Mixtures spinodal

Figure A2.5.16. The coexistence curve, = KI(2R) versus mole fraction v for a simple mixture. Also shown as an abscissa is the order parameter s, which makes the diagram equally applicable to order-disorder phenomena in solids and to ferromagnetism. The dotted curve is the spinodal.

Figure A3.3.2 A schematic phase diagram for a typical binary mixture showmg stable, unstable and metastable regions according to a van der Waals mean field description. The coexistence curve (outer curve) and the spinodal curve (iimer curve) meet at the (upper) critical pomt. A critical quench corresponds to a sudden decrease in temperature along a constant order parameter (concentration) path passing through the critical point. Other constant order parameter paths ending within tire coexistence curve are called off-critical quenches.

Binder K 1983 Collective diffusion, nucleation, and spinodal decomposition in polymer mixtures J. Chem. Phys. 79 6387... 

Figure C2.1.10. (a) Gibbs energy of mixing as a function of the volume fraction of polymer A for a symmetric binary polymer mixture = Ag = N. The curves are obtained from equation (C2.1.9 ). (b) Phase diagram of a symmetric polymer mixture = Ag = A. The full curve is the binodal and delimits the homogeneous region from that of the two-phase stmcture. The broken curve is the spinodal.

Verhaegh NAM, Asnaghi D, Lekkerkerker FI N W, Giglio M and Cipelletti L 1997 Transient gelation by spinodal decomposition in colloid-polymer mixtures Phys/ca A 242 104-18... 

Thermodynamics and kinetics of phase separation of polymer mixtures have benefited greatly from theories of spinodal decomposition and of classical nucleation. In fact, the best documented tests of the theory of spinodal decomposition have been performed on polymer mixtures. 

Short-time Brownian motion was simulated and compared with experiments [108]. The structural evolution and dynamics [109] and the translational and bond-orientational order [110] were simulated with Brownian dynamics (BD) for dense binary colloidal mixtures. The short-time dynamics was investigated through the velocity autocorrelation function [111] and an algebraic decay of velocity fluctuation in a confined liquid was found [112]. Dissipative particle dynamics [113] is an attempt to bridge the gap between atomistic and mesoscopic simulation. Colloidal adsorption was simulated with BD [114]. The hydrodynamic forces, usually friction forces, are found to be able to enhance the self-diffusion of colloidal particles [115]. A novel MC approach to the dynamics of fluids was proposed in Ref. 116. Spinodal decomposition [117] in binary fluids was simulated. BD simulations for hard spherocylinders in the isotropic [118] and in the nematic phase [119] were done. A two-site Yukawa system [120] was studied with... 

Then the mixture with droplets is quenched into the spinodal instability region to some T < Ta (Concentration c(r) within droplets starts to evolve towards the value C(,(T) > C(,(T ), but the evolution type depends crucially on the value Act = cj(T) — Ch(Ta). At small Act we have a usual diffusion with smooth changes of composition in space and time. But when Act is not mall (for our simulations Act O.2), evolution is realised via peculiar wave-like patterning shown in Figs. 8-10. 

A similar treatment applies for the unstable regime of the phase diagram (v / < v /sp), where the mixture decays via spinodal decomposition.For the linearized theory of spinodal decomposition to hold, we must require that the mean square amplitude of the growing concentration waves is small in comparison with the distance from the spinodal curve. 

Akcasu, Z.A., Bahar, L, Erman, B., Feng, Y. and Han, C. C. (1992) Theoretical and experimental study of dissolution of inhomogeneities formed during spinodal decomposition in polymer mixtures. 

Figure 17. Different stages of the spinodal decomposition in a symmetric mixture (4>0 = 0.5) r is the dimensionless time. The Euler characteristic is negative, which indicates that the surfaces are bicontinuous. The Euler characteristic increases with dimensionless time. This indicates that the surface connectivity decreases.

The points of these segments represent the AmixG of two-phase alloys. In the composition range between the maximum and the spinodal (xs) a two-phase alloy, such as a mixture xul + xu2, has therefore an overall free energy lower than that of any single-phase alloy of an intermediate composition, which is therefore unstable. 

Figure 3,10 Solvus and spinodal decomposition fields in regular (B) and subregular (D) mixtures. Gibbs free energy of mixing curves are plotted at various T conditions in upper part of figure (A and C, respectively). The critical temperature of unmixing (or consolute temperature ) is the highest T at which unmixing takes place and, in a regular mixture (B), is reached at the point of symmetry.

If the mixture is subregular, definition of the limits of spinodal decomposition is more complex. For a subregular Margules model (figure 3. IOC and D), we have... 

For analytical comprehension of the kinetics of spinodal decomposition processes, we must be able to evaluate the Gibbs free energy of a binary mixture of nonuniform composition. According to Cahn and Hilliard (1958), this energy can be expressed by the linear approximation... 

Figure 3.14 Stability relations in a binary mixture (A,B)N as a function of temperature. Heavy, solid line activity trend for component (B)N in the case of binodal decomposition. Dashed line activity trend in the case of spinodal decomposition.

The energy of elastic strain modifies the Gibbs free energy curve of the mixture, and the general result is that, in the presence of elastic strain, both solvus and spinodal decomposition fields are translated, pressure and composition being equal, to a lower temperature, as shown in figure 3.16. 

In pyroxenes, exsolutive processes proceed either by nucleation and growth or by spinodal decomposition (see sections 3.11, 3.12, and 3.13). Figure 5.30B shows the spinodal field calculated by Saxena (1983) for Cag sMgo sSiOj (diop-side) and MgSi03 (chnoenstatite) in a binary mixture, by application of the subregular Margules model of Lindsley et al. (1981) ... 

Following Cahn s theory, more extended versions were proposed by Langer et al. [ O] and Binder et al. [ l] Recently, de Gennes [52], and Pincus [53] applied spinodal decomposition to polymer mixtures. Many of the recent experimental studies on spinodal decomposition of polymer mixtures deal with measuring characteristic scattering maxima with various scattering techniques [5A-60]. 

The addition of water to solutions of PBT dissolved in a strong acid (MSA) causes phase separation in qualitative accord with that predicted by the lattice model of Flory (17). In particular, with the addition of a sufficient amount of water the phase separation produces a state that appears to be a mixture of a concentrated ordered phase and a dilute disordered phase. If the amount of water has not led to deprotonation (marked by a color change) then the birefringent ordered phase may be reversibly transformed to an isotropic disordered phase by increased temperature. This behavior is in accord with phase separation in the wide biphasic gap predicted theoretically (e.g., see Figure 8). The phase separation appears to occur spinodally, with the formation of an ordered, concentrated phase that would exist with a fibrillar morphology. This tendency may be related to the appearance of fibrillar morphology in fibers and films of such polymers prepared by solution processing. 

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