Lamellar-to-nematic phase transition in a lipid-surfactant mixture

A lyotropic system, consisting of a lecithin (DMPC) and a non-ionic surfactant (C₁₂E₅) in water was studied. The system exhibits a lamellar-to-nematic phase transition. The nematic phase appears as the temperature is decreased and only exists in a very limited temperature and concentration range, for specific lipid-to-surfactant ratios. While a lamellar phase is found at higher temperatures in both mixed and pure C₁₂E₅ systems, the transition to the nematic phase at lower temperatures coincides with a micellar phase in the pure C₁₂E₅ system. The transition appears to be driven by the strong temperature dependence of the surfactant film spontaneous curvature. The structural properties of the lamellar phase close to the lamellar-to-nematic boundary have been studied by polarised light microscopy and small-angle neutron and X-ray scattering experiments. The signature of a helical defect with Burgers vector of magnitude 2 is apparent in our data, close to the lamellar-to-nematic phase transition. The proliferation of screw dislocations in the lamellar phase might be a plausible mechanism for driving this transition. Received 6 July 1999 and Received in final form 17 April 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     

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     

Scaling theory of mixed amphiphilic monolayers

We predict the elastic properties of mixed amphiphilic monolayers in the swollen state within the blob model using scaling arguments. First the elastic moduli and the spontaneous curvature of a bimodal brush are determined as a function of the composition and the relative chain length. We obtain simple and useful scaling functions which interpolate between the elastic moduli of a pure short-chain brush and a pure long-chain brush. By using the analogy between block copolymer interfaces and polymeric brushes, the effect of mixing on self-assembled diblock copolymer monolayers is investigated in the swollen state. We calculate various interfacial properties, such as the equilibrium surface coverage, interface curvature, and the mixing free energy as a function of the composition. In general, we find a nonlinear dependence on the composition, which deviates from the simple linear averaging of the properties of pure components. Our results are used to discuss a recent experiment on the effect of amphiphilic block copolymers on the efficiency of microemulsions. Received 29 December 2000 and Received in final form 19 March 2001     

N-body study of anisotropic membrane inclusions: Membrane mediated interactions and ordered aggregation

We study the collective behavior of inclusions inducing local anisotropic curvatures in a flexible fluid membrane. The N-body interaction energy for general anisotropic inclusions is calculated explicitly, including multi-body interactions. Long-range attractive interactions between inclusions are found to be sufficiently strong to induce aggregation. Monte Carlo simulations show a transition from compact clusters to aggregation on lines or circles. These results might be relevant to proteins in biological membranes or colloidal particles bound to surfactant membranes. Received 30 July 1999 and Received in final form 8 September 1999     

Membrane-mediated interactions of rod-like inclusions

Inclusions embedded in lipid membranes undergo a mediated force, due to the tendency of the membrane to relax its excess of elastic energy. In this paper we determine the exact shape of a two-dimensional vesicle hosting two different inclusions, and we analyse how the inclusion conformation influences the mediated interaction. We find non-trivial equilibrium configurations for the inclusions along the hosting membrane, and we derive the complete phase diagram of the mediated interaction. In particular, we find a non-vanishing mediated force even when the distance between the inclusions is much greater than their size. Our model can be applied to describe the mediated interactions of parallel, elongated inclusions embedded in three-dimensional membranes. Received 22 October 2001 and Received in final form 8 March 2002     

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     

Effect of electron-phonon interaction on surface states in a ternary mixed crystal

A variational theory is proposed to study the surface states of electrons in a semi-infinite ternary mixed crystal, by taking the effect of electron-surface optical (SO) phonon interaction into account. The energy and the wave function of the electronic surface-states are calculated. The numerical results of the energies of the surface states of the polarons and the self-trapping energies are obtained as functions of the composition x and surface potential V₀ for several ternary mixed crystal materials. The results show that the electron-phonon interaction lowers the surface-state levels with the energies from several to scores of meV. It is also found that the self-trapping energy of the surface polaron has a minimum at some middle value of the composition x. It is indicated that the electron-phonon coupling effect can not be neglected. Received 4 January 1999 and Received in final form 7 January 2000     

