Volume, excess of mixing

Conversion of solubilities from thex-scale to the mol dm-3 scale, c, and vice versa requires knowledge of the volume change on mixing the components (the excess volume of mixing, VE). If this is ignored, then the approximate relationships ... 

The NR/PS is of more interest here because of its similarity to poly-butadiene/PS and polyisoprene/PS which are the pairs most widely studied in block copolymer systems. No excess volume of mixing is predicted for this pair, the v values, 1.172 for NR and 1.152 for PS, changing to 1.162 for the mixture at Wi = 0.5. Although Ah, fv and As, fv fail to cancel each other completely, the net sum of the two is still only about 10% of the total A, indicating that here too the contact term is the most important effect giving rise to the incompatibility of the pair. 

If the excess volume of mixing is zero, then all the volume fraction multipliers cancel out in these forms, because then (f)i = (1 — 2)- Though the present derivation should provide a basis for doing better, this assumption of zero volume of mixing will be our second assumption here. Then Eqs. (4.44) describe a scaling of second virial coefficients that is natural even though special ... 

In comparison, ab initio calculations of the electronic stmcture of Fe-S and Fe-Si compounds by Sherman (1997) indicate that due to large excess volumes of mixing as little as 2-8 wt.% of sulfur is enough to account for the density deficit in the core. Alfe et al. (1999b) estimated that 9-11 wt.% oxygen is required to explain the density deficit. 

Figure 13. Lattice parameters of the CaTiOs-SrTiOs solid solution at room temperature (top), expressed in terms of the reduced pseudocubic unit cell. Open symbols data of Qin et al. (2000) filled symbols data of Ball et al. (1998). In the cubic field, data of Ball et al. ate shown by filled circles and data of Mitsui and Westphal (1961) are shown by stars. The curve for includes a symmetric excess volume of mixing. Spontaneous strains (bottom) calculated from lattice parameter data of Mitsui and Westphal (1961), Ball et al. (1998) and Qin et al. (2000) (crosses, filled symbols, open symbols, respectively). From Carpenter et al. (2000b).

Finally, the excess volume of mixing is obtained from the pressure derivatives of the activity coefficients ... 

In addition, it is generally observed for mixtures of aliphatic hydrocarbons that if there is a difference in molecular size, a negative excess volume of mixing results (21). For the lecithin-cholesterol mixtures molecular area decreases (Figure 7), but it does not decrease with the mixture of the lecithins which forms an ideal mixture. Thus, the mixing of cholesterol and lecithin monolayers is consistent with bulk hydrocarbon mixtures with respect to both positive excess heats and negative excess volumes of mixing. 

It is well known that volume changes on mixing are likely to occur in polymer-solvent systems, and both theoretical and experimental studies have been devoted to this subject (26,27,28). When the volumes of the components are not strictly additive, both theoretical and phenomenological approaches include an excess volume term in the thermodynamic equations for the system. These treatments, however, concern polymeric solutions in equilibrium, i.e. the mixture is liquid or rubbery, not glassy. For solutions in the glassy state, no theoretical descriptions of the excess volume of mixing seems to be available up to date. 

Or, in the absence of excess volumes of mixing, cognizing that = i i (V. being a molar volume), and replacing with equation 40 becomes ... 

Excess Volume of Mix. % Increased Octane, (R + M)/2 Increased Beef Weight Gain With DDG. %... 

Scatchard Hlldebrand regular-solution activity coefficients. Hildebrand (1929) defined a regular solution as the mixture in which components mix with no excess entropy provided there is no volume change on mixing. Scatchard in an independent work arrived at the same conclusion. The definition of regular solutions (Hildebrand and Scott, 1950) is in line with van Laar s assumption that the excess entropy and the excess volume of mixing are negligible. Scatchard and Hildebrand used an approach different from van Laar s to calculate G. They defined parameter C as... 

The effect could be equally well described in terms of a large, negative excess volume of mixing V" = V — (1 - - XjKj. 

The approximation is due to neglecting the relatively small excess volume of mixing, V, of the two components. For water-miscible solvents, the maximal value of C3 is its value for the neat solvent, the reciprocal of its molar volume Sneat = 10(X)/(ys /Cm -mOl" ). 

Incompressible Flory mean-field theory is recovered from Eqs. (5.4) and (5.5) if one assumes the following (i) no excess volume of mixing (ii) a blend composition-independent total packing fraction (iii) the... 

Volume fractions imply a temperature dependence and, as they are defined in eqrration (35), neglect excess volumes of mixing and, very often, the densities of the polymer in the state of the solution are not known correctly. However, volttme fractiorrs can be calculated without the exact knowledge of the polymer molar mass (or its averages). 

SHA Sharma, S.C., Syngal, M., and Sharma, V.K., Enthalpies and excess volumes of mixing of poly(tetramethylene oxide) fractions with tetrachloromethane, 1,2-dichloroethane and 1,1,1 -trichloroethane at 313.15 K, Indian J. Chem., 26A, 285, 1987. 

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