Physics – Condensed Matter – Soft Condensed Matter
Scientific paper
2003-02-01
Phys. Rev. E 68, 021108 (2003)
Physics
Condensed Matter
Soft Condensed Matter
18 pages, 4 eps figures. submitted to PRE
Scientific paper
10.1103/PhysRevE.68.021108
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.
Lubensky Tom. C.
Mukhopadhyay Ranjan
Radzihovsky Leo
Xing Xiangjun
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