Regular solutions definition

Solubility parameters are generally tabulated, together with the corresponding liquid molar volumes, only at 25°C. Although solubility parameters are themselves temperature-dependent, the combination of quantities in Eq. 70 is not. Differentiating Eq. 70 with respect to temperature gives — the excess entropy, a quantity which has been assumed to be zero in accord with the definition of a regular solution. Thus only data at 25°C are needed. Solubility parameters may be... 

The regular solution approximation is introduced by assuming definition) that the excess entropy of mixing is zero. This requires that the excess free energy equal the excess enthalpy of mixing. For binary mixtures the excess enthalpy of mixing is ordinarily represented by a function of the form... 

Since the Flory interaction parameter, x> was derived by considering only interaction energies between the molecules, it should not contain any entropic contributions and Equation (2D-9) should yield the correct value for the Flory-/ parameter. Unfortunately, x contains not only enthalpic contributions from interaction energies, but also entropic contributions. The solubility parameter includes only interaction energies and by the definition of regular solutions does not include any excess entropy contributions. Blanks and Prausnitz (1964) point out that the Flory / parameter is best calculated from... 

The definition of a hostile effect, proposed earlier, as an adverse interaction between polymer and solvent wherein the chemical and/or physical integrity of the polymer is affected without the resultant formation of a "regular solution" has been clearly shown. The need now arises for an improved method by which hostile effects can be predicted. Therefore, if one employs the generalized rule cited by Seymour (14) that compatabillty or solubility on the molecular level can be expected if 61-62 is less than 1.8H and that the swelling of polymers occurs when 6 -62 is equal to 3.2H (20), then one would expect some interaction between PVC and all of the solvents listed on Table I, with the possible exception of methanol and 1-butanol. 

For many solutions, it is not possible to vary the composition of the components over the whole range of mole fractions. This is obviously true of solutions made up of a solid and a liquid. For these systems it is better to choose a standard state which is based on the properties of a dilute solution. This leads to the definition of an ideally dilute solution. Such a system is easily defined on a molecular basis as one in which the solute molecule only comes in contact with solvent molecules, and never with another solute molecule. In the previous discussion of regular solutions it was concluded that, when the two components are of equal size, the coordination number for the other molecules around a central one is twelve. This suggests that an ideally dilute solution must have a solute mole fraction which is less than 1/13, that is, 0.08. 

By introducing an approximation into Eq. IV. 18, we can gain insight into the formula for the heat of transport. It suffices to use the assumption of regular solution theory that the radial distribution function is independent of composition.4 Under this assumption we may differentiate Eq. IV. 19 (using the definition of partial molecular enthalpy) to obtain expressions for ha/ in terms of thermodynamic quantities. Substituting these into Eq. IV. 18 yields... 

Hildebrand has found experimentally that a large number of binary mixtures show a behavior which can be represented quite well by the laws of regular solutions. A regular solution is, by definition, one in which the partial entropies of the various components have ideal forms. In this section, we discuss some of the properties of regular solutions. 

It is known through Ref. [13], that the value /) is defined by interactions of macromolecular coil elements between themselves and interactions polymer-solvent. The regular solutions theory absence complicates the exact definition of interactions of the second group and therefore the following approximate expression was used for determination [15] ... 

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... 

Based on the definition we have just given, it is obvious that the excess entropy of a regular solution is null, as are the excess partial molar entropies of each it its components - i.e. ... 

As strictly-regular solutions are, by definition, regular, we can deduce that the entropy of mixing is the same as that of a perfect solution and therefore that the excess entropy is null. 

Certain authors prefer to choose relation [2.89] from the expression of the excess Gibbs energy as the definition for strictly-regular solutions. This second definition is rigorously identical to that which we have chosen (relation [2.87]), because relation [A.2.32] (see Table A.2.2 in Appendix 2) links the activity coefficients and the partial molar Gibbs energy values. 

On the basis of this definition, we can extend the concept of a strictly-regular solution to systems with more than two components, but preserve the symmetry that is present in binary systems. For instance, for a system with N components, we can say that a solution is strictly regular if its excess molar Gibbs energy takes the form ... 

The structure of the section is as follows. In Section 2.8.2 we give necessary definitions and construct a Borel measure n which describes the work of the interaction forces, i.e. for a set A c F dr, the value /a(A) characterizes the forces at the set A. The next step is a proof of smoothness of the solution provided the exterior data are regular. In particular, we prove that horizontal displacements W belong to in a neighbourhood of the crack faces. Consequently, the components of the strain and stress tensors belong to the space In this case the measure n is absolutely continuous with respect to the Lebesgue measure. This confirms the existence of a locally integrable function q called a density of the measure n such that... 

These two examples show that regular patterns can evolve but, by definition, dissipative structures disappear once the thermodynamic equilibrium has been reached. When one wants to use dissipative structures for patterning of materials, the dissipative structure has to be fixed. Then, even though the thermodynamic instability that led to and supported the pattern has ceased, the structure would remain. Here, polymers play an important role. Since many polymers are amorphous, there is the possibility to freeze temporal patterns. Furthermore, polymer solutions are nonlinear with respect to viscosity and thus strong effects are expected to be seen in evaporating polymer solutions. Since a macromolecule is a nanoscale object, conformational entropy will also play a role in nanoscale ordered structures of polymers. 

Distribution Laws And Regular Solid Solutions. For so-called regular solid solutions (15), Equation (9) still holds but by definition the expression for their enthalpy of mixing is ... 

Substitutional Disorder In Regular Solid Solutions. Most simple ionic solutions in which substitution occurs in one sublattice only are not ideal, but regular 2, J3) Most complex ionic solid solutions in which substitution occurs in more than one sublattice are not only regular in the sense of Hildebrand s definition (15) but also exhibit substitutional disorder. The Equations describing the activities of the components as a function of the composition of their solid solutions are rather complex ( 7, V7, 1 ), and these can be evaluated best for each individual case. Both type II and type III distributions can result from these conditions. 

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