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Microcantilever for biomolecular detections

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].


[1] Park, J.H., Kwon, T.Y., Kim, H.J., Kim, S.R., Yoon, D.S., Chun, C.-I., Kim, H., & Kim, T.S. J. Electrocram. in press

[2] Chun, D.W., Hwang, K.S., Eom, K., Lee, J.H., Cha, B.H., Lee, W.Y., Yoon, D.S., & Kim, T.S. submitted to Sens. Actuat. A.

[3] Lavrik, N.V., & Datskos, P.G. (2003). Appl. Phys. Lett. 82, 2697-2699.

[4] Berger, R., Delamarche, E., Lang, H.P., Gerber, C., Gimzewski, J.K., Meyer, E., & Guntherodt, H.-J. (1997) Science. 276. 2021-2024.

[5] Yang, Y.T., Callergari, C., Feng, X.L., Ekinci, K.L., & Roukes, M.L. (2006). Nano Lett. 6. 583-586.

[6] Illic, B., & Craighead, H.G. (2004). Appl. Phys. Lett. 85. 2604-2606.

[7] Ghatnekar-Nilsson, S., Lindahl, J., Dahlin, A., Stjernholm, T., Jeppensen, S., Hook, F., & Montelius, L. (2005). Nanotechnology. 16. 1512-1516.

[8] Arntz, Y., Seelig, J.D., Lang, H.P., Zhang, J., Hunziker, P., Ramseyer, J.P., Meyer, E., Hegner, M., & Gerber, C. (2003). Nanotechnology. 14. 86-90.

[9] Wu, W., Datar, R.H., Hansen, K.M., Thundat, T., Cote, R.J., & Majumdar, A. (2001). Nat. Biotechnol. 19. 856-860.

[10] Lee, J.H., Yoon, K.H., Hwang, K.S., Park, J., Ahn, S., & Kim, T.S. (2004). Biosens. Bioelectron. 20. 269-275.

[11] Lee, J.H., Hwang, K.S., Park, J., Yoon, K.H., Yoon, D.S., & Kim, T.S. (2005). Biosens. Bioelectron. 20. 2157-2162.

[12] Braun, T., Barwich, V., Ghatkesar, M.K., Bredekamp, A.H., Gerber, C., Hegner, M., & Lang, H.P. (2005). Phys. Rev. E. 72. 031907.

[13] McKendry, R., Zhang, J., Arntz, Y., Strunz, T., Hegner, M., Lang, H.P., Baller, M.K., Certa, U., Meyer, E., Guntherodt, H.-J., & Geber, C. (2002) Proc. Natl. Acad. Sci. USA. 99. 9783-9788.

[14] Hwang, K.S., Lee, J.H., Park, J., Yoon, D.S., Park, J.H., & Kim, T.S. (2004) Lab Chip. 4. 9783-9788.

[15] Backmann, N., Zahnd, C., Huber, F., Bietsch, A., Pluckthun, A., Lang, H.-P., Guntherodt, H.-J., Hegner, M., & Gerber, C. (2005) Proc. Natl. Acad. Sci. USA. 102. 14587-14592.

[16] Wu, G., Ji, H., Hansen, K., Thundat, T., Datar, R., Cote, R., Hagan, M.F., Chakraborty, A.K., & Majumdar, A. (2001) Proc. Natl. Acad. Sci. USA. 98. 1560-1564.

[17] Savran, C.A., Knudsen, S.M., Ellington, A.D., & Manalis, S.R. (2004) Anal. Chem. 76. 3194-3198.

[18] Mukhopadhyay, R., Sumbayev, V.V., Lorentzen, M., Kjems, J., Andreasen, P.A., & Besenbacher, F. (2005) Nano. Lett. 5. 2385-2388.

[19] Shu, W., Liu, D., Watari, M., Riener, C.K., Strunz, T., Welland, M.E., Balasubramanian, S., & McKendry, R. (2005). J. Am. Chem. Soc. 127. 17054-17060.

[20] Zhou, F., Shu, W., Welland, M.E., & Hucks, W.T.S. (2006) J. Am. Chem. Soc. 128. 5326-5327.

[21] Hwang, K.S., Eom, K., Lee, J.H., Chun, D.W., Cha, B.H., Park, J.H., Yoon, D.S., & Kim, T.S. Appl. Phys. Lett. 89, 173905, 2006.


Xi Chen's picture

Many applications of carbon nanotubes are in the form of cantilevers, which takes advantage of the large modulus/density ratio of carbon nanotubes, and thus make them ultrasensitive sensors. When the microcantilever is combined with an indenter tip, it becomes a micro/nanoindenter-alike instrument which could be used to explore the mechanical properties of small material structures (which are otherwise difficult to measure). We have used this technique to measure the elastic modulus and osmotic pressure of colloidosomes, the results were published in a JACS paper.

