Wormlike Micelles in Mixed Surfactant Systems: Effect of Cosolvents

10438

J. Phys. Chem. B 2007, 111, 10438-10447

Wormlike Micelles in Mixed Surfactant Systems: Effect of Cosolvents Dharmesh Varade,† Carlos Rodrı´guez-Abreu,‡,§ Lok Kumar Shrestha,† and Kenji Aramaki*,† Graduate School of EnVironment and Information Sciences, Yokohama National UniVersity, Tokiwadai 79-7, Hodogaya-ku, Yokohama 240-8501, Japan, Departamento de Quı´mica Fı´sica, Facultad de Quı´mica, UniVersidad de Santiago de Compostela, E-15782 Santiago de Compostela, Spain, and Institut d’InVestigacions Quı´miques i Ambientals de Barcelona Consejo Superior de InVestigaciones Cientificas (IIQAB/CSIC), Jordi Girona, 18-26, 08034 Barcelona, Spain ReceiVed: May 27, 2007; In Final Form: July 5, 2007

We have studied the structure and rheological behavior of viscoelastic wormlike micellar solutions in the mixed nonionic surfactants poly(oxyethylene) cholesteryl ether (ChEO15)-trioxyethylene monododecyl ether (C12EO3) and anionic sodium dodecyl sulfate (SDS)-C12EO3 using a series of glycerol/water and formamide/ water mixed solvents. The obtained results are compared with those reported in pure water for the corresponding mixed surfactant systems. The zero-shear viscosity first sharply increases with C12EO3 addition and then decreases; i.e., there is a viscosity maximum. The intensity (viscosity) and position (C12EO3 fraction) of this maximum shift to lower values upon an increase in the ratio of glycerol in the glycerol/water mixed solvent, while the position of the maximum changes in an opposite way with increasing formamide. In the case of the SDS/C12EO3 system, zero-shear viscosity shows a decrease with an increase of temperature, but for the ChEO15/ C12EO3 system, again, the zero-shear viscosity shows a maximum if plotted as a function of temperature, its position depending on the C12EO3 mixing fraction. In the studied nonionic systems, worm micelles seem to exist at low temperatures (down to 0 °C) and high glycerol concentrations (up to 50 wt %), which is interesting from the viewpoint of applications such as drag reduction fluids. Rheology results are supported by smallangle X-ray scattering (SAXS) and dynamic light scattering (DLS) measurements on nonionic systems, which indicate micellar elongation upon addition of glycerol or increasing temperature and shortening upon addition of formamide. The results can be interpreted in terms of changes in the surface curvature of aggregates and lyophobicity.

Introduction The formation of elongated wormlike micelles and their networks in aqueous solutions has been the subject of extensive research due to their interesting properties from both fundamental and practical points of view.1,2 Attention has been mostly focused on cationic surfactant systems, in which the effect of several physicochemical parameters such as temperature, salinity, and solubilizates has already been addressed.3-7 Recently, it was found that the formation of viscoelastic solutions of worm micelles is also possible in mixed and single nonionic systems,8-10 which have the advantage of being less sensitive to salts and showing low Krafft points. Although there are plenty of studies on aqueous systems, the formation of viscoelastic worm micelles in solvents of different polarities has been scarcely reported. The addition of polar organic solvents, such as glycerol or formamide, would provide extra degrees of freedom in tailoring the solution properties. For example, pharmaceutical formulation for drug delivery uses cosolvents such as glycerol and ethanol in order to improve the solubility of the active compounds and/or to aid the sensory perception. There is enough experimental evidence supported by theory11 on the surfactant self-aggregation in solvents such as glycerol and formamide, so that both micelles and lyotropic liquid crystals are formed.12-16 However, the Krafft point tends * Corresponding author. E-mail: [email protected]. Phone & Fax: +81-45-339-4300. † Yokohama National University. ‡ Universidad de Santiago de Compostela. § Institut d’Investigacions Quı´miques i Ambientals de Barcelona (IIQAB/ CSIC).

to increase whereas the stability of aggregates tends to decrease in such solvents,13,17-19 which was attributed to changes in the hydration of surfactant headgroups and in the solvophobic effect. In the water/C12EO8 system, micellar aggregates tend to grow with increasing glycerol content, attributed to the dehydration of the ethylene oxide chain.13 Solvents such as short chain alcohols or formamide cause a decrease in the micellar aggregation number20 and an increase in the cloud point,21 whereas polyols such as glycerol have opposite effects.21,22 One of the practical applications of worm-micellar solutions is their use as drag-reducing fluids, a promising technology for energy saving in district heating/cooling systems.2,23 In this technology, the use of polyols as solvents would allow one to expand the working temperature range and therefore obtain higher cooling capacities. In this context, the investigation on the wormlike micelles of amphiphiles in mixed solvents consisting of water and watermiscible polar organic solvents would be very interesting. As reported by our group, the nonionic surfactants poly(oxyethylene) cholesteryl ether (ChEO15) and anionic sodium dodecyl sulfate (SDS) form highly viscoelastic wormlike micelles in the presence of lipophilic trioxyethylene monododecyl ether (C12EO3) in aqueous systems.24,25 However, we have studied both mixed surfactant systems mentioned above by changing the solvent composition in mixed solvents consisting of water and one of the following cosolvents: glycerol or formamide (with dielectric constants below and above water, respectively). The principal means of characterization are rheology, small-angle

10.1021/jp0740999 CCC: $37.00 © 2007 American Chemical Society Published on Web 08/16/2007

Wormlike Micelles in Mixed Surfactant Systems

J. Phys. Chem. B, Vol. 111, No. 35, 2007 10439

SCHEME 1: Molecular Structure of ChEO15

and were corrected for the background scattering from the capillary and the solvent. The maximum resolution of the measurement, or qmin, was ∼0.08 nm-1, which corresponds to ∼40 nm as the detectable maximum size for a particle. SAXS data can be analyzed by indirect Fourier transformation (IFT) followed by deconvolution.26-29 This method allows us to extract information about the shape and internal structure without having a priori assumption on the model of the aggregate. Only an outline of the principle is presented here. In dilute surfactant solutions, the interparticle interference scattering is negligible and, hence, the structure factor, S(q), is considered to be unity and the spatially averaged q-dependent scattering intensity, I(q), is given by

