Hairy Wormlike Micelles: Structure and ... - American Chemical Society

with the emergence of a broad peak in the structure factor at a finite wave vector. The peak can be related to a liquidlike order of the micelles due ...
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Langmuir 2002, 18, 5687-5694

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Hairy Wormlike Micelles: Structure and Interactions Gladys Massiera*, Laurence Ramos, and Christian Ligoure Groupe de Dynamique des Phases Condense´ es (CNRSsUniversite´ Montpellier 2), CC26, Universite´ Montpellier 2, 34095 Montpellier Cedex 5, France Received March 1, 2002. In Final Form: April 15, 2002 We report on the existence and stability of hairy wormlike micelles, which are obtained by adding in a surfactant solution, an amphiphilic copolymer, whose hydrophobic block anchors onto the micelles and whose hydrophilic tails are swollen in the aqueous solvent. Small angle neutron scattering is performed to characterize the structural properties of the copolymer/surfactant mixture. We first show that the locally cylindrical structure of the micelles is maintained upon copolymer addition over a wide range of copolymer-to-surfactant molar ratio. On the other hand, the addition of amphiphilic copolymer correlates with the emergence of a broad peak in the structure factor at a finite wave vector. The peak can be related to a liquidlike order of the micelles due to steric repulsions induced by the copolymer layer covering the micelles. Finally, we show that the phase diagram of the hairy micelles can be quantitatively interpreted in terms of an effective volume fraction of the cylinders, assuming that the radius of the cylinders is increased by the thickness of the surrounding polymer layer. We find that this thickness is of the same order of magnitude as the radius of gyration of the decorating copolymer and increases with the polymeric layer density.

I. Introduction Interactions between amphiphilic copolymers and surfactants have been explored in a variety of experimental systems,1-7 and also theoretically.8,9 Copolymers have dramatic effects on surfactant self-assemblies by modifying their structural, thermodynamical, and rheological properties. For instance, block copolymers induce the formation of stable monodisperse vesicles10 or strongly enhance the repulsive interaction between membranes in a lamellar phase.11 In this paper, we report on a novel type of mixed self-assembled system: hairy wormlike micelles. It consists of long and flexible surfactant cylinders (wormlike micelles) decorated with amphiphilic copolymers. The hydrophobic block of the copolymer is anchored on the hydrophobic core of the cylinders, whereas the hydrophilic tails remain swollen in the aqueous solvent. The effects of this decoration on the rheological properties of micellar solutions have been described in ref 12. In this paper, we focus on the stability and structure of hairy wormlike micelles. (1) Appell, J.; Porte, G.; Rawiso, M. Langmuir 1998, 14, 4409-4414. (2) Kevelam, J.; Hoffmann, A. C.; Engberts, J. B. F. N.; Blokzijl, W.; De Pas, J. V.; Versluis, P. Langmuir 1999, 15, 5002-5013. (3) Yang, Y.; Prudhomme, R.; MacGrath, K. M.; Richetti, P.; Marques, C. M. Phys. Rev. Lett. 1998, 80, 2729-2732. Yang, B.-S.; Lal, J.; Richetti, P.; Marques, C. M.; Russel, W. B.; Prudhomme, R. Langmuir 2001, 17, 5834-5841. (4) Loyen, K.; Iliopoulos, I.; Audebert, R.; Olsson, U. Langmuir 1995, 11, 1053-1056. Bagger-Jo¨rgensen, H.; Olsson, U.; Iliopoulos, I.; Mortensen, K. Langmuir 1997, 13, 5820-5829. (5) Warriner, H. E.; Idziak, S. H. J.; Slack, N. L.; Davidson, P.; Safinya, C. R. Science 1996, 271, 969-973. Keller, S. L.; Warriner, H. E.; Safinya, C. R.; Zasadzinski, J. A. Phys. Rev. Lett. 1997, 78, 4781-4784. (6) Yang, B.-S.; Lal, J.; Kohn, J.; Huang, J. S.; Russel, W. B.; Prudhomme, R. K. Langmuir 2001, 17, 6692-6698. (7) Cabane, B. J. Phys. Chem. 1977, 81, 1639. (8) Bickel, T.; Jeppesen, C.; Marques, C. M. Eur. Phys. J. E 2001, 4, 33-43. (9) Marques, C. M.; Fournier, J. B. Europhys. Lett. 1996, 35, 361365. (10) Joannic, R.; Auvray, L.; Lasic, D. Phys. Rev. Lett. 1997, 78, 34023405. (11) Castro-Roman, F.; Porte, G.; Ligoure, C. Phys. Rev. Lett. 1999, 82, 109-112. Castro-Roman, F.; Porte, G.; Ligoure, C. Langmuir 2001, 17, 5045-5058. (12) Massiera, G.; Ramos, L.; Ligoure, C. Europhys. Lett. 2002, 57, 127-133.

