Highly Oriented, Charged Multilamellar Membranes Osmotically

while for uncharged chains it is the density of macromolecules which matters. ...... Elodie Soussan , Muriel Blanzat , Isabelle Rico-Lattes , Alic...
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Langmuir 2003, 19, 8235-8244

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Highly Oriented, Charged Multilamellar Membranes Osmotically Stressed by a Polyelectrolyte of the Same Sign G. Brotons,*,†,§ T. Salditt,‡,§ M. Dubois,† and Th. Zemb† Service de Chimie Mole´ culaire, CEA/Saclay, Baˆ t. 125, F-91191 Gif-sur-Yvette Cedex, France, and Experimentalphysik, Universita¨ t des Saarlandes, Postfach 15 11 50, D-66041 Saarbru¨ cken, Germany Received April 30, 2003. In Final Form: July 18, 2003 We report an X-ray reflectivity study on highly charged lamellar phases of the surfactant didodecyldimethylammonium halides (DDA+X- where X- ) Cl- or Br-). A few thousand bilayers are aligned on a flat solid surface with a mosaicity below 0.01° and are swollen under controlled osmotic pressure (Π) from periodicities (d) of a few nanometers up to several tens of nanometers by means of direct immersion in the osmotic stressor reservoir. The high-pressure regime (small d) is obtained by water vapor of controlled relative humidity, while lower pressures (high d) are imposed by means of a novel osmotic stress technique. Accordingly, the solid supported sample is immersed in a high mass polyelectrolyte solution with the same sign and counterions than the membranes under study. Thus, water equilibrating time is reduced from weeks to minutes due to the absence of a semipermeable dialysis membrane. Measurements of the specular and nonspecular X-ray reflectivity are demonstrated to be possible through the osmotic reservoir even with a laboratory X-ray tube which greatly simplifies the establishment of the equation of state Π(d). With the same setup, bilayer undulations and compressibility fluctuations can be studied by peak line shape analysis of high-resolution synchrotron data.

I. Introduction Our aim is to investigate the structure, fluctuations, and interaction forces in highly charged lamellar phases of synthetic surfactant and biomimetic lipid bilayers. Lamellar phases exhibit smectic-A liquid crystal (LC) symmetry and can be easily identified by their characteristic Bragg peaks. In the absence of charged species in the aqueous layers (no added salt and low critical micellar concentration, cmc), charged surfactant membranes can be swollen by dilution with water from contact up to 100 nm of water thickness, as determined from the Bragg peak spacing measured by small-angle X-ray scattering (SAXS) or small-angle neutron scattering (SANS). Accordingly, the inter-bilayer interaction is expected to be dominated by electrostatic repulsion, balanced by the osmotic pressure (Π) imposed by the surrounding medium when water in the multilayer is at equilibrium with water outside (osmotic reservoir). At the same time, high surface charge densities σ (∼0.2 C/m2) are expected to affect the bilayer rigidity κ and to dominate over the intrinsic rigidity which is low for fluid surfactant membranes of short hydrocarbon chains. This purely electrostatic description should lead to a universal scaling behavior of the elasticity constants with the repeat distance d of the lamellar stack independent of the nature of the counterion and surfactant headgroups. In other words, the charge density and the imposed pressure should exclusively determine d (i.e., the swelling behavior), as well as the elasticity constants (compressibility modulus and bending stiffness) and corresponding fluctuation properties. This simplified picture has to be corrected by taking into account additional interactions,1,2 such as dispersion or van der Waals forces, hydration forces, and entropic repulsion. * To whom correspondence may be addressed: e-mail, [email protected]; tel: (49) 551 39 9392. † CEA/Saclay. ‡ Universita ¨ t des Saarlandes. § Present address: Institut fuer Roentgenphysik, Georg-AugustUniversitaet, Geiststr. 11, D-37073 Goettingen, Germany.

Besides, it relies on the critical assumption that the counterions behave in a universal manner, i.e., like pointlike charges (mono- or multivalent) with no specific interaction (i.e., binding to the bilayer, etc.). To this end, the range over which the universal predictions are valid has to be investigated. Most importantly, fundamental aspects of specific counterion effects (e.g., anionic Hofmeister effects) are relevant to the properties and stability of many colloidal phases such as the interactions between biomolecules. All of these effects can be studied in the simple and well-defined geometry of a lamellar phase, which is experimentally amenable to quantitative pressure-distance relationships. As is well-known from linear smectic-A elasticity theory,3,4 two constants characterize a lamellar phase of fluid membranes (bilayers without shear rigidity): the compressional modulus B (J/m3) and the bending modulus K ) κ/d (J/m), where κ is the bending energy (J) or bilayer stiffness (for a textbook treatment see ref 5). Accordingly, in-plane undulations (along r|) and periodicity fluctuations (along z) are thermodynamically constrained and governed by B and K, which quantify the energy costs involved. Both fluctuation modes of the multilayered liquid crystals are thermally excited, and the so-called “Caille´ model”6 built upon this theory predicts the broadening and the smearing of the X-ray diffraction peaks. In practice it is difficult to discriminate between bending and compression modes when studying isotropic bulk samples composed of multilamellar stacks with arbitrary orientations (“powder (1) Parsegian, V. A.; Rand, R. P.; Fuller, N. L.; Rau, D. C. Methods in Enzymology; Packer, L., Ed.; Academic Press: New York, 1986; Vol. 127. (2) Israelachvili, J. N. Intermolecular and Surface Forces: With Applications to Colloidal and Biological Systems; Academic: Orlando, FL, 1985. (3) Landau, L. D. Collected Papers of L. D. Landau; Ter Haar, D., Ed.; Gordon and Breach: New York, 1965; p 209. (4) de Gennes, P. G. J. Phys. (Paris) Colloq. Fr. 1969, 30, 65-71. (5) de Gennes, P. G.; Prost, J. The Physics of Liquid Crystals; Clarendon: Oxford, 1993. (6) Caille, A. C. R. Acad. Sci. Paris 1972, t. 274, 891-893.

10.1021/la034733j CCC: $25.00 © 2003 American Chemical Society Published on Web 08/22/2003

