Mean Field and the Single Homopolymer

We develop a statistical model for a confined chain molecule based on a monomer grand canonical ensemble. The molecule is subject to an external chemical potential, a backbone interaction, and an attractive interaction between all monomers. Using a Gaussian variable formalism and a mean field approximation, we analytically derive a minimum principle from which we can obtain relevant physical quantities, such as the monomer density, and we explore the limit in which the chain is subject to a tight confinement. Through a numerical implementation of the minimization process we show how we can obtain density profiles in three dimensions for arbitraty potentials, and we test the limits of validity of the theory.Comment: 15 pages, 7 figure

The Mechanics and Statistics of Active Matter

Active particles contain internal degrees of freedom with the ability to take in and dissipate energy and, in the process, execute systematic movement. Examples include all living organisms and their motile constituents such as molecular motors. This article reviews recent progress in applying the principles of nonequilibrium statistical mechanics and hydrodynamics to form a systematic theory of the behaviour of collections of active particles -- active matter -- with only minimal regard to microscopic details. A unified view of the many kinds of active matter is presented, encompassing not only living systems but inanimate analogues. Theory and experiment are discussed side by side.Comment: This review is to appear in volume 1 of the Annual Review of Condensed Matter Physics in July 2010 and is posted here with permission from that journa

EPR spectroscopy and molecular dynamics modelling: a combined approach to study liquid crystals

This review outlines the recent theoretical and computational developments for the prediction of motional electron paramagnetic resonance spectra with introduced spin probes from molecular dynamics simulations. The methodology is illustrated with applications to thermotropic and lyotropic liquid crystals at different phases and aggregate states

The Chiral Dipolar Hard Sphere Model

A simple molecular model of chiral molecules is presented in this paper : the chiral dipolar hard sphere model. The discriminatory interaction between enantiomers is represented by electrostatic (or magnetic) dipoles-dipoles interactions : short ranged steric repulsion are represented by hard sphere potential and, in each molecule, two point dipoles are located inside the sphere. The model is described in detail and some of its elementary properties are given ; in particular, it is shown that the that the knowledge of only three multipole spherical components (namely : $Q_{10}$, $Q_{21}$ and $Q_{22}$) allows to compute all multipole spherical components of the model. Despite, the simplicity of the model, it is shown also that the energy landscape of the interaction between two enantiomers is quite rich, this renders systems of chiral dipolar hard sphere very interesting and complicated to study. Few preliminary Monte Carlo simulation results are also reported in the paper. Last, but not least, this paper is dedicated to Jean-Jacques Weis.Comment: 28 pages, 14 Figures, 3 Tables. To appear in Molecular Physic

Properties of the Broad-Range Nematic Phase of a Laterally Linked H-Shaped Liquid Crystal Dimer

In search for novel nematic materials, a laterally linked H-shaped liquid crystal dimer have been synthesized and characterized. The distinct feature of the material is a very broad temperature range (about 50 oC) of the nematic phase, which is in contrast with other reported H-dimers that show predominantly smectic phases. The material exhibits interesting textural features at the scale of nanometers (presence of smectic clusters) and at the macroscopic scales. Namely, at a certain temperature, the flat samples of the material show occurrence of domain walls. These domain walls are caused by the surface anchoring transition and separate regions with differently tilted director. Both above and below this transition temperature the material represents a uniaxial nematic, as confirmed by the studies of defects in flat samples and samples with colloidal inclusions, freely suspended drops, X-ray diffraction and transmission electron microscopy.Comment: 30 pages (including Supplementary Information), 7 Figure

Unwinding of a cholesteric liquid crystal and bidirectional surface anchoring

We examine the influence of bidirectional anchoring on the unwinding of a planar cholesteric liquid crystal induced by the application of a magnetic field. We consider a liquid crystal layer confined between two plates with the helical axis perpendicular to the substrates. We fixed the director twist on one boundary and allow for bidirectional anchoring on the other by introducing a high-order surface potential. By minimizing the total free energy for the system, we investigate the untwisting of the cholesteric helix as the liquid crystal attempts to align with the magnetic field. The transitions between metastable states occur as a series of pitchjumps as the helix expels quarter or half-turn twists, depending on the relative sizes of the strength of the surface potential and the bidirectional anchoring. We show that secondary easy axis directions can play a significant role in the unwinding of the cholesteric in its transition towards a nematic, especially when the surface anchoring strength is large

