Phase diagram spinodal decomposition

Figure 16.5 Time evolution of structure in phase-separating binary homopolymer mixtures. Nucleation and growth result when a homogeneous mixture is thrust into the metastable region of the phase diagram. Spinodal decomposition occurs when a mixture is placed in a thermodynamically unstable state.

Figure 7.15. Phase diagram of a phase showing spinodal decomposition, (a) In a regular solution having positive mixing enthalpy, has an opposite sign on the left and...

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. 

Since the start of modern interpenetrating polymer network (IPN) research in the late sixties, the features of their two-phased morphologies, such as the size, shape, and dual phase continuity have been a central subject. Research in the 1970 s focused on the effect of chemical and physical properties on the morphology, as well as the development of new synthetic techniques. More recently, studies on the detailed processes of domain formation with the aid of new neutron scattering techniques and phase diagram concepts has attracted much attention. The best evidence points to the development first of domains via a nucleation and growth mechanism, followed by a modified spinodal decomposition mechanism. This paper will review recent morphological studies on IPN s and related materials. 

Figure 18 illustrates a model of the three component phase diagram of an IPN, where poljrmer I, poljrmer II, and monomer II are chosen for generality in expressing sequential IPN formation. On poljrmerizatlon of monomer II, first phase separation is initiated, probably by nucleation and growth. However, shortly a modified spinodal decomposition mechanism sets in as the overall composition is driven deeper into the phase separation region. 

The coherency strain energy introduces an additional barrier to spinodal decomposition, which causes a shift on the temperature-composition phase diagram of the chemical spinodal, defined by d2filom/dc% = 0, to the coherent spinodal, defined by... 

The Al-Zn system was the first studied extensively in an attempt to verify the theory for spinodal decomposition [24], The equilibrium diagram for this system, shown in Fig. 18.12, shows a monotectoid in the Al-rich portion of the diagram. The top of the miscibility gap at 40 at. % Zn is the critical consolute point of the incoherent phase diagram. 

Figure 11.22 shows that for compositions for which d2G/dc2 > 0, such spin-odal decomposition is not possible and nucleation of aq and 002 is required. Hence, spinodal reactions are possible only for composition/temperature combinations for which d2G/dc2 is negative. Sometimes this region is shown by dotted lines on phase diagrams, as in Figure 11.23. 

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...

Because of the complexity of the processes involved and the various methods of measuring them, phase diagrams of organogels can be envisioned by different theoretical approaches. In one option, network formation can be considered according to a spinodal decomposition mechanism. Briefly, the spinodal curve in a phase diagram represents the limit of metastability defined by the second derivative of the free energy with respect to concentration Important features of such a mechanism are (1) the phase separation in solute-rich and solute-poor... 

Miscible blends of poly(vinyl methyl ether) and polystyrene exhibit phase separation at temperatures above 100 C as a result of a lower critical solution temperature and have a well defined phase diagram ( ). This system has become a model blend for studying thermodynamics of mixing, and phase separation kinetics and resultant morphologies obtained by nucleation and growth and spinodal decomposition mechanisms. As a result of its accessible lower critical solution temperature, the PVME/PS system was selected to examine the effects of phase separation and morphology on the damping behavior of the blends and IPNs. 

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,...

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