Physics-Informed Displacement Control for Variable Pattern Printing with V-shaped PDMS Stamps in Roll-to-Roll Microcontact Printing

Abstract Roll-to-roll microcontact printing enables high-throughput production of flexible electronic devices by continuously transferring inks onto substrates via polydimethylsiloxane (PDMS) stamps. Traditional rectangular or cylindrical PDMS stamps yield uniform pattern sizes, limiting manufacturing versatility. This study introduces V-shaped PDMS stamps for variable pattern printing using a single stamp geometry. A physics-based deformation model was developed by combining finite element simulations and experiments to characterize the out-of-plane behavior of V-shaped PDMS under displacement. Leveraging this model, we implemented a neural network-based Model Predictive Control (MPC) system to precisely regulate vertical displacement and achieve desired pattern dimensions. Experimental results demonstrate that a single V-shaped PDMS stamp can reliably produce variable pattern sizes with high repeatability, significantly improving the adaptability and process efficiency of microcontact printing for flexible electronics manufacturing.