Effects of functionally graded materials on dynamics of molecular bond clusters

Unlike nonspecific adhesion of conventional hard materials in engineering commonly described by JKR and DMT type models, the molecular adhesion via specific receptor-ligand bonds is stochastic by nature and has the feature that its strength strongly depends on the medium stiffness surrounding the adhesion. In this paper, we demonstrate in a stochastic-elasticity framework that a type of materials with linearly graded elastic modulus can be designed to achieve "equal load sharing" and enhanced cooperative rebinding among interfacial molecular bonds. Upon modulus gradation, multiple molecular bonds can be elastically decoupled but statistically cooperative. In general, uniform molecular adhesion can be accomplished by two strategies: homogeneous materials with sufficient stiffness higher than a threshold or heterogeneous materials satisfying the criterion on modulus gradation. These results not only provide a theoretical principle for possible applications of functionally graded materials in quantitatively controlling cell-matrix adhesion, but also have general implications on adhesion between soft materials mediated by specific molecular binding.