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Langmuir 2001, 17, 6740-6742
Effect of Adsorbed and Anchored Polymers on Membrane Flexibility: A Light Scattering Study of Sponge Phases M. Maugey and A. M. Bellocq* Centre de Recherche Paul Pascal, CNRS, Avenue A. Schweitzer, 33600 Pessac, France Received April 10, 2001. In Final Form: June 28, 2001
Introduction Dilute solutions of surfactant can exhibit several phases in which the molecules self-assemble as extended fluid bilayer membranes. These phases include a smectic A lamellar phase, a bicontinuous isotropic sponge phase, and less frequently a L4 phase of disconnected vesicles.1 In the lamellar phase, the bilayers are stacked periodically in one direction, in the sponge phase they build a random multiply connected surface separating two distinct continuous solvent volumes, and finally in the vesicle phase they form closed aggregates. In many surfactant/solvent systems, both LR and sponge phases are observed over a broad range of surfactant concentrations. As a consequence, the smectic period d and the characteristic size ξ of the sponge random network can be varied typically from 5 nm at high concentrations to more than 1 µm in the very dilute limit. From theoretical grounds, the phase behavior of fluid membranes is controlled by their volume fraction φM and their bending energy which involves two intrinsic parameters, the bending modulus κ and the Gaussian curvature modulus κj.2 One possible way to monitor these moduli is to adsorb or to graft a polymer on the surface of the membranes. These effects have been explored theoretically.3-5 Polymer grafting is predicted to induce a stiffening of the membrane and a decrease of κj, whereas polymer adsorption should decrease the modulus κ and increase the Gaussian modulus κj. Experimentally, numerous studies on doped polymerbilayer phases have focused on the structure of the bilayers and their interactions.6-12 The influence of adsorbed and grafted polymers on the bending properties of membranes is much less documented.12-14 This is the reason we have focused our interest on the determination of the modulus κ in the presence of both types of polymer. In a recent (1) Bellocq, A. M. In Handbook of microemulsion science and technology; Kumar, P., Mittal, K. L., Eds.; Marcel Dekker: New York, 1999; p 139. (2) Morse, D. C. Phys. Rev. E 1994, 50, 2423. (3) Brooks, J. T.; Marques, C. M.; Cates, M. E. J. Phys. II 1991, 1, 673. (4) Hiergeist, C.; Lipowsky, R. J. Phys. II (France) 1996, 6, 1465; Europhys. Lett. 1995, 30, 197. (5) Clement, F.; Joanny, J. F. J. Phys. II 1997, 7, 673. (6) Ligoure, C.; Bouglet, G.; Porte, G. Phys. Rev. Lett. 1993, 71, 3600. Ligoure, C.; Bouglet, G.; Porte, G.; Diat, O. J. Phys. II (France) 1997, 7, 473. (7) Sing, M.; Ober, R.; Kle´man, M. J. Phys. Chem. 1993, 97, 11108. (8) Ficheux, M. F.; Bellocq, A. M.; Nallet, F. J. Phys. II (France) 1995, 5, 823. (9) Porcar, L.; Ligoure, C.; Marignan, J. J. Phys. II (France) 1997, 7, 493. (10) Freyssingeas, E.; Antelmi, D.; Kekicheff, P.; Richetti, P.; Bellocq, A. M. Eur. Phys. J. 1999, B9, 123. (11) Bouglet, G.; Ligoure, C.; Bellocq, A. M.; Dufourc, E.; Mosser, G. Phys. Rev. E 1998, 57, 834. (12) Yang, Y.; Prudhomme, R.; McGrath, K. M.; Richetti, P.; Marques, C. M. Phys. Rev. Lett. 1998, 80, 2729.
