Viscoelastic Wormlike Micellar Solutions Made from Nonionic

Viscoelastic Wormlike Micellar Solutions Made from Nonionic Surfactants: Structural. Investigations by ... Christian Moitzi, Norbert Freiberger, and O...
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J. Phys. Chem. B 2005, 109, 16161-16168

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Viscoelastic Wormlike Micellar Solutions Made from Nonionic Surfactants: Structural Investigations by SANS and DLS Christian Moitzi, Norbert Freiberger, and Otto Glatter* Institut fu¨r Chemie, UniVersita¨t Graz, Heinrichstrasse 28, A-8010 Graz, Austria ReceiVed: December 22, 2004; In Final Form: June 10, 2005

A highly viscoelastic micellar solution of nonionic surfactants in a dilute region was recently reported. A transient network of wormlike micelles formed with the addition of short-EO-chain poly(oxyethylene) dodecyl ether surfactants (C12EOj, j ) 1-4) to poly(oxyethylene) cholesteryl ethers (ChEOm, m ) 10 and 15). A gradual increase in micellar length with an increasing C12EOj concentration was assumed from the results of model calculations and rheological measurements. We report in this study the results of structural investigations with small-angle neutron scattering (SANS) to confirm this assumption. Tuning from spherical to wormlike and to locally flat structures can be achieved by way of three methods. One can either increase the C12EOj concentration or decrease j (smaller headgroup size) at a fixed concentration of C12EOj. The third possibility is to increase the temperature at a fixed composition. All three methods result in the same structural transition. The formation of a transient network of wormlike micelles analogous to polymer solutions can be observed with dynamic light scattering (DLS). A stretched exponential approach was applied to fit the correlation functions.

Introduction Surfactant molecules in aqueous media self-assemble to form a variety of microstructures such as spherical micelles, cylindrical micelles, vesicles, and liquid crystals. Some cationic surfactants,1-4 such as hexadecyltrimethylammonium bromide (CTAB), as well as some nonionic5-9 and anionic surfactant systems can self-assemble into long, flexible wormlike micelles under certain conditions of salinity, temperature, the presence of counterions, etc. The entanglement of these micelles into a transient network imparts useful viscoelastic properties to the surfactant solutions, which are analogous to those observed in solutions of flexible polymers. However, unlike ordinary polymers, wormlike micelles are in equilibrium with their monomers, and micellar chains can reversibly break and recombine and are therefore also called “living polymers”. Most of the literature reports the formation of viscoelastic wormlike micelles in cationic systems in the presence of strongly binding counterions. A highly viscoelastic solution of nonionic surfactants in a dilute region was recently reported by Kunieda and co-workers.10-12 They are of particular interest in basic research as well as within practical applications. The systems are relatively insensitive to ionic strength and are biocompatible. They are widely used in pharmaceutical and cosmetic formulations. It has been indicated by Israelachvili13,14 that the intrinsic geometry of an individual amphiphile has a strong influence on the final shape of the micelle. The various shapes of micellar aggregates can be characterized by the dimensionless critical packing parameter cpp ) υ/a0lc, where a0 is the effective headgroup area and υ and lc are the volume and the critical chain length of the hydrophobic chain, respectively. Spherical micelles, cylindrical micelles, and bilayers are formed for cpp ∼ 1/3, 1/3 < cpp < 1/2, and 1/2 < cpp < 1, respectively. Acharya and Kunieda10 investigated the phase properties and rheological * Corresponding author. E-mail: [email protected].

behavior of mixtures of poly(oxyethylene) cholesteryl ethers (ChEOm, m ) 10 and 15) and short-chain poly(oxyethylene) dodecyl ethers (C12EOj, j ) 1-4) at room temperature. The addition of C12EOj initiates the sphere-to-rod transition by reducing the mean interfacial curvature as a result of its relatively small headgroup size. Acharya and Kunieda also reported the effect of the number of oxyethylene groups of both surfactants (varying m and j). It was found that, with decreasing headgroup size, the unidimensional micellar growth is favored. Another possibility of decreasing the interfacial curvature of aqueous nonionic systems, in general, is to increase the temperature and thereby reducing the hydration of the oxyethylene groups.15 The cholesteryl frame is more bulky and rigid than a conventional hydrocarbon chain. Hence, that is one reason as to why the formation of wormlike micelles is attributed to its unique hydrophobic part. Except from some small-angle X-ray scattering (SAXS) measurements on the binary ChEOm/water system from Sato et al.,12 only indirect experimental methods such as rheology and dynamic light scattering (DLS) were used to confirm the gradual increase in the length of the micelles. In this study, we report the structural investigations mainly by small-angle neutron scattering (SANS) on the transition from a sphere to a rod and further to planar structures in ChEO10/ C12EOj/water systems. SANS is more appropriate for this study than SAXS because of the higher contrast between the particles and the solvent. We report the influence of C12EOj concentration, the number of oxyethylene groups j, and temperature on micellar growth. We also show that it is possible to evaluate the DLS data of viscoelastic solutions of wormlike micelles with a stretched exponential approach analogous to polymer solutions. Theory Indirect Fourier Transformation and Deconvolution. The methodology for analyzing small-angle scattering data using

