Effect of Frustration in Liquid Crystals and Polymers

Abstract

We assign the term of frustration to the general case in which the interactions which compete on short distances in the stability of some material lead to local configurations of molecules which are incompatible on large scales. The standard example in liquid crystals are the blue phases, whose ground state is an assembly of frustrated domains with specific double twist order and characteristic size, separated by defect lines (disclinations). Blue phases are modifications of cholesteric phases with small molecules; the same considerations extend to cholesteric liquid crystal polymers where frustration is also documented. In particular, we discuss observations made in solutions of biological liquid crystal polymers, and in biological objects, like some proteins and the chromosome of dinoflagellate; this last example provides a geometry of double twist different to that one theorized in blue phases. In this model, the finite size of the chromosome is directly related to the characteristic size of the unfrustrated domain of double twist. Finally, we extend the consideration of a space of constant positive curvature already used for blue phases to the case of crystalline arrangements of chiral molecules. The frustration is entirely relieved in such a space. We argue that the same model of curved space could describe short range correlations in chiral or non-chiral amorphous polymers.