theoretical investigation, it is argued that one may extract an estimate for the bilayer bending modulus κ from the dynamic structure factor of a single membrane.15 In this paper, we report about an experimental study using dynamic light scattering of very dilute sponge phases with adsorbed and anchored polymers. The membranes under investigation are made of sodium dodecyl sulfate (SDS) and hexanol, and the polymers used are poly(ethylene glycol) (PEG) and Brij 700. PEG is dissolved in the solvent and is known to adsorb on the surfaces of SDS micelles16 and also SDS-containing membranes.8 Although the strength of the interaction PEG/SDS-hexanol membranes is not known, critical micelle concentration measurements show that the polymer exhibits an attractive interaction with the mixed SDS-hexanol layer.17 The amphiphilic copolymer polyoxyethylene stearyl ether (Brij 700) consists of a short PEG chain with a molecular weight of 4400 Da covalently linked to a hydrophobic group (C18H37). Exposure of the octadecyl chain to the water environment having a high energy cost, Brij 700 is anchored to the SDS-hexanol membranes. The octadecyl chain is inserted into the bilayer, while the PEG chain is in the aqueous solvent. Experimental Section The sponge phases under investigation are composed of SDS and hexanol in a NaCl brine solution at 10 g/L containing 30% glycerol in volume. The phase diagram of this system has been previously studied.18 Both lamellar and sponge phases are found in an extended range of concentrations. Hereafter, we concentrate on the effect of two polymers on the stability of mixtures with a SDS mass fraction of 0.004. In the sponge phase, the membranes have a 2 nm thickness, and the characteristic size ξ of the sponge is approximately 270 nm. Poly(ethylene glycol) with a molecular weight of 20 000 Da was used as an adsorbing polymer. The radius of gyration of isolated PEG macromolecules in water is approximately 3 nm, and the overlap concentration C* is 35 g/L.9 PEG is provided by Fluka, and Brij 700 by Sigma. In the following, Cp denotes the PEG concentration (g/L) in the aqueous solution and X denotes the Brij 700/SDS mass ratio. Cp has been varied between 0 and 50 g/L; and X, between 0 and 0.75. Sample tubes were prepared by weighing in appropriate amounts of SDS, hexanol, and an aqueous solution containing salt, glycerol, and polymer. The tubes were initially mixed using a vortex mixer, then the tubes were allowed to equilibrate at 25 °C for 2 or 3 weeks. Along a line at constant SDS and polymer concentrations, the weight percentage between two tubes is typically equal to 0.02. Phase boundaries were determined by visual inspection in transmitted light and by observation of the samples between crossed polarizers. The experiments were performed using a coherent IK-90 krypton ion laser light source operating at 476 nm and linearly polarized. The scattered light was collected with a photoncounting photomultiplier tube (Hamamatsu) for scattering angles between 20° and 150°. The time autocorrelation function of the scattered light was accumulated using a BI-9000AT correlator from Brookhaven Instruments. (13) Endo, H.; Allgaier, J.; Gompper, G.; Jakobs, B.; Monkenbusch, M.; Richter, D.; Sottman, T.; Strey, R. Phys. Rev. Lett. 2000, 85, 102. (14) Joannic, R.; Auvray, L.; Lasic, D. D. Phys. Rev. Lett. 1997, 78, 3402. (15) Zilman, A. G.; Granek, R. Phys. Rev. Lett. 1996, 77, 4788. (16) Cabane, B.; Duplessix, R. J. Phys. France 1982, 43, 1529; 1987, 48, 651. (17) Javierre, I. Ph.D. Thesis, University of Bordeaux, France, 1999. (18) Alibert, I.; Coulon, C.; Bellocq, A. M.; Gulik-Krzwicki, T. Europhys. Lett. 1997, 39, 563.
10.1021/la010534t CCC: $20.00 © 2001 American Chemical Society Published on Web 09/14/2001
Notes
Langmuir, Vol. 17, No. 21, 2001 6741
Figure 2. Static light scattering for L3 samples at 0.4% SDS in the representation q2I(q) vs q: Cp ) 0 (b); Cp ) 10 g/L (O); Cp ) 20 g/L (4); X ) 0.3125 (+); X ) 0.75 (×). The scattered light intensity has been normalized to the benzene scattered intensity.
intensity is given by Figure 1. Sections of the phase dragrams of the systems (a) SDS-hexanol-PEG and b) SDS-hexanol-Brij 700 in brine and glycerol (T ) 300 K, NaCl ) 10 g/L, glycerol 30% in volume) at fixed mass concentration of SDS (0.4%). Cp is the PEG concentration in aqueous solution, and X is the Brij 700/SDS mass ratio. The dashed line represents the transition line between the micellar phase L1 and the sponge phase L*. The hatched areas correspond to two-phase regions; the symbol 2φ corresponds to liquid-liquid equilibria.
