pubs.acs.org/Langmuir © 2010 American Chemical Society
Growth and Branching of Charged Wormlike Micelles as Revealed by Dilution Laws Martin In,*,† Baroudi Bendjeriou,† Laurence Noirez,‡ and Isabelle Grillo§ †
Laboratoire des Colloı¨des, Verres et Nanomat eriaux, UMR 5587 CNRS-Universit e Montpellier 2, F-34095 Montpellier, France, ‡Laboratoire L eon Brillouin CEA-CNRS, CEA Saclay, F-91191 Gif Sur Yvette, France, and §Institute Max von Laue Paul Langevin, F-38042 Grenoble 9, France Received March 26, 2010. Revised Manuscript Received May 31, 2010 The successive transitions of morphology in aqueous solutions of interacting micelles are directly evidenced by the position q* of the correlation peak of the small angle neutron scattering profiles. As the volume fraction Φ increases, q* successively fits to the dilution laws expected for spheres and cylinders, and eventually gets close to the one expected for sheets when the micelles get branched. Data in between the swelling laws are quantitatively analyzed in terms of aggregation number and junction density. Varying the temperature in the dilute regime yields the end-cap energy which varies with molecular structure and scales as Φ-1/2. In the semidilute regime, the junction density scales as νj ∼ Φ1.8, close but slightly faster than theoretically expected. The boosting effect of intermicellar repulsion on growth and branching is pointed out by the present results which directly show that both condensation processes keep the micelles further apart.
Introduction Giant wormlike micelles consist of long cylindrical supramolecular self-assemblies of amphiphilic molecules.1 They make up the basic nanostructure of aqueous viscoelastic surfactant materials (VES) used to formulate multifunctional materials that combine interfacial tension reduction, high viscosity, and selfhealing ability. The surface activity of VES relies upon the amphiphilic nature of the molecules. The self-healing properties of VES result from the fact that giant micelles form under equilibrium conditions through reversible self-assembling processes. The viscoelastic properties arise from the entanglement of the giant micelles, which can hardly move independently of each other, when their length is much larger than the distance between them. Less than 5% of surfactant in weight can increase the viscosity of an aqueous solution by a factor of 109.1 Like polymers, wormlike micelles can be linear or branched. Their mechanical and thermodynamical properties depend on the number density of ends νe that determines the average length (ÆLæ 1/ νe) and on the branching density νj. For instance, junction points can enhance the elastic properties of VES systems,2 but their profusion leads to phase separation.3-6 The properties of giant micelles are determined by a delicate balance between an effective anisotropic attraction between the building units and the thermal energy, like any stringlike selfassembled system formed under equilibrium conditions.3,6 Anisotropic attraction yields infinitely long strings, while thermal energy tends to disperse the building units in the available volume, *To whom correspondence should be addressed. E-mail: martin.in@ lcvn.univ-montp2.fr. (1) Giant Micelles, Properties and Applications; Zana, R., Kaler, E. W., Eds.; Surfactants Science Series; CRC Press, Taylor & Francis Group: Boca Raton-LondonNew York, 2007. (2) In, M.; Warr, G. G.; Zana, R. Phys. Rev. Lett. 1999, 83, 2278–2281. (3) Tlusty, T.; Safran, S. A. Science 2000, 290, 1328–1331. (4) Porte, G.; Gomati, R.; Elhaitamy, O.; Appell, J.; Marignan, J. J. Phys. Chem. 1986, 90, 5746–5751. (5) Constantin, D.; Freyssingeas, E.; Palierne, J. F.; Oswald, P. Langmuir 2003, 19, 2554–2559. (6) Tlusty, T.; Safran, S. A.; Menes, R.; Strey, R. Phys. Rev. Lett. 1997, 78, 2616– 2619.
