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Colloids and Surfaces A: Physicochem. Eng. Aspects 305 (2007) 83–88
Rheological behavior of gemini-type surfactant/alkanolamide/water systems Suraj Chandra Sharma, Rekha Goswami Shrestha, Dharmesh Varade, Kenji Aramaki ∗ Graduate School of Environment and Information Sciences, Yokohama National University, 79-7 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan Received 10 March 2007; received in revised form 18 April 2007; accepted 18 April 2007 Available online 24 April 2007
Abstract The formation of the viscoelastic wormlike micelles in aqueous solution of mixed surfactant system of anionic gemini-type surfactant without a spacer group, disodium 2,3-didodecyl-1,2,3,4-butanetetracarboxylate (GS), and dodecanoyl-N-methyl ethanolamide (NMEA-12) has been studied at 25 ◦ C. With addition of NMEA-12 to the GS–water binary system, a micellar (Wm )–lamellar (L␣ ) phase transformation takes place at low GS concentration. Within the Wm phase region of GS–NMEA-12–water system, there exists a high viscosity region consisting of a viscoelastic micellar solution of entangled wormlike micelles. On increasing the concentration of GS, micellar growth begins at a slightly lower mixing fraction of NMEA-12. The oscillatory-shear rheological behavior of the viscoelastic solutions can be described by Maxwell model at low -shear frequency region. The increase in viscosity can be simply explained by reducing the effective cross-sectional area per amphiphile upon addition of NMEA-12. © 2007 Elsevier B.V. All rights reserved. Keywords: Gemini surfactant; Alkanolamide; Phase behavior; Wormlike micelles; Rheological behavior
1. Introduction Surfactant molecules in aqueous solution self-assemble to form a variety of microstructures such as spherical micelles, wormlike micelles, vesicles and liquid crystals [1–4]. These different aggregation structures have characteristic rheological properties. Transition from spherical to wormlike micelles corresponds to a drastic increase of elasticity and viscosity of the fluid [5]. The viscoelastic wormlike micelles have attracted much interest in fundamental research and practical applications [5–7]. Formation of viscoelastic wormlike micelles 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 [8], analogous to those observed in flexible polymer solutions, with an important difference from the polymeric network that the micelles can break
∗
Corresponding author. Tel.: +81 45 339 4300; fax: +81 45 339 4300. E-mail address: [email protected] (K. Aramaki).
0927-7757/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.colsurfa.2007.04.044
and recombine on a time scale characteristic of the system [9]. It is well known that cationic surfactants can self-assemble in aqueous solution into long flexible cylindrical micelles (wormlike micelles) upon the addition of salts [5,10–12]. The salt serves to reduce the electrostatic interactions between the cationic headgroups, thus reducing the effective area per head group and thereby promoting the growth of cylindrical aggregates at the expense of spherical ones. There are some recent reports on non-ionic mixed surfactant systems [13–17]. However, not much is known about the formation and rheological behavior of the wormlike micelles in anionic systems except sodium dodecyl sulfate (SDS) [18–21]. Gemini surfactants have a very high potential for practical applications because of their excellent ability to reduce surface tension of water and low Krafft temperatures. Compared to their monomeric analogs, gemini surfactants have much lower critical micelle concentration. Due to their high molecular weight, skin penetration of gemini surfactant is expected to be low, which is one of the desirable properties of a surfactant to be used in body care products such as soaps, shampoos and cosmetics. However, the main factor that has prevented the use of gemini surfac-
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tants in practical applications is their higher cost. Most of the gemini surfactants studied so far have a spacer chain between two hydrophilic groups in the molecule. It is known that the spacer chain largely influences the physicochemical properties of the surfactants [22]. It is known that a cationic gemini surfactant with a short chain shows viscoelastic properties in solution [23,24]. Recently the interfacial properties of aqueous solution of a novel anionic gemini-type surfactant with no spacer group, disodium 2,3-didodecyl-1,2,3,4-butanetetracarboxylate (GS) was studied [25] and its rheological behavior with a short poly(oxyethylene) chain non-ionic surfactant was investigated [26]. In order to enrich the knowledge about the microstructure flow behavior and ability of this anionic gemini surfactant to form wormlike micelles or regarding the rheological properties of these micelles in salt free condition, we want to extend the further study with alkanolamides, well-known as foam boosters in surfactant aqueous solution [27–30] as a thickening agent in shampoos, and also as antistatic and anticorrosion agents in detergents [28]. In this context, we studied the rheological behavior of the viscoelastic wormlike micellar solutions in the aqueous system with mixed anionic gemini surfactant (GS) and dodecanoyl-Nmethylethanolamide (NMEA-12). 2. Experimental 2.1. Materials Gemini surfactant (GS) was kindly supplied from Chukyo Yushi Co., Japan. The synthesis of GS has been described elsewhere [26]. The dodecanoyl-N-methylethanolamide (designated by NMEA-12, purity 99.4%) was received as a gift from Kao Corporation, Japan. All the chemicals were used as received. Deionized (Millipore filtered) water was used to prepare the samples. Schematic molecular structures of GS and NMEA-12 are shown in Scheme 1.
