Effects of charge and its fluctuation on membrane undulation and stability

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Abstract
We study the electrostatic effects on the undulation of a flexible membrane with non-vanishing excess charges and charge fluctuation. It is shown that the membrane becomes unstable to a long-wavelength undulation due to Coulomb repulsion between excess charges on the membrane. This instability is suppressed both by charge fluctuation which induces an effective attraction and by free ions in solution which screen the Coulomb repulsion. Our result explains qualitatively spontaneous vesiculation and also its suppression by added salts observed for mixtures of ionic surfactants. The charge-fluctuation-induced attraction, unless screened by the free ions, softens the membrane by reducing bending rigidity.