Application of the Euler characteristic to the study of homopolymer blends and copolymer melts

The Euler characteristic is applied to study the pi-case separation/ordering phenomena occurring in polymer mixtures. Several methods used to compute Euler characteristics are described and discussed in terms of accuracy and efficiency. A novel, robust and exact algorithm based on simplex decomposition is presented. The simulated morphology of spinodal decomposition and the phase equilibrium diagram of gradient copolymers are analyzed in terms of Euler characteristics. Again, the Euler characteristics are applied to specify the connectivity of bicontinuous patterns, to distinguish the disperse and the bicontinuous morphologies, and to detect the percolation transition. During the spinodal decomposition, the dynamic transformation between the bicontinuous and the droplet patterns is shown to involve the formation of a transient "cylindrical" morphology.