High-temperature flat phase

Recently there has been considerable interest in the phase transition of polymerized (tethered) membranes with attractive interactions [1-4]. In a pioneer work [1], Abraham and Nelson found by molecular dynamics simulations that the introduction of attractive interactions between monomers leads to a collapsed membrane with fractal dimension 3 at a sufficiently low temperature. Subsequently, Abraham and Kardar [2] showed that for open membranes with attractive interactions, as the temperature decreases, there exists a well-defined sequence of folding transitions and then the membrane ends up in the collapsed phase. They also presented a Landau theory of the transition. Grest and Petsche [4] extensively carried out molecular dynamics simulations of closed membranes. They considered flexible membranes the nodes of the membrane are connected by a linear chain of n monomers. For short monomer chains, n = 4, there occurs a first-order transition from the high-temperature flat phase to... 

The phase transition consists of a cooperative mechanism with charge-ordering, anion order-disorder, Peierls-like lattice distortion, which induces a doubled lattice periodicity giving rise to 2 p nesting, and molecular deformation (Fig. 11c). The high temperature metallic phase is composed of flat EDO molecules with +0.5 charge, while the low temperature insulating phase is composed of both flat monocations... 

For molecular crystals in which the molecules are nearly spherical there will frequently be a high-temperature crystal phase of which the site symmetry is higher than the molecular symmetry. These crystals are referred to as plastic crystals and they have unusual properties such as very high temperatures of melting and low anisotropic properties similar to those of liquids. The theory of lattice vibrations of orientationally disordered solids has been addressed, and the results indicate that such disorder should lead to a broadening of the vibrational bands and that all modes may be active in both the infrared and Raman spectra. Spectra of this type are referred to as density-of-states spectra, since the bands correspond to the flat points in the dispersion curve. 

For a real fluid at sufficiently high temperatures the slope [0 /0(l/p)]y is positive for all values of p, in accordance with Eq. (29). At lower temperatures, there can be one or more regions in which [dpld llp)]j, = 0. These flat portions of the curve in the ip,p ) phase diagram possess mathematical singularities at both ends as a consequence of the limiting process V,N -> oo with p,T constant under which we are studying the fluid. The flat portion corresponds to a two-phase coexistence region. 

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