Polymer solutions entropy change

The formation of the solution may be conceived to occur in two steps disorientation of the polymer molecules and mixing of the disoriented polymer with solvent. The separate entropy changes are readily obtained as follows The first is given by Eq. (8) with ni = 0, i.e. 

Cyclisation of polymer chains. Theory and experiment 64 Entropy changes for cyclisation reactions in solution 74... 

The effect of exclusion on the retention volumes of macromolecules was qualitatively explained above. The pioneering work of Casassa [54] has shown that the extent of pore exclusion of macromolecules is controlled by the changes in their (conformational) entropy. The principle is explained in a simplified form in Figure 16.4a through c. A zone of polymer solution with a nonzero concentration travels along a column packed with porous particles. Initially, the concentration of macromolecules within pores is zero (Figure 16.4a). The concentration gradient outside of pore (c > 0) and within pore (c = 0) pulls macromolecules into the pores. 

Here is Boltzmann s constant, or the gas constant per molecule, R/Nq, where No is Avogadro s number (or Na + Nb for one mole of solution) and va and are the volume fractions of solvent and polymer. Comparison of Eq. (2.76) with the entropy of mixing presented earlier in the chapter by Eq. (2.30) shows that they are similar in form, except that now the volume fractions of the components, va and vg, are found to be the most convenient way of expressing the entropy change for polymers, rather than the mole fraction used for most small molecules. This change arises from the differences in size between the large polymer molecules and the small solvent molecules which would normally mean mole fractions close to unity for the solvent, especially when dilute solutions are being studied. 

The addition of a diluent to a crystalline polymer depresses its melting point, as is shown schematically in Figure 2.43. The upper sketch again shows the standard reference case. In the lower sketch, solvent molecules are available to mix with the polymer chains once they separate from the crystalline lattice. The final state is now a polymer solution, instead of a molten polymer. This additional disordering greatly increases the entropy change for the process and therefore decreases the melting point, frequently to the extent of 40-50 °C. 

Nonideal thermodynamic behavior has been observed with polymer solutions in which A Hm is practically zero. Such deviations must be due to the occurrence ofa nonideal entropy, and the first attempts to calculate the entropy change when a long chain molecule is mixed with small molecules were due to Flory [8] and Huggins [9]. Modifications and improvements have been made to the original theory, but none of these variations has made enough impact on practical problems of polymer compatibility to occupy us here. 

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