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Hello,
My question is about PFQNM- sample kit. I measured two samples: PDMS1 and PDMS2. For PDMS1, the value is 8.8 MPa. For PDMS2, the value is 3.7 MPa. The value for PDMS2 is acceptable. But what happened for PDMS1? I did the calibrations of deflection sensitivity, k and tip radius. I measured samples one by one. If I did something wrong, I couldn't get a right value for PDMS2. I know that the difference between PDMS1 and PDMS2 is supposed to be 1 MPa. But I got about 5 MPa difference. Is it possible that the problem is the sample of PDMS1?
Thank you for your help!
fangfang
FangFang,Thanks for your question and the variation could be from a number of things. We can try to troubleshoot a couple here, but may have to put you in touch with one of our Apps Scientists.Just to get this out of the way, could you check the sample under the microscope and make sure the protective film has been peeled off the surface. Do this by carefully picking at the corner with a pair of tweezers. We normally do this before we ship, but there have been instances where this has been missed. (However if this were the case your measurement should be in the 100’s of MPa so this is not likely, but I want to check).Also, I will email you Version F of the QNM manual. This has the latest updates on the calibration process. If you are following this version, I would look to the following:You may be underestimating your tip radius (if you are using a small deformation) and need to use a tip characterization sample other than tip-check. We are finding Nioprobe is a good choice if your indentation is only a few nm.In any case, pay special attention to the note on page 64:The Height from Apex parameter should equal the average penetration depthor the indentation in the force curve. The indentation can be measured as theseparation from the minimum force to the peak force in the loading curve. Formost samples, the indentation is very close to the sample deformation.Therefore, the average deformation can be used as Height from Apexparameter to estimate tip radius. But for very soft samples (<20MPa), theadhesion is very large and the difference between indentation and deformationis large so that the indentation must be measured from the force curves in theForce Monitor window shown in Figure 4.5b.The example shown is for PDMS1 so this is a critical point for your problem.Let me know how it goes,Steve
Hi, Fangfang,
I would like to take a look at your raw data on QNM of the two samples and tip check result if you have. You can send to my email at ang.li@bruker-nano.com
LA
Hi Stephen,
I have a few similar queries and a request.
Request : Could you please send me "practical advice to determine the spring constants of AFM cantilevers" the app note?
Queries:
1. Can you provide a table for AFM tip - indentation depth on Ti tip check sample for the probes that Bruker has? I am not able to decide what indentation depth should be used . I had received a app note with suggestion from Kamaljit to use 10 nm depth for tip radius calibration. This works well with scanasyst air tip, as I could measure the modulus of PDMS 1 within reasonable acuracy. But it would not work for RTESP which is a much harder tip and would possibly indent deeper. What is the protocol to determine the depth? I believe with change in depth, the radius of the tip would change , thereby changing the DMT modulus calculations.
1a. Is there a better and quantitative way to get the penetration depth / height from apex 1 using HSDC ? If so how?
2. What is the best way to choose a tip for a sample of unknown strength? The force curve - approach and withdrawl patterns? Or would you say if we can map the topography well, it should be good enough to indent deep enough as well?
3. After deflection sensitivity , spring constant and tip radius calibration, while imaging the reference sample , which values should be tinkered with more to get the BRUKER DETERMINED modulus - the spring constant or the tip radius?
Thanks
Mithun
Hi, Mithun,
some quick answers to your questions:
1. We don't actually indent Ti tip check sample for tip radius calibration, it's purely topography based method. so you can just set setpoint as auto when you scan the tip check sample, no worry about the indentation depth.
2. If you can posts your contact here, I can send you some materials describing how to choose tips and how to tune the force curves to improve QNM results. Or you can directly send your queries to my email: ang.li@bruker-nano.com
3. It's a combination of spring constant and tip radius, K/sqrt(R), that you can fine tune to get actual modulus.
Ang Li
Hi Ang,
Hi Ang and Bede,
Hi Mithun,
there is a calibration method, which just needs reference samples. It is particularly good, when you have a sample with at least 2 different materials, e.g. PS-LDPE. Surprisingly, this sample can be used to calibrate a quite wide range of cantilevers, I did that successfully with ScanAsyst-Air, FESP and TESP-type levers.
The idea is simple: The most important parameter in the whole calibration procedure is the deflection sensitivity. If you look at some theory (simple Hertz-model), the deflection sensitivity is correctly determined, when the ratio of 2 moduli is measured correctly, independent from the absolute value of the individual moduli. If you have the correct deflection sensitivity, you can do a thermal tune, which gets you an effective spring constant. With deflection sensitivity and spring constant determined, you just need to calculate the tip radius to finally measure the right moduli on your reference sample.
In principle, the values of R, k, and defl sens need not be correct in an absolute way, they just need to produce correct modulus values and force measurements. As all of the mechanical parameter extraction is based on a contact mechanics model (which might be appropriate for the materials or not), this way of seeing the calibration parameters allow some correction of intrinsic errors of the full procedure - just see them as tuning parameters without a deeper meaning.
