Simulation of Polymer Fractal Formation Using a Triangular Network Growth Model

Fractal formation in spin-coated thin-film polymers is of experimental and theoretical interest. Modeling the determinants and dynamics of this process will deepen our understanding of polymer aggregation and the predictability of thin-film structures. This is especially true if the model used has readily interpretable parameters and has been demonstrated to yield a close match to experimental processes under a variety of conditions. In this work, we adapted and applied a relatively new model of fractal growth comprised of a spreading and contracting triangular network, to model spin-coated, thin-film polymers made of poly(vinyl alcohol) on polydimethylsiloxane substrates. We drew clear connections between model parameters and the process of polymer aggregation and we demonstrated the ability of the model to simulate fractal formation under a wide variety of conditions including varying the degree of hydrolysis of the polymer, changing the spin-coating process, and solvent annealing and reforming of polymer fractals under different drying conditions. We also showed how the model is able to replicate idiosyncratic experimental settings yielding novel fractal patterns.