Phase transition spinodal

Phase transitions in two-dimensional (adsorbed) layers have been reviewed. For the multicomponent Widom-Rowlinson model the minimum number of components was found that is necessary to stabilize the non-trivial crystal phase. The effect of elastic interaction on the structures of an alloy during the process of spinodal decomposition is analyzed and results in configurations similar to those found in experiments. Fluids and molecules adsorbed on substrate surfaces often have phase transitions at low temperatures where quantum effects have to be considered. Examples are layers of H2, D2, N2, and CO molecules on graphite substrates. We review the PIMC approach, to such phenomena, clarify certain experimentally observed anomahes in H2 and D2 layers and give predictions for the order of the N2 herringbone transition. Dynamical quantum phenomena in fluids are also analyzed via PIMC. Comparisons with the results of approximate analytical theories demonstrate the importance of the PIMC approach to phase transitions, where quantum effects play a role. 

FIG. 4 Qualitative phase diagram close to a first-order irreversible phase transition. The solid line shows the dependence of the coverage of A species ( a) on the partial pressure (Ta). Just at the critical point F2a one has a discontinuity in (dashed line) which indicates coexistence between a reactive state with no large A clusters and an A rich phase (hkely a large A cluster). The dotted fine shows a metastability loop where Fas and F s are the upper and lower spinodal points, respectively. Between F2A and Fas the reactive state is unstable and is displaced by the A rich phase. In contrast, between F s and F2A the reactive state displaces the A rich phase. 

The systems undergoing phase transitions (like spinodal decomposition) often exhibit scaling phenomena [ 1—4] that is, a morphological pattern of the domains at earlier times looks statistically similar to a pattern at later times apart from the global change of scale implied by the growth of L(f)—the domain size. Quantitatively it means, for example, that the correlation function of the order parameter (density, concentration, magnetization, etc.)... 

The scattered intensity increases with increasing temperature as shown in Fig. 10. The scattered intensity diverges at the spinodal temperature, Ts in this particular case Ts = ca. 34.6 °C. Experimentally such a divergence cannot be expected because a macroscopic phase separation occurs and the scattered intensity remains finite. It is worthy to note that the difference in the scattered intensities between at 34.6 °C and at 35.0 °C clearly indicates that the system undergoes a transition. The critical phenomena of the volume phase transition of non-ionic gels with respect to temperature will be discussed in Sect 5.4. 

However, it remains unknown how heterogeneities affect the phase transition itself. In fact, the perturbation scheme used to derive Eq. (4.52) breaks down near the spinodal point. We can well expect that domains of a shrunken (or swollen) phase are created and pinned around heterogeneities with higher (or lower) crosslink densities. 

Dynamical study of the phase transition of the gels in spinodal regimes was described. The evolution of intensity of light scattered from the gels indicated the applicability of Cahn s linearized theory to the phase transition. Our work offers a basis for the determination of diffusion coefficient of gels in their spinodal regimes. 

Neutral NIPA gel is the most extensively studied among known gels from the standpoint of phase transition, and thus, various physical properties around the transition have been reported. These include the shear and bulk modulus [20, 24], the diffusion constant of the network [25], spinodal decomposition [26], specific heat [21], critical properties of gels in mixed solvents [8] and the effect of uniaxial [27] and hydrostatic [28] pressures on the transition, and so... 

The isotropic-to-nematic transition is determined by the condition [1 — (2/3)TBBWBB/k T] = 0 whereas the spinodal line is obtained when the denominator of XAA is equal to zero. These conditions are evaluated in the thermodynamic limit (Q = 0) in Fig. 7 for a Maier-Saupe interaction parameter Web/I bT = 0.4xAb and for NA = 200, N = 800, vA = vB = 1. When the volume fraction of component A(a) is low, the isotropic-to-nematic phase transition is reached first whereas at high < >A the spinodal line is reached first. In the second case, the macromolecules do not have a chance to orient themselves before the spinodal line is reached. This RPA approach is a generalization of the Doi et al. [36-38] results (that were developed for lyotropic polymer liquid crystals) to describe thermotropic polymer mixtures. Both approaches cannot, however,... 

Fig. 19. From the intersections in this figure, the diffusion coefficients were determined and are presented in Fig. 20. By extrapolating the D pp value to the horizontal axis, the spinodal temperature can be determined. Applying this procedure, we could determine a spinodal temperature of 34.2 °C which was sHghtly higher than the phase transition temperature of 34 °C. Thus, it was verified that the initial sta of the phase separation with the NIPA gel was expressed by Cahn s linearized theory.

F. Bruge and S. L. Fornili, Comput. Phys. Commun., 60, 31 (1990). Concurrent Molecular Dynamics Simulation of Spinodal Phase Transition on Transputer Arrays. 

Herein, we expand on the discussion of our recently observed isothermal amorphous-amorphous-amorphous transition sequence. We achieved to compress LDA in an isothermal, dilatometric experiment at 125 K in a stepwise fashion via HDA to VHDA. However, we can not distinguish if this stepwise process is a kinetically controlled continuous process or if both steps are true phase transitions (of first or higher order). We want to emphasize that the main focus here is to investigate transitions between different amorphous states at elevated pressures rather than the annealing effects observed at 1 bar. The vast majority of computational studies shows qualitatively similar features in the metastable phase diagram of amorphous water (cf. e.g. Fig.l in ref. 39) at elevated pressures the thermodynamic equilibrium line between HDA and LDA can be reversibly crossed, whereas by heating at 1 bar the spinodal is irreversibly crossed. These two fundamentally different mechanisms need to be scrutinized separately. 

Crystallization is thus a two-step process nucleation and growth. The first step is nucleation, which occurs spontaneously when the supersaturation attains the metastable limit at the spinodal curve. Knowledge of the spinodal curve is useful in understanding the mechanism of crystallization. However, the actual metastable limit may often exceed the spinodal curve in certain systems, and in such cases the phase transition mechanism is explained in terms of spinodal decomposition (9) or the solution history, impurities present, or rate of increase of supersaturation. 

For example, iieai a critical point or at a spinodal (i.e., at the stability limit of a fluid phase in the metastable regime), the above is no longer true. However, it should also be noted that, at a discontinuous phase transition (i.e., before entering the metastable regime), Eq. (2.76) still holds. 

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