iMechanica - Microcantilever for biomolecular detections - Comments

Surface stress effect on shear modulus

hamed hamed — Fri, 04 Apr 2008 13:04:00 -0400

does surface stress enfluence on shear modulus?

Lu's paper - some explanation

Stanislaw Kalicinski — Thu, 22 Mar 2007 09:17:43 -0400

Hi,

Can anybody help me with understanding of some terms from Lu's paper? It seems I lack of some principle knowledge about physics at surfaces. My background is mostly micro-electronics and MEMS but I'm doing PhD in reliability of MEMS and would like to understand more what is happening on the surface of semiconductors (from mechanical point of view) in case of adsorption-desorption of different spieces.

I do not understand what is strain-dependent and independent surface stress, the two terms mentioned in the paper mentioned by Mr. Pradeep.

What is still not clear to me is whether the surface stress affect the resonance frequency of cantilevers or not. It seems that what Lagowski have written is not true (see Gurtin et al) but Lu says it true in one case but not in another (strain-dependent surface stress). This is very confusing.

Could you indicate what I should read (books, papers) first to understand it?

Thank you in advance!

ask for a help

Zaiwang Huang — Mon, 18 Dec 2006 21:36:11 -0500

Dear weixu your result is really interesting for me. for my current research, I encounter a problem similar to you. in my experiment of uniaxial compression for micropillar, the elastic modulus of different diameter(micro to submicro-scale) column vary largely, could you provide me some your research details? thanks a lot

Thank you I have posted it!

Weixu Zhang — Mon, 18 Dec 2006 21:17:54 -0500

Thank you Prof. Sharma I have posted the paper on the effect of surface energy on yield strength!

You can (nearly) always post a pre-print.

Pradeep Sharma — Mon, 18 Dec 2006 19:51:24 -0500

You can always post a pre-print. Far as I know, this is not a violation of copyright. You can check rules for each journal on this web site.

To add an attachment, you have to create your own new post which I would encourage you to do.

I am glad to post my manuscript here, but I don't know copyrigh

Weixu Zhang — Mon, 18 Dec 2006 19:32:18 -0500

Prof. Sharma.
Yes I am glad to post my manuscript here, and I think it may be helpful to understand the surface effect more.

But I know nothing about the copyright problem. It is just a manuscript submited to APL under review. Can I post it here ? Of course it is my own manuscript. Another question is that if I have the rights to allow others to download my papers published in a journal?
It is part of my doctoral dissertation. If I can post it here, who will please tell me how to add an attachment here?

Please do post it...

Pradeep Sharma — Mon, 18 Dec 2006 11:10:38 -0500

Weixu, please do post your paper here. Along with me, I am sure, others will be interested to look at it.

Hi Prof. Sharma would like to see my manuscript on surface effe

Weixu Zhang — Mon, 18 Dec 2006 10:28:45 -0500

Hi Prof. Sharma would like to see my manuscript on surface effect on the yield strength of material with nano-inhomogeneities?

I investigated the surface effect on plastic deformation of nanomaterials. The surface effect has influence not only on the elastic moduli but also plastic deformation of materials with nano-inhomogeneities.

Thank you for this very nice

Philip LeDuc — Mon, 25 Sep 2006 19:22:52 -0400

Thank you for this very nice information. This type of technology is becoming more essential as detection of molecules has a wide variety of fields. From my personal interest, quantification of molecules will be a huge advantage when trying to dissect the complex interactions happening at the cellular level. As there are hundreds of thousands of different types of molecules as well as billions of molecules in a single cell, the ability to quantify them may be a tremendous advantage. I applaud you again on this work and look forward to reading more on it in the future! Best wishes! Philip LeDuc

response to Wei Hong's comment

Pradeep Sharma — Sun, 24 Sep 2006 19:28:05 -0400

Wei,

I agree with all of your points. Gurtin's expression is the correct one. The residual surface tension should play no role in this.

Kilho, it would be interesting to take another look at your findings with the aid of Gurtin's expression (and interpreting the resonant frequency change due to surface elasticity rather than surface tension). Incidentally, the following (more recent) paper might be germane as well: Surface stress effects on the resonance properties of cantilever sensors, Lu et al, PRB, 72 (8), 2005, 085405

It more or less summarizes most of the things we have discussed in this post.

The governing equation might be wrong

Wei Hong — Sun, 24 Sep 2006 17:46:12 -0400

Dear Kilho,

I am afraid the governing equation you used might be wrong.

Eq. (1), or eq (21) in Ren and Zhao's paper, is the vibration equation of a beam under external distributed axial load (tau).

It might be a misunderstanding of "surface stress". Surface stress is the variation of surface energy with respect to the strain, often writen as a constant (surface tension) plus a term linear in strain. Neither term depends on spacial coordinates. And the result of it is just a constant tension / compression in the substrate/surface layer. Even in a beam bent by the surface stress, there's no shear stress between the bulk and the surface layer, except on the very end.

Secondly, surface stress is a internal force rather than external. If the central part of the beam is under compression, the surface must be under tension, and they are balanced. One cannot analys the central part of the beam as a prestressed beam, while neglecting the surface tension. This is a similar mistake as that made by Lagowski et al, pointed out by Gurtin et al.