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samples”), leading to concentric Debye-Scherer rings at q ) n2π/d for each Bragg order (n ) 1, 2, 3, ..., where n is the order of reflection). Contrarily, for oriented lamellar phases the scattering is strongly anisotropic in the direction of the stacking (z) and perpendicularly (in-plane of the membranes, r|). In this geometry, all three functions d(P), B(P), and K(P) can be accurately measured by specular 7 and nonspecular X-ray reflectivity, given that the measured fluctuation spectrum conforms to the predictions of the standard Caille´ model. In this case, the line shape of the pseudo-Bragg peaks is determined by d, B, and K. Thus, three functions can in principle be measured and checked against theoretical models. While we do not carry out such analysis in the present paper, we develop and discuss the basic experimental technique to perform such work. Section II discusses the concepts of our approach for probing charged membrane forces within multilayer assemblies. We combine an extension of the classical osmotic stress technique (section II.A) for establishing the equation of state (pressure-distance relation) of highly charged lamellar phases (section II.B), which are oriented on a solid support (section II.C) in order to carry out interface-sensitive scattering methods. Section III (materials & methods) presents the details of the sample preparation and the scattering experiments. Results are discussed in section IV, and finally Section V closes with a summary and a short outlook. II. Equation of State, Thermal Fluctuations, and Scattering Theory (II.A) The Classical Osmotic Stress (OS) Technique for Establishing the Equation of State. Imposing the osmotic pressure (Π, in N/m2) to a swollen lamellar phase (ideally flat and parallel membranes) is strictly equivalent to imposing the net interaction force experienced by the membranes through the water layer. Indeed, the osmotic pressure quantifies the cost or gain in free energy for removing or adding bulk state water molecules (at Π ) 0) to the inter-bilayer solution, and thus, it quantifies the inter-bilayer forces as a function of d. From this general concept, the so-called “osmotic stress (OS) technique” has been developed by Parsegian and coworkers,1 where the sample under investigation is equilibrated with a reservoir of water with known osmotic pressure (i.e., fixed water chemical activity). Repeating the equilibration step at several osmotic pressures combined with microstructural characterization of the sample allows establishing pressure-distance relationships, i.e. the curve d(Π) so-called the equation of state (EOS). In practice this is achieved by combining SAXS or neutron SANS diffraction and the OS technique: low pressures (below ∼106 Pa) are imposed with a hydrophilic neutral polymer solution as a reservoir (usual stressors are poly(ethylene glycol) (PEG), poly(vinylpyrrolidone) (PVP), or dextran) through a dialysis membrane only permeable to water, while high pressures (up to ∼108 Pa) are reached by direct contact with vapor from a saturated salt solution. The OS method has been extended to the use of polyelectrolyte stressor solutions by Morvan and co-workers8 on clay dispersions in order to reach the intermediate stress regime (104-105 Pa) with a low polymeric mass content. The electrostatic repulsions in charged polyelectrolyte solutions drastically increase the pressure in comparison to neutral polymers. (7) Mennicke, U. PhD Dissertation, Georg-August-Universita¨t zu Go¨ttingen, 2003. (8) Morvan, M.; Espinat, D.; Vascon, R.; Lambard, J.; Zemb, T. Langmuir 1994, 10, 2559-2565.

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(II.B) Highly Charged Membranes, Inter-bilayer Force Balance, and Membrane Rigidity. The synthetic surfactant chosen can be considered as a model system. Didodecyldimethylammonium halide (DDAX) bilayers expose about one charge every 70 Å2 (σ ∼ 0.2 C/m2) when the counterions are dissociated from the headgroups. They self-assemble to thin fluid membranes (∼2.4 nm thickness at room temperature) which in turn form lamellar phases over a large dilution range (DDABr: 0.025 < φ < 0.9, where φ is the volume fraction of surfactant). The low cmc (∼5 × 10-5 mol/L) warrants negligible electrostatic screening of membrane interactions. DDABr has relatively short 12-carbon acyl chains, leading to a correspondingly low crystallization temperature (transition from LR to Lβ phase at 18 °C and full hydration). The intrinsic bending stiffness (without electrostatic contribution) is expected to be rather low, e.g., compared to phospholipid bilayers. In parallel, we carry out a study of charged phospholipid systems with a similar charge density but a much greater intrinsic bending rigidity (Mennicke et al., in preparation). The simplest expression for the pressure-distance relation of highly charged lamellar phases is obtained by considering purely electrostatic repulsion and neglecting ions in the aqueous layer. It is known as the Langmuir equation2 for two interacting parallel and highly charged plates

(

ΠLang ) kBT

)

π 2LBeW2

where eW ) d - eB is the water layer thickness for uncompressible bilayers with thickness eB and LB is the Bjerrum length (∼7.2 Å in water at room temperature). The Langmuir equation corresponds to the asymptotic law of the exact analytical solution with no added salt9,10 obtained when the distance between plates eW is much larger than the Gouy-Chapman length here equal to λGC ) s/2πLB ∼ 1.5 Å, where s ∼ 70 Å2 is the DDAX bilayer surface per charge. Derivation of this expression gives the compressibility modulus, i.e., the variation of pressure (Π) associated to a variation of volume (here eW)

( )

BLang ) -d

( )

∂ΠLang π d ) kBT ∂eW LB e 3 W

(1)

These expressions assume flat membranes, i.e., with infinitively large bending modulus (K) or equivalently bending energy (κ). Nallet and co-workers11 have reported laboratory SAXS and SANS intensity profiles of DDABr (φ ) 0.04) and AOT (φ ) 0.14 to 0.62) lamellar phases, which could be modeled by the Caille´ theory simplified to an analytical expression in the limit of small undulations. In these experiments the randomly distributed domains in bulk solution and the relatively low instrumental resolution used (∆q ∼ (2-8) × 10-3 Å-1), might have prevented the detection of in-plane undulation modes. However, these modes are expected for such systems and swellings since bending energies are assumed to be close to kBT (at room temperature), following the prediction of Higgs and Joanny for the electrostatic contribution to κ in lamellar phases with no added salt12 (9) Engstro¨m, S.; Wennerstro¨m, H. J. Phys. Chem. 1978, 82, 27112714. (10) Dubois, M.; Zemb, T.; Belloni, L.; Delville, A.; Levitz, P.; Setton, R. J. Chem. Phys. 1992, 96, 2278-2286. (11) Nallet, F.; Laversanne, R.; Roux, D. J. Phys. II 1993, 3, 487502.

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K)

κ d

in (J/m)

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(2)

where

κ)

(

)

kBT π2 1e πLB 12 W

In many cases, additional specific interactions have also to be included in the EOS and are responsible for particular regimes, e.g., in the EOS and more generally the phase behavior. Examples of such interactions are the charge regulation mechanism established by Ninham and Parsegian13 according to which s increases when counterions bind to the charged membranes, as well as the general formalism recently proposed by Ninham and Yaminsky including the theory of dispersion forces between an ion and an interface14 (subject reviewed recently15), or finally the entropically driven repulsive force introduced by Helfrich,16 which is expected to become relevant at high swellings when van der Waals (VDW) and electrostatic forces compensate. Many more parameters than those of eq 1 and eq 2 can therefore enter the calculation of B and K for charged membranes. Thus, the force balance becomes uncertain and may be based on a high number of assumptions concerning these unknown parameters. Experimental evidence for the validity of the assumptions is needed. Among the questions of interest to be addressed for highly charged membranes are as follows: (i) What is the nature of thermal fluctuations and their role in lamellar stability? (ii) Does the theory of linear smectic elasticity apply, e.g., in the absence of electrostatic screening (no added salt)? Finally, the most interesting issue: (iii) what is the role of counterions with different polarizabilities (interaction forces, membrane rigidity, phase diagram)? Can we measure the ion distribution, investigate ion-ion interactions, and distinguish between classical and more recent theories for ion distribution?17 (II.C) Interface-Sensitive Scattering Techniques and Peak Line Shape Analysis. Specular and nonspecular X-ray reflectivity may provide the key to answer to these questions. Roughly speaking for a multilayered film,18 the specular reflectivity (equal incident and exit angle) can be modeled from the electronic density profile perpendicular to the interfaces (F(z)), while the nonspecular scattering is obtained from the statistical heightheight difference function: gij(r|) ) 〈|ui(r|′) - uj(r|′ + r|)|2〉 where ui(r|) is the displacement of the interface labeled i from its mean z position at the lateral coordinate r|. The experimental distinction between diffuse scattering due to periodicity variations (along z) or due to lateral undulations becomes possible in highly oriented samples, i.e., in samples with a low mosaicity (distribution of bilayer normal vectors with respect to the substrate interface).19 Full range line shape fitting is needed covering several Bragg reflections measured on high-resolution instruments (synchrotron SAXS) in order to be sufficiently sensitive. To this end, we propose to use highly oriented samples which allow the detection of even very weak (12) Higgs, P. G.; Joanny, J.-F. J. Phys. (Paris) 1990, 51, 2307-2320. (13) Ninham, B. W.; Parsegian, V. A. J. Theor. Biol. 1971, 31, 405428. (14) Ninham, B. W.; Yaminsky, V. Langmuir 1997, 13, 2097-2108. (15) Leontidis, E. Curr. Opin. Colloid Interface Sci. 2002, 7, 81-91. (16) Helfrich, W. Z. Naturforsh. 1973, 28C, 693-703. (17) Netz, R. R. Eur. Phys. J. E 2001, 5, 557-574. (18) Daillant, J.; Gibaud, A. Lect. Notes Phys. 1999, 58. (19) Salditt, T.; Li, C.; Spaar, A.; Mennicke, U. Eur. Phys. J. E 2002, 7, 105-116.

