Phase separation thermodynamic miscibility

The spontaneous mixing of the two polymers will transpire at a rate which reflects the degree of miscibility of the system. As X approaches the critical value for phase separation, "thermodynamic slowing down" of the interdiffusion will occur [12]. The rate of increase of the scattering contrast reflects the proximity of the system to criticality, as well as the strong composition dependence of the glass transition temperature of the blend. Extraction of a value for either the self diffusion constants [13,14] or the interaction parameter is not feasible from the presently available data. 

The term compatibility is used extensively in the blend literature and is used synonymously with the term miscibility in a thermodynamic sense. Compatible polymers are polymer mixtures that do not exhibit gross symptoms of phase separation when blended or polymer mixtures that have desirable chemical properties when blended. However, in a technological sense, the former is used to characterize the ease of fabrication or the properties of the two polymers in the blend [3-5]. 

Lattice constants for Pd-Rh alloys quenched from 1300°C vary smoothly with composition, showing only a small positive deviation from Vegard s law, but prolonged vacuum annealing below 850°C revealed the existence of a wide miscibility gap 151). Figure 25 shows the limits of the miscibility gap calculated from the lattice constants of the two-phase system between 825° and 600°C. Recent thermodynamic data (Table I) confirm the tendency to phase separation. The enthalpies of formation are endothermic... 

The information available on aqueous polymer blends is qualitative in nature because of the lack of a suitable theory to interpret the experimental observations. Mixed gels can be comprised of an interpenetrating network, a coupled network (as discussed above), or a phase-separated network [2]. The latter is the most common as the blends have a tendency to form two phases during gelation. In such cases the miscibility and thermodynamic stability have to be empirically investigated and proper conditions for miscible blends identified. This involves a phase diagram study as is described in [3]. 

Thermodynamic Perspective of Miscibility and Phase Separation in Solid Dispersion 503... 

If the drug and polymer are miscible in their Luid state, then as discussed in Section Thermodynamic Perspective of Miscibility and Phase Separation in Solid Dispersions, the mixture may or may not undergo phase separation during solidiLcation, thereby inLuencing the structure of solid dispersion. 

For some particular formulations (e.g., unsaturated polyesters formulated with a high styrene concentration), the primary chains that are first generated are not miscible with the unreacted monomers. In this case, there is a phase separation phenomenon characterized by the appearance of relatively large polymer-rich particles. These microgels are formed by a thermodynamic driving force and their sizes are large enough to be detected in both the course of polymerization and the final materials. 

This article reviews the phase behavior of polymer blends with special emphasis on blends of random copolymers. Thermodynamic issues are considered and then experimental results on miscibility and phase separation are summarized. Section 3 deals with characteristic features of both the liquid-liquid phase separation process and the reverse phenomenon of phase dissolution in blends. This also involves morphology control by definite phase decomposition. In Sect. 4 attention will be focused on flow-induced phase changes in polymer blends. Experimental results and theoretical approaches are outlined. 

The now classical methods used for the preparation of supported gold catalysts are hardly capable of giving particles that are both small and bimetallic, when the precursors in solution do not interact strongly with each other. During the subsequent thermal treatment performed to get metal particles, the metals must have enough mobility to migrate on the support, interact with each other, and form bimetallic particles. However, phase separation can be a common problem, especially when the metal ratio falls in the miscibility gap (Section 2.6), or if the intended composition is not thermodynamically stable. 

On mixing solutions of a protein and a polysaccharide, four kinds of mixed solutions can be obtained. Figure 3.1 shows that two single-phase systems (1 and 3) and two-types of biphase systems (2 and 4) can be produced. The two-phase liquid systems 2 and 4 differ in the distribution of biopolymers between the co-existing phases. The biopolymers are concentrated either in the concentrated phase of system 2 because of interbiopolymer complexing, or within separated phases of system 4 because of incompatibility of the biopolymers. The term biopolymer compatibility implies miscibility of different biopolymers on a molecular level. The terms incompatibility or limited thermodynamic compatibility cover both limited miscibility or limited cosolubility of biopolymers (i.e., system 2) and demixing or phase separation... 

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. 

This growing demand for polymer blends has generated a need for a better understanding of the thermodynamics of miscibility and phase separation in polymer systems. This in turn has generated tremendous interest in techniques that can be used to characterize the thermodynamics of polymer-polymer systems. 

Finally, it has been found that the deuterium staining of individual molecules, commonly used in condensed matter studies, in case of polymers can lead to serious consequences in bulk and surface thermodynamics. This was shown in this work by the phase separation of isotopic blends (Sect. 2.2.2), isotope swapping effect in blend miscibility (Sect. 2.2.3) and surface segregation (Sect. 3.1.2.5) as well as by the specific scaling law (Eq. 61) which governs the polymer brush conformation (Sect. 4.2.1). 

PNDB occurs for blends that are miscible only within a small range of concentration. To understand these systems, the interaction between the flow and the phase separation must be considered. This has become an area of considerable scientific activity. One needs to consider both how the phase separation influences the rheological behavior and how the flow (or stress) affects the thermodynamics of phase separation. 

It is readily seen from Fig. 3.8 that for each value of x above Xc there are two different values of 2 at which the chemical potential of the solvent in the two phases is the same. This implies that solutions with concentrations defined by these two values of 2 can be in thermodynamic equilibrium for X > Xc- Moreover, it implies that a solution with an intermediate value of (j)2 will spontaneously separate into two stable liquid phases defined by these two concentrations this will occur with a concomitant decrease in the free energy. Such phenomena are in fact observed with solutions of flexible polymers for values of x above a critical value (Xc)- Thus, if X is increased by decreasing the temperature, an initially totally miscible system at higher temperatures is transformed to one of limited miscibility by lowering the temperature at some critical temperature Tc, incipient phase separation (as indicated by the onset of an opalescence) is encountered, followed by separation into distinct liquid phases at still lower temperatures. 

Thermodynamic parameters for the mixing of dimyristoyl lecithin (DML) and dioleoyl lecithin (DOL) with cholesterol (CHOL) in monolayers at the air-water interface were obtained by using equilibrium surface vapor pressures irv, a method first proposed by Adam and Jessop. Typically, irv was measured where the condensed film is in equilibrium with surface vapor (V < 0.1 0.001 dyne/cm) at 24.5°C this exceeded the transition temperature of gel liquid crystal for both DOL and DML. Surface solutions of DOL-CHOL and DML-CHOL are completely miscible over the entire range of mole fractions at these low surface pressures, but positive deviations from ideal solution behavior were observed. Activity coefficients of the components in the condensed surface solutions were greater than 1. The results indicate that at some elevated surface pressure, phase separation may occur. In studies of equilibrium spreading pressures with saturated aqueous solutions of DML, DOL, and CHOL only the phospholipid is present in the surface film. Thus at intermediate surface pressures, under equilibrium conditions (40 > tt > 0.1 dyne/cm), surface phase separation must occur. 

---