Dielectric Relaxation Behavior of Aqueous ... - ACS Publications

Langmuir 2001, 17, 6841-6850

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Dielectric Relaxation Behavior of Aqueous Dodecyldimethylamineoxide Solutions Shyuji Itatani and Toshiyuki Shikata* Department of Macromolecular Science, Osaka University, Toyonaka, Osaka 560-0043, Japan Received April 14, 2001. In Final Form: August 23, 2001 Dielectric relaxation behavior was examined for aqueous solutions of dodecyldimethylamineoxide (DDAO) in the range of concentration (cD) from 100 to 500 mM varying the average degree of protonation (〈R〉) by adding HBr. DDAO has an electric dipole moment due to an OrN coordination chemical bond on its headgroup, and the fraction of OrN is reduced by adding HBr, while that of HO-N+ increases. This process was detected as a change in dielectric spectra. Dielectric spectra for aqueous DDAO solutions had four types of relaxation modes. A fast relaxation time (τ1 ∼ 10-10 s) was essentially independent of cD, and the relaxation strength (∆1) was proportional to cD at 〈R〉 ) 0. Moreover, the magnitude of ∆1 decreased with 〈R〉; therefore, it was attributed to the rotational relaxation mode of OrN type headgroups in spherical micelles. A relaxation mode with cD-independent τ2 (∼10-9 s) possessed relaxation strength (∆2) proportional to cD. Because ∆2 increased with 〈R〉 by adding HBr and the number of Br- entrapped in micelles increased with 〈R〉, the mode was assigned to the rotational relaxation mode of an ion pair formed between HO-N+ and Br- on the micellar surface. A relaxation mode with τ3 (∼10-8 s) at 〈R〉 > 0 was attributed to the rotational relaxation mode of intermolecular association particles formed between protonated and unprotonated DDAO molecules due to intermolecular forces such as hydrogen bonding. A slow mode with τ4 (∼10-7 s at 〈R〉 ) 0) was assigned to the relaxation of a counterion distribution around spherical DDAO micelles. When 〈R〉 was higher than 0.5, dielectric behavior of aqueous DDAO solutions was essentially the same as that of aqueous solutions of cationic detergents. The addition of NaBr to aqueous DDAO solutions at 〈R〉 greater than 0.5 made a spherical micellar shape change into a spheroidal shape. This change in micellar shapes made dielectric relaxation spectra much broader.

Introduction Dielectric relaxation spectroscopy is a very powerful method to investigate the motion of molecules possessing electric dipole moments. However, sometimes dielectric spectra are too complicated to understand what happens in a system examined, since all molecular motions changing electric dipole moments are sensitively detected by the dielectric relaxation measurement as a function of the frequency of an applied electric field. In the case of aqueous systems, an electrode polarization effect which frequently occurs on the surface of electrodes is a very serious phenomenon for one to estimate exact dielectric spectra of solute molecules from obtained dielectric data, especially in the low-frequency side. The electrode polarization effect is always beyond control when one employs an ordinary measurement cell consisting of two or three electrodes. Aqueous systems have other problems for precise estimation of the dielectric spectra of solute molecules. One problem is that pure water has a very big dielectric constant of 78 at 25 °C; therefore, the magnitude of an examined dielectric constant for a solute molecule should be greater (for instance, than unity) to be detected precisely. The other problem for aqueous systems is that a general theoretical method to evaluate the dielectric parameters of solute molecules in aqueous systems has not been established so far. Aqueous solutions of some polyelectrolytes such as sodium poly(styrenesulfonate) have been studied by using dielectric relaxation spectroscopy, and molecular dynamics for dissociated sodium ions has been discussed extensively.1,2 The spatial distortion of a dissociated counterion * To whom correspondence should be addressed. Tel: 81-6-68505538. Fax: 81-6-6850-5538. E-mail: [email protected]. (1) Oosawa, F. Biopolymer 1970, 9, 677.

distribution induces a very large electric dipole moment. A time for the distorted distribution of dissociated counterions to relax strongly depends on the size of polyelectrolytes in aqueous solutions, which is sensitively affected by the concentrations of polyelectrolytes and added salts and by the molecular weight of polyelectrolytes. These are the reasons dielectric research for some kinds of aqueous polyelectrolyte solutions has been successfully developed. Some aqueous solutions of detergent molecules such as dodecyltrimethylammonium bromide (DTAB), tetradecyltrimethylammonium bromide (TTAB), sodium dodecyl sulfate (SDS), and so on were investigated dielectrically.3-5 These detergent molecules make spherical micelles in the condition above their critical micelle concentration (cmc). Because spherical micelles formed by such ionic detergent molecules in aqueous solutions always bear ion clouds of dissociated counterions, the distortion of a counterion distribution around spherical micelles induces large electric dipole moments and the relaxation of the counterion distribution is sensitively detected by the dielectric relaxation measurement.4,5 The degree of dissociation for detergent molecules in aqueous spherical micellar systems is not high, and many ion pairs between a detergent ion and counterion exist. Because these ion pairs possess fairly large electric dipole moments, the rotational relaxation mode of detergent molecules in micelles has been detected by the dielectric relaxation measurement.4,5 As pointed out previously, since dielectric relaxation spectroscopy is very sensitive to the motion of molecules bearing dipole moments, it can provide very useful information about (2) Mandel, M.; Odijk, T. Annu. Rev. Phys. Chem. 1984, 35, 75. (3) Barchini, R.; Pottel, R. J. Phys. Chem. 1994, 98, 7899. (4) Shikata, T.; Imai, S. Langmuir 1998, 14, 6804. (5) Imai, S.; Shiokawa, M.; Shikata, T. J. Phys. Chem. B 2001, 105, 4495.

