The transition from bulk to nano as a phase transition

It is demonstrated that the chemical potential of bosons trapped in a harmonic potential shows a discontinuity as a function of the number of particles in the system. In the model used, it is shown that if the number of particles is of the order of 106 or greater, bulk-like behaviour is exhibited by the system. This translates to a ratio of V/Vc>106 for bulk behaviour, where V is the crystallite volume of the experimental sample and Vc is the volume of the unit cell. Several experimental results covering a wide range of physical phenomena that corroborate the fact that such a number-induced phase transition indeed exists are presented.