Binodal decomposition

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.

Figure 3J2 Energy relationships between solvus and spinodal decompositions. (A) Portion of Gibbs free energy of mixing curve in zone between binodal (X ) and spinodal (X ) points. (B) Gibbs free energy variation as a consequence of compositional fluctuations around intermediate points X and X(2). ...

The exsolution process in either binodal or spinodal decomposition may lead to coherent or incoherent interfaces between the unmixed phases (figure 3.15). The... 

Differentiate between binodal and spinodal decomposition in polymer mixtures. 

Binodal and Spinodal Decompositions. As the temperature of a solid solution is lowered, the entropy contribution to the solid Gibbs energy... 

Fig. 17 Phase diagram of a PDMS/PEMS (16.4/48.1) blend. The dashed lines are the binodal and the spinodal. The phase contrast micrographs show typical demixing patterns for spinodal decomposition and nucleation and growth in the respective regions. The bullets mark the initial sample positions. See text for details. Figure from [112]. Copyright (2007) by the American Chemical Society...

In a UCST system, when the temperature is reduced to a final value 7/ that is below the critical temperature Tc, a mixture with a concentration 0 not too far from the critical composition phase separate into two phases whose compositions lie on the opposite sides of the binodal envelope line of Fig. 9-1. The dynamics of the separation process of a single phase into these two phases is controlled by Tf, the composition , the rate of the quench dT/dt, the viscous (or viscoelastic) properties of the phases formed, and the interfacial tension F between the two phases. Although a variety of different kinds of behavior can occur, there are two generic types of phase separation, namely, spinodal decomposition (SD) and nucleation and growth (NG). SD occurs when the mixture is quenched into a part of the phase diagram where the mixture is unstable to small variations in composition, leading to immediate growth of phase-separated domains. When the quenched... 

Figure 9-1 Schematic phase diagram of a binary fluid mixture of small molecules. The two-phase region lies under the binodal line, the apex of which defines the critical temperature Tc and critical composition Between the binodal and the spinodal lines, phase separation is by nucleation and growth (NG), while under the spinodal line it is by spinodal decomposition (SD). Within the region of spinodal decomposition, near the compositional symmetry line, there is a region where the morphology is initially bicontinu-ous. Outside of this region, one of the phases is a discontinuous droplet phase. Eventually,...

From a thermodynamic point of view, phase diagrams may be constructed by changing the temperature (ii), pressure (12). or composition of a material. The present experiments are concerned with changes in composition at constant temperature and pressure, leading to a ternary phase diagram with polymer network I at one corner, monomer II at the second corner, and polymer network II at the third corner. According to classical concepts, at first there should be a mutual solution of monomer II in network I, followed by the binodal (nucleation and growth kinetics) and finally the spinodal (spinodal decomposition kinetics). 

The entire region enclosed by the outer dome represents immiscibility. The inner dome is known as the spinodal. The outer dome is known as the binodal. In the region of composition between the binodal and spinodal lines, phase separation occurs by the nucleation and growth mechanism and leads to the formation of dispersed micro-spherical glass particles in the matrix (see also Shelby, 1997). Spinodal decomposition which takes place inside the dotted region is a special type of phase separation. In order to understand this, consider two materials A and B, melts of which... 

Interpretation of the phase separation fluorescence results requires that accurate values of the equilibrium binodal compositions for a particular temperature be available. These are necessary in order to calculate the volume fraction of the rich phase in the two component system. This volume fraction is assumed to be constant during the early stages of spinodal decomposition. 

FIGURE 6.17 Solubility of a homopolymer according to the Flory-Huggins theory. Variables are the excluded volume parameter ft (or the polymer-solvent interaction parameter y), the net volume fraction of polymer q>, and the polymer-to-solvent molecular volume ratio q. Solid lines denote binodal, the broken line spinodal decomposition. Critical points for decomposition (phase separation) are denoted by . See text. 

In the concentration range between the binodal and the spinodal (not shown), separation may be very slow. Even spinodal decomposition may take long to become visible, because the system often is concentrated and very viscous, implying slow diffusion of the polymers a concentrated phase may even tend to gel. Mostly, one of the phases forms droplets, and the system may be called a water-in-water emulsion. Which phase becomes the continuous one depends on the concentration ratio of both polymers. If c3/c2 is larger than the ratio at the critical point, the continuous phase tends to become the one rich in c2, and vice versa. The interfacial tension between... 

On the other hand, near the critical composition, the binodal and spinodal merge so that the metastable region reduces considerably in size. In this case, it is easier to pass directly into the unstable region by a thermal excursion before phase separation begins. Once in the unstable region, spinodal decomposition is the mechanism of phase separation. 

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