Results and Discussion Phase Behavior. Figure 1 shows the effect of polymer concentration Cp and on the phase behavior observed along the line at 0.4% SDS. In the polymer-free system, four phases (L1 (micellar), L* (sponge), LR (lamellar), and L3 (sponge)) are found with increasing the alcohol content. The continuous phase transition L1-L*, occurring at the hexanol concentration C1, is easily evidenced by a sharp increase of the light scattered intensity. Freeze-fracture electron microscopy results have previously revealed that L* and L3 sponge phases exhibit different topologies. Indeed, sponges evolve from a structure containing vesicles dispersed in membranes in L* toward a continuous membrane network in L3. PEG and Brij 700 are both soluble in the four phases L1, L*, LR, and L3. However, these polymers affect differently the stability of the membrane phases. At fixed alcohol concentration, the solubilization of PEG in the solvent between the bilayers induces the sequence LRfL3 while the anchoring of Brij 700 within the bilayers produces the inverse transformation L3fLR. In addition, PEG reduces the L* region at the benefit of the L3 domain. These results suggest that PEG and Brij 700 have opposite effects on the Gaussian curvature modulus κj. PEG tends to increase κj, and Brij 700 tends to reduce this modulus. Light Scattering Results. In sponge, the existence of a correlation length ξ between membranes is associated to a characteristic bump or break in the neutron or light spectra at q0 ) 2π/ξ. On a length scale much shorter than ξ (q > q0), the membrane does not interact with neighboring membranes. Scattering at such short wavelengths can thus probe the static and dynamic behavior of a single membrane. In the regime of large wave vectors q > q0, the static structure factor of sponges exhibits a q-2 behavior, typical for an ensemble of nearly flat membrane pieces at random orientation.19 In this regime, the scattered (19) Gazeau, D. et al. Europhys. Lett. 1989, 9, 447.
q2I(q) )
A 2 qδ sin 2 qδ 2
(
( ))
2
(1)
with
A ) 2π∆F2 φMδ 2 where δ is the bilayer thickness, φM is the membrane volume fraction, and ∆F is the contrast. In the range qδ , 1, the scattered intensity must reach the asymptotic limit q2I(q) ) A/2. We performed light scattering measurements on L3 samples located close to the alcohol-rich demixing line. Plotting q2I(q) versus q, as shown in Figure 2, we find that all the spectra exhibit the asymptotic behavior expected for bilayers. This observation gives strong evidence that the sponge structure is conserved by addition of polymer. In the case of PEG, as Cp increases from 0 to 50 g/L the plateau covers approximately the same q range (q > q0 ) 2.3 × 107 m-1) but its value decreases. The first point shows that the sponge size ξ ) 2π/q0 ) 273 nm does not change as PEG is added in the solvent. The reduction of the asymptotic limit A/2 is associated to a variation of ∆F. The addition of PEG increases the refractive index of the aqueous solvent and thereby yields a reduction of the contrast ∆F between the bilayer and the solvent. In the case of Brij 700, the plateau is slightly shifted to higher q and higher values. Both effects reflect an increase of φM related on one hand to the incorporation of Brij 700 in the bilayer and on the other hand to an increase of the alcohol content. Since the static light scattering results show that the addition of PEG or Brij 700 does not affect the sponge bilayer structure, we attempt to measure κ by dynamic light scattering. In a recent study, Zilman and Granek have investigated the dynamical structure factor S(q,t) of membrane phases at large wavenumbers q and have calculated the effect of membrane thermal undulations for an ensemble of membrane plaquettes at random orientations.15 They predict a stretched exponential relaxation
S(q,t) ≈ S(q) exp[-(Γqt)R]
(2)
with
( )
R ) 2/3 and Γq ) 0.025γκ
kBT κ
1/2k T B 3
η
q
(3)
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Langmuir, Vol. 17, No. 21, 2001
Figure 3. Dynamical signal at q ) 2.77 m-1 for the L3 sample at 0.4% SDS and Cp ) 20 g/L. The scattering signal has been normalized to the static intensity. The continuous line corresponds to the best fit to eq 2.
