Ligand mediated adhesive mechanics of two deformed spheres

A self-consistent model is developed to investigate attachment / detachment kinetics of two soft, deformable microspheres with irregular surface and coated with flexible binding ligands. The model highlights how the microscale binding kinetics of these ligands as well as the attractive/repulsive potential of the charged surface affects the static deformed configuration of the spheres. It is shown that in the limit of smooth, neutral charged surface (i.e., the Debye length, $\kappa \rightarrow \infty $), interacting via elastic binders (i.e., the stiffness coefficient, $\lambda \rightarrow 0$) the adhesion mechanics approaches the regime of application of the JKR theory, and in this particular limit, the contact radius scales with the particle radius, according to the scaling law, $R_c\propto R^{\frac{2}{3}}$. We show that adhesion dominates in larger particles with highly charged surface and with resilient binders. Normal stress distribution within the contact area fluctuates with the binder stiffness coefficient, from a maximum at the center to a maximum at the periphery of the region. Surface heterogeneities result in a diminished adhesion with a distinct reduction in the pull off force, larger separation gap, weaker normal stress and limited area of adhesion. These results are in agreement with the published experimental findings.