signals due to intrinsically high signal-to-noise ratios. We report here how to prepare such highly oriented lamellar phases made of charged DDAX bilayers and how to use a novel variation of the OS technique, which preserves the high orientational alignment needed for reflectivity measurements. We emphasize the experimental aspects of sample alignment, sample osmotic equilibration, proper choice of osmotic stressor to avoid the use of semipermeable membranes (dialysis bags), and finally the details of the specular and nonspecular reflectivity experiments. We also compare the information extracted from our approach on oriented surfactants to the previous measurements on isotropic bulk suspensions (d(Π) curves). Technically, we compare two complementary approaches: The first one is to use high-resolution synchrotron reflectivity instruments to probe the conformation of the membranes on lateral length scales between some angstroms and several micrometers without model assumptions. The second route is to develop more accessible in-house techniques, since our interest is to explore the pressure-distance diagram (EOS) of many lamellar phases and to connect their structure and fluctuations to molecular and thermodynamical forces. We would like to render laboratory reflectivity experiments on charged membrane multilayers as simple as SAXS experiments which are routinely carried out for isotropic bulk samples. III. Materials and Methods Surfactants. The synthetic surfactant chosen for this study is DDABr ((C12H25)2N+(CH3)2Br- with molar weight of 462.64 g/mol) purchased from Acros Organics (99% purity). We name it DDAX, where in the dissociated state DDA+ stands for the cationic group composed of a hydrophilic quaternary ammonium headgroup with two hydrocarbonated C12H25 tails and X- stands for the anionic counterion (X- being Cl- or Br- in this study). DDABr was highly purified from three recrystallization and filtration steps (one in ethyl acetate and two in acetone/ether oxide mixtures) that allow us to extract several percent in weight of a clear yellow paste. Purified DDABr salt was changed to DDACl through an anion-exchange column in the chloride form (resin Bio-Rad, AG MP-1 extensively washed and filtrated with Milli-Q water) carried out in a 25-75 mixture of ethanol and water. The counterion exchange was checked by capillary electrophoresis (capillary ion analyzer, model Quanta 4000 from Waters). All surfactants have been lyophilized and kept in dry atmosphere before use. Solid Supported and Highly Oriented Lamellar Phases of Charged Bilayers. To this end, spreading lipid surfactants from organic solutions has shown to be an efficient route for preparation of solid supported multilamellar membranes.20 Bilayers can be deposited on solid substrate, and stacks of oriented membranes can be obtained with typically several hundred to thousand layers. This approach has previously been validated for many different neutral or charged phospholipids and lipid mixtures.21 DDAX was dissolved in 2-propanol chosen for its wettability of hydrophilic silicon substrates. The membranes were deposited on rectangular slices (15 × 25 mm2 and 0.5 mm thickness) cut from commercial 5 in. silicon wafers. Substrates were systematically cleaned before deposition by applying three consecutive methanol baths under sonication followed by ultrapure water and 2-propanol rinsing. Since the solid surface must be fully wetted by the spreading solvent, substrates were rendered hydrophilic by an oxygen plasma etching of 30 s with a commercial apparatus (Harrick Scientific-NY) and nitrogen drying was applied just before the deposition. Glass microscopy slides can also be used successfully with the same treatments. Among the advantages of the spreading technique, the control of the deposited volume allows fixing of the total amount of surfactant molecules. To minimize finite size effects that enlarge the (20) Seul, M.; Sammon, M. Thin Solid Films 1990, 185, 287. (21) Lyatskaya, Y.; Liu, Y.; Tristram-Nagle, S.; Katsaras, J.; Nagle, J. F. Phys. Rev. E 2000, 63, 011907.

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diffraction peaks and to minimize the scattering contribution from membranes perturbed by the solid and liquid interface at the crystal borders, we have chosen to work with a high number of membranes. For this reason a DDAX concentration of 100 mg/mL was selected, and the spreading volume was adjusted to 50 µL without tossing from the substrate. If we assume that homogeneous bilayers of about 20 Å thickness cover the substrate just after the fast solvent evaporation, the deposited mass corresponds to a total film thickness of 14 µm and so about 6500 bilayers. Sample homogeneity was checked by optical brightfield microscopy. It looks like a packed flat domain assembly, each one extending over several millimeters square over the whole surface with the exception of edges and first millimeters from borders where excess material is found. With crossed polarizers, contrast is only observed on substrate borders or at the contact lines between the large domains. To avoid that the aligned DDAX lamellar phase crystallizes to a three-dimensional phase (LC appearing as a white hydroscopic powder) just after the solvent evaporation, samples were always kept above 35 °C (15 °C above DDAX chain crystallization temperature) and at relative humidity higher than 80% under circulating air. For this reason, it was not possible to put the samples in high vaccuum to remove residual traces of organic solvent after the evaporation nor was it possible to store the samples in a cold room as it is usually done with phospholipidic films. We have thus no guarantee that the solvent evaporation is completely achieved. Nevertheless alcohol could only be present as traces in the film after the evaporation (as checked by gravimetric measurements during the drying process) and furthermore be reduced in contact with the 5 mL aqueous reservoir in the stress experiment. Sample Environment for X-ray Reflectivity Experiments under Osmotic Stress. Solid supported samples were mounted in a large stainless steel chamber developed for X-ray measurements22 with two large Kapton windows and thermalization by oil circulation regulated at the sample position by a Julabo (Germany) temperature controller. An evacuated chamber around the internal compartment was used for thermal isolation. All measurements were carried out at 30 ( 0.1 °C in the fluid LR phase. High osmotic pressures (low hydration regime) were obtained by contact with water vapor at fixed relative humidity (RH ) p/p0, where p and p0 are the vapor pressure of the reservoir and of pure water). To this end, the osmotic pressure (equivalently the RH) inside the chamber was either controlled by the temperature applied to a large water reservoir or imposed by an aqueous saturated salt solution of K2SO4 at sample temperature. The vapor pressure is calculated from Π ) -(kBT/νwater) ln(RH), where νwater is the water molecular volume, T is the temperature in kelvin, and kB ) 1.381 × 10-23 (J K-1). K2SO4 at 30 °C fixes the RH to 97% corresponding to an osmotic stress of Π ) 106.628 Pa. RH values of other aqueous saturated salt solutions are given in refs 1, 23, and 24. Low osmotic pressures (full hydratation regime) were imposed by direct contact of the solid supported sample with a diluted polyelectrolyte solution in a sealed chamber with a 5 mL capacity (“liquid chamber”22) mounted inside the large temperature-controlled chamber. A sketch of the liquid chamber and of the experimental setup is presented in Figure 1. Polyelectrolyte Stressor Solutions. Since we use a direct contact between the polyelectrolyte osmotic stressor solution and the sample, we have chosen a polyelectrolyte of high mass and with the same sign as the bilayers (with a cationic ammonium monomer group) to prevent its penetration in the swollen DDAX lamellar phase. For this purpose pDADMACl (polydiallyldimethylammonium chloride, Mmono ) 159.66 g/mol) with a molecular weight between 400 kDa and 500 kDa was bought from Aldrich and was highly purified. The as-received 20% weight solution was diluted and dialyzed against pure water using a 100 mL semipermeable bag with a molecular mass cutoff of 12 kDa (Membra-Cell from Merk-eurolab). To ensure the extraction of small residual chains and salts, dialysis was carried out until the out-flowing solution conductivity was below 10 µS/cm. This operation was performed several times in order to reach several (22) Vogel, M. PhD Dissertation, Universita¨t Potsdam, 2000. (23) O’Brien, F. E. M. J. Sci. Instrum. 1948, 23, 73-76. (24) Dubois, M.; Zemb, T. J. Phys. IV 1998, 8, 55-62.

