Inter-lamellar interactions modulated by addition of guest components

Bending elastic modulus of a polymer-doped lyotropic lamellar phase

The effect of inserting a neutral water-soluble adsorbing polymer on the flexibility of amphiphilic bilayers in a lamellar phase is investigated. The L_α system is a stack of charged undulating bilayers composed of sodium dodecyl sulfate (SDS) and octanol separated by aqueous solutions of polyethylene glycol (PEG). The mean bending elastic modulus κ is determined from the quadrupole splittings in the solid state NMR spectra of the perdeuterated octanol chains embedded in the membranes that undergo collective fluctuations. Parameters for describing the membrane behavior (bilayer thickness, elastic compressibility modulus, order parameter) are obtained by supplementing the NMR data with complementary experiments (x-ray scattering), NMR spectral simulations, and theoretical considerations. A fairly complete picture of the membrane rigidity emerges for any location in the lamellar phase thanks to a broad sweep of the lamellar domain by systematically varying the membrane fraction along dilution lines as well as the polymer composition. The most remarkable result is the difference between dilute and semi-dilute regimes. In the dilute PEG solution, no (or slight positive shift) polymer contribution to the rigidity curvature of the layered system is noted within the experimental resolution (≤0.3 k_BT) and κ remains around 2.7 k_BT. In contrast, the membrane rigidity increases steadily upon polymer addition once the crossover concentration c_p* is exceeded, amounting to a 60% increase in κ at polymer concentration 2.5 c_p* in the aqueous interlayers. These results are discussed with regard to the theoretical expectation of membrane rigidification upon irreversible polymer adsorption.

Effect of interlamellar interactions on shear induced multilamellar vesicle formation

Shear-induced multilamellar vesicle (MLV) formation has been studied by coupling the small-angle neutron scattering (SANS) technique with neutron spin echo (NSE) spectroscopy. A 10% mass fraction of the nonionic surfactant pentaethylene glycol dodecyl ether (C₁₂E₅) in water was selected as a model system for studying weak inter-lamellar interactions. These interactions are controlled either by adding an anionic surfactant, sodium dodecyl sulfate, or an antagonistic salt, rubidium tetraphenylborate. Increasing the charge density in the bilayer induces an enhanced ordering of the lamellar structure. The charge density dependence of the membrane bending modulus was determined by NSE and showed an increasing trend with charge. This behavior is well explained by a classical theoretical model. By considering the Caillé parameters calculated from the SANS data, the layer compressibility modulus B¯ is estimated and the nature of the dominant inter-lamellar interaction is determined. Shear flow induces MLV formation around a shear rate of 10 s^-1, when a small amount of charge is included in the membrane. The flow-induced layer undulations are in-phase between neighboring layers when the inter-lamellar interaction is sufficiently strong. Under these conditions, MLV formation can occur without significantly changing the inter-lamellar spacing. On the other hand, in the case of weak inter-lamellar interactions, the flow-induced undulations are not in-phase, and greater steric repulsion leads to an increase in the inter-lamellar spacing with shear rate. In this case, MLV formation occurs as the amplitude of the undulations gets larger and the steric interaction leads to in-phase undulations between neighboring membranes.

Bending stiffness of biological membranes: what can be measured by neutron spin echo?

Large vesicles obtained by the extrusion method represent adequate membrane models to probe membrane dynamics with neutron radiation. Particularly, the shape fluctuations around the spherical average topology can be recorded by neutron spin echo (NSE). In this paper we report on the applicable theories describing the scattering contributions from bending-dominated shape fluctuations in diluted vesicle dispersions, with a focus on the relative relevance of the master translational mode with respect to the internal fluctuations. Different vesicle systems, including bilayer and non-bilayer membranes, have been scrutinized. We describe the practical ranges where the exact theory of bending fluctuations is applicable to obtain the values of the bending modulus from experiments, and we discuss about the possible internal modes that could be alternatively contributing to shape fluctuations.

The intermediate scattering function for lipid bilayer membranes: from nanometers to microns

A numerical scheme based upon established hydrodynamic and elastic considerations is introduced and used to predict the intermediate scattering function for lipid bilayer membranes. The predictions span multiple wavelength regimes, including those studied by dynamic light scattering (DLS; microns) and neutron spin-echo (NSE) spectroscopy (10-100 nm). The results validate a recent theory specific to the NSE regime and expose slight inaccuracies associated with the theoretical results available in the DLS regime. The assumptions that underlie both our numerical methods and the related theoretical predictions are reviewed in detail to explain when certain results can be applied to experiment and where caution must be exercised.

Effect of polymer on the elasticity of surfactant membranes: a light scattering study

We have performed a dynamic light-scattering (DLS) investigation of the effect of a water-soluble polymer, polyethylene glycol (PEG), on the bending elastic modulus κ of surfactant membranes. The polymer, in concentrations ranging from 0 to 8 g/L (0 to 0.4 mM), was incorporated into the solvent of sponge phases of the sodium dodecyl sulfate (SDS)-hexanol-brine system. PEG adsorbs into the SDS membranes. The correlation functions of the polymer-doped sponge phases displayed a stretched-exponential decay, appropriately described by the Zilman-Granek (Z-G) theory for fluctuating membranes. The dynamics of the surfactant bilayers was slowed down by the addition of the polymer: Increasing PEG concentrations increase the DLS relaxation times. From the Z-G model we extracted the membrane-bending elastic modulus, as a function of polymer concentration, C(PEG) = κ increases with C(PEG), a behavior opposite to that expected from available models for the interaction between fluid membranes and adsorbing polymers. Our results suggest that the polymer penetrates to some extent the surfactant bilayers.

