Flory-Huggins Parameter χ, from Binary Mixtures of Lennard-Jones Particles to Block Copolymer Melts

The Flory-Huggins parameter χ, is a quantity of paramount importance in describing the degree of segregation in block-copolymer systems. The parameter is dictated by the differences in the chemical character between the constituent monomers and the detailed molecular architecture of the copolymer. For bead-spring models with impenetrable monomer cores the calculation of χ is difficult, since the free energy of the system is not directly accessible, making additional expensive calculations necessary. We propose a novel approach for determining χ that resolves these issues by decoupling the chemical incompatibility of the monomers from the effects of molecular architecture. In particular, we have performed an extensive set of isobaric-isothermal Monte Carlo simulations of binary mixtures of Lennard-Jones particles with the same size, but with asymmetric energetic parameters. The phase behavior of these monomeric mixtures is then extended to chains with finite sizes through theoretical considerations, where we have taken the effects of molecular architecture into account by estimating an effective molecular size [1]. We demonstrate the applicability of our approach for generating parameters by reproducing the morphology diagram of a specific diblock copolymer, namely, poly(styrene-b-methyl methacrylate), which has been extensively studied in experiments.

[1] A. Chremos, A. Nikoubashman, and A. Z. Panagiotopoulos, J. Chem. Phys. 140, 054909 (2014).