10.1021/la010551i CCC: $20.00 © 2001 American Chemical Society Published on Web 10/06/2001

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molecular dynamics of ionic detergent molecules in micelles, for example, rotational relaxation times of detergents.4,5 Moreover, the estimated magnitude of dipole moments for detergents will be a measure of the strength of intermolecular interaction between detergents in micelles, and it should be relevant to a different factor than the number and length of alkyl tails of detergents and the sizes of their headgroups, which determine the shape of molecular assemblies such as micelles and vesicles. Detergent molecules with an amineoxide group (OrN) such as dodecyldimethylamineoxide (DDAO) are electrically neutral when the pH value of aqueous solutions is higher than 7; however, the amineoxide group is protonated to be (HO-N+) at pH values lower than 7. Because the OrN group has an electric dipole moment, ca. ∼5 D,6 due to OrN coordinate chemical bonding much greater than that of ordinary organic compounds and a solvent, water, the rotational relaxation mode of individual DDAO molecules in spherical micelles is precisely detected at pH values higher than 7 by using the dielectric relaxation measurement. On the other hand, when the pH value is lower than 7 by adding HBr, HO-N+ groups of protonated DDAO might form ion pairs with Br- in micelles as well as DTAB in aqueous solutions. Thus, it is anticipated that the dielectric behavior of DDAO in the condition with the pH value lower than 7 becomes similar to that of DTAB in aqueous solutions. In this study, we discuss the dielectric behavior of aqueous DDAO solutions by changing the concentrations of DDAO, NaBr, and the pH value to elucidate dynamic features in micelles of DDAO in aqueous solutions. Experimental Section Materials. Dodecyldimethylamineoxide, DDAO, was kindly supplied by Nippon Oil & Fats Co. Ltd. (Osaka) and was purified by recrystallization from a mixture of methanol and acetone. Highly deionized water obtained by a MilliQ system possessing a specific resistance higher than 16 MΩ cm was used as a solvent. Aqueous hydrogen bromide (HBr) was added to control pH values (or the degree of protonation, 〈R〉). The concentration (cD) of DDAO was altered from 100 to 500 mM for a system at 〈R〉 ) 0. On the other hand, cD was kept at 100 mM for a system with varying 〈R〉 values from 0 to 1.0. The concentration (cS) of sodium bromide (NaBr) ranged from 0 to 50 mM for a system with cD ) 100 mM and 〈R〉 ) 0, 0.5, and 1.0. Methods. Dielectric relaxation measurements were carried out with an RF LCR meter (Agilent Technologies, 4287A) equipped with a homemade electrode cell4 in the frequency (ω) range from 6.24 × 106 to 6.24 × 109 rad s-1. In the high ω range from 3.1 × 108 to 1.3 × 1011 rad s-1, a dielectric material probe system (Hewlett-Packard, 85070B) which contains a network analyzer (Hewlett-Packard, 8720ES) as a signal analyzer was used.5 The sample temperature in the electrode cells was kept constant at 25 °C with circulating thermostated water. Data obtained with the RF LCR meter were collected in the form of equivalent parallel capacitance (C) and conductance (G) of samples. Dielectric constant (′) and loss (′′) were evaluated as ′ ) C/C0 and ′′ ) G/(C0ω), where C0 was the capacitance of the vacant electrode cell (ca. 0.17 pF). In the case of the dielectric material probe system, ′ and ′′ were automatically generated by a program developed by Hewlett-Packard with water as the standard material. The contribution of DDAO micelles to the dielectric behavior was estimated using following equations: ∆′ ) ′ - fw′ and ∆′′ ) ′′ - fw′′ - Gdc/(ωC0), where w′ and w′′ are the dielectric constant and loss of pure water, respectively, and f means the fractional contribution for pure water to the dielectric behavior of samples. (6) Minkin, V. I.; Osipov, O. A.; Zhdanov, Yu. A. Dipole Moments in Organic Chemistry, Vaughan, W. E., Trans. Ed.; Plenum: New York, 1970.

Itatani and Shikata

Figure 1. Dependence of dielectric constant (′) and loss (′′) on frequency (ω) for an aqueous DDAO solution at DDAO concentration (cD) of 500 mM and for pure water. The obtained ∆′ and ∆′′ were fitted by the sum of Debye type relaxation functions possessing (at maximum) four sets of relaxation time τi and strength ∆i (i ) 1-4). Solutions with high Gdc values had the relationship of ∆′ ∝ ω-2 in the low ω side due to a serious electrode polarization effect. In this case, the contribution of the electrode polarization was removed by subtracting the Gdc2(C0Ce)-1ω-2 value from ∆′ curves according to a correction method used in the previous studies;7,8 Ce represents ω- and Gdc-independent capacitance on the surface of electrodes and was estimated to be 0.3 µF. The concentration of Br- ions ([Br-]) was determined by using a Br- ion selective electrode (8005, Horiba, Kyoto). A homemade Ag-AgCl electrode inserted into a 3.3 M KCl aqueous solution with a salt bridge of 3% agar containing 1.0 M NH4Cl was employed as a reference electrode. A potentiometer (pH meter F-22, Horiba, Kyoto) was used to monitor potential difference between the electrodes. All measurement was carried out at 25 °C. A calibration line between the potential difference and the Br- concentration, [Br-], was obtained using aqueous standard NaBr solutions at 0.001, 0.01, and 0.1 M. A glass pH electrode (6378-10D, Horiba, Kyoto) was used to determine the pH values of sample solutions. The potentiometer mentioned above was used to monitor pH values. The system of pH measurements was calibrated with three kinds of standard solutions at pH ) 2, 7, and 9 prior to each measurement. All pH measurement was carried out at 25 °C.

Results Dependence of Dielectric Spectra on cD. Dielectric spectra, ′ and ′′, for a DDAO aqueous solution at cD ) 500 mM are shown in Figure 1 as functions of ω. Dielectric spectra for pure water are also plotted in the same figure, which can be perfectly reproduced as solid curves by dielectric model functions reported in the literature.9 In the procedure for estimating ∆′ and ∆′′, we assumed that dielectric relaxation times caused by the presence of DDAO micelles were somehow longer than the main relaxation time of τw ) 8.3 × 10-12 s at 25 °C for pure water, and the τw was not affected by the presence of the micelles. Therefore, the f value was determined as spectra, ∆′ and ∆′′, diminished gradually until they disappeared altogether in a ω range higher than 1010 rad s-1 as seen in Figure 2. The next step was the procedure for determining the G0 value. The determined ω dependence of ∆′ was fitted by a model function formed by three Debye type relaxation functions with parameters τ1 ) 1 × 10-10 s, ∆1 ) 5.0, τ2 (7) Imai, S.; Shikata, T. Langmuir 1999, 15, 8388. (8) Shikata, T.; Imai, S. J. Phys. Chem. B 2000, 103, 8694. (9) Kaatze, U. J. Chem. Eng. Data 1989, 34, 371.

