Session R8: Monolayers, Membranes & Microemulsions

Theory of Myelin Coiling

We propose a new model to explain coiling of myelins composed of fluid bilayers. This model allows the bilayer cylinders of a myelin to be non-coaxial and the bilayer lateral tension to vary from bilayer to bilayer. Our calculations suggest that a myelin would bend or coil to lower its free energy when the bilayer lateral tension is sufficiently large. The proposed coiling mechanism is in a sense similar to the classical Euler buckling of a thin elastic rod subject to axial compression. The analysis of a simple two-bilayer case shows that a bilayer lateral tension of about 1 dyne/cm can easily induce coiling of myelins of typical lipid bilayers. This model signifies the importance of bilayer lateral tension in determining the morphology of myelinic structures.   

Curvature condensation and twinning in an indented elastic shell

We study the formation of a localized geometrical defect and its evolution in an elastic shell using a combination of experiment and numerical simulation. We find that as a symmetric localized indentation on a semi-cylindrical shell increases, there is a transition from a global mode of deformation to a localized one which leads to the condensation of curvature along a parabolic crease along the line of symmetry. Further indentation leads to a twinning phenomena wherein the crease bifurcates into two defects that move apart on either side of the line of symmetry. We present a simple theory to explain the main features of the experiments and numerical simulations.   

Anomalous persistence of a pinch in a pipe

The response of low-dimensional solid objects combines geometry and physics in unusual ways, exemplified in structures of great utility such as a tubular shell that is ubiquitous in nature and technology. Here we provide a particularly surprising consequence of this confluence of geometry and physics in tubular structures: the anomalously large persistence of a localized pinch in an elastic pipe whose effect decays very slowly as an oscillatory exponential with a persistence length that scales as $R^{3/2}/t^{1/2}$, diverging as the thickness of the tube vanishes. The result is more a consequence of geometry than material properties, and is thus equally applicable to carbon nanotubes and cytoskeletal microtubules as it is to aircraft fuselages and geological plates, with a number of consequences, some of which we consider.   

Crystalline order on the paraboloid

We describe an experimental and theoretical investigation of crystalline order on a two-dimensional paraboloid. In contrast to the sphere, the paraboloid exhibits both variable Gaussian curvature and a boundary. Both these features must be treated for a thorough theoretical understanding. A macroscopic model of a parabolic crystal can be obtained in the laboratory by assembling a single layer of soap bubbles on the surface of a rotating liquid, thus extending the classic work of Bragg and Nye on planar arrays of soap bubbles.   

Elastic Stiffness of Grain Boundary Scars and Dislocation Dynamics

We analytically calculate the stiffness of finite-length grain boundaries (scars) on a spherical crystal within the continuum elasticity theory. The scar is composed of an isolated disclination with +1 topological charge together with a finite number of dislocations. We determine the elastic free energy of a single finite-grain boundary scar by considering interacting defects, such as Disclination-Disclination (D-D), Disclination-dislocation (D-d), and dislocation-dislocation (d-d). The harmonic potential binding dislocations to the scar is obtained by determining the free energy of a single dislocation perturbed away from its equilibrium position. The elastic spring constants so obtained are compared to experimental data on dislocation dynamics [1]. We conclude with some comments on interstitial dynamics. [1] Lipowsky, P., Bowick, M. J., Meinke, J. H., Nelson, D. R. and Bausch, A. R. Nature Mater. 4, 407-411 (2005).   

Membrane Nano-Structures: The Three Tether Junction

Tethers are robust cylindrical nanostructures of lipid bilayer membranes, including biomembranes. They can be easily produced in experiments and can be found in and on cells. Tethers are useful for probing the mechanical properties of membranes, because the radius of a tether is small enough to make the bending stiffness of the membrane relevant. In an experiment, a glass bead was attached to a tether and pulled with a laser tweezer leading to the formation of a three tether junction. I will present a theory explaining the observed force-displacement relationship and simulation results of the shape of the three tether junction.   

