The name is absent

The analysis was carried out by manually adjusting σ_sampie in force-curve simulations and
comparing it to experimentally measured force curves in the long-range region (1-4
Debye lengths). In Figure 2.3, the best fit of simulation to data is for the charge density
-0.043 C∕m², which is interpreted as the membrane surface charge density. The reference
silicon nitride data were used to characterize σ_tip in a similar manner to that used in the
analytical procedure.

0.08.....................-....................r.....................,..........................................τ.....................;

0.07                                          j

0.06                                       ' Ï

$2 0.05                   ,,.V „    ∙

⅞ 0.04 .        ■ /             J

ra                                z^z                                    :

O 0.03  « Z                     J

0.02     / ,                  J

0.01 7                               ∖

o∕ⁱ.≡....._i................_i.................................>.............i

0    0.1   0.2 0.3 0.4 0.5 0.6

Xps

Figure 2.4: (a) Lipid membrane charge densities and, (b) surface potentials determined by
a numerical analysis of the experimental force curves. The data (squares) follow the
curves predicted by the Gouy-Chapman-Stem model (line).

Unlike the result obtained with Equation 2.1, the numerical data follow the trend
displayed in Figure 2.4. The numerical results shown in Figure 2.4 are in quantitative
agreement with a simple Gouy-Chapman-Stem (GCS) model of the membrane, which
accounts for charge regulation [25]. In the model, electrolyte cations can bind to the PS
headgroups to form a Stem layer that neutralizes their contribution to the effective
surface charge density. The cation binding is described by a Langmuir isotherm and the
effect of the surface potential on the cation surface concentration is taken into account.
The model therefore has only three input parameters: the bulk electrolyte concentration

24

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