Electrostatic Interactions of Asymmetrically Charged Membranes

We predict the nature (attractive or repulsive) and range (exponentially screened or long-range power law) of the electrostatic interactions of oppositely charged and planar plates as a function of the salt concentration and surface charge densities (whose absolute magnitudes are not necessarily equal). An analytical expression for the crossover between attractive and repulsive pressure is obtained as a function of the salt concentration. This condition reduces to the high-salt limit of Parsegian and Gingell where the interaction is exponentially screened and to the zero salt limit of Lau and Pincus in which the important length scales are the inter-plate separation and the Gouy-Chapman length. In the regime of low salt and high surface charges we predict - for any ratio of the charges on the surfaces - that the attractive pressure is long-ranged as a function of the spacing. The attractive pressure is related to the decrease in counter-ion concentration as the inter-plate distance is decreased. Our theory predicts several scaling regimes with different scaling expressions for the pressure as function of salinity and surface charge densities. The pressure predictions can be related to surface force experiments of oppositely charged surfaces that are prepared by coating one of the mica surfaces with an oppositely charged polyelectrolyte

Strain engineered graphene using a nanostructured substrate: I Deformations

Using atomistic simulations we investigate the morphological properties of graphene deposited on top of a nanostructured substrate. Sinusoidally corrugated surfaces, steps, elongated trenches, one dimensional and cubic barriers, spherical bubbles, Gaussian bump and Gaussian depression are considered as support structures for graphene. The graphene-substrate interaction is governed by van der Waals forces and the profile of the graphene layer is determined by minimizing the energy using molecular dynamics simulations. Based on the obtained optimum configurations, we found that: (i) for graphene placed over sinusoidally corrugated substrates with corrugation wave lengths longer than 2\,nm, the graphene sheet follows the substrate pattern while for supported graphene it is always suspended across the peaks of the substrate, (ii) the conformation of graphene to the substrate topography is enhanced when increasing the energy parameter in the van der Waals model, (iii) the adhesion of graphene into the trenches depends on the width of the trench and on graphene's orientation, i.e. in contrast to a small width (3 nm) nanoribbon with armchair edges, the one with zig-zag edges follows the substrate profile, (iv) atomic scale graphene follows a Gaussian bump substrate but not the substrate with a Gaussian depression, and (v) the adhesion energy due to van der Waals interaction varies in the range [0.1-0.4] J/m^2.Comment: 12 pages and 16 figures, To appear in Phys. Rev.

Surface tension in bilayer membranes with fixed projected area

We study the elastic response of bilayer membranes with fixed projected area to both stretching and shape deformations. A surface tension is associated to each of these deformations. By using model amphiphilic membranes and computer simulations, we are able to observe both the types of deformation, and thus, both the surface tensions, related to each type of deformation, are measured for the same system. These surface tensions are found to assume different values in the same bilayer membrane: in particular they vanish for different values of the projected area. We introduce a simple theory which relates the two quantities and successfully apply it to the data obtained with computer simulations

Universal reduction of pressure between charged surfaces by long-wavelength surface charge modulation

We predict theoretically that long-wavelength surface charge modulations universally reduce the pressure between the charged surfaces with counterions compared with the case of uniformly charged surfaces with the same average surface charge density. The physical origin of this effect is the fact that surface charge modulations always lead to enhanced counterion localization near the surfaces, and hence, fewer charges at the midplane. We confirm the last prediction with Monte Carlo simulations.Comment: 8 pages 1 figure, Europhys. Lett., in pres

Self-limited self-assembly of chiral filaments

The assembly of filamentous bundles with controlled diameters is common in biological systems and desirable for the development of nanomaterials. We discuss dynamical simulations and free energy calculations on patchy spheres with chiral pair interactions that spontaneously assemble into filamentous bundles. The chirality frustrates long-range crystal order by introducing twist between interacting subunits. For some ranges of system parameters this constraint leads to bundles with a finite diameter as the equilibrium state, and in other cases frustration is relieved by the formation of defects. While some self-limited structures can be modeled as twisted filaments arranged with local hexagonal symmetry, other structures are surprising in their complexity.Comment: 5 pages, 5 figure

Swelling of particle-encapsulating random manifolds

We study the statistical mechanics of a closed random manifold of fixed area and fluctuating volume, encapsulating a fixed number of noninteracting particles. Scaling analysis yields a unified description of such swollen manifolds, according to which the mean volume gradually increases with particle number, following a single scaling law. This is markedly different from the swelling under fixed pressure difference, where certain models exhibit criticality. We thereby indicate when the swelling due to encapsulated particles is thermodynamically inequivalent to that caused by fixed pressure. The general predictions are supported by Monte Carlo simulations of two particle-encapsulating model systems -- a two-dimensional self-avoiding ring and a three-dimensional self-avoiding fluid vesicle. In the former the particle-induced swelling is thermodynamically equivalent to the pressure-induced one whereas in the latter it is not.Comment: 8 pages, 6 figure

Minimal Bending Energies of Bilayer Polyhedra

Motivated by recent experiments on bilayer polyhedra composed of amphiphilic molecules, we study the elastic bending energies of bilayer vesicles forming polyhedral shapes. Allowing for segregation of excess amphiphiles along the ridges of polyhedra, we find that bilayer polyhedra can indeed have lower bending energies than spherical bilayer vesicles. However, our analysis also implies that, contrary to what has been suggested on the basis of experiments, the snub dodecahedron, rather than the icosahedron, generally represents the energetically favorable shape of bilayer polyhedra

The lamellar-to-isotropic transition in ternary amphiphilic systems

We study the dependence of the phase behavior of ternary amphiphilic systems on composition and temperature. Our analysis is based on a curvature elastic model of the surfactant film with sufficiently large spontaneous curvature and sufficiently negative saddle-splay modulus that the stable phases are the lamellar phase and a droplet microemulsion. In addition to the curvature energy, we consider the contributions to the free energy of the long-ranged van der Waals interaction and of the undulation modes. We find that for bending rigidities of order k_B T, the lamellar phase extends further and further into the water apex of the phase diagram as the phase inversion temperature is approached, in good agreement with experimental results.Comment: LaTeX2e, 11 pages with references and 2 eps figures included, submitted to Europhys. Let

Spicules and the effect of rigid rods on enclosing membrane tubes

Membrane tubes (spicules) arise in cells, or artificial membranes, in the nonlinear deformation regime due to, e.g. the growth of microtubules, actin filaments or sickle hemoglobin fibers towards a membrane. We calculate the axial force exerted by the cylindrical membrane tube, and its average radius, by taking into account steric interactions between the fluctuating membrane and the enclosed rod. The force required to confine a fluctuating membrane near the surface of the enclosed rod diverges as the separation approaches zero. This results in a smooth crossover of the axial force between a square root and a linear dependence on the membrane tension as the tension increases and the tube radius shrinks. This crossover can occur at the most physiologically relevant membrane tensions. Our work may be important in (i) interpreting experiments in which axial force is related to the tube radius or membrane tension (ii) dynamical theories for biopolymer growth in narrow tubes where these fluctuation effects control the tube radius.Comment: 10 pages, 1 figur