The name is absent

The electric double layer force between a spherical tip and planar sample in electrolyte
solution was derived [24] starting from the formula for the pressure between two charged
planes in an electrolyte solution [36]. Accordingly, the force F is given by

P - ^^π^^^σ4p^σ^mple         (2.1 )

electrolyte о

where R is the tip radius, λ is the Debye screening length, σ_lip and σ_sampie ^are the tip and
sample charge densities, and D is the tip-sample separation [36]. This equation was
derived using several assumptions, including small surface potentials, tip-sample
separations larger than the Debye length, and tip radii larger than the separation, R >> D
» λ. In spite of these approximations, this expression has been successfully used to
describe experimental measurements in terms of the force dependence on tip-sample
separation, tip radius, electrolyte concentration, and pH [35, 37-43]. It has been widely
applied to electrostatic interactions between Si3N4 (silicon nitride) probe tips and
inorganic surfaces, as well as lipid membranes [42-47]. Another method of analyzing
AFM force data is to numerically simulate the tip-sample force by solving the full
nonlinear Poisson-Boltzmann equation with proper boundary conditions [36, 48-51]. To
get membrane surface electrostatic information, one can interpret the experimental data
with Equation 2.1 or with a numerical simulation. To make a quantitative measurement
using an analytical approach, one must measure all the constant parameters in Equation
2.1. If one uses a numerical approach, the proper boundary conditions must be chosen. To
test the quantitative surface charge density measurement method for biomembrane
analysis, we have measured force curves over supported lipid membranes of zwitterionic

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