  Colloidal particles with mobile binding molecules constitute a powerful
platform for probing the physics of self-assembly. Binding molecules are free
to diffuse and rearrange on the surface, giving rise to spontaneous control
over the number of droplet-droplet bonds, i.e., valence, as a function of the
concentration of binders. This type of valence control has been realized
experimentally by tuning the interaction strength between DNA-coated emulsion
droplets. Optimizing for valence two yields droplet polymer chains, termed
`colloidomers', which have recently been used to probe the physics of folding.
To understand the underlying self-assembly mechanisms, here we present a
coarse-grained molecular dynamics (CGMD) model to study the self-assembly of
this class of systems using explicit representations of mobile binding sites.
We explore how valence of assembled structures can be tuned through kinetic
control in the strong binding limit. More specifically, we optimize
experimental control parameters to obtain the highest yield of long linear
colloidomer chains. Subsequently tuning the dynamics of binding and unbinding
via a temperature-dependent model allows us to observe the heptamer chain
collapse into all possible rigid structures, in good agreement with recent
folding experiments. Our CGMD platform and dynamic bonding model (implemented
as an open-source custom plugin to HOOMD-Blue) reveal the molecular features
governing the binding patch size and valence control, and opens the study of
pathways in colloidomer folding. This model can therefore guide programmable
design in experiments.
