Surface tension and contact with soft elastic solids

The Johnson-Kendall-Roberts theory is the basis of modern contact mechanics. It describes how two deformable objects adhere together, driven by adhesion energy and opposed by elasticity. Here we characterize the indentation of glass particles into soft, silicone substrates using confocal microscopy. We show that, whereas the Johnson-Kendall-Roberts theory holds for particles larger than a critical, elastocapillary lengthscale, it fails for smaller particles. Instead, adhesion of small particles mimics the adsorption of particles at a fluid interface, with a size-independent contact angle between the undeformed surface and the particle given by a generalized version of the Young's law. A simple theory quantitatively captures this behaviour and explains how solid surface tension dominates elasticity for small-scale indentation of soft materials.

[1]  S. Schmidt,et al.  Characterization of adhesion phenomena and contact of surfaces by soft colloidal probe AFM , 2010 .

[2]  Y. Pomeau,et al.  Solid drops: large capillary deformations of immersed elastic rods. , 2013, Physical review letters.

[3]  P.‐J. Sell,et al.  The Surface Tension of Solids , 1966 .

[4]  Dirk Mayer,et al.  Micropatterned silicone elastomer substrates for high resolution analysis of cellular force patterns. , 2007, The Review of scientific instruments.

[5]  Eric R Dufresne,et al.  Deformation of an elastic substrate by a three-phase contact line. , 2011, Physical review letters.

[6]  A. Jagota,et al.  Surface tension, surface energy, and chemical potential due to their difference. , 2013, Langmuir.

[7]  Y. Pomeau,et al.  Surface instability of soft solids under strain , 2011 .

[8]  H. Butt,et al.  Force measurements with the atomic force microscope: Technique, interpretation and applications , 2005 .

[9]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[10]  B. Persson,et al.  On pattern transfer in replica molding. , 2008, Langmuir.

[11]  D. Luo,et al.  Gravity and surface tension effects on the shape change of soft materials. , 2013, Langmuir : the ACS journal of surfaces and colloids.

[12]  Andrey V Dobrynin,et al.  Adhesion of nanoparticles. , 2010, Langmuir : the ACS journal of surfaces and colloids.

[13]  P. Tracqui,et al.  Optimization of poly-di-methyl-siloxane (PDMS) substrates for studying cellular adhesion and motility , 2008 .

[14]  J. Wettlaufer.  ACCRETION IN PROTOPLANETARY DISKS BY COLLISIONAL FUSION , 2009, 0911.5398.

[15]  Hertz.  On the Contact of Elastic Solids , 1882 .

[16]  J. Frenkel.  Viscous Flow of Crystalline Bodies under the Action of Surface Tension , 1945 .

[17]  S. Gorb,et al.  From micro to nano contacts in biological attachment devices , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[18]  Uzi Landman,et al.  Atomistic Mechanisms and Dynamics of Adhesion, Nanoindentation, and Fracture , 1990, Science.

[19]  S. E. Reynolds,et al.  THUNDERSTORM CHARGE SEPARATION , 1957 .

[20]  B. Luan,et al.  The breakdown of continuum models for mechanical contacts , 2005, Nature.

[21]  M. Dunn,et al.  The role of van der Waals forces in adhesion of micromachined surfaces , 2005, Nature materials.

[22]  Ludwik Leibler,et al.  Static and Dynamic Wetting Properties of Thin Rubber Films , 1996 .

[23]  S. Sherwood,et al.  Small ice crystals and the climatology of lightning , 2006 .

[24]  E. Dufresne,et al.  Universal deformation of soft substrates near a contact line and the direct measurement of solid surface stresses. , 2012, Physical review letters.

[25]  H. Hertz.  Ueber die Berührung fester elastischer Körper. , 1882 .

[26]  A. Jagota,et al.  Growth of adhesive contacts for Maxwell viscoelastic spheres , 1998 .

[27]  A. Chateauminois,et al.  Deformation of elastic coatings in adhesive contacts with spherical probes , 2006 .

[28]  S. Gorb,et al.  Surface roughness of peeled adhesive tape: A mystery? , 2010 .

[29]  D. Tabor.  Surface Forces and Surface Interactions , 1977 .

[30]  D. Maugis.  Extension of the Johnson-Kendall-Roberts theory of the elastic contact of spheres to large contact radii , 1995 .

[31]  A. Jagota,et al.  Solid surface tension measured by a liquid drop under a solid film , 2013, Proceedings of the National Academy of Sciences.

[32]  D. Maugis.  Adhesion of spheres : the JKR-DMT transition using a dugdale model , 1992 .

[33]  R. Cerbino.  Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves , 2006 .

[34]  Anand Jagota,et al.  Surface-tension-induced flattening of a nearly plane elastic solid. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  D. Luo,et al.  A mechanical metamaterial made from a DNA hydrogel. , 2012, Nature nanotechnology.

[36]  S. Suresh,et al.  Graded Materials for Resistance to Contact Deformation and Damage , 2001, Science.

[37]  Jean-Léon Maître,et al.  Adhesion Functions in Cell Sorting by Mechanically Coupling the Cortices of Adhering Cells , 2012, Science.

[38]  Charles M. Lieber,et al.  Chemical Force Microscopy , 1997, Microscopy and Microanalysis.

[39]  Robert W Style,et al.  Patterning droplets with durotaxis , 2013, Proceedings of the National Academy of Sciences.

[40]  M. Shanahan,et al.  Inertial to viscoelastic transition in early drop spreading on soft surfaces. , 2013, Langmuir : the ACS journal of surfaces and colloids.

[41]  Rudolf Merkel,et al.  Cell force microscopy on elastic layers of finite thickness. , 2007, Biophysical journal.

[42]  A. Jagota,et al.  The Role of Viscoelastic Adhesive Contact in the Sintering of Polymeric Particles. , 2001, Journal of colloid and interface science.

[43]  Surface folding-induced attraction and motion of particles in a soft elastic gel: cooperative effects of surface tension, elasticity, and gravity. , 2013, Langmuir : the ACS journal of surfaces and colloids.

[44]  Eric R. Dufresne,et al.  Static wetting on deformable substrates, from liquids to soft solids , 2012, 1203.1654.

[45]  Conceptual aspects of line tensions. , 2007, The Journal of chemical physics.

[46]  K. Kendall,et al.  Surface energy and the contact of elastic solids , 1971, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[47]  Ty Phou,et al.  Capillarity driven instability of a soft solid. , 2010, Physical review letters.

[48]  Kevin T. Turner,et al.  Friction laws at the nanoscale , 2009, Nature.

[49]  B. M. Fulk.  MATH , 1992 .

[50]  Z. Suo,et al.  Surface energy as a barrier to creasing of elastomer films: an elastic analogy to classical nucleation. , 2012, Physical review letters.

[51]  Alexander G. G. M. Tielens,et al.  The Physics of Dust Coagulation and the Structure of Dust Aggregates in Space , 1997 .

[52]  Christian Fretigny,et al.  Friction and shear fracture of an adhesive contact under torsion. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[53]  Amy E. Childress,et al.  Colloidal adhesion to hydrophilic membrane surfaces , 2004 .

[54]  B. Widom.  Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves , 2003 .

[55]  U. Landman,et al.  Nanotribology: friction, wear and lubrication at the atomic scale , 1995, Nature.

[56]  E. Dufresne,et al.  Imaging in-plane and normal stresses near an interface crack using traction force microscopy , 2010, Proceedings of the National Academy of Sciences.