THERMODYNAMICS OF NANOPARTICLE SySTEMS

Classical thermodynamics deals with macroscopic thermal-mechanical properties and their relationships for massive assemblages of atoms or molecules (i.e., 10 fundamental particles) in terms of energy conversion and transformation. Studies of phase/chemical changes and equilibria involving nanoparticles are important areas where the classical thermodynamic approach is effective. Because quantum mechanical effects may be marked (e g., the energy of a nanoparticle may not be continuous) where there are only several hundred (or even only tens) of atoms in a nanoparticle, one may ask, Is classical thermodynamics still valid for nanoparticle systems  

A rigorous thermodynamic treatment of nanoparticle systems should at least contain quantum mechanical corrections. However, these treatments are impractical and difficult, considering the vast diversities of thermodynamic systems and the enormous numbers of fundamental particles involved in each. If thermodynamic quantities of a nanoparticle system are determined by conventional methods (such as calorimetry and equilibrium determinations), these quantities bear contributions from quantum mechanical effects and classical thermodynamics may still be applicable, so long as the number of atoms is not too small. 

At constant temperature and external pressure, there are many ways to approach the minimum free energy state (equilibrium state) for the system  

Minimization of the total free energy by phase transformation 

Given the above assumptions, the independent thermodynamic variables are temperature T, external pressure P and particle size D (diameter). When the three variables change, the change in the total free energy of the system is only due to the change in the free energy of the nanoparticles. The nanoparticles may undergo a phase 

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