Phase and Rheological Behavior of Salt-Free Alkyltrimethylammonium

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Phase and Rheological Behavior of Salt-Free Alkyltrimethylammonium Bromide/ Alkanoyl-N-methylethanolamide/Water Systems Durga P. Acharya,† Koheita Hattori,† Takaya Sakai,‡ and Hironobu Kunieda*,† Graduate School of Environment and Information Sciences, Yokohama National University, 79-7 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan, and Materials Development Research Laboratories, Kao Corporation, 1334 Minato, Wakayama-shi, Wakayama 640-8580, Japan Received May 19, 2003. In Final Form: August 22, 2003 Addition of N-hydroxyethyl-N-methyldodecanamide (NMEA-12) and N-hydroxyethyl-N-methylhexadecanamide (NMEA-16) to dilute solutions of hexadecyltrimethylammonium bromide (CTAB) and dodecyltrimethylammonium bromide (DTAB) in the micellar (Wm) phase results in an increase in viscosity. It is found that the CTAB-NMEA-12 or CTAB-NMEA-16 and DTAB-NMEA-16 surfactant systems show viscoelastic behavior typical of systems containing wormlike micelles. The dynamic viscoelastic behavior of the viscoelastic micellar phase follows the Maxwell model at low shear frequency at the composition of maximum viscosity. The mixing fraction of NMEA in total amphiphile for the maximum viscosity increases with decreasing the total amphiphile concentration. Most probably, in a dilute region, as, the effective cross-sectional area per surfactant at the hydrophobic interface in the micelle, increases and more NMEA is needed to decrease the average as. Assuming that one-dimensional growth of micelles takes place upon addition of NMEA and as for the surfactant and NMEA are constant, the rod-micellar length was calculated as a function of the mixing fraction of NMEA in total amphiphile. As a result, the rodlike micellar length is not largely increased up to certain amount of added NMEA, above which the enormous increase in micellar length takes place. The micellar growth can be simply explained by decreasing the effective cross-sectional area per amphiphile upon addition of NMEA.

Introduction Long-chain cationic surfactants self-assemble into very long, flexible threadlike aggregates. Hexadecyltrimethylammonium bromide (CTAB) in the semidilute1-6 and in the concentrated region7-10 and other long-chain cationic surfactants11-14 have been reported to form wormlike micelles upon addition of counterions such as salicylate or bromide ions. In some short-chain gemini surfactant systems, such a wormlike micellar system is formed even without addition of salt.15 However, most studies report the formation of viscoelastic wormlike micelles in cationic systems in the presence of strongly binding counterions. * To whom correspondence should be addressed. Phone and Fax: +81-45-339 4190. E-mail: [email protected]. † Yokohama National University. ‡ Kao Corp. (1) Kim, W.-J.; Yang, S.-M.; Kim, M. J. Colloid Interface Sci. 1997, 194, 108-119. (2) Kim, W.-J.; Yang, S.-M. J. Colloid Interface Sci. 2000, 232, 225234. (3) Imai, S.; Shikata, T. J. Colloid Interface Sci. 2001, 244, 399-404. (4) Kern, F.; Lemarechal, P.; Candau, S. J.; Cates, M. E. Langmuir 1992, 8, 437-440. (5) Khatory, A.; Lequeux, F.; Kern, F.; Candau, S. J. Langmuir 1993, 9, 1456-1464. (6) Vethamuthu, M. S.; Almgren, M.; Brown, W.; Mukhtar, E. J. Colloid Interface Sci. 1995, 174, 461-479. (7) Shikata, T.; Kotaka, T. J. Non-Cryst. Solids 1991, 131, 831. (8) Hartmann, V.; Cressely, R. Colloids Surf., A 1997, 121, 151. (9) Hartmann, V.; Cressely, R. Colloid Polym. Sci. A 1998, 276, 169. (10) Hartmann, V.; Cressely, R. Europhys. Lett. 1997, 40, 691. (11) Raghavan, S. R.; Kaler, E. W. Langmuir 2001, 17, 300-306. (12) Soltero, J. F. A.; Puig, J. E.; Manero, O. Langmuir 1996, 12, 2654-2662. (13) Montalvo, G.; Rodenas, E.; Valiente, M. J. Colloid Interface Sci. 2000, 227, 171-175. (14) Ponton, A.; Schott, C.; Quemada, D. Colloids Surf., A 1998, 145, 37-45. (15) Kern, F.; Lequeux, F.; Zana, R.; Candau, S. J. Langmuir 1994, 10, 1714-1723.

