The Dependence of Miscibility on Blend Composition and Temperature

In the original Flory-Huggins model, the interaction parameter x (or B) reflected exclusively enthalpic contributions to the free energy of mixing [2]. However, this description was soon extended when assuming that x includes contributions of both enthalpic and entropic nature to AG , [2-5]. As discussed in the preceding sections, specific interactions introduce nonrandomness and other effects that need to be considered for a correct description of the actual behavior of polymer blends. Both, theoretical and empirical corrections to x (or B) have been proposed [8]. Regarding the dependence on composition, the simplest empirical approach assumes a linear dependence of B with composition (B = a + brpi). This type of approach has actually been used in Eq. (2.28) and applied to the PLLA/PVPh system in Section 2.1.6 in this chapter. 

Regarding the temperature dependence of the interaction parameter x (or B), in the original Flory-Huggins model the unfavorable enthalpic term is constant with temperature, but the favorable entropic term increases with temperature (see Eq. (2.14) or (2.17)). The model predicts phase diagrams with an Upper Critical Solution Temperature (UCST), or misdbilization upon heating. However, systems 

According to Eqs (2.20) and (2.30), the following dependence on temperature can be deduced for the interaction energy density B = a + bT. In addition, B depends on composition (recall the simple dependence discussed here, B = a + h(pi). A general expression can be proposed for B combining both dependences B = Ai+A2T+Ai(pi+A4(piT, where the Aj coefficients are now constant coefficients that depend only on the nature of the system. Several expressions of different complexity can be found in the literature [30,31]. 

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