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# Isotropic-cholesteric transition of a weakly chiral elastomer cylinder.

Department of Physics, Syracuse University, Syracuse, New York 13244, USA.
Physical Review E (Impact Factor: 2.31). 09/2008; 78(2 Pt 1):021709. DOI:10.1103/PhysRevE.78.021709
Source: PubMed

ABSTRACT When a chiral isotropic elastomer is brought to the low-temperature cholesteric phase, the nematic degree of freedom tends to order and form a helix. Due to the nematoelastic coupling, this also leads to elastic deformation of the polymer network that is locally coaxial with the nematic order. However, the helical structure of nematic order is incompatible with the energetically preferred elastic deformation. The system is therefore frustrated and appropriate compromise has to be achieved between the nematic ordering and the elastic deformation. For a strongly chiral elastomer whose pitch is much smaller than the system size, this problem has been studied by Pelcovits and Meyer, as well as by Warner. In this work, we study the isotropic-cholesteric transition in the weak-chirality limit, where the pitch is comparable to or much larger than system size. We compare two possible solutions: a helical state as well as a double-twist state. We find that the double-twist state very efficiently minimizes both the elastic free energy and the chiral nematic free energy. On the other hand, the pitch of the helical state is strongly affected by the nematoelastic coupling. As a result, this state is not efficient in minimizing the chiral nematic free energy.

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##### Article: Isotropic-cholesteric transition in liquid-crystalline gels.
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ABSTRACT: In a nematic gel, the appearance of nematic order is accompanied by a spontaneous elongation of the gel parallel to the nematic director. If such a gel is made chiral, it has a tendency to form a cholesteric helical texture, in which local elongation of the gel parallel to the nematic director is suppressed due to the requirement of elastic compatibility. We show that a conical helix in which the director makes an oblique angle with respect to the helix axis serves as an energy minimizing compromise between the competing tendencies for elongation and twisting. We find the dependence of the helical cone angle and pitch on the strength of the chirality, and determine the change in sample shape at the isotropic to cholesteric phase transition.
Physical Review E 10/2002; 66(3 Pt 1):031706. · 2.31 Impact Factor
• ##### Article: Isotropic-to-cholesteric transition in liquid crystal elastomers.
[hide abstract]
ABSTRACT: A liquid crystal elastomer tries to spontaneously elongate on entering the locally nematic phase, but may have to twist to reduce its Frank elastic energy. The extremes are a conventional, transverse cholesteric structure (where it reduces its Frank energy), and a uniformly aligned state (where it can maximally spontaneously extend and reduce its elastic energy). Between these it can adopt a conical state where there is also bend but equally a partial satisfaction of the elastic requirements. A line of first-order transitions between conical and transverse states ends and becomes a line of second-order transitions, depending on chain anisotropy, the ratio of the Frank bend and twist constants, and on the elastic modulus reduced by the bend energy. Continuous and discontinuous variation of cone angles, and spontaneous elongations and shears are given, as are analytic forms for the singular variation of director as cones are lost to the transverse state. The variation of the multicritical point with the ratio of Frank constants is also given.
Physical Review E 02/2003; 67(1 Pt 1):011701. · 2.31 Impact Factor
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##### Book: The Physics of Liquid Crystals
01/1993; Oxford University Press. · 6.76 Impact Factor