Toward a multi-scale simulation of lipid bilayer systems

In numerical simulations of lipid bilayer systems, it has become important to treat the membrane molecules (e.g., lipids, proteins, and drug molecules) explicitly for designing medical drugs and for developing drug delivery systems. However, it is difficult to apply straightforwardly a microscopic simulation technique such as the molecular dynamics method to the large-scale bilayer systems, because the length and the time scales of these systems are very large compared to the scales of the molecules. The authors take two approaches for this problem. First, we use the dissipative particle dynamics method and the coarse grained molecular dynamics method in addition to the standard molecular dynamics method. The results are compared with the molecular-dynamics results and experimental data. Secondly we use a molecular dynamics and continuum hybrid simulation method. In this method, the region near the membrane is computed by an atomistic-simulation method and the solvent region is computed by a continuum-simulation method. (In our study, the coarse grained molecular dynamics was used for the atomistic region.) The validity and availability of this later approach will be discussed.   

Influence of the size of interacting domains on the diffusion of nano-particles

Single particle tracking (SPT) is widely used for investigating the diffusion of proteins in cell membranes. However, short lifetime and the blinking of fluorescent tracers make it difficult to obtain sufficient data on the interactions with the inhomogeneities of the membrane. Langmuir lipid monolayers provide control over obstacle size and the corresponding interaction energy since their condensed domains within liquid phases exhibit a net dipole moment. The diffusion of a stable, negatively charged latex bead in the coexisting liquid phase, with a dipole moment anti parallel to the one of the domain, was observed by SPT. The interaction energy was obtained by Boltzmann statistics of the tracking data. The electric field of the monolayer domains varies with domain size. Its distance dependence can principally change from $E\sim 1/r^3$ for a single dipole to $E\sim 1/r$ for large domains $(R>10µm)$. The influence of this change on the particle diffusion was investigated by Monte Carlo simulations. The analysis shows that the particles are stronger trapped at the domain border of smaller domains and that a change from two to one dimensional diffusion occurs. Recently, we also started analogous experiments using red blood cells and vesicles as biomembrane mimics.   

Control of domain formation and budding in multicomponent bilayer membranes

Phase separation in fluid bilayer membranes, of lipids or block copolymers, can lead to a budding transition when line tension between the two phases comes to dominate the bending rigidity of the membrane. This leads to a nearly spherical bud connected to the membrane by a small neck. We examine the role of molecular architecture and composition on this shape transformation. Specifically we consider the inclusion of twin-tail amphiphiles which lower the free energy of the system by segregating to the interface between the two phases. Such additives can be used to lower the surface tension, thus controlling the critical size at which buds form. In addition they stabilize the neck when budding does occur, by acting essentially as stitches, thereby increasing the energy needed to detach the bud from the membrane. Using dissipative particle dynamics we are able to simulate the dynamics of large mebrane patches over relevant time scales.   

Ordering by collapse: Two-dimensional crystallization of hydrophobic dimers by folding Langmuir monolayers

Synchrotron X-ray studies of arachidic-acid monolayers compressed to the collapse region, beyond their densely packed molecular area, reveal that the resulting structures are stable and exhibit a surprising degree of order. Different structures, depending on whether the monolayer is spread on pure water or on CaCl$_2$ solutions, are identified. On pure water the collapsed monolayer forms a stable crystalline trilayer, with acyl-chain packing practically identical to the 3D crystal structure of fatty acids. For monolayers spread on Ca$^{2+}$ solutions, the collapse regime consists of an inverted bilayer with the hydrophobic tails in contact with the water surface and the calcium ions bridging the polar heads. The inverted bilayer structure possesses a well ordered crystalline slab of calcium-oxalate-monohydrate intercalated between two acyl-chains. We discuss the implications of our findings to recent reports on dewetting of water near hydrophobic surfaces, on the formation of super-lattice structures by ions beneath a monolayer, and the relevance to certain biological processes.   

