Non-extensivity of thermodynamics at the nanoscale in molecular spin crossover materials: a balance between surface and volume.

The spin transition behavior in nanoparticles of molecular spin crossover (SCO) materials is investigated theoretically using a two-variable microscopic Ising-like model solved by Monte Carlo simulations. The extensive nature of the energy, and therefore the whole thermodynamics is affected by the increasing role of surface energetic parameters. As a consequence the pressure inside the nanoparticle is different from the external pressure of the bath. The difference of the surface energies between the low spin (LS) and the high spin (HS) states is the origin of the modification of the SCO properties at finite sizes (downshift of the transition temperature and loss of the hysteresis). On the other hand, the extensivity of the system can be controlled by the form of the nanoparticle. Hollow particles allow control of the surface to volume ratio. An important consequence of this effect is the conservation of the SCO properties as a function of size. A modification of the intermolecular interactions at the surface leads to a modification of the surface rigidity, and will impact also on the extensivity of the system. When increasing/decreasing the surface rigidity the global elasticity of the nanoparticle raises/decreases and enhances/reduces the cooperativity of the SCO material.