Universität Stuttgart
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Item Open Access Metallic glasses and chiral nematic liquid crystals(1987) Trebin, Hans-Rainer; Longa, Lech; Salzgeber, BennoGeometrical frustration exists in both metallic glasses and chiral nematic liquid crystals. Applying results from the Landau-Ginzburg theory of liquid crystals and from polytope models for the amorphous state, a frustrated free-energy density for metallic glasses is derived. It is expressed in terms of an order parameter that characterizes the bond orientation of neighbouring atoms.Item Open Access Structure of the elastic free energy for chiral nematic liquid crystals(1989) Longa, Lech; Trebin, Hans-RainerIn Landau–de Gennes theory, the free energy f of liquid crystals is expanded into powers of a symmetric, traceless tensor order parameter Q αβ and its derivatives Q αβ,γ. The expansion is subject to the condition that f is a scalar, i.e., invariant under all rotations of the group SO(3). Using the method of integrity basis, we have established the most general SO(3)-invariant free-energy density up to all powers in Q αβ and up to second order in Q αβ,γ. It turns out that this free-energy density is composed of 39 invariants, which are multiplied by arbitrary polynomials in TrQ 2 and TrQ 3. On the other hand, these 39 invariants can be expressed as polynomials of 33 so-called irreducible invariants. Interestingly, among the irreducible invariants there are only three chiral terms (i.e., linear in Q αβ,γ). They locally give rise to three independent helix modes in chiral, biaxial liquid crystals. This conclusion generalizes results of Trebin [J. Phys. (Paris) 42, 1573 (1981)] and Govers and Vertogen [Phys. Rev. A 31, 1957 (1985); 34, 2520 (1986)] and contradicts a statement of Pleiner and Brand [Phys. Rev. A 24, 2777 (1981); 34, 2528 (1986)], according to which only one twist term is supposed to exist.Item Open Access Integrity basis approach to the elastic free energy functional of liquid crystals. 1, Classification of basic elastic modes(1989) Longa, Lech; Trebin, Hans-RainerUsing the method integrity basis, the most general SO(3)-invariant free energy density up to all powers in xβ and up to second order in Q xβ,y is established. The method provides all analytically independent elastic modes for nematics and cholesterics in the form of 33 so-called, irreducible invariants. Interestingly, among the irreducible invariants there are only three chiral terms (i.e. linear in Q δ,β,y ). They give rise locally to three independent helix modes in chiral, biaxial liquid crystals. This conclusion generalizes results of Trebin and Govers and Vertogen and contradicts a statement of Pleiner and Brandt, according to which only one twist term is supposed to exist. The most general free energy expansion can be written as sum of 39 additive invariants, which are multiplied by arbitrary polynomials in TrQ 2 and TrQ 3.Item Open Access Phase diagrams of cholesteric liquid crystals obtained with a generalized Landau-de Gennes theory(1989) Longa, Lech; Monselesan, Didier; Trebin, Hans-RainerPhase diagrams of chiral nematic liquid crystals are studied within the framework of a generalized Landau-Ginzburg-de Gennes theory. Using the parametrization of Grebel, Hornreich, and Shtrikman for the tensor order parameter Q, all relevant elastic terms are included for the helicoidal phase and the blue phases of chiral nematic liquid crystals up to fourth order in Q and its gradient ∂Q. The influence of the additional elastic terms on the phase diagrams of the chiral nematic phases is then investigated. The theory correctly describes the variation of the pitch with temperature and the induced biaxiality of the cholesteric phase. The results resolve the discrepancies encountered by Hornreich and Shtrikman in the comparison of experiment and theory. New features in the topology of the phase diagrams of blue phases, like re-entrant phase transitions, are predicted.