Although there are some reports of significant micellar growth and increase in viscosity induced by the addition of nonionic additives such as medium- and long-chain alcohols and amines in dilute solutions of CTAB1 and sodium dodecyl sulfate (SDS),16 formation of a highly viscoelastic micellar system has not been reported in these systems. Formation of a viscoelastic micellar system is a consequence of unidimensional micellar growth. Above some critical concentration, called the overlapping concentration, wormlike micelles entangle with each other to form a transient network and exhibit viscoelastic properties,17 analogous to those observed in flexible polymer solutions, with an important difference from the polymeric network that the micelles can break and recombine on a time scale characteristic of the system. Alkanolamides are well-known as foam boosters in surfactant aqueous solution,18,19 as a thickening agent in shampoos, and also as antistatic and anticorrosion agents in detergents.19 In various areas of detergency, in particular cosmetics, prediction and control of the microstructure, flow behavior, and viscoelastic properties of fluids are important. Therefore, an understanding of the phase and rheological behavior of alkanolamides in surfactant systems is very helpful in the formulation of various industrial and consumer products. However, there (16) Kabir-ud-Din; Kumar, S.; Aswal, V. K.; Goyal, P. S. J. Chem. Soc., Faraday Trans. 1996, 92, 2413-2415. (17) Lin, Z.; Cai, J. J.; Scriven, L. E.; Davis, H. T. J. Phys. Chem. 1994, 98, 5984-5993. (18) Lai, K. Y.; Dixit, N. In Foams: Theory, Measurements and Applications; Prud’homme, R. K., Khan, S. A., Eds.; Marcel Dekker: New York, 1996. (19) Cox, M. F. In Handbook of Applied Surface and Colloid Chemistry; Holmberg, K., Ed.; John Wiley: New York, 2002; Vol. 1.

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Chart 1. Structure of NMEA-n

are very few studies concerning the phase and rheological properties of water/surfactant/alkanolamide systems20,21 Recently, we observed that addition of a small amount of a new foam booster, alkanoyl-N-methylethanolamide (NMEA), to a dilute SDS solution results in an enormous increase in the zero-shear viscosity (of order 5) and forms a viscoelastic micellar system.20 Herb et al. also reported the formation of a viscous micellar phase in the SDS/ commercial dodecanoyl diethanolamide (LDEA)/water system.21 If this increase in viscosity is not attributed to a specific anionic headgroup of the surfactant and hydrophilic group of NMEA, a similar phenomenon could happen in NMEA-cationic surfactant systems. Different from the viscoelastic system including salt, the relation between the packing of amphiphiles in a self-organized structure and its increase in viscosity can be easily figured out in surfactant-cosurfactant systems. In this context, we studied the effect of NMEA on the rheological properties of cationic surfactant solutions. We also studied the phase behavior and rheological properties of different combinations of surfactants/NMEA/water systems by taking surfactants with similar headgroups but different hydrophilic chain lengths within each type of surfactant. Experimental Section Materials. CTAB (purity > 98%) and dodecyltrimethylammonium bromide (DTAB, purity > 99%) were purchased from Tokyo Kasei Kogyo. The alkanoyl-N-methylethanolamides (molecular structure as shown in Chart 1), viz., N-hydroxyethylN-methyldodecanamide (designated by NMEA-12, purity of 99.4%) and N-hydroxyethyl-N-methylhexadecanamide (designated by NMEA-16, purity of 98.0%), were received from Kao Co., Japan. All the chemicals were used as received. Millipore double-distilled water was used. Phase Diagram. For the study of phase behavior, sealed ampules containing the required amounts of reagents were homogenized and left in a water bath at 25 °C for a few days (for the Wm phase) to several weeks (for the liquid crystal phase) for equilibration. Phases were identified by visual observation and/ or small-angle X-ray scattering (SAXS) performed on a smallangle scattering goniometer with a 15 kW Rigaku rotating anode generator (RINT 2500). The samples were covered with plastic films (Mylar seal method) for the measurement. Rheological Measurements. Samples for rheological measurements were prepared by adding the required amount of NMEA-12 or NMEA-16 to a measured volume of CTAB or DTAB solution of the appropriate concentration. The samples were homogenized and left in a water bath at 25 °C for at least 24 h to ensure equilibration before performing measurements. Rheological measurements were performed in an ARES7 rheometer (Rheometric Scientific) at 25 °C using couette (cup diameter, 34 mm; bob diameter, 32 mm; bob length, 33.3 mm) and cone-plate (diameters, 50 and 25 mm each; cone angle, 0.04 rad) geometry, depending on the viscosity of the samples. Similar rheological results were found for a sample regardless of the type of the geometry chosen in the measurement. Dynamic frequency sweep measurements were performed in the linear viscoelastic regime of the samples, as determined previously by dynamic strain sweep measurements. (20) Rodriguez, C.; Acharya, D. P.; Hattori, K.; Sakai, T.; Kunieda, H. Langmuir 2003, 19, 8692-8696. (21) Herb, C. A.; Chen, L. B.; Sun, W. M. In Structure and Flow in Surfactant Solutions; Herb, C. A., Prud’homme R. K., Eds.; ACS Symposium Series 578; American Chemical Society: Washington, DC, 1994.

