Controlled self-assembly using external rotating electric or magnetic fields is an emerging area in soft matter, with applications in creating functional materials, three-dimensional bioprinting, and tissue engineering. Experimental studies in this field are typically conducted on substrates with pinning zones, which affect diffusion and, consequently, self-assembly processes, though the detailed impact of pinning on diffusion has not been systematically studied before. In the present work, we systematically calculate diffusion in a system relevant to a monolayer of colloidal particles with tunable interactions induced by external electric or magnetic fields, placed on a substrate with pinning zones. Using molecular dynamics simulations, we explore the diffusion of particles over a wide range of parameters for attractive and repulsive interaction regimes induced by different field configurations. We derive simple fits that accurately capture the effect of pinning on diffusion across a broad portion of the phase diagram. We believe this fit will be useful for analyzing and designing experiments with two-dimensional soft matter systems with tunable interactions and for various potential applications.

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• Diffusion
• 2-dimensional systems
• Classical fluids
• Colloids
• Brownian dynamics
• Molecular dynamics