Dielectric Relaxation Behavior of DDAO Solutions

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Figure 2. Dependence of dielectric constant difference (∆′) and loss difference (∆′′) on ω for aqueous DDAO solutions at cD ) 100, 300, and 500 mM. Solid lines in this figure represent the best fit curves for the data calculated by Debye type relaxation functions with four elements. The inset shows the relationship between the fractional contribution (f) of the pure water to the dielectric behavior of aqueous DDAO solutions and cD.

) 4 × 10-10 s, ∆2 ) 3.3, τ4 ) 2.4 × 10-8 s, and ∆4 ) 1.1 in this case. From these parameters, the ∆′′ curve was calculated; thus, the value of G0 was determined as the ω dependence of experimental ∆′′ agreed with the calculated one. In this procedure, the entire ω dependence of ∆′′ was determined. In Figure 2, the dependence of ∆′ and ∆′′ on ω for aqueous DDAO solutions at cD ) 100, 300, and 500 mM estimated along the procedure above is shown. Three or four sets of τi and ∆i, i ) 1-4, were necessary to determine the best fit curves for ∆′ and ∆′′ spectra of the solutions. An inset in Figure 2 shows cD dependence of the f value to make the spectra of ∆′ and ∆′′. A solid line in this inset indicates the theoretical prediction for f proposed by Pottel10 assuming only the volume effect of the solute, DDAO. Agreement between experiments and the theoretical prediction is reasonable. This agreement suggests two kinds of possibilities: (i) DDAO micelles have few hydration water molecules. (ii) A few water molecules tightly hydrate to DDAO molecules, and other water molecules with rotational rates as fast as those of water molecules in the bulk state are included in DDAO micelles. In this case, the number of the total hydrated water molecules to DDAO in a micelle should be close to that of water molecules with fast rotational rates. We recently found that two water molecules tightly hydrated to a trimethylamineoxide (TMAO) molecule in aqueous solution.11 Hence, DDAO molecules probably have tightly hydrated a few water molecules even in micelles. We also found that some water molecules possessing very fast rotational rates were included in CTAB micelles formed in aqueous solutions.5 These likely support the latter. The f values for solutions with cD ) 100 mM at various 〈R〉 and cS were essentially independent of 〈R〉 and cS values: ca. f ) 0.96 ( 0.01. The dependencies of τi and the concentration reduced dielectric relaxation strength (∆icD-1, i ) 1-4) on cD at 〈R〉 ) 0 are shown in Figure 3a,b. The fastest relaxation (10) Pottel, R. Water; Franks, F., Ed.; Plenum: New York, 1973; Vol. 3, Chapter 8. (11) Shikata, T.; Itatani, S. Bull. Chem. Soc. Jpn., submitted.

Figure 3. Relaxation times and concentration reduced relaxation strengths (τi (a) and ∆icD-1 (b), i ) 1-4) used to obtain the best fit curves in Figure 2 as functions of cD for aqueous DDAO solutions.

time, τ1, is around 10-10 s, and its strength, ∆1, is essentially proportional to cD. The second relaxation time, τ2, is around 4 × 10-10 s, and its strength, ∆2, is also proportional to cD. However, the reduced strength of ∆4cD-1 decreases with increasing cD. These cD dependencies of relaxation times and strengths imply that the mechanisms of the fastest and second fastest relaxation modes are relevant to molecular motion in micelles of DDAO. The mechanism of the slowest relaxation mode of τ4 is, on the other hand, related to molecular level events which occur outside of the micelles, because both the relaxation time and strength depend on the average distance between micelles in the solutions. In later sections, the fastest and second fastest relaxation modes will be attributed to the rotational motion of a detergent headgroup with OrN coordination bonding and that of an ion pair formed between a protonated detergent headgroup HO-N+ and OH-, respectively. On the other hand, the slowest mode of τ4 will be assigned to the relaxation mode of the electrically bound counterion distribution around DDAO micelles. Dependence of Dielectric Spectra on 〈r〉. The ω dependencies of the relaxation spectra, ∆′ and ∆′′, of the system were strongly affected by the value of 〈R〉 or pH. When 〈R〉 is altered from 0 to 1.0 in aqueous DDAO solutions with cD ) 100 mM, ∆′ and ∆′′ spectra change as shown in Figure 4a,b. Solid lines in Figure 4a,b

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Figure 4. Dielectric spectra, ∆′ and ∆′′ vs ω, for aqueous DDAO solutions at various degrees of protonation (〈R〉) from 0 to 0.5 (a) and from 0.7 to 1.0 (b). Solid lines in this figure represent the best fit curves for the data calculated by Debye type relaxation functions with four elements.

represent the best fit Debye type relaxation functions with three or four sets of τi and ∆i for the experimental spectra. At the condition of 〈R〉 g 0.5, electric conductance, G0, was high and an electrode polarization effect was serious to estimate precise ∆′ and ∆′′. Thus, ∆′ and ∆′′ spectra at 〈R〉 g 0.5 contain slight uncertainty in the low ω side. The most striking point is that the magnitude of the τ2 mode increases its strength remarkably with increasing the value of 〈R〉. The dependencies of relaxation time, τi, and the relaxation strength, ∆i, of each mode on the value of 〈R〉 for the solutions are shown in Figure 5a,b. The values of τ1 and τ3 are kept at constant values of ca. 10-10 and 10-8 s, while τ4 decreases markedly with increasing the value of 〈R〉. Moreover, the value of τ2 (ca. 10-9 s) for the solutions with 〈R〉 g 0.1 is almost twice as large as that at 〈R〉 ) 0, and the magnitude of ∆2 dramatically increases until 〈R〉 ) 0.5 and then approaches a constant value above 〈R〉 ) 0.7. These facts are caused by the addition of HBr to control the value of 〈R〉. As discussed later, the formation of an ion pair between a protonated HO-N+ group and Br- is a key point to make a larger electric dipole moment which is able to show a strong dielectric relaxation process observed as the τ2 mode. At 〈R〉 ) 0, the presence of a small number of ion pairs between HO-N+ and OH- is detected as the τ2 mode. On the other hand, decrease in the magnitude of ∆1 with increasing 〈R〉, especially above 〈R〉 ) 0.5, should be related to a decrease in the number of the coordination chemical bonding, OrN, possessing a dipole moment smaller than that of the ion pair between HO-N+ and Br-. Degree of Protonation of Amineoxide Group. The degree of protonation of amineoxide groups in the system

Itatani and Shikata

Figure 5. Relaxation times and strengths (τi (a) and ∆i (b), i ) 1-4) used to obtain the best fit curves in Figure 4 as functions of 〈R〉.