Figure 1. Phase diagrams of DTAB/NMEA-12/water and DTAB/NMEA-16/water systems at 25 °C. Wm, H1, and LR are micellar, hexagonal, and lamellar phases, respectively. W + S denotes the solid surfactant in excess water.

Results Phase Behavior. Partial phase diagrams of DTAB/ NMEA-12/water and DTAB/NMEA-16/water in a relatively dilute region at 25 °C are shown in Figure 1. NMEA12 forms a lamellar liquid crystal (LR) coexisting with excess water, whereas NMEA-16 is in a solid state in the water-rich region of the NMEA-water binary system.22 In the presence of a small amount of surfactant, both NMEAs form lamellar phases, which contain a large amount of water. A hexagonal liquid crystal (H1) in the water-DTAB system is extended to a relatively dilute region. The aqueous DTAB micellar solution is very fluid, but with successive addition of NMEA to a dilute micellar (Wm) solution, at first an increase in viscosity is observed, which is more pronounced with NMEA-16 than with NMEA-12. These viscous samples were optically isotropic and flowed slowly under gravity. With further addition of NMEA, the viscosity decreases and ultimately the Wm to lamellar liquid crystal (LR) phase transformation occurs. In the figures, the H1 regions include a single-phase and multiphase regions containing H1 phase. The approximate phase boundary is shown by the dotted line in Figure 1. The highly viscous region inside the Wm phase is the region extended from the protruded part of the H1 phase. The maximum-viscosity region inside the single Wm phase is indicated by the broken line in Figure 1. Since the broken line is extended from the top of the H1 phase, rodlike micelles are formed along the line. The phase diagrams of CTAB/NMEA-12/water and CTAB/NMEA-16/water are also shown in Figure 2. As well as the DTAB systems, the H1 phase region extends toward a lower CTAB concentration in the system, much lower than the DTAB systems. Inside the single-micellar solution phase (Wm), the viscosity is very high and the samples did not flow under gravity in a region approximately shown as a shaded area in Figure 2. In both systems, the high-viscosity micellar region is nearly parallel to the CTAB-water axis. This tendency is similar to the locus of maximum viscosity in SDS/dodecyldiethanolamide/water systems.21 Since the H1 phase consists of very long rod-micelles stacked in a hexagonal array, the micelles in the shaded area are also considered to be longrod wormlike ones. In all DTAB and CTAB systems in the low surfactant concentration region, vesicles are separated from the phase boundary of the single-Wm region. This (22) Jin-Feng; Rodriguez, C.; Izawa, T.; Kunieda, H.; Sakai, T. J. Dispersion Sci. Technol., submitted for publication.

