Measurement of Tangential Momentum Accomodation?

Question

(this question is a crosspost from physics.)

• I am using atomic force microscopy (AFM) for characterizing pores of the size of nanometers for application in gas flow. For this, knowing the value of Tangential Momentum Accommodation (TMA) coefficient is an important task. Following is a formalism that describes measurements done by AFM and the formula to compute TMA:

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:

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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Comments

@ Moderators: Since I didn't get a single reply in last 2 days, would it be a good idea if I post this question in Physics.SE? If I do that should I remove this one here or I can simultaneously cross post this question in Physics.SE?

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Sure. Suresh cross-posted this question (http://theoreticalphysics.stackexchange.com/questions/651/lower-bounds-for-quantum-circuits-using-the-geodesic-framework) from cstheory.se. Could you do the same thing (put a link on both questions pointing to the other and explicitly say it is a cross post)? I think what has happened is that while your question seems on topic here, it doesn't really fall into any of the area of interest of many of the current users, which is unfortunate.

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Cross-posted on P.SE: http://physics.stackexchange.com/q/18170/2451

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No one has any insight to share on this question?

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@S_H Perhaps _would like to hear of some general discussion_ isn't the best thing for this site. In [FAQ](http://theoreticalphysics.stackexchange.com/faq) there is _Chatty, open-ended questions diminish the usefulness of our site and push other questions off the front page._. That is, it would be beneficial to ask a precise question.

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@Piotr: I've rephrased the question wording to make it look more precise.

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