Ligand-mediated adhesive mechanics of two static, deformed spheres

Abstract.

A self-consistent model is developed to investigate attachment/detachment kinetics of two static, 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 macroscale static deformed configuration of the spheres. It is shown that in the limit of smooth, neutrally charged surface (i.e., the dimensionless inverse Debye length, $\kappa D \rightarrow \infty$), interacting via elastic binders (i.e., the dimensionless stiffness coefficient, $\gamma \rightarrow 0$) the adhesion mechanics approaches the regime of application of the JKR theory, and in this particular limit, the contact radius, R_c, scales with the particle radius, R, according to the scaling law, $R_{c}\propto R^{2/3}$. We show that static, deformed, highly charged, ligand-coated surface of micro-spheres exhibit strong adhesion. Normal stress distribution within the contact area adjusts with the binder stiffness coefficient, from a maximum at the center to a maximum at the periphery of the region. Although reported in some in vitro experiments involving particle adhesion, until now a physical interpretation for this variation of the stress distribution for deformable, charged, ligand-coated microspheres is missing. Surface roughness results 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.

Graphical abstract