I am very thankful to your comments. Your paper published in JACS seems quite interesting to me.

My works processed for publication to APL is the quantitative study on surface stress driven by protein-protein interactions exerted on a piezoelectric thin film microcantilever capable of self-actuating and electrical sensing using piezoelectric effects.

Application of carbon nanotubes to a cantilever is also of interests. Thanks.


Zhigang Suo's picture

Hi Kilho:

Could you please upload a preprint of your APL to iMechanica? To upload the preprint, click the title of your post, then click edit. Near the bottom of the screen, you will see the button "file attachments"

Uploading preprints is consistent with the policy of APL and many other journals. Use this link to search the policies of journals.

Hello, Prof. Suo.

As you mentioned, I uploaded the preprint to APL.

Rui Huang's picture

Hi Kilho:

We did not get any chance to talk when you were in Austin. Now we can through iMech! Your post is interesting, and I read your pre-print. Somehow I cannot follow through Eq. (1) in the paper, which includes the surface stress effect in the plate equation. Would you give an explanation or point to a reference where the equation was originally derived?

Many thanks. 


Zhigang Suo's picture

Thanks, Rui, for asking.  I was stuck with the same equation. 

More generally, in linear elasticity, how can residual stress affect natural frequency?  Surface stress is just a way to represent residual stress near the surface.

I'm aware of the case that axial load on a column affects the natural frequency of flexural vibration.  But I cannot get the surface stress to work this way.  Please help us through this, Kilho. 

The discussion on surface stress has been very interesting.  At the risk of muddying the waters, I'd like to share some observations from calcuations on surfaces in polycrystal elasticity that I had performed in the past.  The objective was to study the difference between stresses calculated at the surface in a collection on FCC crystal grains and compare that with a like collection embedded in the bulk of the material.  Both collections have the same crystallographic orientations; the difference being that the surface collection has one face exposed as a free surface.

Under the action of a axial load directed along the surface, the surface grain collections develop less strain energy than identical grain collections in the bulk.  The effect is greatest for highly anisotropic crystals and highly random orientations. 

The internal stress field generated by grain boundary incompatibility is the cause of the surface-bulk difference.  A free surface does not have the ability to support internal stress components normal to the surface or shear stresses along the surface.  The grains in the bulk are able to support a general system of internal stresses.

So what appears to occur is a general shedding of suface load, where all stress components are not supported, to the bulk regions, where all components are supported.  The effect could only be seen in the first 2 layers of the polycrystal, so it goes unnoticed at large length scales.  It might come into play in smaller scale components, such as the microcantilevers.  The strain energy drop at the surface was typically 5% for highly anisotropic copper, but did go as low as 13% for individual cases.

The main point - the stresses at the surface may be less than expected if your crystals are highly anisotropic and randomly oriented.

Hope you find this interesting.


Zhigang Suo's picture


I did not appreciate this difference between a free surface and a grain boundary. Do you have a reference to the work that you have just mentioned? 

We have been studying the effect of surface stress on pattern formation for some time.  An early account of our work was presented in Lu and Suo (2001).

Professor Suo, 

The work was included in my thesis 'Surface Effects in Polycrystalline Plasticity', 2004, Northwestern University. 





William John Walsh


Inelastic deformation produced by slip at the surface grains of face center cubic (FCC) polycrystalline materials is studied through the use of finite element modeling.  All of the models calculate the mechanical response of material located at the free surface, and compare the surface response to a similar calculation for the material in the bulk.  Through the application of these models, two competing mechanisms are revealed as being important in determining if the inelastic slip will be greater at the surface or in the bulk. 

The first mechanism examined is the lack of constraint for grains located at the surface.  The lack of constraint results in behavior with less constraint than the interior grains, which are surrounded on all sides by neighboring grains, and a single crystal, which has no external constraints.  The modeling of a single isotropic elastic-plastic grain embedded in an isotropic elastic matrix demonstrates that the lack of constraint at the surface results in greater values of plastic strain at the surface compared to the bulk. 

The second of these mechanisms occurs in the elastic loading range, causing differences in the stress state at the surface compared to the bulk prior to any inelastic deformation.  The constraint between crystal grains of different orientations causes internal stresses within the grains and at the grain boundary.  A free surface does not have the ability to support the internal stress components normal to the surface or shear stresses along the surface.  The grains in the bulk are able to support a general system of internal stresses.  Therefore, the internal stress field caused by grain boundary incompatibility is responsible for different stress states at surface and bulk locations.  The general trend found in this study is a lowering of stresses at the surface.  The lowering of stress at the surface can reduce the resolved shear stress on the slip systems and ultimately result in less inelastic slip at the surface.

