Data-Driven Field Inversion of Molecular Simulations to Construct Free Energy Landscapes of Organic Semiconducting Systems

Constructing the free energy landscape of organic blends is a natural bridge between molecular simulations that faithfully capture molecular architecture effects, and continuum simulations that can account for processing conditions like evaporation rates and fluid shear stresses. Here, we show an approach that computationally extracts the free energy landscape from <b><i>a single MD simulation</i></b>. This is based on the idea that constitutive relations (i.e. the free energy landscape, that is a key ingredient of the continuum simulator) can be extracted from a sequence of spatio-temporal snapshots created from MD simulations using a framework of partial differential equation-constrained optimization. We illustrate this approach by considering the canonical problem of binary phase separation. A single configuration (here, volume fraction of A in a A/B binary mixture) of the system was chosen to perform MD simulation. Snapshots of the MD data was voxelized to construct volume fraction fields. This sequence of volume fraction fields representing a continuum analogue of the MD simulations then served as an input to a PDE constrained optimization framework. The optimization framework tries to fit the best free energy functional that produces a sequence of volume fraction fields that match the MD generated volume fraction fields. The free energy functional is used in a Cahn-Hilliard PDE that describes binary phase separation. We utilize a Bayesian based optimization strategy to identify the best fit free energy functional. We subsequently used this free energy functional to predict the morphology evolution of a A/B blend with a different initial composition, and produced excellent comparisons with MD simulations. This is a significant result since it suggests that a single MD simulation can be informative enough to extract constitutive relationships to enable equivalent continuum simulations. This opens up the way for systematic MD-continuum simulations while ensuring that a minimal number of compute intensive MD simulations are required. This is collaborative work with the Risko group (U Kentucky) and the Bazant group (MIT).