Gurtin et al use energy method to analys the problem, and the result is quite intuitive: a constant surface tension will never change the resonant frequency, only the stiffness of the surface (which makes a thin beam seemingly stiffer) shifts the vibration frequency, just as Pradeep mentioned.

Correct me if I am wrong.

Governing equation

Kilho Eom — Sun, 24 Sep 2006 12:53:56 -0400

Dear. Prof. Suo

For governing equation, I would not go over in detail because details are given in other reference. The governing equation that I used was already suggested by work by Ren and Zhao. The reference is as below:

Ren, Q., Zhao, Y.P. (2004) Microsystem Technologies, 10, p307-314.

In our work, we used governing equation suggested by Ren and Zhao, but we employed the Ritz method for calculating the surface stress driven by myoglobin antigen-antibody interactions. Furthermore, if you would like to pursue further in-depth insight into surface stress, you may use reference as follows:

Ibach, H. (1997) Surface Science Report, 29, p193-263.

ref

Pradeep Sharma — Sun, 24 Sep 2006 11:09:29 -0400

Zhigang,

The ref is, "The effect of surface stress on the natural frequency of thin crystals", Applied Physics Letters, Gurtin, Markenscoff, Thurston, Vol 29, n9, 76, 529

I have also taken the liberty to email you and Rui the paper directly.

Yes, I do mean the supeficial elatic constants--then of course, as you point out also, shift in resonant frequency makes sense.

No, I don't understand Kilho's eq 1.However please refer to Gurtin's eq 1-2, compare with Kilho's eq 1 and finally Gurtin's points after eqs 6, 7 and then the final result.

Do you mean that superficial elastic constant shifts frequency?

Zhigang Suo — Sun, 24 Sep 2006 10:48:15 -0400

Pradeep:

Thanks for the tip. Do you mean that superficial elastic constant shifts frequency? If you do, I think I understand. Any time you modify stiffness in any part of a structure, you modify the natural frequency of the structure.

The atomic arragement at the surface differes from that in the bulk, so that the elastic property should be different from the bulk.

You cannot attach a paper to a comment, but you can give the reference to the paper. I'd be interested in reading this paper.

Still, the question remains, do you understand equation (1) in Kilho's APL, which he did attach to his post.

ref to Rui's and Zhigang's comment

Pradeep Sharma — Sun, 24 Sep 2006 09:25:50 -0400

Dear Rui and Zhigang,

Consistent with what you have indicated in your post, there is an old paper by Gurtin, which expressed that residual surface tension cannot impact the natural frequency. He then (along with a co-worker) proceeds to derive the expression for shift in the natural frequency of a cantilever beam when the deformation dependent part of the surface stress is incorporated. The latter indeed can cause such shift. I hope I did not misunderstand your comments. In any event, I have that paper and would like to attach it to this comment (can someone please tell me how to attach files!). Presumably this is the paper Kilho is referring to?

Microcantilever for biomolecular detections

Kilho Eom — Wed, 20 Sep 2006 07:45:49 -0400

Microcantilevers have taken much attention as devices for label-free detection of molecules and/or their conformations in solutions and air. Recently, microcantilevers have allowed the nanomechanical mass detection of thin film [1-3], small molecules [4, 5], and biological components such as viruses [6] and vesicles [7] in the order of a pico-gram to a zepto-gram. The great potential of microcantilevers is the sensitive, reliable, fast label-free detection of proteins and/or protein conformations. Specifically, microcantilevers are capable of label-free detection of marker proteins related to diseases, even at a low concentration in solution [8-17]. Microcantilevers, operated in a viscous fluid, have also enabled the real-time monitoring of protein-protein interactions [8, 12-15]. Furthermore, microcantilevers are able to recognize the specific protein conformations [18] and/or reversible conformation changes of proteins/polymers [19, 20].

The fundamental principle for label-free detection of molecules is the transduction of molecular adsorption and/or molecular interactions on a cantilever surface into the mechanical response change of a cantilever (e.g. deflection change, resonant frequency shift). Understanding the role of added mass and/or molecular interactions, due to binding events of target molecules to functionalized cantilever, in the mechanical response change is central to quantification of mass of target molecules and/or molecular interactions.

Many recent studies provide that the deflection change of a static microcantilever is induced by molecular interactions. From the classical elasticity (Gurtin, Stoney), the deflection change of a cantilever is ascribed to the surface stress driven by molecular interactions during the binding events. Microcantilevers operated in static mode have allowed many researchers to detect the specific proteins as well as to observe the conformation changes of biological molecules (e.g. DNA). Nevertheless, static microcantilevers exhibit the limitations such that the deflection change is minuscule for a miniaturized (in a micron size) cantilever, leading to error-proneness to measure deflection.

Recently, microcantilevers in vibration (oscillation) mode has been taken account because miniaturization broadens the dynamical range, resulting in increasing the sensitivity of a cantilever. The dynamic behavior of a cantilever for protein-protein interactions on a cantilever surface has been quantitatively understood. We provided the basic principles for dynamical response of a cantilever to biomolecular interactions. It is shown that the surface stress driven by protein-protein interactions play a significant role on the dynamical response of a cantilever. For details, you may refer to my papers, one of which will be published in Applied Physics Letters in the near future [21].

References

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