arXiv subjects

Robert A. Pelcovits

Publications and source records attributed to Robert A. Pelcovits.

At least 37 records · Page 2Linked to original sources

arXiv2013

Instability of flat disks with respect to the formation of twisted ribbons in smectic-A monolayers

Smectic-A monolayers self-assembled from aqueous solutions of chiral fd viruses and a polymer depletant can assume a variety of shapes such as flat disks and twisted ribbons. A theoretical model based on the de Gennes model for the smectic A phase, the Helfrich model of membrane elasticity and a simple edge energy has been previously used to calculate the disk-ribbon phase diagram. In this paper we apply this model to the nucleation process of ribbons. First, we study the "rippled disks" that have been observed as precursors of ribbons. Using a model shape proposed by Meyer which includes rippling in both the in-plane and out of plane directions, we study the energetics of the disks as functions of the edge energy modulus (a measure of the polymer concentration) and the mean curvature modulus k. We find that as the edge energy modulus is reduced the radial size of the ripples grows rapidly in agreement with experimental observations. For small enough k we find that the out of plane size of the ripples grows but its value saturates at a fraction of the twist penetration depth, too small to be experimentally observable. For large k the membrane remains flat though rippled in the radial direction. Such membranes do not have negative Gaussian curvature and thus will not likely spawn twisted ribbons. We also study the creation of twisted ribbons produced by stretching the edge of a flat membrane in a localized region. In experiments using a pair of optical traps it has been observed that once the membrane has been sufficiently stretched a ribbon forms on the stretched edge. We study this process theoretically using a free energy consisting of the Helfrich and edge energies alone. We add a small ribbon-like perturbation to the protrusion producd by stretching and determine whether it is energetically favorable as a function of the size of the protrusion.

cond-mat.soft↗

arXiv2013

Theory of self-assembled smectic-A "crenellated disks"

Smectic-A monolayers self-assembled in aqueous solutions of chiral fd viruses and a polymer depletant have been shown to exhibit a variety of structures including large, flat disks and twisted ribbons. The virus particles twist near the edge of the structure in a direction determined by the chirality of the viruses. When fd viruses and their mutants of opposite chirality are mixed together in nearly equal amounts unusual structures referred to as "crenellated disks" can appear. These disks are achiral overall but the twist at the edge alternates between left- and right-handedness. To minimize the mismatch where the two regions of opposing twist meet, the "crenellated" structure exhibits cusps rising out of the plane of the monolayer. We use a phenomenological elastic theory previously applied to flat disks and twisted ribbons to analyze an analytic model proposed to describe the "crenellated" structure . When compared with flat, circular disks, we find that the model "crenellated disks" are stable or at least metastable in a wide region of the phase diagram spanned by the Gaussian curvature modulus and the edge energy modulus, with a large energy barrier separating the two structures. The director pattern and geometric parameters of the "crenellated disks" are found to be in qualitative agreement with experimental observations.

cond-mat.soft↗

arXiv2012

Nematic topological defects in the presence of axisymmetric fluid flow

Recent numerical simulations of lid-driven cavity flow of a nematic liquid crystal have found dynamical behavior where topological defects rotate about the center of the fluid vortex induced by the lid motion. By considering a simpler geometry of an infinite system with axisymmetric fluid flow we show that the Ericksen-Leslie nematodynamic equation for the director can be solved exactly. The solution demonstrates that any configuration of defects will be advected by the fluid flow, with the defects rotating about the center of the fluid vortex with the angular velocity of the fluid.

cond-mat.soft↗

arXiv2012

Analysis of a Fivefold Symmetric Superposition of Plane Waves

We show that a symmetric superposition of five standing plane waves can be expressed as an infinite series of terms of decreasing wavenumber, where each term is a product of five plane waves. We show that this series converges pointwise in R^2 and uniformly in any disk domain in R^2. Using this series, we provide a heuristic argument for why the locations of the local extrema of a symmetric superposition of five standing plane waves can be approximated by the vertices of a Penrose tiling.

math-ph↗

arXiv2010

Theory of depletion induced phase transition from chiral smectic A twisted ribbons to semi-infinite flat membranes

We consider a theoretical model for the chiral smectic A twisted ribbons observed in assemblies of fd viruses condensed by depletion forces. The depletion interaction is modeled by an edge energy assumed to be proportional to the depletant polymer in solution. Our model is based on the Helfrich energy for surface bending and the de Gennes model of chiral smectic A liquid crystals with twist penetration at the edge. We consider two variants of this model, one with the conventional Helfrich Gaussian curvature term, and a second with saddle-splay energy. A mean field analysis of both models yields a first-order phase transition between ribbons and semi-infinite flat membranes as the edge energy is varied. The phase transition line and tilt angle profile are found to be nearly identical for the two models; the pitch of the ribbon, however, does show some differences. Our model yields good qualitative agreement with experimental observations if the sign of the Gaussian curvature or saddle-splay modulus is chosen to favor negative Gaussian curvature.

