Mixtures spinodal decomposition

Huang, J.S., Goldburg, W.I., and Bjerkaas, A.W. (1974) Study of phase separation in a critical binary liquid mixture spinodal decomposition, Phys. Rev. Lett. 32,921. 

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

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... 

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.

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]. 

Non-Random Systems. As pointed out by Cahn and Hilliard(10,11), phase separation in the thermodynamically unstable region may lead to a non-random morphology via spinodal decomposition. This model is especially convenient for discussing the development of phase separating systems. In the linearized Cahn-Hilliard approach, the free energy of an inhomogeneous binary mixture is taken as ... 

Note 4 If a mixture is thermodynamically metastable, it will demix if suitably nucleated (see Definition 2.5). If a mixture is thermodynamically unstable, it will demix by spinodal decomposition or by nucleation and growth if suitably nucleated, provided there is minimal kinetic hindrance. 

Note Mixtures exhibiting metastable miscibility may remain unchanged or they may undergo phase separation, usually by nucleation or spinodal decomposition. 

Curve defining the region of composition and temperature for a binary mixture across which a transition occurs from conditions where single-phase mixtures are metastable to conditions where single-phase mixtures are unstable and undergo phase separation by spinodal decomposition. 

These observations are analogous to those of phase-separating mixtures by spinodal decomposition mechanism, leading several researchers to invoke the idea that the early stage of polymer crystallization is spinodal decomposition. 

If any of these features is not observed in the early stages of crystallization, the spinodal decomposition mechanism commonly encountered in phase-separating mixtures cannot be associated with polymer crystallization. 

Differentiate between binodal and spinodal decomposition in polymer mixtures. 

Polymer-polymer systems exhibit phase behavior similar to other mixtures, such that an initially uniform system separates into two or more phases as a result of small change in thermodynamic variable. Two mechanisms can be envisioned to explain this phenomenon nucleation and growth (NG), and spinodal decomposition (SD). 

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