The paper is organized as follows: section II is devoted to materials and methods. The experimental results are described in section III. We report how the phase diagram of the surfactant phase is modified by the addition of amphiphilic copolymer. Small angle neutron scattering (SANS) data are then presented. We show, on the one hand, that the cylindrical structure of the micelles is preserved upon copolymer addition and, on the other hand, that the addition of amphiphilic copolymer correlates with the emergence of a broad peak in the structure factor, at a finite wave vector. Finally, the experimental results are discussed in section IV. Interestingly, the structure factor of semidilute solutions of hairy living polymers is quite similar to that of semidilute solutions of highly charged conventional polyelectrolytes. However, in our case, the peak is the signature of a steric polymer-mediated repulsion between micelles. A simple picture is built, in which the relevant radius of the hairy micelles to be considered is the sum of the hydrophobic core radius of the naked micelles plus the thickness of the decorating polymer layer. This effective copolymer layer thickness, h, can be estimated from the phase diagram of the surfactant/copolymer mixture. We find that h is comparable to the radius of gyration of the hydrophilic tail of the polymer, and increases monotonically with increasing polymer density. II. Experimental Methods A. Materials. The surfactant micelles are made of a mixture of cetylpyridinium chloride (CpCl) and sodium salicylate (NaSal) diluted in brine ([NaCl] ) 0.5 mol‚L-1), at a fixed molar ratio [NaSal]/[CpCl] of 0.5. CpCl is purified by successive recrystallizations in water and in acetone, while NaSal and NaCl are used as received. This system is known to form long and flexible micelles even at low concentration.13 We add to this host phase various amounts of amphiphilic copolymers, which are of two types: two triblock copolymers, of trade name Synperonic F108 and F68 (purchased from Serva and used as received) on the one hand, and a diblock copolymer synthesized in our laboratory,14 (13) Rehage, H.; Hoffman, H. J. Phys. Chem. 1988, 92, 4712-4719. (14) Hartmann, P.; Viguier, M.; Collet, A.; Calvet, D. J. Fluorine Chem. 1999, 95, 145-151.

10.1021/la025687a CCC: $22.00 © 2002 American Chemical Society Published on Web 06/21/2002

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noted PC18 hereafter, on the other hand. The Synperonic F108 (F68) consists of two identical hydrophilic polyoxyethylene (POE) blocks of 127 (76) monomers each, symmetrically bounded to a central shorter hydrophobic block of polyoxypropylene (PPO) of 48 (29) monomers. The amphiphilic polymer PC18 consists of a C18 alkyl chain as hydrophobic part, bounded, by a urethane group, to a POE block of 113 monomers. Both types of polymers (Synperonic and PC18) thus possess equivalent POE hydrophilic tails, but differ by their hydrophobic anchor. Because the hydrophobic block of PC18 is of the same chemical nature as the core of the micelles, it is expected to insert into the micelles. By contrast, for Synperonic copolymers, the affinity for the core of the micelles is more complex. Despite the hydrophobicity of PPO, the fact that PPO is of different chemical nature than the micelle core and that the length of PPO is relatively large suggests that a full insertion of the PPO into the core of the cylinders is not realistic. Nevertheless, in all cases, the hydrophobic part anchors onto the fluid surfactant cylinders, while the hydrophilic tails remain swollen in the aqueous medium and decorate the micelles. We define φ as the weight fraction of surfactant (φ ) (wCpCl + wSal)/wtot (g/g)15) and R as the ratio of the number of POE chains to the number of surfactant molecules. In our experiment, φ lies in the interval 0.15-40%; R ranges between 0 and 4.2% for F108 and PC18 and between 0 and 8.4% for F68. Note that, for a direct comparison between F108 and PC18, PC18 must be incorporated at twice the F108 molar content, since PC18 comprises only one POE tail rather than two as in F108. This results in the same POE chains-to-surfactant ratio R. The aqueous solutions are prepared by weight. We dissolve first the copolymer in brine, add then the CpCl to the solution, and add finally the salicylate salt. The samples are stirred several times and left undisturbed at 30 °C for several weeks. All experiments are performed at 30 °C. In the following, since the densities of all composants are nearly identical, we identify mass and volume fractions when H2O is used. For the neutron scattering experiments, H2O is replaced by deuterated water D2O and a correction is then applied to the composition, to account for their difference in molar weight. We have moreover checked that the use of deuterated instead of hydrogenated water does not significantly modify the phase diagrams. Two regimes are expected for the structure of the polymer layer, a mushroom structure at low R values and a brushlike structure at higher R values. The smooth crossover R* between the two regimes corresponds to the overlap threshold value of mushrooms of area σ ) πRG2,17 where RG is the radius of gyration of an hydrophilic tail; RG = 26 Å for F108 and PC18 and RG = 19 Å for F68.18 Calculating the number of spheres of radius RG necessary to form a compact shell of spheres covering a slice of micelle of radius r0 (r0 = 30 Å) and length 2RG, we evaluate R* = 3% for F108 and PC18 and R* = 4.6% for F68. Therefore, for each copolymer, both regimes are investigated experimentally. B. SANS Measurements. Small angle neutron scattering (SANS) experiments are performed at the laboratoire Le´on Brillouin at Saclay (France) on the spectrometer PACE and at the Institut Laue Langevin at Grenoble (France) on the D11 beamline. The scattered intensity is systematically measured on a large range of scattering vectors q, from 3.0 × 10-3 to 3.3 × 10-1Å-1. The data are treated and put on an absolute scale according to standard procedures.19 Deuterated water is used in order to obtain only one contrast factor, namely the contrast between the deuterated compounds and the hydrogenated compounds (surfactant and polymer). As the surfactant polar heads are hydrated and the POE blocks are swollen in water, this method is sensitive to the contrast between the hydrophobic core of the micelles and the D2O solvent. (15) Note that we consider the sodium salicylate ions as part of the surfactant film, because of their strong binding nature.13,16 (16) Magid, L. J.; Han, Z.; Li, Z.; Butler, P. D. J. Phys. Chem. B 2000, 104, 6717-6727. (17) de Gennes, P.-G. Macromolecules 1980, 13, 1069. (18) Cabane, B.; Duplessix, R. J. Phys. (Paris) 1982, 43, 1529. (19) Diffusion des Neutrons aux petits angles; EDP Sciences: Albe´ Massif Vosgien, France, 9, 1998.

