Dear Tran

I suggest you to take a look on the guide made by Bruker here:

https://www.brukerafmprobes.com/

Or the pdf catalogue annexed.

If you have a ScanAsyst or any other equivalent low spring constant cantilever, could be a good way to start.

Best regards

Joao

Hi,

the cantilever stiffness must be of the same order of magnitude as the contact stiffness, which depends on the tip radius and the total load applied (setpoint + adhesion in simplest case). I guess this contact stiffness should be computed with JKR model in your case.

Bruker gives a guide of selection in its application note #128 (figure 3):

https://www.bruker.com/products/surface-and-dimensional-analysis/atomic-force-microscopes/afm-application-notes/an128-quantitative-mechanical-property-mapping-with-peakforce-qnm.html

Best regards

Probably a good way to put in some Physics/Maths is start off with the Hertz equation for your probe:

Conical/Spherical Hertz equations: eg cone:

F = (2/pi) * (E / (1-v^2) ) *[ tan(a)] * [d^2]

Then give yourself an estimated required indentation - you may only want 5-10nm to be in a spherical regime with a standard probe or 100nm to ensure in conical regime.

Then calculate the estimated force (F) required to indent (d) your material of modulus (E) by your required amount, using some estimates for Poisson ratio (v) and cone angle (a).

Most AFM manufacturers will start having non-linearity piezo issues over 2V on photo-detector (PD). So work out the maximum amount of tip deflection required for your cantilever choice to give you 2V on the PD.

Tip defl (nm) = 2 V * inVOLS (nm/V)

inVOLS = the laser sensitivity of the optical pathway - indent a hard surface and dont touch the laser location on the back of lever for entire experiment.

Ideally you want a spring constant (k = F/x) that gives you a reasonable tip deflection for your given material - but I'd not go over the 2V on the PD.

Hope that helps.

Best wishes

Colin

João Paulo Cosas Fernandes This catalogue have not the guide to chose the probes for Peakforce QNM and AFM-nDMA. I need one suitable probe for measuring in these modes

Dear Tran,

Practically any tip can be used with PeakForce QNM, what you need is to choose the one that fits better the range of modulus you want to measure. If you take a closer look, the tables clearly state if the tips can be used for Force Curves/PeakForce. You can also use the search tool in the website to see which probes are recommended for each mode.

Best regards,

Joao

Dear Olivier Arnould,

I fully agree with you that the magnitude of force applied to the sample depends on the tip radius and applied force. Moreover, JKR model was used in my work.

I also think for each probe we have the range of measurement which is suitable to the stiffness of samples for example from a recommended probe of Bruker if I want to measure the modulus of the soft material ( few kPa), I should use the probe have maximum spring constant around 0.1 N/m.

Is there an equation to calculate spring constant of probe form the sample modulus ?

Best regards,

Quynh

Dear Tran Quynh,

the rule of thumb is that the cantilever stiffness kC should be of the same order of magnitude than the normal contact stiffness kN, usually 0.1*kN < kC < 10*kN.

In my case, I can use a DMT model:

F+Fadh = 4/3 M R^0.5 d^1.5,

where M is the indentation (or reduced) modulus and R the tip radius (if your sample surface is flat...). Thus, as kN = ∂F/∂d:

kN = [6 M^2 R (F+Fadh)]^0.33.

That's the way I compute the order of magnitude of the cantilever stiffness knowing the order of magnitude of the tip radius, applied force, adhesion force and mechanical properties of the sample (if it is much softer than the tip).

Best regards,

Olivier

Dear Olivier Arnould,

Thank you for your suggestion. It's very useful for me.

Kind regards,

Quynh

Dear Colin A Grant ,

As you mentioned, I agree that we can use Sneddon, Hertzian, DMT model to estimate the force base on indentation depth or vice versa.

I fully agree that 2V is the maximum value of laser on the photodiode (PD) - Trigger threshold. I wonder the inVOLS(nm/V) that you mentioned is the deflection sensitivity ?

The equation of cantilever sensitivity:

F= k.x

Force (N)= spring constant (N/m). Trigger threshold (V). Sensitivity (nm/V). 10^(-9)

I think that the equation you said.

N/m == nN/nm

:)

There's a lot to be said for trial and error - but as there are not a huge number of possible cantilever spring constants, perhaps look at 2-3 different cantilever stiffness for your materials.

For your modulus range you mentioned (5-200kPa); why not try to make yourself a "test/control" sample?

(elastomers or maybe agar/gelatin gels, where you can control the stiffness by altering the concentration). If you have the facilities, you can do bulk properties/compression tests to try to validate your AFM nanoindentations.

But regardless, if you are indenting visco-elastic materials with AFM; using linear elastic contact models (Hertz, JKR, DMT) - you will always only get approximations/estimations. You should always look to consider viscous behaviour (creep/relaxation) in conjunction with moduli.

Dear Tran Quynh - we actually looked at error propagation and how to calculate the optimal spring constant when knowing the elastic modulus of the sample the, tip radius and the indentation depth (eq. 9 for Hertz contact mechanics): Article Calibration of colloidal probes with atomic force microscopy...

While we were concerned with µm-diameter probes the physics are the same also for sharper probes. I can send you a pdf-copy via private message if this is of interest.

Best, Philipp

You can try MLCT-BIO-F (https://www.brukerafmprobes.com/p-3945-mlct-bio.aspx) and qp-Bio-AC-CI-CB1 (https://www.nanosensors.com/uniqprobe-uniform-quality-bioac-with-rounded-tips-for-cell-imaging-afm-tip-qp-BioAC-CI). Those probes work fine in PeakForce Tapping Mode and we were able to extract the Young’s Modulus of our samples in the range of few tens to hundreds of kPa. You can also play around with the other available tips in the MLCT with different spring constants.

Piuma indenters from https://optics11life.com/ are better for hydrogel characterization (in my opinion) as no sample preparation needed, the cantilever can bend up to 20um (optical fiber readout) so one can use the same probe for a very large range of stiffness and both elastic contact mechanics models (Hertz, JKR, Oliver-Pharr) and viscoelastic (DMA) models are available, latter being more appropriate for hydrogels...