 The Nanoscale World

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Points 38 Good morning,

I have a question about how to calculate the poisson coeficcient. I have a biological material and I measure the Young´s modulus with AFM. To calculate the young´s modulus I need  the poisson coefficient but my problem is that I don´t know how to calculate/measure it. Is there a machine that I can use to measure the poisson coefficient?

Thanks,

Esther

• | Post Points: 16

#### Verified Answer

Verified by EstherNano

Hi Esther,

Wikipedia has a nice writeup about Poisson's ratio that would be a good place to start.  It is not easy to measure this without a bulk sample.  Some methods are:

http://clifton.mech.northwestern.edu/~me381/papers/mechtest/sharpe2.pdf: bulk measurement

http://www.springerlink.com/content/v86m282786m78j1v/: using Nanoindentation -- probably not a good idea for SPM since the level of accuracy is not there.

If you are looking for a way to correct your Modulus measurement by the Poisson's ratio, please note the following (from the PFQNM app note Quantitative Mechanical Property Mapping at the Nanoscale with PeakForce QNM AN128.pdf):

"The Poisson’s ratio generally ranges between about 0.2 and 0.5 (perfectly incompressible) giving a difference between the reduced modulus and the sample modulus between 4% and 25%. Since the Poisson’s ratio is not generally accurately known, many publications report only the reduced modulus. Entering zero for the parameter will cause the system to return the reduced modulus. "

So, it might be best to report the reduced modulus instead of the actual Young's Modulus.

--Bede 17 Posts
Points 184 Verified by EstherNano

Hi Esther,

It is really depends on the sort of material you are dealing with. If you can make a rectangular robust sample of several centimeters, the problem will be trival. Poisson coefficient can be found as a simple geometrical ratio (see, wiki for example). If you have a mechanical engineering dept., they amy have a suitable machine. If not, it would not be difficult to built such device (you would just need basically a ruller...).

If, however, you sample is small, it is far more tricker.. I don't think there  is any universal method allowed to handle such samples. In some cases, there is no much sense to define the Poisson coefficient at all becasue of high complexity of the material itself. For example, biological cells are typically too complicated for mechanical point of view. Even measurements of the Young's modulus are nontrivial. There is variability of the rigidity both along the surface and when the deformation becomes large. Under these uncertainties, people typically introduce so-called apparent Young's modulus, which is equal to the regular Young's modulus divided by (1-Poisson coefficient ). This eliminates the dependence of the apparent Young's modulus on the Poisson coefficient.

Best,
Igor

• | Post Points: 11 9 Posts
Points 77 Verified by EstherNano

Hi Ester,

As the definition of the Poisson’s ration is quite straight forward in the case of an isotropic bulk material, in the case of biological material (I guess cells) its definition is way more complicated if not impossible to be made.

Indeed, mechanically looking, a cell is a cross linked water gel caged within an elastic membrane with a rigid bead more or less in its middle.

Additionally, its mechanical behavior will be quite different whether you use a sharp tip or colloidal probe in order to indent it.

Moreover, given the height of your sample and the amount of indentation applied you may as well feel the influence of your substrate.

Given all these points (and I may even forget some) the best solution may be to make a best guess for the Poisson’s ratio taking as hypothesis that it is an uncompressible material (which is actually the case of its main component, i.e. water).

Or alternatively just calculate the reduced Young’s modulus value and forget to give it a fixed value.

Best regards,

Philippe

• | Post Points: 11

#### All Replies

Verified by EstherNano

Hi Esther,

Wikipedia has a nice writeup about Poisson's ratio that would be a good place to start.  It is not easy to measure this without a bulk sample.  Some methods are:

http://clifton.mech.northwestern.edu/~me381/papers/mechtest/sharpe2.pdf: bulk measurement

http://www.springerlink.com/content/v86m282786m78j1v/: using Nanoindentation -- probably not a good idea for SPM since the level of accuracy is not there.

If you are looking for a way to correct your Modulus measurement by the Poisson's ratio, please note the following (from the PFQNM app note Quantitative Mechanical Property Mapping at the Nanoscale with PeakForce QNM AN128.pdf):

"The Poisson’s ratio generally ranges between about 0.2 and 0.5 (perfectly incompressible) giving a difference between the reduced modulus and the sample modulus between 4% and 25%. Since the Poisson’s ratio is not generally accurately known, many publications report only the reduced modulus. Entering zero for the parameter will cause the system to return the reduced modulus. "

So, it might be best to report the reduced modulus instead of the actual Young's Modulus.

--Bede 17 Posts
Points 184 Verified by EstherNano

Hi Esther,

It is really depends on the sort of material you are dealing with. If you can make a rectangular robust sample of several centimeters, the problem will be trival. Poisson coefficient can be found as a simple geometrical ratio (see, wiki for example). If you have a mechanical engineering dept., they amy have a suitable machine. If not, it would not be difficult to built such device (you would just need basically a ruller...).

If, however, you sample is small, it is far more tricker.. I don't think there  is any universal method allowed to handle such samples. In some cases, there is no much sense to define the Poisson coefficient at all becasue of high complexity of the material itself. For example, biological cells are typically too complicated for mechanical point of view. Even measurements of the Young's modulus are nontrivial. There is variability of the rigidity both along the surface and when the deformation becomes large. Under these uncertainties, people typically introduce so-called apparent Young's modulus, which is equal to the regular Young's modulus divided by (1-Poisson coefficient ). This eliminates the dependence of the apparent Young's modulus on the Poisson coefficient.

Best,
Igor

• | Post Points: 11 9 Posts
Points 77 Verified by EstherNano

Hi Ester,

As the definition of the Poisson’s ration is quite straight forward in the case of an isotropic bulk material, in the case of biological material (I guess cells) its definition is way more complicated if not impossible to be made.

Indeed, mechanically looking, a cell is a cross linked water gel caged within an elastic membrane with a rigid bead more or less in its middle.

Additionally, its mechanical behavior will be quite different whether you use a sharp tip or colloidal probe in order to indent it.

Moreover, given the height of your sample and the amount of indentation applied you may as well feel the influence of your substrate.

Given all these points (and I may even forget some) the best solution may be to make a best guess for the Poisson’s ratio taking as hypothesis that it is an uncompressible material (which is actually the case of its main component, i.e. water).

Or alternatively just calculate the reduced Young’s modulus value and forget to give it a fixed value.

Best regards,

Philippe

• | Post Points: 11 3 Posts
Points 38 Thanks.

• | Post Points: 10
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