The name is absent

2.2.4 Tip radius and spring constant measurement

The radius of each individual AFM tip was measured from scanning electron microscope
(SEM) images using the iterative method described in the literature [1]. The spring
constant of each tip was directly measured by the added mass method [52]. The thermal
resonance frequency of the cantilever was measured before and after the addition of a
known mass, M, by micromanipulation, yielding frequencies vɪ and V2, respectively. The
known mass was a 6 mm spherical silica bead with a well-defined shape and density
(Bangs Laboratories, Fishers, IN). The shift in resonant frequency yields the spring
constant using the following relation:

к = (2л-)²

2.2.5 Finite Element Modeling

Force curves were analyzed with numerical solutions to the full nonlinear Poisson-
Boltzmann equation using a commercial software package (FlexPDE 5.0.8, PDE
Solutions, Antioch, CA). To simulate the interaction between a silicon nitride AFM tip
and a supported lipid membrane, the domains displayed in Figure 2.1 were set up.

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