10.1021/jp0441691 CCC: $30.25 © 2005 American Chemical Society Published on Web 07/29/2005

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indirect Fourier transformation, followed by deconvolution, has been described in detail elsewhere.16-18 The discussion here will only describe the main ideas, as there was a similar analysis described in the references 19 and 20. For a particle of an arbitrary shape with a scattering density difference of ∆F(r), the pair distance distribution function p(r) (PDDF) is given by

p(r) ) r2∆F˜ 2(r)

(1)

where ∆F˜ 2(r) is the convolution square of ∆F(r) averaged for all directions in space. This averaging causes no loss of information in the case of particles with special symmetry, where the neutron scattering length difference (SANS) or the electron density difference (SAXS), ∆Fx(r), is only a function of the radial position. Here, the subscript x refers to the shape of the particle (x ) s for a sphere, c for a circular cylinder, t for a symmetric bilayer). The PDDF is related to the scattered intensity I(q) by the Fourier transformation and enables the determination of the overall shape and size of the scattering objects.21

I(q) ) 4π

∫0∞ p(r)

sin (qr) dr qr

θ 4π sin λ 2

()

(3)

(4)

The cross-section PDDF can be calculated from the scattered intensity via

I(q)q ) πLIc(q) ) 2π2L

∫0∞ pc(r)J0(qr)dr

pt(r) ) ∆F˜ 2t (r)

(6)

and the thickness PDDF is related to the scattered intensity of the thickness It(q) by

I(q)q2 ) 2πAIt(q) ) 4πA

∫0∞ pt(r) cos(qr)dr

(7)

The indirect transformation of eq 7 produces the thickness PDDF, pt(r), which can be deconvoluted to obtain ∆Ft(r). Experimental Section

where λ is the wavelength of the incident radiation, and θ is the angle between the scattered and incident beam. In the case of spherical geometry, the deconvolution of the PDDF gives the radial contrast profile ∆Fs(r). If the scattering objects (micelles) are cylindrical and ∆Fc(r) is only a function of the radial position within the cross section, the situation is similar to the one with spheres. The Fourier transformation of the intensity curve again yields the overall PDDF. The axial length of the cylinder is responsible for a linear region of p(r) for large r, and the distance at which the PDDF decays to zero provides a measure of the length of the micelles. The slope of the linear portion is directly related to the square of the average contrast between the particle and the solvent. If the cylinder is at least 3 times longer than the cross-section diameter, it is possible to study the radial structure of the micelle. The radial profile ∆Fc(r) is related to the PDDF for the cross section pc(r) by22

pc(r) ) r∆F˜ 2c (r)

pt(r) is given by22

(2)

where q is the magnitude of the scattering vector q, defined as

q)

SCHEME 1: Schematic Molecular Structure of Poly(oxyethylene) Cholesteryl Ether (ChEO10).

(5)

where J0(qr) is the zero-order Bessel function. The indirect transformation of eq 5 yields pc(r), which is then used to calculate ∆Fc(r) via the deconvolution technique. The pair distance distribution functions for a vesicle (lamellar) structure show oscillations at large values of r if the vesicles are monodisperse. In most cases, though, the vesicles are polydisperse, and the oscillations are smeared out. The calculation of the scattering contrast profile is similar to that for cylinders. Assuming that the contrast difference ∆Ft(r) within the bilayer is only a function of distance from the midplane, ∆Ft(r) can be evaluated. The thickness pair distribution function

