A Generalized Model Representation Relating the Degree of Mixing to the Mechanical Properties of Physically Blended System of Two Polymer Components

Abstract

The mechanical properties of polymer blends depend on the degree of mixing of the blended components. If the blended polymers are poorly compatible or incompatible, which is oftener met in actual and is more significant in modifying the mechanical properties of a single polymer component in a practical point of view, it presents a sort of physically blending rather than a sort of solvation. This common type of blending usually shows the existence of two glass-transition temperatures which correlate, more or less, to the original glass-transition temperatures of each component and suggest that the physically blending leaves homogeneous regions of each polymer component.
In this paper, it is intended to relate the viscoelastic properties of this type of physically blended system of two polymer components to the degree of mixing by using a generalized model representation, as shown in Fig. 2, consisted of n elements coupled in parallel by the volume fraction λ, in which the ith element consists of two polymer components coupled in series by the volume fraction φ_i.
Considering λ_i as a function of φ_i and n as infinite, then the following mathematical relations will be obtained:
E(T)=∫¹₀E(T, φ_A)λ(φ_A)dφ_A (2')
1=∫¹₀λ(φ_A)dφ_A (3')
VA=∫¹₀λ(φ_A)φ_Adφ_A (4')
and
1/E(T, φ_A)=φ_A/E_A(T)+(1-φ_A)/E_B(T) (1')
where E(T) is temperature dependence of Young's modulus of the whole blended system; E(T, φ_A) is that of the element having the volume fraction of A component φ_A; and V_A, E_A and E_B are volume fraction of A component in the whole system, temperature dependence of Young's modulus of A component and that of B component, respectively.
The degree of mixing, λ(φ_A) is obtained by solving the integral equation (2') under the additional conditions of Eqs. (3') and (4'), since E(T), EA(T) and E_B(T) are measurable functions and thereby E(T, φ_A) is a known function. It is, however, difficult to solve Eq. (2') analytically, and the equation must be solved numerically.
The degree of mixing λ(φ_A) of the blended systems of 30/70 butadiene-styrene copolymer and polystyrene varying V_A from 0 to 100% is determined from the temperature dependence of E(T) of the blended systems given by Tobolsky. λ_i(φ_Ai) determined by the numerical method shows maxima at the extremes of φ_Ai, i.e., near φ_A=0 and 1, and reveals gradual increase of λ_i(φ_Ai≅1) or decrease of λ_i(φ_Ai≅0) with increase of V_A.