Colloids coated with single-stranded DNA (ssDNA) can bind selectively to other colloids coated with complementary ssDNA. The fact that DNA-coated colloids (DNACCs) can bind to specific partners opens the prospect of making colloidal `molecules. However, in order to design DNACC-based molecules, we must be able to control the valency of the colloids, i.e. the number of partners to which a given DNACC can bind. One obvious, but not very simple approach is to decorate the colloidal surface with patches of single-stranded DNA that selectively bind those on other colloids. Here we propose a design principle that exploits many-body effects to control the valency of otherwise isotropic colloids. Using a combination of theory and simulation, we show that we can tune the valency of colloids coated with mobile ssDNA, simply by tuning the non-specific repulsion between the particles. Our simulations show that the resulting effective interactions lead to low-valency colloids self-assembling in peculiar open structures, very different from those observed in DNACCs with immobile DNA linkers.
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