The influence of pressure on the reduction of the agglomeration of nanosolids: a case study for tungsten

The present work suggests a theoretical approach to reduce the agglomeration of nanoparticles by reducing the pressure below ambient. The model considers the increase in the surface energy upon reducing the pressure as an indicator for the reduction of agglomeration. This work relates the surface energy ( γ ) with the shape factor ( μ ) and the applied pressure. The shape factor is defined as the ratio of the surface areas of a deformed to a non-deformed sphere. This proposed model has been applied to the multiply-twinned spherical tungsten nanoparticles prepared by H. K. Kim et al. The shape factor and surface energy have been calculated for tungsten NSs that include ∼ 900 - 7000 atoms. The surface energy γ of an NP/NS has been calculated analytically as a function of size, shape, structure, and pressure. The findings of this work show that as the fraction of the twinning volumes ( ε ) increases, μ decreases. At zero applied pressure, the surface energy has been found to decrease as size decreases for spherical NPs. However, for non-spherical NPs, the surface energy increases as size decreases. Reducing the pressure (with respect to ambient) by 30–50 kPa, the surface energies exceed their corresponding values at zero applied-pressure at all ε . This means that the agglomeration of nanosolids can be reduced by reducing the pressure. Graphical Abstract