Nucleation of phase separation

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. 

The validity of mean field theory for N —y oo has striking consequences for the initial stages of phase separation. " In a metastable state slightly inside the coexistence curve, the nucleation free energy barrier is due to spherical droplets with a radius R The free energy excess of a droplet is written in terms of bulk and surface terms " "... 

The previous discussion has shown that the CIPS technique allows one to produce macroporous epoxy networks with either a narrow or bimodal size distribution. However, no indication has been given on the type of phase separation mechanism to yield these morphologies. As discussed earlier, the formation of a closed cell morphology can result either from a nucleation and growth mechanism or from spinodal decomposition. 

The area of conditions called the metastable zone is situated between the solubility and supersolubility curves on the crystallization phase diagram (Fig. 3.1). The supersolubility curve is defined as the line that separates the conditions where spontaneous nucleation (or phase separation or precipitation) occurs, from those where the crystallization solution remains clear if left undisturbed (Ducruix and Giege, 1992 Ducruix and Giege, 1999). 

The Kelvin equation helps explain an assortment of supersaturation phenomena. All of these —supercooled vapors, supersaturated solutions, supercooled melts —involve the onset of phase separation. In each case the difficulty is the nucleation of the new phase Chemists are familiar with the use of seed crystals and the effectiveness of foreign nuclei to initiate the formation of the second phase. 

While actual chemical events involved in nucleation and crystal growth are not known a phenomenological treatment (gives some insight. Willard Gibbs (9J considered processes of phase separation of two extreme kinds. In the first, fluctuations in concentration occur which are minute in volume but large in extent of departure from the mean (the case of binodal phase separation). In the second the volume of the fluctuation is large but the deviation from the mean for the solution is minute (responsible for spinodal phase separation). In nucleation of zeolites one is conerned only with fluctuations of the first kind. 

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... 

A mechanism for oiling out can be postulated as follows When supersaturation is achieved rapidly such that the concentration is beyond the upper metastable limit—as can often be the case in a nucleation-based process—the substrate is forced to separate into a second phase by the creation of the resulting high solution concentration. However, crystallization is delayed by a slow crystallization rate. This combination may result in the creation of a nonstructured oil or possibly an amoiphous solid. The rates of phase separation and nucleation are relative to each other such that slow nucleation implies only that nucleation was not fast enough to create discrete particles before oil separation. 

The phase-separated droplet/matrix morphology is an outcome of the nucleation and growth mechanism (NG) of phase separation. The phase dimensions are similar to those observed for SD, but in this case the properties are dominated by the matrix polymer with the dispersed phase playing the role of a compatlblllzed filler. A similar dispersed morphology, but with large drops, can be obtained by allowing the SD or NG system to ripen. The coarsening usually leads to a non-uniformity of properties. 

Important aspects of polymer I/monomer Il/polymer II ternary phase diagrams were determined for the system cross-Dolvbutadiene-inter-cross-polystyrene as monomer II, styrene, is polymerized. Information on the mechanisms of phase separation suggest first nucleation and growth, followed by a modified spinodal... 

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... 

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