Phases and transitions in phantom nematic elastomer membranes

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 71, Issue 1, 2005, Pages

  Xing, Xiangjun ^a   Radzihovsky, Leo ^b  

^a University of Illinois at Urbana Champaign   (United States)

^b UNIVERSITY OF COLORADO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

HARMONIC THERMAL FLUCTUATIONS; IN-PLANE SHEAR MODULII; PHANTOM NEMATIC ELASTOMER MEMBRANES; TUBULE-FLAT TRANSITIONS;

COMPUTER SIMULATION; CRYSTAL ORIENTATION; ELASTOMERS; MEMBRANES; MONTE CARLO METHODS; PHASE TRANSITIONS; POISSON RATIO; POLYMERIZATION; THERMODYNAMICS;

NEMATIC LIQUID CRYSTALS;

EID: 41349115004     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.71.011802     Document Type: Article

References (45)

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26. Similar phenomena take place in other "soft" anisotropic sys tems, such as smectic[25] and columnar liquid-crystal phases [25], vortex lattices in putative magnetic superconductor{26], and bulk nematic elastomers[16-18].
27. Stability of an isotropic-flat phase at finite temperature is ensured by a length-scale-dependent bending modulus that is infinitely enhanced by thermal fluctuations. Therefore this finding of a finite, length-scale-independent bending-rigidity modulus for flat nematic elastomer membranes suggests that this nematic-flat phase might indeed be unstable to thermal fluctuations. However, we have also shown that for D<3, new in-plane elastic nonlinearities, which are not included in our analysis near D=4, become qualitatively important and can very well lead to a sufficient enhancement of the bending rigidity sufficient to stabilize a nematic-flat phase of a two-dimensional membrane. At the moment, this question remains unresolved.
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30. As the word "phantom" suggests, we will completely ignore the effects of self-avoiding interactions. It should be made clear that the reason we ignore self-avoidance in this work is not its unimportance. On the contrary, past research experience in this field shows that except for the flat phase, the self-avoiding interaction is qualitatively important to the long-length-scale properties of polymerized membranes. The primary object of this paper is to study the global phase diagram of a liquid-crystalline tethered membrane. We believe that self-avoidance does not destroy, but rather modifies, various phases that we will identify in this paper. Therefore we will leave the technically involved study of self-avoiding interaction to a separate publication.
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39. L. S. Hirst and C. R. Safinya (unpublished).
40. Such an intrinsic nematic order parameterQ may, for example, characterize a spontaneous lipid tilt order or alignment of liquid-crystal polymers making up a nematic elastomer membrane. It should be intuitively clear that the component of such orientational order normal to the membrane should have no anisotropic effects on the elasticity of the tethered membrane. Consequently Q the nematic order parameter is a well-defined reference-space rank-2 tensor that can couple to membrane's metric tensor g. This contrasts qualitatively with distinct physical realization of, for example, a tethered membrane fluctuating inside a nematic liquid crystal. In this latter case the appropriate nematic order parameter is a tensor in the embedding space that can only couple to tangent vectors of a membrane.
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42. This crumpling transition is second order at a mean-field level and is supported by numerical simulation. Renormalization group analysis, however, shows that it may be discontinuous.
43. σ the charge.
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45. This is because in two dimensions the metric tensor g is a 2 × 2 matrix and has only two rotationally invariant independent degrees of freedom - i.e., two eigenvalues.