*(this question is a crosspost from physics.)*

Sneddon demonstrated that for any axisymmetric tip of an AFM, the relation between indentation force and displacement can be written as:

$F=\mathrm{TMA} (Zp-Zc)^n$

Where,

TMA = Tangential Momentum Accommodation

for a spherical tip,
$\mathrm{TMA} = \frac43 E_r R_t^{\frac12}$

$E_r$ = reduced elastic modulus = $\frac{E}{1-\nu^2}$

$n$ = constant between 1 and 2 that depends on the shape of the tip

$Z_p$ = piezoelectric displacement of the chip during indentation

$Z_c$ = cantilever deflection

$R_t$ = tip radius

$E$ = Young's elastic modulus

$\nu$ = Poisson ratio of the sample (for rock minerals it lies between 0.1
and 0.3)

AFM can be used to measure $F$, $Z_p$, $Z_c$ and **Bulk modulus of elasticity of materials**. To obtain the exponent $n$, a log-log plot of $F$ versus $(Zp-Zc)$ is plotted, although TMA is not calculated from this plot because doing so would require accurate knowledge of $(Zp-Zc)$ and, thus, the contact point.

- Based on the above information, I would like to know how we can get TMA from force measurement of molecule and pore wall.

**ABOUT THE EXPERIMENT:**

The goal is to measure TMA by AFM. We measure interactive forces between AFM tip (hemisphere) and planar surface. Using the models for hemisphere and plane surface we can extract necessary data. We extract coefficients that are independent of the shapes to be able to use it in a pore.

The tip measures interactive forces.

In addition to hydrodynamic forces, electrostatic and van der Waals forces are additional forces.

This post has been migrated from (A51.SE)