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leading to breaking and branching of the strings. As a result, the length distribution is broad and the average length and branching ratio depend on concentration and temperature. In giant micelles, the effective anisotropic interaction results from the fact that the spontaneous curvature of the water/micelle interface is cylindrical. Ends and junctions can be regarded as defects, since their curvature differs from the preferred cylindrical one and excess energies are associated to each of them.3 Ends consist of spherical caps, whose curvature is twice the cylindrical spontaneous one and an excess energy ε1 is associated to it. Junctions locally bilayered present an excess of energy ε2 due to a lack of curvature (Figure 1a). Despite clear direct observations of the nanostructure underlying the unique rheological properties of giant micelles,7 the gap between theoretical insight and experiments has been underlined8 and actually persists. Structural characterization of micelles relies on small angle neutron scattering (SANS) experiments,1,9 which are difficult to account for quantitatively when micelles interact strongly. Models were developed from liquid statistical mechanics10 for small spherical micelles, but they do not rely on the relevant interaction potential for giant micelles since growth and branching yield an attractive component in the effective interaction potential. Recent Monte Carlo simulations shed much light in the understanding of the growth of micelles,11 but they also pointed out the difficulty to account for the scattering properties of charged giant micelles and did not yet lead to any fitting function which could be used to analyze experimental data. Calculation of the form factor for the scattering from the surfaces of threefold junctions has improved the analysis of experimental data, but concerns microemulsion systems with high concentrations of junctions.12 (7) Talmon, Y. I., in ref , Chapter 5, pp 163-178. (8) Odijk, T. Curr. Opin. Colloid Interface Sci. 1996, 1, 337–340. (9) Walker, L. M. Curr. Opin. Colloid Interface Sci. 2009, 14, 451–454. (10) Hayter, J. B.; Penfold, J. Mol. Phys. 1981, 42, 109–118. Hansen, J. P.; Hayter, J. B. Mol. Phys. 1982, 46, 651–656. (11) Cannavacciuolo, L.; Pedersen, J. S.; Schurtenberger, P. Langmuir 2002, 18, 2922–2932. (12) Foster, T.; Safran, S. A.; Sottmann, T.; Strey, R. J. Chem. Phys. 2007, 127, 204711.
Published on Web 06/09/2010
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Figure 1. Ends and junctions in giant micelles of gemini type surfactants. (a) Branched cylindrical micelles present curvature heterogeneities: spherical end-caps are associated to an excess of energy ε1, while locally flat junctions are associated to an excess of energy ε2. (b) Surfactant trimer.
The present work shows that the position of the correlation peak that characterizes the SANS profiles of charged wormlike micelles can be analyzed quantitatively in a simple way in terms of growth and branching. This approach is carried out on a series of cationic gemini type surfactants,13 which consist of several amphiphilic moieties (one polar headgroup bound to one fatty chain) tethered at the headgroup level through a spacer of variable length (Figure 1b). Tethering surfactants in this way provides a direct and efficient steric influence over the molecular packing that determines the shape of the micelles. Minute modifications at the molecular level generate all the types of morphologies from spherical micelles to vesicles,14 through branched15 and closedlooped16 wormlike micelles. Surfactant dimers and trimers used in the present study consist of quaternary ammonium C12 amphiphilic moieties with bromide counterions and tethered through polymethylene spacers -(CH2)s- (Figure 1b). They will be referred to as 12-s-12 and 12-s-12-s-12 and can be considered as oligomers of the conventional surfactant dodecyltrimethyl ammonium bromide (DTAB).