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Figure 4. Variation of zero-shear viscosity (η0) as a function of the mixing fraction of NMEA (X) in 0.15 M CTAB or DTABNMEA systems: (A) CTAB-NMEA-12, (B) CTAB-NMEA-16, (C) DTAB-NMEA-16, and (D) DTAB -NMEA-12 systems at 25 °C. Figure 2. Phase diagrams of CTAB/NMEA-12/water and CTAB/NMEA-16/water systems at 25 °C. Phase notations are same as in Figure 1. LC stands for liquid crystal. The shaded region corresponds to the region of the highly viscoelastic micellar phase.

Figure 5. Variation of zero-shear viscosity (η0) as a function of the mixing fraction of NMEA-12 (X) at different CTAB concentrations: (A) 0.20 M, (B) 0.15 M, (C) 0.10 M, and (D) 0.05 M.

Figure 3. Steady shear rate viscosity measurements of 0.15 M DTAB-NMEA-16 (a) and 0.15 M DTAB-NMEA-12 (b) systems at 25 °C. The mole fraction of NMEA in the total amphiphile, X, for each of these systems is shown along with the data points.

means that the surfactant layer curvature becomes zero at a high content of NMEA. It is interesting that a lowviscosity single phase exists beyond the H1 phase and the highly viscous Wm phase (shaded area) at a high mixing fraction of NMEA-12, whereas phase separation takes place without lowering viscosity in the NMEA-16 system. Rheological Properties. Figure 3 shows the variation of steady-shear viscosity (η) measured at equilibrium conditions as a function of shear rate for the DTABNMEA-12 or DTAB-NMEA-16 systems with a fixed concentration of 0.15 M (∼4.6 wt %) DTAB and various mixing fractions of NMEAs, expressed in their mole fraction (X) in total amphiphile. The composition lines are also indicated by arrows in Figures 1 and 2. At all mixing fractions of NMEA-12 (up to X ) 0.68) within the Wm phase, the viscosity is essentially independent of the shear rate (Newtonian fluid behavior) in the low shear rate region (Figure 3b), suggesting that NMEA-12 does not induce pronounced micellar growth in the DTAB system. On the other hand, with a small increase in the concentration of NMEA-16 (from X ) 0.51 to 0.56), an abrupt change in rheological properties is observed, with shear thinning at a shear rate above 1 s-1 (Figure 3a), which shows the presence of a giant micellar structure undergoing structural change at high shear.23 In 0.15 M (23) Rehage, H.; Hoffmann, H. J. Phys. Chem. 1988, 92, 4712-4719.

(∼5.5 wt %) CTAB-NMEA systems, non-Newtonian behavior is noticeable even at a lower concentration of NMEA (X ∼ 0.3), suggesting a pronounced micellar growth at a small mixing fraction of NMEA (data not shown). Figure 4 shows the variation of zero-shear viscosity (η0) with the additive (NMEA) concentrations in the 0.15 M DTAB (∼4.6 wt %) and 0.15 M CTAB (∼5.5 wt %) systems, and the mole fraction of NMEA in total amphiphile is plotted horizontally. The compositional lines are also indicated by arrows in Figures 1 and 2. In the systems showing shear-independent viscosity over a wide range of shear rates, η0 values have been determined by extrapolating the steady-shear viscosity curves to zero shear rate.24 For viscoelastic systems, η0 values have been calculated using eq 3a (given below). Figure 4 shows that with increasing mixing fraction of NMEA (X) in DTAB or CTAB systems, η0 increases gradually at first and then rapidly, which is associated with the unidimensional growth of micelles, and above a critical concentration called the overlapping concentration, the elongated aggregates start to entangle with each other and increase the viscosity of the system. However, as can be seen from Figure 4, the extent of variation of η0, or micellar growth, with X in these different systems depends on the lipophilic chain length of the cationic surfactant as well as NMEA. In the DTAB-NMEA-12 and CTABNMEA-12 systems, a decrease in η0 is observed after the maxima, which clearly shows the structural changes in the aggregate shape. The effect of CTAB concentration on the η0 of CTABNMEA-12 systems is shown in Figure 5. In the systems of each of the series, the concentration of CTAB in the solution is fixed. Figure 5 shows that with increasing concentration of CTAB in the solution, the concentration (24) Manero, O.; Bautista, F.; Soltero, J. A. F.; Puig, J. E. J. NonNewtonian Fluid Mech. 2002, 106, 1-15.

