Fluctuating shells under pressure

Thermal fluctuations strongly modify the large length-scale elastic behavior of crosslinked membranes, giving rise to scale-dependent elastic moduli. While thermal effects in flat membranes are well understood, many natural and artificial microstructures are modeled as thin elastic {\it shells}. Shells are distinguished from flat membranes by their nonzero curvature, which provides a size-dependent coupling between the in-plane stretching modes and the out-of-plane undulations. In addition, a shell can support a pressure difference between its interior and exterior. Little is known about the effect of thermal fluctuations on the elastic properties of shells. Here, we study the statistical mechanics of shape fluctuations in a pressurized spherical shell using perturbation theory and Monte Carlo computer simulations, explicitly including the effects of curvature and an inward pressure. We predict novel properties of fluctuating thin shells under point indentations and pressure-induced deformations. The contribution due to thermal fluctuations increases with increasing ratio of shell radius to thickness, and dominates the response when the product of this ratio and the thermal energy becomes large compared to the bending rigidity of the shell. Thermal effects are enhanced when a large uniform inward pressure acts on the shell, and diverge as this pressure approaches the classical buckling transition of the shell. Our results are relevant for the elasticity and osmotic collapse of microcapsules.Comment: To appear in PNAS; accepted version including Supplementary Informatio

Lateral Diffusion Along Curved Lipid Bilayers

Biomembranes are thin, encapsulating, lipid-based double-layered films prevalently crowded by membrane proteins, and the interactions between the lipids and the embedded proteins are an active field of study with vital relevance for cell biology and biomedicine. Many of these studies approximate lipid bilayers as flat planar structures, even though highly curved membranes, such as membrane tethers and buds, vesicles and liposomes, and in structures like cristae in mitochondria are prevailing. So far, it has been sufficient for scientists to answer simpler questions regarding biomembranes by focusing mainly on planar lipid bilayers. However, the advancements in experimental and computational methods allow and call for a deeper understanding also on how membrane curvature can affect the properties of membranes. This thesis sheds light on the diffusion of proteins and lipids in curved lipid membranes. By presenting the first molecular dynamics simulations on the diffusion of transmembrane proteins in membrane tubes, the dynamics of the lateral diffusion in curved environments are studied in detail. The presented results highlight the importance of nanoscale curvature and compare the effect to macromolecular crowding, another currently confirmed factor related to lateral diffusion in lipid membranes. After a careful comparison between the results of this thesis and both experimental and computational work performed previously, pointers are given on how membrane curvature facilitated effects on lateral diffusion can be studied in the future

Determination of the Bending Rigidity of Graphene via Electrostatic Actuation of Buckled Membranes

The small mass and atomic-scale thickness of graphene membranes make them highly suitable for nanoelectromechanical devices such as e.g. mass sensors, high frequency resonators or memory elements. Although only atomically thick, many of the mechanical properties of graphene membranes can be described by classical continuum mechanics. An important parameter for predicting the performance and linearity of graphene nanoelectromechanical devices as well as for describing ripple formation and other properties such as electron scattering mechanisms, is the bending rigidity, {\kappa}. In spite of the importance of this parameter it has so far only been estimated indirectly for monolayer graphene from the phonon spectrum of graphite, estimated from AFM measurements or predicted from ab initio calculations or bond-order potential models. Here, we employ a new approach to the experimental determination of {\kappa} by exploiting the snap-through instability in pre-buckled graphene membranes. We demonstrate the reproducible fabrication of convex buckled graphene membranes by controlling the thermal stress during the fabrication procedure and show the abrupt switching from convex to concave geometry that occurs when electrostatic pressure is applied via an underlying gate electrode. The bending rigidity of bilayer graphene membranes under ambient conditions was determined to be $35.5^{+20}_{-15}$ eV. Monolayers have significantly lower {\kappa} than bilayers

Black Holes and Biophysical (Mem)-branes

We argue that the effective theory describing the long-wavelength dynamics of black branes is the same effective theory that describes the dynamics of biophysical membranes. We improve the phase structure of higher-dimensional black rings by considering finite thickness corrections in this effective theory, showing a striking agreement between our analytical results and recent numerical constructions while simultaneously drawing a parallel between gravity and the effective theory of biophysical membranes.Comment: v2: 5pp, 3 figures, improved introduction, to be published in PR

