ABSTRACT
The change in entropy of mixing at the glass transition stage of a polymer blend in relation to the changes in heat capacity of the blend at the glass transition can be used to account for the observations of two distinct glass transition temperatures in partially miscible polymer blends. A quadratic expression for the mixed system glass transition temperature is derived:
A Tg2 + B Tg + C = 0, (6.1) where
It can be seen that when α = β = 0, the sum of the roots is (Tg1 +Tg2 ) and the product of the roots is Tg1 Tg2. This is the same as the homopolymer glass transition temperatures, and hence it can denote the immiscible blends. This is the case when ∆∆Smgl is extremely large compared with the ∆Cp12gl or when the heat capacity changes at the glass transition temperature. The case when the change in entropy of mixing is zero results in a miscible blend with a single glass transition temperature. For a symmetric blend when x1 = ½, ∆∆Smgl = 0, and ∆∆Cp12gl = 0, A = 2 ∆Cpgl, B = 0, and C = −2 ∆Cpgl Tg1Tg2. The roots of the quadratic equation are then ±sqrt(Tg1Tg2 ). The partially miscible systems lie intermediate to these two extremes with two real positive roots to the quadratic equation, where
α = +( )∆ ∆
∆∆
C C
1 2 . (6.5)
β = ∆ ∆∆
C
12 . (6.6)
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 polyhydroxybenzoic (PHB), polycarbonate (PC), and styrene acrylonitrile (SAN) have been reported [4]. Very little mathematical description of partially miscible systems is available in the literature.
