Fluctuations and instabilities of model amphiphile interfaces

We study the stability of planar, cylindrical and spherical interfaces with respect to shape and width fluctuations for a model amphiphile solution described by a free energy density functional with square-gradient and square-Laplacian terms. That is, we determine the stability matrix when the stationary state consists of an interface with given geometry that separates two immiscible solvent phases. From the spectrum and the related eigenfunctions of this matrix we establish where lamellar and micellar domain-structured phases occur, and contrast our results with those for a simple square-gradient fluid model for which these phases are always unstable. We also characterize some instability properties such as the buckling of lamella, the undulation of cylindrical structures and the nucleation of micelles.