Materials. Poly(oxyethylene) cholesteryl ether (ChEO10), purchased from Nihon Emulsion Co., Japan, and poly(oxyethylene) dodecyl ethers (C12EOj, j ) 2-4), from Fluka, Switzerland were used as received. The schematic molecular structure of ChEO10 is shown in Scheme 1. The surfactant solutions for SANS experiments were made using D2O (99.96% deuterated, from Aldrich, Germany). Samples for SAXS and DLS were made using distilled H2O. SANS. SANS experiments were conducted at the Institut Laue-Langevin ILL in Grenoble, France, as well as the Forschungszentrum Ju¨lich, Germany. At the ILL in Grenoble (instrument D11), the wavelength of radiation λ was 0.7 nm, with a spread in wavelength ∆λ/λ of 10% fwhm. Data were collected at detector (64 × 64 pixels, each pixel 1 cm2) distances of 2, 8, and 20 m from the sample. Samples were held in 2-mm-thick quartz cells in a temperaturecontrolled chamber. The raw data were corrected for detector efficiency, scattering from the empty cell, and background radiation and placed on an absolute scale using standards provided by the ILL. At the Forschungszentrum Ju¨lich (instrument KWS-1), the wavelength of radiation λ was 0.7 nm, with a spread in wavelength ∆λ/λ of 20% fwhm. Data were collected at the detector (128 × 128 pixels, each pixel 0.22 cm2) distances of 2, 8, and 20 m from the sample. Samples were held in 2-mmthick quartz cells in a temperature-controlled chamber. The raw data were corrected for detector efficiency, scattering from the empty cell, and background radiation and placed on absolute scale using standards provided by the Forschungszentrum. SAXS. The SAXS equipment was a SAXSess camera23 (Anton-Paar, Graz, Austria) using an X-ray generator (Philips, PW 1730/10) operated at 40 kV and 50 mA with a sealed-tube Cu anode. A Go¨bel mirror was used to convert the divergent polychromatic X-ray beam into a focused line-shaped beam of Cu KR radiation (λ ) 0.154 nm). The 2D scattering pattern was recorded by an imaging-plate detector (model Fuji BAS1800 from Raytest, Straubenhardt, Germany) and integrated into the one-dimensional scattering function I(q) using SAXSQuant software (Anton-Paar). The samples were filled at room temperature into the sample holder (quartz capillary in a metal

Viscoelastic Wormlike Micellar Solutions block, temperature controlled by a Peltier element, (0.1 K) and equilibrated at each experimental temperature for at least 10 min. DLS. The DLS measurements were carried out on a laboratory-built goniometer, which is equipped with single-mode fiber optics and an ALV single-photon detector (ALV-Laser Vertriebsgesellschaft, Langen, Germany) for detection. The samples (in 10-mm cylindrical cuvettes) were immersed in a temperaturecontrolled index match bath (decalin). In addition, polarizers before and after the sample were used. The light source was a Verdi V5 diode laser from Coherent, with a wavelength of 532 nm and a maximum output of 5 W. The data acquisition was performed with an ALV 5000 multiple τ digital correlator. The ALV-5000/E software package was used to record and to store the correlation functions. Results and Discussion Small Angle Scattering. The primary results are the experimental SANS and SAXS curves. The geometry of the scattering objects is not assumed but is determined from the pair distribution function p(r) that is obtained from the inverse Fourier transformation of the scattering curve. This operation also includes correction for instrumental broadening. The only assumption of such an analysis is that of monodispersity, namely that all of the particles have the same shape and size. Spherical micelles are the only self-assembled structures that are essentially monodisperse. In the case of cylindrical micelles, it can be assumed that all micelles have about the same diameter, which is usually smaller than the one of spherical micelles that are built up by the same surfactant system, but there is certainly a considerable polydispersity in length. An exponential length distribution is postulated from theory1 and is also in good agreement with some experimental results.24 The length distribution can be seen in the PDDF. If there is no variation in length, the PDDF decays linearly. The distance at which the PDDF decays to zero provides a measure of the length. If there is a polydispersity in length, one obtains the sum of different PDDF functions weighted according to their scattering intensity, i.e., the volume fraction at a fixed concentration. In this case, the decay is not linear but convex. The decay to zero provides information about the maximum length. This value may, however, be biased by the resolution limit (qmin) of the experiment. Such a length polydispersity does not influence the determination of the cross section of the cylindrical micelles. In this contribution, we did not attempt to estimate any length distribution or mean length. For understanding the increase of viscosity, it was sufficient to prove the sphere-to-rod transition and to observe the growth of the length of the cylinders. This growth cannot be directly seen in reciprocal space at low q-values. There is only a more extended q-1 regime visible. Knowledge of the geometry enables the appropriate convolution square root to be taken from the corresponding cross-section distance distribution function. The final results are then the size or local length scale of the aggregates, and the detailed variation of the scattering length density (SANS) or electron density (SAXS) profiles ∆Fx(r) normal to the surface. The obtained data were processed using the program GIFT25-28 for the inverse Fourier transformation and the program DECON29,30 for the deconvolution. The particle interactions were neglected because the volume fraction of the micelles was about 1%, so no structure factor had to be taken into account. It should be noted that samples prepared with D2O and H2O were both measured using X-rays, and the results did not differ significantly. Sphere-to-Rod Transition. The structural transition from nearly spherical to long cylindrical micelles in ChEO10 solutions

