion for an ionic pair formed by a surfactant ion and a counterion in a portion with the opposite sign curvature near the branching point of threadlike micelles should be more or less different from that in other portions far from branching points. Thus, in systems possessing threadlike micelles with so many branching points, it is possible that the contribution of the branch to the dielectric behavior becomes important. In this case, the dependence of dielectric relaxation behavior on the concentration of surfactants would differ from that in Figure 3 observed in the equimolar aqueous CTAB and NaSal system. Hydration of CTA+. The medium (water), ∆′m and ∆′′m, makes a contribution to ∆′ and ∆′′. When the cD-S value was low, the values of ∆′m and ∆′′m were similar to those of pure water, ∆′w and ∆′′w. However, when cD-S was high, the values of ∆′m and ∆′′m were smaller than those of ∆′w and ∆′′w. ∆′w is given as ∆′w-r + ∆∞, where ∆′w-r and ∆∞ mean the relaxing part (∆w/(1 + ω2τw2), ∆w ) 72.7) relevant to the molecular motion of water molecules in the bulk state with a relaxation time of τw (16) Shikata, T.; Sakaiguchi, Y.; Urakami, H.; Tamura, A.; Hirata, H. J. Colloid Inerface Sci. 1987, 119, 291. (17) Fischer, P.; Fuller, G. G.; Lin, Z. Rheol. Act. 1997, 36, 632. (18) Lin, Z.; Hill, R. M.; Scriven, L. E.; Davis, H. T.; Talm, Y. Langmuir 1996, 10, 1008. (19) Lequeux, F. Europhys. Lett. 1992, 19, 675. (20) Khatory, A.; Kern, F.; Lequeux, F.; Appell, J.; Porte, G.; Morie, N.; Ott, A.; Urbach, W. Langmuir 1993, 9, 933.
Shikata and Imai
Figure 6. Relationship between a factor, f, representing the dielectric contribution of pure water molecules at high ω around 1011 rad s-1, and cD-S for an aqueous CTAB and NaSal system.
) 8.3 × 10-12 s and a constant value of 5.3 at the extremely high ω region, due to electron polarizability, respectively.8 Namely, ∆′′w is given as ∆wωτw/(1 + ω2τw2). Barchini and Pottel reported that the contribution of free water molecules to the overall dielectric spectra in aqueous surfactant systems such as CTAB/water decreased with increasing concentration of surfactants. The value of ∆′w-r decreased linearly with the surfactant concentration, whereas ∆∞ was not influenced by adding surfactants at all up to a concentration of 100 m mol kg-1.8 Moreover, ∆′′w also linearly decreased with the surfactant concentration. These findings mean that water molecules form a structure near the headgroup of trimethylammonium, in which water molecules are immobilized and dielectrically dead owing to symmetric orientation. This is very similar to hydration in aqueous tetraalkylammonium salt systems such as tetra-n-butylammonium bromide (TBAB) and tetramethylammonium bromide (TMAB). The estimated numbers of water molecules in the structures of a clathrate hydrate (iceberg) of TBAB and TMAB averaged 33 and 12-18, respectively.21 According to Barchini and Pottel,8 the contribution of free water to the dielectric spectra are given as eq 3 with a factor, f, proportional to the molar fraction of dielectrically free water molecules.
∆′m )
f∆w 2
1 + ω τw
2
+ ∆∞
∆′′m )
f∆wωτw 1 + ω2τw2
(3)
The estimated f vales with which to determine the dielectric spectra for all the examined solutions are plotted as a function of cD-S in Figure 6. The relationship between f and cD-S is perfectly linear. The slope of the solid line in Figure 6 is -0.58 kg mol-1. In an aqueous CTAB and NaSal system, Br- anions are replaced by Sal- anions to form ionic pairs in threadlike micelles.2,11,14 Therefore, solutions in this study contain dissociated Na+ and Br- ions at a concentration identical to cD-S. Solution properties of an aqueous NaBr system were studied in detail using DR22 and nuclear magnetic resonance (NMR)23 spectroscopy, and the number of hydrated water molecules per NaBr was 12-16. (21) McMullan, R.; Jeffrey, G. A. J. Chem. Phys. 1959, 31, 1231. (22) Pottel R.; Lossen, O. Ber. Bunsen-Ges. Phys. Chem. 1967, 71, 135. (23) Hertz, H. G.; Zeidler, M. D. Ber. Bunsen-Ges. Phys. Chem. 1964, 68, 821.
Entanglements in a Threadlike Micellar System
The value of 1 - f means a molar fraction of water molecules immobilized and dielectrically dead in the ω range around 1011 rad s-1, and which form hydration structures with ionic pairs of CTA+-Sal- in threadlike micelles and with NaBr in the bulk water phase. The estimated number of immobilized water molecules per ionic pair of CTA+-Sal- in the threadlike micelle of an aqueous CTAB and NaSal system is 15-19 from the slope in Figure 6, taking into account the hydration number (14-18) of NaBr. The number of immobilized water molecules in the threadlike micelle of a CTAB and NaSal system is a little more than that of hydrated water molecules to TMAB. Although the number of hydrated water molecules to a surfactant molecule in micelles was not considered in detail, it should not differ radically from that of hydrated water molecules to TMAB possessing a similar electrolyte group. Because surfactant molecules do not significantly dissociate in micelles, the hydrophobicity of surfactant molecules would be higher than that of TMAB. Thus, the numbers of hydrated water molecules of alkyltrimethylammonium surfactants may be higher than those of TMAB with similar headgroups. As we described,11 the magnitude of a dipole moment for the ionic pair CTA+-Sal- in threadlike micelles is much larger than that calculated from the value of the elementary charge and the estimated separation, about 0.4 nm, between the center of a trimethylammonium headgroup and that of Sal- in the ionic pair of threadlike micelles. This suggests that a large degree of immobilized water molecules in ionic pairs increases the magnitude of the dipole moment by highly oriented hydration to a trimethylammonium headgroup and Sal- of ionic pairs. The effective size of headgroups for the ionic pair of CTA+-Sal- in threadlike micelles should be evaluated
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taking into account the volumetric contribution of the great number of hydrated water molecules attracted to the ionic pair. Conclusion The presence of contact (or entanglement) points in an aqueous threadlike micellar system of equimolar CTAB and NaSal was discussed with data of dielectric relaxation measurements. Broad dielectric relaxation spectra were found in the micellar system, which were well-fitted by a model function consisting of four Debye-type relaxation functions possessing relaxation times from 1.2 ns to 0.7 µs. The rotational relaxation mode of an ionic pair formed by CTA+ and Sal- in a threadlike micelle was assigned to the fastest mode with the relaxation time of 1.2 ns. The magnitude of concentration-normalized dielectric relaxation strength for the rotational relaxation mode decreased, while that of the second fastest relaxation mode with the relaxation time of 6 ns increased with the concentration of CTAB and NaSal above 30 m mol kg-1. However, the concentration-normalized relaxation strength for other relaxation modes did not change with the concentration of CTAB and NaSal. This suggests that the rotational motion of the ionic pair in micelles is strictly interrupted and slowed at entanglement points between threadlike micelles owing to interaction between two portions on the micellar surface. Acknowledgment. This work was supported by a Grant-in-Aid (11440205) from the Ministry of Education, Science, Culture and Sports, Japan. LA9913248
