Energy of Pt Nanoparticles

For ideal sphCTical particles, the Gibbs-Thompson equation relates the Gibbs energy to the radius. The chemical potential per metal atom of a particle with radius rpt is given by 

Entropy contributions to the Gibbs energy caused by vibrations of atoms in the nanoparticle are small and vary little with particle size. The relation Ecoh(N) tipt(N) is expected to be valid in the range of particle sizes, in which the spherical particle approximation holds. 

In a plot of Ecoh versus the intersection with the ordinate (i.e., in the limit N oo) corresponds to the bulk chemical potential of the metal /rp,, and the slope 

Pt nanoparticles with fewer than 25 atoms. Although their data could be represented reasonably well by a linear relation, these particle sizes are too small for a meaningful extrapolation to the bulk limit. 

FIGURE 3.6 (a) The absolute value of the cohesive energy Ecoh obtained from DFT-based optimization for Pt nanoparticles with up to 92 atoms, as a function of where N is the 

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Developing from this type of approach Tang and colleagues used first principle electronic structure calculations of the surface energy of Pt nanoparticles to develop size-dependent potential pH diagrams and to show, supported by experimental electrochemical scanning tunnelling microscopy, that Pt nanoparticles of diameter less than 4 nm dissolve oxidatively via the direct electrochemical dissolution ... 

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