Brushes on curved surfaces

In many applications, including colloid stabilization, polymers are end-grafted onto large particles which are intermediate between the planar brush and a star. Curved brushes, with either spherical or cyUndrical symmetry, can also be formed by asymmetric diblock copolymers in the strong segregation limit. When the grafting surface curves towards the polymers (concave curvature), the volume available to the polymer chains is lowered compared to a flat surface. In this case, the chains are stretched throughout the brush and the brush is qualitatively unaltered from the flat case. MC simulations on a tetrahedral lattice for chains inside a spherical cavity 

The free end density as a function of the distance from the grafting surface 

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As it is well established, polymer brushes on flat substrates can be treated to a first approximation as a linear string of blobs of equal size [2]. On the other hand, in the case of a brush grafted on a curved surface (convex or concave), the theoretical analysis of the system is somewhat more complicated than the case of flat surfaces, and that is because the surface curvature leads to the modification of the available space for each grafted chain. Following the classic theoretical analysis of Daoud and Cotton for star polymers [3], brushes on curved surfaces can be envisioned as an array of concentric shells of blobs that have variable size as we move away from the... 

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