arXiv subjects

T. C. Lubensky

Publications and source records attributed to T. C. Lubensky.

At least 55 records · Page 3Linked to original sources

arXiv2004

Commentary on "Mechanical properties of mono-domain side chain nematic elastomers" by P. Martinoty et al., Eur. Phys. J. E 14, 311 (2004)

We discuss the rheology experiments on nematic elastomers by Martinoty et al. in the light of theoretical models for the long-wavelength low-frequency dynamics of these materials. We review these theories and discuss how they can be modified to provide a phenomenological description of the non-hydrodynamic frequency regime probed in the experiments. Moreover, we review the concepts of soft and semi-soft elasticity and comment on their implications for the experiments.

cond-mat.soft↗

arXiv2004

Dynamics of nematic elastomers

We study the low-frequency, long-wavelength dynamics of soft and semi-soft nematic elastomers using two different but related dynamic theories. Our first formulation describes the pure hydrodynamic behavior of nematic elastomers in which the nematic director has relaxed to its equilibrium value in the presence of strain. We find that the sound-modes structure for soft elastomers is identical to that of columnar liquid crystals. Our second formulation generalizes the derivation of the equations of nematohydrodynamics by the Harvard group to nematic elastomers. It treats the director explicitly and describes slow modes beyond the hydrodynamic limit.

cond-mat.soft↗

arXiv2004

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 $μ$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.

cond-mat.soft↗

arXiv2003

Anomalous elasticity of nematic and critically soft elastomers

Uniaxial elastomers are characterized by five elastic constants. If their elastic modulus C_5 describing the energy of shear strains in planes containing the anisotropy axis vanishes, they are said to be soft. In spatial dimensions d less than or equal to 3, soft elastomers exhibit anomalous elasticity with certain length-scale dependent bending moduli that diverge and shear moduli that vanish at large length-scales. Using renormalized field theory at d = 3 and to first order in ε= 3 - d, we calculate critical exponents and other properties characterizing the anomalous elasticity of two soft systems: (i) nematic elastomers in which softness is a manifestation of a Goldstone mode induced by the spontaneous symmetry breaking associated with a transition from an isotropic state to a nematic state and (ii) a particular version of what we call a critically soft elastomer in which C_5 = 0 corresponds to a critical point terminating the stability regime of a uniaxial elastomer with C_5 > 0.

cond-mat.soft↗

arXiv2003

Microrheology, stress fluctuations and active behavior of living cells

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 non-thermal 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 $1/ω^2$ power spectrum, as expected for a continuum with a slowly evolving internal prestress.

cond-mat.soft↗

arXiv2003

The Structure of TGB$_C$ Phases

We study the transition from the cholesteric phase to two TGB$_C$ phases near the upper critical twist $k_{c2}$: the Renn-Lubensky TGB$_C$ phase, with layer normal rotating in a plane perpendicular to the pitch axis, and the Bordeaux TGB$_C$ phase, with the layer normal rotating on a cone parallel to the pitch axis. We calculate properties, including order-parameter profiles, of both phases.

cond-mat.soft↗

arXiv2003

Fluctuating Nematic Elastomer Membranes: a New Universality Class

We study the flat phase of nematic elastomer membranes with rotational symmetry spontaneously broken by in-plane nematic order. Such state is characterized by a vanishing elastic modulus for simple shear and soft transverse phonons. At harmonic level, in-plane orientational (nematic) order is stable to thermal fluctuations, that lead to short-range in-plane translational (phonon) correlations. To treat thermal fluctuations and relevant elastic nonlinearities, we introduce two generalizations of two-dimensional membranes in a three dimensional space to arbitrary D-dimensional membranes embedded in a d-dimensional space, and analyze their anomalous elasticities in an expansion about D=4. We find a new stable fixed point, that controls long-scale properties of nematic elastomer membranes. It is characterized by singular in-plane elastic moduli that vanish as a power-law eta_lambda=4-D of a relevant inverse length scale (e.g., wavevector) and a finite bending rigidity. Our predictions are asymptotically exact near 4 dimensions.

