What kind of phases nanoparticles have (gas-solid-liquid)? If a phase transition requires a number of particles that is in the TD-limit, can nanoparticles (~10 atoms) have phase transitions? What kind of phases and transitions nanoparticles have?
 A: We can't really talk generally about the phase of an individual nanoparticle, as we aren't in the thermodynamic limit, as the question you linked to suggests. 
Think about what a gas is, for example: gases have a higher average kinetic energy than a liquid, which causes it to be less dense and occupy a greater volume than liquid. But if we look at the particles comprising the gas at a microscopic level, we see a distribution of velocities - there will be some proportion of the molecules that have less kinetic energy than the average energy of, say, a liquid. But in a liquid, there will be some small proportion of molecules that have more kinetic energy than the average kinetic energy of a gaseous phase. So it makes sense to talk about phases in terms of an average over a large number of particles and not in terms of an individual particle. The number of particles comprising a nanoparticle is many orders of magnitude less than that required for the thermodynamic limit.
I suppose you could describe a single nanoparticle in a Bose Einstein Condensate state, since the BEC phase is described by all particles taking on a common wavefunction which is a different requirement than some sort of average over many particles.
You can, however, talk about the phase of a large collection of nanoparticles; this is no different than how we describe the solid, liquid, or gaseous state of any other material.
