arXiv subjects

T. C. Lubensky

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

83 records · Page 5Linked to original sources

arXiv1996

Soft Condensed Matter Physics

Soft condensed matter physics is the study of materials, such as fluids, liquid crystals, polymers, colloids, and emulsions, that are ``soft" to the touch. This article will review some properties, such as the dominance of entropy, that are unique to soft materials and some properties such as the interplay between broken-symmetry, dynamic mode structure, and topological defects that are common to all condensed matter systems but which are most easily studied in soft systems.

cond-mat↗

arXiv1996

n-atic Order and Continuous Shape Changes of Deformable Surfaces of Genus Zero

We consider in mean-field theory the continuous development below a second-order phase transition of $n$-atic tangent plane order on a deformable surface of genus zero with order parameter $ψ= \langle e^{i n θ} \rangle$. Tangent plane order expels Gaussian curvature. In addition, the total vorticity of orientational order on a surface of genus zero is two. Thus, the ordered phase of an $n$-atic on such a surface will have $2n$ vortices of strength $1/n$, $2n$ zeros in its order parameter, and a nonspherical equilibrium shape. Our calculations are based on a phenomenological model with a gauge-like coupling between $ψ$ and curvature, and our analysis follows closely the Abrikosov treatment of a type II superconductor just below $H_{c2}$.

cond-mat↗

arXiv1996

Interactions between Membrane Inclusions on Fluctuating Membranes

We model membrane proteins as anisotropic objects characterized by symmetric-traceless tensors and determine the coupling between these order-parameters and membrane curvature. We consider the interactions between transmembrane proteins that respect up-down (reflection) symmetry of bilayer membranes and that have circular or non-circular cross-sectional areas in the tangent-plane of membranes. Using a field theoretic approach, we find non-entropic $1/R^{4}$ interactions between reflection-symmetry-breaking transmembrane proteins with circular cross-sectional area and entropic $1/R^{4}$ interactions between transmembrane proteins with circular cross-section that do not break up-down symmetry in agreement with previous calculations. We also find anisotropic $1/R^{4}$ interactions between reflection-symmetry-conserving transmembrane proteins with non-circular cross-section, anisotropic $1/R^{2}$ interactions between reflection-symmetry-breaking transmembrane proteins with non-circular cross-section, and non-entropic $1/R^{4}$ many-particle interactions among non-transmembrane proteins. For large $R$, these interactions might provide the dominant force inducing aggregation of the membrane proteins.

cond-mat↗

arXiv1996

Chiral Lyotropic Liquid Crystals: TGB Phases and Helicoidal Structures

The molecules in lyotropic membranes are typically aligned with the surface normal. When these molecules are chiral, there is a tendency for the molecular direction to twist. These competing effects can reach a compromise by producing helicoidal defects in the membranes. Unlike thermotropic smectics, the centers of these defects are hollow and thus their energy cost comes from the line energy of an exposed lamellar surface. We describe both the twist-grain-boundary phase of chiral lamellar phases as well as the isolated helicoidal defects.

cond-mat↗

arXiv1996

Chiral Fluctuations and Structures

Chiral molecules form a number of non-chiral structures, the simplest being an isotropic fluid phase. In a mesophase of achiral molecules the fluctuations will on average be achiral as well: left-handed twists and right-handed twists will occur with the same probability. In a system composed of chiral molecules, however, the fluctuations will be biased in one direction or the other, and there will be optical effects such as a non-zero fluctuation induced rotary power {\sl in addition} to the molecular rotary power of the individual molecules. We discuss this effect in a number of contexts, including lyotropic lamellar phases. When the tendency to twist is strong enough or the line energy of having an exposed edge is small enough, a new, defect riddled ground state of a lyotropic lamella, akin to the Renn-Lubensky twist-grain-boundary phase of thermotropic smectics, can occur.

cond-mat↗

arXiv1995

Disclination Asymmetry in Deformable Hexatic Membranes and the Kosterlitz-Thouless Transitions