Experimental Section Materials. Surfactant oligomers 12-2-12, 12-3-12, 12-3-12-312, and 12-6-12-6-12 were synthesized by quaternization of the corresponding permethylated polyamine with bromododecane.13 The permethylated amines were either commercially available (tetramethylethylene diamine, tetramethylpropylene diamine) or permethylated by reductive alkylation with formaldehyde as alkylating agent and formic acid or sodium borohydride as reducing agent. Details of the synthesis procedure and purification can be found in ref 13. DTAB is commercially available and has been used as received. The critical micelle concentration (CMC) of each surfactant has been measured in D2O by conductimetry. It corresponds to the slope break in the concentration dependence of the conductivity. CMC values are reported in Table 1 of the Supporting Information SI 1. Surfactants were studied by SANS in deuterated water, over a broad range of volume fractions from Φ = 0.02% to 25%, in the micellar phase. Small Angle Neutron Scattering. The SANS data have been collected during several runs at the Laboratoire Leon Brillouin in Saclay, France using different beamlines (PAXY and PACE). The range of scattering vector covered is 0.007 A˚-1< q < 0.4 A˚-1, using two combinations of sample-detector distance and wavelength. The temperature was controlled via a circulating fluid in the sample holder rack and controlled by using an internal probe located in one of the sample cells. The samples were held in Hellma quartz cells with 1 or 2 mm pathway. Samples at very low concentration were studied on the high flux line D22 at the (13) In, M.; Bec, V.; Aguerre-Chariol, O.; Zana, R. Langmuir 2000, 16, 141–148. (14) Zana, R.; Talmon, Y. Nature 1993, 362, 228–230. (15) Danino, D.; Talmon, Y.; Levy, H.; Beinert, G.; Zana, R. Science 1995, 269, 1420–1421. (16) In, M.; Aguerre-Chariol, O.; Zana, R. J. Phys. Chem. B 1999, 103, 7747– 7750.
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Figure 2. (Inset) Scattering pattern I(q) of charged micelles characterized by a correlation peak at a scattering vector qImax; 12-3-123-12 at various volume fractions. As maximum intensity increases, Φ = 0.45, 0.90, 1.80, 3.60, 5.40, 9.0, 13.5, and 18.0%. (Main frame) Position of the correlation peak as a function of Φ. (þ) DTAB; () 12-6-12-6-12; (2) 12-3-12; (O) 12-2-12; (0) 12-3-12-3-12 in D2O at 25 C. The equations of the continuous lines from the thinnest to the thickest one are qI* = 0.227Φ1/3, qI* = 0.207Φ1/2, qI* = 0.254Φ1.
Institute Laue Langevin in Grenoble, France. Raw data were radially averaged when necessary (PAXY and D22 spectrometers), normalized for incident flux, transmission, sample thickness, and detector sensitivity using standard procedures. The incoherent background scattering has been determined from the slope of Iq4 versus q4 plots and subtracted from the normalized data. The position of the peak of the intensity I(q) and of the apparent structure factor ÆS(q)æ have been determined by fitting of the data around the correlation peak by a Gaussian function. ÆS(q)æ is obtained by dividing the scattering profile I(q) by a calculated form factor estimated from high q data, where S(q) oscillates around 1 by less than 1%: ÆS(q)æ = I(q)/[νf 2P(q)]. P(q) is the normalized form factor (P(0) = 1), ν is the number density of micelles, and f is the scattering power of the micelles determined by their volume and their composition. For surfactants prone to form giant micelles, there is a range of volume fraction close to the onset of the semidilute regime where it is not possible to satisfactorily fit the high q data with the form factor of either spheres or cylinders. In such cases, P(q) has been estimated using the Guinier approximation: P(q)= K exp[-(Rgq)2/3].
Results and Discussion Transitions of Shape. Due to electrostatic repulsion, charged micelles are not distributed randomly in aqueous solution. They adopt a preferred first neighbor distance d, and their SANS profiles I(q) are therefore characterized by a correlation peak at q*(Figure2, I inset).The way qI* varies with concentration can be quite irregular for one particular surfactant (Figure 2). However, the whole set of data is framed by a succession of three power laws, the so-called dilution or swelling laws: qI* Φ1/D. They are reminiscent of the ones observed for the first Bragg peak in liquid crystals.17 The characteristic exponent of the dilution law is related to the dimensionality of the crystalline structure: D = 3 for the packing of spheres, D = 2 for infinite cylinders, and D=1 for lamellar stackfrom ing. In liquid crystals, phase transitions lead to jumps of q*(Φ) I one dilution law to the other. In the present study, the three dilution laws are observed in a single phase and qI*(Φ) is continuous all over the volume fraction range. It reflects the continuous morphological transitions, from spherical to cylindrical and branched cylindrical (17) Hyde, S. T. Colloids Surf., A 1995, 103, 227–247.
