Flory-Huggins theory limitations

According to Flory-Huggins theory, in the limit of x the critical x parameter is 0.5.(H) Below this value the polymer and solvent will be miscible in all proportions. Above this value, the solvent will not dissolve the polymer, but will act only as a swelling solvent. Thus, the pure solvent may not dissolve the polymer even though it is not crosslinked. If x is not , the critical value of x is larger, but the same qualitative arguments regarding mutual solubility of the solvent and polymer hold. Thus, the application of Equation 1 does not require that the pure solvent be able to completely dissolve the polymer, only that the solvent dissolve into the polymer by an amount that can be measured. 

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

Equation (12-23) suffers from the same limitations as the simple solubilty parameter model, because the expression for Wm is derived by assuming that in-termolecular forces are only nondirectional van der Waals interactions. Specific interactions like ionic or hydrogen bonds arc implicitly eliminated from the model. The solubility parameter treatment described to this point cannot take such inler-actions into account because each species is assigned a solubility parameter that is independent of the nature of the other ingredients in the mixture. The x parameter, on the other hand, refers to a pair of components and can include specific interactions even if they are not explicitly mentioned in the basic Flory-Huggins theory. Solubility parameters are more convenient to use because they can be assigned a priori to the components of a mixture, x values are more realistic, but have less predictive use because they must be determined by experiments with the actual mixture. 

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. 

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. 

Extrapolating Flory-Huggins theory to the dilute limit (beyond the assumption of the theory) also provides... 

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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