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Journal Club Theme of April 2011: Adhesion of Thin Membranes and Shells

Adhesion is ubiquitous in virtually all materials.  The most general definition is intersurface forces between two surfaces.  In one extreme, gravitational pull between planets can also be considered to be long range adhesion.  If a piece of wood is dropped to the floor, attraction is present due to gravity.  But if now water is introduced at the interface as a “medium”, intersurface interaction turns repulsive and the object floats.  A more pragmatic definition, of course, is related to the interactions between small objects, which is particularly relevant in micro- and nano- scale biological sciences and electronics.  Since the colossal works by Derjaguin in the 1930s, followed by Tabor and Johnson-Kendall-Roberts (JKR), then Maugis-Barquins, adhesion becomes a hardcore science with rigorous physical and mathematical backbones.   The celebrated JKR paper in 1971 becomes one of the most cited papers in the history of science.  Adhesion between “small” solids grows into a gigantic field of study when nano-science, nano-materials and nano-technology virtually take the central stage in the scientific arena these days.  In the past 4 decades, theoretical and experimental investigations fill the literature and are expected to grow even further with an explosive momentum.  In the past decade or so, I am gradually convinced that solid-solid adhesion become inadequate in many advanced technology.  In this monthly journal club theme, I would like to discuss several future directions that might grow out of the conventional core of adhesion mechanics.

Adhesion at membrane-membrane and membrane-substrate interfaces is a very important subject.  Cell-cell adhesion is essential in building our body parts and governing our physiological functions, albeit a key to our survival.  It is obvious that cells are not solid spheres or rubber balls, but viscous cytoplasm encapsulated by membranes.  So when cells stick together, it is membrane-membrane adhesion coupled with elastic deformation of the entire cell that serves as the underlying physics.  Unlike the JKR solids where the Hertz compressive stress developed at the contact interface, flexible membranes conform to the substrate geometry and thus reduces the internal stress to null though stress concentration at the contact edge remains.  Rather than the JKR surface traction, it is now mixed plate-bending and membrane-stretching which dominate the membrane deformation.  The subsequent adhesion-delamination (or detachment) mechanics is therefore expected to be distinctly different from the JKR model.  Should the surface force range exceeds the membrane thickness, a number of new models parallel to the classical JKR solids will be necessary such as (i) a modified Derjaguin-Muller-Toporov (DMT) model, (ii) a modified Maugis’ JKR-DMT transition, and (iii) a new Tabor parameter.  Applying such models to the life sciences might be tricky because the biological community has a different understanding of “Nano-Bio-Mechanics”.  In general, “mechanics” is referred to the interactions of ligand-receptor, proteins etc, rather than the mysterious engineering stress and strain; and “adhesion” must be chemistry oriented.  I greatly appreciate the new book,  Kevin Kendall, Michaela Kendall, and Florian Rehfeldt, “Adhesion of Cells, Viruses and Nanoparticles”, Springer (2010), which details the misunderstanding of both the mechanics and biology communities.  I earnestly look forward to a marriage of the two seemingly mutually exclusive fields in the near future.  

Beyond life sciences, thin film adhesion is an important topic in many nano-structures and nano-devices.  The 2010 Nobel Prize further catalyzes the interests in graphene based technology.  Graphene adhesion on electronic substrates thus plays a crucial role in design criteria and reliability assessment. Notwithstanding the voluminous and excellent molecular dynamics simulation and computation, experimental mechanical characterization methods remain rare, let alone adhesion-delamination.  I earnestly hope that more empirical data in fundamental mechanical behavior will become available soon to benefit both industrial developments and scientific endeavors.

Adhesion of shells is another relevant subject.  The long list of applications includes flexible-stretchable electronics, NEMs / MEMs with moveable parts (e.g. bridges, diaphragms, cantilever, intriguing truss structures), soft hydrogel contact lenses, bacteria adhesion etc.  Similar to membranes, serious treatment of shell adhesion leads to new JKR, DMT, JKR-DMT transition models and Tabor parameter.  Let me discuss two examples here.  

Many brands of contact lenses are commercially available in the market, some good, some bad, and some evilly bad.  In the worst scenario, taking the spherical hydrogel shell (lens) off the cornea can peel off epithelial cells due to strong adhesion in dry eyes.  Bacteria adhesion and subsequent infection are also problematic.  Therefore, mechanical characterization and adhesion measurement of convex shells, construction of rigorous mechanical adhesion models, the extraction of materials properties such as elastic modulus and adhesion energy in the presence of body fluids of specific ionic strength are essential in design and fabrication.

