Free energy and critical force for adhesion clusters.

Cooperative clusters of $N$ parallel bonds confined to an anchoring surface by springs of stiffness ${k}_{s}$ are considered. The free energy of a cluster can be obtained from its force-displacement relation. The dissociation kinetics of the cluster can be modeled as the dissociation of an effective single bond. There is a critical force ${F}_{c}$ beyond which the barrier for the cluster dissociation vanishes. ${F}_{c}$ scales such as ${k}_{s}^{1/2}$ and ${F}_{c}/N$ is small compared to the critical force of a single bond. The theoretical predictions of free energy landscape and cluster lifetime are supported by numerical simulations for large number of bonds. Our study suggests that experiments measuring force-displacement relations could be useful in exploring the dynamics of adhesion clusters.