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Figure 1. Sketch of the experimental geometry used for applying osmotic stress by immersion of the solid supported and charged lamellar phase in a polyelectrolyte solution of the same sign. A typical out-of-plane diffuse scattering pattern recorded on a CCD detector is shown in gray scale for a DDACl sample at Π ) 105.49 Pa. grams of the polymer. Since the polyelectrolyte and surfactant counterions can exchange during the experiment, pDADMABr (with bromide counterions, Mmono ) 204.11 g/mol) was prepared for stressing the DDABr lamellar phases. For this purpose, a 1% pDADMACl weight solution was prepared by dissolution in a brine solution of 7 M NaBr under strong steering. It is then extensively dialyzed until no salt exits the dialysis bag as checked by conductivity measurements. The exchange from chloride to bromide was achieved after two repeating cycles as revealed by capillary electrophoresis measurements of the polymer solution (Cl-, Br-, and Na+ were dosed). Finally, all polyelectrolytes were lyophilized and dissolved in milli-Q water for preparation of the osmotic stressor solutions. Dextran (MW of 110 kDa and 500 kDa from leuconostoc ssp.) and PEG (8 kDA poly(ethylene glycol)) were purchased from Fluka and used with no further treatment. Osmotic pressure (Π) of the polymer stressor solutions was measured by means of vapor pressure reduction using a commercial tonometer (Knauer model K-7000, Germany) in the highpressure regime extending from 104 to 106 Pa. The instrument was first calibrated with NaCl standard solutions. Lower osmotic pressures from diluted polyelectrolyte and neutral hydrosoluble polymer solutions where measured with two membrane osmometers (Knauer model A0330 and model V7091 both limited to Π ) 8 × 103 Pa) used in parallel with cellulose acetate membranes (cutoff ∼10 kDa). X-ray Specular and Nonspecular Reflectivity Measurements. In-house reflectivity was carried out on a laboratorybuilt setup (Saarbrucken University, Germany) with a molybdenum X-ray tube generator (17.48 keV) delivering a direct beam with full width at half maximum (fwhm) of ∼0.007°, an integrated intensity of ∼1.6 × 106 (counts/s), measured with a NaI scintillation counter after reflection from a graphite crystal selecting the KR radiation. High-resolution measurements were carried out at the ID01 variable energy undulator beamline at ESRF (European Synchrotron Radiation Facility, Grenoble France). Scans in the plane of incidence (specular, longitudinal and transverse scans) where collected with a fast NaI scintillation counter (Cyberstar, Oxford). The specular reflection from the film at an angle (Rout) equal to the angle of incidence (Rin) was measured by coupled (Rin/2Rin) reflectivity scans corresponding to the momentum transfer perpendicular to the multilayered sample (q ) qz). To record nonspecular intensities, we have carried out standard “longitudinal scans” (offset scans) and “rocking scans” (transverse scans). The longitudinal scan is similar to the reflectivity scan except that the detection angle is intentionally off-set by a fixed angle ∆Roffset. In the rocking scan, the detector is held fixed during the measurement (i.e., the sum θ ) Rin + Rout is fixed) while the sample is rocked around the axis normal to the plane of reflection so that Rin varies from 0 to 2θ. A sketch of the scattering geometry and a typical intensity distribution measured by a 2d Princeton CCD located at 1455 mm from the sample is presented in Figure 1. In addition to scans described above, the CCD was used to measure the diffuse (nonspecular) scattering simultaneously in and out of the plane of incidence at small fixed angle of incidence Rin. No radiation

Oriented Charged Membranes under Osmotic Stress

Figure 2. Osmotic pressure-distance relation of DDABr (diamonds) and DDACl (circles) lamellar phases measured on isotropic bulk samples (empty symbols25) or solid supported and oriented samples (solid symbols). The osmotic stressor used for oriented samples is indicated on the right of the data. PolyBr and polyCl stand for the bromide and the chloride form of the pDADMA+X- polyelectrolyte stressor solution with indicated polymer weight percent (wt %). The continuous line represents the Poisson-Boltzmann calculation for a constant surface charge density from ref 25. Bromide presents an equilibrium plateau pressure (horizontal stripe) where a swollen lamellar phase (LR) and a condensed one (LR′) coexist. damage was observed during the exposure times needed in our measurements when using high-energy X-rays (above 17 keV). Nevertheless, after several tens of minutes of illumination, the beam footprint became visible on the sample (a white spot) and the highest diffraction orders where lost (indicating decreasing order). Therefore the beam was moved to different spots on the sample. Lower energy X-rays (∼8 keV) were found to damage the sample instantaneously at the synchrotron and are almost totally absorbed in the water reservoir at in-house X-ray tube generators.

IV. Results and Discussion DDAX Lamellar Phases Can Be Considered as a Binary Model System of Highly Charged Membranes. Swelling versus osmotic pressure of DDABr and DDACl lamellar phases has been measured on spontaneously forming bulk assemblies by combining SAXS and the osmotic stress (OS) technique over 5 orders of magnitude in pressure (ranging from ∼2 × 102 to ∼5 × 107 Pa, equivalently ∼0.16 × 10-3 to ∼493 atm).25 These measurements are reported as empty symbols in the pressure-distance diagram of Figure 2 with circles and diamonds for DDACl and DDABr, respectively. The experimental EOS curve can be accurately modeled taking into account an electrostatic double-layer (ESDL) repulsion, an attractive VDW force and a short-range exponential repulsion (the so-called “hydration force”). Membrane undulation forces such as the Helfrich force or molecular protrusion forces where shown to be negligible for such surfactants in the dilution range explored.26 For the bulk experiments in the low-pressure range, samples were measured with the classical OS technique. Few (25) Dubois, M.; Zemb, T.; Fuller, N.; Rand, R. P.; Parsegian, V. A. J. Chem. Phys. 1998, 108, 7855-7869. (26) Tsao, Y.; Evans, D. F.; Rand, R. P.; Parsegian, V. A. Langmuir 1993, 9, 233-241.