Figure 6. Relationship between the degree of protonation of DDAO ([N+-OH]cD-1) and 〈R〉 for aqueous DDAO solutions.

by the addition of HBr can be estimated from the value of pH and 〈R〉 assuming the presence of molecularly dispersed DDAO to be negligible, since the cmc of DDAO is very much lower than 100 mM. Figure 6 shows the relationship between the degree of actual protonation of DDAO ([HO-N+]cD-1) and 〈R〉 for the system with cD ) 100 mM. Until 〈R〉 ) 0.6, the value of [HO-N+]cD-1 is proportional to 〈R〉, whereas [HO-N+]cD-1 reaches a constant value of 0.75 in the high 〈R〉 side. The relationship between the degree of Br- binding to the micellar interior ([Br-]boundcD-1) and 〈R〉 for the DDAO


Figure 7. Dependencies of the degree of Br- binding to the micellar interior ([Br-]boundcD-1) and relaxation strength of the τ2 mode (∆2) on 〈R〉 for aqueous DDAO solutions.

solution with cD ) 100 mM is shown in Figure 7; [Br-]bound represents the concentration of Br- bound to the micellar interior. Because [Br-]boundcD-1 is roughly proportional to the 〈R〉 value with a proportional constant of 0.5 and approaches the constant value of 0.35 when 〈R〉 is greater than 0.6, it is possible that a half number of HO-N+ generated by the addition of HBr makes ion pairs between HO-N+ and Br- in the aqueous DDAO solution at cD ) 100 mM. In other words, the degree of counterion binding to protonated DDAO in micelles in the aqueous DDAO system with HBr is about 0.5 over a wide 〈R〉 range. It was also reported that the degree of counterion binding to protonated DDAO in micelles was not so different from 0.5 over a wide 〈R〉 range in the aqueous DDAO system with HCl.12,13 In Figure 7, the magnitude of dielectric relaxation strength, ∆2, for the same system is also plotted as a function of 〈R〉. The relationship between [Br-]boundcD-1 and 〈R〉 is reasonably proportional to that between ∆2 and 〈R〉. Thus, this implies that the magnitude of relaxation strength for the τ2 mode reflects the concentration of the ion pair between HO-N+ and Br- existing in micelles. The magnitude of ∆2 for an aqueous DDAO solution at cD ) 100 mM and 〈R〉 ) 1.0 is smaller by a factor of 0.65 than that of a dielectric relaxation mode found in an aqueous CTAB solution with the same cD value in which solution about 77% of CTAB forms ion pairs between CTA+ and Br-.5 The fact that 75% of DDAO in spherical micelles is protonated by the addition of HBr and 35% of DDAO forms ion pairs between HO-N+ and Br- in the range of 〈R〉 higher than 0.6 suggests that the magnitude of a dipole moment for an ion pair between HO-N+ and Br- is slightly greater than that for an ion pair between CTA+ and Brin the aqueous CTAB by a factor of 1.2. Dependence of Dielectric Spectra on cS at Various 〈r〉 Values. The dependencies of ∆′ and ∆′′ spectra on ω at various concentrations, cS, of NaBr for solutions with cD ) 100 mM and 〈R〉 ) 0 are shown in Figure 8. The shape of ∆′ and ∆′′ in the ω range from 109 to 1010 rad s-1 does not change so much with cS, whereas that in the low ω side alters remarkably with cS. Spectra in the low ω side at cS > 30 mM are not so precise because of the serious electrode polarization effect due to high electric conduc(12) Imaishi, Y.; Kakehashi, R.; Nezu, T.; Maeda, H. J. Colloid Interface Sci. 1998, 197, 309. (13) Garamus, V.; Kameyama, K.; Kakehashi, R.; Maeda, H. Colloid Polym. Sci. 1999, 277, 868.

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Figure 8. Dielectric spectra at various NaBr concentrations (cS) for aqueous DDAO solutions at 〈R〉 ) 0 and cD ) 100 mM. Solid lines in this figure represent the best fit curves for the data calculated by Debye type relaxation functions.

tance. Solid lines in Figure 8 represent the best fit Debye type relaxation curves for experimental ∆′ and ∆′′ spectra. The relationships between τi and cS and between ∆i and cS are shown in Figure 9a,b. Three sets of relaxation parameters are necessary in solutions at cS g 10 mM. It is likely that the values of τ1 and τ2 are essentially independent of the cS value, while the τ4 value dramatically decreases with increasing cS. The magnitudes of ∆1, ∆2, and ∆4 are independent of cS at cS g 10 mM as anticipated from Figure 8. These results suggest that the rotational molecular motion of DDAO molecules in the micellar interior is not affected so much by changing the cS value; however, molecular dynamics for ion pairs between HON+ and OH- in micelles and that out of the micellar surface are affected by the presence of NaBr. The addition of NaBr should substitute Br- for some OH- of the ion pair between HO-N+ and OH-. Thus, increase in ∆2 with cS in a cS range from 0 to 10 mM seen in Figure 9b means that an ion pair between HO-N+ and Br- should have a dipole moment slightly larger than that of an ion pair between HO-N+ and OH-. Although the addition of NaBr substitutes Br- for the electrically bound OH- around micelles causing the τ4 mode, the number of Br- bound to micelles does not increase with increasing cS. Figure 10 shows the ω dependencies of ∆′ and ∆′′ spectra at various cS values for the solutions with cD ) 100 mM and 〈R〉 ) 0.5. It is clear that the relaxation strength around ω ) 10-9 rad s-1 reduces with cS. The shape of spectra in the slow ω side at the higher 〈R〉 value is much broader than that in Figure 8 at 〈R〉 ) 0. These cS dependencies of ∆′ and ∆′′ spectra are very similar to those observed in aqueous cationic detergent systems such as CTAB.7 Figure 11a shows the relationship between relaxation times, τi, and cS for the aqueous DDAO solutions at 〈R〉 ) 0.5. It is likely that the values of τi have little cS dependence. The dependence of ∆1 on cS for the system is weak as shown in Figure 11b. The value of ∆2 decreases with increasing cS in the system (Figure 11b) as observed in the rotational relaxation mode of ion pairs between a CTA+ cation and a Br- anion in aqueous CTAB solution.4,7 However, the value of ∆4 increases with cS in the system. In an aqueous CTAB system, the shape of micelles changes from a sphere to a rodlike (or threadlike) shape

