Thermal Fluctuations Limit the Adhesive Strength of Compliant Solids

Abstract

For compliant solids, the stress required to separate an interface (its adhesive strength) appears to be much lower than that calculated by computing intersurface interactions. We explore the hypothesis that the adhesive strength is limited in value by thermal fluctuations. In a simple model of an interface, molecules bridging the two surfaces are represented by linear entropic springs. Asymptotic and numerical analyses are carried out to evaluate the adhesive strength and effective work of adhesion. For stiff materials, adhesive strength is found to be equal to the intrinsic strength—the maximum value of intersurface stress computed ignoring fluctuations. For compliant materials, adhesive strength is significantly reduced and is on the order of the elastic modulus. The effective work of adhesion agrees with the intrinsic work of adhesion for stiff materials and can decay slowly with increasing compliance.

Keywords:

• Adhesive strength
• Compliance
• Statistical model
• Thermal fluctuation
• Work of adhesion

ACKNOWLEDGMENTS

This work was supported in part by the National Science Foundation, grant CMS-0527785.

Notes

One of collection of papers honoring Hugh R. Brown, who received The Adhesion Society Award for Excellence in Adhesion Science, Sponsored by 3M, in February 2006.