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milliliters of a DDAX solution (composed of multilamellar vesicles, MLV) were introduced in a dialysis cassette (i.e., bag) which was immersed in a neutral polymer stressor solution of few weight percent. The thermodynamical equilibrium is reached when the lamellar period becomes stable as checked by SAXS measurements and it corresponds to the equivalence of the chemical potentials of permeating species inside and outside the bag (water and DDAX monomers). The main constraint of the method is that the low molecular mass cutoff of the semipermeable membrane necessitates considerable equilibration times. For instance, a month is needed for a molecular cutoff of 8 kDa (∼20 Å permeation holes) and lower cutoffs exceed reasonable periods. Since the outflow of DDAX into the reservoir is a source of artifacts, the membrane pore size cannot be increased. Other difficulties may complicate dialysis experiments such as widening of the pores in time or on the contrary clogging when association occurs with the stressor macromolecules, bacterial decomposition, permeation of small stressor chains, or impurity releases from the dialysis cassette. Note the difference between the EOS and the swelling law (SL), i.e., spacing vs volume fraction of surfactant (curve d(φ)), that is obtained by simple dilution. The time needed for establishing an EOS or a SL is limited by the sample preparation and the X-ray exposure time, typically hours at a laboratory source and less than a second at synchrotron sources. Additionally, establishing the EOS demands the preparation of many osmotic stressor solutions. Osmotic Stress from Charged Polymer Solutions Compared to Classically Used Neutral Ones. To proceed toward faster methods for imposing osmotic pressure and establishing the EOS of electrostatically swollen lamellar phases, we have adopted an approach avoiding the use of dialysis bags: in order to reach the full hydration regime, the solid supported sample is immersed in a high mass polyelectrolyte stressor solution with the same sign and counterions as the bilayers under study. In this case, the scattering experiment can be conducted through the solution as described in the materials and methods section. The required calibration curves (Π as a function of pDADMAX concentration, where X- ) Cl- or Br-) has been established and are shown in Figure 3 with circles and diamonds for the chloride and the bromide form, respectively. Measurements were conducted on the solutions subsequently used in the osmotic stress experiment. Note that multiple pressure values plotted for the same polymer weight content correspond to independent measurements coming for instance from different osmometers. This gives an idea of the uncertainty associated with this calibration. For comparison, additional measurements on the neutral Dextran 110 kDa stressor (empty symbols) have been carried out on the same instruments and membranes. These data points agree well with the master curve (dashed line) obtained previously by fitting many dextran solutions simultaneously. In the explored pressure range, the use of charged species reduces the polymer weight content of the stressor solution by more than a factor 20 as can be seen by comparing the master curve of dextran, 500 kDa, and the DADMAX, 450 kDa, data. This is a clear advantage in our experiment since the X-ray beam goes through the solution. Generally speaking, for polyelectrolyte solutions it is the density of counterions which determines the pressure while for uncharged chains it is the density of macromolecules which matters. This simple picture would predict an ideal gas law of counterions plotted for chloride ions (upper dotted line in Figure 3). Since the size distribution of the polyelectrolyte used is broad and moreover since its degree

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Figure 3. Osmotic pressure Π (Pa) calibration measurements given as a function of the stressor weight percent (wt %) at T ) 30 °C. Solid circles and diamonds correspond respectively to the chloride and to the bromide form of the polyelectrolyte used on oriented samples (pDADMA+X-). The theoretical dotted curves are described in the text and are to be compared to the data. The dashed curves were obtained from many measurements of different classically used neutral hydrosoluble osmotic stressors (It follows at pH ) 7: 0.40806 + 133.17w + 68.797w2 + 8.7837w3 for dextran, 500 kDa; 5.3567 + 280.44w + 118.12w2 - 2.4549w3 for dextran 110 kDa; see ref 1 for PEG 20 kDa. Open circles correspond to dextran 110 kDa calibrations carried out with the same setup as that for the polyelectrolyte measurements.

of branching is not known, it is hard to determine precisely its critical concentration (C*) above which the chains start to overlap. Nevertheless, the semidilute regime (C > C*) is evidently reached for concentrations higher than w ) 1% and the slope of the linear fit through the high-pressure values (Π > 104 Pa in Figure 3) scales with the power law Π/RT ∼ C9/8 predicted for this regime by Odijk27 in the absence of added salt and taking into account the electrostatic screening caused by uncondensed counterions only (we obtain the slopes 1.27 ( 0.048 for Br and 1.1 ( 0.025 for Cl form). Linear fits which also include the lowpressure data (solid lines) give a higher slope (log(Π) ) 4.492 + 1.362 log(w) for Br and log(Π) ) 4.667 + 1.358 log(w) for Cl) and show that a deviation from the linear trend occurs with decreasing concentration. To reproduce this behavior we have used a model solving the PB equation in the cylindrical cell geometry,28,29 assuming reasonable structural parameters for the polyelectrolyte (namely a monomer length of 3 Å and a chain radius of 5 Å). Small variations of these parameters do not drastically modify the calculation which shows a strong discrepancy with the data at low concentrations (middle dotted line of Figure 3 for the Cl form). To obtain a good agreement (lower dotted line), we had to assume that residual salt (∼10-4 M) is present in the pDADMAX solution. Nevertheless the decrease of pressure at low concentrations may also come from a molecular weight dependence of the osmotic pressure in the diluted regime (C < C*) as discussed for PSS-Na+ in ref 30. Note that since we wanted to compare DDABr and DDACl samples stressed at the same osmotic pressures, we have systematically worked with lower weight percent polyelectrolyte when using the chloride forms (in the proportion of the monomer molar ratio, as visible in Figure 3). (27) Odijk, T. Macromolecules 1979, 12, 688. (28) Katchalsky, A.; Alexandrowicz, Z.; Keden, O. Chemical physics of ionic solutions; Conway, B. E., Barradas, R. G., Eds.; Wiley: New York, 1966; p 295. (29) Belloni, L.; Drifford, M.; Turq, P. Chem. Phys. 1984, 83, 147154. (30) Wang, L.; Bloomfield, V. A. Macromolecules 1990, 23, 804-809.

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Figure 4. Swelling law (d(1/φ), periodicity versus inverse surfactant volume fraction) for the bromide (diamonds) and the chloride (circle) forms of the surfactant. Measurements taken from ref 24 are reported with empty symbols while new ones measured identically are plotted as solid symbols. A zoom into the high osmotic pressure region (small 1/φ values) is given as an inset.

To increase the pressure imposed for a given weight percent of polymer, smaller neutral chains are often used such as PEG, 20 kDa, or PVP, 40 kDa.1 However, our attempts to use hydrosoluble neutral stressors (such as dextran 100 kDa and 500 kDa) in direct contact with aligned as well as with bulk charged surfactant phases lead to complexation and destruction of the lamellar phase. On the other hand, when taking chains with comparable size but with charged monomers of the same sign as the bilayers, penetration of the chains into the sample was prevented, and a stable swelling was observed in perfect agreement with the surfactant EOS as measured in bulk. To validate our method, we have plotted all results obtained on oriented samples immersed in polyelectrolyte stressor solutions as solid symbols in Figure 2. In this way, they can be compared to the values presented previously (empty symbols) from SAXS experiments on bulk samples prepared according to the classical OS technique which combines dialysis bags and neutral polymer stressors. For both series, circles and diamonds represent DDACl and DDABr, respectively. As shown on the graph, all values fall onto the same line for periodicities extending from 29 to 342 Å over almost 3 orders of magnitude in pressure which validates the assumption that the high mass pDADMAX does not penetrate the DDAX swollen crystal. Accordingly, electrostatic repulsion between the polyelectrolyte chains and the charged bilayers of the multilayer must be sufficiently strong for keeping well separated phases, and thus only water molecules, surfactant monomers, and counterions can exchange from one phase to the other. Furthermore, just above the LR′-LR biphasic pressure plateau (105.6 ( 0.1 Pa), the DDABr oriented lamellar phase collapses (d ) 31.2 Å at Π ) 105.97) while the DDACl one stays swollen (d ) 56.8 Å at Π ) 105.96) as seen in bulk experiments.25 Reproducibility of the Method and Uncertainties on the EOS Coordinates. The uncertainty associated with Π in the pressure-distance diagrams (Figure 2) comes mainly from the reproducibility of the calibration measurements. It is on the order of few percent but varies strongly with the pressure range and the instrumentation used. For instance it is less precise around 8000 Pa where the membrane osmometer saturates and where the vapor osmometer is poorly sensitive. In addition, we expect that part of the sample dissolves during the experiment such as the excess material on the substrate edges or at least

