Lubensky, Tom C
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Publication Elongation and Fluctuations of Semi-flexible Polymers in a Nematic Solvent(2004-03-26) Dogic, Z.; Zhang, J.; Discher, Dennis E; Lau, A. W.C.; Janmey, Paul; Aranda-Espinoza, Helim; Kamien, Randall; Dalhaimer, Paul M; Lubensky, Thomas C.; Yodh, ArjunWe directly visualize single polymers with persistence lengths ranging from lp = 0:05 to 16 µm, dissolved in the nematic phase of rod-like 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.Publication Electrostatic Repulsion of Positively Charged Vesicles and Negatively Charged Objects(1999-07-16) Aranda-Espinoza, Helim; Chen, Yi; Lubensky, Thomas C.; Dan, Nily; Nelson, Philip; Ramos, Laurence; Weitz, David AA positively charged, mixed bilayer vesicle in the presence of negatively charged surfaces (for example, colloidal particles) can spontaneously partition into an adhesion zone of definite area, and another zone that repels additional negative objects. Although the membrane itself has nonnegative charge in the repulsive zone, negative counterions on the interior of the vesicle spontaneously aggregate there, and present a net negative charge to the exterior. Beyond the fundamental result that oppositely charged objects can repel, our mechanism helps explain recent experiments on surfactant vesicles.Publication Smectic-A Elastomers with Weak Director Anchoring(2008-07-08) Adams, J. M.; Stenull, Olaf; Warner, Mark; Lubensky, Thomas C.Experimentally it is possible to manipulate the director in a (chiral) smectic-A elastomer using an electric field. This suggests that the director is not necessarily locked to the layer normal, as described in earlier papers that extended rubber elasticity theory to smectics. Here, we consider the case that the director is weakly anchored to the layer normal assuming that there is a free energy penalty associated with relative tilt between the two. We use a recently developed weak-anchoring generalization of rubber elastic approaches to smectic elastomers and study shearing in the plane of the layers, stretching in the plane of the layers, and compression and elongation parallel to the layer normal. We calculate, inter alia, the engineering stress and the tilt angle between director and layer normal as functions of the applied deformation. For the latter three deformations, our results predict the existence of an instability towards the development of shear accompanied by smectic-C-like order.Publication Elasticity of a filamentous kagome lattice(2013-04-09) Stenull, Olaf; Mao, Xiaoming; Lubensky, Thomas C.The diluted kagome lattice, in which bonds are randomly removed with probability 1−p, consists of straight lines that intersect at points with a maximum coordination number of 4. If lines are treated as semiflexible polymers and crossing points are treated as cross-links, this lattice provides a simple model for two-dimensional filamentous networks. Lattice-based effective-medium theories and numerical simulations for filaments modeled as elastic rods, with stretching modulus μ and bending modulus κ, are used to study the elasticity of this lattice as functions of p and κ. At p=1, elastic response is purely affine, and the macroscopic elastic modulus G is independent of κ. When κ=0, the lattice undergoes a first-order rigidity-percolation transition at p=1. When κ>0, G decreases continuously as p decreases below one, reaching zero at a continuous rigidity-percolation transition at p=pb≈0.605 that is the same for all nonzero values of κ. The effective-medium theories predict scaling forms for G, which exhibit crossover from bending-dominated response at small κ/μ to stretching-dominated response at large κ/μ near both p=1 and pb, that match simulations with no adjustable parameters near p=1. The affine response as p→1 is identified with the approach to a state with sample-crossing straight filaments treated as elastic rods.Publication Fluctuating Hydrodynamics and Microrheology of a Dilute Suspension of Swimming Bacteria(2009-07-22) Lau, A W.C.; Lubensky, Thomas C.A bacterial bath is a model active system consisting of a population of rodlike motile or self-propelled bacteria suspended in a fluid environment. This system can be viewed as an active, nonequilibrium version of a lyotropic liquid crystal or as a generalization of a driven diffusive system. We derive a set of phenomenological equations, which include the effects of internal force generators in the bacteria, describing the hydrodynamic flow, orientational dynamics of the bacteria, and fluctuations induced by both thermal and nonthermal noises. These equations violate the fluctuation dissipation theorem and the Onsager reciprocity relations. We use them to provide a quantitative account of results from recent microrheological experiments on bacterial baths.Publication Dynamics