Entropy, configurational of mixing

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]

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. 

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... 

More than 50 years ago, Flory and Huggins [13-17] formulated a lattice model which captures the essential features of this competition between configurational entropy of mixing and enthalpy contributions, and even today this extremely simplified model is the basic ground on which most of the discussion... 

Equation (9.4) represents the local increase in free energy due to the formation of a nucleus, and not the total free energy of the system. The latter must include the configurational entropy of mixing of n nuclei in the liquid. When that term is included, the total free energy of the system decreases as it must (see App. 9A). 

This gives the configurational entropy of mixing for any number of components. It can be used to calculate residual entropies at absolute zero due to impurities, imperfections, nuclear spin, isotojjes, etc., simply by considering the imperfections as one component of a mixture. Equation (6.37) applies equally well to ideal mixtures at higher temperatures, as we shall see in Chapter 10. 

The first two terms result from the configurational entropy of mixing and are always negative. For AG to be negative, the value must be as small as possible. The theory assumes that the parameter does not depend on concentration without experimental confirmation. 

The restrictions of the initial version of Flory-lluggins lattice model (P-pLMWL mixtures) were obvious from the very beginning and, first and foremost, to the authors themselves. Indeed, the model did not foresee the chang< in volume on mixing and, as a sequence, the additional variation of the configurative entropy of mixing, x, was considered to have a reciprocal dependence on 7 which specifics the existence of the HOST only. 

Fig. 1 Configurational entropy of mixing per mole of CaMgSi O (diopside) - CaAlSi O (CaTs) pyroxenes, for completely disordered and unit cell charge balanced models.

The molar configurational entropy of mixing follows from equation... 

Fig, 1, Configurational entropy of mixing per mole of CaMgSi206 CaA.l2Si06 clino-pyroxene as a function of composition for the completely disordered" and "unit cell local charge balance" models. 

The entropy of mixing was calculated by counting the number of possible configurations the chain can assume on the lattice. With the reference states taken as the pure solvent and the pure, perfectly ordered polymer, the configurational entropy of mixing, AS, is given by... 

Equation (2) contains contributions from two processes the disorientation of the perfectly ordered polymer molecules and the mixing of the disoriented polymer with solvent. In order to determine the configurational entropy of mixing an amorphous polymer with a solvent, AS, the disorientation entropy term, obtained from Eq, (2) by setting n 0, must be subtracted from AS, ... 

It must be stressed that this is only the configurational entropy of mixing and it is also possible that there may be entropy contributions from specific interactions between polymer and solvent molecules. These will be discussed later. 

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