Discovering New Ordered Phases of Block Copolymers

We propose a new and general method for discovering novel ordered phases of block copolymer melts. The method involves minimizing a free energy functional in an arbitrary unit cell with respect to the composition profile and the dimensions of the unit cell, without any prior assumption of the microphase symmetry. Varying the initial conditions allows to search for different stable and metastable structures. Application of this method to ABC star and linear triblock copolymers using an approximate free energy reveals new morphologies not yet observed in experiment

Reversible Association of Telechelic Molecules: An Application of Graph Theory

We develop a method for calculating the exact free energy of tree clusters formed from associating telechelic molecules. The method uses the concept of rooted trees from the graph theory to enumerate all topologically distinct trees having a maximum degree of branching; it recursively separates the trees into different classes based on their connectivity, thus enabling the exact summation of the trees weighted by their respective Boltzmann factors. We apply our method to studying the pregel properties in pure telechelic solutions and in mixed telechelic and single-associating-end polymer solutions. We highlight the effect of energetic tendency for branching in the former and the effect of competitive association in the latter