Regular solution model mixing entropy

The regular solution model provides no explanation of this excess entropy, nor can it account for a volume change on mixing. To study these problems we need a more detailed model of the liquid state which will enable us to relate these excess quantities to intermolecular forces. 

In ideal solutions, the pure solute and solvent mix with no heat of mixing, AH"" = 0, and the heat of dissolution is numerically equal to the heat of fusion. However, only a limited number of systems form ideal solutions. A less restrictive assumption is that the solution is represented by a regular solution model. This model assumes the heat of mixing is nonzero, but independent of solution composition and temperature (i.e., AH= constant) (Hildebrand and Scott 1950). For a regular solution the differential entropy of mixing is also assumed ideal (i.e., AS = —R In x). 

We modify the conventional regular solution model [5] of low-molecular weight molecules to apply it to solutions of long chain molecules in which the molecular weight of the solute molecules is much larger than that of the solvent molecules. The entropy of mixing decreases with the molecular weight of polymers due to the reduction of the freedom in the translational motion of the molecules. 

A special variant is the regular solution model . Here, the entropy of mixing is supposed to be just the ideal entropy of mixing, = —R[XAlnxA + (1 —... 

If the second term in the configurational entropy of mixing, eq. (9.42), is zero, the quasi-chemical model reduces to the regular solution approximation. Here, Aab is given by (eq. (9.21). If in addition yAB =0the ideal solution model results. 

The mixing entropy of a liquid can be calculated using the model of a regular solution ... 

In the model of regular solution (or its extension to polymer mixtures), the Aj2 term is purely enthalpic and Ajj is thus a true constant. In a real mixture, Aj is a function of T, p, and the composition of the mixture, but the utility of Eq. (1) relies on the fact that the dependence of Ajj on these variables is only moderate in most cases. Only in the case of the systems exhibiting LCST behavior is the temperature dependence of Aj2 appreciable. The strong concentration dependence of Xi2> often found with dilute polymer solutions, is not encountered with polymer mixtures. This is mainly due to the fact that the mean-field approximation, as stated earlier, is fairly satisfactory and the entropy of mixing two polymeric components is reasonably well represented by the combinatory entropy term. 

We ha c developed a model for the thermodynamic properties of ideal and regular solutions. Two components A and B will tend to mix because of the favorable entropy resulting from the many different ways of interspersing A and B particles. The degree of mixing also depends on w hether the. 46 attractions are stronger or weaker than the AA and BB attractions. In the next chapters we will apply this model to the properties of solutions. 

Equation (5.1) includes only the ideal, combinatorial entropy of mixing and the simplest conceivable regular solution type estimate of the enthalpy of mixing based on completely random mixing of monomers mm ( ) = 1 in the liquid state language i referred to as the bare chi parameter since it ignores all aspects of polymer architecture and Interchain nonrandom correlations. For these reasons, the model blend for which Eq. (5.1) is thought to be most appropriate for is an interaction and structurally symmetric polymer mixture. The latter is defined such that the only difference between A and B chains is a v (r) tall potential, which favors phase separation at low temperatures. The closest real system to this idealized mixture is an isotopic blend, where the A and B... 

Statistical thermodynamics can be used to calculate both the enthalpic and the entropic contributions to the free energy of mixing by means of statistical calculations. Attempts were first made to apply a theory appropriate to simple regular solutions, the Hildebrand model, to the case of macromolecular solutions. This model does not adequately account for the specific behavior of polymer solutions primarily because the entropy of mixing in a polymer solution is strongly affected by the connectivity of the polymer—that is, by the existence of covalent bonds between the repetitive units. 

One model that has found applicability in the lipids area is the regular solution theory developed by Hildebrand and Scott [9] and Scatchard [10]. Incorporating a partial molar entropy of mixing term [11-14] into the regular solution theory yields the following expression for the activity of a component in a liquid mixture ... 

The entropy of mixing of many real solutions will deviate considerably from the ideal entropy of mixing. However, accurate data are available only in a few cases. The simplest model to account for a non-ideal entropy of mixing is the quasi-regular model, where the excess Gibbs energy of mixing is expressed as... 

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