Redox Behavior of Nanoparticules: Nonextensive Thermodynamics Approach

We show here that the concepts of nonextensive thermodynamics (NET), described previously ( J. Phys. Chem. B, 2004, 108, 18980), can be used to express the variations of a redox couple according to the size of the reduced solid species by a power law. The Gibbs−Thompson relation then appears as a particular case of this formulation. The NET adopts the same conceptual basis as classical thermodynamics but uses an extensity, χ, in the expression of internal energy. This extensity is an Euler’s function of the particle mass with a homogeneity degree, m, which can be other than one; m is the thermodynamic dimension of the system. The consequences are that the functions of state are no longer extensive and that the magnitudes such as the chemical potential or the pressure are no longer intensive extents. This approach can be used to describe complex systems (for example, nanoparticles, porous substrates, and dispersed or interpenetrated phases). We checked the validity of the relations established by considering experimental data concerning the Ag/Ag + system. The silver clusters which grow on AgBr and AgBr in the presence of gelatin indeed have the properties of nonextensive phases of which we specify the characteristics.