Massiera et al.

Figure 1. Sketch of a wormlike micelle decorated with amphiphilic copolymers. The hydrophobic block anchors onto the micelle while the hydrophilic part remains swollen in the solvent.

Figure 2. Phase diagrams of solutions of wormlike micelles decorated with amphiphilic copolymer. Two copolymers are used: (a) F68; (b) F108. For each POE chains-to-surfactant molar ratio, R, the symbols denote the surfactant volume fraction φT that separates homogeneous isotropic samples (φ < φT) from multiphasic samples (φ > φT).

III. Results A. Phase Diagram. The phase diagram of the CpClNaSal mixture in brine has been extensively studied by Rehage et al.13 and Berret et al.20 Without copolymer, the micellar solutions are homogeneous and isotropic for surfactant weight fraction φ less than φT ) 36%. At 36%, the solution phase separates: for 36% < φ < 38%, an isotropic and a nematic phase coexist, while for 38% < φ < 43%, a nematic and a hexagonal phase coexist. Finally, for φ greater than 43%, a hexagonal phase is obtained. Parts a and b of Figure 2 show how the phase diagram of the initial CpCl/NaSal/Brine cylindrical self-assemblies (20) Berret, J.-F.; Roux, D.; Porte, G. J. Phys. II 1994, 4, 1261-1279.

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through a comparison between the effect of the various decorating polymers. It is shown that the existence of the correlation peak is due to the copolymer layer that covers the micelles. The position dependence of the peak is described as a function of both parameters, the polymer ratio R and the surfactant concentration φ. 1. Local Structure. The scattered intensity I(q) of a set of N identical uncorrelated particules of volume VP in a total volume V can be written as22

N I(q) ) (∆F)2 VP2〈|F(q b)|2〉 V

Figure 3. Scattered intensity normalized by surfactant volume fraction φ as a function of wave vector q. The surfactant volume fraction is φ ) 9%. Curves are labeled by the POE chains-tosurfactant molar ratio, R. The decorating copolymer is PC18.

(1)

where ∆F is the difference in scattering length density between deuterated (solvent) and hydrogenated (hydrophobic core) compounds (∆F ) FD2O - Fcore = 6.1 × 1010 cm-2), and the quantity F(q b) is the Fourier transform of the contrast function. The term 〈|F(q b)|2〉, which depends only on the shape of the particles, is defined as the form factor P(q) of the objects. The morphology of the scattering objects can therefore be extracted from the scattered intensity of very dilute solutions, for which interactions between objects can be neglected. The form factor of rigid cylinders of finite size L and radius r has been calculated, in the limit L . r:19,22

is modified by the addition of F68 and F108, respectively.21 The salient features of these phase diagrams are the following. First of all, there is a large domain, for both guest polymers, where the mixed system remains homogeneous and isotropic and consists of a single phase of hairy wormlike micelles. However, the threshold surfactant concentration φT, above which phase separations occur, depends on the quantity of copolymer R. The transition from a homogeneous isotropic solution to a nonhomogeneous one is reported to lower surfactant concentration as R increases. This effect is more pronounced for the longer copolymer F108 than for the shorter one F68. For naked micelles, φT = 36%, while for R ) 4.2% φT is equal to 17% (26%) for F108 (F68). Above φT, multiphasic solutions are obtained. Very often three phases coexist. One of them is birefringent and reveals an ordering of the cylinders. Note that the coexistence of three phases instead of two in the case of naked micelles is a simple consequence of the Gibbs phase rule, since addition of copolymer corresponds to an extra degree of freedom in the mixture composition. Nevertheless, a biphasic sample is also obtained for a molar ratio of 2.1% in F108 and a surfactant concentration of 22%; the biphasic sample consists of two isotropic phases. The origin of the phase separation is discussed in section IV, in terms of effective volume of the micelles. Both phase diagrams show nevertheless that homogeneous and isotropic solutions extend over a large region of the phase diagram, allowing a systematic study of the structural properties of hairy wormlike micelles. B. Neutron Scattering. The SANS patterns obtained for F108-decorated micelles are reported in Figure 3, for a fixed surfactant concentration (φ ) 9%) and increasing polymer ratio R. It clearly shows that the solubilization of F108 into wormlike micelle solutions leads to the emergence of a correlation peak in the low q range, while the superimposition of the curves in the high q range evidences that the local structure is not affected by the copolymer incorporation. In the following, we will first show that the local structure of the micelles remains essentially cylindrical. The structure factor and the emergence of a correlation peak at low q are then detailed