cond-mat.soft↗

arXiv2007

Nematic cells with defect-patterned alignment layers

Using Monte Carlo simulations of the Lebwohl--Lasher model we study the director ordering in a nematic cell where the top and bottom surfaces are patterned with a lattice of $\pm 1$ point topological defects of lattice spacing $a$. We find that the nematic order depends crucially on the ratio of the height of the cell $H$ to $a$. When $H/a \gtrsim 0.9$ the system is very well--ordered and the frustration induced by the lattice of defects is relieved by a network of half--integer defect lines which emerge from the point defects and hug the top and bottom surfaces of the cell. When $H/a \lesssim 0.9$ the system is disordered and the half--integer defect lines thread through the cell joining point defects on the top and bottom surfaces. We present a simple physical argument in terms of the length of the defect lines to explain these results. To facilitate eventual comparison with experimental systems we also simulate optical textures and study the switching behavior in the presence of an electric field.

cond-mat.soft↗

arXiv2007

Role of electrostatics in the texture of islands in free standing ferroelectric liquid crystal films

Curved textures of ferroelectric smectic C* liquid crystals produce space charge when they involve divergence of the spontaneous polarization field. Impurity ions can partially screen this space charge, reducing long range interactions to local ones. Through studies of the textures of islands on very thin free-standing smectic films, we see evidence of this effect, in which materials with a large spontaneous polarization have static structures described by a large effective bend elastic constant. To address this issue, we calculated the electrostatic free energy of a free standing film of ferroelectric liquid crystal, showing how the screened coulomb interaction contributes a term to the effective bend elastic constant, in the static long wavelength limit. We report experiments which support the main features of this model.

cond-mat.soft↗

arXiv2007

Dynamics of the molecular orientation field coupled to ions in two-dimensional ferroelectric liquid crystals

Molecular orientation fluctuations in ferroelectric smectic liquid crystals produce space charges, due to the divergence of the spontaneous polarization. These space charges interact with mobile ions, so that one must consider the coupled dynamics of the orientation and ionic degrees of freedom. Previous theory and light scattering experiments on thin free-standing films of ferroelectric liquid crystals have not included this coupling, possibly invalidating their quantitative conclusions. We consider the most important case of very slow ionic dynamics, compared to rapid orientational fluctuations, and focus on the use of a short electric field pulse to quench orientational fluctuations. We find that the resulting change in scattered light intensity must include a term due to the quasistatic ionic configuration, which has previously been ignored. In addition to developing the general theory, we present a simple model to demonstrate the role of this added term.

cond-mat.soft↗

arXiv2007

Vesicle shape, molecular tilt, and the suppression of necks

Can the presence of molecular-tilt order significantly affect the shapes of lipid bilayer membranes, particularly membrane shapes with narrow necks? Motivated by the propensity for tilt order and the common occurrence of narrow necks in the intermediate stages of biological processes such as endocytosis and vesicle trafficking, we examine how tilt order inhibits the formation of necks in the equilibrium shapes of vesicles. For vesicles with a spherical topology, point defects in the molecular order with a total strength of $+2$ are required. We study axisymmetric shapes and suppose that there is a unit-strength defect at each pole of the vesicle. The model is further simplified by the assumption of tilt isotropy: invariance of the energy with respect to rotations of the molecules about the local membrane normal. This isotropy condition leads to a minimal coupling of tilt order and curvature, giving a high energetic cost to regions with Gaussian curvature and tilt order. Minimizing the elastic free energy with constraints of fixed area and fixed enclosed volume determines the allowed shapes. Using numerical calculations, we find several branches of solutions and identify them with the branches previously known for fluid membranes. We find that tilt order changes the relative energy of the branches, suppressing thin necks by making them costly, leading to elongated prolate vesicles as a generic family of tilt-ordered membrane shapes.

cond-mat.soft↗

arXiv2006

Untwisting of a Strained Cholesteric Elastomer by Disclination Loop Nucleation

The application of a sufficiently strong strain perpendicular to the pitch axis of a monodomain cholesteric elastomer unwinds the cholesteric helix. Previous theoretical analyses of this transition ignored the effects of Frank elasticity which we include here. We find that the strain needed to unwind the helix is reduced because of the Frank penalty and the cholesteric state becomes metastable above the transition. We consider in detail a previously proposed mechanism by which the topologically stable helical texture is removed in the metastable state, namely by the nucleation of twist disclination loops in the plane perpendicular to the pitch axis. We present an approximate calculation of the barrier energy for this nucleation process which neglects possible spatial variation of the strain fields in the elastomer, as well as a more accurate calculation based on a finite element modeling of the elastomer.

cond-mat.soft↗

arXiv2004

Liquid crystals in random porous media: Disorder is stronger in low--density aerosils

