MODELING POLYMER ADSORPTION THROUGH THE USE OF PHYSICS INFORMED NEURAL NETWORKS (PINN’s)

Polymer adsorption on charged surfaces has garnered considerable attention in the last decades, beyond being a fundamental model for the statistical mechanics of macromolecules, its results have served as a basis for the study of several biologic processes. This work investigates the intricate interplay between polymer conformations and electrostatic interactions driving adsorption phenomena. We employ physics-informed neural networks (PINN's) to solve the Edwards equation, a fundamental equation governing polymer configurations, in the presence of external electric fields. This approach allows us to determine the probability density of polymer segments at different positions relative to the surface. By incorporating the underlying physics into the neural network architecture, this model may enable us to capture more details between polymer flexibility and the interactions arising from electrostatic forces. The results provide valuable insights into the adsorption process, revealing how polymer chain length, surface charge density, and solution conditions influence the equilibrium distribution of adsorbed polymers. This work demonstrates the power of PINN's as a robust and versatile tool for unraveling complex polymer adsorption mechanisms.