Solution, athermal regular

REGULAR SOLUTIONS AND ATHERMAL SOLUTIONS 1. Regular Solutions. 

The term athermal mixtures refers to those in which the heat of mixing A i H is very small but S differs considerably from zero, for example, polymer solutions. In regular mixtures differs considerably from zero but S is negligible, for example, mixtures of highly polar low-molecular substances such as nitriles/esters. 

Although they are partially ideal systems, the athermal solutions are completely different in character from regular solutions while regular solutions consist of molecules of similar shape and size, the constituents of athermal solutions are polymers whose molecular weights are much larger than those of the solvents, which are in general common organic molecules. 

Thus, the molar heat capacity is the same as that for a perfect solution and therefore obeys Kopp s additivity law [A.2.14]. This law can be said to be fairly widely applicable, because we have seen it at woik with perfect solutions, regular solutions, athermic solutions and approximately with dilute ideal solutions. 

Solutions can be classified into five main categories—ideal, athermic, regular, irregular, and theta ... 

Evaluate ASj for ideal solutions and for athermal solutions of polymers having n values of 50, 100, and 500 by solving Eqs. (8.28) and (8.38) at regular intervals of mole fraction. Compare these calculated quantities by preparing a suitable plot of the results. 

In the phenomenological characterization of small deviations from SI solutions, the concepts of regular and athermal solutions were introduced. Normally, the theoretical treatment of these two cases was discussed within the lattice theories of solutions. Here, we discuss only the very general conditions for these two deviations to occur. First, when Pt ab does not depend on temperature, we can differentiate (6.19) with respect to T to obtain... 

When molecular size differences, as reflected by liquid molal volumes, are appreciable, the following Flory-Huggins size correction for athermal solutions can be added to the regular solution free energy contribution... 

Hildebrand and Rotariu [14] have considered differences in heat content, entro])v and activity and classified solutions as ideal, regular, athermal, associated and solvated. Despite much fundamental work the theory of binary liquid mixtures is still e.ssentiaUy unsatisfactory as can be seen from the. systematic treatment of binar> mi.Ktures by Mauser-Kortiim [15]. The thermodynamics of mixtures is presented most instructively in the books of Mannchen [16] and Schuberth [17]. Bittrich et al. [17a] give an account of model calculations concerning thermophysical properties of juire and mixed fluids. 

In practical cases, we have two components which are quite similar (in the usual sense) but not similar (in the sense of the definition of the previous section) and therefore we expect (4.118) to be a valid approximation. In fact, first-order theories of regular and athermal solutions are special cases of (4.118), although their phenomenological characterization is more general [for more details, see Guggenheim (1952)]. 

A mixture for which (4.121) is valid may be referred to as a simple mixture. Within the realm of simple solutions, one may further distinguish between regular and athermal solutions as two special cases. 

At the end of this chapter the calculated and exjKjrimental (chromatographic) data are compared this is preceded by a presentation of some important models which have been put forward for regular solutions and athermal solutions, together with the theories of contact points and segments, perturbation and Plory s equation of state. It should be mentioned that only theories verified by chromatographic data are considered. 

The term general solution was introduced by Flory to characterize polymer solutions whose enthalpy of mixing is not zero. The model of general solutions borrows the formula of excess enthalpy from regular systems and the excess entropy from athermal solutions. Thus, a treatment of non-ideal polymer solutions arises which is simpler than the conventional methods applied to real systems this allows the deduction, on the basis of the known relationships, of the expressions of functions of deviation from ideality. Thus, for the activity coefficients of components in a binary system the following relations were established ... 

Alongside regular solutions (see section 2.5.1), we can define athermic solutions, which are primarily found when amorphous or molten pol5miers are dissolved in solvents. 

In the same way as we defined a regular solution as one which has the same entropy of mixing as a perfect solution, we shall define an athermic solution as one which has the same enthalpy of mixing as a perfect solution - i.e. zero. Of course, its excess molar enthalpy is also null. 

Note 2.3.- a solution which is both regular and athermic is a perfect solution, because these two solutions have the same enthalpy and the same entropy, and therefore the same Gibbs energy. Hence, they are identical. 

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