Binding of oppositely charged membranes and membrane reorganization

We consider the electrostatic interaction between two rigid membranes, with different surface charge densities of opposite sign, across an aqueous solution without added salt. Exact solutions to the nonlinear Poisson-Boltzmann equation are obtained and their physical meaning discussed. We also calculate the electrostatic contribution to the free energy and discuss the renormalization of the area per head group of the charged lipids arising from the Coulomb interaction. Received 13 October 1998     

Adsorption of a Gaussian random copolymer chain at an interface

We consider the adsorption of an isolated, Gaussian, random, and quenched copolymer chain at an interface. We first propose a simple analytical method to obtain the adsorption/depletion transition, by averaging over the disorder the partition function instead of the free energy. The adsorption thresholds obtained by previous authors at a solid/liquid and at a liquid/liquid interface for multicopolymer chains can be rederived using this method. We also compare the adsorption thresholds obtained for bimodal and for Gaussian disorder; they only agree for small disorder. We focus on the specific case of an ideally flat asymmetric liquid/liquid interface, and consider the situation where the chain is composed of monomers of two different chemical species A and B. The replica method is developed for this case. We show that the Hartree approximation, coupled to a replica symmetry assumption, leads to the same adsorption thresholds as obtained from our general method. In order to describe the properties of the adsorbed (or depleted) chain, we develop a new approximation for long chains, within the framework of the replica theory. In most cases, the behavior of a random copolymer chain can be mapped onto that of a homopolymer chain at an asymmetric attractive interface. The values of the effective adsorption energy are different for a random and a periodic copolymer chain. Finally, we consider the case of uncorrelated annealed disorder. The behavior of an annealed chain can be mapped onto that of a homopolymer chain at an asymmetric non attractive interface; hence, an annealed chain cannot adsorb at an asymmetric interface. Received 21 January 1999     

Thermoelastic behaviour of polyvinylacetate monolayers at the air-water interface: Evidences for liquid-solid phase transition

The thermoelastic behaviour of polyvinylacetate monolayers spread on an aqueous subphase has been studied using rheological data previously published (Monroy et al., Phys. Rev. E 58, 7629 (1998)). The results show fluid-like viscoelastic behaviour well above a transition temperature , while at lower temperatures a soft solid-like behaviour emerges. The correlation between thermodynamic and elastic properties below can be described in terms of scaling laws. Received 12 January 1999 and Received in final form 11 June 1999     

Stiffening of fluid membranes and entropy loss of membrane closure: Two effects of thermal undulations

The problem of membrane softening by thermal undulations is revisited. In contrast to general belief, fluid membranes are predicted to be stiffened, not softened, by their undulations. Equal values of the effective bending rigidity are calculated from the interplay of local mean curvature modes (hats) on the basically flat membrane and from the coupling of spherical harmonic modes with spherical curvature. In addition, a conjecture is made on the entropy of membrane closure. It relies on a similarity of membrane closure to periodic boundary conditions. Received: 10 June 1997 / Revised: 7 October 1997 / Accepted: 2 December 1997     

Adsorption of hydrophobic polyelectrolytes at the air/water interface: Conformational effect and history dependence

We present an experimental study of the adsorption of hydrophobic highly charged polyelectrolytes on a neutral and hydrophobic surface, the air/water interface. The polymer was a randomly sulphonated polystyrene with charge fractions between 0.3 and 0.9 and the adsorbed layers were characterised by Langmuir through measurements, ellipsometry and X-ray reflectivity. The adsorption rate is always very slow and the resulting layers are very thin (< 3 nm). A maximum of adsorption with the charge fraction is observed which we relate to the conformation of the chains in solution. We show that adsorption is partially irreversible, strongly hysteretic and that the state of an adsorbed layer depends on its history. Received 16 June 2000     

Fluctuation-magnification of non-equilibrium membranes near a wall

Membranes in thermal equilibrium are well known to exhibit Brownian motion type shape fluctuations. Membranes containing active force centers -- such as chemically active membrane proteins -- suffer additional non-equilibrium shape fluctuations due to the activity of these force centers. We demonstrate, using scaling arguments, that non-equilibrium shape fluctuations are in general greatly amplified by the presence of a nearby wall or membrane due to the absence of a fluctuation-dissipation theorem. For adhesive membranes, this fluctuation magnification effect may facilitate the establishment of bonding. For non-adhesive membranes, fluctuation magnification produces a long-range repulsive pressure which can exceed the well known Helfrich repulsion due to purely thermal fluctuations. Received: 1 September 1997 / Accepted: 3 December 1997     