Effect of calcium ions and pH on the morphology and mechanical properties of hyaluronan brushes

Hyaluronan (HA) is a linear, regular polysaccharide that plays as a chief structural and functional component in peri- and extracellular matrices, thus contributing significantly to many basic cellular processes. To understand more comprehensively the response of the supramolecular organization of HA polymers to changes in their aqueous environment, we study the effects of Ca 2þ concentration and pH on the morphology and rigidity of films of end-grafted HA polymers on planar supports (HA brushes), as a well-defined in vitro model system of HA-rich matrices, by reflection interference contrast microscopy and quartz crystal microbalance. The thickness and softness of HA brushes decrease significantly with Ca 2þ concentration but do not change with pH, within the physiological ranges of these parameters. The effect of Ca 2þ on HA brush thickness is virtually identical to the effect of Na þ at 10-fold higher concentrations. Moreover, the thickness and softness of HA brushes decrease appreciably upon HA protonation at pH less than 6. Effects of pH and calcium ions are fully reversible over large parameter ranges. These findings are relevant for understanding the supramolecular organization and dynamics of HA-rich matrices in biological systems and will also benefit the rational design of synthetic HA-rich materials with tailored properties

High and low molecular weight crossovers in the longest relaxation time dependence of linear cis-1,4 polyisoprene by dielectric relaxations

The dielectric relaxation of cis-1,4 Polyisoprene [PI] is sensitive not only to the local and segmental dynamics but also to the larger scale chain (end-to-end) fluctuations. We have performed a careful dielectric investigation on linear PI with various molecular weights in the range of 1 to 320 kg/mol. The broadband dielectric spectra of all samples were measured isothermally at the same temperature to avoid utilizing shift factors. For the low and medium molecular weight range, the comparisons were performed at 250 K to access both the segmental relaxation and normal mode peaks inside the available frequency window (1 mHz–10 MHz). In this way, we were able to observe simultaneously the effect of molecular mass on the segmental dynamics—related with the glass transition process—and on the end-to-end relaxation time of PI and thus decouple the direct effect of molecular weight on the normal mode from that due to the effect on the monomeric friction coefficient. The latter effect is significant for low molecular weight (M w < 33 kg/mol), i.e., in the range where the crossover from Rouse dynamics to entanglement limited flow occurs. Despite the conductivity contribution at low frequency, careful experiments allowed us to access to the normal mode signal for molecular weights as high as M w = 320 kg/mol, i.e., into the range of high molecular weights where the pure reptation behavior could be valid, at least for the description of the slowest chain modes. The comparison between the dielectric relaxations of PI samples with medium and high molecular weight was performed at 320 K. We found two crossovers in the molecular weight dependence of the longest relaxation time, the first around a molecular weight of 6.5 ± 0.5 kg/mol corresponding to the end of the Rouse regime and the second around 75 ± 10 kg/mol. Above this latter value, we find a power law compatible with exponent 3 as predicted by the De Gennes theory

Constant-angle surfaces in liquid crystals

We discuss some properties of surfaces in R3 whose unit normal has constant angle with an assigned direction field. The constant angle condition can be rewritten as an Hamilton-Jacobi equation correlating the surface and the direction field. We focus on examples motivated by the physics of interfaces in liquid crystals and of layered fluids, and discuss the properties of the constant-angle surfaces when the direction field is singular along a line (disclination) or at a point (hedgehog defect

Snap evaporation of droplets on smooth topographies

Droplet evaporation on solid surfaces is important in many applications including printing, micro-patterning and cooling. While seemingly simple, the configuration of evaporating droplets on solids is difficult to predict and control. This is because evaporation typically proceeds as a “stick-slip” sequence—a combination of pinning and de-pinning events dominated by static friction or “pinning”, caused by microscopic surface roughness. Here we show how smooth, pinning-free, solid surfaces of non-planar topography promote a different process called snap evaporation. During snap evaporation a droplet follows a reproducible sequence of configurations, consisting of a quasi-static phase-change controlled by mass diffusion interrupted by out-of-equilibrium snaps. Snaps are triggered by bifurcations of the equilibrium droplet shape mediated by the underlying non-planar solid. Because the evolution of droplets during snap evaporation is controlled by a smooth topography, and not by surface roughness, our ideas can inspire programmable surfaces that manage liquids in heat- and mass-transfer applications