Controlling curvature of self-assembling surfaces via patchy particle design

Abstract Curved surfaces in soft matter and biological systems commonly emerge as a result of self-assembly processes where building blocks aggregate in a controlled manner, giving rise to specific system structure and properties. However, achieving precise control of curvature in assembled structures remains challenging and usually requires tuning of complex interactions between particles. We present an inverse design approach to target self-assembly into surfaces with a specified spherical curvature in a one-component system of model patchy particles. Our optimization framework leverages automatic differentiation and addresses the challenge of exploding gradients when differentiating over chaotic molecular dynamics trajectories, yielding stable gradients suitable for general optimization schemes. We outline the model requirements for successful optimization and determine the significant hyperparameter choices influencing algorithm performance. Finally, we demonstrate that the proposed approach allows us to design interactions for self-assembly into structures with a tunable target curvature, paving the way for new functional materials with precisely controlled geometries.