Macromolecules, Vol.36, No.13, 5032-5038, 2003
A general method for calculating bending moduli and spontaneous curvature of polymer brushes in terms of local density functional theory
A general method for calculating the spontaneous curvature and the bending modulus of surfactant monolayers or grafted polymer brushes is presented which is based on a density functional theory, where the bending parameters and the spontaneous curvature are analytically represented in terms of integral moments of the solution for the flat geometry. The novelty here is that the problem is solved for an arbitrary form of the free energy density function with the only requirement being that the energy functional is local. The difference compared to other approaches is that for the case of local density functional theories; the lateral pressure and its derivatives with respect of curvature could be expressed analytically in terms of the density profiles of the flat geometry. This general approach enables a variety of problems involving polymer brushes, surfactants, and amphiphilic diblock copolymers to be treated directly and has direct application in modeling the phase behavior of microemulsions and surfactant solutions. As particular examples we consider the cases of low-density arbitrary solvent, arbitrary density in ideal solvent and Theta solvent of a polymer brush and an amphiphilic diblock copolymer.