Polymer brushes at curved surfaces

Abstract

In this paper we use the polymer adsorption theory of Scheutjens and Fleer to describe polymer brushes at spherical and cylindrical surfaces that are immersed in a low molecular weight solvent. We analyze the volume fraction profiles of such brushes, focusing our attention on spherical brushes in athermal solvents. These are shown to generally consist of two parts: a power law-like part and a part that is consistent with a parabolic potential energy profile of the polymer segments. Depending on the curvature of the surface, one of these two parts is more important, or may even dominate completely. We especially consider the distribution of the free end segments and the possible existence of a "dead zone" for these segments. Such a dead zone is actually found and is seen to follow a scaling law in the case of large curvatures. Furthermore, the effect of diminishing the solvent quality is considered for both the total volume fraction profile and the distribution of the end segments.

Exclusion zone of convex brushes in the strong-stretching limit

“…However, such a difference is not surprising, as these authors have found that exact solution for the cylindrical brush is also significantly lower than the value predicted from variational approach. Additionally, lower size of the exclusion zone predicted in this work is in line with later simulations by Grest [14] and numerical calculations by Wijmans and Zhulina [19], and Dan and Tirrell [20].…”

“…Several simulations [14,15,16,17,18], semi-analytical calculations [13,19], and numerical approaches [19,20] have been introduced. However, none of these fully exploits the limit of strong stretching to provide an analytical result at intermediate curvatures, or gives a quantitative answer in the limit of very strong curvatures.…”

Spherical polymer brushes under good solvent conditions: Molecular dynamics results compared to density functional theory

“…In order to study the crossover of the average brush height H av from the flat brush limit to the star polymer limit in detail, we follow Wijmans and Zhulina 45 by defining H av from the second moment of the monomer density profile as follows shown as a broken straight line. The DFT results converge to a power law with slope of minus one third (or -2/6), (full straight line).…”

“…From the SCFT treatment of Wijmans and Zhulina 45 we conclude that in the limit R c → ∞, N → ∞ (these limits need to be taken together such that 0 < H 0 /R c < ∞) a scaling property holds, where f ( H 0 Rc ) is some scaling function,…”

Effect of Chain Tilt on the Interaction between Brush-Coated Colloids

“…First of all, eq 5 overlooks the presence of zones where the free chain ends are excluded from next to convex grafting surfaces (i.e., wedges with S′( ) > 0). 17 The proper treatment of these exclusion zones is sufficiently complex that the full solution has only been formulated for cylindrical brushes in the melt state (i.e., φ( ) ) 1). 18 Nevertheless, this one example demonstrates that the zones have an absolutely negligible effect on the free energy, even in the limit of infinite surface curvature.…”