where rC is the mean radius of the hydrophobic core. In the case of naked micelles, the excellent agreement between the fit and the experimental data allows one to establish the locally cylindrical structure of the micelles and to determine the hydrophobic radius rC of the cylinders. We find rC = 21.5 Å, in agreement with previous measurements.23

(21) Because of unidentified impurities remaining after the synthesis of the polymer PC18, the solution containing PC18 is turbid, which renders the identification of the phases quite difficult at high polymer content. We therefore did not succeed in obtaining a systematic and reliable phase diagram.

(22) Glatter, O.; Kratky, O. Small-angle X-ray scattering; Academic Press: New York, 1982. (23) Marignan, J.; Appell, J.; Bassereau, P.; Porte, G.; May, R. P. J. Phys. Fr. 1989, 50, 2553-2566. Appell, J.; Marignan, J. J. Phys. II Fr. 1991, 1, 1447-1454.

P(q,r) )

(

)

2π 2J1(qr) qL qr

2

(2)

where J1 is the Bessel function of first order. In our system, long-range Coulombic interactions are screened because of a high NaCl concentration (0.5 M). Therefore, micelles in dilute solutions do not interact. Experimental results for naked (R ) 0) and hairy micelles are presented in Figure 4. To emphasize the local morphology of the aggregates, the scattered intensity I times q4 is plotted as a function of the wave vector q, showing the form factor oscillations in the high-q range. The data are fitted with a relation derived from eq 2. In addition, we assume a very narrow Gaussian distribution for the radius of the cylinder section (σ = 3 Å), which accounts for the damping oscillations observed experimentally on the q4I versus q plot. The resulting form factor is also convoluted with the instrumental function to account for the poor resolution obtained in SANS, which is dominated by the polychromaticity of the incident wavelength. We take for this function a Gaussian distribution of width ∆q ) q(∆λ/λ), with ∆λ/λ = 10%.19 (Note that we have not taken into account the lack of resolution due to angular dispersion of the beam, its contribution at high q being negligible.) The final form factor reads

∫

N I(q) ) (∆F)2 VP2 exp[-(r - rC)2/σ2] × V

∫

( exp[-(q′ - q)2/(∆q)2] P(q′,r) dq′) dr (3)

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Figure 5. Scattered intensity normalized by surfactant concentration φ, for various φ values (1.4% < φ < 11.8%). The polymer (PC18) to surfactant molar ratio is fixed at R ) 2.1%. The overlap of all curves at high q shows that the local structure of the micelles remains the same upon increasing φ.

Figure 4. Form factor normalized by the surfactant volume fraction φ on a q4I versus q representation for wormlike micelles decorated with (a) PC18 amphiphilic copolymer for various copolymer-to-surfactant molar ratios (R ) 0, 0.9%, 0.2%). The arrow indicates a departure from the fitting function, due to the intermicellar interactions for high R and high φ values. (b) F108 amphiphilic copolymer for various polymer molar ratios (R ) 0, 1%, 2.1%). The surfactant volume fraction is (a) 9% and (b) 3%. For both (a) and (b), the continuous line is the best fitting function, using eqs 2 and 3.

As shown in Figure 4a, when PC18 is used as decorating copolymer, the form factor of hairy micelles exactly superimposes on the form factor of naked micelles, in the range of copolymer ratio investigated (R e 4.2%). Note that for both large φ and R a difference is obtained at low q, before the first maximum of the form factor oscillations (arrow in Figure 4a). In this case, the approximation of uncorrelated micelles is no longer valid: a peak is indeed obtained in the structure factor as detailed in the next paragraph. Nor are strong modifications of the form factor observed for the Synperonic F108 (Figure 4b), as long as R e 2.1%. For a given POE chains-to-surfactant molar ratio R, systematic measurements are performed as a function of the surfactant concentration φ. The φ-normalized scattered intensities, I/φ, obtained for various φ values at a given R, overlap in the high-q range (see Figure 5). Thus, the locally cylindrical structure of the micelles is not affected by the addition of copolymer, and is moreover maintained upon increasing the surfactant concentration. In the case of Synperonic copolymers, above R ) 2.1%, a departure from the form factor of ideal long cylinders is observed in the whole range of q vectors (Figure 6). The fact that a similar deformation of the form factor is also obtained if a linear chain of PPO24 of length comparable to the length of the PPO block of F108 (47 monomers) is