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Figure 1. Scattered intensity I(q) from SANS experiments on samples containing 1 wt % of ChEO10 and an increasing concentration of C12EO3. The fractions of C12EO3 are 0 wt % (squares), 0.05 wt % (circles), 0.10 wt % (upward-pointing triangles), and 0.15 wt % (downwardpointing triangles). The top three curves are offset by scale factors for better visibility. A slope of q-1 is indicated for the comparison to the intensity at low values of q.

can be accomplished by way of three different methods. One can either add different amounts of a second surfactant with a smaller packing ratio (C12EO3) or one can add different surfactants with a decreasing headgroup size (C12EO4-C12EO3C12EO2). The third, and maybe most interesting, possibility for application is to increase the temperature at a fixed composition. For all three paths, the viscosity of the sample increases for some orders of magnitudes if the surfactant concentration is high enough to achieve the entanglement of the micelles into a transient network. The mesh size in the highly viscous regime cannot be determined with scattering methods because of the limit of resolution of the experiments (rmax ) π/qmin). In the case of our SANS experiments, the resolution limit was about 115 nm. However, the calculation to slightly larger dimensions is possible qualitatively. In this study, trends were followed up to lengths of 200 nm. The maximum length of the wormlike micelles is expected to be much larger. Figure 1 shows a plot of I(q) vs q for a series of samples containing 1 wt % of ChEO10 and an increasing concentration of C12EO3 (0, 0.05, 0.10, and 0.15 wt %) in D2O. All of the curves were measured at 20 °C with SANS. With increasing C12EO3 concentration, a transition from a horizontal low q regime to a q-1 decay at low q-values occurs, which is a typical signature for a sphere-to-rod transition. However, all of the information about micellar size and shape is derived from the pair distribution function21. The slope of the scattering curve in the low q-regime was only used to confirm the micellar shape. The first step in the analysis of the scattering data is the indirect Fourier transformation, which yields the pair distance distribution function p(r). The most important information obtained from the PDDF is the geometry of the aggregate, by comparing them with theoretically calculated PDDF for a given geometry and contrast profile. Figure 2 shows the calculated PDDF for the SANS curves shown in Figure 1. The p(r) functions indicate that the globular geometry is close to a sphere for ChEO10 alone (see also magnification in Figure 5) and show increasing elongation for an increasing concentration of C12EO3, in agreement with the conclusions drawn by Acharya and Kunieda10 from rheology. The length of the micelles increases from about 17 nm (1 wt % of ChEO10 without C12EO3) to about 120, 160, and 200 nm for 0.05, 0.10, and 0.15 wt % C12EO3, respectively. The decay to large r values is not linear, but is slightly convex. This indicates polydispersity in length. It has to be noted that a length of 200 nm is higher than the resolution

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Figure 2. Pair distance distribution functions p(r) obtained from the intensities shown in Figure 1. The samples contain 1 wt % of ChEO10 and 0 wt % (squares), 0.05 wt % (circles), 0.10 wt % (upward-pointing triangles), and 0.15 wt % (downward-pointing triangles) C12EO3, respectively.

Figure 3. Scattered intensity I(q) from SANS experiments on samples containing 1 wt % of ChEO10 and 0.043 wt % C12EO4 (squares), 0.050 wt % C12EO3 (circles), and 0.057 wt % C12EO2 (upward-pointing triangles), respectively. The different weight fractions of C12EOj in the three samples all correspond to the same molar concentration (∼1.57 mM). The top two curves are shifted by scale factors. A slope of q-1 is indicated for the comparison to the intensity at low values of q.

limit; in fact, the micelles may be even longer. However, the proceeding elongation can be clearly confirmed. This elongation can be understood by the smaller packing ratio of C12EO3 compared to that of ChEO10. The cross-section diameter (inflection point in p(r)) indicated by the arrow, is approximately 12 nm and does not change significantly in this series. In Figures 3 and 4, the same evaluation procedure as described above is shown for a series of samples containing 1 wt % of ChEO10 (∼12 mM) and 1.57 mM of C12EO4, C12EO3, and C12EO2. The molar concentration of 1.57 mM corresponds to 0.057 (j ) 4), 0.05 (j ) 3), and 0.043 wt % (j ) 2) of C12EOj. An elongation can be seen for decreasing headgroup size. The micellar length increases from about 17 nm for C12EO4 to 120 nm for C12EO3, and 160 nm for C12EO2. A magnification of the PDDF of the globular micelles is shown in Figure 5. The addition of C12EO4 has almost no effect on the geometry of the micelles. Acharya and Kunieda10 reported that no gellike phase is formed by the addition of C12EO4. Apparently, C12EO4 has a comparable packing ratio to ChEO10. The easiest way to increase the packing ratio and to achieve the formation of elongated micelles is by increasing the temperature and, therefore, reducing the headgroup size by the dehydration of the oxyethylene groups. The results of a temperature series of SANS measurements on a sample containing 1 wt % of ChEO10 are shown in Figures 6 and 7. A very

