Multiscale numerical approximation of morphology formation in ternary mixtures with evaporation : Discrete and continuum models for high-performance computing

Abstract

We propose three models to study morphology formations in interacting ternary mixtures with the evaporation of one component. Our models involve three distinct length scales: microscopic, mesoscopic, and respectively, macroscopic. The real-world application we have in mind concerns charge transport through the heterogeneous structures arising in the fabrication of organic solar cells. As first model, we propose a microscopic 3-spins lattice dynamics with short-range interactions between the considered species. This microscopic model is approximated numerically via a Monte Carlo Metropolis-based algorithm. We explore the effect of the model parameters (volatility of the solvent, system's temperature, and interaction strengths) on the structure of the formed morphologies. Our second model is built upon the first one, by introducing a new mesoscale corresponding to the size of block spins. The link between these two models as well as between the effects of the model parameters and formed morphologies are studied in detail. These two models offer insight into cross-sections of the modeling box. Our third model encodes a macroscopic view of the evaporating mixture. We investigate its capability to lead to internal coherent structures. We propose a macroscopic system of nonlinearly coupled Cahn-Hilliard equations to capture numerical results for a top view of the modeling box. Effects of effective evaporation rates, effective interaction energy parameters, and degree of polymerization on the wanted morphology formation are explored via the computational platform FEniCS using a FEM approximation of a suitably linearized system. High-performance computing resources and Python-based parallel implementations have been used to facilitate the numerical approximation of the three models