Phase Diagrams Upper and Lower Miscibility Gap

Phase diagrams of polymer blends under atmospheric pressure are usually presented in terms of the variables (pA and T. Emanating from the discussed universal phase diagram in terms of x and /a these can be obtained by introducing the temperature dependence of the Flory-Huggins parameter into the consideration. This function x T) then solely determines the appearance. For 

Let us first consider an endothermal polymer mixture with negligible entropic contributions to the local Gibbs free energy, i.e., a system with X = xh 0. Here the temperature dependence of x is given by Eq. (4.22) 

The consequences for the phase behavior are evident. Perfect miscibility can principally exist at high temperatures, provided that the molar mass of the components are low enough. The increase of x with decreasing temperature necessarily results in a termination of this region and the formation of a miscibility gap, found when x Xc- For a symmetric mixture we obtained Xc = (Eq. (4.36)). If Xc is reached at a temperature Tc, we can write 

The resulting phase diagram is shown in Fig. 4.6, together with the temperature dependence of x- The binodal follows from Eq. (4.38), as 

It marks the boundary between the homogeneous state at high temperatures and the two-phase region at low temperatures. 

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