Behavior of Binary Mixtures

Process engineering often deals with multicomponent mixtures. The behavior of multicomponent mixtures in general does not differ from the behavior of two component mixtures, which are technically and practically easier to describe. Therefore, it is advantageous to acquire the basics for the behavior of binary systems. How the equations can be transferred to fit multicomponent mixtures is shown in Chap. 5. 

A closed, binary two-phase system is in thermorfynamic equilibrium if the entropy 5 of the whole system has reached its rrraximrrm. For two-phase systerrrs of liquid (L) and vapor (G ) the already merrtioned conditiorrs for equilibria are 

Description of eqtrihbria becomes particrrlarly easy when dealing with dilute solu-tiorrs. A solrrtion is cortsidered to be dilute if there is just one molecrrle of dissolved srrbstarrce in about 100 or more molecrrles of solvent. The dissolved molecule is then orrly irtfluenced by the interaction energy with the solvent molecrrles, but not by the irrteraction energy with molecrrles of its own kind. Therefore, the assumption of a dilute solution is orrly vahd for a mole fraction of the dissolved substance smaller than 0.01. 

Mole fraction is one possible measure for the composition of a rrrixtrrre. It relates the amoimt of srrbstance of one component to the total amormt of srrbstances in the system. In analogy, the mass fraction is defined. Other measrrres for the composition of a mixtirre (mass or molar loading) are given in Table 2.1-1. In addition, this table also gives the rules of conversion between these measures. The term concentration c or c shall only be used if the amoimt of a substance is related to the volume. 

In a gas, every gas component aims to disperse into the whole space available, and dissolved components in a mixture of hquids aim to disperse all over the liquid. 

---

To see whether or not knowledge of the behavior of binary mixtures of chemically homogeneous copolymers can be applied to natural co-... 

Chapter 14 describes the phase behavior of binary mixtures. It begins with a discussion of (vapor -l- liquid) phase equilibria, followed by a description of (liquid + liquid) phase equilibria. (Fluid + fluid) phase equilibria extends this description into the supercritical region, where the five fundamental types of (fluid + fluid) phase diagrams are described. Examples of (solid + liquid) phase diagrams are presented that demonstrate the wide variety of systems that are observed. Of interest is the combination of (liquid + liquid) and (solid 4- liquid) equilibria into a single phase diagram, where a quadruple point is described. 

Table 3B.1 The performance of three equations of state for predicting the phase behavior of binary mixtures of hydrogen sulfide and other components in the acid gas mixture.

Peritectics are observed in mixed saturated-unsaturated systems. Figure 17.12(c) is a theoretical peritectic phase diagram. Several authors have reported mixtures of SOS and SOO to exhibit peritectic behavior (Rossell 1976). The peritectic mixture contained 24%SOS melted at 27.4°C, determined using differential thermal analysis. Table 17.4 list common phase behaviors of binary mixtures for different triacyl-glycerides adapted from Rossell (1967). 

Table 17.4. Phase behavior of binary mixtures of triacylglycerides adapted from Rossell (1967). (M) represents monotectic phase behavior, (E) represents euteetie phase behavior and (P) represents peritectic phase behavior.

TABLE 7. Phase Behavior of Binary Mixtures of Saturated-unsaturated Diacid and Triacid TAGs. 

Chatteijee S., Debenedetti P. (2006) Fluid-phase behavior of binary mixtures in which one component can have two critical points, J. Chem. Phys. 124, 154503. 

The phase behavior of single-component systems has been discussed as part of thepVT relationship presented in Section 4.2.1. Examiifing the phase behavior of mixtures, we observe that, with mixtures, phase behavior remains one facet of the pVT relationship. But a new phenomenon is encountered with mixtures phases at equilibrium are generally of different compositions. These mixtures show a great variety of phase behavior that can often be exploited to make separations. We examine in broad terms the qualitative features of the phase behavior of binary mixtures of various types. Experience has shown a wealth of phenomena displayed by binary mixtures. 

