Molar Mass Dependence of Phase Diagrams

For strictly binary systems, appropriate differentiation of the free enthalpy of mixing leads to 

The last three terms in eqn (8.38) reduce to —2Zi2 and in eqn (8.39) to zero. If JTi2 does not depend on concentration then the critical points can be identified  

Binodals (heavy curves) as described by eqn (8.36) and (8.37) and spinodals (light curves) according to eqn (8.38) showing the effect of molar mass size milm2). Open circles are critical points specified by eqn (8.40) and (8.41) and connected by the dash-dot curve.  

For small molecules mi = m2 = 1 but for high polymer solutions mi = 1, m2 1, the critical value of X12 approaches for very large m2 and the critical volume fraction of polymer becomes very small. When both mi and m2 are very large l i2c is very small. 

In general, as the molecular mass of the polymer is increased the minimum temperature at which phase separation starts is reduced. For an 

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