Self-similarity and finite-size effects in nano-indentation of highly cross-linked polymers

The scalability of thermomechanical polymer deformations in the sub-10 nm regime is of particular importance for nano-imprint techniques, hardness measurements of thin films by nano-indentations, and scanning-probe-based thermomechanical data storage. We investigate nano-indentation in the sub-10 nm regime performed on highly cross-linked polymer films of different thicknesses. It is shown that the lateral and vertical geometric characteristics of the indents independently scale down to an indent depth of 1 nm and that the scaling parameters are functions of the film thickness and the temperature of the indenter. However, in the limit of shallow indents the scaling of the cross-coupling between lateral and vertical dimensions is lost. It is argued that the breakdown of self-similarity is due to a minimum strain requirement originating from the co-operative nature of the polymer response induced by a transitions which lock the indent in the deformed state. The results shed new light on the fundamental processes and size effects involved in nanoscale plastic replication, in general.