Modeling the assembly of oppositely charged lock- and key-colloids

The interaction of oppositely charged lock- and key-colloids is investigated using computer simulations. We show that indented spheres, i.e., lock-particles, can be specifically assembled with spherical key-particles using solely electrostatic interactions in addition to a hard overlap potential. An analytic description of the entropic and energetic contributions is derived and supported by simulations and explicit energy calculations, respectively. The analytic expression of the electrostatic contribution is further employed to build up a schematic model allowing for efficient large-scale Monte Carlo simulations. The influence of the charge/ionic strength, the degree of indentation, and the size/number ratio is discussed by analyzing the specific and unspecific associations from the simulations. Herein, both particle design and mixing conditions lead to the formation of stable specific clusters analogous to colloidal molecules whose valence is defined by the number of lock-particles associated with a key-particle. In addition, the approach is extended to the encapsulation of an excess of small key-particles in largely indented lock-particles. These two examples exemplify that highly specific pairwise interactions can be implemented by using solely oppositely charged particles with complementary geometries, which opens the road for a rational design of complex hierarchical self-assemblies of complementary building blocks.