Interaction parameter, polymer-solute, definition

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. 

Figure AVI.l Relationship between solvent-solvent, segment-segment. and solvent-segement interaction energies, and the definition of the interaction parameter, X, for polymer solutions.

As it has been noted above, the fractal dimension macromolecu-lar coil in solution is determined by two interactions groups interactions polymer-solvent and interactions of coil elements between themselves. Such definition allows to link between themselves the dimension and Flory-Huggins interaction parameter which was determined as follows [1] ... 

Originally x was stated to be independent of polymer concentration. The X-parameters determined by many investigators using one or another of the methods for measuring colligative properties of polymer-liquid solutions (mentioned below) show that this is not the case (see Tables 3-22 of Reference 43) nor does x vary linearly with 1/T as stated in Eq. 7. Later [44] a quantity Aws representing an entropic contribution from contact interaction was added to the Flory-Huggins definition of x to produce a relationship linear in 1/T. 

Five parameters classify the main types of linear polyelectrolytes the fraction / of charged monomers, the strength of the Coulomb interaction normalized to ksT, A, the added salt concentration Cs, the polymer concentration c and of coiuse the chain length L. One other important quantity is the valence of the counterions or salt ions. For the most part only monovalent ions have been considered to date in simulations and theory. To completely understand polyelectrolytes requires studying the variation of each of these quantities which is a formidable task. The understanding of polyelectrolytes in solution is just beginning. While much work has been done on these systems, by no means is there a definitive understanding of their properties and structure. 

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