Figure 6. Form factors obtained for F108 (crosses) and PPO (empty circles) at high polymer content (R ) 4.2%). The surfactant volume fraction is φ ) 9%. The line is the form factor obtained for cylinders of radius 24 Å. The arrow denotes the second maxima of the form factor oscillations, which constitutes the main difficulty in fitting the data.

used instead of F108 allows us to reject the hypothesis of a second type of aggregates in solution such as copolymer spherical micelles.25 Moreover, we checked that the form factor of cylinders with a core-shell contrast (to take into account an eventual additional contrast due to the PPO shell) does not lead to a satisfying description of the experimental form factor obtained at high F108 copolymer content. The difficulty in fitting the data lies in fact essentially in the second maxima of the oscillations obtained around 0.17 Å-1, indicated by an arrow in Figure 6. The discrepancy between the theoretical form factor and the experimental one, observed at high enough polymer concentration, is obviously due to the hydrophobic PPO block, since no deformation is obtained for PC18. This may be due to the fact that the PPO block is relatively large and may deform the locally cylindrical shape of the micelles; for instance, it no longer has a constant circular (24) For the PPO linear chains, the polymer content used is simply the number of PPO linear chains over surfactant molar ratio. (25) Besides, due to the large difference of volume between spherical micelles and long cylinders, the contribution of a spherical micelle to the scattering intensity (I ∝ VP2) is negligible compared to the contribution of a long cylinder. Thus, the number of spherical micelles necessary to give an efficient contribution to the scattered intensity would not be realistic.

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Figure 7. Scattered intensity normalized by surfactant volume fraction φ as a function of wave vector q for samples without polymer (empty circles), with linear PPO chains (crosses), with linear POE chains (diamonds), and with F108 (empty triangles). The surfactant volume fraction is φ ) 9%, and the polymer molar ratio is R ) 0.9%.

Figure 8. Peak position q* as a function of the copolymer molar ratio R for F108 (circles) and PC18 (triangles). The straight line is a power law fit yielding an exponent of 0.24 ( 0.08.

cross section. However, such an assumption remains to be confirmed. 2. Copolymer Induced Interactions. While the SANS scattering patterns for solutions of naked and hairy micelles superimpose at high q (see Figure 3), a marked difference is observed in the low-q range upon increasing the copolymer fraction. Figure 7 shows the variation of the φ-normalized SANS scattering intensity, I(q)/φ, at a given surfactant concentration φ ) 9%, for various types of samples. In the case of naked micelles the intensity decreases monotonically with increasing q. The scattering intensity, in this case, is analogous to that of a semidilute solution of conventional neutral homopolymers, as expected from the close similarity between the structure of semidilute solutions of polymers and of wormlike micelles.26,27 If we then add either PPO or POE linear chains into the micellar solutions of CpCl/NaSal, the shape of the experimental intensity curves is not strongly modified. For instance, contrary to the deformation observed in the high-q range, the experimental spectrum of a mixture of PPO24 and CpCl/NaSal cylindrical micelles superimpose (26) Schurtenberger, P.; Scartazzini, R.; Magid, L. J.; Leser, M. E.; Luisi, P. L. J. Phys. Chem. 1990, 94, 3695-3701. (27) Jerke, G.; Pedersen, J. S.; Egelhaaf, S. U.; Schurtenberger, P. Phys. Rev. E 1997, 56, 5772-5788.

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Figure 9. Position q* of the maximum of the structure factor as a function of surfactant concentration φ, for samples with F108 copolymer, R ) 1% (full circles) and R ) 3.2% (empty triangles), and with PC18, R ) 2.1% (squares). The data are fitted with a power law yielding an exponent 0.5 ( 0.1.

exactly on the spectrum of naked micelles. For mixtures of POE chains and CpCl/NaSal micelles, a monotonic decrease of I(q) with q is also obtained, with however a higher increase of I(q) toward small q, with respect to the case of naked micelles. This indicates the presence of supplemental attractive interactions between the cylinders, induced by homopolymers chains, presumably due to a depletion effect.28 In the case of hairy micelles, a very distinct and broad peak with an upturn in the small q range is observed in the intensity spectrum, for the three types of amphiphilic copolymers, and shown in Figure 7 for F108. The peak is only observed for sufficiently large surfactant volume fraction φ, and in all cases larger than the overlap concentration of the micelles, which varies between 0.3% and 1.05% for F108, when R increases.12 Figure 3 shows the evolution of the scattering intensity for a fixed surfactant concentration of 9%, when increasing the copolymer fraction. For this series, a peak begins to emerge at R ) 0.9%, which roughly corresponds to a linear density of copolymer chains along the cylinders of ∼1/50 Å-1. The intensity of the maximum depends clearly on the copolymer-to-surfactant ratio R: the higher R, the more pronounced is the peak. However, as shown in Figure 8, the peak position q* depends only weakly on the copolymer density. Data obtained for two different copolymers F108 and PC18 exactly superimpose, and give q* ∼ R0.24(0.08. By contrast, q* varies significantly with the surfactant concentration and scales as φ0.5(0.1 (Figure 9). The whole of these results unambiguously shows that the interaction peak is induced by the POE chains grafted onto the cylinders. This in turn provides supplementary experimental evidence that surfactant micelles are indeed decorated with the amphiphilic copolymers. IV. Discussion From the whole of the results obtained on the structure factor of hairy micelles, we can infer that a broad peak arises from additional steric repulsions between the cylinders, due to the copolymer layer grafted onto the wormlike micelles. The steric interaction is obviously short range, with a typical range on the order of the thickness of the copolymer layer. What is the physical origin of this peak? To address this question, it is interesting to go back (28) Israelachvili, J. Intermolecular and surface forces; Academic Press: San Diego, 1992.

