Continuum modeling of the cohesive energy for the interfaces between films, spheres, coats and substrates

Explicit solutions of the cohesive energy for the interfaces between film/coat, sphere/coat, sphere/matrix and sphere/substrate are obtained by continuum modeling of the van der Waals interaction between them. The analytical results show that the cohesive energy strongly depends on their size and spacing. For a given film thickness and sphere radius, the cohesive strength increases with increasing coat thickness and then tends to a constant when the coat thickness is up to a critical value. The cohesive strength for the interface between sphere/matrix keeps a constant when the sphere radius is up to a critical value. Checking against full atom molecular mechanics calculations show that the continuum solution has high accuracy. The established analytical solutions should be of great help for understanding the interactions between the nanostructures and substrates, biomaterials, designing nanocomposites and nanoelectromechanical systems.