Entropic-elastic coupling in fibrillar adhesion: A unified analytical framework

Fibrillar adhesive systems are ubiquitous in nature and serve as powerful blueprints for the design of advanced bioinspired interfaces. Their performance arises from a subtle interplay between molecular-scale entropic effects, elastic deformation within the adhering layer, and the external work applied by actuating elements—factors that have seldom been treated within a unified theoretical framework. Here, we introduce a minimal analytical model that, for the first time, captures this energetic competition across multiple scales, from molecular interactions to mesoscopic and macroscopic adhesion responses such as those measured by Atomic Force Microscopy. Using a simple lattice representation, we derive closed-form expressions for key quantities – strength, stiffness, peel force, strain, and stored energy – thereby elucidating the critical roles of thermal fluctuations, material compliance, and actuator elasticity. The model successfully reproduces temperature-dependent decohesion behavior in artificial fibrillar adhesive systems, confirming its predictive capability. This framework not only reconciles experimental observations across biological and synthetic systems but also provides a quantitative basis for tuning adhesion through molecular and mechanical design. In particular, it yields a closed-form regime map separating ductile and fragile decohesion at fixed temperature. By coupling entropic and elastic contributions within a single analytical description, the study establishes a rigorous foundation for understanding contact mechanics in fibrillar architectures and for guiding the rational development of next-generation bioinspired adhesives.