We calculate the membrane-induced interaction between inclusions, in terms of the membrane stretching and bending moduli and the spontaneous curvature. We find that the membrane-induced interaction between inclusions varies nonmonotonically as a function of the inclusion spacing. The location of the energy minimum depends on the spontaneous curvature and the membrane perturbation decay length, where the latter is set by the membrane moduli. The membrane perturbation energy increases with the inclusion radius. The Ornstein-Zernike theory, with the Percus-Yevick closure, is used to calculate the radial distribution function of inclusions. We find that when the spontaneous curvature is zero, the interaction between inclusions due to the membrane deformation is qualitatively similar to the hard-core interaction. However, in the case of finite spontaneous curvature, the effective interaction is dramatically modified.
We investigate the formation of polymer vesicles, or polymersomes, of polystyrene-block-poly(ethylene oxide) diblock copolymers using double emulsion droplets of controlled architecture as templates. To engineer the structure of the polymersomes, it is important to consider the concentration of diblock copolymer in the middle phase of the double emulsion. We describe how the presence of excess polymer can induce a transition from complete wetting to partial wetting of the middle phase, resulting in polymer shells with inhomogeneous thicknesses.
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