Phase transitions molecular approaches

It turns out that a third order process is possible which combines Vi and the k-f interaction characterized by (A,. T) = (1,1). Details can be found in Fulde (1975). The net result is that this time the quadrupole susceptibility diverges as TJ T - Tc) in molecular field approximation as the magnetic phase transition is approached from above. This would imply that an elastic constant becomes soft at a second order magnetic phase transition. In practice this requires the presence of the interaction (A, i ) = (1, 1) with reasonable strength. 

Phase transitions in two-dimensional layers often have very interesting and surprising features. The phase diagram of the multicomponent Widom-Rowhnson model with purely repulsive interactions contains a nontrivial phase where only one of the sublattices is preferentially occupied. Fluids and molecules adsorbed on substrate surfaces often have phase transitions at low temperatures where quantum effects have to be considered. Examples are molecular layers of H2, D2, N2 and CO molecules on graphite substrates. We review the path integral Monte Carlo (PIMC) approach to such phenomena, clarify certain experimentally observed anomalies in H2 and D2 layers, and give predictions for the order of the N2 herringbone transition. Dynamical quantum phenomena in fluids are analyzed via PIMC as well. Comparisons with the results of approximate analytical theories demonstrate the importance of the PIMC approach to phase transitions where quantum effects play a role. 

The layer spacing for smectic Ad and Cd phases significantly exceeds the molecular length (d/L = 1.35-1.65) and increases as the Ad<= Cd transition is approached from above. However, the temperature variations of the layer spacing in the Cd phase are very small in comparison to the classical smectic A-smectic C transition (Fig. 14). This unique behaviour results from the fact that both the tilt angles for different molecular moieties and the relative... 

The simulation of a first-order phase transition, especially one where the two phases have a significant difference in molecular area, can be difficult in the context of a molecular dynamics simulation some of the works already described are examples of this problem. In a molecular dynamics simulation it can be hard to see coexistence of phases, especially when the molecules are fairly complicated so that a relatively small system size is necessary. One approach to this problem, described by Siepmann et al. [369] to model the LE-G transition, is to perform Monte Carlo simulations in the Gibbs ensemble. In this approach, the two phases are simulated in two separate but coupled boxes. One of the possible MC moves is to move a molecule from one box to the other in this manner two coexisting phases may be simulated without an interface. Siepmann et al. used the chain and interface potentials described in the Karaborni et al. works [362-365] for a 15-carbon carboxylic acid (i.e. pen-tadecanoic acid) on water. They found reasonable coexistence conditions from their simulations, implying, among other things, the existence of a stable LE state in the Karaborni model, though the LE phase is substantially denser than that seen experimentally. The re-... 

From the previous demonstration of various phase transitions in small molecular systems, photochemical image recording on polymer films with amplification seems to be a promising approach to a new information storage material. While use of a polymer film will improve image stability when the polymer is kept below T , the restricted molecular motion in the solid polymer may reduce6the response time. 

An important step in developing the mean-field concept was done by Landau [8, 10]. Without discussing the relation between such fundamental quantities as disorder-order transitions and symmetry lowering, we just want to note here that his theory is based on thermodynamics and the derivation of the temperature dependence of the order parameter via the thermodynamic potential minimization (e.g., the free energy A(r),T)) which is a function of the order parameter. It is assumed that the function A(rj,T) is analytical in the parameter 77 and thus near the phase transition point could be expanded into the series in 77 usually it is a polynomial expansion with temperature-dependent coefficients. Despite the fact that such a thermodynamical approach differs from the original molecular field theory, they are quite similar conceptually. In particular, the r.h.s. of the equation of state for the pressure of gases or liquids and the external field in ferromagnetics, respectively, have the same polynomial form. 

To extract concrete predictions for experimental parameters from our calculations is a non-trivial task, because neither the energetic constant B nor the rotational viscosity yi are used for the hydrodynamic description of the smectic A phase (but play an important role in our model). Therefore, we rely here on measurements in the vicinity of the nematic-smectic A phase transition. Measurements on LMW liquid crystals made by Litster [33] in the vicinity of the nematic-smectic A transition indicate that B is approximately one order of magnitude less than Bo. As for j we could not find any measurements which would allow an estimate of its value in the smectic A phase. In the nematic phase y increases drastically towards the nematic-smectic A transition (see, e.g., [51]). Numerical simulations on a molecular scale are also a promising approach to determine these constants [52],... 

Our quantum chemical approach has been applied to explain the thermodynamics of the TKHS-like materials on the level of simple mean (molecular) field approximation [1,4] which, however, is not well adapted to provide for quantitative estimations of the critical temperature of phase transitions. To examine the... 

Micellar aggregates are considered in chapter 3 and a critical concentration is defined on the basis of a change in the shape of the size distribution of aggregates. This is followed by the examination, via a second order perturbation theory, of the phase behavior of a sterically stabilized non-aqueous colloidal dispersion containing free polymer molecules. This chapter is also concerned with the thermodynamic stability of microemulsions, which is treated via a new thermodynamic formalism. In addition, a molecular thermodynamics approach is suggested, which can predict the structural and compositional characteristics of microemulsions. Thermodynamic approaches similar to that used for microemulsions are applied to the phase transition in monolayers of insoluble surfactants and to lamellar liquid crystals. 

Theoretical approaches to total energy as a function of volume predict a phase transition to the rock salt structure under high pressure [11,12], The transition is calculated to occur at a pressure of about 245 GPa and an experimental value of 230 GPa [13] has been quoted [9], but other workers quote 10 -14 GPa [14]. The critical volume ratio [11] is V/V0 = 0.83, equivalent to a molecular volume reduction from 31 to 27 A3. 

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