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Figure 5. (a) Time-resolved low-resolution X-ray reflectivity measurements carried out during the water equilibration process for a solid supported DDACl lamellar phase immersed in a 2% weight pDADMACl stressor solution. The two upper curves are a specular and a longitudinal scan measured before immersion, while all other curves are longitudinal scans shifted with a vertical factor of 10 each time. The time corresponding to the beginning of each measurement is reported on the right axis of the figure (hours:minutes:seconds). (b) An intensity pattern of the stable state obtained from the succession of many rocking scans (so-called “mesh scan”) plotted with a gray scale colorbar in log scale of counts per seconds.

in the range of the surfactant cmc (note that ∼5 × 10-5 mol/L is reached if 1/30 of the deposited material dissolves). This should slightly modify the equilibrium osmotic pressure in a subtle way related to the Donnan effect31 where the equilibrium state corresponds to the equality of the DDAX salt chemical potential in both charged phases. Thus the salt concentration may differ in the sample and in the reservoir. This effect should be very small at the swellings explored for the polyelectrolyte and for the lamellar phase.10 The water layer thickness (eW) was chosen as the abscissa of the graph due to its pertinence in the pressure calculations. It is obtained by subtraction of the bilayer thickness (eB) from the lamellar periodicity (d), measured with an excellent accuracy ((0.5 Å) since four Bragg reflections are observed. Thus the uncertainty on eW is due to the uncertainty in eB, which increases at high Π when the bilayers come into contact as known from a previously measured decrease in the mean surface per headgroup (e.g., see Figure 5 in ref 25). These measurements are reported in Figure 4 (empty symbols) as well as new ones (solid symbols) from the highly purified surfactants used here. In this way residual ions and impurities are excluded and as a consequence the maximum swelling of the DDACl lamellar phase has been doubled (up to φm ) 0.1 while previously published papers give φm ∼ 0.2 at room temperature25,32). The SL of DDABr and DDACl Figure 4 shows a linear trend in full hydration upon dilution which means that all available water goes between the membranes and so that d ) eB/φ. A linear fit through these data gives the same bilayer thickness for both counterions (eB ) 23 ( 0.2 Å for Cl and eB ) 22.75 ( 0.3 Å for Br) while a 3 Å increase of eB is expected in the range of the vapor pressures used for some of the oriented samples (d ∼ 29 Å) (from ref 25 in insert of Figure 4). We did not include this correction in Figure 2 because of the difference in purity of the surfactant used in both studies which might also affect the bilayer thickness close to contact. In addition, the value of the osmotic pressure imposed on DDACl with vapor from a temperature-controlled water bath is not as precisely known as the pressure imposed by a saturated K2SO4 solution used for DDABr. Therefore, an uncertainty on eW on ther order of a few angstroms is expected in our high(31) Kenworthy, S. R. Nature 1947, 160, 408-410. (32) Changjiang, K.; Ali, K. J. Colloid Interface Sci. 1993, 156, 218228.

pressure measurements when comparing DDACl and DDABr. In the future, saturated salt solutions will be preferred to the water bath method since they give a higher reproducibility and control of relative humidity. From Dry State to Full Hydration. The stability of the stressed DDAX film has been studied by means of a time-resolved in-house X-ray reflectivity experiment: An oriented DDACl film deposited on a silicon wafer is first equilibrated in high humidity atmosphere as described previously but mounted in the small “liquid chamber” with opened tap. The lamellar periodicity stabilized at 29 Å with small fluctuations until the chamber is sealed tight. The corresponding X-ray specular and longitudinal reflectivity scans are plotted in Figure 5a (two top curves with the starting time index 0:0:0 for hours:minutes: seconds). They show a first-order Bragg reflection with a large broadening due to the low instrumental resolution. The specular curve shows a critical angle (below which reflectivity is 1) that is not very well-defined and that is between the values expected for the silicium/water and silicium/air interface (corresponding respectively to qz ) 0.023 Å-1 and qz ) 0.0316 Å-1). Since the electron densities of DDACl, DDABr, and pure water are close (0.298, 0.324, and 0.333 Å-3, respectively, from density measurements), the mean scattering length density (X-ray contrast) of swollen DDAX multilayers is expected to be similar to that of pure water (∼9.33 × 10-6 Å-2). The experiment starts upon injection of 5 mL of a nonviscous 2% weight pDADMACl solution into the chamber. The syringe is not directed to the vertical sample surface. The chamber is closed and time-resolved specular and longitudinal reflectivity scans are conducted through the stressor solution one after the other. Longitudinal scans over a period of 18 h and 30 min are plotted in Figure 5a. We have shifted curves with a vertical factor of 10 each time, and the size of the error bars differs because of differences in counting times. Specular reflectivity scans where also conducted in parallel but are not shown. A representative picture of how water equilibrates between the multilayer and the reservoir is obtained: (i) first, the Bragg peak of the dry state immediately disappears in contact with the aqueous phase and the first specular scan (measured 50 s after start) shows the critical angle of the silicium/water (equivalently silicium/film) interface as all subsequent scans; (ii) a few minutes after immersion, scattering increases close to the qz value expected for the equilibrium

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Table 1. Tested Couples of Solid Supported Samples under Imposed Osmotic Pressure (from a vapor phase or a polyelectrolyte solution) osmotic stressor reservoir counterion form (X-) of DDAX sample

wpoly (pDADMAX wt %)

Cl-

Cl-

vapor cell with pure water, T ) 30°C vapor from saturated K2SO4 salt, T ) 30°C 10% 12.83% 3.98% 5.15% 2% 2% with Clcounterions 0.97%

BrBr-

1.29% 0.32%

BrClBrClBrClBr-

C (mol/L), monomer concn

ΠExp (Pa), measd osmotic pressure

29.6; 29.1

lab; lab

29.7; 29.4

0.627

∼97 ( 2% rel humidity 106.628 (≡97% rel humidity) 105.96 105.97 105.49 105.46 105.16 105.16

ESRF (Figure 7); ESRF ESRF ESRF ESRF (Figure 1) ESRF lab; lab lab (Figure 5)

