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Adhesion phenomena play an important role in different areas of science and technology including tribology, colloidal science, materials science, biophysics and biochemistry. They are of paramount importance for colloidal stabilization, drug delivery, interfacial friction and lubrication, nanofabrication and nanomolding, cell mechanics and adhesion, and contact mechanics. The modern approach to adhesion between elastic bodies in a contact is based on the classical work by Johnson, Kendal and Roberts (JKR) that extended the Hertz theory of the elastic contact by accounting for the effect of the adhesion in the contact area. According to this model a contact radius a of an elastic sphere of radius R_p with the shear modulus G in a contact with a solid substrate is proportional to a~R_p (W/GR)^1/3  where W is the work of adhesion.  The analysis of this scaling relation indicates that the importance of the adhesive forces increases for ‘soft’ highly compliant materials such as elastomers, living cells and soft tissues.

We have developed a new model of nanoparticle adhesion which explicitly takes into account the change in the nanoparticle surface energy.  Using combination of the molecular dynamics simulations and theoretical calculations we have showed that the deformation of the adsorbed nanoparticles is a function of the dimensionless parameter β=γ_p(GR_p)^-2/3 W^-1/3, where G is the particle shear modulus, R_p is the initial particle radius, γ_p is the polymer interfacial energy and W is the particle work of adhesion. In the case of small values of the parameter β<0.1, which is usually the case for strongly cross-linked large nanoparticles, the particle deformation can be described in the framework of the classical Johnson, Kendall, and Roberts (JKR) theory. However, we observed a significant deviation from the classical JKR theory in the case of the weakly cross-linked nanoparticles that experience large shape deformations upon particle adhesion. In this case the interfacial energy of the nanoparticle plays an important role controlling nanoparticle deformation. Our model of the nanoparticle adhesion is in a very good agreement with the simulation results and provides a new universal scaling relationship for nanoparticle deformation as a function of the system parameters.