Layer frustration

Rod-Like Liquid Crystals with Two Fluorinated Chains at Opposite Ends Layer Frustration... 

Sliding between concentric multiwalled carbon nanotubes presents a simple geometry, which restricts interlayer motion to a single (axial) direction with a fixed interlayer orientation of stiff, smooth layers. Each layer in a concentric multiwalled carbon nanotube is indexed by two integers (n, m) that give the circumference in graphitic lattice coordinates. The difference in radii between successive layers frustrates the circumferential interlayer registry. The axial... 

Keith, C. Reddy, R. A. Prehm, M. Baumeister, U. Kresse, C. H. Chao, J.L. Hahn, H. Lang, H. Tschierske, C. Layer frustration, polar order and chirality in liquid crystalline phases of silyl-terminated achiral bent-core molecules. Chem. Eur. J. 2007, 13, 2556-2577. 

More than with continuous improvement in the preparation of clean surfaces in electrochemistry, the measurement of 0 is rather casual in surface science at present. In particular, work functions are mostly measured for d-metals rather than for sp-metals, which are more common in electrochemical double-layer studies. As a consequence, compilations of work function values report data for sp-metals that are 20 to 30 years old.63,856,857 This does not imply that the data are unreliable, but imparts to the situation a sense of frustration related to the immobility in one of the variables. 

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. 

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. 

Unlike the bulk morphology, block copolymer thin films are often characterized by thickness-dependent highly oriented domains, as a result of surface and interfacial energy minimization [115,116]. For example, in the simplest composition-symmetric (ID lamellae) coil-coil thin films, the overall trend when t>Lo is for the lamellae to be oriented parallel to the plane of the film [115]. Under symmetric boundary conditions, frustration cannot be avoided if t is not commensurate with L0 in a confined film and the lamellar period deviates from the bulk value by compressing the chain conformation [117]. Under asymmetric boundary conditions, an incomplete top layer composed of islands and holes of height Lo forms as in the incommensurate case [118]. However, it has also been observed that microdomains can reorient such that they are perpendicular to the surface [ 119], or they can take mixed orientations to relieve the constraint [66]. 

For polycatenar hydrogen bonded complexes with fluorinated chains at both ends (e.g., 138,139, see Fig. 36) formation of columnar phases was observed [246]. However, compound 137, having a branched Rp-chain at one end and three RH-chains at the other has a sequence of three distinct phases in the unusual sequence Cub-Col-SmA-Iso. For the SmA phase of compound 137 a structure with intercalated aromatic cores and RF-chains and separated layers of the hydrocarbon chains was proposed. At lower temperature, when incompatibility rises and the aromatics and Rp-chains disintegrate, all three components form their own layers. However, this produces interface curvature and a columnar phase with square lattice is formed. On further cooling a transition to a cubic phase with Im3m lattice takes place which is most likely of the bicontinuous type [262]. This leads to the unusual phase sequence Cubv-Col-SmA where the positions of the Cubv and Col phases are exchanged with respect to the usually observed phase sequences. The Col-Cub transition at lower temperature could be the result of the decreased conformational disorder of the terminal chains which reduces the steric frustration and hence reduces the interface curvature. 

In this work, we have focused on strong surface preference with only mutual transition between the symmetrical and asymmetrical layer-type structures. SSL theory and MC simulation are further applied to investigate the self-assembled morphology of diblock copolymers confined in the nanopore. MC simulation shows that the Niayer of the concentric cylinder barrel changes with respect to the extent of frustration between the exterior radius Rex and the bulk lamellar period L0. Simultaneously, the predictions of SSL theory also show that both... 

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