Vertical melting of a stack of membranes

A stack of tensionless membranes with nonlinear curvature energy and vertical harmonic interaction is studied. At low temperatures, the system forms a lamellar phase. At a critical temperature, the stack disorders vertically in a melting-like transition. Received 26 April 2000 and Received in final form 16 August 2000     

Effect of thermal undulations on the bending elasticity and spontaneous curvature of fluid membranes

We amplify previous arguments why mean curvature should be used as measure of integration in calculating the effective bending rigidity of fluid membranes subjected to a weak background curvature. The stiffening of the membrane by its fluctuations, recently derived for spherical shapes, is recovered for cylindrical curvature. Employing curvilinear coordinates, we then discuss stiffening for arbitrary shapes, confirm that the elastic modulus of Gaussian curvature is not renormalized in the presence of fluctuations, and show for the first time that any spontaneous curvature also remains unchanged. Received 19 April 1999 and in Received in final form 7 January 2000     

Growth and shapes of a cubic lyotropic liquid crystal

Monocrystals of the cubic lyotropic liquid crystal phase V₁ are studied in droplets of the mixture C ₁₂ EO ₆/water surrounded by water vapor of controlled pressure p. Shapes of monocrystals are found to depend on the conditions of growth from the lamellar phase and on the nature of the substrate. After the growth, when the lamellar phase is exhausted and crystals are in equilibrium with water vapors, their shapes are shown to depend on the pressure p. Thermodynamic aspects of these phenomena are discussed. Received 22 November 2000     

Structure factor of a lamellar smectic phase with inclusions

Motivated by numerous X-ray scattering studies of lamellar phases with membrane proteins, amphiphilic peptides, polymers, or other inclusions, we have determined the modifications of the classical Caillé law for a smectic phase as a function of the nature and concentration of inclusions added to it. Besides a fundamental interest on the behavior of fluctuating systems with inclusions, a precise characterization of the action of a given protein on a lipid membrane (anchoring, swelling, stiffening ...) is of direct biological interest and could be probed by way of X-ray measurements. As a first step we consider three different couplings involving local pinching (or swelling), stiffening or curvature of the membrane. In the first two cases we predict that independent inclusions induce a simple renormalization of the bending and compression moduli of the smectic phase. The X-ray experiments may also be used to probe correlations between inclusions. Finally we show that asymmetric coupling (such as a local curvature of the membrane) results in a modification of the usual Caillé law. Received 10 March 2000 and Received in final form 30 August 2000     

Kinetics of shape equilibration for two dimensional islands

We study the relaxation to equilibrium of two dimensional islands containing up to 20 000 atoms by Kinetic Monte Carlo simulations. We find that the commonly assumed relaxation mechanism - curvature-driven relaxation via atom diffusion - cannot explain the results obtained at low temperatures, where the island edges consist in large facets. Specifically, our simulations show that the exponent characterizing the dependence of the equilibration time on the island size is different at high and low temperatures, in contradiction with the above cited assumptions. Instead, we propose that - at low temperatures - the relaxation is limited by the nucleation of new atomic rows on the large facets: this allows us to explain both the activation energy and the island size dependence of the equilibration time. Received 7 December 1998 and Received in final form 18 March 1999     

Exact treatment of interface fluctuations in a two-dimensional emulsion

Summary We present a model for a polydisperse ensemble of two-dimensional droplets wich accounts for the effects of arbitrarily large distortions of the droplet shape. Interactions within a droplet include bending rigidity and spontaneous curvature. Interactions between droplets are omitted. Even at high temperatures, the effects of the shape fluctuations on the droplet size distribution remain small, as they are dominated by the contributions from the mixing entropy. In contrast, shape fluctuations lead to a pronounced peak in thermodynamic quantities like specific heat. This peak occurs at temperatures where thermal excitations become of the order of the bending energies of the droplet surface. The fluctuation-dominated regime extends to temperatures far lower than expected from a mean-field calculation. Paper presented at the I International Conference on Scaling, Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Microscopic membrane elasticity and interactions among membrane inclusions: interplay between the shape, dilation, tilt and tilt-difference modes

