Lower miscibility gap

Since there had not been any measurements of thermal diffusion and Soret coefficients in polymer blends, the first task was the investigation of the Soret effect in the model polymer blend poly(dimethyl siloxane) (PDMS) and poly(ethyl-methyl siloxane) (PEMS). This polymer system has been chosen because of its conveniently located lower miscibility gap with a critical temperature that can easily be adjusted within the experimentally interesting range between room temperature and 100 °C by a suitable choice of the molar masses [81, 82], Furthermore, extensive characterization work has already been done for PDMS/PEMS blends, including the determination of activation energies and Flory-Huggins interaction parameters [7, 8, 83, 84],... 

The measurements near the critical point have been performed with a PDMS/ PEMS blend with molar masses of Afw = 16.4kgmol 1 (PDMS, Mw/Mn= 1.10) and Afw = 22.8 kg mol 1 (PEMS, Afw/Mn =1.11). The corresponding degrees of polymerization are N = 219 and N = 257, respectively. The phase diagram shows a lower miscibility gap with a critical composition of cc = 0.548 (weight fractions... 

G985). Upper miscibility gap calculated by Harrison et al. (2000b). Lower miscibility gap is schematic (modified from Burton 1985). Boundaiy between CAF and FM depends on thermal history (represented by broad shaded region). Other lines are guides to the eye. 

As predicted by the Flory-Huggins theory, such a system shows a lower miscibility gap characterized by an upper critical point, at temperature Ta, which depends on both the oil and the amphiphile structure (Figure 3.11a). The critical composition is usually not far from the pure oil side. 

Figure 3.11b shows the lower miscibility gap between some n-alkanes and C6E5 (pentaethylene glycol monohexyl ether). The upper critical temperature Ta increases with increasing hydrocarbon chain length (hydrophobicity). 

The binary water-ethoxylated nonionic system usually includes two distinct miscibility gaps the lower miscibility gap which is generally found below room temperature and which is delimited by an UCT (upper consolute temperature), and the upper miscibility gap which often has, for thermodynamical reasons, the shape of a closed loop and is thus delimited by both UCT and LCT (lower consolute temperature). This last LCT is better known by formulators as the cloud point. ... 

Fig. 3.17. Endothermal symmetrical mixture with a constant heat of mixing. Temperature dependence of the Flory-Huggins parameter (left) and phase diagram showing a lower miscibility gap right)...

If we wish to account for both upper and lower miscibility gaps, we may write in linear approximation... 

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. 4. 8. Phase diagrams for different PS/PB-mixtures, exhibiting lower miscibility gaps, (a) M(PS) = 2250gmol, M(PB) = 2350gmol (b) M(PS) = 3500gmol , M(PB) = 2350gmon (c) M(PS) = 5200gmol , M(PB) = 2350gmol . Data from Roe and Zin [19]...

The miscibility gap becomes progressively more lopsided as n increases. This means that c occurs at lower concentrations and that the tie line coordinates—particularly for the more dilute phase-are lower for large n. 

It is particularly helpful that we can take the Cu-Ni system as an example of the use of successive deposition for preparing alloy films where a miscibility gap exists, and one component can diffuse readily, because this alloy system is also historically important in discussing catalysis by metals. The rate of migration of the copper atoms is much higher than that of the nickel atoms (there is a pronounced Kirkendall effect) and, with polycrystalline specimens, surface diffusion of copper over the nickel crystallites requires a lower activation energy than diffusion into the bulk of the crystallites. Hence, the following model was proposed for the location of the phases in Cu-Ni films (S3), prepared by annealing successively deposited layers at 200°C in vacuum, which was consistent with the experimental data on the work function. 

In the Au-Bi system the compound Au2Bi is stable in a restricted range of temperature only it is formed by a peritectic reaction (371°C) and, at a lower temperature (116°C), it is decomposed according to the eutectoidal reaction Au2Bi — (Au) + (Bi). In the Zn-Te system, finally, we have the congruently melting compound ZnTe. In this system a miscibility gap in the liquid state may also be noticed. 

We can observe that for values of B/RT greater than 2, the curves have two concave upward sections, and points between the concave upward sections have a greater value of G , than the minima, thus showing that two immiscible phases have lower values of G , than a single phase, even though the single phase has a lower value of G , than do the pure components. A more advanced treatment of the miscibility gap can be found in Guggenheim s treatise [13]. 

Note A miscibility gap is observed at temperatures below an upper critical solution temperature (UCST) or above the lower critical solution temperature (LCST). Its location depends on pressure. In the miscibility gap, there are at least two phases coexisting. 

Pb, where retrograde solubility for the solid in equilibrium with the liquid can also occur. As a critical value of n " is approached the liquid forms its own miscibility gap and the diagram then exhibits two forms of liquid invariant reaction, the lower temperature reaction being either eutectic or peritectic, while the higher temperature reaction becomes monotectic. Examples of such systems are Cu-Pb and Cu-Tl. When n becomes even larger, the top of the liquid miscibility gap rises above scale of the graph and there is little solubility of either element in the liquid. Such a diagram is typical of Mg systems such as Mg-Fe or Mg-Mn. 

The existence of these isostructural compounds suggests that solid solutions could be formed between two end members via isomorphous substitution for Fe " by other cations. The likelihood of substitution depends on the similarity of the ionic radii and the valency of the cations (Goldschmidt, 1937). m " is the most suitable cationic species and a radius about 18% higher or lower than that of high-spin Fe " in sixfold coordination can be tolerated. Isomorphous replacement of Fe in Fe oxides by a number of cations has been observed in nature and, more frequently, in the laboratory. As far as is known, however, almost all these solid solutions have broad miscibility gaps, possibly induced by development of structural strain as substitution rises. 

Many minerals show exsolution textures. For these minerals, there is complete solid solution at sufficiently high temperatures, but a miscibility gap at lower temperatures. The alkali feldspar, (Na, K)AlSi30s, is an example. Suppose a roughly homogenous mineral of intermediate composition cools down and into... 

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