Commercial Blends That Are Partially Miscible

Most polymer blends that are commercial products in the industry are partially miscible. Partially miscible polymer blends are those that exhibit some shift from their pure component glass transition temperatures. Thus, a binary miscible blend will exhibit one glass transition temperature [1], and a partially miscible blend may exhibit two distinct glass transition temperatures other than their pure component values [2,3]. Some experimental systems such as polyethylene terepthalate (PET) and poly-hydroxybenzoic (PHB), polycarbonate (PC), and styrene acrylonitrile (SAN) have been reported [4]. Very little mathematical description of partially miscible systems is available in the literature. 

Mixed system glass transition temperature, Tg is defined by the requirement that entropy for the glassy state is identical to that for the rubbery state [5]. A revisit of the Couchman equation without neglecting the differences of entropy of mixing in the glassy and rubbery state is used to develop a mathematical framewoilc to represent multiple glass transition tanperatures in partially miscible copolymers in blends. 

For blends, at a molecular level during phase transition the molar volume and bulk density changes along with the heat capacity. This implies that ASg, the entropy of mixing in the glassy state, is different from ASJn, the entropy of mixing in the rubbery phase. The mixed system entropy is given by 

The entropy at the glassy and rubbery states is then calculated as 

From the continuity of entropy considerations at the glass transition the Equations (6.10) and (6.11) are equated, i.e., 5 = 5. Then, 

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