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Figure 3. Growth of the micelles in the dilute regime. (a) Aggregation number N versus surfactant volume fraction Φ at T = 25 C; (2) 12-3-
12; (O) 12-2-12; (0) 12-3-12-3-12 in D2O. (b) N versus rescaled inverse of the temperature in semilogarithmic scale; (2)12-3-12 at 1.5%, ε1 = 38 ( 5kT; (O) 12-2-12 at 1.0%, ε1 = 40 ( 6kBT; (0) 12-3-12-3-12 at 0.5%, ε1 = 54 ( 8kBT. (c) End-cap energies ε1 versus the inverse of the square root of the volume fraction; (2) 12-3-12; (O) 12-2-12; (0) 12-3-12-3-12 in D2O.
micelles. This interpretation is supported by closer analysis of the high q data (see Supporting Information Figure 2). It is also supported by the known structure of solutions of charged colloids and macromolecules: Solutions of colloidal particles interacting at distances larger than their own size, either spherical18 or rodlike,19 are characterized by qI* Φ1/3. In this regime, the peak position is determined by the number density ν of particles and the prefactor of this dilution law depends on the size of the micelles. When flexible one-dimensional objects get longer than their first neighbor distance, then qI* Φ1/2.11 This defines the semidilute regime of solutions of charged macromolecules and giant cylindrical micelles, where q*I reflects the mesh size of the entanglement network. remains close to Φ1/3 up to For 12-6-12-6-12 and DTAB, q*(Φ) I 13%, which means that those surfactants do not form entangled giant micelles. On the contrary, upon increasing Φ of short spacer through a maximum at Φ = Φc and dimers and trimer, q*goes I then decreases until it reaches the minimum at Φ = Φ* that marks the onset of the semidilute regime. Between Φc and Φ*, an increase of Φ does not lead to an increase of the number density of micelles, otherwise q*I would increase. This reflects a condensation process and reveals that the micelles get larger. For Φ > Φ*, qI* Φ1/2, but for the surfactants 12-2-12 and 12-3-12-3-12 qI*(Φ) eventually deviates from Φ1/2: It increases more slowly and gets closer to Φ1. This suggests a second condensation process that could correspond to the formation of either ribbons or junctions. However, the scattered intensity at high q is still close to the one calculated for cylinders. Moreover, cryo-TEM showed that both these surfactants are prone to form branched wormlike micelles9,10 and their solutions present an enhanced elasticity.2,13 In the following section, the quantitative interpretation is carried out on q*, S the position of the maximum of the measured structure factor ÆS(q)æ. It is obtained by dividing I(q) by the average form factor of an ensemble of polydispersed micelles.18 Note that qI* and qS* did not differ by more than 15% in our samples, so that considering either one for the above qualitative discussion is equivalent. Aggregation Number and End Energies. In the dilute regime (Φ < Φ*), the nearest-neighbor distance d = 2π/qS* is determined by the number density of micelles νM: d νM-1/3. It means that measuring d is equivalent to counting the micelles. Since the number density of micellized surfactant νs is known, the number N of amphiphilic moieties a micelle is made of can be thus expressed as20 !3 1 pffiffiffi2π 3 νs N ¼ ð1Þ 4 qS (18) D’Aguanno, B.; Klein, R. J. Chem. Soc., Faraday Trans. 1991, 87, 379–390. (19) Schneider, J.; Karrer, D.; Dhont, J. K. G.; Klein, R. J. Chem. Phys. 1987, 87, 3008–3015. (20) Chen, S. H.; Sheu, E. Y.; Kalus, J.; Hoffmann, H. J. Appl. Crystallogr. 1988, 21, 751–769.
