Instability and Periodic Deformation in Bilayer Membranes Induced by Freezing

The instability and periodic deformation of bilayer membranes during freezing processes are studied as a function of the difference of the shape energy between the high and the low temperature membrane states. It is shown that there exists a threshold stability condition, bellow which a planar configuration will be deformed. Among the deformed shapes, the periodic curved square textures are shown being one kind of the solutions of the associated shape equation. In consistency with recent expe rimental observations, the optimal ratio of period and amplitude for such a texture is found to be approximately equal to (2)^{1/2}\pi.Comment: 8 pages in Latex form, 1 Postscript figure. To be appear in Mod. Phys. Lett. B. 199

Molecular twist transition in chiral and racemic phospholipid monolayers detected by Maxwell-displacement-current measurements

The molecular basis for the little (lit) mouse phenotype, characterized by a hypoplastic anterior pituitary gland, is the mutation of a single nucleotide that alters Asp 60 to Gly in the growth hormone releasing factor receptor. Detailed analysis of the lit mouse anterior pituitary reveals spatially distinct proliferative zones of growth hormone-producing stem cells and mature somatotrophs, each regulated by a different trophic factor. This sequential growth factor requirement for a specific cell type may exemplify a common strategy for regulating cellular proliferation in other mammalian organs

Lipid membranes with an edge

Consider a lipid membrane with a free exposed edge. The energy describing this membrane is quadratic in the extrinsic curvature of its geometry; that describing the edge is proportional to its length. In this note we determine the boundary conditions satisfied by the equilibria of the membrane on this edge, exploiting variational principles. The derivation is free of any assumptions on the symmetry of the membrane geometry. With respect to earlier work for axially symmetric configurations, we discover the existence of an additional boundary condition which is identically satisfied in that limit. By considering the balance of the forces operating at the edge, we provide a physical interpretation for the boundary conditions. We end with a discussion of the effect of the addition of a Gaussian rigidity term for the membrane.Comment: 8 page

Second-order susceptibility tensor of a monolayer at the liquid-air interface: SHG spectroscopy by compression

The complete expression for the macroscopic second-order susceptibility (SOS) tensor chi((2)) for a monolayer with C-infinity symmetry at the air-liquid interface is derived as functions of the molecular SOS tensor alpha((2)) and the orientational order parameters. The chiral (non-chiral) terms of chi((2)) distinguished by their association with even (odd) order parameters, by which a second-harmonic generation (SHG) circular-dichroism effect can be better understood. An SHG experiment of a 4-cyano-4'-5-alkyl-biphenyl monolayer on an air-water interface by monolayer compression is also discussed. (C) 2000 Elsevier Science B.V. All rights reserved

Pattern formation and chiral phase separation by compression: Racemic monolayer viewed as Bragg-Williams binary cholesterics

The monolayer of racemic amphiphiles is studied as a film of cholesteric liquid crystal (ChLC), mixed by the left- and right-handed chiral enantiomers. The chiral phase separation (CPS) and molecular orientation pattern are analyzed by Bragg-Williams theory for binary mixtures and the curvature-elastic model of ChLC. It is shown that below a certain critical temperature a compression can induce transition from racemic phase to CPS phase with a stripe-pattern formation. This gives a clear explanation of CPS in a racemic monolayer recognized by Lundquist [Ark. Kemi. 17, 183 (1960)], and observed recently by Eckhardt ct al. [Nature (London) 362, 614 (1993)]. [S1063-651X(99)11301-1]

Modeling analysis of molecular chiral effect detected by Maxwell-displacement-current measurements

Based on Maxwell displacement current (MDC) and surface pressure measurements by monolayer compression, the physicochemical properties of chiral and racemic phospholipid [alpha-phosphatidylcholine dipalmitoyl (DPPC)] monolayers at the air-water interface were investigated. It was found that at a temperature of 20 degrees C, the chiral and racemic phospholipid monolayers exhibited similar pressure-area isotherms with a pressure plateau between 65 and 85 Angstrom(2), usually attributed to the two-dimensional (2D) phase transition from expanded monolayer to condensed one. Nevertheless, with MDC measurement some critical peaks in the 2D pressure plateau region with different amplitude and sign were detected related to the chirality of the phospholipid samples. This result clearly demonstrates that microscopic chirality affects the electrical properties of monolayers. To investigate the chiral effect theoretically, a twist-conformation molecular model was raised by a modification of the simple rodlike model and biaxial rodlike model, which were developed in our previous work. The analysis based on this modified model reveals that the monolayer properties, especially the MDC behavior by compression, are profoundly influenced by the chirality of molecules. (C) 1999 American Institute of Physics. [S0021-9606(99)70724-5]

Linear and nonlinear dielectric constant tensor for monolayer films in terms of orientational order parameters

We give a general expression of the dielectric constant tensor in orientational orders in the applied static or low-frequency electric field for the semi-two-dimensional monolayer films with C-infinity upsilon symmetry. The dielectric anisotropic orientational tensor and orientational polarization tensor are derived in orientational order parameters. The nonlinear electro-optical Pockels effect including the local-field influence is also discussed using the orientational orders. A numerical calculation result shows that the first orientational order parameter S-1 is a destructive order while the second orientational orientational order parameter S-2 is a constructive one to the dielectric constant in the normal direction of monolayer films. (C) 2000 American Institute of Physics. [S0021-9606(00)70323-0]

Helfrich-Canham bending energy as a constrained non-linear sigma model

The Helfrich-Canham bending energy is identified with a non-linear sigma model for a unit vector. The identification, however, is dependent on one additional constraint: that the unit vector be constrained to lie orthogonal to the surface. The presence of this constraint adds a source to the divergence of the stress tensor for this vector so that it is not conserved. The stress tensor which is conserved is identified and its conservation shown to reproduce the correct shape equation.Comment: 5 page

Nematic Films and Radially Anisotropic Delaunay Surfaces

We develop a theory of axisymmetric surfaces minimizing a combination of surface tension and nematic elastic energies which may be suitable for describing simple film and bubble shapes. As a function of the elastic constant and the applied tension on the bubbles, we find the analogues of the unduloid, sphere, and nodoid in addition to other new surfaces.Comment: 15 pages, 18 figure