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Dear All,
I am a research associate in the University of Melbourne, Australia, and have several questions on how to calculate the normal loading force (not include the adhesion force) exerted on a sample imaged using a Nanoscope IV AFM (software Nanoscope 5.31r1).
Some guys suggested that the normal loading force could be calculated by two steps: a) using the deflection data from the image to subtract the value of the out-of-contact of a force curve that was collected immediately after imaging the sample; b) multiplying the calculated data by the spring constant of the cantilever used. According to the manual of the instrument, however, it seems that this force should be calculated by adding the deflection data to the value calculated by using the set-point to subtract the out-of-contact value before multiplying by the spring constant. So, which one is correct? If I change set-point values continuously during the imaging process, then, how could I calculate the force exerted on the sample? I found that the force curves collected at different set-point values have different out-of-contact values (not caused by drift)? My last question is: if I choose Friction in the Data Type in the force calibration window, does the curve obtained provide information on lateral signals for a tip approaching and retracting from a sample?
It would be much appreciated if you could help me with any of these questions.
Cheers,
Huabin Wang
Hi Huabin,
The normal loading force for imaging or force curves is simply calculated using Hookes law F=kz. There are various ways to determine the spring constant k [N/m] (see one of our application notes regarding this). z [m] is determined by multiplying the deflection sensitivity [m/V] by the setpoint [V] and by setpoint I mean difference between photodiode signal when cantilever is far from surface and when it is at setpoint i.e. 0v and 3V, or -1V and 2V would be the same setpoint.
Secondly, yes the Friction data type will display twisting motion of the cantilever during a force curve.
Best regards
Ian
Many Thanks, Ian. I think I did not describe my problems clear enough. More straightforward, my question is how to calculate the normal force exerted on a sample from an image captured with the Data Type set to Deflection?
Huabin
Hi again Huabin,
The deflection channel is literally an image of the variation in your setpoint, so on average it should be some definite value (your setpoint - apart from peaks and troughs when the probe encounters sharp height variation). So you can take this value and use it as the "z" value in the Hookes' law equation I mentioned previously. Note you will still have to pay attention to the deflection sensitivity and the units either in [V] or [m].
Cheers
Dear Ian,
Many thanks! Do you mean that we still need to collect a force curve (without changing the set point) immediately after the collection of the deflection image since we need to know the non-contact value of the cantilever in order to determine the z value?
In my experiment, the sample is a 1-D array of trapezoidal steps (TGF11, MikroMasch) and I need to know the normal force exerted on the slopes and horizontal planes, respectively. How could I do it properly? Does it make sense if I calculate their corresponding z values by considering the deflection data on these different features, respectively?
If ten different set-point values were used in one deflection image, then how to calculate the normal force exerted on the slopes and horizontal planes at different set-point values?
I found that force curves collected at different set-point values have different non-contact values.
I am sorry for asking these tedious questions, however, it is necessary for the lateral force calibration using a ‘wedge-method’.
Kind regards.
Yes you will need to collect at least one force curve at some point to look at the gradient of the contact region or constant compliance zone. This will tell you the deflection sensitivity i.e. what voltage on the photodetector corresponds to what deflection of the cantilever. Unless this is done your deflection image is not calibrated. The deflection sensitivity is nominal for a given type of cantilever but will still vary amongst them. Obviously different cantilevers with different length/ width/ material etc... will have drastically different deflection sensitivity.
You could use the deflection channel differences on the horizontal planes and slopes to calculate the normal force, sure.
If you use ten different set point values you will see 10 corresponding differences in the deflection image so this is the same as the previous question in essence. It just goes back to Hookes law and plugging in the relevant numbers i.e. spring constant multiplied by deflection sensitivity multiplied by setpoint or if you have done the deflection sensitivity first and updated this in the detector setting in the software you could just do spring constant multiplied by deflection image value.
I dont understand when you say force curves at different loading force have different "out of contact" value. You mean "out of contact" value for force? as by definition this should be zero every time. Note by "zero" this could mean arbitrary number or offset. You can send me some example force curves to my email: ian.armstrong@bruker-nano.com
Hi Ian,
In my experiment, I usually calibrate the cantilever before performing other measurements. So, it’s no problem to convert the data from volts to nanometers. As to ‘out-of-contact’, I am sorry for this confusion, which actually means the value (nm) of the baseline of a force curve, or ‘photodiode signal (nm) when cantilever is far from a surface’ (please see sample forces emailed to you).
Since the z value (nm) is determined by the difference between photodiode signal when cantilever is far from a surface (out-of-contact) and when it is at set-point, I may need to calculate the z value by subtracting the out-of-contact value (nm) of a force curve from the deflection data (nm) of an image. Does this make sense? If the above discussion is correct, then a force curve is needed to get the out-of-contact value.
I used ten different set-point values in one deflection image, and definitely saw ten corresponding differences in the image. My problem is at which set-point should I do a force curve, in order to get the out-of-contact value? I found that the force curves collected at different set-point values have different out-of-contact values. Do I need to collect ten force curves at corresponding ten different set-set point values and then calculate z values, respectively?