A Theory of Polymer Blend, as Extension of the Theory of Filler Reinforcement and of a Theoretical View of Stress-Strain Behavior of Model Polymer Blend System

Abstract

The molecular theory of filler reinforcement which was previously proposed by one of the authors (Y.S.) has been applied by extension to the analysis of the mechanical properties of polymer blends. Almost the same model has been used in the present experiment of the theory of filler reinforcement as those which were used in the previous experiment of the theory of the same, and almost the same assumptions are made for the present theory as was made for the previous theory, except that the dispersed spherical particles are rigid, because the spherical particles dispersed in polymers as demonstrated in the present theory are no longer to be necessarily designated rigid, but only deformable bearing the rigidity G0.Of the blend of two kinds of polymers with rigidity G and G0, the stress-strain relation of simple extension is obtained as follows where σ denotes the tension at extension ratio α, Y and (1-ζ) denote the volume fraction of the dispersed polymer and the degree of adhesion, respectively, and K is the ratio of the surface modulus to the volume modulus and is a parameter expressing the surface effects, φ is the ratio of the volume of the sample before and after deformations, γ1 and γ represent the deformation of the inner surface of the medium facing the dispersed particles in the direction of extension in a perfect adhesion state and an actual adhesion state, respectively, γ1' and γ' represent the deformation perpendicular in the direction of extension in perfect adhesion state and an actual adhesion state, respectively. Upon this relation, it has been examined theoretically how Y or X (Volume ratio of two polymers), (1-ζ) and K will affect the stress-strain behavior of polymer blends. The two cases of blend system have been considered; the system composed of two kind of polymers in which a polymer medium with rigidity of 2.5 includes softer polymer particles with rigidity of 1.25, and harder polymer particles with rigidity of 5.0. The results show that in the case of a perfect adhesion state, the calculated tension σ for both the systems increased with increasing α and X, while in the case of a perfect non-adhesion state, σ increased with α but the rate of increase changed at an extension ratio of about 1.5 or 2.0 and decreased with increasing X. It was also found that σ was fairly sensitive to the change in the value of K.