Quasi-ideal solutions

Several examples of both association and complex formation are discussed in detail in the following paragraphs. Quasi-ideal solutions are assumed in all cases. First we assume that the first component exists in monomeric and dimeric forms only. The equilibrium reaction is... 

Figure 11.1. Activity coefficients for a binary quasi-ideal solution involving a 1-1 complex.

A long flexible polymer chain is a typical object addressed by meso thermodynamics. In dilute solutions a polymer chain can exhibit either a random walk or a self-avoiding walk." These two regimes are separated by the theta point, the point of polymer-solvent phase separation in the limit of infinite degree of polymerization." The random walk occurs when the polymer chain and the solvent form either ideal or quasi-ideal solutions. The ideal polymer chain exhibits Gaussian fluctuations of the distance R between the two ends of the... 

From these results, the thennodynamic properties of the solutions may be obtamed within the McMillan-Mayer approximation i.e. treating the dilute solution as a quasi-ideal gas, and looking at deviations from this model solely in temis of ion-ion interactions, we have... 

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. 

Temkin was the first to derive the ideal solution model for an ionic solution consisting of more than one sub-lattice [13]. An ionic solution, molten or solid, is considered as completely ionized and to consist of charged atoms anions and cations. These anions and cations are distributed on separate sub-lattices. There are strong Coulombic interactions between the ions, and in the solid state the positively charged cations are surrounded by negatively charged anions and vice versa. In the Temkin model, the local chemical order present in the solid state is assumed to be present also in the molten state, and an ionic liquid is considered using a quasi-lattice approach. If the different anions and the different cations have similar physical properties, it is assumed that the cations mix randomly at the cation sub-lattice and the anions randomly at the anion sub-lattice. 

Figure 42 Bode plots of an epoxy-resin-based coating on phosphated steel exposed to 0.5 M NaCl solution, (a) Quasi-ideal coating, (b) Sample exposed for 1 hour, (c) Sample exposed for 48 h. (From J. Titz, G. H. Wagner, H. Spahn, M. Ebert, K. Juttner, W. J. Lorenz. Corrosion 46, 221 (1990).)...

The first turning point occurred in the beginning of 1972 when the Kirkwood-BufF theory was found useful in interpreting some properties of water and aqueous solutions. The main idea was to apply the Kirkwood-BufF theory of solutions, to pure one-component systems viewed as a mixture of various quasi-component systems. The KB theory was also applied in the analysis of various ideal solutions on a molecular level (Ben-Naim 1973b, 1974). 

A special situation occurs when the attraction between the segments exactly compensates the (hard-core) excluded volume efifeet In dilute solutions the chains then behave quasi-ideal. This situation is commonly referred to as the -solvent condition. 

In 8 1 it was shown that equations (14 4)-(14 6) lead to a statistical deduction of the laws of ideal solutions. For this purpose it was supposed that a solid or liquid solution can be approximated by a quasi-crystalline lattice, and also that the A and B molecules are of a sufficiently equal shape and size for them to be interchangeable between the lattice sit without change of lattice structure and without change in the lattice vibrations or the internal states of the molecules. Before mixing there is only one geometrical arrangement and after mixing there are... 

A dependence of w upon composition must also be adduced in the case of the Fe-Ni solid solutions. Over the range from 0 to 56 at. per cent Ni, these solid solutions exhibit essentially ideal behavior,39 so that w 0. Since the FeNi3 superlattice appears at lower temperatures, either w is markedly different at compositions about 75 at. per cent Ni than at lower Ni contents, or w 0 for the solid solutions about the superlattice. Either possibility represents a deviation from the requirements of the quasi-chemical theories. 

Table II also demonstrates the discrepancy existing between E0/RTe calculated by the Yang-Li quasi-chemical theory and the experimental ratio. E0 is the energy difference between a fully ordered superlattice and the corresponding solid solution with an ideally random atom species distribution. It is a quantity that can only be estimated from existing experimental information, but the disparity between theory and experiment is beyond question.

It is simplest to consider these factors as they are reflected in the entropy of the solution, because it is easy to subtract from the measured entropy of solution the configurational contribution. For the latter, one may use the ideal entropy of mixing, — In, since the correction arising from usual deviation of a solution (not a superlattice) from randomness is usually less than — 0.1 cal/deg-g atom. (In special cases, where the degree of short-range order is known from x-ray diffuse scattering, one may adequately calculate this correction from quasi-chemical theory.) Consequently, the excess entropy of solution, AS6, is a convenient measure of the sum of the nonconfigurational factors in the solution. 

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... 

---