X-ray scattering (SAXS) and dynamic light scattering (DLS) measurements. The variables that we examined include the content of the polar organic solvent in the mixed solvent with water and the temperature. We have tried to provide a comprehensive picture of how the presence of cosolvents affects the formation of wormlike micelles. From the application viewpoint, such a fundamental information would be very much beneficial. Experimental Section Materials. The nonionic surfactant poly(oxyethylene) cholesteryl ether (ChEO15, number of oxyethylene units m ) 15) and anionic sodium dodecyl sulfate (SDS, purity >99%) were purchased from Nihon Emulsion Co. and Aldrich Chemicals, respectively. The schematic molecular structure of the ChEO15 surfactant is shown in Scheme 1. A highly pure sample of trioxyethylene monododecyl ether (C12EO3) was purchased from Nikko Chemical Co., Japan. Glycerol and formamide were AR grade solvents from TCI Chemicals, Japan. All of the chemicals were used as received. Millipore-filtered water was used for the preparation of all samples. Rheological Measurements. Samples for rheological measurements were homogenized and kept in a water bath at a specified temperature for at least 24 h to ensure equilibration before performing measurements. The measurements were performed in a stress-controlled rheometer, AR-G2 (TA Instrument), using cone-plate geometry with the plate temperature controlled by a 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. The zero-shear viscosity of the samples was determined from steady shear-rate measurement of samples by extrapolating the viscosity-shear-rate curve to zero-shear rate. Small-Angle X-ray Scattering (SAXS). For the SAXS measurements on micellar solution, we used a SAXSess camera (Anton Paar), a new and powerful updated version of the socalled Kratky compact camera, which is attached to a PW3830 laboratory X-ray generator with a long fine focus sealed glass X-ray tube (KR wavelength of 0.1542 nm). The apparatus was operated at 40 kV and 50 mA. The SAXSess camera is equipped with focusing multiplayer optics and a block collimator for an intense and monochromatic primary beam with low background, and a translucent beam stop for the measurement of an attenuated primary beam at q ) 0. Samples were enclosed into a vacuum tight thin quartz capillary with an outer diameter of 1 mm and thickness of 10 µm, and the same capillary was used in each measurement to attain the exactly same scattering volume and background contribution. The sample temperature was controlled with a thermostated sample holder unit (TCS 120, Anton Paar). The scattered intensities were measured with an imaging plate (IP) detection system, Cyclone (Perkin-Elmer, U.S.A.), and via SAXSQuant software (Anton Paar), twodimensional intensity data were transformed to the onedimensional scattering curves as a function of the magnitude of the scattering vector. All data were normalized to the same incident primary beam intensity for the transmission calibration

I(q) ) 4π

∫0∞p(r) sinqrqr dr

(1)

where p(r) is the pair-distance distribution function (PDDF), involving the information about the particle size, shape, and internal core-shell structure of the particles. In general, the intraparticle scattering contribution is related to the form factor, P(q), theoretically corresponding to the Fourier transformation of p(r), and the interparticle interference scattering is connected to the structure factor, S(q), given as the Fourier transformation of the total correlation function, h(r) ) g(r) -1, as

S(q) ) 1 + 4πn

∫0∞[g(r) - 1]r2 sinqrqr dr

(2)

where n is the particle number density and g(r) is the paircorrelation function. In the case of monodisperse spherical systems, the total scattering intensity, I(q), can simply given by

I(q) ) nP(q) S(q)

(3)

For the dilute systems, S(q) is equivalent to unity and I(q) is simply given by P(q). This equation is strictly valid only for a monodisperse spherical system. However, it can be extended to polydisperse and elongated particle systems up to a certain theoretical and practical limit.30-32 For a particle of an arbitrary shape having a scattering density difference of ∆F(r), the pair-distance distribution function (PDDF) is given by

p(r) ) r2∆F˜ 2(r)

(4)

where ∆F˜ 2(r) is the convolution square of ∆F(r) averaged over all directions in space. For spherical particles, averaging is not necessary because the scattering density difference, or electron density difference, ∆Frs(r), is only a function of the radial position and deconvolution of the PDDF gives the radius contrast profile. Dynamic Light Scattering (DLS). DLS measurements were performed with a DLS-7000 instrument (Otsuka Electronics Co., Ltd.). The DLS instrument consists of a goniometer, a 75 mW Ar ion laser (λ ) 488 nm), and a multiple tau digital real time correlator (ALV-5000/EPP, Germany). The intensity correlation function, g2(t), is given by33

g2(t) - 1 ) β|g1(t)|2

(5)

where g1(t) is the field correlation function, which is fitted by the regularization CONTIN program, and β is an adjusted parameter depending on the performance of the instrument. When aggregates of different sizes are formed in solution, g1(t) includes all of the individual relaxation processes and can

10440 J. Phys. Chem. B, Vol. 111, No. 35, 2007

Varade et al.

Figure 1. Steady shear-rate plots of micellar solutions of the 0.06 M ChEO15 system in glycerol/water mixed solvent ratio 50/50 (expressed in wt %) at different mixing fractions of C12EO3, X, in the total surfactant at 25 °C. Lines are only visual guides.

be expressed as follows

x(g2(t) - 1) ) xβ∫0 A(Γ) exp(-Γt) dΓ ∞

(6)

where A(Γ) is the relaxation rate distribution function and Γ is the relaxation rate

Γ ) Dq2

(7)

where D is the effective diffusion coefficient and q is the scattering vector, whose amplitude is

q ) (4πn/λ) sin(θ/2)

(8)

where n is the refractive index of the solvent, λ is the laser beam wavelength, and θ is the scattering angle. Results and Discussion Rheology. ChEO15/C12EO3/CosolVent Systems. In water, poly(oxyethylene) cholesteryl ether (ChEO15) forms spherical or ellipsoidal micelles and the resulting solutions have a low viscosity similar to that of the solvent.24 Addition of trioxyethylene monododecyl ether (C12EO3) to these solutions increases the viscosity dramatically. This is evident even by visual observation. To quantify the effect of cosolvents, we carried out rheological measurements in a series of glycerol/water and formamide/water mixed solvents (25/75, 50/50, and 75/25; expressed in wt %) at a fixed ChEO15 concentration of 0.06 M (≈6 wt %) and with increasing concentration of C12EO3 expressed in weight fraction of C12EO3 in total amphiphiles, X. The obtained results were compared with that in plain water,24 in order to get an insight of the mixed solvent effect on the formation and viscoelasticity of the wormlike micellar solution. In the present systems, the overall surfactant concentration has not been fixed while varying the C12EO3 concentration. Figure 1 shows the representative plots for steady shear-rate (γ˘ )-viscosity (η) curves at 25 °C for the 0.06 M ChEO15 in glycerol/water mixed solvent ratio 50/50 at various concentrations of C12EO3, X. At lower C12EO3 content (up to X ∼ 0.18) in the system, the solution shows Newtonian behavior over the entire range of shear rates studied. At X g 0.19, the viscosity increases sharply and a shear thinning is observed at a higher γ˘ , which is typical of wormlike micelles because above a critical γ˘ value the viscosity decreases due to shear alignment of the micelles as well as the breaking of the structured networks. With an increase in X, the wormlike micelles become more structured and the critical γ˘ value shifts to lower values, and at X ∼ 0.22, the sample becomes highly viscoelastic and attains a maximum viscosity. With further increase in C12EO3 concentration (X ∼