Tbe basic scheme for modeling the phase behavior of binary mixtures is first to input the pure component characteristic parameters Tc, Pc, and to, and then determine the binary mixture parameters, kj. and iij., by fitting data such as pressure-composition isotherms. Normally k.. and tIj. are expected to be lie between 0.200. If the two species are close in chemical ize and intermolecular potential, the binary mixture parameters will have values very close to zero. In certain cases a small value of either of these two parameters can have a large influence on the calculated results. 

Sections 9.3-9.S present the common phase behavior of binary mixtures 9.3 describes vapor-liquid, liquid-liquid, and vapor-liquid-liquid equilibria at low pressures 9.4 considers solid-fluid equilibria and 9.5 discusses common high-pressure fluid-phase equilibria. Then 9.6 briefly describes the basic vapor-liquid and liquid-liquid equilibria that can occur in ternary mixtures. This chapter describes many apparently different phase behaviors, and so we try to show when those differences are more apparent than real. The organization is intended to bring out underlying similarities, thereby reducing the number of different things to be learned. 

Second, recall the many analogies that occur in the phase behavior of binary mixtures. For example, many features that occur on binary vapor-liquid phase diagrams have counterparts on liquid-solid diagrams. Some of those equivalent features are listed in Table 9.2. Furthermore, such equivalences include not only the kinds of behavior but may also extend to the general shapes of two-phase lines. That is, many... 

D.M. Baek, C.D. Han, Rheological behavior of binary-mixtures of a block copolymer and a homopolymer, Macromolecules 25 (1992) 3706-3714. 

Kiselev, S.B. (1997) Prediction of the thermodynamic properties and the phase behavior of binary mixtures in the extended critical region. Fluid Phase Equilibria 128, 1-28. 

The comparison of the compressional behavior of binary mixtures of DPPC and CnCONH-j8-CD with those of... 

Nockemann, P., Binnemans, K., Thijs, B., Parac-Vogt, T.N., Merz, K., Mudring, A.-V, Menon, P.C., Rajesh, R.N., Cordoyiannis, G., Thoen, J., Leys, J. and Glorieux, C., Temperature-driven mixing-demixing behavior of binary mixtures of the ionic liquid choline bis(trifluoromethylsulfonyl)imide and water, J. Phys. Chem. B 113 (5), 1429-1437 (2009). 

From another point of view, the determination of the thermodynamic parameters gives valuable information about the donor properties of the solvents and the behavior of binary mixtures. A particularly interesting... 

Illian et al. [82] studied the pressure effect on the phase transition behavior of binary mixtures of terminally polar and nonpolar components which exhibit induced SmA phases. The re-entrant N phase is stabilized by increasing pressure and at about 101 MPa the SmA-re-entrant N phase boundary meets the N-SmA one. At higher pressures a nematic gap appears and finally the SmA phase on the polar side of the temperature-mole fraction diagram (175 MPa) disappears. 

A bicritical point is a point in the temperature-concentration or pressure-temperature plane at which two second-order phase boundaries and one first-order phase boundary meet. In order to find such a bicritical point in the pressure-temperature plane Rahr et al. [105] studied the pressure-temperature phase behavior of binary mixtures of4-(4- -butyloxybenzoyloxy)-4 -nitroazo-benzene and 4-(4- -nonyloxybenzoyloxy)-4 -cyanoazobenzene. From the p-T phase diagrams of the pure components which are also presented a bicritical behavior of their mixtures can be expected. Two mixtures with molar fractions of about 0.80 for the cyano component show an abrupt change of... 

YEL Yelash, L.V. and Kraska, T., The global phase behavior of binary mixtures of chain molecules. Theory and application, Phys. Chem. Chem. Phys., 1, 4315, 1999. 

We examine the prediction of the volumetric behavior of binary mixtures in the next two Examples 11.5 and 11.6 and the evaluation of interaction coefficients, in Example 11.7. We proceed, then, with some general comments on the estimation of mixture properties, followed by the discussion of fiigacities in mixtures. 

---