Lubensky, Tom C
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Publication Elasticity and Response in Nearly Isostatic Periodic Lattices(2009-11-13) Souslov, Anton; Liu, Andrea J.; Lubensky, Tom C.The square and kagome lattices with nearest-neighbor springs of spring constant k are isostatic with a number of zero-frequency modes that scale with the perimeter. We analytically study the approach to this isostatic limit as the spring constant k' for the next-nearest-neighbor bond vanishes. We identify a characteristic frequency ω* ~ √(k') and length ω* ~ √(k/k' ) for both lattices. The shear modules C44 = k' of the square lattice vanishes with k', but that for the kagome lattice does not.Publication Electrostatic Repulsion of Positively Charged Vesicles and Negatively Charged Objects(1999-03-01) Aranda-Espinoza, Helim; Chen, Yi; Lubesnky, T C; Dan, Nily; Nelson, Philip C; Ramos, Lauren; Weitz, D. 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-C Tilt Under Shear in Smectic-A Elastomers(2008-08-08) Stenull, Olaf; Lubensky, Thomas C.; Adams, J. M.; Warner, MarkStenull and Lubensky [Phys. Rev. E 76, 011706 (2007)] have argued that shear strain and tilt of the director relative to the layer normal are coupled in smectic elastomers and that the imposition of one necessarily leads to the development of the other. This means, in particular, that a smectic-A elastomer subjected to a simple shear will develop smectic-C-like tilt of the director. Recently, Kramer and Finkelmann [e-print arXiv:0708.2024; Phys. Rev. E 78, 021704 (2008)], performed shear experiments on smectic-A elastomers using two different shear geometries. One of the experiments, which implements simple shear, produces clear evidence for the development of smectic-C-like tilt. Here, we generalize a model for smectic elastomers introduced by Adams and Warner [Phys. Rev. E 71, 021708 (2005)] and use it to study the magnitude of SmC-like tilt under shear for the two geometries investigated by Kramer and Finkelmann. Using reasonable estimates of model parameters, we estimate the tilt angle for both geometries, and we compare our estimates to the experimental results. The other shear geometry is problematic since it introduces additional in-plane compressions in a sheetlike sample, thus inducing instabilities that we discuss.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 Effect of Randomness on Critical Behavior of Spin Models(1975) Lubensky, Thomas C.; Harris, A. BrooksRenormalization group methods are used to analyze the critical behavior of random Ising models. The Wilson‐Fischer ε‐expansion for the recursion relations for n‐component continuous spin models are developed for randomly inhomogeneous systems. In addition to the usual variables for a homogeneous system there appears a variable which in essence describes local fluctuations in T c . From the structure and stability of the fixed points we conclude that critical exponents are unaffected by randomness for n≳4 but are renormalized by randomness for 1Publication Rheological Microscopy: Local Mechanical Properties from Microrheology(2003-03-14) Chen, D. T.; Crocker, John C; Weeks, E. R.; Islam, M. F.; Verma, R.; Gruber, J.; Lubensky, Thomas C.; Levine, A. J.; Yodh, A. G.We demonstrate how tracer microrheology methods can be extended to study submicron scale variations in the viscoelastic response of soft materials; in particular, a semidilute solution of lambda-DNA. The polymer concentration is depleted near the surfaces of the tracer particles, within a distance comparable to the polymer correlation length. The rheology of this microscopic layer alters the tracers’ motion and can be precisely quantified using one- and two-point microrheology. Interestingly, we found this mechanically distinct layer to be twice as thick as the layer of depleted concentration, likely due to solvent drainage through the locally perturbed polymer structure.Publication Critical Properties of Spin-Glasses(1976-02-23) Harris, A. Brooks; Lubensky, Thomas C; Chen, Jing-HueiThe critical properties of the model of a spin-glass proposed by Edwards and Anderson are studied using the renormalization group. The critical exponents are calculated in 6−ε spatial dimensions. It is argued that a tricritical point can exist where the nonordering field is the skewness of the distribution of J.Publication Direct Determination of DNA Twist-Stretch Coupling(1996-11-01) Kamien, Randall; Lubensky, Tom; Nelson, Philip C; O'Hern, Corey S.The symmetries of the DNA double helix require a new term in its linear response to stress: the coupling between twist and stretch. Recent experiments with torsionally constrained single molecules give the first direct measurement of this important material parameter. We extract its value from a recent experiment of Strick et al. [Science 271 (1996) 1835] and find rough agreement with an independent experimental estimate recently given by Marko. We also present a very simple microscopic theory predicting a value comparable to the one observed.Publication Soft Elasticity in Biaxial Smectic and Smectic-C Elastomers(2006-11-26) Stenull, Olaf; Lubensky, Thomas CIdeal (monodomain) smectic-A elastomers cross-linked in the smectic-A phase are simply uniaxial rubbers, provided deformations are small. From these materials smectic-C elastomers are produced by a cooling through the smectic-A to smectic-C phase transition. At least in principle, biaxial smectic elastomers could also be produced via cooling from the smectic-A to a biaxial smectic phase. These phase transitions, respectively, from D∞h to C2h and from D∞h to D2h symmetry, spontaneously break the rotational symmetry in the smectic planes. We study the above transitions and the elasticity of the smectic-C and biaxial phases in three different but related models: Landau-like phenomenological models as functions of the Cauchy-Saint-Laurent strain tensor for both the biaxial and the smectic-C phases and a detailed model, including contributions from the elastic network, smectic layer compression, and smectic-C tilt for the smectic-C phase as a function of both strain and the c-director. We show that the emergent phases exhibit soft elasticity characterized by the vanishing of certain elastic moduli. We analyze in some detail the role of spontaneous symmetry breaking as the origin of soft elasticity and we discuss different manifestations of softness like the absence of restoring forces under certain shears and extensional strains.Publication Dynamics of Smectic Elastomers(2007-03-30) Stenull, Olaf; Lubensky, Tom CWe study the low-frequency, long-wavelength dynamics of liquid crystal elastomers, crosslinked in the smectic-A phase, in their smectic-A, biaxial smectic and smectic-C phases. Two different yet related formulations are employed. One formulation describes the pure hydrodynamics and does not explicitly involve the Frank director, which relaxes to its local equilibrium value in a nonhydrodynamic time. The other formulation explicitly treats the director and applies beyond the hydrodynamic limit. We compare the low-frequency, long-wavelength dynamics of smectic-A elastomers to that of nematics and show that the two are closely related. For the biaxial smectic and the smectic-C phases, we calculate sound velocities and the mode structure in certain symmetry directions. For the smectic-C elastomers, in addition, we discuss in some detail their possible behavior in rheology experiments.