Moitzi et al.

Figure 4. Pair distance distribution functions p(r) obtained from the intensities shown in Figure 3. The samples contain 1 wt % of ChEO10 and 0.043 wt % C12EO4 (squares), 0.050 wt % C12EO3 (circles), and 0.057 wt % C12EO2 (upward-pointing triangles), respectively.

Figure 5. Comparison of the pair distance distribution functions p(r) determined from SANS data of a sample containing 1 wt % of ChEO10 (full line) and a sample containing 1 wt % of ChEO10 and 0.043 wt % of C12EO4 (dashed line).

Figure 6. Scattered intensity I(q) from SANS experiments on a sample containing 1 wt % of ChEO10 at varying temperatures (20 °C (squares), 35 °C (circles), 40 °C (upward-pointing triangles), and 55 °C (downward-pointing triangles)). The top three curves are offset by scale factors. A slope of q-1 is indicated for the comparison to the intensity at low values of q.

small elongation can be seen in the temperature range from 20 to 35 °C (from 17 to 25 nm in length). Then the elongation proceeds much faster, and the length becomes 60 nm at 40 °C and 180 nm at 55 °C. Again, the value of 180 nm has to be regarded as an indication for the proceeding elongation and not as an absolute value because it is beyond the resolution limit of the measurement. In Figure 8, the viscosity data of the binary system ChEO10/ water at varying temperatures is shown. At low temperatures,

Viscoelastic Wormlike Micellar Solutions

Figure 7. Pair distance distribution functions p(r) obtained from the intensities shown in Figure 6 (1 wt % of ChEO10 at 20 °C (squares), 35 °C (circles), 40 °C (downward-pointing triangles), and 55 °C (upward-pointing triangles)).

Figure 8. Viscosity of a micellar solution of 1 wt % ChEO10 in water at various temperatures (25 °C (squares), 50 °C (circles), 55 °C (upwardpointing triangles), 60 °C (downward-pointing triangles), 65 °C (diamonds), 70 °C (left-pointing triangles), and 75 °C (right-pointing triangles)).

the viscosity is low. At 40 °C, the micelles are not spherical any more but are already elongated (length about 60 nm, see Figure 7). A slight increase in viscosity can be seen at 55 °C, where the micelles have a length of about 180 nm (Figure 7). At a further increase of the temperature, the viscosity increases over more than 1 order of magnitude even at this low concentration of surfactant (1 wt %). Pronounced shear thinning can be observed. At very high temperatures, when locally flat structures are formed (75 °C), the viscosity drops. Formation of Flat Bilayer Structures. At a further increase of the C12EO3 concentration or at a further increase of the temperature in samples containing wormlike micelles, the decay of the intensity at low q-values changes from q-1 to q-2, which strongly supports the presumption of a transition from rodlike to locally flat bilayer structures. In Figure 9, SANS curves of a temperature series are shown to illustrate this transition. The sample contains 1 wt % of ChEO10 and 0.15 wt % of C12EO3. In Figure 10, the corresponding PDDF are shown. At 35 °C, a clear signature of cylindrical micelles with a length of about 170 nm is found. At 50 and 60 °C, practically the same flat bilayer structure can be seen. This locally flat bilayer structure might be a vesicular phase, as postulated by Kunieda and colleagues,10 or a bicontinuous zero mean curvature phase (L3), as found in other nonionic surfactant systems.31 Our data do not permit the exclusion of one of these possible structures, but the fact that the phase is stable against dilution down to 0.05 wt %, and that no shear birefringence has been found,

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Figure 9. Scattered intensity I(q) from SANS experiments on a sample containing 1 wt % of ChEO10 and 0.15 wt % of C12EO3 at different temperatures (35 °C (squares), 40 °C (circles), 50 °C (upward-pointing triangles), and 60 °C (downward-pointing triangles)). The top three curves are offset by scale factors for better visibility. Slopes of q-1 and q-2 are indicated for the comparison to the intensity at low values of q.