Figure 2. Variation of zero-shear viscosity, η0, for the 0.06 M ChEO15 system at different mixing fractions of C12EO3, X, in the total surfactant, in water (/) and various glycerol/water (open symbols) and formamide/ water (closed symbols) mixed solvent ratios: 25/75 (circles), 50/50 (triangles), and 75/25 (squares) expressed in wt % at 25 °C. Lines are only visual guides.

0.23), the viscosity decreases which corresponds to a structural change in the system (probably branching) and finally there is a phase separation above X ) 0.29. Figure 2 shows the change in the zero-shear viscosity, η0, of 0.06 M ChEO15 as a function of the C12EO3 concentration, X, in a series of glycerol/water and formamide/water contents in mixed solvents. The values of η0 were obtained from steady shear rheological experiments in the limit of low shear rates, where the viscosity asymptotically approached a plateau. The figure clearly depicts the effect of increasing glycerol or formamide content in the mixed solvent with water. In aqueous 0.06 M ChEO15, upon gradual addition of C12EO3, the viscosity at first shows a slow and then a sharp increase until a maximum and then finally phase separation takes place. However, the situation changes in the presence of mixed solvents. The zeroshear viscosity first sharply increases with C12EO3 addition and then decreases; i.e., there is a viscosity maximum. The magnitude of viscosity and position (C12EO3 fraction) of this maximum shift to lower values upon increasing glycerol content in glycerol/water mixed solvent, while the position of the maximum changes in the opposite way with increasing formamide in formamide/water. The samples are strongly flow birefringent; small stresses induced by a tilt or mild tapping of a sample vial are enough to cause intense birefringence when viewed under crossed polarizers. There is no birefringence at rest, however. Upon addition of glycerol, the zero-shear viscosity curve shifts to the lower C12EO3 fraction, indicating that glycerol favors the formation of wormlike micelles compared to the case of pure water. Addition of glycerol to water has been reported to result in a higher micelle association number (resulting from an increasing solvophobic effect) and a pronounced dehydration of the EO groups, which promoted micellar growth,13,15,34 as the specific surface area of aggregates decreases. A closer look at Figure 2 reveals that the viscosity of ChEO15 solutions increases with X up to 2 orders of magnitude in the presence of 75% glycerol (the viscosity of glycerol/water being about 2 orders of magnitude higher than that of pure water); however, further increase in glycerol content results in formation of lamellar liquid crystals, which support the claim that there is a reduction of specific surface area and surface curvature as glycerol is added. Opposite to glycerol, increasing formamide content in the mixed solvent shifts the entire curve toward a higher concentration of C12EO3 with a significant drop in the viscosity maxima. Above 40 wt % formamide in the mixed solvent, the network structure of wormlike micelles is completely lost, and at 75 wt



Figure 3. (a) Variation of the storage modulus, G′ (circles), and viscous modulus, G′′ (squares), as a function of oscillatory shear frequency, ω, for the 0.06 M ChEO15 system in glycerol/water mixed solvent ratio 50/50 (expressed in wt %) at different mixing fractions of C12EO3, X, in the total surfactant at 25 °C: (A) X ) 0.22; (B) X ) 0.20. The solid lines are best fits to eqs 9 and 10. (b) Cole-Cole plot of corresponding dynamic data.

%, the peak viscosity drops by 4 orders of magnitude. The formamide/water mixed solvent seems to become a better solvent for the surfactant compared to water and thus disfavors the formation of micelles.15,34 Addition of formamide to water reduces the solvophobicity and increases the solubility of surfactant. This in turn lowers the interfacial tension between the hydrophobic chains and the solvent, so that shrinking and disruption of micelles becomes more energetically favorable than in plain water.15,34 At a fixed ChEO15 concentration, an increase in the C12EO3 content leads to a rapid increase and viscosity goes through a maximum. It is widely accepted that there is a transition from linear to branched micelles at the peak,35 according to which micelles grow linearly before the peak composition and thereafter tend to form branches rather than continue growing axially. As branching proceeds, the viscosity drops because the branch points are not fixed but are free to slide along the micelle, providing an additional mode of stress relaxation.35 To characterize the viscoelasticity of ChEO15/C12EO3/cosolvent systems, we turned to dynamic rheology. Oscillatory shear (frequency sweep) measurements were performed on the viscoelastic samples formed around the viscosity maximum. Representative plots of elastic modulus, G′, and viscous modulus, G′′, as a function of angular frequency, ω, for 0.06 M ChEO15 in glycerol/water mixed solvent ratio 50/50 at various mixing fractions of C12EO3, X, are shown in Figure 3a. These systems show a liquidlike behavior (G′ < G′′) at the low frequency region, but G′ increases with ω, and solidlike behavior (G′ > G′′) is observed at the high frequency region. This is the typical viscoelastic behavior shown by wormlike micellar solutions. In the Maxwell model of viscoelastic fluids with a single relaxation time, τR, the elastic modulus, G′, and viscous modulus, G′′, obey the following relations as a function of ω.36

G′(ω) )

G′′(ω) )

(ωτR)2

G0

(9)

G0 1 + (ωτR)2

(10)

1 + (ωτR)2 ωτR

The plateau modulus, G0, is given by G′(ω) at high ω. The relaxation time, τR, may be estimated from the relation τR ) 1/ωc. Once G0 and τR are available, η0 can be calculated using the following relation:

η0 ) G0τR

(11)

Alternately, the following relationship allows one to estimate η0 by extrapolating the complex viscosity values, |η*|, to zeroshear frequency:

|η*| )

(G′2 + G′′2)1/2 ) ω

η0

x1 + ω2τR2

(12)

Also of interest is a linear plot of G′′ and G′ which reveals the semicircle (Cole-Cole) characteristic of a Maxwell fluid, which is expressed as eqs 9 and 10.

