# Measurement of Tangential Momentum Accomodation?

(this question is a crosspost from theoretical 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

$Z_c$ = 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 hear of some general discussion on how we can get TMA from force measurement of molecule and pore wall.