The nature of glass phases of liquid crystals in random porous media depends on the effective disorder strength. We study how the disorder strength depends on the density of the porous media and demonstrate that it can increase as the density decreases. We also show that the interaction of the liquid crystal with random porous media can destroy long--range order inside the pores.

cond-mat.soft↗

arXiv2002

Optomechanical Properties of Stretched Polymer Dispersed Liquid Crystal Films for Scattering Polarizer Applications

A scattering polarizer is created by subjecting a polymer dispersed liquid crystal (PDLC) film to tensile strain. The optomechanical properties of the film are investigated by simultaneously measuring the stress-strain and polarization dependent optical transmission characteristics. The correlation between transmittances of two orthogonal polarizations and the stress-strain curve reveals that the polymer orientation as well as the droplet shape anisotropy influences the liquid crystal alignment within the droplets. A Monte-Carlo simulation based on the Lebwohl-Lasher model is used to explain the subtle influence of polymer orientation on liquid crystal alignment.

cond-mat.soft↗

arXiv2002

The isotropic-cholesteric transition in liquid-crystalline gels

In a nematic gel, the appearance of nematic order is accompanied by a spontaneous elongation of the gel parallel to the nematic director. If such a gel is made chiral, it has a tendency to form a cholesteric helical texture, in which local elongation of the gel parallel to the nematic director is suppressed due to the requirement of elastic compatibility. We show that a conical helix in which the director makes an oblique angle with respect to the helix axis serves as an energy minimizing compromise between the competing tendencies for elongation and twisting. We find the dependence of the helical cone angle and pitch on the strength of the chirality, and determine the change in sample shape at the isotropic to cholesteric phase transition.

cond-mat.soft↗

arXiv2002

Virtual surfaces, director domains and the Freedericksz transition in polymer stabilized nematic liquid crystals

The critical field of the Freedericksz transition and switching dynamics are investigated for polymer stabilized nematic liquid crystals as a function of polymer concentration. A simple phenomenological model is proposed to describe the observed critical field and dynamic response time behaviors as a function of concentration. In this model the polymer fibrils form director domains, which are bounded by virtual surfaces with a finite anchoring energy. The Freedericksz transition occurs independently within each of these domains.

cond-mat.soft↗

arXiv2002

The electroclinic effect and modulated phases in smectic liquid crystals

We explore the possibility that the large electroclinic effect observed in ferroelectric liquid crystals arises from the presence of an ordered array of disclination lines and walls. If the spacing of these defects is in the subvisible range, this modulated phase would be similar macroscopically to a smectic A phase. The application of an electric field distorts the array, producing a large polarization, and hence a large electroclinic effect. We show that with suitable elastic parameters and sufficiently large chirality, the modulated phase is favored over the smectic A and helically twisted smectic C* phases. We propose various experimental tests of this scenario.

cond-mat.soft↗

arXiv2002

Coarsening Dynamics of Biaxial Nematic Liquid Crystals

We study the coarsening dynamics of two and three dimensional biaxial nematic liquid crystals, using Langevin dynamics. Unlike previous work, we use a model with no a priori relationship among the three elastic constants associated with director deformations. We find a rich variety of coarsening behavior, including the simulataneous decay of nearly equal populations of the three classes of half-integer disclination lines. The behavior we observed can be understood on the basis of the relative values of the elastic constants and the resulting decay channels of the defects.

cond-mat.soft↗

arXiv2001

Disclination loop behavior near the nematic-isotropic transition

We investigate the behavior of disclination loops in the vicinity of the first order nematic-isotropic transition in the Lebwohl-Lasher and related models. We find that two independent measures of the transition temperature, the free energy and the distribution of disclination line segments, give essentially identical values. We also calculate the distribution function D(p) of disclination loops of perimeter p and fit it to a quasiexponential form. Below the transition, D(p) falls off exponentially, while in the neighborhood of the transition it decays with a power law exponent approximately equal to 2.5, consistent with a "blowout" of loops at the transition. In a modified Lebwohl-Lasher model with a strongly first-order transition we are able to measure a jump in the disclination line tension at the transition, which is too small to be measured in the Lebwohl-Lasher model. We also measure the monopole charge of the disclination loops and find that in both the original and modified Lebwohl-Lasher models, there are large loops which carry monopole charge, while smaller isolated loops do not. Overall the nature of the topological defects in both models is very similar.

cond-mat.soft↗

arXiv2000

Cluster Monte Carlo Simulations of the Nematic--Isotropic Transition

We report the results of simulations of the Lebwohl-Lasher model of the nematic-isotropic transition using a new cluster Monte Carlo algorithm. The algorithm is a modification of the Wolff algorithm for spin systems, and greatly reduces critical slowing down. We calculate the free energy in the neighborhood of the transition for systems up to linear size 70. We find a double well structure with a barrier that grows with increasing system size, obeying finite size scaling for systems of size greater than 35. We thus obtain an estimate of the value of the transition temperature in the thermodynamic limit.

cond-mat.soft↗