The relative amount of inelastic slip occurring in grains at the surface compared to those in the bulk is ultimately a result of which of these competing mechanisms predominates.  The results of the finite element analysis indicate that the lack of constraint factor does not appear to influence the FCC polycrystals, presumably because of their high degree of symmetry in the slip systems.  None of the polycrystalline finite element models demonstrated greater slip at the surface compared to the bulk.  Greater amounts of slip were demonstrated in the bulk when the elastic properties of the polycrystals are highly anisotropic, and the crystallographic orientation of the grains is random.  When both of these conditions are satisfied, the slip in the bulk grains is typically greater than the surface grains. 

Polycrystalline materials are modeled with elastic crystal properties of varying degrees of elastic anisotropy.   The greatest differences between the surface and bulk behavior is found in the highly anisotropic copper, the least in the nearly anisotropic aluminum, and a response between these two extremes is seen in the mildly anisotropic nickel material. 

Please let me know if I can help you obtain a copy.


Origin of surface stress

Before I discuss the equation of motion, I would like to review the static-type microcantilever (i.e. measuring deflection rather than resonant frequency) for biomolecular detection. The main idea of biomolecular detection is to estimate the deflection change due to protein-protein interactions on a cantilever surface. It is well known that the deflection change induced by biomolecular interactions are determined by not molecular mass effect but the molecular interactions. This case is well described by Stoney's equation (see Ref. 4, 9, 16). Specifically, when molecular adsorption occurs on a surface, the molecular interaction induces the surface stress (consequently causing the buckling of a cantilever) responsible for deflection change.

For dynamic-mode cantilevers, many researchers suspects that molecular mass induces the resonant frequency shift due to protein-protein interactions. However, it was observed that molecular mass effect due to binding events does not contribute the resonant frequency shift. For instance, for C reactive protein (CRP) antigen-antibody interactions, the molecular mass effect drives the resonant frequency shift on the order of a Hz, whereas the resonant frequency shift due to CRP antigen-antibody interaction was experimentally observed on the order of 100 Hz. This result suggests that molecular interactions somehow affects the resonant frequency. For describing this effect, Lee and coworkers estimates the change in stiffness of a cantilever (at that time, they only can describe the stiffness change) for CRP antigen-antibody interaction. For details, you may refer to a couple of references (Lee, J.H., Kim, T.S., Yoon, K.H., Appl. Phys. Lett., 2003, 84, p3187).

Empirically, it is appealing that surface stress (consequently causing buckling of a cantilever) induced by protein-protein interaction may play a role in dynamic behavior of a cantilever. This idea is consistent with static case that the deflection change of a cantilever due to protein-protein interactions is driven by surface stress originated from molecular interactions during ligand-binding events. Accordingly, I establish the equation of motion for a cantilever empirically in order to consider buckling of a cantilever due to protein-protein interactions. The equation of motion that I established can be found in other reference (Dorignac, J., Kalinowski, A., Erramilli, S., Mohanty, P., Phys. Rev. Lett., 2006, 96, 186105). In the reference by Mohanty, they consider the quantum effect because they consider the nano-scale effect (thermal fluctuations), while we do not consider thermal fluctuation effects since our cantilever for experiment is in the order of 100 micrometer (continuum effect is sufficient).

In summary, protein-protein interactions on a cantilever surface (i.e. ligand-binding events on a cantilever) drives the buckling of a cantilever, typically described by surface stress. The original article on surface stress due to molecular adsorption may be referred to several articles (maybe including Gurtin's paper; but now I cannot give you details of an article by Gurtin because I am taking a vacation for weekend so that I am not able to access my research data). Furthermore, I suggest that, for details on physics for this case, you may consider articles as follows:

Wu, G., et al (2001), PNAS, 98, p1560.

Dorignac, J., et al. (2006), Phys. Rev. Lett., 96, 186105

I hope that my comments may be helpful for understanding on this topic. Prof. Huang, and Prof. Suo, thank you for your asking on my topic. I hope that we may have a chance to talk for some interesting topics on mechanics in the future. Thank you again.


Pradeep Sharma's picture

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?

Zhigang Suo's picture


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.

Pradeep Sharma's picture


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.

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.

Wei Hong's picture

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.

Pradeep Sharma's picture


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.



 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!

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

Weixu Zhang's picture

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.

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

Pradeep Sharma's picture

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

Weixu Zhang's picture

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?

Pradeep Sharma's picture

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.

Weixu Zhang's picture

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

does surface stress enfluence on shear modulus?

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