of Gas-Fluidized Granular Rods(2009-04-01) Daniels, L. J.; Lubensky, Thomas C.; Park, Y.; Durian, Douglas J.We study a quasi-two-dimensional monolayer of granular rods fluidized by a spatially and temporally homogeneous upflow of air. By tracking the position and orientation of the particles, we characterize the dynamics of the system with sufficient resolution to observe ballistic motion at the shortest time scales. Particle anisotropy gives rise to dynamical anisotropy and superdiffusive dynamics parallel to the rod’s long axis, causing the parallel and perpendicular mean-square displacements to become diffusive on different time scales. The distributions of free times and free paths between collisions deviate from exponential behavior, underscoring the nonthermal character of the particle motion. The dynamics show evidence of rotationaltranslational coupling similar to that of an anisotropic Brownian particle. We model rotational-translational coupling in the single-particle dynamics with a modified Langevin model using nonthermal noise sources. This suggests a phenomenological approach to thinking about collections of self-propelling particles in terms of enhanced memory effects.Publication Stripes, Zigzags, and Slow Dynamics in Buckled Hard Spheres(2009-01-29) Shokef, Yair; Lubensky, Thomas C.We study the analogy between buckled colloidal monolayers and the triangular-lattice Ising antiferromagnet. We calculate free-volume-induced Ising interactions, show how lattice deformations favor zigzag stripes that partially remove the Ising model ground-state degeneracy, and identify the martensitic mechanism prohibiting perfect stripes. Slowly inflating the spheres yields jamming as well as logarithmically slow relaxation reminiscent of the glassy dynamics observed experimentally.Publication Microrheology, Stress Fluctuations, and Active Behavior of Living Cells(2003-11-03) Lau, A. W. C.; Hoffman, Brenton D; Crocker, John C; Davies, A.; Lubensky, Thomas C.We report the first measurements of the intrinsic strain fluctuations of living cells using a recently developed tracer correlation technique along with a theoretical framework for interpreting such data in heterogeneous media with nonthermal driving. The fluctuations’ spatial and temporal correlations indicate that the cytoskeleton can be treated as a course-grained continuum with power-law rheology, driven by a spatially random stress tensor field. Combined with recent cell rheology results, our data imply that intracellular stress fluctuations have a nearly 1/ω2 power spectrum, as expected for a continuum with a slowly evolving internal prestress.Publication Effective-medium theory of a filamentous triangular lattice(2013-04-09) Stenull, Olaf; Mao, Xiaoming; Lubensky, Thomas C.We present an effective-medium theory that includes bending as well as stretching forces, and we use it to calculate the mechanical response of a diluted filamentous triangular lattice. In this lattice, bonds are central-force springs, and there are bending forces between neighboring bonds on the same filament. We investigate the diluted lattice in which each bond is present with a probability p. We find a rigidity threshold pb which has the same value for all positive bending rigidity and a crossover characterizing bending, stretching, and bend-stretch coupled elastic regimes controlled by the central-force rigidity percolation point at pCF≃2/3 of the lattice when fiber bending rigidity vanishes.Publication Influence of Particle Shape on Bending Rigidity of Colloidal Monolayer Membranes and Particle Deposition during Droplet Evaporation in Confined Geometries(2012-06-01) Yunker, Peter J; Gratale, Matthew; Lohr, Matthew A; Lubensky, Thomas C.; Still, Tim; Yodh, Arjun G.We investigate the influence of particle shape on the bending rigidity of colloidal monolayer membranes (CMMs) and on evaporative processes associated with these membranes. Aqueous suspensions of colloidal particles are confined between glass plates and allowed to evaporate. Confinement creates ribbonlike air-water interfaces and facilitates measurement and characterization of CMM geometry during drying. Interestingly, interfacial buckling events occur during evaporation. Extension of the description of buckled elastic membranes to our quasi-2D geometry enables the determination of the ratio of CMM bending rigidity to its Young’s modulus. Bending rigidity increases with increasing particle anisotropy, and particle deposition during evaporation is strongly affected by membrane elastic properties. During drying, spheres are deposited heterogeneously, but ellipsoids are not. Apparently, increased bending rigidity reduces contact line bending and pinning and induces uniform deposition of ellipsoids. Surprisingly, suspensions of spheres doped with a small number of ellipsoids are also deposited uniformly.