Mixtures regular mixture

Many liquid mixtures behave approximately as regular mixtures [3], which are characterized by... 

They generally exhibit a UCST, To, = bf,B(T)/2R. It must be remembered that only pairs of liquids that mix at least partly behave as regular mixtures and that Eqs. (2.5) and (2.6) cannot be used for the general case of any two liquids, except as a very rough approximation. The value of bA iT) can be estimated from the properties of the individual liquids to be mixed, by invoking their solubility parameters [Eq. (2.1)]. The expression is ... 

Nemst distribution law for regular mixtures and solvents ) it The non-electrolyte solute A in water A... 

Figure 3.9 Conformation of Gibbs free energy curve in various types of binary mixtures. (A) Ideal mixture of components A and B. Standard state adopted is that of pure component at T and P of interest. (B) Regular mixture with complete configurational disorder kJ/mole for 500 < r(K) < 1500. (C) Simple mixture IF = 10 - 0.01 X r(K) (kJ/ mole). (D) Subregular mixture Aq = 10 — 0.01 X T (kJ/mole) = 5 — 0.01 X F (kJ/ mole). Adopting corresponding Margules notation, an equivalent interaction is obtained with IFba = 15 - 0.02 X r(kJ/mole) Bab = 5 (kJ/mole).

Regular Mixtures with Complete Configurational Disorder (Zeroth Approximation)... 

Let us now imagine that we are dealing with a regular mixture (A,B)N with an interaction parameter W = +20 kJ/mole. The Gibbs free energy of mixing at various temperatures will be... 

Figure 3,10 Solvus and spinodal decomposition fields in regular (B) and subregular (D) mixtures. Gibbs free energy of mixing curves are plotted at various T conditions in upper part of figure (A and C, respectively). The critical temperature of unmixing (or consolute temperature ) is the highest T at which unmixing takes place and, in a regular mixture (B), is reached at the point of symmetry.

To reproduce the binary loops of the system Mg2Si04-Fe2Si04 accurately, Fei and Saxena (1986) use a (symmetric) regular mixture model for a-jS-y phases with the following interaction parameters (cf section 3.8.4) = —8.314 kJ/... 

The parameters of the thermodynamic model of Lindsley et al. (1981) are reported in table 5.38. The mixing properties described are those of a regular mixture for orthopyroxene and of a subregular mixture (asymmetric with Mar-... 

In a regular mixture, the activity coefficient of component i is associated with the interaction parameter W through... 

The first term in parentheses on the right side of equation 5.213 is the distribution coefficient (K ), and the second groups activity coefficients related to the mixing behavior of components in the two phases. The equilibrium constant is thus related to the interaction parameters of the two phases at equilibrium. For example, the equilibrium between two regular mixtures is defined as... 

Immiscibility phenomena in silicate melts imply positive deviations from ideality in the mixing process. Ghiorso et al. (1983) developed a mixing model applicable to natural magmas adopting the components listed in table 6.12. Because all components have the same standard state (i.e., pure melt component at the T and P of interest) and the interaction parameters used do not vary with T, we are dealing with a regular mixture of the Zeroth principle (cf sections 2.1 and 3.8.4) ... 

With regular mixtures, in which, therefore, no volume effect occurs on mixing, AF and A G are identical (p A V = o). According to the derivation given above we have in this case ... 

The quaternary solid solution GaxIni tNy Si , can be considered as a regular mixture of four binary compounds GaN, GaAs, InN and InAs in respective proportions [4], Chemical reactions governing the growth of GaJni tNy. S j, layer and the evaporation of main elements from its surface are the following ... 

This energy equation is a mean-field description of all binary regular mixtures regular solutions, polymer solutions, and polymer blends. 

The opposite case where the energy dominates is found at r=0 K. because the entropic contribution vanishes. The free energy only has an energetic part given, for example, by Eq. (4.22) for regular mixtures. Differentiating Eq. (4.22) twice with respect to composition determines whether the blend is locally stable at 0 K... 

To compare the excess Gibbs function of mixtures of carbon tetrachloride and cyclohexane with a simple formula for regular mixtures. 

Here 6, = FitOi is the monolayer coverage, Fi is the adsorption, n = yo - y is the surface pressure, yo is the surface tension of solvent, n, = coj/too, and coo are the partial molar surface areas of the surfactant and solvent, respectively, bi is the adsorption constant, Cj is the surfactants concentration in the solution bulk. The Frumkin parameters ai and a2 represent the interactions of components 1 and 2 with the solvent, while the parameter ai2 accounts for interactions between the two surfactants 1 and 2 in the ternary regular mixture (see Eq. 2.32) a,=HJ,/RT aj=HJ2/RT a,2=(Ho,+Ho2-HJj)/2RT, where Hy=A,jRT. Choosing the dividing surface after Lucassen-Reynders (cf. Chapter 2), one can eliminate the contributions from the entropic non-ideality of the solvent, thus reducing Eq. (3.27) to a much simpler form... 

The term athermal mixtures refers to those in which the heat of mixing A i H is very small but S differs considerably from zero, for example, polymer solutions. In regular mixtures differs considerably from zero but S is negligible, for example, mixtures of highly polar low-molecular substances such as nitriles/esters. 

Mixtures that obey (5.6.1) and (5.6.7)-(5.6.9) are variously called simple mixtures, symmetric mixtures, or sometimes regular mixtures (but this last is a misnomer). We follow Rowlinson and Swinton [13] and call them quadratic mixtures, because for such mixtures all the excess properties are parabolic in a mole fraction Xj. 

Note also that the same molecule can belong to different species at different times. This is quite different from a regular mixture having a fixed composition but similar to a mixture of inter-converting molecules at equilibrium. 

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