Fig. 1
a Schematic representation of the in-liquid SDM setup in force detection mode used to measure the dielectric properties of single liposomes adsorbed on a functionalized metallic substrate. b Schematic representation of the theoretical model used to compute the tip-liposome capacitance gradient, dC/dz, for the case of an adsorbed bi-lamellar liposome, with the different parameters indicated. Not included in the scheme: tip height H, disc cantilever length Lc and cantilever thickness, W. c (continuous lines) Numerically calculated dependence of the tip-liposome capacitance gradient, dC/dz, for a bi-lamellar liposome as a function of the separation between the lamellae, d, for three different conductivities of the internal solution, σlip = 0.01 S/m, 0.1 S/m, 1 S/m. The dashed and dot-dashed lines correspond to the capacitance gradient values, dC/dz, for a uni-lamellar model with membrane capacitances cm = 0.76 µF/cm2 and cm/2 = 0.38 µF/cm2, respectively. Parameters of the calculations: tip radius, R = 30 nm, half cone angle, θ = 20°, cone height, H = 12.5 µm, cantilever disc radius, Lc = 3 µm, cantilever disc thickness, W = 3 µm, tip-substrate distance, z = 150 nm, spherical cap liposome shape with height, h = 100 nm and diameter, D = 500 nm, internal and external solution dielectric constants, εsol = εlip = 78, external solution conductivity, σsol = 0.2 µS/m, tip interfacial capacitance, ctip = 2.7 µF/cm2, substrate interfacial capacitance, csubs = 0.65 µF/cm2, frequency of the applied voltage, fel = 5 MHz