Figure 10. PDDF p(r) obtained from the intensities shown in Figure 9 (1 wt % ChEO10 and 0.15 wt % of C12EO3 at 35 °C (squares), 40 °C (circles), 50 °C (upward-pointing triangles), and 60 °C (downwardpointing triangles)).

favors a vesicular phase. The measurement at 40 °C shows some kind of mixed structure. Deconvolution. Once the geometry of the aggregates is established, it is possible to calculate the cross-sectional PDDF, px(r) (x ) c for cylindrical geometry and t for planar geometry). The px(r) are useful because the r value, for which px(r) ) 0, provides an estimate of the maximum cross-sectional dimension of the aggregate. Figure 11 shows the p(r) of a nearly spherical micelle (1 wt % ChEO10 in D2O at 20 °C) and two crosssectional PDDF for cylindrical geometry pc(r). The sphere-torod transition was achieved for one curve by increasing the temperature (55 °C), for the other pc(r), C12EO3 was added (1 wt % ChEO10 + 0.15 wt % C12EO3) at 20 °C. Both pc(r) functions are practically the same. Furthermore, two crosssectional PDDF for planar geometry pt(r) are shown: one produced by way of heating of the sample, which shows a cylindrical geometry at room temperature (1 wt % ChEO10 + 0.15 wt % C12EO3) to 80 °C, and the other one produced by a further increase of the C12EO3 concentration (1 wt % ChEO10 + 0.40 wt % C12EO3) at 20 °C. Again both pt(r) functions are practically the same. With the later sample, SAXS measurements were also performed in order to clarify the internal structure of the bilayer. Although the overall contrast of the micelles is rather low, as it often is for nonionic surfactants, it was possible to calculate the pt(r). The bilayer thickness corresponds very well with the thickness obtained from SANS measurements on the

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Figure 11. PDDF p(r) of 1 wt % ChEO10 in D2O at 20 °C (squares), compared with two cross-sectional PDDF pc(r) (1 wt % ChEO10 at 55 °C (circles) and 1 wt % ChEO10 + 0.15 wt % C12EO3 at 20 °C (upwardpointing triangles)) and two thickness PDDF pt(r) (1 wt % ChEO10 + 0.15 wt % C12EO3 at 80 °C (downward-pointing triangles) and 1 wt % ChEO10 + 0.40 wt % C12EO3 at 20 °C (diamonds)) obtained from SANS data. Additionally, the thickness PDDF pt(r) of the sample containing 1 wt % of ChEO10 and 0.40 wt % of C12EO3 at 20 °C obtained from SAXS data is shown (dashed line). All of the curves are normalized to a maximum value of 1.

Figure 12. Contrast profiles obtained by deconvolution of the PDDF shown in Figure 11 for three different geometries. SANS data: spherical (∆F(r)), 1 wt % ChEO10 at 20 °C (squares); rodlike (∆Fc(r)), 1 wt % ChEO10 at 55 °C (circles); and 1 wt % ChEO10 + 0.15 wt % C12EO3 at 20 °C (upward-pointing triangles); planar (∆Ft(r)), 1 wt % ChEO10 + 0.15 wt % C12EO3 at 80 °C (downward-pointing triangles); and 1 wt % ChEO10 + 0.40 wt % C12EO3 at 20 °C (diamonds). The dashed curve is the contrast profile for the sample containing 1 wt % of ChEO10 and 0.40 wt % of C12EO3 at 20 °C, obtained from SAXS data.

same sample (∼8 nm). The length of one ChEO10 molecule is ∼3.85 nm (meander configuration of the oxyethylene part). Two of these molecules add up nearly perfectly to the measured bilayer thickness. The diameter of the cylindrical micelles (∼12 nm) is larger than the thickness of the bilayer. This increase is a general behavior because of packing constraints, but the difference is rather large compared to that of other surfactant systems. This is most probably due to the bulky and rigid cholesteryl frame of ChEO10. The maximum dimension of a spherical micelle is, for the same reasons, again larger than the cross-sectional diameter of the cylindrical micelles, but from this p(r), one can conclude that the micelles are already slightly elongated. The maximum dimension corresponds to the length of the micelle. Deconvolution of the px(r) results in the contrast profile ∆Fx(r) normal to the interface; these functions are shown in Figure 12. As for the SANS measurements, the surfactants are fully hydrogenated, and the solvent is deuterated; there is no change in the sign of the contrast within the micelle. The profile starts

