Phase transition complete miscibility

Even when complete miscibility is possible in the solid state, ordered structures will be favored at suitable compositions if the atoms have different sizes. For example copper atoms are smaller than gold atoms (radii 127.8 and 144.2 pm) copper and gold form mixed crystals of any composition, but ordered alloys are formed with the compositions AuCu and AuCu3 (Fig. 15.1). The degree of order is temperature dependent with increasing temperatures the order decreases continuously. Therefore, there is no phase transition with a well-defined transition temperature. This can be seen in the temperature dependence of the specific heat (Fig. 15.2). Because of the form of the curve, this kind of order-disorder transformation is also called a A type transformation it is observed in many solid-state transformations. 

Differentiation between ideal miscibility and complete immiscibility is possible by evaluating surface pressure/area isotherms. According to the phase rule of Defay and Crisp 53-67) in a completely immiscible monolayer the surface pressures observed for phase transitions or collapse points are equal to those of the pure components. This case of a completely immiscible monolayer is schematically illustrated in Fig. 29 (left). In a completely miscible lipid monolayer these surface pressures vary with different molar ratios of the lipid components. 

There is a large body of experimental work on ternary systems of the type salt + water + organic cosolvent. In many cases the binary water + organic solvent subsystems show reentrant phase transitions, which means that there is more than one critical point. Well-known examples are closed miscibility loops that possess both a LCST and a UCST. Addition of salts may lead to an expansion or shrinking of these loops, or may even generate a loop in a completely miscible binary mixture. By judicious choice of the salt concentration, one can then achieve very special critical states, where two or even more critical points coincide [90, 160,161]. This leads to very peculiar critical behavior—for example, a doubling of the critical exponent y. We shall not discuss these aspects here in detail, but refer to a comprehensive review of reentrant phase transitions [90], We note, however, that for reentrant phase transitions one has to redefine the reduced temperature T, because near a given critical point the system s behavior is also affected by the existence of the second critical point. An improper treatment of these issues will obscure results on criticality. 

A very important aspect of phase behavior in a system consisting of a volatile organic solvent, such as ethanol, and a supercritical fluid, such as CO2, is that the mixture critical pressure coincides with the liquid vapor phase transition. This means that above a single phase exists for all solvent compositions, whereas the (ethanol-rich and C02-rich) two-phase region lies below this curve. This fact has important implications for the mass transfer and precipitation mechanisms. Complete miscibility of fluids above P means that there is no defined or stable vapor liquid or liquid liquid interface, and the surface tension is reduced to zero and then thermodynamically becomes... 

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. 

The UC2 phase is stable above about 1500°C and undergoes phase transition from a (tetragonal CaCj type) to p phase (cubic KCN type) at 1765°C (92). The C/U ratio of the UCj phase never reaches 2.00, the ratio being usually near 1.90 in coexistence with graphite (93). There exists a miscibility gap between UC. and UC2 below 2050°C, while above this temperature a complete solid solution is formed, as described above. 

The most important transition metal nitride, TiN, has complete miscibility with ZrN, HfN, VN, and NbN at high temperatures but miscibility gaps occur upon lowering the temperature [36]. The two-phase mixtures which form upon demixing have increased hardness and are thus interesting for commercial applications. 

SMP based on miscible blends of semicrystalline polymer/amorphous polymer was reported by the Mather research group, which included semicrystalline polymer/amorphous polymer such as polylactide (PLA)/poly vinylacetate (PVAc) blend [21,22], poly(vinylidene fluoride) (PVDF)/PVAc blend [23], and PVDF/polymethyl methacrylate (PMMA) blend [23]. These polymer blends are completely miscible at all compositions with a single, sharp glass transition temperature, while crystallization of PLA or PVDF is partially maintained and the degree of crystallinity, which controls the rubbery stiffness and the elasticity, can be tuned by the blend ratios. Tg of the blends are the critical temperatures for triggering shape recovery, while the crystalline phase of the semicrystalline PLA and PVDF serves well as a physical cross-linking site for elastic deformation above Tg, while still below T ,. 

Another miscible semicrystalline polymer/amorphous polymer blend SMP is a polyethylene oxide (PEO)/novolac-type phenolic resin blend [24]. The blend was found to be completely miscible in the amorphous phase when the phenolic content is up to 30 wt%, and the crystalline melting temperature (T,f) of the PEO phase working as a transition temperature can be tuned. 

Fig. 4.2 Miscibility diagram Ref and Inv mean the reference compound with well known phase sequence and unknown compound to be investigated. Starting with molar content c = 1 and proceeding to the left while measuring phase transition temperatures one finally arrives at c = 0 with complete phase diagram, therefore, having information about the unknown compound...

Miscibility in polymer blends has been studied by both theoreticians and experimentalists. The number of polymer blend systems that have been found to be thermodynamically miscible has increased in the past 20 years. Systems have also been found to exhibit the upper or lower critical solution temperatures. So complete miscibility is found only in limited temperature and composition ranges. A large number of polymer pairs form two-phase blends. This is consistent with the small entropy of mixing that can be expected of high polymers. These blends are characterized by opacity, distinct glass transition temperatures, and deteriorated mechanical properties. Some two-phase blends have been made into composites with improved mechanical properties. Often, incompatibility is the general rule, and miscibility or even partial miscibility is the exception. 

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