Folds and Buckles at the Nanoscale: Experimental and Theoretical Investigation of the Bending Properties of Graphene Membranes

The elastic properties of graphene crystals have been extensively investigated, revealing unique properties in the linear and nonlinear regimes, when the membranes are under either stretching or bending loading conditions. Nevertheless less knowledge has been developed so far on folded graphene membranes and ribbons. It has been recently suggested that fold-induced curvatures, without in-plane strain, can affect the local chemical reactivity, the mechanical properties, and the electron transfer in graphene membranes. This intriguing perspective envisages a materials-by-design approach through the engineering of folding and bending to develop enhanced nano-resonators or nano-electro-mechanical devices. Here we present a novel methodology to investigate the mechanical properties of folded and wrinkled graphene crystals, combining transmission electron microscopy mapping of 3D curvatures and theoretical modeling based on continuum elasticity theory and tight-binding atomistic simulations

Viscous regularization and r-adaptive remeshing for finite element analysis of lipid membrane mechanics

As two-dimensional fluid shells, lipid bilayer membranes resist bending and stretching but are unable to sustain shear stresses. This property gives membranes the ability to adopt dramatic shape changes. In this paper, a finite element model is developed to study static equilibrium mechanics of membranes. In particular, a viscous regularization method is proposed to stabilize tangential mesh deformations and improve the convergence rate of nonlinear solvers. The Augmented Lagrangian method is used to enforce global constraints on area and volume during membrane deformations. As a validation of the method, equilibrium shapes for a shape-phase diagram of lipid bilayer vesicle are calculated. These numerical techniques are also shown to be useful for simulations of three-dimensional large-deformation problems: the formation of tethers (long tube-like exetensions); and Ginzburg-Landau phase separation of a two-lipid-component vesicle. To deal with the large mesh distortions of the two-phase model, modification of vicous regularization is explored to achieve r-adaptive mesh optimization

Optimization of Cricket-inspired, Biomimetic Artificial Hair Sensors for Flow Sensing

High density arrays of artificial hair sensors, biomimicking the extremely sensitive mechanoreceptive filiform hairs found on cerci of crickets have been fabricated successfully. We assess the sensitivity of these artificial sensors and present a scheme for further optimization addressing the deteriorating effects of stress in the structures. We show that, by removing a portion of chromium electrodes close to the torsional beams, the upward lift at the edges of the membrane due to the stress, will decrease hence increase the sensitivity.Comment: Submitted on behalf of EDA Publishing Association (http://irevues.inist.fr/EDA-Publishing

Critical points in the analysis of membrane pore structures by thermoporometry

Several ultrafiltration membranes of the anisotropic and isotropic type were characterized by means of the thermoporometry. Successive cooling and heating runs were performed in order to investigate the effects of the water-ice and ice-water phase transitions on the structure of the membranes. The results found for membranes having different casting thicknesses indicate that, in some cases, pores in the sublayer of anisotropic UF membranes frustrate the measurement of the, for the separation, relevant porse present in the top layer

Negative electrostatic contribution to the bending rigidity of charged membranes and polyelectrolytes screened by multivalent counterions

Bending rigidity of a charged membrane or a charged polyelectrolyte screened by monovalent counterions is known to be enhanced by electrostatic effects. We show that in the case of screening by multivalent counterions the electrostatic effects reduce the bending rigidity. This inversion of the sign of the electrostatic contribution is related to the formation of two-dimensional strongly correlated liquids (SCL) of counterions at the charged surface due to strong lateral repulsion between them. When a membrane or a polyelectrolyte is bent, SCL is compressed on one side and stretched on the other so that thermodynamic properties of SCL contribute to the bending rigidity. Thermodynamic properties of SCL are similar to those of Wigner crystal and are anomalous in the sense that the pressure, compressibility and screening radius of SCL are negative. This brings about substantial negative correction to the bending rigidity. For the case of DNA this effect qualitatively agrees with experiment.Comment: 8 pages, 2 figure