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Figure 9. Relaxation times and strengths (τi (a) and ∆i (b), i ) 1-4) used to obtain the best fit curves in Figure 8 as functions of cS.

Figure 10. Dielectric spectra at various NaBr concentration (cS) for aqueous DDAO solutions at 〈R〉 ) 0.5 and cD ) 100 mM. Solid lines in this figure represent the best fit curves for the data calculated by Debye type relaxation functions.

with addition of simple salts such as NaBr.7 The viscosity of the aqueous CTAB system is very low like that of water even at the concentration of 100 mM, whereas the addition of NaBr to the system dramatically increases its viscosity due to the change in the micellar shape.7 Maeda et al. reported that the aggregation number (Nagg) of micelles formed in aqueous DDAO solutions at a NaCl concentration higher than 100 mM showed the maximum obviously at 〈R〉 ) 0.5.13,14 Because the maximum value of Nagg at 〈R〉 ) 0.5 and the NaCl concentration of 50 mM was

Itatani and Shikata


estimated to be ca. 100,14 which was not so different from that of spherical micelles, increase in viscosities for aqueous DDAO solutions at 〈R〉 ) 0.5 caused by the addition of NaCl was small. The value of Nagg became greater than 600 and the shape of micelles was rodlike at 〈R〉 ) 0.5 and the concentration of NaCl higher than 200 mM.13 In the case of aqueous DDAO solutions with NaBr, the viscosity of a solution at 〈R〉 ) 0.5 and cS ) 50 mM was 15 times as high as that of pure water. Thus, the maximum Nagg value in the solution with NaBr at 〈R〉 ) 0.5 should be much larger than that of the solution with NaCl. The ω dependencies of dielectric spectra, ∆′ and ∆′′, for aqueous DDAO solutions with cS ranging from 0 to 50 mM at 〈R〉 ) 1 are shown in Figure 12. Figure 13a,b shows τi and ∆i for the best fit curves seen in Figure 12. The magnitude of relaxation strength, ∆2, around 10-9 rad s-1 slightly decreases with cS. The dielectric spectra for the solution at cS g 30 mM look very similar to those for a solution at 〈R〉 ) 0.5 and cS ) 50 mM. The magnitude of ∆1 is independent of cS, while that of ∆2 slightly decreases with cS, like the behavior in solutions with 〈R〉 ) 0.5. On the other hand, the ∆4 value increases with increasing cS at cS > 30 mM as seen in Figure 13b. Maeda et al. reported that micelles formed by DDAO in D2O solutions at 〈R〉 ) 1 with a NaCl concentration higher than 200 mM possessed not a spherical shape but an elongated shape by use of a small-angle neutron scattering technique as observed in solutions at 〈R〉 ) 0.5.13 Thus, the increase in the ∆4 value with increasing cS at cS > 30 mM seen in Figure 13b reflects a change in the (14) Ikeda, S.; Tsunoda, S.; Maeda, H. J. Colloid Interface Sci. 1979, 70, 448.


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Figure 14. Dependence of the ratio of Br- concentration bound to the micellar interior to that at cS ) 0 mM ([Br-]bound/[Br-]bound0) on cS. Figure 12. Dielectric spectra at various NaBr concentrations (cS) for aqueous DDAO solutions at 〈R〉 ) 1.0 and cD ) 100 mM. Solid lines in this figure represent the best fit curves for the data calculated by Debye type relaxation functions.

suggests that the number of the ion pair between HO-N+ and Br- formed in micelles is kept at constant and independent of cS. Discussion Dipole Moments. The τ1 mode found around ω ) 1010 rad s-1 in all the systems examined in this study is assigned to the rotational relaxation mode of unprotonated headgroups of DDAO which have OrN coordination chemical bonding with a dipole moment. Because most of the DDAO molecules are not protonated at 〈R〉 ) 0, the value of ∆1cD-1, ca. 12 M-1 (Figure 3b), should correspond to the product between the number density of OrN coordination chemical bonding in the system and the square of the magnitude of its dipole moment (µ). The value of µ should include the dielectric contribution of two methyl groups and a dodecyl group. If the dielectric interaction among the headgroup of DDAO and water molecules is not so strong, the following relationship approximately holds in this system.5,11

∆1cD-1 ) ANAµ2/(2vkBT)

(1)

where A, NA, v, and kBT represent a numerical factor, Avogadro’s number, the permittivity of a vacuum, and the product between Boltzmann’s constant and the absolute temperature, respectively. In the case of homogeneous systems such as an aqueous TMAO system,11 eq 2 was proposed to describe A:

A ) (1 + z cos γµwater µ-1)


micellar shape from a sphere to an elongated spheroidal shape. Br- Binding to Micellar Interior. The ratio of Brconcentration bound to the micellar interior at various cS values relative to that at cS ) 0 mM ([Br-]bound/[Br-]bound0) estimated by using a Br- ion selective electrode is plotted in Figure 14 as a function of cS. The value of [Br-]bound/ [Br-]bound0 is essentially kept at unity at every condition examined. Thus, Br- anions supplied by the addition of NaBr are not bound to the micellar interior anymore. This

(2)

where z, γ, and µwater represent the number of the first neighbor water molecules surrounding a tested solute (TMAO), the average angle between dipole moments of the tested TMAO and surrounding water molecules, and the magnitude of the dipole moment of a water molecule, respectively. By substitution of z ) 35, γ ) 54.7° due to the random orientational condition, and µwater ) 1.85 D into eqs 2 and 1, µ ) 3.9 D was obtained for TMAO.11 Then, A ) 11 is obtained for a homogeneous aqueous TMAO solution. However, eq 2 cannot be directly applied to micellar solutions, because micelles have molecular level order structure and detergents do not dissolve homogeneously. Here, we propose eq 3 to describe A for micellar solutions as a very rough approximation. We assume that detergent headgroups with dipoles such as OrN are arranged twodimensionally on the surface of micelles and the contribu-

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Itatani and Shikata

tion of alkyl tails of detergents to dielectric behavior is negligibly small.

