  Developing construction methods of materials tailored for given applications
with absolute control over building block placement poses an immense challenge.
DNA-coated colloids offer the possibility of realising programmable
self-assembly, which, in principle, can assemble almost any structure in
equilibrium, but remains challenging experimentally. Here, we propose an
innovative system of linker-mediated mobile DNA-coated colloids (mDNACCs), in
which mDNACCs are bridged by the free DNA linkers in solution, whose two
single-stranded DNA tails can bind with specific single-stranded DNA receptors
of complementary sequence coated on colloids. We formulate a mean-field theory
efficiently calculating the effective interaction between mDNACCs, where the
entropy of DNA linkers plays a nontrivial role. Particularly, when the binding
between free DNA linkers in solution and the corresponding receptors on mDNACCs
is strong, the linker-mediated colloidal interaction is determined by the
linker entropy depending on the linker concentration.
