Trains, tails and loops of partially adsorbed semi-flexible filaments

Polymer adsorption is a fundamental problem in statistical mechanics that has direct relevance to diverse disciplines ranging from biological lubrication to stability of colloidal suspensions. We combine experiments with computer simulations to investigate depletion induced adsorption of semi-flexible polymers onto a hard-wall. Three dimensional filament configurations of partially adsorbed F-actin polymers are visualized with total internal reflection fluorescence microscopy. This information is used to determine the location of the adsorption/desorption transition and extract the statistics of trains, tails and loops of partially adsorbed filament configurations. In contrast to long flexible filaments which primarily desorb by the formation of loops, the desorption of stiff, finite-sized filaments is largely driven by fluctuating filament tails. Simulations quantitatively reproduce our experimental data and allow us to extract universal laws that explain scaling of the adsorption-desorption transition with relevant microscopic parameters. Our results demonstrate how the adhesion strength, filament stiffness, length, as well as the configurational space accessible to the desorbed filament can be used to design the characteristics of filament adsorption and thus engineer properties of composite biopolymeric materials

Bonded straight and helical flagellar filaments form ultra-low-density glasses

We study how the three-dimensional shape of rigid filaments determines the microscopic dynamics and macroscopic rheology of entangled semi-dilute Brownian suspensions. To control the filament shape we use bacterial flagella, which are micron-long helices assembled from flagellin monomers. We compare the dynamics of straight rods, helical filaments, and shape diblock copolymers composed of seamlessly joined straight and helical segments. Caged by their neighbors, straight rods preferentially diffuse along their long axis, but exhibit significantly suppressed rotational diffusion. Entangled helical filaments escape their confining tube by corkscrewing through the dense obstacles created by other filaments. By comparison, the adjoining segments of the rod-helix shape-diblocks suppress both the translation and the corkscrewing dynamics, so that shape-diblocks become permanently jammed at exceedingly low densities. We also measure the rheological properties of semi-dilute suspensions and relate their mechanical properties to the microscopic dynamics of constituent filaments. In particular, rheology shows that an entangled suspension of shape rod-helix copolymers forms a low-density glass whose elastic modulus can be estimated by accounting for how shear deformations reduce the entropic degrees of freedom of constrained filaments. Our results demonstrate that the three-dimensional shape of rigid filaments can be used to design rheological properties of semi-dilute fibrous suspensions.Comment: 24 pages, 7 figure

Nematic Ordering of Rigid Rods in a Gravitational Field

The isotropic-to-nematic transition in an athermal solution of long rigid rods subject to a gravitational (or centrifugal) field is theoretically considered in the Onsager approximation. The new feature emerging in the presence of gravity is a concentration gradient which coupled with the nematic ordering. For rodlike molecules this effect becomes noticeable at centrifugal acceleration g ~ 10^3--10^4 m/s^2, while for biological rodlike objects, such as tobacco mosaic virus, TMV, the effect is important even for normal gravitational acceleration conditions. Rods are concentrated near the bottom of the vessel which sometimes leads to gravity induced nematic ordering. The concentration range corresponding to phase separation increases with increasing g. In the region of phase separation the local rod concentration, as well as the order parameter, follow a step function with height.Comment: Full article http://prola.aps.org/abstract/PRE/v60/i3/p2973_

Elongation and fluctuations of semi-flexible polymers in a nematic solvent

We directly visualize single polymers with persistence lengths ranging from $\ell_p=0.05$ to 16 $\mu$m, dissolved in the nematic phase of rod-like {\it fd} virus. Polymers with sufficiently large persistence length undergo a coil-rod transition at the isotropic-nematic transition of the background solvent. We quantitatively analyze the transverse fluctuations of semi-flexible polymers and show that at long wavelengths they are driven by the fluctuating nematic background. We extract both the Odijk deflection length and the elastic constant of the background nematic phase from the data.Comment: 4 pages, 4 figures, submitted to PR

Achiral symmetry breaking and positive Gaussian modulus lead to scalloped colloidal membranes