2.3. Rheological measurements Samples for rheological measurements were homogenized and kept in water bath at specified temperature for at least 24 h to ensure equilibration before performing measurements. The rheological measurements were performed in a stress controlled rheometer, AR-G2 (TA Instrument) using cone-plate geometries (diameters 60 mm for low-viscosity sample and 40 mm for highviscosity sample, each with a cone angle of 1◦ ) with the plate temperature controlled by peltier unit. A sample cover provided with the instrument was used to minimize the change in sample composition by evaporation during the measurement. Frequency sweep measurements were performed in the linear viscoelastic regime of the samples, as determined previously by dynamic strain sweep measurements. 3. Results and discussion 3.1. Phase behavior The partial phase diagram of the GS/NMEA-12/water system at 25 ◦ C in a water-rich region is shown in Fig. 1. In water–GS binary system micellar solution appears up to about 25 wt% of surfactant concentration at 25 ◦ C after which hexagonal (H1 ) phase forms [26]. NMEA-12 forms a lamellar liquid crystal (L␣ ) coexisting with excess water in the waterrich region of NMEA-12/water binary system [31]. Aqueous GS micellar solution is very fluid, but with successive addition of NMEA-12 to a dilute micellar (Wm ) solution, the viscosity of the solution increases gradually at first, then rapidly and a viscous solution is observed. The minimum concentration of 3.6 wt% NMEA-12 is required in total system to increase the viscosity of 5 wt% GS solution significantly. The viscous solution is isotropic at rest but shows birefringence when applied a shear, such as sudden jerk. The shaded region shows the region of increased viscosity within the Wm domain of the phase diagram tentatively. With further addition of NMEA-12, an isotropic micellar phase is still observed but the viscosity decreases and ultimately
2.2. Phase diagram For the study of phase behavior, sealed ampoules containing required amount of reagents were homogenized and kept in a water bath at 25 ◦ C for equilibration. Phases were identified by visual observation (through crossed polarisers).
Scheme 1. Schematic molecular structures of GS (a) and NMEA-12 (b).
Fig. 1. Partial phase diagram of water/GS/NMEA-12 ternary diagram at 25 ◦ C. Wm stands for the isotropic micellar solution, H1 and L␣ are the hexagonal and the lamellar liquid crystalline phases.
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˙ Fig. 2. Steady shear-rate (γ)–viscosity (η) curves for 5% GS + NMEA-12 systems at various mixing fraction of NMEA-12 in total surfactant, X.
Wm to lamellar liquid crystal (L␣ ) phase transformation occurs which corresponds to a decrease in surfactant layer curvature with the incorporation of the NMEA-12 in the palisade layer of the surfactant aggregate. The viscosity of 5 wt% GS solution starts decreasing appreciably on addition of 5.1 wt% NMEA-12 in total system. 3.2. Rheology of micellar solutions ˙ Fig. 2 shows the steady shear-rate (γ)–viscosity (η) curves for the aqueous 5% GS + NMEA-12 systems at different mixing fraction of NMEA-12, expressed in weight fraction of NMEA12 in total surfactant (X) at 25 ◦ C. ˙ i.e., At lower value of NMEA-12, η is independent of γ, Newtonian flow behavior is observed up to γ˙ ∼ 1000 s−1 . At X ∼ 0.462 and above, however, the Newtonian behavior is limited to low shear rate, and viscosity decreases monotonically with increasing shear rate, which can be taken as the evidence of the formation of giant aggregates that break at high shear. The decrease in viscosity with increasing shear rate corresponds to a shear thinning behavior. With increasing X up to X ∼ 0.515, the critical γ˙ for shear thinning shifts gradually to lower value and also the viscosity in the plateau region (low γ˙ region) increases which shows that the system is getting more structured. This rheological behavior is typical of systems consisting of network structure formed by wormlike micelles. When network structure is deformed by applying a shear, shear thinning occurs due to alignment of aggregates under flow if the deformation is faster than the time required to regain equilibrium network structure, and with increasing network density the relaxation becomes slower, i.e., shear thinning begins at lower shear rate [32]. However, with further increase in NMEA-12 concentration (at X = 0.524 and 0.569) the viscosity decreases and higher deformation rate is required to induce shear thinning. This indicates that some structural transformation occurs at X > 0.515. The explanation for the change in the rheological behavior is that with increasing X, spontaneous interfacial curvature of aggregate gradually decreases and, with this, energy cost for the formation of hemispherical end caps of the cylindrical aggregates becomes higher. The endcap energy is minimized if the free ends fuse with cylindrical part of its own or another micelles,
Fig. 3. Variation of zero-shear viscosity (η0 ) with the mixing fraction of NMEA12 (X) in GS + NMEA-12 systems at different GS concentrations.