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Figure 10. Hexagonal (a) and cubic (b) lattices used for the calculation of the dependence of the position peak q* on the surfactant concentration φ; d is the mean distance between the cylinders.

Figure 11. (a) Phase separation concentrations φTI/N and φTI/I plotted versus thickness h of the copolymer layer, as obtained respectively from the Onsager theory eq 4 (dotted line) and from a compact cubic lattice eq 5 (line) as described in the text. Symbols are experimental results. (b) Normalized thickness h* ) h/RG (RG is the gyration radius of the two POE parts of the Synperonic: RG = 19 Å for F68 and RG = 26 Å for F108), as a function of the normalized Ω ) R/R* polymer ratio. For the dotted line, h* ) Ω. Symbols are the same for both figures: F68 (empty circles) and F108 (full circles).

to the deep analogy between semidilute polymer solutions and semidilute solutions of wormlike micelles,26,27,29,30 or (29) Candau, S.; Hirsch E.; Zana, R. J. Phys. (Paris) 1984, 45, 12631270. (30) Appell, J.; Porte, G. Europhys. Lett. 1990, 12, 185-190.

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between charged wormlike micelles and polyelectrolyte solutions.31 A. Analogy with Polyelectrolyte Semidilute Solutions. Static scattering experiments on salt-free solutions of polyelectrolytes always exhibit a maximum at a certain scattering wave vector q*. It has been shown by several authors32-35 that, in the semidilute regime, q* scales with the polyelectrolyte concentration as φ1/2. Moreover, the scattering intensity maximum disappears progressively as salt is added and is consequently interpreted as resulting from long-range electrostatic interactions. Many theoretical attempts have been made to understand more quantitatively the features of polyelectrolyte systems.36-41 However, there are still not generally accepted interpretations for the origin of the peak. Three interpretations are proposed: (i) The peak is not due to some order in the solution but is related to the very small value of the scattering intensity when q tends to zero, I(q)0), which is indeed dominated by the osmotic compressibility of the small free ions, due to the constraint of electroneutrality in the solution.41,42 For values of q larger than 2π/ξ (ξ being the mesh size of the semidilute solution), the chain has a rodlike structure, and I(q) scales as 1/q. As a result, a maximum is found between these two regimes, at q* = 1/ξ. (ii) In the isotropic model of de Gennes,37 each chain is surrounded by a correlation hole from which other chains are expelled. The corresponding correlation length ξ is such that for distance r < ξ the electrostatic forces are dominant and the section of the chain has the same extended configurations as in dilute solutions. For r > ξ, both electrostatic and excluded volume interactions are screened and the chain follows random walk statistics. The correlation length ξ is proportional to κ-1, the Debye screening length, and thus scales as φ-1/2. (iii) Finally, the third interpretation43 postulates that electrostatic interactions impose a preferential distance between charged cylinders leading to an “organized structure” characteristic of a local cylindrical hexagonal packing (q* ∼ φ1/2) in the semidilute regime. Since the three different pictures imply a same scaling for q*, q* ∼ φ1/2, experiments cannot discriminate between them. Hairy wormlike micelle solutions are also constituted of long entangled chains interacting with each other, and they exhibit a similar broad peak in the structure factor. However, the difference between both types of systems lies in the range of the interactions, which is short range in the case of micelles covered with a swollen polymeric chain layer. Moreover, as opposed to polyelec(31) Magid, L. J. J. Phys. Chem. B 1998, 102, 4064-4074. (32) Nierlich, M.; Williams, C. E.; Boue´, F.; Cotton, J.-P.; Daoud, M.; Farnoux, B.; Jannink, G.; Picot, C.; Moan, M.; Wolf, X.; Rinaudo, M.; de Gennes, P.-G. J. Phys. (Paris) 1979, 40, 701-704. (33) Cotton, J.-P.; Moan, M. J. Phys. Lett. (Paris) 1976, 37, L-75. (34) Drifford, M.; Dalbiez, J.-P. J. Phys. Chem. 1984, 88, 5368. (35) Kaji, K.; Hurakawa, H.; Kanaya, T.; Kitamaru, R. J. Phys. (Paris) 1988, 49, 993. (36) de Gennes, P.-G. Scaling concepts in polymer Physics; Cornell University Press: Ithaca, NY, 1979. (37) Hayter, J.; Janninck, G.; Brochard-Wyart, F.; de Gennes, P.-G. J. Phys. Lett. (Paris) 1980, 41, L-451-L-454. (38) Odijk, T. J. Polym. Sci., Polym. Phys. Ed. 1977, 15, 477. Odijk, T. Macromolecules 1994, 27, 4998. (39) Ise, N. Angew. Chem., Int. Ed. Engl. 1986, 25, 323. (40) Weil, G. J. Phys. (Paris) 1988, 49, 1049-1054. (41) Barrat, J.-L.; Joanny, J.-F. Adv. Chem. Phys. 1996, 94, 1. (42) des Cloizeaux, J.; Jannink, G. Les Polyme` res en solution: Leur Mode´ lisation et leur structure; Les Ed. de la Physique: Les Ulis, France, 1987. (43) Ise, N.; Okubo, T.; Yamamoto, K. I.; Kawai, H.; Hashimoto, T.; Fujimura, M.; Hiragi, Y. J. Am. Chem. Soc. 1980, 102, 7901. Ise, N.; Okubo, T.; Kunugi, S.; Matsuoka, H.; Yamamotoand, K.; Ishii, I. Y. J. Chem. Phys. 1984, 81, 3294.