A ) (1 + zd cos γd + z cos γµwater µ-1)

(3)

where zd and γd represent the number of detergent headgroups surrounding a tested detergent headgroup, NrO, and the average angle between dipoles of the tested headgroup and of surrounding headgroups, respectively. Here, we take the value of zd to be the total number of the first and second neighbor detergent headgroups of the tested headgroup; zd ∼ 12. The value of γd might be 54.7° again. The value of z in eq 3 is estimated to be about 10, which is one-third of the value used in eq 2 for homogeneous solutions, because water molecules surrounding the tested detergent headgroup exist only outside the micellar surface. Then, one obtains eq 4′ for micellar solutions.

A ) 8.0 + 11µ-1

(4)

When µ is larger than 10 D as in the case of aqueous CTAB solutions,5 the constant value of A ) 9 is useful for practical estimation of µ. Even if one uses the value of A ) 9 for an aqueous micellar system with µ ) 4 D, the estimated value of µ is 4.4 D, which is only 10% larger than the real value. This means that the estimated values of µ for micellar solutions with µ g 4 by using A ) 9 contain errors of only 10%. Hence, we accept the value of A ) 9 for discussion below as done in the aqueous CTAB system.5 Consequently, the value of µ for the aqueous DDAO system at 〈R〉 ) 0 is estimated to be 1.3 × 10-27 C cm () 3.8 D) by applying eq 1 and A ) 9 to the value of ∆1cD-1 ) 12 M-1 (Figure 3b). The magnitude of a dipole moment of OrN coordination chemical bonding including the contribution of three methyl groups bound to a nitrogen atom was estimated to be µ ) 4.9 D with TMAO solutions in nonpolar solvents.6 The difference between the values of µ ) 3.8 D for DDAO in aqueous micellar solution and 4.9 D for TMAO could be explained in the following two ways. (i) In micelles, dipole-dipole interaction between DDAO molecules is so strong that the total electric displacement is reduced by making pairwise molecular association possessing the antiparallel arrangement of dipole moments. (ii) Some water molecules tightly hydrate to the headgroup of DDAO to reduce the magnitude of µ to 3.8 D. Because TMAO molecules of course do not form micelles, the value of µ ) 3.8 D for DDAO, very close to 3.9 D for TMAO in aqueous solutions, supports the conclusion that the essential reason for the µ ) 3.8 D is tight hydration of some water molecules to the headgroup of DDAO as observed in aqueous TMAO solutions.11 Since the degree of protonation is determined in Figure 6 for solutions with cD ) 100 mM, the concentration (cUP) of unprotonated DDAO can be estimated. Then, the value of ∆1cUP-1 is estimated to be 18-22 M-1 at 〈R〉 g 0.1 from Figures 5b and 6. From the estimated value of ∆1cUP-1, µ can be evaluated to be 4.7-5.2 D at 〈R〉 g 0.1. Furthermore, in the following section we propose a model for the τ3 mode. In the model, we assume that some protonated DDAO molecules form intermolecular association particles with protonated and unprotonated DDAO molecules due to intermolecular forces such as hydrogen bonding, and the dielectric relaxation process of unprotonated DDAO molecules in the association particles appears in the τ3 mode. Thus, the concentration of unprotonated DDAO effective to the τ1 mode should be slightly less than cUP; therefore, the true µ value of DDAO at 〈R〉 g 0.1 is not different from 4.9 D. Consequently, we

conclude that the addition of HBr not only protonates DDAO but also removes water molecules which are hydrated to the headgroup of unprotonated DDAO. A similar conclusion was obtained in dielectric behavior for aqueous TMAO solutions at varying 〈R〉.11 The magnitude of a dipole moment of an ion pair between HO-N+ and Br- is also estimated in a similar way. Because the τ2 mode is assigned to the rotational relaxation motion of the ion pair between HO-N+ and Br- in micelles, the value of ∆2cD-1 ) 130 M-1 at a high 〈R〉 side seen in Figure 5b is adopted as the reduced magnitude of the ion pair. As discussed in the previous section, 35% of DDAO in the system forms the ion pair at high 〈R〉; the reduced magnitude of the ion pair should be converted to be ∆2cIP-1 ) 370 M-1 (cIP represents the concentration of the ion pair). Consequently, the value of a dipole moment for the ion pair is evaluated to be µIP ) 7.1 × 10-27 C cm () 21 D) using eq 1 and A ) 9. From this µIP value, the separation between HO-N+ and Br- in the ion pair is calculated as rIP ) 0.45 nm, if hydration of water molecules to the ion pair is neglected. The rIP seems to be a plausible value for the ion pair in the micelle of DDAO molecules and is slightly larger than the value of the ion pair of CTAB micelles in aqueous solutions.5 Dielectric Relaxation Due to Associated DDAO. The protonated headgroup of DDAO, HO-N+, would have the ability to make hydrogen bonding between other protonated and/or unprotonated headgroups of DDAO molecules as schematically depicted in Figure 15. Recently, this idea was proposed by Maeda et al. to interpret their potentiometric titration experiments on DDAO.12,15 Dielectric study in aqueous TMAO solutions also suggested the presence of hydrogen bonding between two TMAO molecules at 〈R〉 g 0.1.11 Thus, we postulate the presence of the hydrogen bonding between two DDAO molecules at 〈R〉 g 0.1. In this case, associated DDAO particles, dimers or trimers of DDAO molecules, generate in micelles at 〈R〉 g 0.1, which have two or three alkyl chain tails and have rotational rates lower than that of a single DDAO molecule. Hence, we assign the τ3 mode to the rotational motion of the associated DDAO molecules. Supposing a DDAO micelle formed in the system is a rigid sphere with a radius (rm) of ca. 2 nm,13,16 the rotational relaxation time (τrot) of the micelle in the system can be estimated to be 24 ns using the following equation: τrot ) 4πηwrm3/(kBT), where ηw is the viscosity of water. If the rotational relaxation time of the associated DDAO particle formed in micelles is much longer than τrot, the obtained τ3 value corresponds to τrot. The greatest contribution to the strength of the τ3 mode should be the ion pair formed between a protonated DDAO and Br-, because a protonated DDAO cation not forming the ion pair and an unprotonated DDAO in the associated particle have much smaller dipole moments than the ion pair. Therefore, we should discuss the relationship between ∆2 + ∆3 and 〈R〉 rather than that between ∆2 and 〈R〉 in Figure 7. The proportionality between ∆2 + ∆3 and [Br-]bound/[Br-]total looks reasonable also (Figure 7). When one estimates the magnitude of µIP, the value of ∆2 + ∆3 at a high 〈R〉 range should be used instead of ∆2 for precise discussion. However, the contribution of ∆3 is slight. The value of ∆3cD-1 is small at 〈R〉 ) 0 as seen in Figures 3b and 5b. The reason for this small value should be that few DDAO molecules are protonated by water molecules (15) Maeda, H. Colloids Surf., A 1996, 109, 263. (16) Maeda, H.; Muroi, S.; Kakehashi, R. J. Phys. Chem. B 1997, 101, 7378.