G′/G′′ ) ωτR

(

G′′2 + G′ -

(13)

) ( )

G0 2 G0 ) 2 2

2

(14)

Figure 3a shows that in the low ω region the data points of G′ and G′′ could be fitted to Maxwell equations, but in the high ω region, experimental data deviate from the model, where an upturn in G′′ occurs due to the appearance of “breathing” or Rouse relaxation modes. Maxwellian type oscillatory rheological behavior of viscous micellar solutions can be related to the transient network formed by the entanglement of wormlike micelles. With increasing C12EO3 concentration, i.e., X from 0.20 to 0.22, the G′-G′′ crossover frequency, ωc, shifts to the low values which suggests slower relaxation processes. It can be expected that micelles with longer lengths would form an entangled network and therefore undergo stress relaxation slowly. It is sometimes difficult to determine how good a Maxwell model fits the data from the dynamic plots. A good indication of single exponential stress relaxation is the semicircular form of the so-called Cole-Cole figure (Figure 3b), where the normalized plot of G′′ as a function of G′ is depicted for the corresponding system shown in a dynamic plot. The semicircles represent the best fits of the low frequency data to the Maxwell model. It can be seen from the figure that a large deviation from the Maxwellian behavior is observed at higher frequency due to the presence of different relaxation modes. The estimated values for G0 and τR obtained from the Maxwell fit to the experimental data at 25 °C for the 0.06 M ChEO15 system as a function of X in the mixed solvents are plotted in Figure 4. Data at higher formamide (>25 wt %) content are not shown because these samples were too thin to perform the dynamic rheology. The value of G0 is related to the number of entanglements between wormlike micelles or the mesh size of the network; then, the increase in G0 with X is attributed to an increase in the network density of the wormlike aggregates. The magnitude of G0 is almost the same in various mixed solvents, indicating


Figure 4. Variation of the plateau modulus, G0, and relaxation time, τR, for 0.06 M ChEO15 at different mixing fractions of C12EO3, X, in the total surfactant at 25 °C in (A) formamide/water mixed solvent ratio 25/75 and various glycerol/water mixed solvent ratios: (B) 25/ 75; (C) 50/50; (D) 75/25. Lines are only visual guides.

Figure 5. Variation of zero-shear viscosity, η0, for the 0.15 M SDS system at different mixing fractions of C12EO3, X, in water (/) and in various glycerol/water (open symbols) and formamide/water (closed symbols) mixed solvent ratio 10/90 (circles) and 25/75 (triangles) expressed in wt % at 25 °C. Lines are only visual guides.

a minor effect of solvent quality on network density. On the other hand, with the increase in X, τR increases, which may be associated with the increase in the micellar length. However, with a successive increase in X, τR decreases, indicating a structural change in the micellar network that allows a faster mechanism of stress relaxation other than reptation. The variation in η0 reflects the variations observed in τR. Addition of moderate amounts of cosurfactant leads to an increase in the average micellar length, whereas, above a certain cosurfactant concentration, structural transitions lead to faster relaxation.37,38 It is generally admitted that increasing the cosurfactant concentration amounts to increasing the curvature energy of the surfactant molecules in the end-cap, leading to an increase in the average micellar length. Branching is energetically favorable due to the disappearance of end-caps with the formation of junctions. τR also tends to decrease with glycerol content for the given C12EO3 concentration, X, but as discussed above, the rheological, and hence relaxation behavior, depends much on this parameter. SDS/C12EO3/CosolVent Systems. Anionic sodium dodecyl sulfate (SDS) also forms the elongated wormlike micellar solution in the presence of C12EO3 in aqueous media.25 Thus, we thought it to be interesting to examine the similar effect of cosolvents in this ionic system. Figure 5 shows the change in the zero-shear viscosity, η0, for 0.15 M SDS (≈ 4.32 wt %) with the C12EO3 concentration, X, in a glycerol/water and formamide/water content in mixed solvents (10/90 and 25/75; expressed in wt %). Increased Krafft temperature of SDS at higher glycerol content limits the rheological measurements to 25 wt % glycerol.

Varade et al.

Figure 6. Variation of the storage modulus, G′ (circles), and loss modulus, G′′ (squares), as a function of oscillatory shear frequency, ω, at 25 °C for the 0.15 M SDS system at mixing fractions of C12EO3, X ) 0.65, in glycerol/water mixed solvent ratio (A) 10/90 and (B) 25/ 75 expressed in wt %. The solid lines are best fits to eqs 9 and 10.

The experimental evidence indicates that increasing formamide content in mixed solvent with water has a similar effect on both ionic and nonionic surfactant, causing the disruption of wormlike micelles, whereas the presence of glycerol shows a different trend in the case of the ionic as compared to the nonionic surfactant system discussed earlier. Increasing the glycerol content in mixed solvent with water tends to decrease the viscosity of the system but does not affect much the position (X value) of the maximum. However, in the case of ionic surfactants, the main effect of the cosolvent is considered to be the change of the dielectric constant of the medium, which in turn affects the electrostatic interaction in solution.39 The glycerol dielectric constant (r ) 42.5) is substantially lower than that of water (r ) 78.5); consequently, increasing the glycerol concentration enhances the electrostatic interactions in solution, which opposes the self-aggregation of surfactant molecules.40 Furthermore, the increased repulsion among the SDS anionic headgroups also causes an increase of the micellar curvature, leading to the formation of smaller aggregates. Hence, the extent of glycerol effects and the mechanism through which they are supposed to act depend on the considered surfactant. Figure 6 shows the representative dynamic rheological data (elastic modulus, G′, and loss modulus, G′′), as functions of frequency, ω, for two samples containing 0.15 M SDS and mixing fractions of C12EO3, X ) 0.65, in different glycerol contents in the glycerol/water mixed solvent. The data clearly reveal the viscoelastic response of these samples. That is, at high ω, the samples show elastic behavior, with G′ tending to a plateau and dominating over G′′, while, at low ω, the samples show viscous behavior. The crossover point shifts to higher frequency as the glycerol content is increased from 10 wt % to 25 wt %, indicating a decrease in relaxation time, τR, which in turn indicates the decrease in micellar length. Effect of Temperature. Plots of η0 as a function of temperature for 0.15 M SDS at X ) 0.63 in glycerol/water mixed solvent ratio 25/75 and 0.06 M ChEO15 at X ) 0.20, 0.22, and 0.27 in glycerol/water mixed solvent ratio 50/50 are shown in parts a and b of Figure 7, respectively. In the case of the SDS/C12EO3 surfactant system (Figure 7a), the behavior is typical (at least qualitatively) of ionic surfactant systems; namely, when a wormlike micellar solution is heated, the micellar contour length, L, decays with temperature according to36