cond-mat.soft↗

arXiv2002

Anomalous elasticity of nematic elastomers

We study the anomalous elasticity of nematic elastomers by employing the powers of renormalized field theory. Using general arguments of symmetry and relevance, we introduce a minimal Landau-Ginzburg-Wilson elastic energy for nematic elastomers. Performing a diagrammatic low temperature expansion, we analyze the fluctuations of the displacement fields at and below the upper critical dimension 3. Our analysis reveals an anomaly of certain elastic moduli in the sense that they depend on the length scale. In $d = 3$ this dependence is logarithmic and below $d=3$ it is of power law type with anomalous scaling exponents. One of the 4 relevant shear moduli vanishes at long length scales whereas the only relevant bending modulus diverges.

cond-mat.soft↗

arXiv2002

Phase Transitions in Lyotropic Nematic Gels

In this paper, we discuss the equilibrium phases and collapse transitions of a lyotropic nematic gel immersed in an isotropic solvent. A nematic gel consists of a cross-linked polymer network with rod-like molecules embedded in it. Upon decreasing the quality of the solvent, we find that a lyotropic nematic gel undergoes a discontinuous volume change accompanied by an isotropic-nematic transition. We also present phase diagrams that these systems may exhibit. In particular, we show that coexistence of two isotropic phases, of two nematic phases, or of an isotropic and a nematic phase can occur.

cond-mat.soft↗

arXiv2001

Symmetries and Elasticity of Nematic Gels

A nematic liquid-crystal gel is a macroscopically homogeneous elastic medium with the rotational symmetry of a nematic liquid crystal. In this paper, we develop a general approach to the study of these gels that incorporates all underlying symmetries. After reviewing traditional elasticity and clarifying the role of broken rotational symmetries in both the reference space of points in the undistorted medium and the target space into which these points are mapped, we explore the unusual properties of nematic gels from a number of perspectives. We show how symmetries of nematic gels formed via spontaneous symmetry breaking from an isotropic gel enforce soft elastic response characterized by the vanishing of a shear modulus and the vanishing of stress up to a critical value of strain along certain directions. We also study the phase transition from isotropic to nematic gels. In addition to being fully consistent with approaches to nematic gels based on rubber elasticity, our description has the important advantages of being independent of a microscopic model, of emphasizing and clarifying the role of broken symmetries in determining elastic response, and of permitting easy incorporation of spatial variations, thermal fluctuations, and gel heterogeneity, thereby allowing a full statistical-mechanical treatment of these novel materials.

cond-mat.soft↗

arXiv2001

Effective index of refraction, optical rotation, and circular dichroism in isotropic chiral liquid crystals

This paper concerns optical properties of the isotropic phase above the isotropic-cholesteric transition and of the blue phase BP III. We introduce an effective index, which describes spatial dispersion effects such as optical rotation, circular dichroism, and the modification of the average index due to the fluctuations. We derive the wavelength dependance of these spatial dispersion effects quite generally without relying on an expansion in powers of the chirality and without assuming that the pitch of the cholesteric $P$ is much shorter than the wavelength of the light $λ$, an approximation which has been made in previous studies of this problem. The theoretical predictions are supported by comparing them with experimental spectra of the optical activity in the BP III phase.

cond-mat.soft↗

arXiv2001

The Fractional Quantum Hall effect in an array of quantum wires

We demonstrate the emergence of the quantum Hall (QH) hierarchy in a 2D model of coupled quantum wires in a perpendicular magnetic field. At commensurate values of the magnetic field, the system can develop instabilities to appropriate inter-wire electron hopping processes that drive the system into a variety of QH states. Some of the QH states are not included in the Haldane-Halperin hierarchy. In addition, we find operators allowed at any field that lead to novel crystals of Laughlin quasiparticles. We demonstrate that any QH state is the groundstate of a Hamiltonian that we explicitly construct.