thus forming micellar joints, or branching [33,34]. Such joints reduce the viscosity because when a stress is applied micellar joint can slide along the cylindrical body (contour) thereby allowing a fast stress relaxation process. In some surfactant systems, micellar connections or branching points have been detected by cryogenic transmission electron microscopy (cryoTEM), especially in the region where the viscosity decreases after the maximum [35–38]. Steady shear measurements on 10% GS + NMEA-12 systems show similar trend with increasing concentration of NMEA-12. The Newtonian behavior is observed at low NMEA-12 concentration while shear-thinning is noticed at high NMEA-12 concentration. The effect of NMEA-12 concentration on the viscosity growth for the systems described in Fig. 2 can be seen more clearly in Fig. 3 where zero shear viscosity, η0 is plotted as a function of X at different GS concentrations. The η0 values for the Newtonian systems of low viscosity have been determined by extrapolating the viscosity to zeroshear rate. In the case of high-viscosity samples, the η0 values can be estimated from the values of G0 and τ R as obtained from oscillatory measurements (see Eq. (3)). With increasing NMEA12 concentration, the zero-shear viscosity increases at first, attains a maximum, and then decreases, suggesting structural changes in the system with increasing NMEA-12 concentration. On increasing the concentration of GS in GS + NMEA-12 systems, increase in viscosity, or in other words, a micellar growth begins at a slightly lower mixing fraction of NMEA-12. At similar mixing ratio (X) of the NMEA-12, the η0 shows a large increase on increasing GS concentration, which can be attributed to the decrease in the interfacial cross-sectional area, as , of surfactant at the interface with increasing surfactant concentration, and hence, less mixing fraction of NMEA-12 is needed to induce unidimensional micellar growth. Oscillatory-shear (frequency sweep) measurements were performed on the viscous samples. Fig. 4 shows plots of elastic modulus (G ) and loss modulus (G ) as a function of oscillatoryshear frequency (ω) for a sample of 5% GS + NMEA-12 system at X = 0.490, 0.515 and 0.524, where X = 0.515 is the composition corresponding to the viscosity maximum (see Fig. 3).
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Fig. 5. Cole–Cole plots for the 5% GS + NMEA-12 system shown in Fig. 4.
Fig. 4. Variation of elastic modulus, G (open symbols) and viscous modulus, G (filled symbols) as a function of oscillatory-shear frequency (ω) as obtained by frequency sweep measurement at 25 ◦ C in 5% GS + NMEA-12 surfactant systems at different mixing fraction of NMEA-12 in total surfactant, X = 0.490 (circles), X = 0.515 (triangles) and X = 0.524 (squares). The lines show the best fitting to Eqs. (1) and (2).
These systems show a liquid-like behavior (G < G ) at the low-frequency region, but both G and G increase with ω, and solid-like behavior (G > G ) is observed at the high-frequency region. This is the typical viscoelastic behavior shown by wormlike micellar solution. The viscoelastic behavior in the solutions of wormlike micelles is attributed to the entanglement of the wormlike micelles to form a transient network. As it can be seen from Fig. 4, with increasing X, plateau value of G increases monotonically whereas G –G crossover frequency shifts to the lower value and attains the lowest value at a composition corresponding to viscosity maximum (X = 0.515) but shifts to higher value again. This shifting of crossover frequency to the highfrequency region suggests faster relaxation processes resulting from the formation of micellar joints. When a strain is applied to wormlike micelles, the stress relaxation occurs by reptation, that is, a reptile-like motion of the micelle along its own contour. Besides this, micelles may undergo reversible scission [9]. When the time scale of the reptation for an average micellar contour length (τ rep ) is too slow in comparison to the time scale of the scission (τ b ), that is τ rep τ b, the viscoelastic micellar solutions behave as a Maxwell-fluid described by following equations [39]: G (ω) =
ω2 τR2 G0 1 + ω2 τR2
(1)
G (ω) =
ωτR G0 1 + ω2 τR2
(2)
As it is evident from the Maxwell equations, at low-frequency region ω ωc , G and G scale with ω according to G ∼ ω2 and G ∼ ω. In the high-frequency region, or more specifically, in the region of ω ωc , however, G attains a plateau value equal to G0 whereas G shows a monotonic decrease. The shear frequency corresponding to G –G , crossover ωc is equal to the inverse of τ R . Considering reptation or diffusion of wormlike micelles along its own contour as the mechanism of stress relaxation in the entangled network, as proposed by Cates and co-worker, the
magnitude of τ R is related to the average length of the wormlike micelles whereas G0 is related to the number density of entanglement in the transient network [9,40]. The parameters G0 and τ R are related to η0 by following relation: η0 = G0 τR
(3)
The rheological behavior in low-ω region (below ωc ) can be described by the Maxwell’s model but at high-ω region, experimental data show significant deviation, which is generally considered to be due to faster relaxation processes such as Rouse modes [41]. This is more clearly shown in normalized Cole–Cole plots (Fig. 5), that is, the plots of G /Gmax against G /Gmax . A Maxwell material is characterized by a semicircle centered at G /Gmax = 1. Variation of G0 and τ R with X is shown more clearly in Fig. 6. These parameters were obtained by fitting of the experimental data from frequency sweep measurements, especially the data in low-frequency region, to the Maxwell equations. As in the case of the systems described in Fig. 4, G at the high-ω region (say G∞ ) is often higher than perfect plateau value (G0 ) as predicted by Maxwell equations. Therefore, the values of G0 estimated from Maxwell equations should be considered as the lower limit for the shear modulus. The increase in plateau modulus G0 with increasing X may be taken as the evidence of the one-dimensional micellar growth, and consequently, an increase in the degree of the entanglement of the wormlike micelles. The relaxation time (τ R ), on the other hand, shows an increase to a maximum value at a composition
Fig. 6. Variation of plateau modulus (G0 ) and relaxation time (τ R ) for 5% GS + NMEA-12 system with the mixing fraction of NMEA-12.