L ) φ1/2 exp

[ ] Ec 2kBT

(15)

where φ is the volume fraction of worms, Ec is the end-cap



Figure 7. Variation of η0 as a function of temperature for (a) 0.15 M SDS in glycerol/water mixed solvent ratio 25/75 at the mixing fraction of C12EO3, X ) 0.63, and (b) 0.06 M ChEO15 in glycerol/water mixed solvent ratio 50/50 at the mixing fraction of C12EO3, X ) 0.20, 0.22, and 0.27. Lines are only visual guides.

energy (i.e., the excess energy associated with the hemispherical caps compared to the cylindrical body of the worm), and kB is Boltzmann’s constant. The reason for this behavior is that, at higher temperatures, surfactant unimers can hop more rapidly between the cylindrical body and the hemispherical end-cap of the worm.36 Thus, because the end-cap constraint is less severe at higher temperatures, the worms grow to a lesser extent. The reduction in micellar length, in turn, leads to a decrease in η0 and the relaxation time, τR. On the other hand, as shown in Figure 7b, for 0.06 M ChEO15/ C12EO3 at fixed X, the viscosity increases with increasing temperature up to a certain limit, it then decreases, and finally phase separation takes place. Therefore, eq 15 is not valid in this case. The position of the maxima depends upon C12EO3 concentration, X. Enhanced one-dimensional micellar growth with increasing temperature is consistent with the fact that with increasing temperature as decreases gradually due to the dehydration of EO groups, and such changes would reduce the spontaneous curvature and increase end-cap energy. One important feature here is that worm micelles seem to exist at low temperatures (down to 0 °C) and high glycerol concentrations (up to 50 wt %) in the case of 0.06 M ChEO15/C12EO3 at X ) 0.27, which is interesting from the point of view of applications such as drag-reducing fluids for cooling systems. From a comparison of the cosolvent effects with temperature effects on 0.06 M ChEO15/C12EO3 mixed systems, we can see that the addition of formamide causes a micelle structural change similar to that caused by a reduction in temperature. On the contrary, the addition of glycerol into water leads to a micelle structure change comparable to that caused by an increase of temperature. Micellar growth is also observed with an increase in temperature in plain water. From the above results, we can say that temperature and cosolvents can act in tandem or in opposition. Figure 8 shows representative dynamic rheological data for 0.15 M SDS at the mixing fraction of C12EO3, X ) 0.63, in glycerol/water mixed solvent ratio 25/75 at 5, 10, 15, 20, 25, and 30 °C. Fits are shown at 5 °C to a Maxwell model, given by eqs 9 and 10. As the temperature increases, the entire frequency spectrum moves to the right, i.e., to higher frequencies or shorter time scales, but at the same time, the plateau modulus, G0, remains constant. The shift in crossover frequency, ωc, to higher values means that the relaxation time decreases with temperature.41-43 Figure 9 shows the variation of rheological parameters G0 and τR with temperature for the corresponding mixed systems. In 0.15 M SDS, the τR values clearly decrease with an increase in temperature (Figure 9a). The scission and recombination kinetics determine the average length of the wormlike micelles.36 As

Figure 8. Variation of the elastic modulus, G′ (circles), and viscous modulus, G′′ (squares), as a function of oscillatory shear frequency, ω, at different temperatures for 0.15 M SDS in glycerol/water mixed solvent ratio 25/75 (expressed in wt %) at mixing fractions of C12EO3, X ) 0.63. The solid lines are best fits to eqs 9 and 10.

mentioned earlier, the micellar contour length predicted to decrease with temperature according to eq 15 would affect the dynamics of micellar stress relaxation. Thus, as the worms grow shorter, they will relax faster. The plateau modulus, G0, is related to the mesh size, ξ, of the entangled network according to G0 ) kBT/ξ3. Since G0 remains constant as a function of temperature, it seems that there is a certain increase in the mesh size (lower network density), contrary to that stated by Tung et al.44 For 0.06 M ChEO15/C12EO3 (Figure 9b), with increasing temperature, G0 increases within the composition range studied, which is expected from the increase in network density (shorter ξ) as micelles grow upon increasing temperature. The trends of τR-T plots at different X values appear essentially similar to those of η0-T plots (Figure 7b). τR at first increases along with the increasing G0 as temperature increases, which may be associated with the increase in the micellar contour length. However, with a successive increase in the temperature, τR decreases, indicating a structural change in the micellar network (formation of micellar joints) that allows a faster mechanism of stress relaxation. The magnitude of G0 and τR increases with an increase in C12EO3 content (indicating micellar growth). SAXS Measurements. SAXS measurement was carried out to investigate the structure of aggregates in the 0.06 M ChEO15/ C12EO3 systems in water as well as in mixed solvent of water with glycerol and formamide to provide supportive evidence for rheological data. The SAXS data were analyzed by the generalized indirect Fourier transformation (GIFT) method,45-47 which determines the form factor and the structure factor simultaneously from the scattering data without any assumption


Figure 9. Variation of the plateau modulus, G0, and relaxation time, τR, for (a) 0.15 M SDS in glycerol/water mixed solvent ratio 25/75 at the mixing fraction of C12EO3, X ) 0.63, and (b) 0.06 M ChEO15 in glycerol/water mixed solvent ratio 50/50 at the mixing fraction of C12EO3, X ) 0.20, 0.22, and 0.27. Lines are only visual guides.

for the form factor, P(q). In the cases of colloidal systems, P(q) can be fixed from the measurement of dilute solutions or theoretical calculation, and the experimental structure factor, S(q)exptl, can be deduced by dividing the normalized scattered intensity, I(q)/c (where c is the surfactant concentration), by the defined P(q) value.48 However, for self-assembled systems such as micellar solutions, P(q) is a function of concentration and temperature, and is to be determined from experiments. In the GIFT analysis of SAXS data, we have used the averaged structure factor model for a hard sphere (HS) interaction, S(q)av,49,50 which considers the Gaussian distribution of the interaction radius, σ, for individual monodisperse systems for polydispersity, µ, and a Percus-Yevick (PY) closure relation to solve the Ornstein-Zernike (OZ) equation. The detailed theoretical description on the method has been reported elsewhere.51, Figure 10 shows the scattering functions, I(q), and the corresponding pair-distance distribution functions (PDDFs), p(r), for the 0.06 M ChEO15/C12EO3 (X ) 0.22) in pure water as a function of temperature. With increasing temperature, the minimum in the scattering function is shifting toward the lower q side. Micellar growth in the homogeneous monodisperse system leads to this kind of behavior in the scattering function. The temperature effect on the micellar aggregates is more clearly reflected from the PDDF curves. The PDDF curve at 10 °C exhibits typical features of core-shell type globular particles with maximum dimension of ∼14 nm. Increasing temperature favors one-dimensional micellar growth, and elongated particles are observed at 25 and 35 °C. The maximum dimension of the micelles, Dmax, extracted by the GIFT method shown in the PDDF curves may not be the exact dimension of the micelles. This is because the addition of low contrast cosurfactant C12EO3 to the ChEO15 aqueous system reduces the overall contrast of the system, and therefore, it is difficult to estimate the real size of the micelles by SAXS. Sato et al.51 have studied the

