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Polyethylene (PE) chains, with CH2 groups replaced by CBr2 at regular intervals ("precision PE"), have been observed to exhibit competing polymorphs driven by a preference for quantized fold lengths by Tasaki et al. Motivated by this recent discovery, the crystallisation behaviour of such precision PE chains, 400 carbons long with CBr2 groups placed regularly at every 21st carbon, is investigated using molecular dynamics simulations. The united-monomer model of PE is extended to include dibromo groups, with steric clashes at the bromines reflected in a triple-well bending potential, demonstrating its function as a preferred fold site. Different crystallisation protocols, continuous-cooling and self-seeding, reveal remarkably different crystals. Using self-seeding, the crystalline lamellar thickness increases monotonically with temperature, in quantized multiples of the distance between dibromo units. Polymer chains are observed to fold preferentially at the dibromo groups and such groups appear to be tolerated within the crystal lamellae. On quenching the bromos assemble to form registered layers, not unlike Smectic phases observed in liquid crystals, which confirms the experimental observation of competing Form I and Form I' polymorphs.

A novel model, devised to describe spontaneous chirality synchronization in complex liquids and liquid crystals, is proposed and studied. Segments of ribbon-like molecular columns with left- or right-handed 180degree twist lie on the bonds of a honeycomb lattice so that three ribbons meet in a vertex of the hexagonal honeycomb. The energy of each vertex is a minimum if the three ribbons have the same chirality, -E, and is +E otherwise, and the ground state is homochiral, i.e. all ribbons have the same hand. The energy levels for two vertices linked by a single ribbon are either -2E, 0 and +2 E in this vertex model. Monte Carlo simulations demonstrate that this model is identical to an Ising spin model on a Kagome lattice, for which the site energy structure is quite different. The equivalence of the ordering of the vertex and Ising spin models is also shown analytically. The energy difference between the disordered and ground states, 4J in the spin model, is related to the transition temperature for the Kagome lattice using the exact result, Tc=2.14J. The ordering energy difference for a single site is 50% higher for the vertex model. The thermodynamic energy for the vertex model is corrected by a factor of 1/3 due to double counting and this makes the specific heat of the vertex model also equal to that of the spin model as expected. Other similar models where there is an unusual relation between the site and thermodynamic energies are discussed briefly., Comment: 17 pages, 9 figures

We have performed Monte Carlo simulations to investigate the temperature dependence of the ordering of the side chains of the X-shape liquid crystal molecules which are arranged in a hexagonal array. Each hexagon contains six side chains, one from each side of the hexagon. Each liquid crystal molecule has two, dissimilar, side chains, one that contains silicon and one containing fluorine. Like chains attract each other more strongly than unlike chains and this drives an order-disorder transition. The system is frustrated because it is not possible to find a configuration in which all the hexagons are occupied by either all silicon or all fluorine chains. There are two phase transitions. If only pairwise interactions are included it is found that there is a novel fluctuating phase between the disordered phase and the fully ordered ground state. This did not agree with the experiments where an intermediate phase was seen that had long range order on one of the three sublattices. Agreement was found when the calculations were modified to include attractive three body interactions between the silicon chains., Comment: Accepted in Physical Review E 26 pages including 7 figures