S.C. Sharma et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 305 (2007) 83–88
Fig. 7. Variation of elastic modulus, G (open symbols) and viscous modulus, G (filled symbols) as a function of oscillatory-shear frequency (ω) as obtained by frequency sweep measurement at 25 ◦ C in 10% GS + NMEA-12 surfactant systems at different mixing fraction of NMEA-12 in total surfactant, X = 0.372 (circles), X = 0.393 (triangles) and X = 0.435 (squares). Fittings to the Maxwellian equations are shown by solid lines.
corresponding to the maximum viscosity of 5% GS + NMEA-12 series (see Fig. 3), followed by a sharp decrease. It means without breaking the network structure, the aggregates undergo structural changes that provide a faster process of stress relaxation. One of the possibilities is that after the saturation of micellar growth, further increase of X 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. With successive addition of the NMEA-12, the viscosity decreases continuously and ultimately the L␣ phase separates out, as shown by the phase diagram (see Fig. 1). Fig. 7 shows the results of oscillatory-shear measurements of 10% GS + NMEA-12 systems having compositions in the vicinity of maximum-viscosity region (see Fig. 3). Like 5% GS systems shown in Fig. 4, these systems follow Maxwell model in low-ω region. The variation of plateau modulus (G0 ) and relaxation time (τ R ) for 10% GS + NMEA-12 systems with the mixing fraction of NMEA-12 is shown in Fig. 8. The G0 increases continuously with increasing X but τ R increases up to X ∼ 0.393 (viscosity-maximum).
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Further increase in X results a sharp decrease in τ R which indicates a structural change, probably the formation of micellar joints as mentioned above. Comparison of the values of G0 of 10% GS system with the corresponding values of 5% GS system reveals that enhanced micellar growth can be achieved at higher GS concentration. The lower value of τ R at the maximum in 10% GS + NMEA-12 system in comparison to that in 5% GS + NMEA-12 system should not be considered as a lower extent of micellar growth in the former system. Instead, it might have arisen from the fact that with increasing surfactant concentration the spontaneous curvature decreases and the system favors micellar branching even at lower value of X so as to minimize energy cost of the formation of end caps. Continuous increase of G0 in the given composition range where η0 and τ R decrease shows that after branching the network density increases until the phase separation occurs. 4. Conclusions Addition of NMEA-12 to dilute solution of GS in the micellar (Wm ) phase results in an increase in viscosity. Above a certain concentration of NMEA, the viscosity increases steeply and a viscoelastic solution of wormlike micelles is formed, which is followed by a rapid viscosity drop. The viscosity drop is a consequence of a sharp decrease in stress relaxation time, which is attributed to the formation of micellar joints, which allow fast stress relaxation process. With further addition of NMEA-12, a Wm –lamellar (L␣ ) phase transformation takes place. The rheological behavior of the viscoelastic micellar solutions follows the Maxwell model at low-shear frequency. The micellar growth can be simply explained by decreasing the effective cross-sectional area per amphiphile upon addition of NMEA-12. Acknowledgements This work was supported by The Ministry of Education, Culture, Sports, Science and Technology, Grant-in-Aid for Young Scientists (B), No. 18780094 and partly supported by Core Research for Evolution Science and Technology (CREST) of JST Corporation. S.C. Sharma is grateful to the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan for given the Monbukagakusho Scholarship. DV is thankful to the Japan Society for Promotion of Science (JSPS) for financial support. References
Fig. 8. Variation of plateau modulus (G0 ) and relaxation time (τ R ) for 10% GS + NMEA-12 system with the mixing fraction of NMEA-12 (X).