Adhesion of binary giant vesicles containing negative spontaneous curvature lipids induced by phase separation

We report the adhesion of binary giant vesicles composed of two types of phospholipids, one has negative spontaneous curvature which tends to bend toward the head group and the other has zero spontaneous curvature. In a homogeneous one-phase region, the giant vesicles do not adhere to each other, whereas in a coexisting two-phase region, the giant vesicles show adhesion. A fluorescence microscope observation reveals that the adhesion takes place through the domains rich in phospholipids having negative spontaneous curvature. We propose a phase separation induced hemifusion model where two apposed monolayers of adjacent vesicles are hemifused in order to reduce the bending energy of monolayers with negative spontaneous curvature and the boundary energy between the domains and matrix. We provide a strong evidence for the hemifusion model by lipid transfer experiments.     

Van der Waals interaction between flux lines in high- superconductors: A variational approach

In pure anisotropic or layered superconductors thermal fluctuations induce a van der Waals attraction between flux lines. This attraction together with the entropic repulsion has interesting consequences for the low field phase diagram; in particular, a first order transition from the Meissner phase to the mixed state is induced. We introduce a new variational approach that allows for the calculation of the effective free energy of the flux line lattice on the scale of the mean flux line distance a, which is based on an expansion of the free energy around the regular triangular Abrikosov lattice. Using this technique, the low field phase diagram of these materials may be explored. The results of this technique are compared with a recent functional RG treatment of the same system. Received: 25 June 1996 / Revised: 18 August 1998 / Accepted: 21 August 1998     

Influence of surface ordering on the wetting of structured liquids

The substrate is shown to induce substantial ordering in diblock copolymer thin films above the bulk order-disorder transition (ODT) where, thermodynamically, a phase mixed state is favored. Initially, uniform films reorganize to form a hierarchy of transient surface patterns and stable film thicknesses that depend on the initial film thickness and on the substrate. Self-consistent field calculations of the free energy of the system for different situations, depending on the relative tendency for the different block components to be attracted to the substrate and/or free surface, provide an explanation of the formation of the stable film thicknesses. A continuum picture proposed earlier by Brochard et al.rovides an explanation of the wetting characteristics of this system. In some cases the ordering destabilizes the film so that dewetting occurs (wetting autophobicity), whereas in other cases the surface ordering results in a kinetic stabilization of a film that would otherwise dewet. Received 3 August 2001 and Received in final form 1 November 2001     

Attractive forces between anisotropic inclusions in the membrane of a vesicle

The fluctuation-induced interaction between two rod-like, rigid inclusions in a fluid vesicle is studied by means of canonical ensemble Monte-Carlo simulations. The vesicle membrane is represented by a triangulated network of hard spheres. Five rigidly connected hard spheres form rod-like inclusions that can leap between sites of the triangular network. Their effective interaction potential is computed as a function of mutual distance and angle of the inclusions. On account of the hard-core potential among these, the nature of the potential is purely entropic. Special precaution is taken to reduce lattice artifacts and the influence of finite-size effects due to the spherical geometry. Our results show that the effective potential is attractive and short-range compared with the rod length L. Its well depth is of the order of , where is the bending modulus. Received 5 February 1999 and Received in final form 14 May 1999     

Radiation pressure induced instabilities in laser interferometric detectors of gravitational waves

The large scale interferometric gravitational wave detectors consist of Fabry-Perot cavities operating at very high powers ranging from tens of kW to MW for next generations. The high powers may result in several nonlinear effects which would affect the performance of the detector. In this paper, we investigate the effects of radiation pressure, which tend to displace the mirrors from their resonant position resulting in the detuning of the cavity. We observe a remarkable effect, namely, that the freely hanging mirrors gain energy continuously and swing with increasing amplitude. It is found that the “time delay”, that is, the time taken for the field to adjust to its instantaneous equilibrium value, when the mirrors are in motion, is responsible for this effect. This effect is likely to be important in the optimal operation of the full-scale interferometers such as VIRGO and LIGO. Received 12 July 1999     

