Transport in Phase Separated Blends

For phase separated blends, permeability versus composition can be more complex at intermediate compositions. However, at the extremes of composition, where component 1 is entirely the continuous phase or the dispersed phase, the parallel and series models can be employed. 

These are the limiting cases for permeability of a polymer, which comprise the continuous or dispersed phases and the parallel model represents the upper bound and the series model represents the lower bound. Another model typically employed, where spheres of one polymer are dispersed in a matrix of the other, is the Maxwell s equation  

An analysis (equivalent box model) proposed by Kolarik, employing the universal constants predicted by the DeGennes percolation theory, can be used to predict the permeability of phase separated blends [162]. The universal constants can also be considered adjustable variables to fit the specific data. The EBM approach employs a series and parallel combination and is virtually identical to the EBM model described earlier in this chapter for modulus, except P is substituted for E. Thus  

The primary studies involving permeability of miscible blends have been conducted at the Royal Institute of Technology (Sweden) and at the University of Texas. Shur and Ranby studied a series of PVC blends believed to be miscible or partially miscible, including PCL [163], NBR [164], chlorinated PE [165], EVA [166] and ABS [167]. The results showed good agreement of the permeability composition behavior in accord with phase separation, partial miscibility or miscibility data determined by other methods (e.g., dynamic mechanical). Departure from the semi-logarithmic relationship expected of miscible blends was observed, when the composition of the copolymers (e.g., chlorinated PE, NBR, EVA) composition was varied such that partial miscibility or phase separation was observed. 

Studies at the University of Texas on miscible blends included PPO/PS [168], PVF2/PMMA [169, 170], PMMA/SAN [171], TMPC/PS [172], and polymethyl acrylate (PMAc)/polyepi- 

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