Pacman percolation: a model for enzyme gel degradation

We study a model for the gel degradation by an enzyme, where the gel is schematized as a cubic lattice, and the enzyme as a random walker, that cuts the bonds over which it passes. The model undergoes a (reverse) percolation transition, which for low density of enzymes falls in a universality class different from random percolation. In particular we have measured a gel fraction critical exponent beta=1.0+-0.1, in excellent agreement with experiments made on the real system.Comment: 4 pages, 7 eps figure

Long-range Casimir interactions between impurities in nematic liquid crystals and the collapse of polymer chains in such solvents

The elastic interactions between objects embedded in a nematic liquid crystal are usually caused by the average distorsion-rather than by the fluctuations-of the nematic orientational field. We argue that for sufficiently small particles, the nematic-mediated interaction originates purely from the fluctuations of the nematic director. This Casimir interaction decays as d^(-6), d being the distance between the particles, and it dominates van der Waals interactions close to the isotropic-to-nematic transition. Considering the nematic as a polymer solvent, we show that the onset of this Casimir interaction at the isotropic-to-nematic transition can discontinuously induce the collapse of a flexible polymer chain from the swollen state to the globular state, without crossing the Theta-point.Comment: 6 pages, 1 figur

Theory of photoferroelectric response in SmC* liquids

We are concerned with the modification of liquid crystalline and polar order in SmC* liquids by illumination. In particular we show that non-uniformity due to absorption and also dynamics, can be complex. The variation of polarization with temperature, while illuminated, is modified from that assuming uniformity. Apparent changes of polarization with illumination will be shown to be underestimated due to non-uniformity. The dynamics is shown to depend on propagating fronts of photo-conversion penetrating the sample.Comment: 6 pages, 7 figure

Splitting of Surface Plasmon Frequencies of Metal Particles in a Nematic Liquid Crystal

We calculate the effective dielectric function for a suspension of small metallic particles immersed in a nematic liquid crystal (NLC) host. For a random suspension of such particles in the dilute limit, we calculate the effective dielectric tensor exactly and show that the surface plasmon (SP)resonance of such particles splits into two resonances, polarized parallel and perpendicular to the NLC director. At higher concentrations, we calculate this splitting using a generalized Maxwell-Garnett approximation, which can also be applied to a small metal particle coated with NLC. To confirm the accuracy of the MGA for NLC-coated spheres, we also use the Discrete Dipole Approximation. The calculated splitting is comparable to that observed in recent experiments on NLC-coated small metal particlesComment: 11 pages, 2 figures. To be published in Appl. Phys. Let

Topological Constraints at the Theta Point: Closed Loops at Two Loops

We map the problem of self-avoiding random walks in a Theta solvent with a chemical potential for writhe to the three-dimensional symmetric U(N)-Chern-Simons theory as N goes to 0. We find a new scaling regime of topologically constrained polymers, with critical exponents that depend on the chemical potential for writhe, which gives way to a fluctuation-induced first-order transition.Comment: 5 pages, RevTeX, typo

Untwisting of a cholesteric elastomer by a mechanical field

A mechanical strain field applied to a monodomain cholesteric elastomer will unwind the helical director distribution. There is an analogy with the classical problem of an electric field applied to a cholesteric liquid crystal, but with important differences. Frank elasticity is of minor importance unless the gel is very weak. The interplay is between director anchoring to the rubber elastic matrix and the external mechanical field. Stretching perpendicular to the helix axis induces the uniform unwound state via the elimination of sharp, pinned twist walls above a critical strain. Unwinding through conical director states occurs when the elastomer is stretched along the helical axis.Comment: 4 pages, RevTeX 3 style, 3 EPS figure

Chirality transfer and stereo-selectivity of imprinted cholesteric networks

Imprinting of cholesteric textures in a polymer network is a method of preserving a macroscopically chiral phase in a system with no molecular chirality. By modifying the elastics properties of the network, the resulting stored helical twist can be manipulated within a wide range since the imprinting efficiency depends on the balance between the elastics constants and twisting power at network formation. One spectacular property of phase chirality imprinting is the created ability of the network to adsorb preferentially one stereo-component from a racemic mixture. In this paper we explore this property of chirality transfer from a macroscopic to the molecular scale. In particular, we focus on the competition between the phase chirality and the local nematic order. We demonstrate that it is possible to control the subsequent release of chiral solvent component from the imprinting network and the reversibility of the stereo-selective swelling by racemic solvents

First-order scaling near a second-order phase transition: Tricritical polymer collapse

The coil-globule transition of an isolated polymer has been well established to be a second-order phase transition described by a standard tricritical O(0) field theory. We provide compelling evidence from Monte Carlo simulations in four dimensions, where mean-field theory should apply, that the approach to this (tri)critical point is dominated by the build-up of first-order-like singularities masking the second-order nature of the coil-globule transition: the distribution of the internal energy having two clear peaks that become more distinct and sharp as the tricritical point is approached. However, the distance between the peaks slowly decays to zero. The evidence shows that the position of this (pseudo) first-order transition is shifted by an amount from the tricritical point that is asymptotically much larger than the width of the transition region. We suggest an explanation for the apparently contradictory scaling predictions in the literature.Comment: 4 pages, 2 figures included in tex

Stereo-selective swelling of imprinted cholesteric networks

Molecular chirality, and the chiral symmetry breaking of resulting macroscopic phases, can be topologically imprinted and manipulated by crosslinking and swelling of polymer networks. We present a new experimental approach to stereo-specific separation of chiral isomers by using a cholesteric elastomer in which a helical director distribution has been topological imprinted by crosslinking. This makes the material unusual in that is has a strong phase chirality, but no molecular chirality at all; we study the nature and parameters controlling the twist-untwist transition. Adding a racemic mixture to the imprinted network results in selective swelling by only the component of ``correct'' handedness. We investigate the capacity of demixing in a racemic environment, which depends on network parameters and the underlying nematic order

Imprinted Networks as Chiral Pumps

We investigate the interaction between a chirally imprinted network and a solvent of chiral molecules. We find, a liquid crystalline polymer network is preferentially swollen by one component of a racemic solvent. This ability to separate is linked to the chiral order parameter of the network, and can be reversibly controlled via temperature or a mechanical deformation. It is maximal near the point at which the network loses its imprinted structure. One possible practical application of this effect would be a mechanical device for sorting mixed chiral molecules.Comment: 4 pages, 5 figure