In spite of enormous research on gold nanoparticles, are there any theories established which explain the stability of it, when they are not stabilised by polymer or other stability imparting agents?
There are lot of theoretical and experimental studies on metal clusters. They are generated in vacuum and analyzed by means of MS revealing magic numbers. These studies are often accompanied by computations explaining the stability.
Check the magic numbers theory. It describe the stability of the metal nanoparticles based on the number of metal atoms. You can simply calculate the number of metal atoms in your gold nanoparticles. Use the TEM to determine the size of the particle then use the standard size of gold atom to calculate the number of gold atoms in your particles. Note: you should consider the shape of the particles. Away from the theory the stability of the gold nanoparticles/ gold colloidal sol is different from one system to another and it depends on many factor like the particle size, shape, solvent, surfactant, preparation method, etc.