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Surface effects on thin film wrinkling

Rui Huang's picture

A recent discussion here about the effect of surface stress on vibrations of microcantilever has gained some interest from our members. A few years ago, Zhigang and I looked at surface effect on buckling of a thin elastic film on a viscous layer (Huang and Suo, Thin Solid Films 429, 273-281, 2003). Although the physical phenomena (buckling vs vibrations) are different, the conclusion is quite consistent with Wei Hong and Pradeep's comments toward the end of the discussion. That is, surface stress only contributes as a residual stress and thus does not affect the buckling wavelength (frequency in space in analogy to frequency in time for vibrations).

More recently, a group at NIST has found that, for ultrathin polystyrene films (h < 40 nm) on PDMS, the buckle wavelength depends on the film thickness nonlinearly, different from a conventional theory commonly used for sandwich plates with stiff skin layers. Using the conventional theory, they found that the elastic modulus of polystyrene decreases by an order of magnitude when the film thickness changes from 100 nm to 5 nm. I worked with them and proposed an explanation based on surface effects (see Stafford et al., Macromolecules 39, 5095-5099, 2006). Here again, we found that surface stress alone does not help with the change of buckle wavelength. As pointed out in one of Zhigang's comments, we had to introduce a superficial elastic modulus. To include both surface stress and surface modulus, we assumed a surface layer of finite thickness, where the surface stress can be accounted for as a residual stress in this surface layer. By using a relatively soft surface layer of about 2 nm, we were able to reasonably reproduce the measured thickness-dependence of buckle wavelength.

It is intuitively plausible that, for ultrathin films (or cantilever beams), surface properties (not just surface stress) can affect the mechanical behavior. For polymer thin films, a 2 nm surface layer is possible based on molecular dynamics simulations of polymer density near a free surface. This leads to an observable change of buckling behavior for film thickness less than about 50 nm. For other materials (metals or Si), I expect some differences: the surface layer should be thinner (< 1 nm?); the surface modulus could be higher than bulk (hard surface), etc. For more details of our model and some general discussions about surface effects on thin film buckling, please see a pre-print here (Huang et al., J. Aerospace Engineering, to appear in January 2007); Update on December 28, 2006: now published as J. Aerospace Engineering 20, 38-44 (2007).


Zhigang Suo's picture

Dear Rui: 

Thank you very much for bring up our old paper.   I took liberty to add another tag, "suo group research", to your post, so I'll not have to post this paper in iMech myself. 

Also, we don't have copyright to post the pdf file of the paper prepared by the journal.  Could you please replace it with a preprint, or simply link to the web page of the journal?  People will see the abstract of this paper.  To download the full text, they will need to add a proxy string to the URL.  This last technique is general and easy to apply.  It will enanble us to deal with all papers published in journals.

Rui Huang's picture


Thanks for your suggestions. The work was certainly a "suo group research".  As for the links, I am struggling here because all the links I get from my computer are associated with UT-Austin userid that requires login, somewhat different from the proxy string you described before. Please see an example by clicking the link to our Thin Solid Films paper above. I could not find a way to get a link generally accessible. Please help.


Zhigang Suo's picture

Rui:  The new version of your post has gone way beyond the joint paper of Huang and Suo (2003).  Your post is no longer an atomic post:  it is a very nice molecular post.  The tag "suo group research" no longer belongs.  You may want to remove it.  Best wishes, Zhigang 

Rui Huang's picture

After I submitted the previous comment, I played a little with the links to journal articles and would like to share with you some experience (seems to be good, to be confirmed by you).  For three of my articles in question, I have three different stories to tell. I hope this covers the situation with a large group of journals.

First, for Thin Solid Films, an Elsevier journal, each paper is given a Digital Object Identifier (DOI) number with a link. According to ScienceDirect, a DOI is guaranteed never to change, so you can use it to link permanently to electronic documents. I believe that access to the full paper would still require subscription (you may check with the link above), but the link should work for everyone from anywhere.

Second, for Macromolecules, a ACS journal, I found an URL to the pdf file from the journal web page that does not require subscription. It seems to me this journal (as well as other ACS journals, perhaps) is open access.

The third article that concerned me was posted by my student, which is published in Physical Review B, a AIP journal. It also has a DOI number, but no link is provided from the journal. Instead, an URL is given for the abstract page. Again, the URL should work for everyone from everywhere. If you or your institution has subscription to AIP journals, it automatically allows access to the full paper.

All the three articles are now linked as described above. This seems to solve the copyright problem. Please let me know if you cannot access any one of them. Thanks.


Zhigang Suo's picture

The status of open access of any journal can be found on this web site.   The site has labeled the journal Macromolecules gray:  authors cannot even post preprints.  So please just give a full citation of the paper in your post, with no hyperlink.  Let us know if you have more up-to-date information on this journal.

By publishing in such a journal, the authors must have made a decision to give up their rights to post preprint.  iMechanica should always honor the decisions of the original authors, as well as any copyright.  Since we are not lawyers, we welcome knowledgeable people to educate us.

Rui Huang's picture

Indeed, ACS journals (Macromolecules in particular) are not open access (I was too hopeful). I have fixed the link above using DOI. Again, you will need subscription to access the full article, but ACS provides a nice image from the paper in addition to the abstract. Please give it a try and let me know how this works. Thanks.


Zhigang Suo's picture


Since this question arises so often among the users, I have summarized our discussion as an entry in FAQ, 

How to cite a journal article in your post?  (and how to access a paper cited in someone else’s post?)

Please feel free to edit. 

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