Coating thickness and coverage effects on the forces between silica   nanoparticles in water
  The structure and interactions of coated silica nanoparticles have been studied in water using molecular dynamics simulations. For 5 nm diameter amorphous silica nanoparticles we studied the effects of varying the chain length and grafting density of polyethylene oxide (PEO) on the nanoparticle coating's shape and on nanoparticle-nanoparticle effective forces. For short ligands of length $n=6$ and $n=20$ repeat units, the coatings are radially symmetric while for longer chains ($n=100$) the coatings are highly anisotropic. This anisotropy appears to be governed primarily by chain length, with coverage playing a secondary role. For the largest chain lengths considered, the strongly anisotropic shape makes fitting to a simple radial force model impossible. For shorter ligands, where the coatings are isotropic, we found that the force between pairs of nanoparticles is purely repulsive and can be fit to the form $(R/2r_\text{core}-1)^{-b}$ where $R$ is the separation between the center of the nanoparticles, $r_\text{core}$ is the radius of the silica core, and $b$ is measured to be between 2.3 and 4.1. 
K. Michael Salerno, Ahmed E. Ismail, J. Matthew D. Lane, and Gary S.   Grest
cond-mat.soft