Limitations of the Flory-Huggins Theory

Experiments tend to show that the major contribution comes from the Xs component, indicating that there is a large decrease in entropy (noncombinatorial), which is acting against the dissolution process of a polymer in a solvent. 

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Discuss ( -one page) some of the limitations of the Flory-Huggins theory. 

The deficiencies of the Flory-Huggins theory result from the limitations both of the model and of the assumptions employed in its derivation. Thus, the use of a single type of lattice for pure solvent, pure polymer and their mixtures is clearly unrealistic since it requires that there is no volume change upon mixing. The method used in the model to calculate the total number of possible conformations of a polymer molecule in the lattice is also unrealistic since it does not exclude self-intersections of the chain. Moreover, the use of a mean-field approximation to facilitate this calculation, whereby it is assumed that the segments of the previously added polymer molecules are distributed uniformly in the lattice, is satisfactory only when the volume fraction (f>2 of polymer is high, as in relatively concentrated polymer solutions. 

As we can see, in the limit fc 0, the stability criterion of the Flory-Huggins theory, x < Xsp is recovered. For finite fc s, the criterion becomes modified. 

It can be seen that for small values of z, the perturbation second virial coefficient given by Eq. (3.117) is equal to the factor in parenthesis. Since N is proportional to M2, the virial coefficient should be independent of molecular weight in the limit of small z. This is the same result we have derived earlier from the Flory-Huggins theory. In the limit of small z, Eq. (3.117) is frequently combined with Eq. (3.86) to yield... 

In brief, it can be said that in the attractive domain, the Flory-Huggins theory describes the demixtion curve in a reasonable way. However, the renormalization theory of critical phenomena shows that the top of the demixtion curve is not parabolic but much flatter. Moreover, the tricritical theory shows that when cp increases, there is no oblique asymptote but a limiting logarithmic curve (see Section 6). Actually, experiments seem to confirm these more recent theories. Nevertheless, the Flory-Huggins theory remains a very interesting approximation whose continuous limit will now be studied. 

The Flory-Huggins theory, RPA, and SCFT, along with the information in Tables 19.1 and 19.2 enable prediction of the sfructure and phase behavior of complex polymer mixtures in the mean-field limit. We discuss two illustrative examples of such predictions. More details regarding these examples can be found in the original references [18,45,46]. 

Although the Flory-Huggins theory is not truly valid at low-volume fractions of solute, it is useful to examine the dilute limiting law for the osmotic pressure. The expression In (l - x) = -x - / 2--is used ... 

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