Binary mixture thermodynamic stability

Thermodynamic stability. Let us consider a liquid binary mixture of two species, a and b, crystallizing to a solid solution. Let G be the free enthalpy (Gibbs) function of each phase, either solid or liquid. Calculate the change AG in molar free enthalpy when a liquid of molar composition XUqb crystallizes to a solid of molar composition... 

A promising way to create LLC systems with sufficient stability is the use of immiscible ternary mixtures to create what is called a dynamic (or solvent-generated ) LLC system. The principle of such a phase system is illustrated in figure 3.9. This figure shows an example of a thermodynamic phase diagram of a mixture of three components (A, B and C). Both the binary mixtures A + B and A + C are miscible in all proportions. 

Earlier versions (12-13,22) of this new mixture theory have predicted and reproduced experimental trends in various thermodynamic and molecular ordering properties [such as phase transition temperatures, phase stabilities (including of the N LC phase and the I liquid phase), curvatures of lines of coexisting phases, and orientational order P2] in binary mixtures as a function of T, P, system composition, and molecule chemical structures. 

As shown in section C2,6,6.2. hard-sphere suspensions already show a rich phase behaviour. This is even more the case when binary mixtures of hard spheres are considered. First, we will mention the case of moderate size ratios, around 0.6. At low concentrations these form a mixed fluid phase. On increasing the overall concentration of mixtures, however, binary crystals of type AB2 and ABj were observed (where A represents the larger spheres), in addition to pure A or B crystals [105. 106]. An example of an AB2 structure is shown in figme C2.6.11. Computer simulations confirmed the thermodynamic stability of the structures that were observed [107. 108]. 

The question of polymer blend miscibility derives out of the nineteenth century development of thermodynamics and studies in the same periodic of binary mixtures of low molecular weight liquids. From a thermodynamic viewpoint, Gibbs (23) formulated the stability of multiphase systems in terms of the quantity G defined by (in modem notation (24))... 

Thermodynamic Stability in Binary Mixtures Via Energy Minimization... 

The thermodynamic stability of a binary liquid mixture can be characterized by the condition [1-3]... 

An optimisation framework to identify liquid-liquid separation in binary mixtures of n-alkanes is presented. A general thermodynamic criterion, based on the concept of stability limits, is introduced to identify the largest short-chain n-alkane which is immiscible in a given long-chain polymer-like n-alkane. 

The thermodynamic condition for stability towards composition fluctuations in a binary mixture is ... 

In theory, if composition of the mixture is known, then calculation of any characteristic property of the multi-component mixture can be performed by the classical physical and chemical analysis methods. For binary liquid system, it is possible only if all chemical forms (including all possible associates), their stoichiometry, stability constants, and their individual physical and chemical properties are well determined. A large volume of correct quantitative thermodynamic data required for these calculations is not available. Due to these obstacles, data on permittivity, viscosity and other macro-properties of mixed solvents with interacting components are obtained by empirical means. Data on empirical physical properties of liquid systems can be found in published handbooks.Principles of characteristic changes due to the compositional change of liquid mixtures with interacting components are discussed here. Assessment of nature of such interactions can only be made after evaluation of the equilibrium constant (energy) of such interactions between solvents. 

Figure 12.1 Gibbs free energy functions (left column) and phase diagrams (right column) for binary systems with different thermodynamic properties of the co-crystal former B. The free energy functions are plotted for the separate liquid phases of A and B ((A)iiq + (B)iiq) as the reference state (AG = 0). Relative to this, the 1 1 mixture of liquid A and B ((A + B)iiq) is stabilized by 2Rrin(0.5) as a result of the mixing entropy. The melting points of A and AB are fixed and indicated by open circles, whereas the variable melting point of B is indicated by a solid circle. The liquidus curves in the phase diagrams are calculated based on the assumption of ideal behavior (Equations (12.1) to (12.3)).

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