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(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:

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


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


  1. 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.

  2. The tip measures interactive forces.

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

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What do you want, the TMA of the pore-flow, or that of the AFM tip? You seem to be confusing the two. I assume you are interested in measuring the TMA of the pore alone, not the tip, so that the tip is only used to drive fluid into the pore, and from these measurements you wish to extract the tma of the pore. It would help if you described the geometry better--- for exmaple, does the tip cover the pore completely? Can you get it to jam in the pore? Are there forces (other then hydrodynamic ones) between the tip and the pore, etc. It is difficult to know what the question is, beyond "find TMA". –  Ron Maimon Dec 12 '11 at 10:42
Cross-posted on TP.SE: theoreticalphysics.stackexchange.com/q/660/189 –  Qmechanic Dec 12 '11 at 19:03
Thanks for providing a link to the cross post, Qmechanic. –  S_H Dec 12 '11 at 21:02
@Ron Maimon: Please see the updated part in the question above. Those points answer your questions. I am sorry that it took time to get back to your comment. Thanks. –  S_H Dec 15 '11 at 22:36
I shared a link to this question on Facebook in hopes of reaching someone who can get you a good answer. It's a shame we don't have more experts in this sort of thing, but hopefully someone can answer... –  David Z Dec 18 '11 at 3:44
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