Another example is that of adhesion in bacteria and protozoa, since it is responsible for adhesion-aggregation-transportation of pollutant and micro-organisms in porous medium (e.g. sand), water treatment facilities, and colloidal filtration.  Though ligand-receptor interactions remain operational, the complex interplay of non-specific interactions of electrostatic double layer repulsion and van der Waals attraction has long been reckoned by the environmental engineering community to be more relevant.  In fact, the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory is deemed the most pertinent.  The most comprehensive model available for colloidal filtration is the statistical description of the dual fast/slow deposition in standard column test where particles (e.g. latex spheres) pass down a sand packed column.  It is quite promising that a scientifically sound model of shell adhesion mechanics for bacteria with stiff glycoprotein walls will yield physical interpretation to the phenomenological statistical parameters.  For instance, how well the particle sticks to the collector substrate is predominantly governed by the “pull-off” force, which is in turn related to the intersurface force magnitude and range, as well as the shear in a liquid flow.



Qiming Wang's picture

Hi Dr. Wan,

 Thank you so much for posting this interesting thread. One quick question, is there any review paper about adhesion between bacteria and polymers (or related), eapecially in mechanics approach? Thanks.


If you type “Adhesion, Bacteria” in google search, you mostly like get tons of papers on biochemistry or some mechanical characterization technique, or molecular dynamics simulation of polymer chains and ligand-receptor interaction.  There isn’t much in the conventional stress-strain mechanics, as the word “mechanics” is understood by the biologists and even bioengineers from a very different perspective.  I personally believe that there is a good future for the solid-mechanicians to contribute to life sciences such regards.  The top priority is probably to build a good communication channels with the environmental engineers and biologists, otherwise, whatever efforts you put in building excelling mechanics models will be by and large ignored altogether.  A few years ago, we started some adventures along this line and published some papers that are cited by quite a number of investigators: KK Liu, HG Wang, KT Wan, T Liu, Z Zhang, “Characterizing capsule-substrate adhesion in presence of osmosis”, Colloids and Surfaces B: Biointerfaces 25 [4] 293-298 (2002).  KT Wan, KK Liu, “Contact mechanics of a thin walled capsule adhered onto a rigid planar substrate”, Medical and Biological Engineering and Computing 39 605-608 (2001).  We also started lately to look into shell adhesion that will be ultimately extended to the adhesion mechanics of bacteria glycoprotein shell adhesion to another particle or substrates.  Here are a few of our latest work:  Jiayi Shi, Sinan Müftü, Kai-Tak Wan, “Adhesion of an Elastic Convex Shell onto a Rigid Plate”,  in press, Journal of Adhesion (2011). C Majidi, KT Wan, “Adhesion between thin cylindrical shells with parallel axes”, Journal of Applied Mechanics 77 041013  DOI: 10.1115/1.4000924 (2010).  

Jayadeep U. B.'s picture

Dear Dr. Wan,

Thanks for posting this journal club theme, which is very much related to my PhD work.  I hope there will be a thorough discussion on this topic, which could be very helpful for me.

One thing I would like to point out is that, when we think of very small objects, the forces causing adhesion (mainly van der Waals forces) can not be considered as surface forces, but rather should be treated as body forces, distributed over (atleast a part of) the volume.  There are some works already done in this direction by using numerical methods (FEA) by Cho and Park , Sauer and colleagues (for eg ) and a paper from our group.

Thanks and regards,


You raise an interesting point.  I agree that in specific situations the full body forces should be considered, especially when the objects are much smaller than the surface range (if you treat the substrate as half continuum).  For instance, in case of particle filtration, particulates adhere in the presence of long range electrostatic forces.  It is probably just a scaling problem.  At least in the biological world, even the smallest organelles, vesicles or viruses possess dimensions larger or much larger than the surface force range.  Large computational efforts might prove to be unnecessary and probably not convincing to the biologists nonetheless.  

It is worthwhile to note that the surface potential (e.g. DLVO theory) due to van der Waals forces is derived from integration over all atoms in the adhering bodies.  But since the mechanical deformation of solids is usually confined to the surface layers, vdW is considered to be surface force which is after all a good and reasonable approximation.   If a comprehensive consideration of coupled body forces with mechanical deformation is considered, the results will depend heavily on the variation of mass density, atomic arrangement or crystallography, and the stress distribution etc, and must be repeated every time when a new geometry is concerned.  Though justifiable strictly in the academic sense, I doubt if the chemists and biologists will bother to look into such fine details, when simple results like the JKR “pull-off” force is applicable (though not accurate).

