Mixing configurational entropy

Since the entropy of mixing (configurational entropy) is a function of W ... 

Although the right-hand sides of Eqs. (8.27) and (8.28) are the same, the former applies to the mixture (subscript mix), while the latter applies to the mixing process (subscript m). The fact that these are identical emphasizes that in Eq. (8.27) we have calculated only that part of the total entropy of the mixture which arises from the mixing process itself. This is called the configurational entropy and is our only concern in mixing problems. The possibility that this mixing may involve other entropy effects—such as an entropy of solvation-is postponed until Sec. 8.12. 

Remember that the hump which causes the instability with respect to phase separation arises from an unfavorable AH considerations of configurational entropy alone favor mixing. Since AS is multiplied by T in the evaluation of AGj, we anticipate that as the temperature increases, curves like that shown in Fig. 8.2b will gradually smooth out and eventually pass over to the form shown in Fig. 8.2a. The temperature at which the wiggles in the curve finally vanish will be a critical temperature for this particular phase separation. We shall presently turn to the Flory-Huggins theory for some mathematical descriptions of this critical point. The following example reminds us of a similar problem encountered elsewhere in physical chemistry. 

The configurational entropy of the mobile guest ions, assuming random mixing and a concentration x, residing in x° lattice sites of equal energy, is... 

With the introduction of these relations into Eq. (41), the configurational entropy change (the entropy of mixing solvent and polymer excluded see Chap. XII) relative to the initial state ax = ay = az = l becomes... 

If each solvent molecule may occupy one of the remaining lattice sites, and in only one way, 0 represents also the total number of configurations for the solution, from which it follows that the configurational entropy of mixing the perfectly ordered pure polymer and the pure solvent is given hy Sc —k In Introduction of Stirling s approximations for the factorials occurring in Eq. (7) for fi, replacement of no with Ui+xn[Pg.501]

If the configurational entropy A>Sm is assumed to represent the total entropy change LSm on mixing, the free energy of mixing is simply obtained by combining Eqs. (10) and (20). That is,... 

Hence the theoretical configurational entropy of mixing AaSm cannot be compared in an unambiguous manner with the experimentally accessible quantity ASm- It should be noted that the various difficulties encountered, aside from those precipitated by the character of dilute polymer solutions, are not peculiar to polymer solutions but are about equally significant in the theory of solutions of simple molecules as well. 

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 regular solution parameters are still assumed to be enthalpic in nature. In other words, the vibrational entropy is, as earlier, considered not to be affected by the mixing. The last term of eq. (9.83), the configurational entropy, is also unaffected by this modification. 

Application of Stirling s formula to equation 5.191 and comparison with the configurational state of pure components lead to the definition of a configurational entropy of mixing term in the form... 

There is evidence that random mixing of partially charge-neutralized hydrated polyelectrolyte complexes inside the coacervate phase imparts higher configurational entropy to these less stiff polyelectrolyte molecules as compared to those in the pre-coacervation phase (Kaibara et al.,... 

The simplest approximation to the total entropy of mixing is the mean-field Bragg-Williams-Gorsky configurational entropy, proportional to X > lnp [4J 3... 

Finally, the entropy of mixing or configurational entropy, must have a maximum value. The configurational entropy is given by (Nordstrom and Munoz, 1986)... 

Flory ) and Huggins ) derived a now classical mean-field expression for the configurational entropy and energy of mixing, using a lattice model. The solution, containing moles of solvent and n moles of polymer, is described as a lattice of sites, of which are occupied by solvent and N

[Pg.619]

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