Langmuir, Vol. 17, No. 22, 2001 6849

Figure 15. Schematic representation of intermolecular association particles in DDAO micelles due to hydrogen bonding between protonated and unprotonated DDAO molecules.

at 〈R〉 ) 0, and the number of associated DDAO molecules is also small in this condition. Dielectric Relaxation Due to Counterion Clouds. Micelles formed in all samples examined in this study have more or less electric charges on their surface due to the protonation of OrN groups. Counterions such as OHand Br- make counterion clouds around micelles. In the case of solutions with high cS values at 〈R〉 ) 0.5 and 1.0, the shape of micelles changes from spherical to an elongated spheroidal shape. The slowest dielectric relaxation mode, τ4, for these solutions containing elongated spheroidal micelles would reflect complicated molecular dynamics in the micelles. However, in solutions containing spherical micelles the slowest τ4 mode should reflect the relaxation of a counterion distribution in counterion clouds around micelles as observed in aqueous CTAB solution.5 The number of counterions entrapped in counterion clouds around micelles is roughly estimated from the difference between G0 and the value of electric conductance (G0c) estimated from the concentrations of dissociated ions such as Br- and H+ using the limiting molar conductances of the ions (λBr-∞ and λH+∞) given in the literature.17 The concentration ([Br-]) of dissociated Br- was determined by using a Br- ion selective electrode, and [OH-] or [H+] was determined by a pH electrode in this study. The mole fraction of Br- electrically bound into counterion clouds in the total number of Br- (β) was estimated in aqueous DDAO solutions with 〈R〉 from 0.3 to 0.9 at cD ) 100 mM and cS ) 0 mM. The estimated β values are summarized in Table 1. Assuming Nagg ) 8013,14 and the concentration of micelles [M] ) cDNagg-1 ) 1.25 × 10-3 M in the solutions, most of the evaluated number of Br- bound to each counterion cloud (ni) is less than unity (see Table 1). Therefore, many micelles possess no counterion clouds. A number of Br- bound into the counterion cloud as small as that observed in this case was also found in aqueous CTAB solutions.5 A dielectric relaxation time for a system consisting of uniform size spheres possessing counterion clouds was theoretically considered by Schwarz.18 Here, we assume that the relaxation time, τ4, found in aqueous DDAO (17) Robinson, R. A.; Stokes, R. H. Electrolyte Solutions, 2nd ed.; Butterworths: London, 1959. (18) Schwarz, G. J. Phys. Chem. 1962, 66, 2636.

Table 1. Mole Fraction of Br- Electrically Bound to Counterion Clouds in the Total Br- Number, β, the Number of Br- in Each Counterion Cloud, ni, and cCI/[M] for Aqueous DDAO Solutions at cD ) 100 mM and cS ) 0 mM with Various 〈r〉 from 0.3 to 0.9 [H+]/mM [Br-]/mM G0c/mS cm-1 a G0/mS cm-1 βb nic cCI/[M]d

〈R〉 ) 0.3

〈R〉 ) 0.5

〈R〉 ) 0.7

〈R〉 ) 0.9

0.0123 17.3 1.36 1.35-1.39 0-0.018 0-0.42

0.162 24.1 1.94 1.82-2.00 0-0.031 0-1.2 ∼0.11

1.35 36.1 3.29 3.21-3.30 0-0.014 0-0.86 ∼0.29

13.8 56.6 9.25 9.12-9.22 0.004-0.023 0.27-1.3 ∼0.56e

a G c ) [H+]λ +∞ + [Br-]λ -∞, λ +∞ ) 349.8 S cm2 mol-1 (ref 17), 0 H Br H λBr-∞ ) 78.1 S cm2 mol-1 (ref 17). b β ) (G0c - G0)/(λBr-∞ cD〈R〉).c ni ) (G0c - G0)/(λBr-∞ [M]). d See text. e The quality of estimated ∆4 is not high.

solutions containing only spherical micelles corresponds to the time considered by them. According to Schwarz,18 the relaxation time, τ4, is given as

τ4 ) l2/(2DCI)

(5)

where l and DCI are the average distance between the center of a micelle and the location of an electrically bound counterion and the self-diffusion constant of the counterions in water at 25 °C, respectively. In aqueous DDAO solutions with various cD at 〈R〉 ) 0, only spherical micelles are formed with a constant radius, rm, of ca. 2 nm.13,16 From the data of τ4 in Figure 3a, the values of l are estimated as a function of cD using eq 5 supposing DCI () DOH-) ) 5 × 10-5 cm2 s-1 17,19 (Figure 16). When one considers the physical meaning of l, the sum of rm and Debye length (κ-1) for the system examined is one of the plausible candidates for l. Figure 16 contains the value of rm + κ-1 and the average separation between micellar centers (λS) as functions of cD. Because the pH values of the aqueous DDAO solutions at 〈R〉 ) 0 were determined to be about 8.5, the concentration of dissociated (19) Here, we employ Nernst’s equation for the self-diffusion coefficient of an ionic species. The self-diffusion coefficient of ion I is given as DI ) NAkBTλI∞/(|zI|F2), where λI∞, zI, and F represent the limiting molar conductance of ion I, electric charge number of ion I, and Faraday's constant, respectively. λOH-∞ ) 198 S cm2 mol-1 (ref 17).

