Binary mixture symmetric

Similar calculations have been carried out for an equimolar binary mixture of associating Lennard-Jones particles with spherically symmetric associative potential [173]. The interaction between similar species is given by Eq. (87), whereas the interaction between different species is chosen in the form... 

To illustrate, let us consider a simple, symmetric binary mixture at some fixed temperature and 1-atm pressure. For this liquid mixture, let us assume that... 

We consider a binary liquid mixture of components 1 and 3 to be consistent with our previous notation, we reserve the subscript 2 for the gaseous component. Components 1 and 3 are completely miscible at room temperature the (upper) critical solution temperature Tc is far below room temperature, as indicated by the lower curve in Fig. 27. Suppose now that we dissolve a small amount of component 2 in the binary mixture what happens to the critical solution temperature This question was considered by Prigogine (P14), who assumed that for any binary pair which can be formed from the three components 1, 2 and 3, the excess Gibbs energy (symmetric convention) is given by... 

Let us consider a dynamically symmetric binary mixture described by the scalar order parameter field < )(r) that gives the local volume fraction of component A at point r. The order parameter < )(r) should satisfy the local conservation law, which can be written as a continuity equation [143] ... 

For these experiments, a binary mixture of sieved fractions of 150-250 pm (nominally 200 pm) and 710-840 pm (nominally 775 pm) glass beads was used. A symmetrical initial condition (top-to-bottom loading) is implemented. The blender is run at constant rotation rate a segregation pattern was assumed to be stable when it did not discernibly change for 100 revolutions. In many pharmaceutical operations, the mixing time is on the order of 100 500 revolutions, and experiments are run with regard to this timeframe. 

While the half-width w1/2 is related to the maximum slope, only the interfacial width w also takes into account the relevant concentration range (see Fig. 2). An analytical expression of the equilibrium profile < )(z) may be obtained only near the critical point of the symmetric binary mixture (NA=NB) with ( -independent interaction parameter % [49] ... 

Fig. 46. Schematic illustration of the interfacial brush formed by the binary mixture of short symmetric (S) and long asymmetric (L) copolymers with identical anchoring blocks. Depicted situation corresponds to Figs. 44 and 45. Short and long components of the mixed brush are characterized by mean inter-anchor spacings Xs1/2 and XL1/2 or equivalently by respective interfacial coverages os and oL...

Parameter will henceforth be referred to as the asymmetry of the model mixture, where xb > 1 characterizes a binary mixture in which the formation of B-B pairs is energetically favored, whereas for XB < L this is the case for A-A pairs. For the special case xb 1 the asymmetric mixture degenerates to the symmetric case previously studied in Refs. [84] and [85]. In addition, we define the selectivity of the solid surfaces by specifying Xs in Eq. (4.125d) in a fashion similar to xb in Eq. (4.125c). Hence, the parameter space of our model is spanned by the set , aBi s, Xb> X s -... 

In the limit ab = 10, the symmetric binary mixture degenerates to a pure fluid. In this case Tcep —> 0 and the A-linc becomes formally indistinguishable from the /r-axis (and therefore physically meaningless). The remaining coexistence line /Xxb = -3 = /icb (i e-, the phase diagram) involving gas (G) and liquid phases (L) becomes parallel with the T-axis and ends at the critical point where Tcb = as expected for the bulk lattice gas [16] [see, for example, Fig. 4.12(a)]. 

The Porter equation is the simplest realistic expression for gE- It is appropriste for "symmetrical binary mixtures shewing small deviations from ideality, for example, the acetone-methanol system depicted in Fig. 1.4-1,... 

Few if any binary mixtures are exactly symmetrical around x = 1/2, and phase diagrams like that sketched in figure A2.5.5(c) are typical. In particular one can write for mixtures of molecules of different size (different molar volumes F° and F °g) the approximate equation... 

Dioxane is a cyclic diether forming a six-membered ring [20]. Thus it is a nearly nonpolar symmetric molecule. 1,4-Dioxane is an extraordinary solvent, capable of solubilizing most organic compounds, and water in all proportions, and many inorganic compounds. The self-diffusion coefficient of dioxane is 1.1 x 10 cm /s, about half that of a water molecule. The effective diameter of dioxane is 5.5 A - about twice that of a water molecule. One should not forget that a water-dioxane mixture narrowly avoids a lower critical consolute point. However, the effects of criticality are reflected in the values of ffie mutual diffusion coefficient and viscosity. Note that binary mixtures are often chosen so that they are mixable (do not phase separate). Thus, the two components interact attractively and strongly. 

An important point to note from Figures 5.2-5.4 is that g is a weak function of temperature and is more nearly symmetric in composition than either or s. These features are common to many binary mixtures the nonidealities, as functions of composition, are more uniform in g than in either of the separate contributions, and s. ... 

We caution that a binary mixture may obey the Porter equation (5.6.1) but still not be a quadratic mixture that is, may be parabolic in composition but and may not be. An example is the hexane-cydohexane mixture shown in Figure 5.2. Such behavior occurs because as)unmetries in and approximately cancel when they combine via the Legendre transform (5.2.18) to form g. Such cancellations are the norm rather than the exception. To say this another way, the Redlich-Kister expansion for (5.6.3) is usually dominated by the first term, which is symmetric in Xj and Xi-However, in the analogous expansions for and s, asymmetric terms are frequently important. 

C. Recent Fluid Mixture Theory.—The system CF4 + CH4 is at present unique among binary mixtures because (i) it is composed of simple non-polar spherically symmetric molecules, (ii) the system exhibits considerable deviations from ideality, and (iii) and x known explicitly and with high accuracy. G and F have been measured with high precision and (and hence TS ) can be estimated with somewhat lower precision. This binary system has therefore been used to assess the merits of various rival statistical theories of fluid mixtures. Some of these theoretical predictions are shown in Table 3. It is seen... 

It is well known that coexistence curves for binary mixtures are frequently more nearly symmetric in a T, representation than in a T, x representation." Simon, Fannin, and Knobler found, in analysing their vapour-pressure measurements on the system CH4 + CF4, that plots of A vs. [where their definition of takes the molar volumes in equation (28) as those of the pure... 

---