Figure 46.

Engulfment regimes for weakly curved mother membranes as a function of particle radius $R_{\mathrm{p}\mathrm{a}}=a$ and spontaneous curvature $m_{\mathrm{b}\mathrm{o}}=c_0$ of the membrane segment bound to the nanoparticle. Both quantities are given in units of the modified adhesion length ${\widehat{R}}_{\mathrm{W}}=\sqrt{2\kappa /w}$. The direction of negative spontaneous curvature coincides with direction of the curvature of the particle surface. Complete-wrapped states ${\mathcal{C}}_{\mathrm{s}\mathrm{t}}$ (blue) are found between the two regimes with non-wrapped states, ${\mathcal{F}}_{\mathrm{s}\mathrm{t}}^{<}$ and ${\mathcal{F}}_{\mathrm{s}\mathrm{t}}^{>}$ (yellow). The phase boundaries are given by $R_{\mathrm{p}\mathrm{a}}=1/({\widehat{R}}_{\mathrm{W}}^{-1}-m_{\mathrm{b}\mathrm{o}})$ for $m_{\mathrm{b}\mathrm{o}}<1/{\widehat{R}}_{\mathrm{W}}$ and $R_{\mathrm{p}\mathrm{a}}=1/(|m_{\mathrm{b}\mathrm{o}}|-{\widehat{R}}_{\mathrm{W}}^{-1})$ for $m_{\mathrm{b}\mathrm{o}}<-1/{\widehat{R}}_{\mathrm{W}}$. Reprinted with permission from [42]. Copyright (2015) American Chemical Society.