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Figure 6. Variation of the storage modulus G′ (circles), the loss modulus G′′ (squares), and the complex viscosity |η*| (triangles) as a function of oscillatory shear frequency (ω) at 25 °C for 0.15 M CTAB-NMEA-12 systems at different mixing fractions of NMEA-12 (X).

of NMEA-12 required to induce a rapid micellar growth (or η0) decreases. As described in the phase behavior section, in all the systems, more or less, the composition of the maximum viscosity is almost parallel to the watersurfactant axis as shown in Figures 1 and 2. Hence, in all the systems, with decreasing surfactant concentration, more NMEA is needed to obtain the maximum viscosity. In CTAB-NMEA-12 and also in DTAB-NMEA-16 systems, viscoelastic micellar solutions are formed at compositions around the maximum-viscosity region. Under oscillatory shear, the viscoelastic micellar solutions usually behave as a Maxwell fluid with a single relaxation time,23 and the elastic or storage modulus G′(ω) and the viscous or loss modulus G′′(ω) obey the following relations as a function of the oscillatory shear frequency (ω):

G′(ω) )

G′′(ω) )

(ωτR)2

G0

(1)

G0 1 + (ωτR)2

(2)

1 + (ωτR)2 ωτR

The plateau modulus, G0, is given by G′(ω) at high ω. The relaxation time, τR, can be estimated as (ωR)-1 where ωR is the frequency at which two moduli are equal. The zero-shear viscosity (η0) is given by the relation

η0 ) G0τR

(3a)

The complex viscosity, η*, is related to the storage and loss moduli by the relation

|η*| )

(G′2 + G′′2)1/2 ω

(3b)

Figure 6 shows the results of oscillatory shear measurements for 0.15 M CTAB-NMEA-12 systems at different concentrations of NMEA-12. At X ) 0.40 (Figure 6a), the loss modulus (G′′(ω)) is greater than the storage modulus (G′(ω)) at low oscillatory shear frequency (ω), and the system still shows a liquidlike behavior in this region. The G′(ω)-G′′(ω) crossover takes place at crossover frequency ωR ) 1 rad s-1, and above this frequency G′(ω) > G′′(ω), and therefore the system is viscoelastic. However, in the high-frequency region, G′(ω) does not attain a welldefined plateau value (G0), and there is no minimum of G′′(ω), indicating various processes of stress relaxation. Increasing the NMEA-12 concentration to X ) 0.44 results in a shifting of ωR to a lower value (Figure 6b), which corresponds to a longer relaxation time (τR). Moreover, an overall increase in the magnitude of G′(ω) in the high-frequency region with a well-defined plateau is observed, and the rheological pattern comes closer to the Maxwell model. These developments in the rheological

Figure 7. Cole-Cole plots of 0.15 M CTAB-NMEA-12 systems at various mixing fractions of NMEA-12 (X).

properties can be associated with the increase in the micellar length and degree of entanglements leading to the promotion of the network density of wormlike micelles. With a further increase in NMEA concentration to X ) 0.49 (Figure 6c), the relaxation time again becomes shorter, with a wide spectrum of relaxation processes in the high-frequency region as suggested by a nearly constant G′′(ω) at ω > ωR and an ill-defined plateau value. This shows a weakening of the transient network of the micellar system due to which stress relaxation may occur by different processes other than those considered by the Maxwell and Rouse model. Figure 7 shows normalized Cole-Cole plots, that is, the plots of G′′(ω)/G′′max against G′(ω)/G′′max for different 0.15 M CTAB-NMEA-12 systems, where G′′max corresponds to the maximum of G(ω)′′ at ω ∼ ωR. A Maxwell material is characterized by a semicircle centered at G′(ω)/ G′′max ) 1 in the Cole-Cole plot. It can be seen from the Cole-Cole plot that a large deviation from the Maxwellian behavior is observed at low and high concentrations of NMEA-12. The values of G0 and τR may be calculated for the 0.15 M CTAB-NMEA-12 systems as follows. Since ωR corresponds roughly to the maximum of G(ω)′′, that is, G(ω)′′max), Maxwell equations allow us to make the following estimation at ωR:

G0 ) 2G′(ω) = 2G(ω)′′max For the systems showing deviation from Maxwell behavior, the G0 estimated from G′′max is considered as the lower limit for the plateau modulus. The calculated values of G0 and τR are plotted as a function of NMEA-12 concentration and shown in Figure 8. Since G0 is usually proportional to the number density of the micellar aggregates and therefore reflects the mesh size of the network, the increase in the plateau modulus G0 with NMEA concentration corresponds to the increase in the degree of entanglements. With a successive increase in NMEA concentration, a decrease in G0 and a sharp decrease in the relaxation time (τR) and consequently the zero-shear viscosity (η0 ) G0τR) are observed in the high NMEA-12 concentration region, as shown by Figure 8. These changes in τR and G0, and also the G′′(ω) in the high-frequency region (shown in Figure 6c), indicate a structural change in the network that allows stress relaxation to occur by a faster process other than the reptation of the micelles. One of the possibilities is that after the saturation of micellar growth, further addition of cosurfactant (NMEA) to the system results in the connection of the wormlike micelles with each other, forming a joint that can slip along its length, thereby allowing a faster and easier way of stress relaxation.25,26,27 (25) Khatory, A.; Kern, F.; Lequeux, F.; Appell, J.; Porte, G.; Morie, N.; Ott A.; Urbach, W. Langmuir 1993, 9, 933-939.

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Figure 9. Variation of G′, the loss modulus G′′, and |η*| as a function of shear frequency (ω) at 25 °C for the 0.15 M DTABNMEA-16 system. Notations are the same as in Figure 6. The solid lines are the corresponding Maxwell fitting.

Figure 8. Variation of the plateau modulus, G0 (circles), and relaxation time, τR (squares), with the mixing fraction of NMEA12 (X) in 0.15 M CTAB-NMEA-12 systems (a) and CTAB concentrations along the locus of maximum viscosity (b).

In a number of surfactant systems,28-29,30,31 such micellar connections or branching points have been detected by cryogenic transmission electron microscopy (cryo-TEM), especially in the region where the viscosity decreases after a maximum as a function of increasing concentration of surfactant or counterion. With the successive addition of cosurfactant (NMEA), viscosity continuously decreases and ultimately the LR phase separates out, as shown by the phase diagram (Figure 2). Here, it is not understood clearly how the interconnected rodlike aggregates transform to a lamellar structure with increasing amount of cosurfactant. Probably, with an increase in cosurfactant concentrations the connecting points gradually grow to form a disklike aggregate. In 0.10 and 0.20 M CTAB-NMEA-12 systems also, the evolution of viscoelastic behavior with increasing the mixing fraction, X, follows a trend that is more or less similar to that shown by 0.15 M CTAB systems. G0 and τR values of samples with maximum viscosity at different CTAB concentrations (0.10, 0.15, and 0.20 M) in CTABNMEA-12 systems are plotted as a function of CTAB concentration and shown in Figure 8b. This plot gives information on the structural change in the surfactant system along the locus of maximum viscosity, or the most favorable composition of micellar growth, with increasing CTAB concentration. Increases in G0 and decreases in τR with increasing CTAB concentration show that the stress relaxation becomes faster with decreasing mesh size of the network, which may be due to an increasing number of micellar connections or branching with increasing CTAB. Figure 9 shows the result of oscillatory shear measurements for the 0.15 M DTAB-NMEA-16 system at a composition corresponding to maximum η0. The data points in the low ω region can be fitted to the Maxwell model (solid line in the figure). The G0 and also τR for this system are smaller than those observed in the CTABNMEA-12 system in the region of maximum η0, which corresponds to a micellar network of bigger mesh size or (26) Magid, L. J. J. Phys. Chem. B 1998, 102, 4064-4074. (27) Candau, S. J.; Oda, R. Colloids Surf., A 2001, 183-185, 5-14. (28) Lin, Z. Langmuir 1996, 12, 1729-1737. (29) Danino, D.; Talmon, Y.; Levy, H.; Beinert, G.; Zana, R. Science 1995, 269, 1420-1421. (30) In, M.; Aguerre-Chariol, O.; Zana, R. J. Phys. Chem. B 1999, 103, 7747-7750. (31) Zana, R. Adv. Colloid Interface Sci. 2002, 97, 205-253.