In the presence of a non-adsorbing polymer, monodisperse rod-like particles assemble into colloidal membranes, which are one rod-length thick liquid-like monolayers of aligned rods. Unlike 3D edgeless bilayer vesicles, colloidal monolayer membranes form open structures with an exposed edge, thus presenting an opportunity to study physics of thin elastic sheets. Membranes assembled from single-component chiral rods form flat disks with uniform edge twist. In comparison, membranes comprised of mixture of rods with opposite chiralities can have the edge twist of either handedness. In this limit disk-shaped membranes become unstable, instead forming structures with scalloped edges, where two adjacent lobes with opposite handedness are separated by a cusp-shaped point defect. Such membranes adopt a 3D configuration, with cusp defects alternatively located above and below the membrane plane. In the achiral regime the cusp defects have repulsive interactions, but away from this limit we measure effective long-ranged attractive binding. A phenomenological model shows that the increase in the edge energy of scalloped membranes is compensated by concomitant decrease in the deformation energy due to Gaussian curvature associated with scalloped edges, demonstrating that colloidal membranes have positive Gaussian modulus. A simple excluded volume argument predicts the sign and magnitude of the Gaussian curvature modulus that is in agreement with experimental measurements. Our results provide insight into how the interplay between membrane elasticity, geometrical frustration and achiral symmetry breaking can be used to fold colloidal membranes into 3D shapes.Comment: Main text: 25 pages, 6 figures. Supplementary information: 6 pages, 6 figure

Radius and chirality dependent conformation of polymer molecule at nanotube interface

Temperature dependent conformations of linear polymer molecules adsorbed at carbon nanotube (CNT) interfaces are investigated through molecule dynamics simulations. Model polyethylene (PE) molecules are shown to have selective conformations on CNT surface, controlled by atomic structures of CNT lattice and geometric coiling energy. PE molecules form entropy driven assembly domains, and their preferred wrapping angles around large radius CNT (40, 40) reflect the molecule configurations with energy minimums on a graphite plane. While PE molecules prefer wrapping on small radius armchair CNT (5, 5) predominantly at low temperatures, their configurations are shifted to larger wrapping angle ones on a similar radius zigzag CNT (10, 0). A nematic transformation around 280 K is identified through Landau-deGennes theory, with molecule aligning along tube axis in extended conformationsComment: 19 pages, 7 figure2, submitted to journa

Isotropic-nematic phase transition in suspensions of filamentous virus and the neutral polymer Dextran

We present an experimental study of the isotropic-nematic phase transition in an aqueous mixture of charged semi-flexible rods (fd virus) and neutral polymer (Dextran). A complete phase diagram is measured as a function of ionic strength and polymer molecular weight. At high ionic strength we find that adding polymer widens the isotropic-nematic coexistence region with polymers preferentially partitioning into the isotropic phase, while at low ionic strength the added polymer has no effect on the phase transition. The nematic order parameter is determined from birefringence measurements and is found to be independent of polymer concentration (or equivalently the strength of attraction). The experimental results are compared with the existing theoretical predictions for the isotropic-nematic transition in rods with attractive interactions.Comment: 8 Figures. To be published in Phys. Rev. E. For more information see http://www.elsie.brandeis.ed

Parity Breaking in Nematic Tactoids

We theoretically investigate under what conditions the director field in a spindle-shaped nematic droplet or tactoid obtains a twisted, parity-broken structure. By minimizing the sum of the bulk elastic and surface energies, we show that a twisted director field is stable if the twist and bend elastic constants are small enough compared to the splay elastic constant, but only if the droplet volume is larger than some minimum value. We furthermore show that the transition from an untwisted to a twisted director-field structure is a sharp function of the various control parameters. We predict that suspensions of rigid, rod-like particles cannot support droplets with a parity broken structure, whereas they could possibly occur in those of semi-flexible, worm-like particles.Comment: 20 pages, 9 figures, submitted to Journal of Physics: Condensed Matte

Banding, Excitability and Chaos in Active Nematic Suspensions

Motivated by the observation of highly unstable flowing states in suspensions of microtubules and kinesin, we analyze a model of mutually-propelled filaments suspended in a solvent. The system undergoes a mean-field isotropic-nematic transition for large enough filament concentrations when the nematic order parameter is allowed to vary in space and time. We analyze the model in two contexts: a quasi-one-dimensional channel with no-slip walls and a two-dimensional box with periodic boundaries. Using stability analysis and numerical calculations we show that the interplay between non-uniform nematic order, activity, and flow results in a variety of complex scenarios that include spontaneous banded laminar flow, relaxation oscillations, and chaos.Comment: 15 pages, 15 figure