So you can just start with putting in some nominal values for deflection sensitivity, spring constant and radius (e.g. nominal values). Then you take a measurement on the PS-LDPE sample, and adjust imaging force and peak force tapping amplitude such, that you get good force curves - with at least 1/4 to 1/3 of the cycle time in contact, such that you have enough data points on the contact part (of course setpoint set constant, not using scan asyst setpoint control). After that, you do a line scan over an area with both LDPE and PS. You inspect the log-DMT channel, and note down the difference of log-DMT on PS and LDPE. If this difference is 1.431 (which is log[2.7GPa] - log[100MPa], or equivalent to a ratio of 27 of the moduli of PS and LDPE), you have the correct deflection sensitivity. If not, you change the deflection sensitivity in calibrate - detector (don't forget to autoconfigure the force curve, or restart a new scan, to make the change active) till you get the right logarithmic difference. With some experience, this goes pretty fast - after a few scans you will have it. Typically, the difference follows monotonically the deflection sensitivity - smaller sensitivity, smaller logarithmic difference. You will see immediately, when the deflection sensitivity is chosen too high: The modulus data will show extremely high variations. Then you reach the point, when the force-vs.-separation curve reaches infinite slope (that's just math - because one uses the deflection sensitivity to calculate separation from the cantilever deflection and piezo z-position). If you can't get the right logarithmic difference without reaching that point, you need to readjust setpoint, peak force amplitude, or even change to different cantilever type...however, with my own experience with the cantilevers mentioned above, this was never necessary for me.
After you have determined the deflection sensitivity in that way (better call it an effective sensitivity), you withdraw and do a thermal tune. Then you have an effective spring constant. After that, you look at the absolute modulus values from your very first measurement with nominal values (call the parameters R_nom (radius), s_nom (deflection sens), and k_nom (spring constant), and the measured modulus on one of the materials E_nom). The correct modulus E_corr, you will get with R_corr (still unknown), s_corr (measured via modulus ratio), k_corr (measured via thermal tune after determination of the deflection sensitivity). From Hertz model (assuming that setpoint in volt always stays constant, and z amplitude stays constant as well throughout the measurements), you get the following relation between the nominal E (measured with nominal parameters) and the correct E:
E_corr/E_nom = (k_corr/k_nom)*(s_corr/s_nom)*(R_nom/R_corr)^0.5
The only unknown here is the effective tip radius R_corr, which can easily be extracted. You can check consistency, just by using above equation on both materials - you should get quite similar values for R_corr.
After that, you can use these parameters to measure your unknown samples (it is quite correct as long as the modulus is between the moduli of the 2 materials, I can't give an estimation how far it will be off, if you exceed that range, but it might be worth to give it a try). As well, you should keep imaging force and peak force amplitude similar to the measurements on your reference samples.
Of course, this method can be applied as well for samples, which do not intrinsically consist of 2 materials - e.g. the 2 PDMS-samples from the PFQNM-kit. In that case, it is a bit more tedious, because one needs to move several times from one sample to the other one to determine the deflection sensitivity correctly. But that's possible as well. Actually, that is similar to the way, how it was done in the NPL study about quantification of QNM (Young et al, Meas. Sci Technol. 22, 125703).
So maybe this suggestion might help you for some further trials,
Good luck,
Hartmut.
Thanks Hartmut for explaining the process so nicely and in such great detail. The insight on the use of the PS-LDPE reference sample ( the modulus of which was not mentioned in any of the Bruker app notes incidentally ) for a wide range of tips would certainly be a great help. I would try to implement your suggestions and get back with other questions / feedback when ready.
Regards
no problem...
Btw., I made 2 mistakes in my last post, which might lead you to an error. I was too fast
(1) Actually, you should NOT use your very first reference measurement (with all parameters k, R, s, E nominal) for determination of the effective radius. Instead, you should use the reference measurement after you have determined the correct deflection sensitivity as described in my last post. In that measurement (with correct s), the parameters k, R, and E still can stay nominal. Only in that case, one can simplify the relation between nominal modulus and correct modulus into a simple equation to extract correct radius, after spring constant has been measured right.
(2) Additionally, the given equation is incorrect.
I add the explanation for that and the correct equation below...
Consider Hertz-model. E can be calculated from loading force and deformation at loading force. Deformation d can be calculated from z-position (z) and deflection (x), deflection from sensitivity (s) and deflection voltage (V). With that, you get for modulus:
E=0.75*[k/sqrt(R)]*s*V/(z-s*V)^1.5 or E=0.75*[k/sqrt(R)]*s*V/(d^1.5)
A ratio between two moduli E1 and E2 will be then in general (assuming constant V, which is given at the peak force=maximum loading force):
E1/E2=(k1/k2)*(R2/R1)^0.5*(s1/s2)*[(z-s2*V)/(z-s1*V)]^1.5 or E1/E2=(k1/k2)*(R2/R1)^0.5*(s1/s2)*(d2/d1)^1.5
This shows on one hand, that the value of the modulus ratio of the 2 reference materials is only determined by the value of the deflection sensitivity and the deformation ratio at peak force, when we use nominal values for k, R, and s. In the reference measurement on 2 materials, we have k1=k2, R1=R2, s1=s2 (because we use a single set of nominal parameters for measurement of both materials). Then the modulus ratio is solely determined by the deformation ratio of the 2 materials. If sensitivity is correct, deformation ratio is correct, hence modulus ratio is correct. Therefore we can use the reading of a modulus ratio to adjust the deflection sensitivity.
On the other hand, we see, what happens, when we have the correct sensitivity, but a modulus measurement with nominal k and R on a single reference material (where we actually know the correct modulus). In that case, we can set s1=s2=s_corr and d1=d2=d_corr (because it is the same material and s is correct). Then we get:
E1/E2=(k1/k2)*(R2/R1)^0.5
or in terms of E_corr (known reference modulus), E_nom (modulus measured on the same material with correct sensitivity, but nominal k and R):
E_corr/E_nom=(k_corr/k_nom)*(R_nom/R_corr)^0.5
This relation should be used to finally calculate R and replaces the equation given in my last post.
Hope, not too confusing...
Regards,