The lattice model thus provides the capability to obtain good, quantitative fits to experimental VLE data for binary mixtures of molecules below their critical point. Its value lies in the fact that it performs equally well regardless of the size difference between the component molecules. [Pg.94]

In view of these observations, one would like to establish the Ising-like nature of the critical point by an RG treatment. Unfortunately, lattice models, as successfully applied to describe the criticality of nonionic fluids, may be of little help in this regard, because predictions for the Coulomb gas have proved to be surprisingly different from those for the continuum RPM. Discretization effects—and, more generally, the relevance of the results of lattice models with respect to the fluid—still need to be explored in detail. On the other hand, an RG treatment of the RPM or UPM is still lacking and, as Fisher [278] notes, the way ahead remains misty. [Pg.56]

A. Ciach, J. S. Hoye, G. Stell. Microscopic model for microemulsion. II. Behavior at low temperatures and critical point. J Chem Phys 90 1222-1228, 1989. A. Ciach. Phase diagram and structure of the bicontinuous phase in a three dimensional lattice model for oil-water-surfactant mixtures. J Chem Phys 95 1399-1408, 1992. [Pg.743]

Abstract. A phase equilibriums in intermetallic compounds hydrides in the area of disordered a-, (3-phase in the framework of the model of non-ideal lattice gas are description. LaNi5 hydride was chosen as the subject for the model verification. Position of the critical point of the P—w.-transition in the LaNi5-hydrogen system was definite. [Pg.187]

However, as discussed below critical concentrations for cellulose, in a variety of solvents, and based on optical observations under crossed polars are much lower than predicted using eauation 1 and kw = 2 q. Como et al. (4 point out one has to consider the possibili that the lattice model does not accuratelv predict the values of V2 and that V2 values using the Onsager (28) and Isihara (30) theories are about half that predicted by equation 1. [Pg.262]

In considering the vibronic side-bands to be expected in the optical spectra when we augment the static crystal field model by including the electron-phonon interaction, we must know the frequencies and symmetries of the lattice phonons at various critical points in the phonon density of states. We shall be particularly interested in those critical points which occur at the symmetry points T, A and at the A line in the Brillouin zone. Using the method of factor group for crystals we have [Pg.529]

One of the consequences of the suppression of the phase transition is the presence of a special critical point, Tc = 0 K. This point, called the quantum displacive limit, is characterized by special critical exponents. Its presence gives rise to classical quantum crossover phenomena. Quantum suppression and the response at and near this limit, Tc = 0 K, have been extensively studied on the basis of lattice dynamic models solved within the framework of both classical and quantum statistical mechanics. Figure 8 is a log-log plot of the 6 T) results for ST018 [15]. The expectation from theory is that in the quantum regime, y = 2 at 0.7 kbar, after which y should decrease. The results in Fig. 8 quantitatively show the expected behavior however, y is < 2 at 0.70 kbar. Despite the difference in the methods to suppress Tc in ST018, the results in Fig. 4a and Fig. 8 are quite similar. As shown in the results in Fig. 3b, uniaxial pressure also can be a critical parameter S for the evolution of ferroelectricity in STO. [Pg.100]

Determination of pure component parameters. In order to use the EOS to model real substances one needs to obtain

Eight variants of the DD reaction mechanism, described by Eqs. (21-25) have been simulated. The simplest approach is to neglect B2 desorption in Eq. (22) and the reaction between AB species (Eq. (25)). For this case, an IPT is observed at the critical point Tib, = 2/3. Thus this variant of the model has a zero-width reaction window and the trivial critical point is given by the stoichiometry of the reaction. For Tb2 < T1B2 the surface becomes poisoned by a binary compound of (A -I- AB) species and the lattice cannot be completely covered because of the dimer adsorption requirement of a [Pg.420]

© 2019 chempedia.info