Forces and Excess Functions

We shall now consider more closely the relation between inter-molecular forces and excess functions. 

Let us introduce (8.5.1) into the expression (8.4.3) for the excess volume. Neglecting terms of order higher than the second in d or 6. we find 

If we only retain the first order term all excess functions become proportional to B and have the same sign. This is in agreement with the theory of conformal solutions (Ch. IV, 3-4). However, as we have already seen in the case of the one dimensional model, the second order terms destroy this ample relation between the excess fnnctions. Let us consider in more detail a few typical cases which may arise (a) Geometrical or arithmetical mean (2.7.9, 2.7.11). In these cases 02 

The model predicts here contraction on mixing, positive deviations from Raoult s law, absorption of heat on mixing and finally negative excess entropy. This fe in complete agreement with the conclusions we obtained in Ch. VI, 4-5 using the rigorous one dimensional model. 

If we take the arithmetical mean (8.3.7) we still have contraction on mixing and positive deviations from Raoult s law, but the heat of mixing becomes negative. 

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Model 149. 4. Smoothed Potential Cell Model 151. 5. Intermolecular Forces and Excess Functions 153. 

We may compare (17.6.2) with the corresponding expression (10.7.4) for monomer mixtures. Apart from the combinatorial entropy and factors qjqA and CA/iA, these formulae are exactly the same, when the mole fractions xa and xb are replaced by Xa and Xb- We must also notice that in our present model the configurational specific heat at constant volume cvA vanishes as a consequence of our assumption that the cell partition functions do not depend on the temperature. Therefore the detailed discussion of the effect of intermolecular forces on excess functions presented in Ch. IX-XI, applies also to polymer mixtures. For example p will again give rise to positive deviations from ideality, positive excess entropy and heat absorption. We shall not go into more detail. 

Plastic solids derive their functionality from their unique plastic nature. Three conditions are essential for plasticity (5) (1) both liquid and solid phases must be present (2) the solid phase must be so finely dispersed that the entire solid-liquid matrix can be effectively bound together by internal cohesive forces and (3) proper proportions must exist between the phases. Incorrect phase ratios adversely influence product rheology. For example, deficient solids content may result in oil separation, whereas excessive solids can cause hardness or brittleness instead of the desired viscous flow. 

The above method can be apphed to a calculation of other excess functions in terms of intermolecular forces. We may note that the excess entropy of mixing is closely related to the excess volume and to the change of the free volume of the solution with composition. We shall not, however, go into any further details here. 

Thus, the excess functions (e.g., g , ftE, and sE) also reflect the contributions of interorolecular forces to mixture property tn. Partial molar property m, corresponding to molar mixture property m is defined in the usual way ... 

Fugacity and activity are basically compositional terms. In ideal solutions they are not necessary pressure and various composition terms can be directly linked to the Gibbs energy. Real solutions have a variety of intermolecular forces, so that ideal solution models need correction factors. These corrections can be made either to the composition terms (fugacity and activity coefficients) or to the thermodynamic potentials (excess functions), and efforts to model these correction factors in mathematical terms have always been, and likely always will be, an important research field. 

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