Hairy Wormlike Micelles

trolyte solutions, it is possible to monitor independently the magnitude and the range of the interactions, by varying the copolymer-to-surfactant ratio R and the size of the hydrophilic chain on the one hand and the cylinder concentration on the other hand. In principle, one should thus be able to distinguish the different mechanisms at the origin of the peak. In our case, interpretation (ii) of the existence of the peak in terms of a correlation hole from which the other micelles would be expelled has to be rejected. The size of the correlation hole would indeed be expected to scale as the thickness of the polymeric shell h, which is tuned by the ratio R. One expects h to increase with R and to be independent of φ. This would imply that q* decreases with R but does not vary with φ. Exactly the opposite is observed experimentally: q* increases slightly with R and is essentially fixed by the cylinder concentration φ, as clearly shown in Figure 9. By contrast, this peak position dependence can be simply obtained by assuming that infinite cylinders are locally arranged parallel to each other on a hexagonal lattice (Figure 10a) or that the cylinders are ordered on a cubic lattice as shown in Figure 10b. For the hexagonal, respectively cubic, lattice, the volume fraction can be written [(2π)/x3](r/d)2, respectively [(3π)/x4](r/d)2, with r the radius of the cylinders and d the hexagonal, respectively cubic, lattice parameter. This implies that q*, which is proportional to 1/d, scales as φ1/2. The value of q* provides also an evaluation of the mean distance between the cylindrical micelles at a given surfactant concentration φ, which is found to range between 100 and 250 Å for the range of φ investigated (5% < φ < 25%). Thus, the broad peak observed in the structure factor is presumably related to a locally organized structure. Moreover, it is interesting to notice that the mesh size ξ, in our system, scales as φ-3/4 12,44,45 as for neutral polymer semidilute solutions. Therefore, the first (i) interpretation for which q* scales as 1/ξ ∼ φ3/4 is also irrelevant. Finally, our system may provide a simple alternative experimental model to discuss the origin of the peak in semidilute solutions of polymers with additional interactions (polyelectrolytes or charged wormlike micelles are examples of such systems, but hairy micelles are another with a different extra contribution). Among the three pictures, the third (i.e., a local ordering of the chains) is in accordance with the whole set of our experimental results, suggesting that the broad peak observed in the structure factor is related to a soft ordering of the cylinders. B. Polymeric Shell Thickness. In a coarse grain approach, an effective thickness of the copolymer layer, h(R), can be attributed to the hairy wormlike micelles. The effective volume fraction of the micelles, φeff, is in turn larger than their “naked” volume fraction φ. Assuming that the micelles are infinitely long, one obtains φeff ) φ(1 + [h(R)/r0])2, where r0 is the radius of the naked micelles (r0 = 30 Å). The phase diagrams described in section III (Figure 2) allow a determination of the effective polymer thickness h(R), using simple models for phase separations. The phase separation observed at φT for a solution of hairy micelles may originate from two distinct mechanisms. The first one is a transition toward order, and leads to the isotropic/nematic (I/N) transition in the case of naked micelles. The second mechanism results from a close packing of the cylinders because of their high effective (44) Buhler, E.; Munch, J. P.; Candau, S. J. J. Phys. II Fr. 1995, 5, 765-787. (45) Berret, J. F.; Appell, J.; Porte, G. Langmuir 1993, 9, 28512854.

