Nonlinear elasticity, fluctuations and heterogeneity of nematic elastomers

Annals of Physics

Volumn 323, Issue 1, 2008, Pages 105-203

  Xing, Xiangjun ^a   Radzihovsky, Leo ^b  

^a SYRACUSE UNIVERSITY   (United States)

^b UNIVERSITY OF COLORADO   (United States)

Author keywords

61.41.+e; 64.60.Ak; 64.60.Fr; Anomalous elasticity; Critical phase; Fluctuations; Goldstone modes; Liquid crystals; Micropolar elasticity; Nematic elastomer; Nonlinear elasticity; Poisson ratio; Quenched disorders; Renormalization group; Scaling; Symmetry breaking; Zero temperature fixed point

Indexed keywords

EID: 37349090460     PISSN: 00034916     EISSN: 1096035X     Source Type: Journal    
DOI: 10.1016/j.aop.2007.10.009     Document Type: Article

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80. We emphasize that nematic elastomers are amorphous solids with no microscopic lattice structure, or long-range translational order of any kind. This is an essential feature that distinguishes them (and other amorphous solids) from crystalline solids and liquid crystals with quenched structural disorder. In the latter systems, there is a natural periodic reference state with perfect long range translational order that is deformed by local heterogeneity and is a natural reference state about which to expand any other (including a true ground) state. By contrast, in amorphous solids like nematic elastomers, no such natural reference state exists other than the true ground state. Since our isotropic reference state is not the ground state, it is completely arbitrary, a conceptually convenient construction. Consequently, the "phonon field" over(u, →) defined relative to this fictitious reference state, has a priori no absolute meaning, i.e., is "fictitious". However, for a given realization of disorders, there is a well-defined relation between the physical phonon field δ over(r, →), defined relative to the true ground state, and the fictitious phonon field over(u, →), which is defined relative to the IRS. As we shall show later in this paper, the quenched correlation function of over(u, →) encodes information about the correlation of the nonaffine displacement field when the system is macroscopic strained.
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