Chapter 14: Continuum-limit Modelling of Structure Evolution in Active Blends for Organic Solar Cells

This chapter focuses on modelling the spinodal decomposition of solution processed polymer:PCBM blends under evaporative conditions. This mode of phase separation has been experimentally observed for a wide range of polymer:PCBM blends, especially in the absence of co-solvents. Dry-film morphologies characteristically comprise droplet-shaped PCBM-rich domains dispersed in a matrix of predominantly polymer. The modelling approach is based on a drastically coarse-grained treatment, involving solute and solvent concentrations as field-based order parameters. Structure evolution is driven by the minimization of a Flory–Huggins–Cahn–Hilliard-type free energy functional including local and non-local contributions. The model considers purely diffusive transport, either based on slow- or fast-mode dynamics. Solvent evaporation drives isothermal destabilization of the liquid blend giving spinodal decomposition. Linearization of the diffusion equation and solution of the rate equation for the growth of density fluctuations show that, due to evaporation, the spinodal wavelength initially decreases with time and only emerges as structural length scale after a given lag time. The lag time and emerging wavelength exhibit power-law behavior as a function of the evaporation rate with exponents of −2/3 and −1/6. The model predicts an increasing feature size and decreasing fullerene concentration in the polymer-rich phase with the increasing drying time, in accordance with experimental observations and device performance measurements.