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The numerical prefactors come from the hypothesis of the facecentered cubic local ordered structure of the solution.20 It can be shown that aggregation numbers obtained this way are number averaged in the case of wormlike micelles (see Supporting Information SI 3). The volume fraction dependence of N is presented in Figure 3a. For DTAB, N ≈ 50-60, in good agreement with the values obtained from explicit expression of S(q) using statistical mechanics of liquids.21 For short spacer dimers and trimers, we can distinguish two regimes of growth: a slow one for Φ < Φc, followed by a rapid growth regime beyond Φc. This is theoretically expected for charged micelles22 and has also been observed in molecular dynamics simulations for gemini surfactants.23 Aggregation numbers up to N = 1000 have been measured which corresponds to a length of about 40 nm. N approximately scales as N ∼ L ∼ Φ1.4, faster than expected for noninteracting micelles (N ∼ Φ1/2). Figure 3b shows that N increases as the temperature decreases according to: N exp(ε1/2kBT).24 ε1 varies from 10 to 60kT depending on the molecular structure of the surfactant but also on Φ: ε1 = ε1 - RΦ-1/2 (Figure 3c), with R = 2.9kBT. ε1 increases when the spacer length s decreases and when the oligomerization degree increases. It equals 50, 70, and 90kBT for 12-3-12, 12-2-12, and 12-3-12-3-12, respectively. The volume fraction dependence of ε1 and the different regimes of growth can result from intramicellar interactions between surfactant molecules,22 which correspond to forces acting parallel to the water/micelle interface. However, the role of the repulsions between the micelles working perpendicular to the interface is strongly suggested in Figure 2, since the transition from sphere to rod keeps the micelles further apart. The growth of micelles has been shown to be enhanced by excluded-volume interactions at high Φ.25 The same influence is expected at lower Φ for electrostatic repulsions, since they are equivalent to a padding of the excluded-volume dimension.11,25 Junction Density. In the semidilute regime (Φ > Φ*), branching shifts the peak toward low q values in the solutions of 12-212 and 12-3-12-3-12 (Figure 2). This is interpreted as being due to the local excess of surfactant concentration in the vicinity of the junction that leads in turn to a depletion of surfactant in the remaining volume containing strictly linear segments of wormlike micelles. For low concentrations of junctions, the micellar (21) Hayter, J. B. Physics of Amphiphiles: Micelles, Vesicles and Microemulsions; International School of Physics “Enrico Fermi”; North-Holland: Amsterdam, 1985; p 76. (22) Mackintosh, F. C.; Safran, S. A.; Pincus, P. A. Europhys. Lett. 1990, 12, 697–702. (23) Maiti, P. K.; Lansac, Y.; Glaser, M. A.; Clark, N. A.; Rouault, Y. Langmuir 2002, 18, 1908–1918. (24) In the dilute regime, the junction density is supposed so low that the temperature dependence of the aggregation number is solely determined by the end energy ε1. (25) Gelbart, W. M.; Ben-Shaul, A.; McMullen, W. E.; Masters, A. J. Phys. Chem. 1984, 88, 861–866.
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Figure 4. Formation of junctions in the semidilute regime. (a) Number density of junctions νj versus volume fraction Φ in 12-3-12-3-12 solutions at T = 25 C. (b) Volume fraction of the junction domains νjVj (b) and normalized interjunction (9) distance versus Φ; data corresponding to gray symbols were not taken into account for the fit in (a). (c) Position of the correlation peak q* I as a function of rescaled inverse temperature, between 25 and 62 C.
