The name is absent

2.3 Results and discussion

Fits to Equation 2.1 yield the lipid surface charge density σ_sampie, as a function of X_ps as
shown in Figure 2.2. The error bars reflect contributions from the uncertainty in each

„ 001

CM
E

U 0.008
o>

E 0.006
cc
ω

Ü

I 0.004

0.002

0
0    0.1   0.2 0.3 0.4 0.5 0.6

Xps

Figure 2.2: The lipid membrane charge densities determined by applying Equation 2.1 to
the experimental force curves. The data do not follow the expected trend with DOPS
mole fraction.

The use of Equation 2.1 in interpreting the data gives a result that shows no discernable
trend, and the variation cannot be accounted for by the error. This is not entirely
unexpected, considering the approximations that go into the derivation of Equation 2.1.
In our measurements, the tip radii are significantly larger than the Debye length. In
addition, the values of D that must be fit, approach λ at short range and exceed R at long
range. Also, the surface potentials greatly exceed the range where the linearized Poisson-
Boltzmann equation is applicable. Note that the negative result of Figure 2.2 does not
necessarily mean that the functional dependences in Equation 2.1 are inaccurate. Several
experiments have confirmed that Equation 2.1 accurately predicts the force dependence

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