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Dear All,
I have question about the reading the Young's modulus from the force curve. I used PeakForce QNM for measuring mechanical properties for nanocarbon fibers. After tip calibration, I can have mechanical images (ie. DMT modulus, log DMT modulus, Adhesion, deformation, disserpation). Yes, I can have modulus data by making a line on the DMT modulus image, but I don't know how to read modulus from force curve. For example, in the force (nN) vs. separation (nm) curve with two cursor, I did Hertzian fit and there is a number in 'square equation' y=(37.5 (nN/nm^2))*sqrt(1nm)*(x nm)^3/2. Is the number of 37.5 for Young's modulus? If not, please tell me how to read Young's modulus from force curve. Second question, will the DMT modulus match the modulus data from force curve?
Thanks for helping,
Iwei
Hi Iwei,
The Hertzian model uses the equation F=1.33*E*R^0.5*d^1.5 where F is the force, d is the deformation of the sample, and E is the reduced modulus. You must use the "Separation" plot, not the "Z" plot to get the deformation for the fit. If you do, the Nanoscope Hertzian fit reports the equation that fit the data, so 1.33*E*R^0.5=37.5 nN/nm^1.5 or E=(28.1 nN/nm^1.5)/R^0.5 in your case.
Assuming that everything is calibrated correctly and the sample doesn't have any significant time-dependent deformation mechanisms like viscoelasticity, you should get about the same number for the two techniques.
Please refer to http://nanoscaleworld.bruker-axs.com/nanoscaleworld/media/p/418.aspx for more information on the fitting in PeakForce QNM and results where did comparisons with either the literature or SPM nanoindentation (which is essentially what you are doing).
--Bede
Hi Bede,
Thanks for the information. It is exact what I need. Thanks a lot
Hi,
I was also wondering how to get the Young's modulus using DMT model. It seems that this fit is based on the flat substrate, right? If I use a sphere particle sample on the flat substrate, can I use this same approach to calculate the Young's modulus? I think it is defined as 1/R=1/r_tip+1/r'_sample. If r'_sample is flat, 1/R=1/r_tip. If I use the sample that I mentioned above, R should be 1/r_tip+1/r'_sample, not tip radius, right?
Correct. The R given in the Hertzian model equation above is an effective radius which is defined as you have stated. Usually the AFM tip end radius is much smaller than the radius of curvature of the sample. If that is not the case, the sample radius of curvature must also be considered.
Thank you for your answer. I also have questions about the calibration. For the calibration, we need three parameters; deflection sensitivity, spring constant, tip radius. I can follow the manual to get the deflection sensitivity. Let me talk about the absolute method first.
1. For the spring constant, I put the nominal value from the manufacturer. (309N/m, PDNISP-HS) Is it ok to use this value?
2. I got the tip radius by scanning a reference sample (polystyrene) with PDNISP-HS. I don't understand what the tip characterizer sample (a tip calibration artifact) is. (section 4.5) So I used the reference sample (polystyrene) to get the tip radius of PDNISP-HS. When I checked the tip radius value suggested by the manufacturer on the website, it should be from 40nm to 50nm. I got 50.19nm for this following the 4.5 section. But i'm not sure that is correct or not. Is it ok to put this value to the cantilever parameters.
After getting these three values, I can put those parameters to the cantilever parameters. Assuming that I finished the calibration, I started imaing the sample.
Let me talk about the relative method.
2. To get the tip radius, I can image the reference sample (polystyrene) using PeakForce QNM. Then how can I adjust the tip radius parameter to make the measured Modulus equal the known value of the ref. sample? What I'm understanding is the following. For the ref. sample, let's assume I got y=37.5nN/nm^2*sqrt(1nm)*(xnm)^3/2 Hertz fit. And F=1.33E*R^0.5d^1.5. So 1.33E*R^0.5=37.5. If we know E value, we can calculate the R value. Is this correct?
So after that, I can put the values to the cantilever parameters. Than I can start imaging the unknown sample. In the manual, it says "image the unknown sample adjusting the peak force set point to match the deformation depth used during imaging of the reference sample. How can I know the deformation depth of the ref. sample? Is it the difference b/t the separation point at which the force is zero and the separation point at which the force is max. (the end of the force-separation curve)? Also How can I adjust the peak force setpoint to match the deformation depth?
I'm struggling to solve above questions even though I already took a look at the manual. Please let me know the procedure in detail for both absolute and relative method. Thanks.
Hosop
Hi, Hosop,
Though your post is some while ago, hope you have already solved your porblem, just some quick reply to your questions.
In absolute method, the characterizer sample is refered to as RS sample in this post: http://nanoscaleworld.bruker-axs.com/nanoscaleworld/forums/t/792.aspx, you need to use the captured data on this sample as the reference to calculate the tip radius. In this method, a small trick is to record the deformation channel (this will appear later in relative method again) in your QNM test on your sample, then use the average deformation value as input for 'Height 1 from Apex' in tip characterizing. This is critical since for different deformation (penetration depth), the apparent/effective tip radius will be different. Other steps have been clearly stated in the manual.
In relative method, for your diamond tip, you should use and can rely on the quoted nominal value for both deflection sensitivity and spring constant, they have been calibrated. The procedure for tip radius calibration is indeed as you have realized, to back calculate R from known E. Since apparent/effective R is dependent on the penetration depth (this can be observed from deformation channell), it's important to keep consistent average deformation for both calibrationi sample and your own sample. A systematic way to calibrate your tip radius is to scan the calibration sample at different deformation and plot the relationship between tip radius vs. deformation (should be a continuous curve) and then use this curve to choose the radius for your own sample at given deformation.
LA