Lock and key (and nanoparticle) with appropriate radii,
r, labelled. The size and extent of the lock 'mouth' can be described as a spherical indentation of a 'cutting sphere' with radius
rC.
### Depletion-driven self-assembly of lock and key colloidal fluids.
Imagine a box filled with three kinds of particles. Two of these particles are called the lock and the key (approximately the same size), whilst the third is denoted the nanoparticle (approximately one tenth the radii of a lock). The lock is a sphere with a spherical indentation and the key and nanoparticle are both spherical. For the system in question, there are generally many more nanoparticles than locks or keys. The system is free to sample any (physical) configuration it likes, within the confines of the box, and in fact, favours a combined lock and key set up. Why is this?
Our closed system will approach a state of minimum free energy: the more volume available to the nanoparticles, the lower the free energy. If you sat down and looked at the volumes of a separate lock and a separate key compared to a so called 'dimer', you'd find the dimer's volume is less. Therefore, the configurations in which the lock and key are 'locked' are the preferred states for the whole system. The nanoparticles 'force' the locks and keys into bound states so they can have more entropy, and hence the overall free energy of the system will reach a minimum.
### Current Work