A disclination in a hexatic membrane favors the development of Gaussian curvature localized near its core. The resulting global structure of the membrane has mean curvature, which is disfavored by curvature energy. Thus a membrane with an isolated disclination undergoes a buckling transition from a flat to a buckled state as the ratio $κ/K_{A}$ of the bending rigidity $κ$ to the hexatic rigidity $K_{A}$ is decreased. In this paper we calculate the buckling transition and the energy of both a positive and a negative disclination. A negative disclination has a larger energy and a smaller critical value of $κ/K_{A}$ at buckling than does a positive disclination. We use our results to obtain a crude estimate of the Kosterlitz-Thouless transition temperature in a membrane. This estimate is higher than the transition temperature recently obtained by the authors in a renormalization calculation.

cond-mat↗

arXiv1995

Kosterlitz-Thouless Transitions on Fluctuating Surfaces

We investigate the Kosterlitz-Thouless transition for hexatic order on a free fluctuating membrane and derive both a Coulomb gas and a sine-Gordon Hamiltonian to describe it. In the former, both disclinations and Gaussian curvature contribute to the charge density. In the latter, there is a linear coupling between a scalar field and the Gaussian curvature. We derive renormalization group recursion relations that predict a transition with decreasing bending rigidity $κ$. Using the sine-Gordon model, we show that there is no KT transition on a deformable sphere.

cond-mat↗

arXiv1995

Topological Defects on Fluctuating Surfaces: General Properties and the Kosterlitz-Thouless Transition

We investigate the Kosterlitz-Thouless transition for hexatic order on a free fluctuating membrane and derive both a Coulomb gas and a sine-Gordon Hamiltonian to describe it. The Coulomb-gas Hamiltonian includes charge densities arising from disclinations and from Gaussian curvature. There is an interaction coupling the difference between these two densities, whose strength is determined by the hexatic rigidity, and an interaction coupling Gaussian curvature densities arising from the Liouville Hamiltonian resulting from the imposition of a covariant cutoff. In the sine-Gordon Hamiltonian, there is a linear coupling between a scalar field and the Gaussian curvature. We discuss gauge-invariant correlation function for hexatic order and the dielectric constant of the Coulomb gas. We also derive renormalization group recursion relations that predict a transition with decreasing bending rigidity $κ$.

cond-mat↗

arXiv1995

Sine-Gordon Field Theory for the Kosterlitz-Thouless Transitions on Fluctuating Membranes

In the preceding paper, we derived Coulomb-gas and sine-Gordon Hamiltonians to describe the Kosterlitz-Thouless transition on a fluctuating surface. These Hamiltonians contain couplings to Gaussian curvature not found in a rigid flat surface. In this paper, we derive renormalization-group recursion relations for the sine-Gordon model using field-theoretic techniques developed to study flat space problems.

cond-mat↗

arXiv1994

Measure Factors, Tension, and Correlations of Fluid Membranes

We study two geometrical factors needed for the correct construction of statistical ensembles of surfaces. Such ensembles appear in the study of fluid bilayer membranes, though our results are more generally applicable. The naive functional measure over height fluctuations must be corrected by these factors in order to give correct, self-consistent formulas for the free energy and correlation functions of the height. While one of these corrections -- the Faddeev-Popov determinant -- has been studied extensively, our derivation proceeds from very simple geometrical ideas, which we hope removes some of its mystery. The other factor is similar to the Liouville correction in string theory. Since our formulas differ from those of previous authors, we include some explicit calculations of the effective frame tension and two-point function to show that our version indeed secures coordinate-invariance and consistency to lowest nontrivial order in a temperature expansion.

cond-mat↗

arXiv1993

Twisted Line Liquids

We propose a model of directed lines where the average direction has the nature of a cholesteric liquid crystal. This model, for instance, would describe the liquid of screw dislocations in the twist-grain-boundary (TGB) phase of liquid crystals. We show that the presence of lines does not alter the long wavelength elasticity of a cholesteric and, therefore, does not stabilize Landau-Peierls instability of the cholesteric phase. We discuss other possible mechanisms for stabilizing the twist-grain-boundary phase.

cond-mat↗