Mixtures phase separation

Here we shall consider two simple cases one in which the order parameter is a non-conserved scalar variable and another in which it is a conserved scalar variable. The latter is exemplified by the binary mixture phase separation, and is treated here at much greater length. The fonner occurs in a variety of examples, including some order-disorder transitions and antrferromagnets. The example of the para-ferro transition is one in which the magnetization is a conserved quantity in the absence of an external magnetic field, but becomes non-conserved in its presence. 

Within this general framework there have been many different systems modelled and the dynamical, statistical prefactors have been calculated. These are detailed in [42]. For a binary mixture, phase separating from an initially metastable state, the work of Langer and Schwartz [48] using die Langer theory [47] gives the micleation rate as... 

A method has been developed for the continuous removal and reuse of a homogeneous rhodium hydroformylation catalyst. This is done using solvent mixtures that become miscible at reaction temperature and phase separate at lower temperatures. Such behavior is referred to as thermomorphic, and it can be used separate the expensive rhodium catalysts from the aldehydes before they are distilled. In this process, the reaction mixture phase separates into an organic phase that contains the aldehyde product and an aqueous phase that contains the rhodium catalyst. The organic phase is separated and sent to purification, and the aqueous rhodium catalyst phase is simply recycled. 

It has been long established that 3He/4He liquid mixtures phase separate at temperature below 0.9 K. (see Fig. 5.9), and the theoretical explanation for this, first advanced by Prigogine, has been outlined above. Similarly, mixtures of solid 3He/4He (formed at elevated pressure) and mixtures of solid H2/D2 both phase separate, but liquid mixtures of H2 and D2 do not, although they do show appreciable nonideality. No other small molecule isotopomer mixtures phase separate, but... 

This mirrors the experience of everyday life, where if you try to get one thing to mix with another you often heat them (Figure 11-15). However, as we will see later, polymers can also give counter-intuitive behavior, where mixtures phase-separate upon heating ... 

In this and the following sections we shall mostly restrict ourselves to fully miscible mixtures. Phase separation in the bulk or at the surface leads to inhomogeneous surfaces, of which the tension cannot be unambiguously measured. For an illustration of such an zmalysis, see ref., which concerns the influence of the temperature on water-2,6 dimethylpyridine mixtures which phase-separate below T = 33.87°C. 

The critical mixture curve is measured in the following manner (Occhio-grosso et al., 1986). At a temperature slightly higher than the UCEP temperature, a vapor-liquid mixture at a fixed overall concentration is compressed to a single phase. The pressure is then isothermally decreased very slowly until the system becomes turbid and a second phase just begins to precipitate. A critical mixture point is obtained if critical opalescence is observed during the transition process and if two phases of equal volume are present when the mixture phase-separates. 

In Figure 20.17, we compare a polymer-surfactant mixture, a nonionic polyoxyethylene surfactant and dextran, with a related polymer-polymer mixture, poly(ethylene glycol) and dextran. We can see that the two mixtures phase-separate in qualitatively the same way. 

The criticality conditions of a mixture are different from those of a pure fluid. The fluid mixture phase-separates at finite compressibility because it becomes materially unstable it can lower its free energy by splitting into two phases of different composition. For a binary mixture of mole fraction x, the criticality conditions, in terms of the Gibbs free energy G(P,T), are... 

Therefore if Xamixture phase separates into phase a and phase If 0 < 2 < and < x < 1, the fiee energy increases if the mixture... 

When a colloid-polymer mixture phase separates into a coUoid-rich and polymer-rich phase an interface appears in between. For a colloidal gas-liquid... 

By the addition of non-adsorbing polymers to colloidal suspensions the mixture phase separates into a coUoid-rich and a polymer-rich phase, as discussed above. The understanding of this polymer-induced phase separation is very important, not only for colloid science but also for industrial systems, such as food dispersions [74, 77, 236, 237]) and paint [238]. In these systems colloids and polymers (or surfactants) are jointly present and influence the stability and hence related processing issues. 

Similar to the fluorous biphasic concept, a system was developed that formed a homogenous phase at elevated temperature, but phase-separated at room temperature [49c]. It was found that a mixture of functionalized PNIPAM polymer, ethanol, heptane and water exhibited these properties. The hydrogenation of 1-octadecene and 1-dodecene using a phosphine functionalized PNIPAM with a rhodium precursor were taken as test reactions and the high activity was foimd was similar to that of RhCl(PPh3)3. At room temperature the mixture phase separated and the catalysis stopped since the catalyst is completely insoluble in heptane. The substrate is dissolved in the heptane allowing a facile catalyst/product separation without the loss of activity. The concept is obviously limited to substrates that show... 

The dependence of AGm on composition cpi and x 12 for a binary blend consisting of two polymers of equal molar mass can be determined from equation 21, and it is similar to that reported for polymer solutions. As temperature increases, the specific interactions between the two components weaken owing to molecular motion and the mixture phase separates. A large number of polymer blends show LCS behavior represented in Figure fib. However, a UCST may still be observed in some polymeric binary systems, particularly low molecular weight nonpolar mixtures. In this case, even if the entropic term is small it is still larger than Aifm. and ASm governs the miscibility. 

Blending of two or more polymers to improve properties is becoming increasingly important. It can reduce the cost of an expensive thermoplastic, ease the processibility of a heat-sensitive plastic or improve impact resistance. It can be a homogeneous mixture, phase-separated systems or a combination of both. 

An additional complexity is the existence of two critical temperatures. When the temperature of an initially homogeneous mixture is lowered below the phase boundary, phase separation begins to occ-ur. The temperature of phase separation is dependent on composition and the critical point associated with the cloud point curve is called upper critical solution temperature. (UCST) For some polymer-solvent and polymer-polymer mixtures phase separation is also olDserved when the temperature of the mixture is raised.The corresponding critical point is called lower critical solution temperature (LCST),... 

Upon cooling a homogeneous mixture, phase separation at first sets in for samples with the critical composition, = 0.5, at the temperature Tc. For the other samples demixing occurs at lower temperatures, as described by the binodal. We observe here a lower miscibility gap. A second name is also... 

Fig. lOa-f 2D sliced images taken by LSCM for the DPB/PB mixture phase-separated for 1,675 min at 40 °C. The depth of the image increases in the order of image a-f with the increment of 1.0 jim. The point marked by an arrow corresponds to the same pixel position in all images... 

Phase Diagram in the Temperature vs. composition plane. Below the binodal the mixture is stable and only one phase exists. Above the binodal the mixture phase separates. Phase separation occurs via nucleation and growth if the mixture is initially in the metastable region. If it begins in the unstable region phase separation occurs by spinodal decoposition. 

FIGURE 3.3 Plots of the chemical potential difference Ti - ft as a function of polymer volume fraction for different values of %. For x < X . this function is monotonically decreasing and the one-phase mixture is stable for all values of V2. For % > Xc, this function goes through a minimum and a maximum, and the mixture phase separates. 

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