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Rheological behavior of gemini-type surfactant/alkanolamide/water systems Suraj Chandra Sharma, Rekha Goswami Shrestha, Dharmesh Varade, Kenji Aramaki ∗ Graduate School of Environment and Information Sciences, Yokohama National University, 79-7 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan Received 10 March 2007; received in revised form 18 April 2007; accepted 18 April 2007 Available online 24 April 2007
Abstract The formation of the viscoelastic wormlike micelles in aqueous solution of mixed surfactant system of anionic gemini-type surfactant without a spacer group, disodium 2,3-didodecyl-1,2,3,4-butanetetracarboxylate (GS), and dodecanoyl-N-methyl ethanolamide (NMEA-12) has been studied at 25 ◦ C. With addition of NMEA-12 to the GS–water binary system, a micellar (Wm )–lamellar (L␣ ) phase transformation takes place at low GS concentration. Within the Wm phase region of GS–NMEA-12–water system, there exists a high viscosity region consisting of a viscoelastic micellar solution of entangled wormlike micelles. On increasing the concentration of GS, micellar growth begins at a slightly lower mixing fraction of NMEA-12. The oscillatory-shear rheological behavior of the viscoelastic solutions can be described by Maxwell model at low -shear frequency region. The increase in viscosity can be simply explained by reducing the effective cross-sectional area per amphiphile upon addition of NMEA-12. © 2007 Elsevier B.V. All rights reserved. Keywords: Gemini surfactant; Alkanolamide; Phase behavior; Wormlike micelles; Rheological behavior
1. Introduction Surfactant molecules in aqueous solution self-assemble to form a variety of microstructures such as spherical micelles, wormlike micelles, vesicles and liquid crystals [1–4]. These different aggregation structures have characteristic rheological properties. Transition from spherical to wormlike micelles corresponds to a drastic increase of elasticity and viscosity of the fluid [5]. The viscoelastic wormlike micelles have attracted much interest in fundamental research and practical applications [5–7]. Formation of viscoelastic wormlike micelles 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 [8], analogous to those observed in flexible polymer solutions, with an important difference from the polymeric network that the micelles can break
∗
Corresponding author. Tel.: +81 45 339 4300; fax: +81 45 339 4300. E-mail address: [email protected] (K. Aramaki).
0927-7757/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.colsurfa.2007.04.044
and recombine on a time scale characteristic of the system [9]. It is well known that cationic surfactants can self-assemble in aqueous solution into long flexible cylindrical micelles (wormlike micelles) upon the addition of salts [5,10–12]. The salt serves to reduce the electrostatic interactions between the cationic headgroups, thus reducing the effective area per head group and thereby promoting the growth of cylindrical aggregates at the expense of spherical ones. There are some recent reports on non-ionic mixed surfactant systems [13–17]. However, not much is known about the formation and rheological behavior of the wormlike micelles in anionic systems except sodium dodecyl sulfate (SDS) [18–21]. Gemini surfactants have a very high potential for practical applications because of their excellent ability to reduce surface tension of water and low Krafft temperatures. Compared to their monomeric analogs, gemini surfactants have much lower critical micelle concentration. Due to their high molecular weight, skin penetration of gemini surfactant is expected to be low, which is one of the desirable properties of a surfactant to be used in body care products such as soaps, shampoos and cosmetics. However, the main factor that has prevented the use of gemini surfac-
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tants in practical applications is their higher cost. Most of the gemini surfactants studied so far have a spacer chain between two hydrophilic groups in the molecule. It is known that the spacer chain largely influences the physicochemical properties of the surfactants [22]. It is known that a cationic gemini surfactant with a short chain shows viscoelastic properties in solution [23,24]. Recently the interfacial properties of aqueous solution of a novel anionic gemini-type surfactant with no spacer group, disodium 2,3-didodecyl-1,2,3,4-butanetetracarboxylate (GS) was studied [25] and its rheological behavior with a short poly(oxyethylene) chain non-ionic surfactant was investigated [26]. In order to enrich the knowledge about the microstructure flow behavior and ability of this anionic gemini surfactant to form wormlike micelles or regarding the rheological properties of these micelles in salt free condition, we want to extend the further study with alkanolamides, well-known as foam boosters in surfactant aqueous solution [27–30] as a thickening agent in shampoos, and also as antistatic and anticorrosion agents in detergents [28]. In this context, we studied the rheological behavior of the viscoelastic wormlike micellar solutions in the aqueous system with mixed anionic gemini surfactant (GS) and dodecanoyl-Nmethylethanolamide (NMEA-12). 2. Experimental 2.1. Materials Gemini surfactant (GS) was kindly supplied from Chukyo Yushi Co., Japan. The synthesis of GS has been described elsewhere [26]. The dodecanoyl-N-methylethanolamide (designated by NMEA-12, purity 99.4%) was received as a gift from Kao Corporation, Japan. All the chemicals were used as received. Deionized (Millipore filtered) water was used to prepare the samples. Schematic molecular structures of GS and NMEA-12 are shown in Scheme 1.
