Bilayer Membrane in Confined Geometry: Interlayer Slide and Steric Repulsion

We derived free energy functional of a bilayer lipid membrane from the first principles of elasticity theory. The model explicitly includes position-dependent mutual slide of monolayers and bending deformation. Our free energy functional of liquid-crystalline membrane allows for incompressibility of the membrane and vanishing of the in-plane shear modulus and obeys reflectional and rotational symmetries of the flat bilayer. Interlayer slide at the mid-plane of the membrane results in local difference of surface densities of the monolayers. The slide amplitude directly enters free energy via the strain tensor. For small bending deformations the ratio between bending modulus and area compression coefficient, Kb/KA, is proportional to the square of monolayer thickness, h. Using the functional we performed self-consistent calculation of steric potential acting on bilayer between parallel confining walls separated by distance 2d. We found that temperature-dependent curvature at the minimum of confining potential is enhanced four times for a bilayer with slide as compared with a unit bilayer. We also calculate viscous modes of bilayer membrane between confining walls. Pure bending of the membrane is investigated, which is decoupled from area dilation at small amplitudes. Three sources of viscous dissipation are considered: water and membrane viscosities and interlayer drag. Dispersion has two branches. Confinement between the walls modifies the bending mode with respect to membrane in bulk solution. Simultaneously, inter-layer slipping mode, damped by viscous drag, remains unchanged by confinement.Comment: 23 pages,3 figures, pd

Front Propagation in the Pearling Instability of Tubular Vesicles

Recently Bar-Ziv and Moses discovered a dynamical shape transformation induced in cylindrical lipid bilayer vesicles by the action of laser tweezers. We develop a hydrodynamic theory of fluid bilayers in interaction with the surrounding water and argue that the effect of the laser is to induce a sudden tension in the membrane. We refine our previous analysis to account for the fact that the shape transformation is not uniform but propagates outward from the laser trap. Applying the marginal stability criterion to this situation gives us an improved prediction for the selected initial wavelength and a new prediction for the propagation velocity, both in rough agreement with the experimental values. For example, a tubule of initial radius 0.7\micron\ has a predicted initial sinusoidal perturbation in its diameter with wavelength 5.5\micron, as observed. The perturbation propagates as a front with the qualitatively correct front velocity a bit less than 100\micron/sec. In particular we show why this velocity is initially constant, as observed, and so much smaller than the natural scale set by the tension. We also predict that the front velocity should increase linearly with laser power. Finally we introduce an approximate hydrodynamic model applicable to the fully nonlinear regime. This model exhibits propagating fronts as well as fully-developed ``pearled" vesicles similar to those seen in the experiments.Comment: 42 pages, 6 eps figures included with text in uuencoded file, ps file available from ftp://dept.physics.upenn.edu/pub/Nelson/pearl_propagation.ps submitted to Journal de Physiqu

Autonomous engines driven by active matter: Energetics and design principles

Because of its nonequilibrium character, active matter in a steady state can drive engines that autonomously deliver work against a constant mechanical force or torque. As a generic model for such an engine, we consider systems that contain one or several active components and a single passive one that is asymmetric in its geometrical shape or its interactions. Generally, one expects that such an asymmetry leads to a persistent, directed current in the passive component, which can be used for the extraction of work. We validate this expectation for a minimal model consisting of an active and a passive particle on a one-dimensional lattice. It leads us to identify thermodynamically consistent measures for the efficiency of the conversion of isotropic activity to directed work. For systems with continuous degrees of freedom, work cannot be extracted using a one-dimensional geometry under quite general conditions. In contrast, we put forward two-dimensional shapes of a movable passive obstacle that are best suited for the extraction of work, which we compare with analytical results for an idealised work-extraction mechanism. For a setting with many noninteracting active particles, we use a mean-field approach to calculate the power and the efficiency, which we validate by simulations. Surprisingly, this approach reveals that the interaction with the passive obstacle can mediate cooperativity between otherwise noninteracting active particles, which enhances the extracted power per active particle significantly.Comment: 21 pages, 8 figure

Hydrodynamic lift on bound vesicles

Bound vesicles subject to lateral forces such as arising from shear flow are investigated theoretically by combining a lubrication analysis of the bound part with a scaling approach to the global motion. A minor inclination of the bound part leads to significant lift due to the additive effects of lateral and tank-treading motions. With increasing shear rate, the vesicle unbinds from the substrate at a critical value. Estimates are in agreement with recent experimental data.Comment: 9 pages, one figur

Mapping vesicle shapes into the phase diagram: A comparison of experiment and theory

Phase-contrast microscopy is used to monitor the shapes of micron-scale fluid-phase phospholipid-bilayer vesicles in aqueous solution. At fixed temperature, each vesicle undergoes thermal shape fluctuations. We are able experimentally to characterize the thermal shape ensemble by digitizing the vesicle outline in real time and storing the time-sequence of images. Analysis of this ensemble using the area-difference-elasticity (ADE) model of vesicle shapes allows us to associate (map) each time-sequence to a point in the zero-temperature (shape) phase diagram. Changing the laboratory temperature modifies the control parameters (area, volume, etc.) of each vesicle, so it sweeps out a trajectory across the theoretical phase diagram. It is a nontrivial test of the ADE model to check that these trajectories remain confined to regions of the phase diagram where the corresponding shapes are locally stable. In particular, we study the thermal trajectories of three prolate vesicles which, upon heating, experienced a mechanical instability leading to budding. We verify that the position of the observed instability and the geometry of the budded shape are in reasonable accord with the theoretical predictions. The inability of previous experiments to detect the ``hidden'' control parameters (relaxed area difference and spontaneous curvature) make this the first direct quantitative confrontation between vesicle-shape theory and experiment.Comment: submitted to PRE, LaTeX, 26 pages, 11 ps-fi

Ab initio simulations of liquid systems: Concentration dependence of the electric conductivity of NaSn alloys

Liquid NaSn alloys in five different compositions (20, 40, 50, 57 and 80% sodium) are studied using density functional calculations combined with molecular dynamics(Car-Parrinello method). The frequency-dependent electric conductivities for the systems are calculated by means of the Kubo-Greenwood formula. The extrapolated DC conductivities are in good agreement with the experimental data and reproduce the strong variation with the concentration. The maximum of conductivity is obtained, in agreement with experiment, near the equimolar composition. The strong variation of conductivity, ranging from almost semiconducting up to metallic behaviour, can be understood by an analysis of the densities-of-states.Comment: LaTex 6 pages and 2 figures, to appear in J.Phys. Cond. Ma

Tubular structures of GaS

In this Brief Report we demonstrate, using density-functional tight-binding theory, that gallium sulfide (GaS) tubular nanostructures are stable and energetically viable. The GaS-based nanotubes have a semiconducting direct gap which grows towards the value of two-dimensional hexagonal GaS sheet and is in contrast to carbon nanotubes largely independent of chirality. We further report on the mechanical properties of the GaS-based nanotubes