cond-mat.mes-hall↗

arXiv2001

Sliding Luttinger liquid phases

We study systems of coupled spin-gapped and gapless Luttinger liquids. First, we establish the existence of a sliding Luttinger liquid phase for a system of weakly coupled parallel quantum wires, with and without disorder. It is shown that the coupling can {\it stabilize} a Luttinger liquid phase in the presence of disorder. We then extend our analysis to a system of crossed Luttinger liquids and establish the stability of a non-Fermi liquid state: the crossed sliding Luttinger liquid phase (CSLL). In this phase the system exhibits a finite-temperature, long-wavelength, isotropic electric conductivity that diverges as a power law in temperature $T$ as $T \to 0$. This two-dimensional system has many properties of a true isotropic Luttinger liquid, though at zero temperature it becomes anisotropic. An extension of this model to a three-dimensional stack exhibits a much higher in-plane conductivity than the conductivity in a perpendicular direction.

cond-mat.str-el↗

arXiv2001

Two-point microrheology and the electrostatic analogy

The recent experiments of Crocker et al. suggest that microrheological measurements obtained from the correlated fluctuations of widely-separatedprobe particles determine the rheological properties of soft, complex materials more accurately than do the more traditional particle autocorrelations. This presents an interesting problem in viscoelastic dynamics. We develop an important, simplifing analogy between the present viscoelastic problem and classical electrostatics. Using this analogy and direct calculation we analyze both the one and two particle correlations in a viscoelastic medium in order to explain this observation.

cond-mat.soft↗

arXiv2001

Phase transitions in a ferrofluid at magnetic field induced microphase separation

In the presence of a magnetic field applied perpendicular to a thin sample layer, a suspension of magnetic colloidal particles (ferrofluid) can form spatially modulated phases with a characteristic length determined by the competition between dipolar forces and short-range forces opposing density variations. We introduce models for thin-film ferrofluids in which magnetization and particle density are viewed as independent variables and in which the non-magnetic properties of the colloidal particles are described either by a lattice-gas entropy or by the Carnahan-Starling free energy. Our description is particularly well suited to the low-particle density regions studied in many experiments. Within mean-field theory, we find isotropic, hexagonal and stripe phases, separated in general by first-order phase boundaries.

cond-mat.soft↗

arXiv2001

Dislocation Geometry in the TGB-A Phase: Linear Theory

We demonstrate that an arbitrary system of screw dislocations in a smectic-A liquid crystal may be consistently treated within harmonic elasticity theory, provided that the angles between dislocations are sufficiently small. Using this theory, we calculate the ground state configuration of the TGB-A phase. We obtain an estimate of the twist-grain-boundary spacing and screw dislocation spacing in a boundary in terms of the macroscopic parameters, in reasonable agreement with experimental results.

cond-mat.soft↗

arXiv2000

Granular Shear Flow Dynamics and Forces : Experiment and Continuum Theory

We analyze the main features of granular shear flow through experimental measurements in a Couette geometry and a comparison to a locally Newtonian, continuum model of granular flow. The model is based on earlier hydrodynamic models, adjusted to take into account the experimentally observed coupling between fluctuations in particle motion and mean-flow properties. Experimentally, the local velocity fluctuations are found to vary as a power of the local velocity gradient. This can be explained by an effective viscosity that diverges more rapidly as the random-close-packing density is approached than is predicted by Enskog theory for dense hard sphere systems. Experiment and theory are in good agreement, especially for the following key features of granular flow: The flow is confined to a small shear band, fluctuations decay approximately exponentially away from the sheared wall, and the shear stress is approximately independent of shear rate. The functional forms of the velocity and fluctuation profiles predicted by the model agree with the experimental results.

cond-mat.stat-mech↗

arXiv2000

A Crossed Sliding Luttinger Liquid Phase

We study a system of crossed spin-gapped and gapless Luttinger liquids. We establish the existence of a stable non-Fermi liquid state with a finite-temperature,long-wavelength, isotropic electric conductivity that diverges as a power law in temperature $T$ as $T\to 0$. This two-dimensional system has many properties characteristic of a true isotropic Luttinger liquid, though at zero temperature it becomes anisotropic. This model can easily be extended to three dimensions.

cond-mat.str-el↗