Varade et al. phase and self-organized structures in water/poly(oxyethylene) cholesteryl ether systems. They found the core-shell type of globular micelles with maximum dimensions of ∼13 nm in the ChEO15/water system at 25 °C. The surfactant concentration could not modulate the shape and size of the micellar aggregates appreciably within the studied surfactant concentration limit of 1-20%. Moreover, Moitzi et al.52 by a SANS study have shown that addition of C12EO3 to the cholesterol ether/water system favors the one-dimensional micellar growth, forming viscoelastic wormlike micellar solutions, and they have presented the micelles with maximum dimensions of a few tens of nanometers to hundreds of nanometers. Thus, in the present system, also the real size of the micelles could be of a few tens to hundreds of nanometers. If we compare the micellar size of the present mixed surfactant system with that reported in ref 51 for the ChEO15/water system, the observed dimension of the micelles, i.e., Dmax ∼ 16 nm, indicates the micellar growth induced by the C12EO3. However, at present, we are not focused to determine the exact micellar size. Our main strategy is to investigate the temperature-induced microstructure changes and its impact on the rheological behavior in water and the mixed solvent systems. As shown in Figure 10b, all PDDF curves exhibit a pronounced local maximum and minimum in the low r side, indicating the presence of a typical core-shell type of structure in the studied system. This maximum and minimum in the low r region is the contribution of the negative and positive electron density from the hydrophobic core and hydrophilic shell, respectively, which gives quantitative information about the internal structure of the micellar aggregates. The inflection point between the local maximum and minimum, and that after the local minimum, semiquantitatively gives the cross-sectional radius and diameter of the micellar core. Those points do not change much with temperature; namely, the cross-sectional diameter seems to remain constant, indicating that micellar growth is one-dimensional. The local maximum and minimum in the p(r) functions is the contribution of the low contrast cosurfactant, C12EO3. No such behavior in the PDDF curves is seen in the absence of the C12EO3 (see ref 51). We have investigated the influence of temperature on the 0.06 M ChEO15/C12EO3 system in the glycerol/water mixed solvent. When glycerol is added to water, the average electron density of the solvent will increase, thus decreasing the overall contrast of the system. Under such conditions, it is difficult to estimate the core-shell structure of the particle. Nevertheless, it is possible to see the core structure. In Figure 11, we present the scattering functions and the PDDF curves as a function of temperature for the system at a glycerol/water mixing ratio of 50/50. The shape of the scattering intensity changes significantly as compared with plain water, reflecting the changes in the micellar structure. As can be seen from Figure 10a, the forward scattering intensity, I(qf0), increases with increasing temperature and follows I(q) ∝ q-1 behavior at high temperature. Micellar growth from short to long rodlike particles should lead to this kind of behavior in the scattering function (Figure 11a).53 Glycerol causes a major change in the structure mainly in terms of the shape of the aggregates. Upon addition of 50% glycerol, nearly globular core-shell type particles present in the aqueous system transform into the rodlike particles; it shows one-dimensional growth with an increase in temperature, keeping the cross-section diameter virtually constant (indicated by a broken line in Figure 11b). Microstructure changes induced by glycerol in the mixed solvent system can be clearly seen from the shape of the p(r) functions. For example, at 10 °C, p(r) is symmetric (at high q) in the absence of glycerol, as seen in Figure 10b, suggesting quasi-spherical micelles. On the other



Figure 10. (a) Scattering functions, I(q), of the 0.06 M ChEO15/C12EO3 (X ) 0.22) aqueous solutions as a function of temperatures10 °C (circles), 25 °C (squares), and 35 °C (triangles)sobtained in absolute units. (b) The corresponding pair-distance distribution functions, p(r), extracted from the GIFT analysis of the scattering functions. The broken and solid lines in panel a represent the form factor and GIFT fit, respectively.

Figure 11. (a) Scattering functions, I(q), of the 0.06 M ChEO15/C12EO3 (X ) 0.22) system with a glycerol/water mixing ratio of 50/50 as a function of temperatures10 °C (circles), 25 °C (squares), and 35 °C (triangles)sobtained in absolute units. (b) The corresponding pair-distance distribution functions, p(r), extracted from the GIFT calculation.

hand, at the same temperature and in the presence of glycerol, p(r) is not symmetric as for long micelles, which indicates that addition of glycerol at constant temperature also induces micellar growth. The modulation in the structure of the particle in the mixed solvent system is the contribution of glycerol, which decreases the degree of hydration of the ethylene oxide head group of the surfactant. Due to strong hydrogen bonding between water and glycerol molecules, the volume fraction of water at the surfactant head group decreases and the lipophilic character of the surfactant consequently increases. As a result of smaller head groups, the surfactant molecules tend to form cylindrical aggregates. The increase of zero-shear viscosity with increasing glycerol content at a fixed amount of surfactant/ cosurfactant ratio (see Figure 2) is thus attributed to the microstructure change of the aggregates. Temperature has a major influence on the phase behavior and self-organized microstructure on the poly(oxyethylene) type nonionic surfactant systems. These types of surfactants in aqueous systems show a miscibility gap at high temperature (clouding behavior) due to dehydration of the water molecules. With an increase in temperature, the hydrophilic-lipophilic interface of the micelles becomes dry due to thermal dehydration of the water molecules, and hence, the micelles grow due to a decrease in the effective cross-sectional area of the surfactant head group. In the present mixed solvent system, the onset of micellar growth with temperature is in good agreement with the rheological data, namely, increase of viscosity with temperature. However, in the viscosity-temperature plot, we observed a viscosity maximum; i.e., after a certain temperature (∼25 °C), the viscosity decreases with further increasing temperature (see Figure 7). Nevertheless, the SAXS data

