Type Seminar in the framework of the DK Winter Workshop and SFB Internal Meeting
Time 11:10 - 11:55
Speaker Paolo Piovano (University of Vienna)
Title Analytical validation of the Young-Dupré law for epitaxially-strained thin films
Abstract A variational model for epitaxially-strained thin films on substrates is derived both by $\Gamma$-convergence from the transition-layer setting, and by relaxation from a sharp-interface description available in the literature for regular configurations.
The model is characterized by a configurational energy that accounts for both the competing mechanisms responsible for the film shape. On the one hand, the lattice mismatch between the film and the substrate generates large stresses, and corrugations may be present because film atoms move to release the elastic energy. On the other hand, flatter profiles may be preferable to minimize the surface energy.
The regularity of energetically-optimal film profiles is then studied by extending previous methods and by developing new ideas based on transmission problems. The achieved regularity results relate to both the Stranski-Krastanow and the Volmer-Weber modes, the possibility of different elastic properties between the film and the substrate, and the presence of the surface tensions of all three involved interfaces: film/gas, substrate/gas, and film/substrate.
Finally, geometrical conditions are provided for the optimal wetting angle, i.e., the angle formed at the contact point of films with the substrate. In particular, the Young-Dupré law is shown to hold, yielding what appears to be the first analytical validation of such law for a thin-film model in the context of Continuum Mechanics. This is a joint work with Elisa Davoli (University of Vienna).