The Role of Repulsion in Colloidal Crystal Engineering with DNA

Hybridization interactions between DNA-functionalized nanoparticles (DNA-NPs) can be used to program the crystallization behavior of superlattices, yielding access to complex three-dimensional structures with more than 30 different lattice symmetries. The first superlattice structures using DNA-NPs as building blocks were identified almost a decade ago, yet the role of repulsive interactions in guiding structure formation is still largely unexplored. Here, a comprehensive approach is taken to study the role of repulsion in the assembly behavior of DNA-NPs, enabling the calculation of interparticle interaction potentials based on experimental results. In this work, we used two different means to assemble DNA-NPs - Watson-Crick base-pairing interactions and depletion interactions - and systematically varied the salt concentration to study the effective interactions in DNA-NP superlattices. A comparison between the two systems allows us to decouple the repulsive forces from the attractive hybridization interactions that are sensitive to the ionic environment. We find that the gap distance between adjacent DNA-NPs follows a simple power law dependence on solution ionic strength regardless of the type of attractive forces present. This result suggests that the observed trend is driven by repulsive interactions. To better understand such behavior, we propose a mean-field model that provides a mathematical description for the observed trend. This model shows that the trend is due to the variation in the effective cross-sectional diameter of DNA duplex and the thickness of DNA shell.