Simple models of proteins with repulsive non-native contacts

The Go model is extended to the case when the non-native contact energies may be either attractive or repulsive. The folding temperature is found to increase with the energy of non-native contacts. The repulsive non-native contact energies may lead to folding at T=0 for some unusual two-dimensional sequences and to reduction in complexity of disconnectivity graphs for local energy minima. Received 10 May 1999 and Received in final form 13 October 1999     

Elastic property of bilayer membrane in copolymer-homopolymer mixtures

We study the domain morphology in a phase separated state of diblock copolymer-homopolymer mixtures. In the situation that one of the blocks of copolymers is incompatible with homopolymers, formation of a bilayer membrane of block copolymers is shown to be possible in the matrix of homopolymers. Starting with the free energy functional in terms of the local volume fractions of each monomer, we derive the bending and curvature rigidities in the Helfrich free energy for a membrane. It is found that the curvature modulus is negative only in a limited region of the parameters, where a closed shape of a membrane like a vesicle is possibly formed. We establish a method to calculate the rigidities without a molecular picture in a consistent way with the field theoretic model free energy. Stability of a bilayer membrane compared with micelles is also investigated. Received: 22 July 1997 / Received in final form: 1 December 1997 / Accepted: 22 January 1998     

TA1[110] phonon dispersion and martensitic phase transition in ordered alloys Fe3Pt

In a previous neutron scattering study, we had observed that the TA phonon softening in L1₂-ordered ferromagnetic Fe₇₂Pt₂₈ Invar is pronounced at the zone boundary M-point and leads to an antiferrodistortive phase transition at low temperatures. Here, we report on similar neutron scattering investigations on two ordered crystals with higher Fe content to investigate the relation between the TA phonon softening and the martensitic transformation, which occurs in Fe-rich ordered Fe-Pt. We find that the TA phonon softening, especially at the M-point zone boundary, does not depend on the composition of the investigated crystals. In Fe_74.5Pt_25.5, however, the antiferrodistortive phase transition temperature is enhanced due to tetragonal strain preceding the martensitic transition. In Fe₇₇Pt₂₃ a precursor driven premartensitic phase transition is not observed. The structure of the martensite is, however, influenced by the soft mode lattice instability of the austenite. This would explain the origin of structural details found previously for Fe₃Pt thermoelastic martensite. Received 18 January 1999 and Received in final form 11 March 1999     

Elastic energy of tilt and bending of fluid membranes

Tilt of hydrocarbon chains of lipid molecules with respect to membrane plane is commonly considered to characterize the internal structure of a membrane in the crystalline state. However, membranes in the liquid state can also exhibit tilt resulting from packing constraints imposed on the lipid molecules in diverse biologically relevant structures such as intermediates of membrane fusion, pores in lipid bilayers and others. We analyze the energetics of tilt in liquid membranes and its coupling with membrane bending. We consider three contributions to the elastic energy: constant tilt, variation of tilt along the membrane surface and membrane bending. The major assumption of the model is that the core of a liquid membrane has the common properties of an elastic continuum. We show that the variation of tilt and membrane bending are additive and that their energy contributions are determined by the same elastic coefficient: the Helfrich bending modulus, the modulus of Gaussian curvature and the spontaneous curvature known from previous studies of pure bending. The energy of a combined deformation of bending and varying tilt is determined by an effective tensor accounting for the two factors. In contrast, the deformation of constant tilt does not couple with bending and its contribution to the elastic energy is determined by an independent elastic constant. While accurate determination of this constant requires additional measurements, we estimate its value using a simplified approach. We discuss the relationships between the obtained elastic Hamiltonian of a membrane and the previous models of membrane elasticity. Received 10 February 2000 and Received in final form 19 June 2000