Nanosphere Embedment into Polymer Surfaces: A Viscoelastic Contact Mechanics Analysis

Teichroeb and Forrest (\textit{Phys. Rev. Lett.}, \textbf{91}, 1, 016104-1(2003)) image gold nanosphere embedment into a polystyrene surface and imply the existence of a liquid surface layer. We use a viscoelastic contact mechanics model of their results to give a contrary interpretation. The surface interactions between gold and polystyrene and the indentation depth determine the loads on the nanospheres. Using bulk properties, quantitative agreement between the model and the data is obtained, implying little or no, depression in the glass temperature or existence of a liquid layer at the polystyrene surface. An important aspect of the present analysis is that it is the first to solve the problem for the time dependent Poisson's ratio. The fact that this varies from 0.33 to 0.5 upon traversing the glass transition (time) flattens the nanosphere embedment profile with increasing time.