Bending moduli of polymeric surfactant interfaces

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Abstract
Our recent theory of the free energy and conformations of end-grafted polymer « brushes » is extended to polymers attached to curved surfaces. Several important systems, e.g., layers of polymeric surfactants or of strongly segregated diblock copolymers, can be well described as brushes. By expanding in powers of the curvature the free energy of a brush on a curved surface, the mean and Gaussian bending moduli may be obtained analytically. Results for K and K of monodisperse brushes are consistent with scaling arguments, which imply K, K ∼ N3 σ 5 for melt conditions and ∼ N3 σ 7/3 for moderate-density brushes with solvent. The important case of a brush composed of a mixture of long- and short-chain molecules is also treated analytically. The replacement of a small fraction of long-chain molecules in a brush by short chains is shown to dramatically reduce the bending moduli