0.0627

104.85

160.0 ; 177.6

0.0157

104.799 103.82

168 341.6

0.251 0.125

state expected at the imposed pressure (d ∼ 114 Å for Π ) 105.17 Pa) but in addition also a range of smaller periodicities seems to be present; (iii) over the first hour, the first Bragg peak intensity of the swollen state increases slowly while smaller periodicity contributions disappear progressively; then (iv) the broadening of the peaks diminishes. It is surprising that under complete immersion, several tens of minutes are needed to reach the stable state with 90 Å water layers between membranes. Finally, no significant evolution takes place indicating that the equilibrium state has been reached. This state has been checked to be stable over a period of 3 days for this sample. This means that the polyelectrolyte does not penetrate the swollen DDAX thick film and that the film does not dissolve noticeably in the aqueous reservoir. This arrangement is convenient for time-consuming so-called “mesh scans” performed for mapping the reciprocal space and collecting the nonspecular reflectivity accessible in the plane of incidence ((q bz,q bx) in Figure 1). An intensity map obtained in 6 h from the succession of 80 rocking scans, each one composed of 90 accumulations of 3 s is presented in Figure 5b with a gray scale colorbar in log scale of counts per seconds. Three Bragg reflections are evident at scattering vectors equal to n2π/d with n ) 1, 2, 3 on the qz axis. Each one has broad diffuse tails extending in the qx direction, the so-called “Bragg sheets” (BS). Since they are peaked at the qz coordinates of Bragg reflections, they can be explained by conformal roughness or fluctuations of the membranes due to thermally excited fluctuations. A pronounced specular contribution (vertical line with qx ) 0) is also clearly observed in Figure 5b, as well as the unaccessible regions of reciprocal space which are located on both sides of the map with no intensity (background level). These regions correspond to negative incident angles (Rin) or exit angles (Rout) with the scattering blocked by the sample horizon. To reach higher projections of the wavevector transfer in the direction parallel to the membranes (q| ) (qx2 + qy2)1/2) and since the range accessible for in plane of incidence measurements (qz,qx) is small (qx < 10-2, qy ∼ 0), we have also performed out-of-plane measurements (qz,qy). They had to be performed with a beam collimated in vertical and horizontal directions, and thus high brilliance synchrotron radiation was needed. A sketch of the setup and a typical CCD detector image of the scattering plotted with linear gray scale are shown in Figure 1. The particular data set corresponds to a DDACl sample stressed with a 4% weight pDADMACl solution. The incidence angle of the 20 keV X-ray beam is fixed at

reflectivity experiments d (Å)

56.8 31.2 87.4 84.9 110 ; 114.3 114.0

instrument

ESRF (Figure 6a); lab (Figure 6b) ESRF ESRF (Figure 8)

Rin ) 0.3°. The transmitted beam was cut just after the sample cell with a slit (shadow in the picture). We emphasize that this incidence angle does not satisfy the Bragg law for the multilayer, and thus no scattering would be measured for perfectly flat and aligned membranes. In that case, the only signal expected would be the specular spot (qz ) 4π/λ sin(Rin) and qy ) 0) and part of the direct beam defining the reciprocal space origin (qz ) 0 and qy ) 0). The membranes of our samples are perfectly oriented at macroscopic scale but undergo thermally excited undulations and compressibility fluctuations leading to diffuse scattering measured for large qy values extending up to 0.25 Å-1. Here, the scattering has been accumulated for 60 s in order to observe the low intensity tails while the center of the Bragg peaks are saturated (white spots). A thin ring with low intensities crosses the first Bragg peak and can be attributed to multilamellar vesicles equilibrated at the same pressure. Such multilamellar vesicles sometimes form at the water/film interface as reported in microscopy studies for phospholipid multilayers.22 The experimental conditions of all tested couples of oriented DDAX samples and pDADMAX stressor solutions are reported in Table 1 (solid symbols of Figure 2). X-ray reflectivity experiments were carried out either at the ESRF synchrotron (ID01 beam line) or using a laboratorybuilt setup (Saarbrucken University). Several combinations were tested independently (different sample, solution and instrument) to check the reproducibility of the method. Note that a DDABr and a DDACl samples were stressed with the same 2% weight pDADMACl solution. They reached the same swelling (d ) 114 Å) as expected since counterions can exchange and Cl- is in excess from the reservoir. Reflectivity with High (Synchrotron) or Low (Laboratory) Resolution. Figure 6 shows the in-plane of incidence (qz,qx) reflectivity curves (specular, longitudinal, and transverse) measured both at the in-house X-ray tube and once at the synchrotron for an oriented DDACl crystal stressed by a 1% pDADMACl solution (Π ) 104.85 Pa). A strong scattering is evidenced between the Bragg peaks of the specular curve (Rin/2Rin scan) which does not appear in the longitudinal curve (offset scan Rin/2Rin + ∆Roffset). This effect is due to the substrate reflectivity and can be a source of complications for weakly scattering and highly swollen systems, since the width and the shape of the Bragg peaks measured in the specular scan (Figure 6) cannot be resolved anymore.19 Contrarily, the longitudinal scans intersect the Bragg sheets with a high peak

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Figure 6. Comparison between (a) laboratory and (b) synchrotron X-ray reflectivity measurements of a solid supported DDACl lamellar phase, fully hydrated at imposed osmotic pressure by direct contact with a 1% pDADMACl weight stressor solution (Π ) 104.85 Pa). Specular and longitudinal scans are plotted with no corrections (raw intensities in counts/s). (c) Corresponding transverse scans on the first Bragg peaks, as well as the fits to the data described in the text.

to tail intensity ratio; see Figure 5a. The longitudinal curve is measured by a coupled reflectivity scan with an intentional constant angular offset (∆Roffset). By choosing this offset to be slightly larger than the width of the reflected incident beam, we avoid collecting the intense specular contribution owing to the macroscopic flatness and we measure the Bragg sheets at the same qz. Due to the small mosaicity, longitudinal scans can be carried out with small offsets (∆Roffset ) -0.05° in Figure 6b and -0.1° in Figure 6a) and conversely small qx wavevectors. For instance, the first Bragg sheets in the high-resolution longitudinal scan is measured with qx ∼7 × 10-5 Å-1. The effect of the instrumental resolution on the rocking curves is obvious in Figure 6c. A good fit to the highresolution measurement is obtained with a Lorentz function of full width at half-maximum equal to fwhm ) 0.0036 ( 0.0001° ()63 µrad). A Gauss function gives a less convincing fit in the tails of the curve but results in the same width (0.0038 ( 0.0001°). If we now look at the in-house measurement, it is strongly convoluted by the angular spreading of the laboratory beam and shows a Gaussian shape with approximately twice the width of the primary beam (fwhm ) 0.0176°). Since the shape and width of the curve come mainly from the convolution by the beam, it would be misleading to use it as a determination of the film mosaicity. Indeed, the mosaicity measured from the width of the high resolution rocking scan on the first Bragg peak is found to be at least five times smaller. Thus we can consider these samples as perfect smectic-A swollen liquid crystals, at least on the macroscopic scale probed in the high resolution rocking scan. We again emphasize that the clear separation between the specular and the nonspecular scattering is a consequence of the flatness of the multilayer on large length scales. Obviously the surface orientation prevents the Landau-Peierls instability33 which predicts a divergence of the lateral correlation length (ξ|) of the membranes due to the thermally excited fluctuations. At large length scales the bilayers in the lamellar assembly are flat and parallel to the substrate, similarly to what has been reported for aligned phospholipid multilayers34 but here (33) Peierls, R. E. Helv. Phys. Acta 1934, 7. (34) Salditt, T.; Mu¨nster, C.; Lu, J.; Vogel, M.; Fenzl, W.; Souvorov, A. Phys. Rev. E 1999, 60, 7285.

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Figure 7. Synchrotron X-ray specular reflectivity measurement of a solid supported DDABr oriented lamellar phase under high humidity atmosphere controlled with water vapor from a K2SO4 saturated salt solution at 30 °C (equivalently Π ) 106.628 Pa). A rocking scan measured at the first Bragg peak is shown in the inset and is fitted with the sum of a large Gaussian and a sharp Lorentzian function.