Moitzi et al. at a maximum negative value and becomes zero at the maximum dimension. There is a decrease in contrast in the region of the headgroups because of increasing hydration of the oxyethylene groups with a deuterated solvent. Again, it should be noted that the dimension of the contrast profile for the spherical micelle is slightly overestimated because of the elongation of the micelles. For the SAXS measurement, the contrast profile ∆Ft(r) changes its sign within the micelle because the aliphatic tail has a lower electron density than water, while the oxyethylene headgroup has a higher one. Together, the overall contrast is rather low, which makes SAXS data of nonionic surfactant systems in general difficult to evaluate, and they are afflicted with rather large error bars. Nevertheless, the data correspond well, together with the SANS data. The thickness is the same as that obtained with SANS, and one can also see the coreheadgroup interface (zero-crossing). The length of the hydrophobic cholesteryl part obtained with SAXS is an underestimation of the actual length (∼1.85 nm). This can be attributed to the rather poor quality of the SAXS data because of very low overall contrast. Interdigitation is unlikely because of the nearly perfect match of the bilayer thickness to the double length of a ChEO10 molecule in the more accurate SANS measurements. DLS. Wormlike micelles can entangle with each other and form a transient network with viscoelastic properties. This entanglement can be observed with DLS, analogous to solutions of flexible polymers in the semidilute regime.32-35 In contrast to rheology, one can look at the formation of entanglements without applying any shearing. It is not possible to fit the whole correlation function with the simple cumulant fit method,36 as performed by Acharya et al.,10 as soon as entanglements are present. It is just the first decay that can be fitted well, but the essential changes are happening at long relaxation times. The decays in the correlation function can be well described by two modes, initially a single exponential, followed by a stretched exponential at longer times:

g(1)(t) ) Af exp(- t/τf) + As exp[-(t/τs)β]

(8)

The quantities Af and As are the amplitudes for the fast and slow relaxation modes, respectively. The sum Af + As is the intercept of the instrument (close to 1). The fast mode τf is related to a collective diffusion coefficient Dc (τ-1 ) Dcq2), f which reflects a concerted motion of the wormlike micelles relative to the solvent. Its long-time behavior is associated with the disentanglement relaxation of individual chains or cluster relaxation. The variable τs is an effective slow relaxation time, and the stretched exponent β (0 < β e 1) is inversely proportional to the width of the distribution of relaxation times. The correlation functions were analyzed by using a nonlinear fitting algorithm to obtain best-fit values for Af, τf, τs, and β. The coupling approach of Ngai37 provides a general description of the dynamics in constrained and interacting systems. The value of the coupling parameter n (n ) 1 - β) is a direct measure of the coupling strength of the relaxation mode to its complex environments. A high value of n (or a low value of β) indicates strong coupling effects and a large width of the distribution of relaxation times. The model treats the system under consideration as a combination of basic units that interact nonlinearly with each other. At short times, the basic units relax independently. At longer times, the cooperative constraints between the basic units come into play. In this case, the relaxation function depends on the coupling strength (n) between basic units, so that this function is characterized by a slowed

Viscoelastic Wormlike Micellar Solutions

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Figure 13. Correlation functions from DLS measurements from a sample containing 5 wt % ChEO10 and 0.25 wt % C12EO3 (a) and from a sample containing a 5-fold lower concentration of both surfactants (b) at varying temperatures (20 °C (squares), 25 °C (circles), 30 °C (upward-pointing triangles), 35 °C (downward-pointing triangles), 40 °C (diamonds), 45 °C (left-pointing triangles), 50 °C (right-pointing triangles), 60 °C (stars), and 70 °C (plus signs)). The correlation times are normalized to 20 °C with respect to changing temperatures and solvent viscosity to make them directly comparable (eq 9).

stretched exponential function. The basic prediction of this model is that n raises (or β decreases) and the slow relaxation time τs increases as the strength of the interaction between the basic units is increased. In Figure 13, examples of correlation functions from DLS measurements at different temperatures and two different surfactant concentrations are shown (a: 5 wt % ChEO10 and 0.25 wt % C12EO3; b: 1 wt % ChEO10 and 0.05 wt % C12EO3). To make the correlation functions directly comparable, normalization is necessary in order to consider changing solvent viscosity with temperature. For that reason, a normalized correlation time t* was calculated:

T ηnorm t* ) t Tnorm η

(9)

where T is the temperature of the measurement, and Tnorm is the normalization temperature (20 °C). η is the viscosity of water at the measuring temperature, and ηnorm is the viscosity of water at 20 °C in our case. In Figure 13a, the correlation functions of a sample containing 5 wt % of ChEO10 and 0.25 wt % of C12EO3 at different temperatures are shown. At temperatures up to 35 °C, globular micelles are present. The correlation functions are shifted only very little and up to higher correlation times with increasing temperature because of the slight elongation of the micelles. At about 40 °C, rapid micellar growth starts and the viscosity increases. Because of entanglements, a tail to longer correlation

