Numerical study of DNA-functionalized microparticles and nanoparticles: explicit pair potentials and their implications for phase behavior.

DNA-coated colloids have great potential for the design of complex self-assembling materials. In order to predict the structures that will form, knowledge of the interactions between DNA-functionalized particles is crucial. Here, we report results from Monte Carlo simulations of the pair-interaction between particles coated with single-stranded DNA sticky ends that are connected to the surface by relatively short and stiff surface tethers. We complement our calculations with a study of the interaction between two planar surfaces coated with the same DNA. Based on our simulations we propose analytical expressions for the interaction potentials. These analytical expressions describe the DNA-mediated interactions well for particle sizes ranging from tens of nanometers to a few micrometers and for a wide range of grafting densities. We find that important contributions to both the repulsive and attractive parts of the free energy come from purely entropic effects of the discrete tethered sticky ends. Per bond, these entropic contributions have a magnitude similar to the hybridization free energy of a free pair of sticky ends in solution and they can thus considerably change the effective sticky-end binding strength. Based on the calculated interaction potentials, we expect that stable gas-liquid separation only occurs for particles with radii smaller than a few tens of nanometers, which suggests that nanoparticles and micrometer-sized colloids will follow different routes to crystallization. Finally, we note that the natural statistical nonuniformities in the surface distribution of sticky ends lead to large variations in the binding strength. This phenomenon may compromise the reliability of tests that aim to detect specific DNA targets in diagnostics. In addition to guiding the design of novel self-assembling materials and gene-detection assays, the insights presented here could also shed more light on (multivalent) interactions in other systems with tethered binding groups, for instance in the areas of supramolecular chemistry or ligand-receptor mediated biorecognition.