Phase transition density-functional theories

Key words Entropic phase transition - Density functional theory - Nematic liquid crystal - Freezing... 

S. Chains in the S phase are also oriented normal to the surface, yet the unit cell is rectangular possibly because of restricted rotation. This structure is characterized as the smectic E or herringbone phase. Schofield and Rice [204] applied a lattice density functional theory to describe the second-order rotator (LS)-heiTingbone (S) phase transition. 

J.W.D. Coimolly and A.R. W hiams, Density-functional theory applied to phase transformations in transition metals, Phys. Rev. B 27 5169 (1983). 

Ab initio calculations and density functional theory studies of the gas-phase addition of HF to CH2=CH2 have revealed the possibility of forming trimolecular (two HF and one ethylene) and dimolecular (one FIF and one ethylene) complexes and transition-state structures and of the catalytic effect of the second molecule of the reagent. An energetically favourable pathway was selected on the basis of the computed potential-energy surface for these two reactions. ... 

A systematic study to identify solid oxide catalysts for the oxidation of methane to methanol resulted in the development of a Ga203—M0O3 mixed metal oxide catalyst showing an increased methanol yield compared with the homogeneous gas-phase reaction.1080,1081 Fe-ZSM-5 after proper activation (pretreatment under vacuum at 800-900°C and activation with N20 at 250°C) shows high activity in the formation of methanol at 20°C.1082 Density functional theory studies were conducted for the reaction pathway of the methane to methanol conversion by first-row transition-metal monoxide cations (MO+).1083 These are key to the mechanistic aspects in methane hydroxylation, and CuO+ was found to be a likely excellent mediator for the reaction. A mixture of vanadate ions and pyrazine-2-carboxylic acid efficiently catalyzes the oxidation of methane with 02 and H202 to give methyl hydroperoxide and, as consecutive products, methanol and formaldehyde.1084 1085... 

Another approach to liquid glass transition is the self-consistent phonon theory or density functional theory applied to aperiodic structures [112-114]. These theories predict the Lindemann stability criterion for the emergence of a density wave of a given symmetry. Although the finite Lindemann ratio implies a first-order phase transition, the absence of latent heat in glassy systems suggests the presence of an exponentially large number of aperiodic structures that are frozen in at Tg [94,95,110,111],... 

Density functional theory is used for band structure calculations of hydrogen storage materials. This method has been applied to a variety of hydrides such as ABs [77-79], AB [77], transition metals [53, 80], Laves phases [81], and complex hydrides [82[. Theoretical investigation is not only useful for the prediction of the heat of formation but it could also assess the elastic and mechanical properties of these materials, properties which are usually difficult to measure in the case of hydrides [78[. 

Over the years, vapour adsorption and condensation in porous materials continue to attract a great deal of attention because of (i) the fundamental physics of low-dimension systems due to confinement and (ii) the practical applications in the field of porous solids characterisation. Particularly, the specific surface area, as in the well-known BET model [I], is obtained from an adsorbed amount of fluid that is assumed to cover uniformly the pore wall of the porous material. From a more fundamental viewpoint, the interest in studying the thickness of the adsorbed film as a function of the pressure (i.e. t = f (P/Po) the so-called t-plot) is linked to the effort in describing the capillary condensation phenomenon i.e. the gas-Fadsorbed film to liquid transition of the confined fluid. Indeed, microscopic and mesoscopic approaches underline the importance of the stability of such a film on the thermodynamical equilibrium of the confined fluid [2-3], In simple pore geometry (slit or cylinder), numerous simulation works and theoretical studies (mainly Density Functional Theory) have shown that the (equilibrium) pressure for the gas/liquid phase transition in pores greater than 8 nm is correctly predicted by the Kelvin equation provided the pore radius Ro is replaced by the core radius of the gas phase i.e. (Ro -1) [4]. Thirty year ago, Saam and Cole [5] proposed that the capillary condensation transition is driven by the instability of the adsorbed film at the surface of an infinite... 

This equation states that the change in the free energy of the critical germ with the chemical potential per molecule of species / in the original phase (i.e., the mother liquor) equals the negative of the excess number An of molecules of type i in the nucleus over that present in the same volume of original space. The nucleation theorem is independent of the model and of the transition it holds true for classical nucleation theory, density functional theory, or cluster kinetic analysis and for gas-to-liquid or liquid-to-solid conversions. 

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