Figure 10. (a) Schematic model of a rodlike micelle. (b) Variation of the length of the cylindrical part of the micelle, L, with the mole fraction of NMEA in the total amphiphile, X, for the CTAB-NMEA-16 system (I), the CTAB-NMEA-12 system (II), the DTAB-NMEA-16 system (III), and the DTAB-NMEA12 system (IV).

a smaller number density of the aggregates in the DTAB system. Considering the similar concentration of cationic surfactant in both systems, this difference in the rheological properties is possibly due to a shorter chain length of wormlike micelles in the DTAB-NMEA-16 system than in the CTAB-NMEA-12 system. Discussion Micellar Growth. When the total surfactant becomes less hydrophilic by mixing with cosurfactant, a spherical micelle grows up. There are two types of micellar growth: one-dimensional growth causes the formation of rodlike micelles, whereas a disklike micelle is formed due to twodimensional growth. If the structure of a rodlike micelle can be ideally expressed as in Figure 10a, the total volume (V h ) and surface (A) of the mixed micelle are written as in the following equations:

4 V h ) πlh3 + πlh2L ) Nvj 3

(4)

js A ) 4πlh2 + 2πlhL ) Na

(5)

where L is the cylindrical length (excluding the hemispherical endcaps) of a rodlike micelle composed of N amphiphilic monomers having average hydrophobic chain length hl, average interfacial cross-sectional area a j s, and average lipophilic volume vj . Since hl is close to the hydrocarbon chain length in its extended form for spherical and rodlike micelles in the very dilute region, the following approximation may be applied:

hl ) lcatXcat + lNMEAXNMEA

(6)

where l is the extended chain length of an amphiphile and X is its mole fraction in the mixed system. Similarly, at

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Table 1. Values of the Length of the Lipophilic Chain (l), the Cross-Sectional Area of the Headgroup (as), and the Volume of the Lipophilic Chain (v) of Each of the Amphiphiles Used to Calculate the Micellar Length, L l/nm as/nm2 v/nm3

CTAB

DTAB

NMEA-12

NMEA-16

2.18 0.62 0.46

1.68 0.62 0.35

1.54 0.30 0.32

2.05 0.30 0.43

a very low concentration of surfactant, the screening of electrostatic repulsion between positive headgroups by NMEA can be neglected and the cross-sectional area of the cationic surfactant may be assumed to be constant. Thus, the a j s and vj in the mixed surfactant aggregate may be obtained from the following approximations:

a j s ) as catXcat + as NMEAXNMEA

(7)

vj ) vcatXcat + vNMEAXNMEA

(8)

Note that eq 8 is a good approximation, but a j s is sometimes negatively deviated from the ideal case in eq 7. The l and v of each of the amphiphiles may be calculated from Tanford equations:32

l ≈ (0.154 + 0.1265n) nm and

v ≈ (27.4 + 26.9n) × 10-3 nm3 where n is the number of carbons in the hydrocarbon chain of the amphiphile. The as for a cationic surfactant in its pure aggregate may be estimated, assuming a spherical shape of aggregate consisting of N monomers (using the literature values of N ) 100 for CTAB and N ) 60 for DTAB33). The as for NMEA is assumed to be 0.30 nm2 as suggested by the experimental result.34 The values of l, as, and v for each of the amphiphiles (shown in Table 1) may be substituted in eqs 6-8 to obtain the variation of hl, a j s, and vj at different values of XNMEA in the mixed system. From eqs 4 and 5, we obtain

hl L)

