Fig. 3

a (symbols) Equivalent homogeneous dielectric constant of the liposomes, ε_eq, (N = 81) as a function of their height for the liposomes electrically detected in Fig. 2e. The vertical error bars correspond to the fitting error, while the horizontal ones to the uncertainty of the height determination. The model used in the calculations is shown in the bottom inset. The height and width have been determined from the topographic image in Fig. 2a. The tip geometry has been calibrated by using dC/dz approach curves acquired on a bare part of the substrate, giving R = 43 nm, θ = 20°, C'_offset = 1.5 aF/nm and c_subs = 0.6 µF/cm². The remaining parameters of the tip and solution are the same as in Fig. 1c. Theoretical values for ε_eq predicted from the uni-lamellar liposome model shown in the top inset (red continuous lines), with membrane specific capacitances c_m = 0.78 µF/cm², c_m/2 and c_m/3. For the internal solution we took σ_lip = 0.8 S/m, ε_sol = 78, corresponding to the solution used to prepare the liposomes. Theoretical values for ε_eq predicted for a bi-lamellar liposome model (grey dashed lines) with c_m = 0.78 µF/cm² and interlamellar separations d = 5 nm, 10 nm and 15 nm. b Distribution of lamellarity values obtained from the analysis in a and corresponding to the liposomes electrically detected in Fig. 2e