Entropy Driven Self-Assembly in Charged Lock-Key Particles

In this work we study the lock-key model successfully used in supramolecular chemistry and particles self-assembly and gain further insight into the infinite diluted limit of the lock and key, depletant mediated, effective attraction. We discuss the depletant forces and entropy approaches to self-assembly and give details on the different contributions to the net force for a charged lock and key pair immersed in a solvent plus a primitive model electrolyte. We show a strong correlation of the force components behavior and the underlying processes of co-ion and solvent release from the cavity. In addition, we put into context the universal behavior observed for the energy-distance curves when changing the lock and key to solvent size ratio. Basically, we now show that this behavior is not always achieved and depends on the particular system geometry. Finally, we present a qualitative good agreement with experiments when changing the electrolyte concentration, valence, and cavity-key size ratio.