(

)

js 4a hl - 4 3 vj a js 2 - hl vj

(9)

Then, the change in L as a function of XNMEA is calculated, and the result is shown in Figure 10b. It can be seen that this simple calculation predicts a small unidimensional micellar growth initially with increasing concentration of NMEA, followed by a rapid growth at high NMEA content. Since the zero-shear viscosity of a wormlike micellar solution increases with the micellar length,12 this simple theoretical model describes qualitatively the increase in zero-shear viscosity with X, as shown in Figure 4. Here, the value of L reflects the favorability of the formation of a rodlike aggregate instead of its actual length. Once the packing constraint favors the formation of a cylindrical aggregate, the equilibrium length of the cylinder is determined by the (32) Israelahvili, J. N. In Intermolecular and Surface Forces, 2nd ed.; Academic Press: San Diego, 1992; Chapter 17. (33) Stam, J. V.; Depaemelaere, S.; De Schryver, F. C. J. Chem. Educ. 1998, 75, 93-98. (34) Kunieda, H. Unpublished data.

stability of the endcaps where the amphiphiles are forced to pack into hemispherical caps with a headgroup area (as ec) determined by vj /as echl ) 1/3.32 Since vj /a j shl > 1/3 for rodlike aggregates, we get as ec > a j s, which is energetically unfavorable. The unfavorable end-energy of cylindrical micelles may be eliminated if the two ends join, thereby inducing unidimensional growth. Since we have not considered the contribution of the free energy of the endcaps to the length of the micellar aggregate, the estimated value of L is likely to be lower than the equilibrium length of a wormlike micelle in the real system. We used as values for the surfactant in a very dilute region, and the data in Figure 10 can be applied only in a dilute region. With increasing surfactant concentration, as decreases even in a water-surfactant system. In fact, as is small and around 0.4 nm2 in the H1 phase region. Hence, with increasing surfactant concentration and decreasing as, the mixing fraction of NMEA for the maximum viscosity decreases as is shown in Figures 1, 2, and 5. However, the mixing fraction of NMEA for a rapid increase in zero-shear viscosity depends on the cationic surfactant CTAB or DTAB, as is shown in Figure 4. Our model predicts a much smaller effect than is observed. This limitation of the model is probably associated with the difference in the as of CTAB and DTAB amphiphiles in the mixed surfactant system at a high concentration. The difference in the phase benavior of CTAB and DTAB systems (Figures 1 and 2), especially the ability of CTAB to form the H1 phase at a low concentration, indicates that the as values of these amphiphiles may vary to different extents with increasing concentration. Despite these limitations, this simple model predicts unidimensional micellar growth in dilute systems of cationic surfactant and NMEA. Conclusion Addition of NMEA to dilute solutions of CTAB and DTAB in the micellar (Wm) phase results in an increase in viscosity. CTAB-NMEA-12 or CTAB-NMEA-16 and DTAB-NMEA-16 surfactant systems show viscoelastic behavior typical of systems containing wormlike micelles within a narrow range of NMEA concentration. The dynamic viscoelastic behavior of the micellar phase formed at the composition of maximum viscosity follows the Maxwell model at low shear frequency. The mixing fraction of NMEA in total amphiphile for the maximum viscosity decreases on increasing the total amphiphile concentration. Most probably, with increasing surfactant concentration, as, the effective cross-sectional area per surfactant at the hydrophobic interface in the micelle decreases and less NMEA is needed to decrease the average as and induce unidimensional micellar growth. The micellar growth can be simply explained by decreasing the effective crosssectional area per amphiphile upon addition of NMEA. Assuming constant as for the surfactant and NMEA in the very dilute region, the rod-micellar length was calculated as a function of the mixing fraction of NMEA in total amphiphile. It is found that the rodlike micellar length increases gradually up to a certain concentration of NMEA, above which an enormous increase in micellar length takes place. This result is consistent with the variation of rheological properties with NMEA concentration. Acknowledgment. D.P.A. thanks Kathmandu University, Nepal, for providing a study leave. LA0348618