Two complementary theoretical approaches are used to study the effect of polydispersity on (anti)fouling properties of a neutral polymer brush. Polydispersity is described using the Schulz−Zimm distribution. The Scheutjens−Fleer self-consistent-field (SF-SCF) formalism is used to consider the interaction between a single particle and a polydisperse brush with grafting density σ, focusing on the influence of the polydispersity index. The larger the polydispersity, the easier it is for a small particle (with radius R ∼ 1/(2 √ σ)) to penetrate the brush. Hence, the monodisperse brush is better suited to protect a surface against the adsorption of small particles compared to a corresponding polydisperse brush. The brush grafting density, however, remains the most important parameter for tuning the brush antifouling properties against small particles. For large particles (modeled as a flat wall) an opposite effect of polydispersity is found: it is harder to compress a polydisperse brush than a corresponding monodisperse brush, and thus a polydisperse brush is better suited to protect the surface against adsorption of large particles. A less-detailed approach, based on the stacking of Alexander−de Gennes boxes, is used to study the adsorption of many particles into a polydisperse brush. Consistent with the single-particle data generated by the SF-SCF theory, for weak attraction between the particles and the brush the absolute adsorbed amount remains low but increases strongly as a function of polydispersity (from M w / M n = 1−2 by a factor of 2−4). Obviously, at higher attraction between the particles and the brush the adsorption increases, but a less strong dependence on the polydispersity index is observed.
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Vos et al. (2009) studied this question.