2.3. Rheological measurements Samples for rheological measurements were homogenized and kept in water bath at specified temperature for at least 24 h to ensure equilibration before performing measurements. The rheological measurements were performed in a stress controlled rheometer, AR-G2 (TA Instrument) using cone-plate geometries (diameters 60 mm for low-viscosity sample and 40 mm for highviscosity sample, each with a cone angle of 1◦ ) with the plate temperature controlled by peltier unit. A sample cover provided with the instrument was used to minimize the change in sample composition by evaporation during the measurement. Frequency sweep measurements were performed in the linear viscoelastic regime of the samples, as determined previously by dynamic strain sweep measurements. 3. Results and discussion 3.1. Phase behavior The partial phase diagram of the GS/NMEA-12/water system at 25 ◦ C in a water-rich region is shown in Fig. 1. In water–GS binary system micellar solution appears up to about 25 wt% of surfactant concentration at 25 ◦ C after which hexagonal (H1 ) phase forms [26]. NMEA-12 forms a lamellar liquid crystal (L␣ ) coexisting with excess water in the waterrich region of NMEA-12/water binary system [31]. Aqueous GS micellar solution is very fluid, but with successive addition of NMEA-12 to a dilute micellar (Wm ) solution, the viscosity of the solution increases gradually at first, then rapidly and a viscous solution is observed. The minimum concentration of 3.6 wt% NMEA-12 is required in total system to increase the viscosity of 5 wt% GS solution significantly. The viscous solution is isotropic at rest but shows birefringence when applied a shear, such as sudden jerk. The shaded region shows the region of increased viscosity within the Wm domain of the phase diagram tentatively. With further addition of NMEA-12, an isotropic micellar phase is still observed but the viscosity decreases and ultimately
2.2. Phase diagram For the study of phase behavior, sealed ampoules containing required amount of reagents were homogenized and kept in a water bath at 25 ◦ C for equilibration. Phases were identified by visual observation (through crossed polarisers).
Scheme 1. Schematic molecular structures of GS (a) and NMEA-12 (b).
Fig. 1. Partial phase diagram of water/GS/NMEA-12 ternary diagram at 25 ◦ C. Wm stands for the isotropic micellar solution, H1 and L␣ are the hexagonal and the lamellar liquid crystalline phases.
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˙ Fig. 2. Steady shear-rate (γ)–viscosity (η) curves for 5% GS + NMEA-12 systems at various mixing fraction of NMEA-12 in total surfactant, X.
Wm to lamellar liquid crystal (L␣ ) phase transformation occurs which corresponds to a decrease in surfactant layer curvature with the incorporation of the NMEA-12 in the palisade layer of the surfactant aggregate. The viscosity of 5 wt% GS solution starts decreasing appreciably on addition of 5.1 wt% NMEA-12 in total system. 3.2. Rheology of micellar solutions ˙ Fig. 2 shows the steady shear-rate (γ)–viscosity (η) curves for the aqueous 5% GS + NMEA-12 systems at different mixing fraction of NMEA-12, expressed in weight fraction of NMEA12 in total surfactant (X) at 25 ◦ C. ˙ i.e., At lower value of NMEA-12, η is independent of γ, Newtonian flow behavior is observed up to γ˙ ∼ 1000 s−1 . At X ∼ 0.462 and above, however, the Newtonian behavior is limited to low shear rate, and viscosity decreases monotonically with increasing shear rate, which can be taken as the evidence of the formation of giant aggregates that break at high shear. The decrease in viscosity with increasing shear rate corresponds to a shear thinning behavior. With increasing X up to X ∼ 0.515, the critical γ˙ for shear thinning shifts gradually to lower value and also the viscosity in the plateau region (low γ˙ region) increases which shows that the system is getting more structured. This rheological behavior is typical of systems consisting of network structure formed by wormlike micelles. When network structure is deformed by applying a shear, shear thinning occurs due to alignment of aggregates under flow if the deformation is faster than the time required to regain equilibrium network structure, and with increasing network density the relaxation becomes slower, i.e., shear thinning begins at lower shear rate [32]. However, with further increase in NMEA-12 concentration (at X = 0.524 and 0.569) the viscosity decreases and higher deformation rate is required to induce shear thinning. This indicates that some structural transformation occurs at X > 0.515. The explanation for the change in the rheological behavior is that with increasing X, spontaneous interfacial curvature of aggregate gradually decreases and, with this, energy cost for the formation of hemispherical end caps of the cylindrical aggregates becomes higher. The endcap energy is minimized if the free ends fuse with cylindrical part of its own or another micelles,
Fig. 3. Variation of zero-shear viscosity (η0 ) with the mixing fraction of NMEA12 (X) in GS + NMEA-12 systems at different GS concentrations.