Figure 8. Synchrotron X-ray specular and longitudinal reflectivity measurements of a solid supported DDABr oriented lamellar phase immersed in a 0.32% pDADMABr weight osmotic stressor solution (Π ) 103.82 Pa). Five rocking scans measured on the successive Bragg peaks are shown in the inset.

for giant swellings with measured periodicities up to 15 times larger than the bilayer thickness. We conclude from the two experiments with low (Figure 6a) and high (Figure 6b) resolution that notwithstanding the fact that the signal-to-noise ratio is impressively increased when using a synchrotron beam, the use of a commercially available X-ray reflectometer is well adapted when the interest is focused on the periodicity determination (for instance when establishing the EOS). We now compare the high-resolution reflectivity of a DDABr film stressed at the higher and the lower osmotic pressures tested. The corresponding equilibrium periodicities are 29.7 Å (Figure 7 within vapor from a saturated K2SO4 solution) and 341.6 Å (Figure 8 within a 0.32% pDADMABr solution), respectively. Through the vapor phase, four extremely sharp and intense Bragg-like peaks are measured indicating a well-defined lamellar periodicity with a high degree of translational order. The peak intensities and the whole reflectivity profile are modulated by the single bilayer form factor which shows an oscillation between the first and second Bragg peaks. Note that the total reflection plateau is lower than the first peak maximum due to illumination footprint. The rocking curve through the first Bragg peak was analyzed with a simple structural approach with no model assumptions: a fit is

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obtained from the sum of a sharp Lorentzian function for the central specular peak and a broad Gaussian function for the nonspecular (diffuse) scattering (solid line shown in Figure 7). The fwhm of the sharp peak is smaller than 0.001°, which is characteristic of a very small mosaic spreading, and its clear separation from the diffuse scattering reveals macroscopic flatness at large length scales. The broad Gaussian form is due to the presence of height-height structural correlations in the plane of the membranes and at smaller length scale. It can be analyzed in terms of a lateral cutoff length ξ| ) 1/∆qx, where ∆qx ) qz tan((θ - ∆Rhwhm)/2), θ is fixed to 1.86° during the rocking scan, and the Gaussian hwhm is ∆Rhwhm ) 0.73°.35 Hence, the maximum correlation length measured is on the order of ξ| ∼ 480 Å and corresponds to the larger wavelength of thermally excited undulations in the membrane direction. Under the conditions of full hydration (Figure 8), the first Bragg peak is shifted to qz ) 0.0184 Å-1 below the angle of total external reflection for the silicium/water interface. The corresponding difficulty to observe the peak is circumvented by the longitudinal scan which allows us to evidence five sharp reflections without contributions from the substrate reflectivity. Similarly to all other samples, no Kiessig fringes were detected. These oscillations are expected between the Bragg peaks of the specular curve when the film thickness is small and well defined.18 The resolution limited fwhm of the first Bragg peak for all our samples is very small (in the range of ∆qz ∼ 0.001 Å-1) setting a lower bound on the number, N, of membranes which scatter coherently (N ∼ 300 at Π ) 106.628 Pa). The diffuse scattering measured in the rocking curves (Figure 8 inset) is totally flat and several orders of magnitude lower than the specular peak. Unexpectedly, dynamical effects appear in the form of resonant sharp peaks in the diffuse scattering under the conditions that the incidence or exit angle equals a Bragg angle of the specular curve: Rin or Rout equal to Rn ≡ arcsin(nλ/2d).36 Thus, multiple reflections at the bilayer interfaces add up coherently in the form of a standing wave with the lamellar periodicity. This is once again a clear indication of the high degree of ordering and orientation of the charged bilayers within the multilayered assembly. V. Summary and Conclusions Our method opens new routes for establishing the equation of state (EOS, pressure-distance relation) of charged lamellar phases. It combines perfectly aligned bilayers on a flat solid support, X-ray interface-sensitive scattering techniques (such as reflectivity or grazing incidence diffraction), and an extension of the osmotic stress (OS) technique using polyelectrolytes solutions in direct contact with the sample. An outstanding feature is the high number of charged membranes which selfassemble parallel to the solid substrate keeping a high degree of alignment under the conditions of full hydration. These films can be considered as perfect smectic-A crystals since their mosaic spread is less than a hundredth of a degree. Thus, specular and nonspecular scans can be carried out within the different symmetry axes of the (35) Sinha, S. K. J. Phys. III 1994, 4, 1543-1557. (36) Sinha, S. K. Mater. Res. Soc. Symp. Proc. 1995, 376, 175.

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multilayer. Measurements can be performed using laboratory X-ray instrumentation with the beam path going through the stressor solution, owing to the alignment which leads to high-intensity peaks which are smeared out by the powder averaging for isotropic bulk samples (MLV, multilamellar vesicles). Without the use of semipermeable membranes (dialysis bags), reflectivity measurements can be performed on highly swollen solid supported membranes. Under these conditions, hydrophilic neutral polymers could not be used with charged didodecyldimethylammonium halides (DDA+X- where X- ) Cl-, Br-) since they penetrate the sample and destroy the smectic order. On the contrary, we report that high mass polyelectrolytes with the same sign as the sample bilayers stay well separated and revealed to be an extremely convenient osmotic stressor since: (i) It allows coverage of a large pressure range by simple dilution (here tested from 103.82 to 105.97 Pa) and allows an easier coverage of the difficult domain around 105 Pa, intermediate between membrane and vapor pressure techniques. (ii) It considerably reduces the polymer weight content of the osmotic stressor reservoir. Further advantages are as follows: (a) the water exchange goes faster (equilibration times are reduced to an hour); (b) the X-ray beam is less affected when propagating through the stressor solution before and after diffraction from the sample. Additionally, the use of vapor phases from saturated salt solutions allowed us to cover a large hydration range extending from few water molecule layers (eW ∼ 5 Å at Π ) 106.628 Pa) up to high swellings with water layers 15 times thicker than the bilayers (eW ∼ 319 Å at Π ) 103.82 Pa). Under these conditions we obtained an excellent agreement with previous results from bulk solutions studied by the classical OS technique (dialysis bags and neutral polymer stressor25) which validates our approach. Finally, the approach presented necessitates only small sample quantities. Indeed, the sample covers ∼4 cm2 but only consumes 5 mg of surfactant. This ensures very good conditions for the osmotic stress experiment since the reservoir is a hundred times larger than the sample in our experiments. Moreover, a single solid supported sample can be used with successive osmotic stressor solutions to establish the whole EOS. This is particularly interesting in studies of biomolecular samples and/or in studies of osmotic pressure dependent phase transitions, such as the lamellar to vesicle transition by simple dilution of the osmotic reservoir. For such rather slow transitions, time-resolved X-ray experiments are particularly promising and have been shown to be possible using conventional in-house reflectivity instruments. Acknowledgment. We thank U. Mennike and C. Li for their help during the X-ray experiments and preparation. L. Belloni is acknowledged for sharing his experience of charged systems, as well as helpful discussions in many other aspects. We are grateful for the excellent working conditions provided by the ESRF and particularly our ID01 local contacts A. Mazuelas and B. Jean, as well as H. Metzger. We thank P. Lixon for help in the electrophoresis analysis and A. Aroti for carrying out some of the swelling law data. LA034733J