Effects of Branching on Apparent Theta-Temperature

In Flory s theory (/ ), a polymer-solvent system is characterized by a temperature 0 at which (i) excluded-volume effects are just balanced by polymer-solvent interactions, so that os=l, (ii) the second virial coefficient is zero, irrespective of the MW of the polymer, and (iii) the polymer, of infinite molecular weight, is just completely miscible with the solvent The fundamental definition of the temperature is a macroscopic one, namely that for T near 0 the excess chemical potential of the solvent in a solution of polymer volume fraction v2 is of the form (18)  

Casassa (S3) has modified a theory of the configuration of polymer molecules in solution due to Vrij (84) and applied it to branched molecules. If certain terms neglected in Flory s derivation are retained, Eq. (6.10) becomes  

A different approach to the problem has been adopted by Candau and co-workers (85), They make a useful distinction between the temperature 0 that occurs in their equations as a parameter characterizing the polymer-solvent interactions which may be assumed to be independent of MW or branching,- and the temperatures 0Al and 0a at which A2 =0 and os = I respectively, which do depend on both factors. They assume that the free energy of mixing AGm of nl molecules of solvent with n2 molecules of polymer is given by  

Then by solving for the condition os= 1 they find that  

Unless, 42 0, the solution would be unstable. For positive A, the expression on the right of (6.17) is also positive, and 0tt 0. If A is small, 0a 0Ai 0, though in the general case Ai may be less than 0a. However, as M-kx , 0a- 0 and 0A2-+0, so that the value of is experimentally obtainable. 

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