thus forming micellar joints, or branching [33,34]. Such joints reduce the viscosity because when a stress is applied micellar joint can slide along the cylindrical body (contour) thereby allowing a fast stress relaxation process. In some surfactant systems, micellar connections or branching points have been detected by cryogenic transmission electron microscopy (cryoTEM), especially in the region where the viscosity decreases after the maximum [35–38]. Steady shear measurements on 10% GS + NMEA-12 systems show similar trend with increasing concentration of NMEA-12. The Newtonian behavior is observed at low NMEA-12 concentration while shear-thinning is noticed at high NMEA-12 concentration. The effect of NMEA-12 concentration on the viscosity growth for the systems described in Fig. 2 can be seen more clearly in Fig. 3 where zero shear viscosity, η0 is plotted as a function of X at different GS concentrations. The η0 values for the Newtonian systems of low viscosity have been determined by extrapolating the viscosity to zeroshear rate. In the case of high-viscosity samples, the η0 values can be estimated from the values of G0 and τ R as obtained from oscillatory measurements (see Eq. (3)). With increasing NMEA12 concentration, the zero-shear viscosity increases at first, attains a maximum, and then decreases, suggesting structural changes in the system with increasing NMEA-12 concentration. On increasing the concentration of GS in GS + NMEA-12 systems, increase in viscosity, or in other words, a micellar growth begins at a slightly lower mixing fraction of NMEA-12. At similar mixing ratio (X) of the NMEA-12, the η0 shows a large increase on increasing GS concentration, which can be attributed to the decrease in the interfacial cross-sectional area, as , of surfactant at the interface with increasing surfactant concentration, and hence, less mixing fraction of NMEA-12 is needed to induce unidimensional micellar growth. Oscillatory-shear (frequency sweep) measurements were performed on the viscous samples. Fig. 4 shows plots of elastic modulus (G ) and loss modulus (G ) as a function of oscillatoryshear frequency (ω) for a sample of 5% GS + NMEA-12 system at X = 0.490, 0.515 and 0.524, where X = 0.515 is the composition corresponding to the viscosity maximum (see Fig. 3).
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Fig. 5. Cole–Cole plots for the 5% GS + NMEA-12 system shown in Fig. 4.
Fig. 4. Variation of elastic modulus, G (open symbols) and viscous modulus, G (filled symbols) as a function of oscillatory-shear frequency (ω) as obtained by frequency sweep measurement at 25 ◦ C in 5% GS + NMEA-12 surfactant systems at different mixing fraction of NMEA-12 in total surfactant, X = 0.490 (circles), X = 0.515 (triangles) and X = 0.524 (squares). The lines show the best fitting to Eqs. (1) and (2).
These systems show a liquid-like behavior (G < G ) at the low-frequency region, but both G and G increase with ω, and solid-like behavior (G > G ) is observed at the high-frequency region. This is the typical viscoelastic behavior shown by wormlike micellar solution. The viscoelastic behavior in the solutions of wormlike micelles is attributed to the entanglement of the wormlike micelles to form a transient network. As it can be seen from Fig. 4, with increasing X, plateau value of G increases monotonically whereas G –G crossover frequency shifts to the lower value and attains the lowest value at a composition corresponding to viscosity maximum (X = 0.515) but shifts to higher value again. This shifting of crossover frequency to the highfrequency region suggests faster relaxation processes resulting from the formation of micellar joints. When a strain is applied to wormlike micelles, the stress relaxation occurs by reptation, that is, a reptile-like motion of the micelle along its own contour. Besides this, micelles may undergo reversible scission [9]. When the time scale of the reptation for an average micellar contour length (τ rep ) is too slow in comparison to the time scale of the scission (τ b ), that is τ rep τ b, the viscoelastic micellar solutions behave as a Maxwell-fluid described by following equations [39]: G (ω) =
ω2 τR2 G0 1 + ω2 τR2
(1)
G (ω) =
ωτR G0 1 + ω2 τR2
(2)
As it is evident from the Maxwell equations, at low-frequency region ω ωc , G and G scale with ω according to G ∼ ω2 and G ∼ ω. In the high-frequency region, or more specifically, in the region of ω ωc , however, G attains a plateau value equal to G0 whereas G shows a monotonic decrease. The shear frequency corresponding to G –G , crossover ωc is equal to the inverse of τ R . Considering reptation or diffusion of wormlike micelles along its own contour as the mechanism of stress relaxation in the entangled network, as proposed by Cates and co-worker, the
magnitude of τ R is related to the average length of the wormlike micelles whereas G0 is related to the number density of entanglement in the transient network [9,40]. The parameters G0 and τ R are related to η0 by following relation: η0 = G0 τR
(3)
The rheological behavior in low-ω region (below ωc ) can be described by the Maxwell’s model but at high-ω region, experimental data show significant deviation, which is generally considered to be due to faster relaxation processes such as Rouse modes [41]. This is more clearly shown in normalized Cole–Cole plots (Fig. 5), that is, the plots of G /Gmax against G /Gmax . A Maxwell material is characterized by a semicircle centered at G /Gmax = 1. Variation of G0 and τ R with X is shown more clearly in Fig. 6. These parameters were obtained by fitting of the experimental data from frequency sweep measurements, especially the data in low-frequency region, to the Maxwell equations. As in the case of the systems described in Fig. 4, G at the high-ω region (say G∞ ) is often higher than perfect plateau value (G0 ) as predicted by Maxwell equations. Therefore, the values of G0 estimated from Maxwell equations should be considered as the lower limit for the shear modulus. The increase in plateau modulus G0 with increasing X may be taken as the evidence of the one-dimensional micellar growth, and consequently, an increase in the degree of the entanglement of the wormlike micelles. The relaxation time (τ R ), on the other hand, shows an increase to a maximum value at a composition
Fig. 6. Variation of plateau modulus (G0 ) and relaxation time (τ R ) for 5% GS + NMEA-12 system with the mixing fraction of NMEA-12.
