Miscibility gap

Figure 1 compares data reduction using the modified UNIQUAC equation with that using the original UNIQUAC equation. The data are those of Boublikova and Lu (1969) for ethanol and n-octane. The dashed line indicates results obtained with the original equation (q = q for ethanol) and the continuous line shows results obtained with the modified equation. The original equation predicts a liquid-liquid miscibility gap, contrary to experiment. The modified UNIQUAC equation, however, represents the alcohol/n-octane system with good accuracy. 

Therefore, the locus of the values ( ) with a vanishing second derivative of A delimits the region of the miscibility gap in which spinodal decomposition occurs. This locus is referred to as the spinodal (figure C2.1.10 (bl). The length scale of the concentration fluctuations at the beginning of the separation process is controlled by... 

Figure 8.2b is a schematic representation of versus X2 for a system which shows a miscibility gap. Any attempt to prepare a mixture between P and Q in composition will result in separation into the two phases P and Q at equilibrium. 

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. 

Gold and gold-based alloys ate used for corrosion-resistant equipment. Gold—platinum alloys, 75 Au-25 Pt or 84 Au-15 Pt-1 Rh, ate used as cmcible material for many molten salts (98). Spinnerets for rayon manufacture ate based on the Au—Pt system which exhibits a broad miscibility gap in the soHd state so that the alloys can be age-hardened. Spinneret alloys contain 30—40% or mote platinum modified by small additions of usually rhodium (99). Either gold or gold—platinum alloys ate used in mpture disks for service with corrosive gases (100). 

Colloidal suspensions are, per definition, mixtures of mesoscopic particles and atomic liquids. What happens if there are several different species of particles mixed in the solvent One can invent several different sorts of mixtures small and large particles, differently charged ones, short and long rods, spheres and rods, and many more. Let us look into the literature. One important question when dealing with systems with several components is whether the species can be mixed or whether there exists a miscibility gap where the components macroscopically phase-separate. 

Of course, LC is not often carried out with neat mobile-phase fluids. As we blend solvents we must pay attention to the phase behavior of the mixtures we produce. This adds complexity to the picture, but the same basic concepts still hold we need to define the region in the phase diagram where we have continuous behavior and only one fluid state. For a two-component mixture, the complete phase diagram requires three dimensions, as shown in Figure 7.2. This figure represents a Type I mixture, meaning the two components are miscible as liquids. There are numerous other mixture types (21), many with miscibility gaps between the components, but for our purposes the Type I mixture is Sufficient. 

If the miscibility gap of Pri+xl2 is temperature dependent (which they usually are), then Prl2 could be a line phase at, say, ambient temperature, i.e., x = 0. Hence, on quenching or when the annealing process progresses, the metastable i+xh phase must release praseodymium metal. This surplus praseodymium metal can be released from both the 3 a (heavily under-occupied) and 3 b (fully occupied) positions combined with site changes from 3 b to 3 a, or not. These... 

In the case on the left, a composition exists which in which a minimum melting point exists. Again, A and B form a which partially melts to form a + L. However, two forms of a edso exist, a compositional area known as a "miscibility gap", i.e.- " ai and aa". But at higher temperatures, both of these melt into the single phase, a. Finally, we obtain the melt plus a. Note that at about 80% ttj-20% Uj, a melting point minimum is seen where it melts directly instead of forming the two-phase system, a -i- L. 

Miner et al. [50] prepared monodispersed AuPt and PdPt alloys by simultaneous reduction of the corresponding salt mixtures at various molar ratios. They confirmed that AuPt alloys are formed at any atomic ratio, even if the two metals show a broad miscibility gap between 2 and 85wt% Au [51]. The homogeneous character of the various AuPt alloys was proven by means of optical spectra, sedimentation measurements, and electron microscopy. 

Mixtures forming two phases a priori, or at a given miscibility gap, or around the latter, because small temperature or volume changes can cause demixing. 

Figure 3 shows the excess enthalpy v . composition measured for aqueous solutions of n-butanol and water at 30.0 °C Figure 4 shows corresponding results for the amphiphilic side of the miscibility gap at... 

C. Each Figure shows titration data for compositions inside of the miscibility gap (where the "curve" is linear), as well as enthalpies in a single-phase region. Data from the literature are also shown for comparison with the present results (13-161. Table I shows values of the compositions of the aqueous and amphiphilic phases for n-butanol/water at 30.0 and 55.0 °C and for n-butoxyethanol/water at... 

Fig. 1. Variation of free energy of mixing with composition for a binary alloy system possessing a miscibility gap in the range X-Z.

It is also of interest to note that starting from miscibility gap data, attempts have been made to derive thermodynamic properties, i.e., free energies of mixing, and Sundquist (23) summarizes information and discusses a number of binary alloy systems. 

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. 

Finally, with respect to successive evaporation, Pd-Rh films used for CO oxidation (34) are an example of preparing alloy films where a miscibility gap exists and interdiffusion rates are slow. These Pd-Rh films were prepared by depositing layers of palladium and rhodium at 0°C, followed by annealing in 50 Torr hydrogen at 400°C for 21 hr. The apparent surface compositions, evaluated from the CO oxidation rate as described in Section IV, and information on film structure obtained by X-ray diffraction (XRD) are recorded in Table II. 

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