Solution pseudoideal

Interpretation of the second and third virial coefficients, A2 and A3, in terms of Floiy-Huggins theory is apparent from Eq. (3.82). The second virial coefl[icient A2 evidently is a measure of the interaction between a solvent and a polymer. When A2 happens to be zero, Eq. (3.82) simplifies greatly and many thermodynamic measurements become much easier to interpret. Such solutions with vanishing A2 may, however, be called pseudoideal solutions, to distinguish them from ideal solutions for which activities are equal to the molar fractions. Inspection of Eq. (3.83) reveals that A2 vanishes when the interaction parameter X equal to. We should also recall that %, according to its definition given by Eq. (3.40), is inversely proportional to temperature T. Since x is positive for most polymer-solvent systems, it should acquire the value at some specific temperature. 

The pseudoideal or theta solution is an important special case of irregular solutions in macromolecular science. The enthalpy of mixing and the excess entropy of mixing exactly compensate each other at a certain temperature with the dilute theta solution. Theta solutions at this theta temperature thus behave like ideal solutions. In contrast to ideal solutions, however, the enthalpy of mixing is not zero and the entropy of mixing differs considerably from the ideal entropy of mixing. Thus, an ideal solution exhibits ideal behavior at all temperatures, the pseudoideal solution only behaves ideally at... 

If the polymer concentration increases so that the number of high order bead-bead interactions is significant, c>>c =p, (when c is expressed as the polymer volume fraction. Op), the fluctuations in the polymer density becomes small, the system can be treated by mean-field theory, and the ideal model is applicable at all distance ranges, independent of the solvent quaUty and concentration. These systems are denoted as concentrated solutions. A similar description appHes to a theta solvent, but in this case, the chains within the blobs remain pseudoideal so that =N (c/c ) and Rg=N, i.e., the global chain size is always in-... 

Thus, at some special temperature T = 9, A2 vanishes and the solutions become pseudoideal. Such solutions are also called theta solutions. The second virial coefficient is positive at temperatures higher than 9 and negative at lower temperatures. 

To emphasize this circumstance, polymer solutions at T = 0 are sometimes called pseudoideal, or just solutions in the theta solvent. 

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