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Fig. 7. Variation of elastic modulus, G (open symbols) and viscous modulus, G (filled symbols) as a function of oscillatory-shear frequency (ω) as obtained by frequency sweep measurement at 25 ◦ C in 10% GS + NMEA-12 surfactant systems at different mixing fraction of NMEA-12 in total surfactant, X = 0.372 (circles), X = 0.393 (triangles) and X = 0.435 (squares). Fittings to the Maxwellian equations are shown by solid lines.
corresponding to the maximum viscosity of 5% GS + NMEA-12 series (see Fig. 3), followed by a sharp decrease. It means without breaking the network structure, the aggregates undergo structural changes that provide a faster process of stress relaxation. One of the possibilities is that after the saturation of micellar growth, further increase of X 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. With successive addition of the NMEA-12, the viscosity decreases continuously and ultimately the L␣ phase separates out, as shown by the phase diagram (see Fig. 1). Fig. 7 shows the results of oscillatory-shear measurements of 10% GS + NMEA-12 systems having compositions in the vicinity of maximum-viscosity region (see Fig. 3). Like 5% GS systems shown in Fig. 4, these systems follow Maxwell model in low-ω region. The variation of plateau modulus (G0 ) and relaxation time (τ R ) for 10% GS + NMEA-12 systems with the mixing fraction of NMEA-12 is shown in Fig. 8. The G0 increases continuously with increasing X but τ R increases up to X ∼ 0.393 (viscosity-maximum).
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Further increase in X results a sharp decrease in τ R which indicates a structural change, probably the formation of micellar joints as mentioned above. Comparison of the values of G0 of 10% GS system with the corresponding values of 5% GS system reveals that enhanced micellar growth can be achieved at higher GS concentration. The lower value of τ R at the maximum in 10% GS + NMEA-12 system in comparison to that in 5% GS + NMEA-12 system should not be considered as a lower extent of micellar growth in the former system. Instead, it might have arisen from the fact that with increasing surfactant concentration the spontaneous curvature decreases and the system favors micellar branching even at lower value of X so as to minimize energy cost of the formation of end caps. Continuous increase of G0 in the given composition range where η0 and τ R decrease shows that after branching the network density increases until the phase separation occurs. 4. Conclusions Addition of NMEA-12 to dilute solution of GS in the micellar (Wm ) phase results in an increase in viscosity. Above a certain concentration of NMEA, the viscosity increases steeply and a viscoelastic solution of wormlike micelles is formed, which is followed by a rapid viscosity drop. The viscosity drop is a consequence of a sharp decrease in stress relaxation time, which is attributed to the formation of micellar joints, which allow fast stress relaxation process. With further addition of NMEA-12, a Wm –lamellar (L␣ ) phase transformation takes place. The rheological behavior of the viscoelastic micellar solutions follows the Maxwell model at low-shear frequency. The micellar growth can be simply explained by decreasing the effective cross-sectional area per amphiphile upon addition of NMEA-12. Acknowledgements This work was supported by The Ministry of Education, Culture, Sports, Science and Technology, Grant-in-Aid for Young Scientists (B), No. 18780094 and partly supported by Core Research for Evolution Science and Technology (CREST) of JST Corporation. S.C. Sharma is grateful to the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan for given the Monbukagakusho Scholarship. DV is thankful to the Japan Society for Promotion of Science (JSPS) for financial support. References
Fig. 8. Variation of plateau modulus (G0 ) and relaxation time (τ R ) for 10% GS + NMEA-12 system with the mixing fraction of NMEA-12 (X).
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