Liquid , generally spinodal

Figure 7. Time dependence of the wavelength of the fastest growing density fluctuation (Affiax) during a molecular dynamics simulation of isothermal liquid-vapor spinodal decomposition in the three-dimensional Lennard-Jones fluid kT/e = 0.8 p

In Fig. 1.14, the dotted lines for each curve show the activity of the coexisting phases at chemical equilibrium. Similarly in Fig. 1.16 the dotted line BDF shows the activity of the coexisting phases (5 = 0.185 and 0.815). The coexisting phases, which have the same structure, differ in the concentration of vacancies. This phenomenon is generally called phase separation or spinodal decomposition (it is observed not only in the solid phases but also in the liquid phases), and originates from the sign of the interaction energy... 

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,... 

Generally, the metastability is a phenomenon associated with the persistence of the given phase well below the stability domain, bordered by the first order transition, for instance (/) the glass transition phenomenon, (//) metastable systems studies linked to spinodals - absolute stability limits, with particular attention towards the inherently metastable negative pressure domain (///) metastability near a critical point, (/v) the quest for the liquid - liquid near-critical transition in one component liquid, (v) the issue of liquid crystals where... 

Figures. 9 and 10 represent the most expressive confirmation of the latent symmetry in the HPD for water obtained by the generalized WMG-model. It was suggested the existence of the quasicritical point to extrapolate the low-temperature results of Figs. 6,7 and predict the whole quasibinodal. It is the point (Fig. 9) in which the branch of negative pressures P (Tintersects the liquid branch of the WMG-spinodal Plp(T) at the parameters T°j, 605K and...

Figure 6A is a general representation of the pressure-composition diagrams for systems that display liquid -liquid phase separation. The binodal boundary represents the equilibrium demixing pressures for a monodisperse polymer system. Below the binodal there is another boundary known as the spinodal boundary. The binodal and the spinodal envelopes determine the metastable region (shaded area in between). They... 

Finally, for PRISM/R-MPY theory the thermodynamic consistency between the free energy and compressibility route calculations of the chi parameter and spinodal phase boundaries has been shown to be remarkably good. Moreover, in the long-chain limit the predicted chi parameter and phase boundary appear to be exactly equivalent, which is a unique circumstance for liquid-state theories. However, this is not a general feature of PRISM with the molecular closures but rather derives from the fact that in the long-chain limit the critical temperature becomes arbitrarily high, the HTA is rigorous, and thus the symmetric blend reference system reduces to a composition-independent homopolymer melt. 

We also note that in principle, Eq. (6.17) is really a transcendental equation for the spinodal temperature if the polymer density and/or statistical segments length depend on temperature as generally true for real systems. This aspect can lead to apparent N dependences of the spinodal temperature, which do not follow the classic Flory scaling relation of T,. N. A liquid-gas-type transition is also predicted, but since it is driven by density, not concentration, fluctuations the relevant temperature scale is independent of N, and thus is expected to be well below Tj for macromolecules. 

Thus, while liquid-hquid and polymer-solvent mixtures (that are borderline in miscibility) usually exhibit upper critical solution temperatures (ucst), polymer-polymer mixtures generally exhibit lower critical solution temperatures (lest). This behavior is illustrated in Fig. 2.1 with an illustration of the free energy composition at key temperatures noted in Fig. 2.2. The binodal and spinodal curves (binodal and spinodal phase separation processes are discussed later in this chapter) are illustrated on the phase diagrams. The spinodal curve is related to the position where... 

Whether nudeation or spinodal dewetting dominates the rupture of a liquid film depends on the specific system. The A oc Hq dependence predicted by Eq. (7.34) has been observed in polymer [815, 816, 820] and metal ]821] films. For polymer films in many cases, nudeation is faster [818, 820]. For aqueous films on hydrophobic surfaces, small bubbles are generally accepted to initiate nudeation and nudeation dominates ]813, 814]. 

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