Figure 4. Relaxation frequencies Γq vs q3 for two L3 samples at 0.4% SDS: Cp ) 0 (b) and Cp ) 20 g/L (4).
η is the solvent viscosity and γκ is a weak monotonically increasing function of κ/kBT and approaches unity for κ/kBT > 1. The universal scaling law Γq ∝ q3 and the trend of Γq to decrease with increasing κ are in agreement with experiments previously carried out for dilute sponges.20 We report in Figure 3 a typical L3 dynamic autocorrelation function normalized to the static intensity for a scattering angle corresponding to q/q0 ) 1.2. The time decay of the scattering signal in the regime q/q0 > 1 is definitively nonexponential for all the studied samples. As also illustrated in Figure 3, a stretched exponential function yields a good fit to the data. The stretching exponent R takes for all the samples a constant value close to 0.77 which is slightly larger than the theoretical value (R ) 2/3). The typical shape of the dispersion relation Γq is reported in Figure 4 for two samples with Cp ) 0 and Cp ) 20 g/L. As expected for the dynamics of a single membrane, a q3 scaling is observed for all the L3 samples whatever Cp or X. The reduced relaxation frequency Γ* ) Γq/q3 is polymer dependent. Γ* remains almost constant as Brij 700 is added and decreases by addition of PEG. Using eq 3 and taking into account the changes in solvent viscosity η,21 we deduce the rigidity κ of the bilayer; Figure 5 compares the X and Cp dependences of κ. We (20) Freyssingeas, E.; Roux, D.; Nallet, F. J. Phys. II (France) 1997, 7, 913.
Notes
Figure 5. Variation of the elastic constant κ as a function of Cp (9) and X (×).
find that the relatively small grafting densities investigated in this study (1 Brij molecule/20 SDS molecules) do not modify the bilayer rigidity. This finding agrees with previous results obtained for vesicles stabilized by grafted polymers.14 In contrast, the addition of PEG leads to a strong decrease of κ from 3.1 kBT for Cp ) 0 to 1.7 kBT for Cp ) 50 g/L. The contribution of added PEG to the rigidity appears to decrease steeply with Cp at small concentrations and seems to slightly level off to a mininum value of 1.7 kBT at polymer concentrations above C*. In qualitative agreement with theoretical predictions, the adsorbed polymer makes the membrane less stiff and has a positive contribution to κj whereas the anchored polymer has a negative contribution to κj. This last effect is similar to that seen upon addition of an amphiphilic block copolymer to a bicontinuous microemulsion.13 In addition, the value of κ found in the presence of Brij 700 is compatible with the small size of the polymer and its low concentration in the membrane.4 In the regime of strong adsorption, it has been theoretically found that adsorbed polymers of degree of polymerization N induce a reduction of κ proportional to log N.3 Thus, to see if the observed effect is compatible with a polymer-induced softening of the membrane a systematic study of κ as a function of PEG molecular weight is required. Among the other possible reasons for a decrease of κ, an increase in the area per polar head Σ on the surfactant should be considered since κ is expected to scale as Σ-5.22 The estimation of this effect needs the determination of Σ as a function of Cp. Acknowledgment. Useful discussions with Frederic Nallet and Isabelle Javierre are gratefully acknowledged. LA010534T (21) In both polymer-doped systems, the oxyethylene chains of the polymers are in the solvent. Therefore, we assume that the solvent of the membranes contains brine, glycerol, and the oxyethylene chains of the polymers. Values of solvent viscosity: Cp ) 0, η ) 2.05 cP; Cp ) 10 g/L, η ) 2.6 cP; Cp ) 20 g/L, η ) 3.7 cP; Cp ) 50 g/L, η ) 6.6 cP. Considering the low concentration of Brij 700 in water (
