Theoretical Evaluation of the Extent of the Mesophase in Particulate and Fibrous Composites

Abstract

The concept of the mesophase and its extension in fibrous and particulate composite polymers has been investigated experimentally in the past. A theoretical method for the evaluation of the thickness of the mesophase is introduced in this paper. The method was based on the unfolding models, which describe the variation of the variable elastic- modulus, E,(r), of the mesophase material with respect to its thickness. By applying to E 1(r) the restriction based on the principle of continuity, that its variation curve must be tangent to the value of the constant elastic-modulus of the polymeric matrix, the thickness of the mesophase may be analytically determined. This is accomplished, of course, by the use of the appropriate models describing the properties of the com posite. A review of the properties of the existing unfolding models indicated the possibility of a modification of these models. This modified unfolding model, with the already existing two-term model, yields a band, as lower and upper bounds respectively, in which lie all existing experimental values for the thickness of the mesophase for fibrous composites. Numerical results derived from this theoretical treatment are in satisfactory agree ment with experimental values for fibrous composites, while for particulate composites there is a divergence between the theoretical and experimental values. The reasons of this fact are known and are explained in the appropriate section of this paper.