2D capsid formation within an oscillatory energy landscape: orderly self-assembly depends on the interplay between a dynamic potential and intrinsic relaxation times.

Multiple dissipative self-assembly protocols designed to create novel structures or to reduce kinetic traps have recently emerged. Specifically, temporal oscillations of particle interactions have been shown effective at both aims, but investigations thus far have focused on systems of simple colloids or their binary mixtures. In this work, we expand our understanding of the effect of temporally oscillating interactions to a two-dimensional coarse-grained viral capsid-like model that undergoes a self-limited assembly. This model includes multiple intrinsic relaxation times due to the internal structure of the capsid subunits and, under certain interaction regimes, proceeds via a two-step nucleation mechanism. We find that oscillations much faster than the local intrinsic relaxation times can be described via a time averaged inter-particle potential across a wide range of interaction strengths, while oscillations much slower than these relaxation times result in structures that adapt to the attraction strength of the current half-cycle. Interestingly, oscillation periods similar to these relaxation times shift the interaction window over which orderly assembly occurs by enabling error correction during the half-cycles with weaker attractions. Our results provide fundamental insights to non-equilibrium self-assembly on temporally variant energy landscapes.