Mechanical Properties of an Actin Filament Network Monolayer

Actin filament networks present a model system to study the mechanical properties of semi-rigid polymer networks. Because they are a network, the filaments can display behavior that deviates from continuum elasticity theory on sufficiently short length scales, resulting in interesting nonlinear response of the system to applied stresses and strains. We have developed a Couette (concentric cylinders) style apparatus to study monolayers of actin confined to the air-water interface. This talk will present results characterizing the response of the monolayer to continuous and step-wise strains. We will report on measurements of the viscosity of the actin network, as a macroscopic characterization, and on tracking of particles embedded in the network. The particle tracking is used to probe local displacements of the network in response to applied strain. We will report on tests of the predicted transition between affine and non-affine displacements as a function of cross-linking density.   

Shape Selection in Self-Assembled Chiral Membranes: New Mechanism Based on the Flexoelectric Effect

Many biological materials self-assemble into chiral microstructures such as cylindrical tubules and helical ribbons. A chiral elastic theory proposed by Selinger et al., based on the elastic properties and chirality of amphiphilic lipid molecules, has been successful in explaining the formation of tubules and helical ribbons. Recently, an experiment has shown that achiral lipid molecules can also form chiral microstructures. This challenges the previous theory based on molecular chirality. Toward understanding this problem, we develop a new model for membrane shape selection based on the flexoelectric effect. We investigate this model through both analytical calculations and dissipative particle dynamic simulations on tethered membranes.   

Bile Salt Mediated Growth of Reverse Wormlike Micelles in Nonpolar Liquids

We report the growth of reverse wormlike micelles induced by the addition of a bile salt in trace amounts to solutions of the phospholipid, lecithin in nonpolar organic solvents. Previous recipes for reverse wormlike micelles have usually required the addition of water to induce reverse micellar growth; here, we show that bile salts, due to their unique ``facially amphiphilic'' structure, can play a role analogous to water and promote the longitudinal aggregation of lecithin molecules into reverse micellar chains. The formation of transient entangled networks of these reverse micelles transforms low-viscosity lecithin organosols into strongly viscoelastic fluids. The zero{\-}shear viscosity increases by more than five orders of magnitude, and it is the molar ratio of bile salt to lecithin that controls this viscosity enhancement. The growth of reverse wormlike micelles is also confirmed by small-angle neutron scattering (SANS) experiments on these fluids.   

Mesoscopic simulations of binary mixtures and microemulsions using a stochastic, particle-based algorithm

Particle-based simulation techniques provide an attractive alternative to traditional methods for the coarse-grained modeling of a fluctuating solvent. A particularly appealing algorithm introduced by Malevanets and Kapral[1], called Stochastic Rotation Dynamics, describes a fluid with an ideal gas equation of state. The algorithm has been successfully applied to study polymers, colloids, and vesicles in shear flow. Recently, this algorithm has been generalized to model fluids with non-ideal equations of state[2]. We will discuss how this can be used to study binary mixtures with a miscibility gap. Results for the demixing such as the phase diagram and measurements of interface fluctuations and the surface tension of a droplet will be shown. By tuning the ratio of surface tension and viscosity both damped and overdamped capillary waves were obtained.The coarsening of domains during spinodal decomposition is also investigated. In order to describe microemulsions, the model is further extended to include surfactant molecules. Preliminary results for the onset of emulsification will be presented. [1] A. Malevanets, R. Kapral, J. Chem. Phys. 110, 8605 (1999). [2] T. Ihle, E. Tuzel, D. M. Kroll, cond-mat/0509631; cond-mat/0511312.   

On the bouncing of rigid spheres on thin polymer films

We report on a study of the rebound of stainless steel spheres on thin polymer films. After the sphere is dropped it bounces off the plastic sheet and the evolution in time of the subsequent rebounds are recorded. Experiments are performed varying the sphere radius, the impact velocity, and the film tension. The variations of the contact time, the amplitude of deformation of the film, and the loss of energy of the sphere after impact, as reported via a coefficient of restitution, lead to a number of scaling relations. These results are interpreted in terms of linear and nonlinear theories of the elasticity of membranes.