unambiguously show a continuous increase of the micellar size with temperature. This indicates that the decrease of viscosity with temperature after the viscosity maximum may be due to some other major changes in the structure of the particles such as formation of micellar joints or branching. Next, we have studied structural transition of the micellar aggregates for 0.06 M ChEO15/C12EO3 in various ratios of formamide/water mixed solvent at 25 °C. We are able to detect the changes in the dimensions of the micelles, although the system has low contrast. In comparison to glycerol, formamide has the opposite effect on the geometry of the micellar aggregates (as revealed from rheology). The geometry of the micellar aggregates of 0.06 M ChEO15/C12EO3 undergoes a rod-sphere transition, forming short, globular micelles in the presence of formamide. The scattering functions and the corresponding PDDFs curves for the 0.06 M ChEO15/C12EO3 (X ) 0.28) system are presented in Figure 12. As we can clearly see from the scattering curves, with an increase in formamide content, the scattering intensity in the low q region decreases, indicating the strong repulsive interactions.48 When the formamide content approaches 50%, the shape of the scattering intensity differs significantly and the forward scattering intensity decreases sharply compared to the system with less formamide. Such dramatic changes in the scattering intensity may be caused by the worse contrast of the system. The effect of formamide/water mixing ratio on the dimensions of the micellar aggregates is clearly reflected in the PDDF curves. All of the PDDF curves exhibit a local maximum and minimum in the low r side, which is the signature of the coreshell type of micellar structure in the system. In the absence of formamide, elongated rodlike micelles with maximum dimen-


Varade et al.

Figure 12. (a) Scattering functions, I(q), of the 0.06 M ChEO15/C12EO3 (X ) 0.28) system in various formamide/water mixed solvents obtained in absolute units. (b) The corresponding pair-distance distribution functions, p(r). The broken and solid lines in panel a represent the form factor and GIFT fit, respectively, and the arrow in panel b indicates the maximum dimension of the micelles.

Figure 13. (a) Correlation function ge ) g2(t) - 1 and (b) DLS relaxation time as a function of the inverse of the scattering vector for the 0.06 M ChEO15/C12EO3 system at X ) 0.22 and 25 °C in pure water (circles), glycerol/water ) 50/50 (squares), and formamide/water ) 50/50 (triangles).

sions of ∼18 nm are observed in the 0.06 M ChEO15/C12EO3 (X ) 0.28) system. However, when 25% formamide is added into the system, the micellar size is significantly reduced and the micellar disruption continues with increasing formamide content in the mixed solvent. The decrease in the micellar length with the formamide concentration supports the rheological data, namely, decrease of steady shear viscosity with increasing mixing ratio of formamide/water at a fixed concentration of the surfactants (see Figure 2). DLS Measurements. To gather further evidence on the solvent-induced morphological changes, DLS measurements were taken from samples in solvents of different quality, and representative results are shown in Figure 13. Only single decay can be clearly resolved in Figure 13a, and such a decay shifts to longer times in the presence of glycerol and to shorter times in the presence of formamide, indicating changes in the relaxation processes. The relaxation time, τ (τ ) 1/Γ, eq 6), taken from the main peak of the distribution calculated by the CONTIN method is plotted in Figure 13b as a function of the inverse of the square of the scattering vector, q-2. A log-log representation of the experimental data gives straight lines with a slope close to 1, in agreement with eq 7, which indicates that the main relaxation process comes from diffusive modes. We cannot rule out completely the presence of other modes associated with longer relaxation times, especially in glycerol systems, but they were not clearly resolved in the CONTIN distribution, which prevented further analysis. Compared to the system in pure water, the fitting line shifts to higher τ (slower relaxation) upon addition of glycerol and to lower τ (faster relaxation) when formamide is added, in line with the glycerolinduced micellar growth and formamide-induced micellar

TABLE 1: Effective Diffusion Coefficients and Apparent Hydrodynamic Radius in Solvents of Different Quality for 0.06 M ChEO15 Systems at X ) 0.22 and 25 °C solvent

Deff (m2/s)

RH (nm)

water glycerol/water ) 50/50 formamide/water ) 50/50

1.8 × 1.4 × 10 -12 2.6 × 10 -11

12 30 6

10 -11

disruption evidenced by rheometry and SAXS. This is more clearly observed in Table 1, in which the apparent hydrodynamic radius has been calculated by the Stokes-Einstein equation. Although RH values might not represent the actual micellar size due to the effect of interactions on the diffusion coefficient, there is a clear tendency: larger micelles are formed upon addition of glycerol, and smaller micelles are present when formamide is added. Conclusions Viscoelastic solutions of wormlike micelles are formed in an aqueous solution of hydrophilic nonionic surfactant, ChEO15, and anionic SDS in the presence of a small amount of lipophilic amphiphile, C12EO3. The effects of polar solvents such as glycerol and formamide on the structure of wormlike micelles in water have been investigated as a function of the cosolvent content in the mixed solvent and solution temperature using rheology, SAXS, and DLS. The addition of formamide to water causes micellar disruption, which is attributed to lower hydrocarbon-solvent interfacial tension and a reduction in the solvophobic effect, while the progressive increase of glycerol in water-glycerol mixed solvent reduces the hydration of surfactant head groups and induces smaller surfactant surface

