Particle Penetration into Polydisperse Polymer Brushes: A Theoretical Analysis

Based on theoretical analysis, the effect of polydispersity on particle penetration into polydisperse polymer brushes is investigated. Three different polydispersities representing sharp, moderate, and extremely wide chain length distributions are chosen, since the corresponding explicit expressions of brush density at these polydispersities are available. To simplify the discussion, this study is restricted to spherical particles of small size which ensure that the particle insertion only causes local conformational perturbations. By analyzing the particle distribution, it is found that polydispersity always facilitates particle penetration. This prediction is confirmed by analyzing the surface fluctuations of the brushes. Interestingly, uniform scaling relations are observed for particles penetrating into monodisperse and moderately polydisperse brushes. The uniformity predicted by monodisperse and moderately polydisperse brushes originates from the same asymptotic behavior of their densities approaching the brush edge. This indicates that polydispersity brings significant influence only at high polydispersities.