6850


Figure 16. Relationship between estimated characteristic distances, l, λs, and rm + κ-1, and cD for aqueous DDAO solutions at 〈R〉 ) 0 and cS ) 0 mM.

Figure 17. Relationship between estimated characteristic distances, l and rm + κ-1, and cS for aqueous DDAO solutions at cD ) 100 mM and 〈R〉 ) 0.

OH- was on the order of 10-5 M. As seen in this figure, rm + κ-1 is much longer than λS and is not recognized as l in the condition at 〈R〉 ) 0. The value of λS looks like a much better measure for l in this condition. In such a case, micelles do not behave as individual dielectric spheres bearing counterion clouds. Then, using eq 5 does not make sense. A new model should be necessary for dielectric consideration of aqueous DDAO solutions which do not contain NaBr or HBr. On the other hand, in aqueous DDAO solutions with various cS at cD ) 100 mM and 〈R〉 ) 0, a change in the estimated l value from τ4 in Figure 9a using eq 5 supposing DCI () DBr-) ) 2 × 10-5 cm2 s-1 17,19 is perfectly described by the sum rm + κ-1 in the range of cS higher than 10 mM as seen in Figure 17. Moreover, in aqueous DDAO solutions at 〈R〉 g 0.3 and cS ) 0 mM, the values of l estimated from τ4 in Figure 5a reasonably agree with rm + κ-1. Reasonable agreement between l and rm + κ-1 was also found in aqueous CTAB solutions.5 Thus, in systems containing numbers of ions which make the value of rm + κ-1 close to rm, micelles well behave as individual dielectric spheres bearing counterion clouds. Supposing the number of electrically bound counterions to one counterion cloud is unity, the magnitude of the dipole moment for a micelle bearing a counterion cloud is roughly estimated in the manner of µCI ) e0l, where e0 represents the elementary electric charge.5 By converting eq 5, one can calculate the concentration (cCI) of micelles bearing a counterion cloud as cCI ) 2vkBT ∆4/(ANAµCI2). Then, a fraction of micelles bearing a counterion cloud (cCI/[M] ) ni) in the total concentration of micelles, [M], must be equal to or smaller than unity. In the case of aqueous DDAO solutions with cS ) 30 and 50 mM at cD

Itatani and Shikata

) 100 mM and 〈R〉 ) 0, the values of l ∼ 3 nm and ∆4 ) 0.8 are obtained from Figures 17 and 9b; then, cCI/[M] is estimated to be 0.090 using Nagg ) 8013,14 and A ) 4. The value of µCI (∼ 140 D) is much greater than that of µwater in eq 2 for homogeneous systems. The value of z should be the number of the first neighbor water molecules surrounding a micelle, which can be roughly estimated as (l/rwater)2 ∼ 400, where rwater (∼ 0.15 nm) is the average radius of a water molecule. Thus, the value of A ) 4 is obtained in this rough estimation. In aqueous NaBr-free DDAO solutions at 〈R〉 g 0.3, the value of cCI/[M] can be estimated in the same way from the data of τ4 and ∆4 in Figure 5a,b with A ) 4 and is summarized in Table 1. Although the value of cCI/[M] for the system does not agree with the values of ni, the fact that the value of cCI/[M] is smaller than unity is important considering the quality of experimental results. Consequently, we conclude that the number of electrically bound counterions to one counterion cloud does not exceed unity and the fraction of micelles bearing the counterion cloud is smaller than unity, as observed in aqueous CTAB solutions.5 Concluding Remarks DDAO has an electric dipole moment due to the OrN coordination chemical bond on its headgroup, and the fraction of OrN type headgroups is reduced by adding HBr, while that of HO-N+ type headgroups increases. Dielectric spectra for aqueous DDAO solutions had four types of relaxation modes. The fastest relaxation time (τ1 found around 10-10 s) was almost independent of cD, and the relaxation strength (∆1) was proportional to cD at 〈R〉 ) 0. Moreover, the magnitude of ∆1 decreased with increasing 〈R〉; therefore, it was attributed to the rotational relaxation mode of OrN type headgroups in spherical micelles. The second fastest relaxation time (τ2 ∼ 10-9 s) was essentially independent of cD, and the relaxation strength, ∆2, was proportional to cD. Because both the magnitude of ∆2 and the number of Br- anions entrapped in micelles increased with increasing 〈R〉, the τ2 mode was assigned to the rotational relaxation mode of an ion pair formed between HO-N+ and Br- at 〈R〉 g 0 on the micellar surface. The third relaxation mode (τ3 ∼ 10-8 s) was attributed to the rotational relaxation mode of intermolecular association particles formed between protonated and unprotonated DDAO molecules due to intermolecular forces such as hydrogen bonding. The slowest mode with a relaxation time (τ4 ∼ 10-7 s) was assigned to the relaxation of a counterion distribution in a counterion cloud formed around spherical DDAO micelles. When 〈R〉 g 0.5, dielectric behavior of aqueous DDAO solutions was essentially the same as that of aqueous solutions of ionic detergents such as cetyltrimethylammonium bromide. The addition of NaBr to aqueous DDAO solutions at 〈R〉 g 0.5 made the shape of micelles change into a spheroidal shape. The frequency dependence of dielectric relaxation spectra for aqueous DDAO solutions containing spheroidal micelles is much broader than that for solutions containing only spherical micelles as observed in aqueous cationic detergent solutions. The number of electrically bound counterions to one counterion cloud is unity, and the fraction of micelles bearing the counterion cloud is lower than unity. Acknowledgment. This work was financially supported by a Grant-in-Aid (11440205) from the Ministry of Education, Science, Culture and Sports, Japan. LA010551I

Dielectric Relaxation Behavior of Aqueous ... - ACS Publications

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