The stability of a nanoparticle is a term often used to describe the preservation of a specific, usually size-dependent, property of the particle. It can refer to e.g.: its size, shape, composition, crystalline structure, surface properties or dispersion within a solution. The interfacial layer of a nanoparticle can aid these types of stabilities in different ways.
The ligands can bind to the different facets of a nanoparticle, the size and type of which will determine the way the ligands will be ordered. The way the ligands are attached to the particle, ordered disordered or somewhere in between, plays a crucial role in the way different particles will interact. This in turn affects the reactivity of the nanoparticle, which is another way to look at the stability of the particle.