Fractional dynamics of interfaces between soft-nanoparticles and rough substrates

A theoretical model is presented to describe the spatiotemporal behavior of complex liquid-solid interfaces bordered by the contact line formed between liquid-like particle and solid-rough substrate. The analysis helps us to determine the soft-nanoparticle adhesion. When the interfacial temperature is above the glass transition and the substrate is rough, we find that surface forces can change by orders of magnitude depending on the temperature, contact time, and particle size varying from atoms to microns. The critical surface tension of solid substrates and the temperature-dependent structural relaxation of soft nanoparticles are shown to have significant effects on the size-dependent adhesion.