Figure 14. Fitted values of β (a) and τs (b) for samples containing 5 wt % of ChEO10 and 0 wt % (squares), 0.125 wt % (circles), 0.25 wt % (upward-pointing triangles), and 0.50 wt % (downward-pointing triangles) of C12EO3. The values were fitted to the correlation functions measured with DLS using eq 8.

times occurs. This tail becomes more pronounced up to 50 °C. At even higher temperatures, when locally flat structures are formed, the fast decay is shifted to the right, but the tail has vanished because no entanglements are present any more and the viscosity is lower again. A similar series, but with a 5-fold lower concentration, is shown in Figure 13b (1 wt % ChEO10, 0.05 wt % C12EO3). Basically, the same behavior was found, only the temperature regime, where wormlike micelles are present, is smaller and has lower temperatures (from 35 to 40 °C). So even at this low concentration of 1.05 wt % surfactant, the change in dynamics resulting from the entanglements can be seen with DLS. Slow relaxation times can be used qualitatively to characterize the differences in the viscoelastic response of the system. β and τs are the most sensitive parameters for the development of slow diffusion modes caused by entanglement of the wormlike micelles. A low value of β indicates a broad distribution of relaxation times. In Figure 14, the fitted values of β (a) and τs (b) for samples containing 5 wt % of ChEO10 and an increasing concentration of C12EO3 (0, 0.125, 0.25, and 0.50 wt %) are shown. As soon as wormlike micelles are formed (viscoelastic phase), the width of the distribution of the slow relaxation times increases. The fitting parameter β passes a pronounced minimum at the temperature where the viscosity enhancement of the system is highest. The effective slow relaxation time τs is increasing at the same time. After approaching the vesicular phase (low viscosity), β is increasing and τs is decreasing. For the first two samples, a further temperature increase would have been necessary to reach this regime. Both predictions of the coupling model (increasing τs and decreasing β when a transient network of wormlike micelles is formed) are in agreement with the experimental findings.

16168 J. Phys. Chem. B, Vol. 109, No. 33, 2005 Conclusions Unidimensional micellar growth in ChEO10/water systems can be initiated in different ways. All of the possibilities are based on a reduction of the mean curvature of the aggregate-solvent interface by making the average headgroup size smaller. This can either be achieved by adding a second nonionic surfactant with a smaller headgoup size (e.g., C12EO3) or by increasing the temperature. The concentration of the second surfactant necessary for the sphere-to-rod transition is decreasing for surfactants with smaller headgroups. The results of our structural investigations confirm the assumptions drawn by Acharya and Kunieda10 from indirect methods, such as rheology and DLS, and calculations based on the packing of the surfactants in the aggregates on the gradual growth in length of the micelles. It was shown that the same structural transition from spherical to cylindrical or from cylindrical to planar can be achieved by increasing the C12EO3 concentration or by increasing the temperature. The geometry of the aggregates as well as the increase in viscosity are the same independent of the way one achieves the transition. The viscosity increase is dependent on the total surfactant concentration during the sphere-to-rod transition; it drops again when planar structures are formed. The possibility to tune the viscosity over some orders of magnitude by simply changing the temperature can be of great importance for applications. In the system ChEO10/C12EO3/ water, the viscosity at room temperature can be adjusted by the C12EO3 concentration, while a dramatic change in viscosity (either increase or decrease) can be achieved by changing the temperature. The concentration of C12EOj can be used to tune the transitions to a special temperature. For some applications, the independence of the formed structures from ionic strength might be useful. The evaluation of DLS data with the approach of stretched exponentials is a quick and easy method for estimating the entanglements within a transient network of wormlike micelles. This can be performed without any structural changes introduced by external forces. The predictions of the coupling model of Ngai37 are in agreement with the experimental findings. Acknowledgment. We are grateful for financial support from the Christian Doppler Society. The Christian Doppler Laboratory for Advanced Functional Materials is a part of the long-term research program of AT&S. This work was also supported by the Austrian Science Fund (FWF) under grant P15698. The results from SANS were obtained partly at the Institut LaueLangevin ILL in Grenoble (experiment number 9-11-1061). We would like to acknowledge the help of our local contact, Peter Lindner. This research project has been supported by the European Commission under the 6th Framework Program through the Key Action: Strengthening the European Research

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