A phenomenological Landau elasticity for the shape, dilation, and lipid-tilt of bilayer membranes is developed. The shape mode couples with the sum of the monolayers' tilt, while the dilation mode couples with the difference of the monolayers' tilts. Interactions among membrane inclusions within regular arrays are discussed. Inclusions modifying the membrane thickness and/or inducing a tilt-difference due to their convex or concave shape yield a dilation-induced attraction and a tilt-difference-induced repulsion. The resulting interaction can stabilize 2D crystal phases, with the possible coexistence of different lattice spacings when the dilation-tilt-difference coupling is large. Inclusions favoring crystals are those with either a long-convex or a short-concave hydrophobic core. Inclusions inducing a local membrane curvature due to their conical shape repel one another. At short inclusions separations, a tilt comparable with the inclusion's cone angle develops: it relaxes the membrane curvature and reduces the repulsion. At large separations the tilt vanishes, whatever the value of the shape-tilt coupling. Received 23 October 1998 and Received in final form 12 January 1999     

Transition from small to big charged unilamellar vesicles

The transition from small to big unilamellar vesicles predicted by a Poisson-Boltzmann Cell Model for the thermodynamics of a dilute phase of unilamellar charged vesicles is characterized. The radius as a function of experimental parameters is calculated and the coexistence region of small and big vesicles is identified. We further investigate the physical meaning in terms of simplified models, which allow for an identification of the role of parameters like the surface charge density or the Debye-length. Connections to experiments are discussed. Received: 20 October 1997 / Received in final form: 9 February 1998 / Accepted: 9 March 1998     

Inclusions induced phase separation in mixed lipid film

The effect of rigid inclusions on the phase behavior of a film containing a mixture of lipid molecules is investigated. In the proposed model, the inclusion-induced deformation of the film, and the resulting energy cost are strongly dependent upon the spontaneous curvature of the mixed film. The spontaneous curvature is in turn strongly influenced by the composition of film. This coupling between the film composition and the energy per inclusion leads to a lateral modulation of the composition, which follows the local curvature of the membrane. In particular, it is shown that inclusions may induce a global phase separation in a film which would otherwise be homogeneously mixed. The mixed film is then composed of patches of different average composition, separated by the inclusions. This process may be of relevance to explain some aspects of lipid-protein association in biological membranes. Received 8 April 1999 and Received in final form 4 October 1999     

An auger investigation of oxygen-enhanced tin segregation on a liquid Pb−Sn alloy

Summary Auger measurements of the surface composition have been performed on solid and molten Pb-5at%Sn alloys. They confirm the theoretical predictions that, in the absence of oxygen, liquid or solid alloys exhibit no significant surface segregation. On the contrary, surface composition measurements and simultaneous surface tension measurements clearly show that oxygen adsorption strongly affects the segregation of tin at the liquid-vapour interface. This surface enrichment is driven by the contribution of the reaction free energy and of the products surface tension.     

Separation of enantiomers in a diol monolayer studied by fluorescence microscopy and grazing incidence X-ray diffraction

Summary Monolayers of a racemic mixture and of the pure S- and R-enantiomers of 3-hexadecyloxy-propane-1,2-diol have been investigated by fluorescence microscopy and grazing incidence X-ray diffraction. Above the transition pressureΠ _c domains with a polygonal shape appear. On compressing the monolayers shape instabilities occur. While the spirals of the S-enantiomer turn clockwise and the spirals of the R-enantiomer turn counterclockwise, the spirals from one domain of the racemate exhibit opposite handedness. This behaviour is explained by a separation of enantiomers on the molecular level. At all pressures investigated the enantiomers exhibit an oblique lattice. The tilt angle of the molecules decreases with increasing pressure. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Studies on behaviors of dipalmitoylposphatidylcholine and bilirubin in mixed monolayer at the air/water interface

Mixed monolayers of dipalmitoylposphatidylcholine (DPPC) and bilirubin (BR) were prepared on different subphases. The properties of DPPC/BR monolayer, such as collapse pressure (π_coll), limiting area per molecule (A_lim), surface compressibility modulus, free energy (ΔG_mix) and excess free energy (ΔG_ex), were investigated based on the analysis of the surface pressure-area isotherms on pure water. The results showed that DPPC and BR were miscible and formed non-ideal mixed monolayers at the air/water interface. With the molar fraction of BR (X_BR) increasing, the LE-LC coexistence region of DPPC monolayer was eliminated gradually. The DPPC/BR complex (M_D-B) of 1:2 stoichiometry formed as a result of the strong hydrogen bonds between the polar groups of DPPC and BR. The studies of effects of pH values and calcium ions in subphase on the DPPC/BR monolayers showed that the mixed monolayer became expanded on alkali aqueous solution and on 1 mmol/L CaCl₂ aqueous solution. The orientation of DPPC and BR at air/water interface was also discussed.