solution can be assumed to be composed of νj spherical junction domains per unit volume, independent of each other, each of volume Vj, and characterized by an average volume fraction Φj > Φ. The principle of conservation of matter leads to νj ¼
1 Φ - Φapp V j Φj - Φapp
ð2Þ
where Φapp is the apparent volume fraction of the micelles segments that are strictly linear and supposed to dominate the scattering pattern. Φapp is obtained from the experimentally established dilution law for cylinders: qS* = 0.20Φapp1/2. Due to the radial geometry of the junction, the local excess of volume fraction in the vicinity of a junction vanishes as one gets further from the junction center. This defines the size of the junction domain: Rj = (3/4)1/2(CSb/qS*), from which Vj and Φj are computed using results from ref 26 (see Supporting Information SI 4 for details). As shown in Figure 4a, νj in 12-3-12-3-12 solutions increases by a factor of 10 from Φ = 0.016 to Φ = 0.066 and scales as Φ1.8(0.3. Application of eq 2 was limited to the low volume fractions of the semidilute regime (Φ < 0.07), where the fraction of volume occupied by the junction domains νjVj remains below 15%, so that the assumption of the scattering profile being dominated by the packing of the linear segments of the micelles is probably correct. Moreover, in this range, the average distance between two junctions djj ≈ νj-1/3 remains larger that the characteristic distance of the system 2π/qS* (Figure 4b). Finally, the molar fraction of surfactant in the junctions remains below 10%. The volume fraction dependence of νj is in good agreement but slightly higher than theoretical expectation (νj ∼ Φ1.5) for neutral micelles.3,27 The discrepancy could be explained by the fact that part of the interaction energy between micelles is relaxed by branching because of the associated increase of the mesh size. Moreover, the excess energy ε2 associated with the junctions is related to the curvature and depends on the fraction of condensed bromide counterions.28 As volume fraction increases, more counterions are expected to condense and this could lead to a decrease of ε2. Experiments were carried out at increasing temperatures for 12-3-12-3-12 at Φ = 0.15. q*I is observed to decrease toward the cylinder dilution law as temperature decreases (Figure 4c). Although this volume fraction is out of range to apply eq 2, the shift of qI* qualitatively shows that the concentration of junctions decreases as temperature rises, contrarily to expectations for a defect of constant excess energy. However, an increase in tem(26) May, S.; Bohbot, Y.; Ben-Shaul, A. J. Phys. Chem. B 1997, 101, 8648–8657. (27) Drye, T. J.; Cates, M. E. J. Chem. Phys. 1992, 96, 1367–1375. (28) Andreev, V. A.; Victorov, A. I. Langmuir 2006, 22, 8298–8310.
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perature releases counterions and probably rises ε2, as opposed to what is observed with nonionic surfactants, where an increase in temperature favors lower curvature and branching due to progressive dehydration of oxyethylene moieties.29
Conclusion Strongly interacting micelles of short spacer gemini surfactants undergo two types of morphological transition: The first is the growth from spheres to wormlike micelles and the second one corresponds to branching. Both correspond to condensation processes that maintain average intermicellar distances larger than expected when increasing the volume fraction of micelles of constant morphology. That is why they are directly revealed by the concentration dependence of the position of the correlation peak of SANS patterns. Growth and branching of wormlike micelles are triggered by an overall attractive effective interaction determined by spontaneous curvature. However, these condensation processes reduce the number density of micelles and keep them further apart, they also relax some of the energy associated with repulsive forces, so that electrostatic repulsions have a probably a boosting effect on growth and branching. To quantitatively address this contribution is difficult because screening intermicellar interaction by adding salt would also increase the effective attraction since it reduces the preferred curvature through counterion condensation. The approach presented here can be extended to other self-assembled network based materials provided that long-range repulsions take part in the interactions between the building units. Acknowledgment. The Laboratoire Leon Brillouin and the Institut Laue Langevin are acknowledged for the beam time allocated. This work has been conducted within the scientific program of the European Network of Excellence Softcomp: Soft Matter Composites: an approach to nanoscale functional materials, supported by the European Commission. P. Delors, M. Abkarian, and J. Oberdisse are gratefully acknowledged for fruitful discussions. Supporting Information Available: Table SI I: CMC of surfactants in D2O. Figure SI 1: Various representations of the scattering profile for spherical cylindrical and branched cylindrical micelles. (a) log-log and comparison with calculated ones for spheres and cylinders; (b) Porod plot; (c) Kratky plot. SI3: Explanations on the polydispersity issue and the kind of average q* provides. SI4: Details on the model to determine νj from q*. S This material is available free of charge via the Internet at http://pubs.acs.org. (29) Zilman, A.; Safran, S. A.; Sottmann, T.; Strey, R. Langmuir 2004, 20, 2199– 2207.
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