page_title: Nanotribology
section_title: Adhesion
hierarchical_section_title: Nanotribology / Properties / Adhesion
caption_attribution_description: English: force-displacement curves showing the effect of adhesion force
context_page_description: Nanotribology is the branch of tribology that studies friction, wear, adhesion and lubrication phenomena at the nanoscale, where atomic interactions and quantum effects are not negligible. The aim of this discipline is characterizing and modifying surfaces for both scientific and technological purposes.
  Nanotribological research has historically involved both direct and indirect methodologies. Microscopy techniques, including Scanning Tunneling Microscope, Atomic-Force Microscope and Surface Forces Apparatus, have been used to analyze surfaces with extremely high resolution, while indirect methods such as computational methods and Quartz crystal microbalance have also been extensively employed.
  Changing the topology of surfaces at the nanoscale, friction can be either reduced or enhanced more intensively than macroscopic lubrication and adhesion; in this way, superlubrication and superadhesion can be achieved. In micro- and nano-mechanical devices problems of friction and wear, that are critical due to the extremely high surface volume ratio, can be solved covering moving parts with super lubricant coatings.
context_section_description: Adhesion is the tendency of two surfaces to stay attached together.
  The attention in studying adhesion at the micro- and nanoscale increased with the development of AFM: it can be used in nanoindentation experiments, in order to quantify adhesion forces
  According to these studies, hardness was found to be constant with film thickness, and it's given by:
  where  is the indentation's area and  is the load applied to the indenter.
  Stiffness, defined as , where  is the indentation's depth, can be obtained from , the radius of the indenter-contact line.
   is the reduced Young's modulus,  and  are the indenter's Young's modulus and Poisson's ratio and ,  are the same parameters for the sample.
  However,  can't always be determined from direct observation; it could be deduced from the value of  (depth of indentation), but it's possible only if there is no sink-in or pile-up (perfect Sneddon's surface conditions).
  If there is sink in, for example, and the indenter is conical the situation is described below.
  From the image, we can see that:
   and 
  From Oliver and Pharr's study
  where ε depends on the geometry of the indenter;   if it's conical,  if it's spherical and  if it's a flat cylinder.
  Oliver and Pharr, therefore, did not consider adhesive force, but only elastic force, so they concluded:
  Considering adhesive force
  Introducing  as the adhesion energy and  as the work of adhesion:
  obtaining
  In conclusion:
  The consequences of the additional term of adhesion is visible in the following graph:
  During loading, indentation depth is higher when adhesion is not negligible: adhesion forces contributes to the work of indentation; on the other hand, during unloading process, adhesion forces opposes indentation process.
  Adhesion is also related to capillary forces acting between two surfaces when in presence of humidity.
caption: Load-displacement curves that shows the effect of adhesion force
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