Systems, binary, critical phenomena

In solutions, depending on the temperature, the various components can segregate into separate phases. For simplicity, we shall only consider binary mixtures. The phenomenon is similar to the critical phenomenon in a liquid-vapor transition in that across one range of temperature the system is in one homogeneous phase (solution) but across an another range of temperature the system becomes unstable and the two components separate into two phases. The critical temperature that separates these two ranges depends on the composition of the mixture. This can happen in three ways, as illustrated by the following examples. 

As mentioned previously (see Section 1.3.5) the binary M-X system shows a phase separation phenomenon in which the phase decomposes into two phases, having lower and higher concentrations of vacancies, below the critical temperature f, under the condition < 0, i.e. there is an attractive force between vacancies. In Section 1.3.5 it was not possible to refer to the details of those structures, because the model was less than simple. In any case, it can be safely said that if s < 0, vacancies cluster at low temperatures (from a thermodynamic point of view). Here let us briefly review the non-stoichiometry of 3d transition metal monoxides Mj- O, and then discuss the Fej system as a typical example of the clustering of vacancies in detail. 

Figure 5.2. Critical solution phenomenon in a binary system.

The intensity of light scattered from a fluid system increases enormously, and the fluid takes on a cloudy or opalescent appearance as the gas-liquid critical point is approached. In binary solutions the same phenomenon is observed as the critical consolute point is approached. This phenomenon is called critical opalescence.31 It is due to the long-range spatial correlations that exist between molecules in the vicinity of critical points. In this section we explore the underlying physical mechanism for this phenomenon in one-component fluids. The extension to binary or ternary solutions is not presented but some references are given. 

The cosolvency phenomenon was discovered in 1920 s experimentally for cellulose nitrate solution systems. Thereafter cosolvency has been observed for numerous polymer/mixed solvent systems. Polystyrene (PS) and polymethylmethacrylate (PMMA) are undoubtedly the most studied polymeric solutes in mixed solvents. Horta et al. have developed a theoretical expression to calculate a coefficient expressing quantitatively flie cosolvent power of a mixture (dTydx)o, where T,. is the critical temperature of the system and x is the mole fraction of hquid 2 in the solvent mixture, and subscript zero means x—>0. This derivative expresses the initial slope of the critical line as a function of solvent composition (Figure 5.4.1). Large negative values of (dT/dx) are the characteristic feature of the powerful cosolvent systems reported. The theoretical expression developed for (dT dx)o has been written in terms of the interaction parameters for the binary systems ... 

Early studies by Bates et al. [106,107] and by Sakurai et al. [87] reveal that these systems exhibit an upper critical solution temperature (UCST), i.e., undergo phase separation upon cooling. Subsequent investigations have focused on the combined influence of isotope effects and the blend microstructure on the miscibility patterns of these random copolymer binary mixtures. In particular, a series of systematic SANS experiments by Jinnai et al. [53] demonstrate that the UCST phase behavior that had previously been observed for these systems [87,106,107] remarkably converts to a lower critical solution temperature (LCST) phase separation with an increase in the vinyl content of the HPB component when the vinyl content of the DPB component remains flxed. This phenomenon cannot be explained by the traditional extension of FH theory to random copolymers since this theory is derived under the assumption that the individual Xap are of purely energetic origin. Thus, the FH random copolymer theory [88] is capable, at most, of predicting the conversion of a UCST phase separation system into a completly miscible system. 

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