Interactions between nanoparticles and fractal surfaces.

This study evaluated attachment of a 30-nm nanoparticle to and detachment from fractal surfaces by calculating Derjaguin-Landau-Verwey-Overbeek (DLVO) interaction energies in three-dimensional space using the surface element integration technique. The fractal surfaces were generated using the Weierstass-Mandelbrot function with varying values of fractal dimension D (2.3 ≤ D ≤ 2.7) and fractal roughness G (0.000136 ≤ G ≤ 0.136). Results show that maximum energy barrier is reduced at peak areas of a fractal surface, and hence attachment in primary minima is favored. Some nanoparticles attached in primary minima at the peak areas can be detached by decreasing ionic strength (IS) due to monotonic decrease of interaction energy with increasing separation distance at low ISs. While the attachment in primary minima at valley areas is irreversible to IS reduction, the attachment is inhibited due to enhanced maximum energy barrier at these areas. A nonmonotonic variation of attachment efficiency in primary minimum (AEPM) with IS is present at high fractal dimension (D ≥ 2.4) or low fractal roughness (G < 0.00136), whereas the AEPM decreases monotonically with decreasing IS at low fractal dimension (D < 2.4) or high fractal roughness (G ≥ 0.00136). The AEPM decreases monotonically with increasing D or decreasing G at ISs from 1 mM to 200 mM. The decrease of AEPM with D or G is much slower at 10 mM compared to other ISs. These theoretical findings can explain various experimental observations in the literature, and can have important utility to development of water filtration techniques in engineered systems and to assessment of environmental risks of nanoparticles.