Random Polymer Models and their Applications

Statistical copolymers refer to a class of copolymers in which the distribution of the monomer counits follows Markovian statistics [1,2]. In these polymeric materials, since the different chemical units are joined at random, the resulting polymer chains would be expected to encounter difficulties in packing into crystaUine structures with long-range order however, numerous experiments have shown that crystallites can form in statistical copolymers under suitable conditions [2], In this section, we will discuss the effects of counit incorporation on the solid-state structure and the crystallization kinetics in statistical copolymers. A number of thermodynamic models, which have been proposed to describe the equilibrium crystallization/melting behavior in copolymers, vill also be highlighted, and their applicability to describing experimental observations will be discussed. 

In order to prediet the stiffness, the strain concentration tensor A is needed. Mori and Tanaka (1973) eonsidered a composite model where the heterogeneities are diluted in the matrix. This model takes into account an interaction between the inclusion and the surroimdings (inelusions and polymer matrix) in their original model, the inclusions were considered to have the same shape and orientation. Benveniste (1987) made a reconsideration and reformulation of the Mori-Tanaka s theory in its application to the computation of the effective properties of composite. In this model the inclusions can be considered either aligned or randomly oriented. This formulation is more suitable for the morphology of clays dispersed in a polymer. The expression of the strain concentration tensor A is written as follows ... 

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