That said, I appreciate the several reference papers you cite.  I strongly encourage you to find pragmatic systems that prove such body force consideration is necessary.  The new grounds will definitely be a blessing to the solid mechanics community.

  Dear Dr. Wan,

  Please look at the adhesion theory paper:  V. K. Nevolin  and F. R. Fazylov
 On the adhesion theory of solids in terms of the dielectric formalism”  here:
  The free version (on Russian) is here:

   The calculated dependences for computing the energy and strength of the  ideal adhesion for solids (metals, semiconductors, and dielectrics) have been obtained and there is a good agreement of the calculated values with the available data.

   “At large distances between the bodies, the expression for the interaction strength takes the form of the van der Waals expression, and when the interaction distance tends to zero, the expression for the interaction strength does not diverge, which allows one to obtain the results comparable to the data on the theoretical tensile strength of the materials.” 

    It was shown that the nature of the adhesion (cohesion) interaction lies in the interaction of quasiparticles on the solid surface.

   The related paper is V. K. Nevolin, F. R. Fazylov, and T. D. Shermergor -Phys. Chem. Mech. Surf. (UK) 5, 1749 (1990)

   Thanks and Regards,

   Foat Fazylov 


Thanks for the comments and paper.  I'll certainly read it. KT

Yanfei Gao's picture


Nice discussion. For adhesion (in the context of JKR etc.), I think one can easily use ABAQUS to define ad hoc contact interaction or to write user element subroutines to simulate adhesive contact. Having said that, the problem lies on the definition of adhesieve forces as the interaction of surface and surface, which may not always be true. 

For adhesion in the context of fracture toughness (e.g., adhesion energy of integrated structures, layered interconnects, etc.), the measurement is a toughness measurement method. Usually a long crack is induced and one can equate the cacluated energy release rate to the toughness. My view on this is that the crack tip process zone can not be easily directly studied. 


I enjoy reading the paper which is useful in semi-conductors and nano-structures with well defined crystallography. It is, however, quite irrelevant to biomembranes in the presence of an aqueous environment at room temperature. The intersurface forces model is already a little too sophisticated to the experimentalists. After all, we are interested in "membranes" not "solids".

Thanks a lot for your
interest on this paper.  I’d like only to
emphasize that the nature of adhesion (cohesion) forces is unique   for “structures
with well defined crystallography” and for “membranes”. It lies in the
interaction of quasiparticles on the solid surface.

Like what Jayadeep mentioned above, Roger Sauer have done an excellent job in incorporating JKR to define contact interaction, especially in his work on the gecko feet.  For membranes, things are in fact more complicated, because solid adhesion involves Hertz contact but membranes and shells require bending-stretching deformation.  It is necessary to derive a Green function to derive the deformed profile of a membrane in a force field in a sefl-consistent manner, unless you have a simple step function like our latest work and Maugis’. You are very correct that the long crack assumption is necessary to investigate fracture toughness. However, there is an urgent need for adhesion-delamination or adhesion-aggregation description for small objects, especially single cells and vesicles.  This is why I sort of abandon the high level description using stress intensity factors in a mode mixity format.  These small objects are already small enough to violate the classical fracture mechanics theory. Besides, the conventional chemistry approach in the biomedical community prefers an energy description such as strain energy release rate instead of the ideal stress singularity at crack tip or crack front.  Again, the bottom line is to build a communication channel with the biomedical community with sufficiently simple math instead of highly sophisticated but exact mathematical solutions. It is very true that direct investigation of the cohesive zone is a tricky business.  But its relevance in so many fields such as bacteria / particle aggregation and biofilm formation in environmental and colloidal sciences require some simple but sufficiently rigorous models.  For instance, the DLVO theory, the long range surface forces and the subsequent cohesive zone model have been in use since 1930s.  Somehow we need a strategy to convince the community of the importance of solid-mechanics.

Adhesion to smooth surfaces is relatively well understood and crack propagation in that limit can be predicted using existing theory.  That's not the case for rough surfaces, particularly if the roughness has a small length scale.  Simulations provide a way out.  But they are not very satisfying in the sense that our understanding rarely goes beyond the particular aspects we choose to look at (i.e., blind men vs. elephant syndrome). 

Has anyone had a chance to examine "Wrapping an adhesive sphere with an elastic sheet" bu Hure, Roman, and Bico,  [Phys. Rev. Lett. 106, 174301] Published Mon Apr 25, 2011 ?  Comments on that work are eagerly sought.

-- Biswajit



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