Interpreting membrane scattering experiments at the mesoscale: the contribution of dissipation within the bilayer

Neutron spin-echo spectroscopy provides a means to study membrane undulation dynamics over length scales roughly spanning 10-100 nanometers. Modern interpretation of these measurements relies on the theoretical predictions of Zilman and Granek; however, it is necessary to introduce an anomalously large solvent viscosity within this theory to obtain quantitative agreement with experiment. An extended theoretical treatment is presented that includes the effects of internal dissipation within the bilayer. Within the length and time regimes appropriate to neutron spin-echo experiments, the results of Zilman and Granek are largely recovered, except that the bilayer curvature modulus kappa appearing in their theory must be replaced with an effective dynamic curvature modulus kappa =kappa+2d(2)k(m), where d is a distance comparable to the monolayer thickness (the height of the neutral surface from bilayer midplane) and k(m) is the monolayer compressibility modulus. Direct comparison between theory and experiment becomes possible without any rescaling of physical parameters.

Influence of a triblock copolymer on phase behavior and shear-induced topologies of a surfactant lamellar phase

The influence of a triblock copolymer, poly(ethylene oxide)20-b-poly(propylene oxide)70-b-poly(ethylene oxide)20 (Pluronic P123) on the phase behavior and on the shear-induced multilamellar vesicle (MLV, also called Onion) formation in the lyotropic lamellar phase of the nonionic surfactant C10E3 was investigated by means of rheology, small-angle neutron scattering (SANS), and microscopy. Added triblock copolymer shifted the Lalpha-L3 phase transition to lower temperatures. In the presence of triblock copolymer, MLV structure was not stable and easily transformed back into the lamellar phase with increasing polymer concentration and temperature. In the study of the shear-induced MLV formation, we found an increase of the critical shear rate for the onset of the shear-thickening, which also indicates the instability of MLV in the presence of the triblock copolymer. No MLV formation was observed at high polymer concentration. Suppression of the shear-induced MLV formation might be attributed to the enhancement of the effective surface tension originating from the excluded volume effect between polymers adsorbed onto the membranes.

Effects of grafted polymer chains on lamellar membranes

We have investigated the effects of grafted polymer chains [poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide)] on the bending modulus and the intermembrane interactions of lamellar membranes (C(12)E(5) water) by means of a neutron spin-echo and a small-angle x-ray scattering technique. In this study the hydrophilic chain takes the mushroom configuration on the membrane. The bending modulus of the polymer-grafted membranes increases in proportion to the square of the end to end distance of the polymer chain, which agrees well with the theoretical prediction of Hiergeist and Lipowsky [J. Phys. II 6, 1465 (1996)]. From the interlamellar interaction point of view, the mushroom layer is renormalized to the membrane thickness, which enhances the repulsive Helfrich interaction. When the size of the decorated polymer chain increases to the interlamellar distance, however, the mushroom is squeezed so as to optimize the interlamellar potential. Further increase of the grafted polymer size brings a lamellar-lamellar phase separation, where the grafted polymer chains are localized in the dilute lamellar phase and the concentrated lamellar phase forms the onionlike texture.

Quantitative analysis of lyotropic lamellar phases SANS patterns in powder oriented samples

We have developed a detailed numerical method based on the Caillé model to fit Small Angle Neutron Scattering profiles of powder-oriented lyotropic lamellar phases. We thus obtain quantitative values for the Caillé parameter and the smectic penetration length from which we can derive the smectic compression modulus and the membrane mean bending modulus. Our method, applied to a surfactant lamellar phase system decorated by amphiphilic copolymers, provides excellent fits for any intermembrane spacing or membrane concentration over the entire q-range of the SANS experiments. We compare our fits with those obtained from the model of Nallet et al. (J. Phys. II 3, 487 (1993)), which is reviewed. Good fits are obtained with both methods for samples exhibiting "hard" smectic order (sharp Bragg peak, moderate small angle scattering). Only our procedure, however, gives good fits in the case of "soft" smectic order (smooth Bragg peak, strong small angle scattering). A quantitative criterion to discriminate between these "soft" and "hard" samples is also proposed, based on a simple analogy with smectic-A liquid crystal in contact with an undulating solid surface. This allows us to anticipate the type of thermodynamic information that can be derived from the fits.

Statistical mechanics of a colloidal suspension in contact with a fluctuating membrane

Surface effects are generally prevailing in confined colloidal systems. Here we report on dispersed nanoparticles close to a fluid membrane. Exact results regarding the static organization are derived for a dilute solution of nonadhesive colloids. It is shown that thermal fluctuations of the membrane broaden the density profile, but on average colloids are neither accumulated nor depleted near the surface. The radial correlation function is also evaluated, from which we obtain the effective pair potential between colloids. This entropically driven interaction shares many similarities with the familiar depletion interaction. It is shown to be always attractive with range controlled by the membrane correlation length. The depth of the potential well is comparable to the thermal energy, but depends only indirectly upon membrane rigidity. Consequences for the stability of the suspension are also discussed.