The name is absent

silicon nitride tip (ε = 7), Domain III the 5 nm thick lipid bilayer membrane (ɛ = 2), and
Domain IV the mica substrate {ε = 6). Since there are no free charges in domain II, III
and IV, the electrostatics potential in these domains are governed by the Laplace equation
vV = o            (²∙⁵)

On line ABCDEF, the zero charge density boundary condition was applied:

V ψ ∙ n = 0            (2.6)

Over line FGIJKA, radial symmetry holds as

^ = O          (2.7)

dr

Constant charge density boundary conditions (Neumann’s condition) were applied [48] at
the surface of the AFM tip (GHI) and at the upper surface of the lipid membrane (line
JD):

ε₁V^tl⅛∕∙ιι-ε₂V^p⅛∕∙n = -σ∕ε₀    (2.8)

where n represents the vector normal to the surface in the direction pointing to the
electrolyte solution. At the interface between the membrane and mica (line CK),
continuity holds. To simulate the force curves between the silicon nitride AFM tip and
the flat silicon nitride substrate, regions III and IV were merged into one layer and set to
ε = 7. FlexPDE employs a modified Newton-Raphson iteration procedure to solve the
nonlinear equations. An initial rough mesh was generated at the beginning of the
simulation and an adaptive mesh algorithm iterated via a mesh refinement procedure until
a tolerance of 10^⁵ was achieved. A portion of the refined mesh and the resulting
electrostatic potentials are plotted in Figure 2.1 (bottom). The electrostatic potential and
the electric field were evaluated at the tip-electrolyte boundary and exported for force
calculations. Rotation of the tip curve r(z) by 2π around the z-axis generates the closed

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