The name is absent

Another charge regulation mechanism is protonation of the PS headgroup. The pK of that
group is < 2 and since our pH is much larger, we can ignore this as a possible cause of the
short range variation [1, 55]. As a control, we have shown below that counterion binding
alone is sufficiently strong to account for short range variations from the constant surface
charge model in the case of a surface with immobile charge groups, specifically, a silicon
nitride surface. In contrast to the mobile lipid charges, silicon nitride is an example of an
inorganic surface which has immobile discrete charges. When force curves taken over
silicon nitride surfaces are fit using the constant surface charge density model, we see the
same type of long-range fit and short range deviation as seen in the lipid bilayer data. We
use Equation 3.5 with association constant K = IO'⁷ M^¹ [23] and consider counterion
binding to the Si3N4 surface in our simulation. In contrast to the lipid case, we see an
effect on the short range fit when the cation binding is included. Figure 3.9 shows such a
fit to a Si3N4 sample.

Figure 3.9: AFM data for a Si3N4 sample fit with a model that includes charge regulation
due to cation binding via a Langmuir isotherm. (Black, solid curve) - AFM data, (Red,
dashed curve) - constant surface charge electrostatic model, (Blue, solid curve) - cation
binding model.

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