Crystal frustration

Keywords Smectic liquid crystals, Molecular conformations, polar and steric frustrations, Polyphilic and perfluorinated mesogens. X-ray diffraction... 

The frustration effects are implicit in many physical systems, as different as spin glass magnets, adsorbed monomolecular films and liquid crystals [32, 54, 55], In the case of polar mesogens the dipolar frustrations may be modelled by a spin system on a triangular lattice (Fig, 5), The corresponding Hamiltonian consists of a two particle dipolar potential that has competing parallel dipole and antiparallel dipole interactions [321, The system is analyzed in terms of dimers and trimers of dipoles. When the dipolar forces between two of them cancel, the third dipole experiences no overall interaction. It is free to permeate out of the layer, thus frustrating smectic order. 

Similar frustration has been evidenced for the crystal structure of isotactic poly(2-vinylpyridine)150 161 (Figure 2.28). Also in this case three independent threefold helices are included in the trigonal unit cell and the frustration is related to a different azimuthal orientation of the chains due to the different interactions between the chains.160 Two chains (chains A in Figure 2.28) maximize their interactions at the expense of the third one (chain B). 

The examples of polymer crystal structures shown in the previous sections are ideal structures, which can be described with the traditional concepts of the principles of equivalence and close packing or the new concepts of symmetry breaking146 and frustration.154 The models of perfect crystals are characterized by a long-range positional order for all the atoms (disregarding thermal motion). The X-ray diffraction patterns of such crystals, oriented with the chain axes along one direction (as in oriented fibers), present sharp reflections organized in layer lines. 

Thermotropic liquid crystals, 15 86-98 bent-core, 15 98 discotic phases of, 15 96 frustrated phases of, 15 94-96 metallomesogens, 15 97 nematic liquid crystals, 15 86-92 smectic liquid crystals, 15 92-94 Thermotropic mesophases, 20 79 Thermotropic polycarbonates, 19 804 Thermotropic polyesters, liquid-crystalline, 20 34... 

Figure 7 shows a plot of x as a function of cp. A rough correlation can be seen if cp is positive then x is positive and if cp is negative then x is negative. The crystal structure of XAGWUX contains two independent molecules with opposite conformations. One of the molecules is syn-syn the other is anti-anti. This occurrence frustrates any attempts to correlate the conformation of the cation with the acidic strength of the anion or other counter ion effects. 

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