Predicting the mechanical properties of immiscible binary polymer blends, particularly Young’s modulus and tensile strength, has long been challenging due to their strong dependence on complex parameters such as microstructure, interfacial properties, and percolation thresholds. Mathematical modeling provides a powerful tool for understanding these relationships and reducing laboratory costs. The main objective of this article is to provide a systematic review of two foundational analytical models that have served as the basis for many more advanced models and are grounded in the microstructural variations of immiscible polymer blends: the Cross-Orthogonal Skeleton (COS) model and the Knitted-Interlocked Skeleton Structure (KISS) model.
In this review, the fundamental assumptions, mathematical details, and predictive mechanisms of each model are thoroughly elaborated. Emphasis is placed on analyzing how these semi-empirical models account for the effects of phase microstructure (such as the arrangement of dispersed and matrix phases) and interfacial conditions. Subsequently, the strengths of each model, including their relative simplicity and ability to provide an initial analytical framework, are discussed alongside their inherent limitations, such as oversimplification in the face of complex microstructures or insufficient attention to nonlinear dependencies. Finally, the importance of these fundamental models as a bridge to developing more sophisticated and accurate models capable of overcoming some of these limitations is explained.