Pores shrinkage and growth in polycrystalline hollow nanoparticles and nanotubes

We propose a model of internal pore shrinkage in hollow polycrystalline nanoparticles controlled by surface and grain boundary diffusion. The latter significantly accelerates the pore shrinkage as compared to single crystalline nanoparticles. Moreover, further shrinkage acceleration is achieved by allowing material accretion/depletion at the grain boundaries and concomitant drift of the grain's lattice toward the center of the particle. Our model predicts that above a certain critical number of grain boundaries in the particle the central pore becomes thermodynamically stable and cannot be removed by annealing.