Thermodynamics of Polymer Solutions Flexible Chains

The hrst efforts at understanding polymer solutions were in the 1930s [23 to 25]. Deviations from solution ideality, Eqs. 3.8 and 3.9 (Raoult s Law), were found to be very large. It was also found that heats of solution were generally small, so that deviations from ideality seemed due to the entropy of mixing. 

The major step to understanding the mechanism of polymer solution non-ideality was achieved in 1939 by K. H. Meyer [25], who first realized that the length of polymer chains reduced the number of configurations possible after mixing. He developed a new lattice treatment, which is indicated in Fig. 3.2. The formulation of Meyer was subsequently extended by Huggins [26] and Flory [27], The argument of this formulation is as follows. If there are i polymer chains with x units in a lattice, the number of conformations for the i + 1 macromolecule is 

The entropy of mixing of a flexible polymer solution was expressed 

Using as before Stirling s approximation (Eq. 3.3b) leads to after subtracting the configurational entropy [27] an entropy of mixing of 

The heat of solution for polymer solutions should be similar to that for low molecular weight liquids. Huggins and Flory used a formulation of the heat of solution similar to the regular solution. Hildebrand and Scott [5], thinking in terms of thevanLaar-Scatchard-Hildebrand regular solutions, simply wrote this as in Eq. 3.16 

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