Wormlike Micelles in Mixed Surfactant Systems areas, which in turn causes micellar growth. Increasing the temperature increases the extent of one-dimensional micellar growth in ChEO15/C12EO3, which is mainly attributed to the decrease in the spontaneous curvature of the aggregates. The temperature range in which viscoelastic worm micelles are present can be tuned with the amount of nonionic cosurfactant, which is an important finding for possible applications. Acknowledgment. D.V. thanks Japan Society for Promotion of Science (JSPS) for financial support. 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. Fruitful suggestion on SAXS measurements from Dr. Takaaki Sato (Waseda University) is gratefully acknowledged. References and Notes (1) Walker, L. M. Curr. Opin. Colloid Interface Sci. 2001, 6, 451. (2) Yang, J. Curr. Opin. Colloid Interface Sci. 2002, 7, 276. (3) Acharya, D. P.; Hattori, K.; Sakai, T.; Kunieda, H. Langmuir 2003, 19, 9173. (4) Kalur, G. C.; Frounfelker, B. D.; Cipriano, B. H.; Norman, A. I.; Raghavan, S. R. Langmuir 2005, 21, 10998. (5) Shashkina, J. A.; Philippova, O. E.; Zaroslov, Y. D.; Khokhlov, A. R.; Pryakhina, T. A.; Blagodatskikh, I. V. Langmuir 2005, 21, 1524. (6) Couillet, I.; Hughes, T.; Maitland, G.; Candau, F.; Jean Candau, S. Langmuir 2004, 20, 99541. (7) Raghavan, S. R.; Edlund, H.; Kaler, E. W. Langmuir 2002, 18, 1056. (8) Varade, D.; Ushiyama, K.; Shrestha, L. K.; Aramaki, K. J. Colloid Interface Sci. 2007, 312, 489. (9) Acharya, D.; Sharma, S. C.; Rodrı´guez, C.; Aramaki, K. J. Phys. Chem. B 2006, 110, 20224. (10) Rodrı´guez, C.; Aramaki, K.; Tanaka, Y.; Lo´pez-Quintela, M. A.; Ishitobi, M.; Kunieda, H. J. Colloid Interface Sci. 2005, 291, 560. (11) Nagarajan, R.; Wang, C.-C. Langmuir 2000, 16, 5242. (12) Auvray, X.; Petipas, C.; Anthore, R.; Rico, I.; Lattes, A. J. Phys. Chem. 1989, 93, 7458. (13) Aramaki, K.; Olsson, U.; Yamaguchi, Y.; Kunieda, H. Langmuir 1999, 15, 6226. (14) Lin, Z.; Davis, H. T.; Scriven, L. E. Langmuir 1996, 12, 5489. (15) Alexandridis, P.; Yang, L. Macromolecules 2000, 33, 5574. (16) Ivanova, R.; Lindman, B.; Alexandridis, P. Langmuir 2000, 16, 3660. (17) Kumar, A.; Kunieda, H.; Vazquez, C.; Lopez-Quintela, M. A. Langmuir 2001, 17, 7245. (18) Martino, A.; Kaler, E. W. Colloids Surf., A 1995, 99, 91. (19) Rodrı´guez, C.; Shigeta, K.; Kunieda, H. J. Colloid Interface Sci. 2000, 223, 197.

J. Phys. Chem. B, Vol. 111, No. 35, 2007 10447 (20) Perche, T.; Auvray, X.; Petipas, C.; Anthore, R. Langmuir 1997, 13, 1475. (21) Iwanaga, T.; Suzuki, M.; Kunieda, H. Langmuir 1998, 14, 5775. (22) Penfold, J.; Staples, E.; Tucker, I.; Cummins, P. J. Colloid Interface Sci. 1997, 185, 424. (23) Zhang, Y.; Schmidt, J.; Talmon, Y.; Zakin, J. L. J. Colloid Interface Sci. 2005, 286, 696. (24) Acharya, D. P.; Kunieda, H. J. Phys. Chem. B 2003, 107, 10168. (25) Acharya, D. P.; Sato, T.; Kaneko, M.; Singh, Y.; Kunieda, H. J. Phys. Chem. B 2006, 110, 754. (26) Glatter, O. J. Appl. Crystallogr. 1977, 10, 415. (27) Glatter, O. J. Appl. Crystallogr. 1981, 14, 101. (28) Glatter, O. Prog. Colloid Polym. Sci. 1991, 84, 46. (29) Strey, R.; Glatter, O.; Schubert, K.-V.; Kaler, E. W. J. Chem. Phys. 1996, 105, 1175. (30) Shrestha, L. K.; Sato, T.; Acharya, D. P.; Iwanaga, T.; Aramaki, K.; Kunieda, H. J. Phys. Chem. B 2006, 110, 12266. (31) Shrestha, L. K.; Sato, T.; Aramaki, K. J. Phys. Chem. B 2007, 111, 1664. (32) Shrestha, L. K.; Sato, T.; Aramaki, K. Langmuir 2007, 23, 6606. (33) Berne, B. J.; Pecora, R. Dynamic Light Scattering with Applications to Chemistry, Biology, and Physics; Robert E. Krieger: Malabar, FL, 1990. (34) Lin, Y.; Alexandridis, P. J. Phys. Chem. B 2002, 106, 12124. (35) Lequeux, F. Europhys. Lett. 1992, 19, 675. (36) Cates, M. E.; Candau, S. J. J. Phys.: Condens. Matter 1990, 2, 6869. (37) Khatory, A.; Lequeux, F.; Candau, S. J. Langmuir 1993, 9, 1456. (38) Hassan, P. A.; Candau, S. J.; Kern, F.; Manohar, C. Langmuir 1998, 14, 6025. (39) Palepu, R.; Gharibi, H.; Bloor, D. M.; Wyn-Jones, E. Langmuir 1993, 9, 110. (40) D’Errico, G.; Ciccarelli, D.; Ortona, O. J. Colloid Interface Sci. 2005, 286, 747. (41) Kern, F.; Zana, R.; Candau, S. J. Langmuir 1991, 7, 1344. (42) Fischer, P.; Rehage, H. Langmuir 1997, 13, 7012. (43) Raghavan, S. R.; Kaler, E. W. Langmuir 2001, 17, 300. (44) Tung, S. H.; Huang, Y.-E.; Raghavan, S. R. Langmuir 2007, 23, 372. (45) Brunner-Popela, J.; Glatter, O. J. Appl. Crystallogr. 1997, 30, 431. (46) Weyerich, B.; Brunner-Popela, J.; Glatter, O. J. Appl. Crystallogr. 1999, 32, 197. (47) Brunner-Popela, J.; Mittelbach, R.; Strey, R.; Schubert, K.-V.; Kaler, E. W.; Glatter, O. J. Chem. Phys. 1999, 21, 10623. (48) Stradner, A.; Sedgwick, H.; Cardinaux, F.; Poon, C. K. W.; Egelhaaf, S. U.; Schurtenberger, P. Nature 2004, 432, 492. (49) Pusey, P. N.; Fijnaut, H. M.; Vrijm, A. J. Chem. Phys. 1982, 77, 4270. (50) Salgi, P.; Rajagopolan, R. AdV. Colloid Interface Sci. 1993, 43, 169. (51) Sato, T.; Hossain, Md. K.; Acharya, D. P.; Glatter, O.; Chiba, A.; Kunieda, H. J. Phys. Chem. B 2004, 108, 12927. (52) Moitzi, C.; Freiberger, N.; Glatter, O. J. Phys. Chem. B 2005, 109, 16161. (53) Glatter, O.; Fritz, G.; Lindner, H.; Brunner-Popela, J.; Mittelbach, R.; Strey, R.; Egelhaaf, S. U. Langmuir 2000, 16, 8692.

Wormlike Micelles in Mixed Surfactant Systems: Effect of Cosolvents

Recommend Documents