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 φi.Considering λi as a function of φi and n as infinite, then the following mathematical relations will be obtained:E(T)=∫10E(T, φA)λ(φA)dφA (2')1=∫10λ(φA)dφA (3')VA=∫10λ(φA)φAdφA (4')and1/E(T, φA)=φA/EA(T)+(1-φA)/EB(T) (1')where E(T) is temperature dependence of Young's modulus of the whole blended system; E(T, φA) is that of the element having the volume fraction of A component φA; and VA, EA and EB 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(φA) is obtained by solving the integral equation (2') under the additional conditions of Eqs. (3') and (4'), since E(T), EA(T) and EB(T) are measurable functions and thereby E(T, φA) 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(φA) of the blended systems of 30/70 butadiene-styrene copolymer and polystyrene varying VA from 0 to 100% is determined from the temperature dependence of E(T) of the blended systems given by Tobolsky. λi(φAi) determined by the numerical method shows maxima at the extremes of φAi, i.e., near φA=0 and 1, and reveals gradual increase of λi(φAi≅1) or decrease of λi(φAi≅0) with increase of VA.
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