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volume fraction, and implicitly assumes that the compression or interpenetration of the copolymer layer is energetically less favorable than a phase separation. This is expected to lead to an isotropic/isotropic (I/I) phase separation, consistent with what is observed experimentally (see section III). Simple models enable prediction of the surfactant concentrations φTI/N and φTI/I at the I/N and I/I transition, respectively, as a function of h, the effective copolymer thickness. The isotropic/nematic transition can be analyzed in the framework of the Onsager theory.46,47 This theory predicts that the transition concentration depends only on the aspect ratio of the anisotropic objects, which implies that φTI/N(L/r) is a constant, where L and r are respectively the length and the radius of the cylinders. From the phase diagram, one knows that φTI/N(0) ) 36% for naked micelles (Figure 2). Assuming that the average length L of the micelles remains essentially unchanged, one therefore predicts φTI/N(0)(L/r0) ) φTeff[L/(r0 + h)] at the transition. Thus

(

φTI/N ) φTI/N(0) 1 +

)

-1

h(R) r0

(4)

Note that a similar approach has been used for charged rods47 and for aqueous suspensions of mineral ribbons.48 Similarly, the concept of effective volume has allowed a qualitative description of the morphological sequence of aggregates of block copolymers in a selected solvent.49 The phase separation into two isotropic phases is predicted to occur at φTI/I, the surfactant concentration at which the effective cylinders start to overlap. We assume that the cylinders are packed on a cubic lattice as sketched in Figure 10b, which is compact for a volume fraction φcompact ) 58.9%. Using the definition of φeff, this leads to

(

φTI/I ) φcompact 1 +

)

h(R) r0

-2

(5)

The two surfactant concentrations φTI/I and φTI/N are plotted in Figure 11a as a function of the effective thickness h. For h ) 19 Å, φTI/N ) φTI/I ) 22%. For h < 19 Å, φTI/N < φTI/I, while for h > 19 Å, φTI/N > φTI/I. For a given h, and thus a given copolymer content, the relevant transition is the one that involves the lowest surfactant concentration. This indicates that, at low h, the transition would be governed by the ordering of the micelles, while at higher h it would be controlled by the compactness of the network due to the effective volume of the cylinders. Thus, from the experimental values of φT, one can determine the effective polymer thickness, which is calculated using eq 4 for φT e 22%, and eq 5 for φT g 22%. At a zero order of approximation, h is expected, below the overlap ratio R*, to vary linearly with the amount of copolymer and to be equal to RG for R ) R*. In this regime, h could thus be approximated by h ) RG(R/R*). By contrast, above the overlap concentration, in the brush regime, h is expected to vary more slightly with R. To allow a comparison between the results obtained for both copolymers F68 and F108, the thickness h is therefore normalized by RG, h* ) h/RG, and the copolymer ratio by the molar ratio at the overlap R*, Ω ) R/R*. The following values are (46) de Gennes, P.-G.; Prost, J. The Physics of Liquid Crystals; Oxford Science: New York, 1993. (47) Vrooege, G. J.; Lekkerkerker, H. N. W. Rep. Prog. Phys. 1992, 55, 1241-1309. (48) Pelletier, O.; Davidson, P.; Bourgaux, C.; Livage, J. Europhys. Lett. 1999, 48, 53-59. (49) Hanley, K. J.; Lodge, T. P.; Huang, C.-I. Macromolecules 2000, 33, 5918-5931.

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used: for F68, R* ) 4.6%, RG = 19 Å; for F108, R* ) 3%, RG = 26 Å. In Figure 11b, h* is reported as a function of Ω, for the two copolymers together with the prediction h* ) Ω for Ω e 1. For the larger (F108) copolymer, the experimental data are in very good agreement with this prediction up to Ω ) 0.6, and start to level off for higher densities. For F68, h* varies linearly with Ω in the whole range of Ω investigated (up to Ω ) 1.7) and is systematically lower than expected; the origin of this remains to be clarified. In all cases, the effective thickness of the copolymer layer is on the order of magnitude of the radius of gyration of the polymer, and increases with the polymeric layer density. Thus, despite its crudeness, our simple model leads to very satisfying results.

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has been determined from the phase diagram of the surfactant/polymer mixture. Interestingly, the structure factor of hairy wormlike micelles exhibits features similar to those of the structure factor of polyelectrolyte solutions. While polyelectrolytes interact through a long-range repulsive potential, hairy wormlike micelles interact through a copolymer-mediated short-range steric potential. On the other hand, as opposed to polyelectrolytes, the range of the repulsive potential (on the order of h) and the concentration in micelles are decoupled. One therefore hopes that the study of hairy wormlike micelles may shed some light on the still debated origin of the peak in the structure factor of polyelectrolytes. In this view, a more quantitative analysis of the structure factor of hairy linear chains is needed.

V. Conclusion We have studied a novel self-assembled system consisting of surfactant wormlike micelles onto which are anchored amphiphilic block copolymers. The effective thickness of the copolymer layer h covering the micelles

Acknowledgment. We are grateful to R. Aznar for the synthesis of the PC18. Local contacts L. Auvray at LLB and B. Deme and J. Zipfel at ILL are acknowledged. LA025687A