Effects of nanoscale thickness and elastic nonlinearity on measured mechanical properties of polymeric films

Scanning probe microscope-enabled nanoindentation is increasingly reported as a means to assess the mechanical properties of nanoscale, compliant material volumes such as polymeric films and bio-membranes. It has been demonstrated experimentally that the Hertzian contact model developed for linear elastic materials of semi-infinite thickness fails to accurately predict the nominal elastic modulus E for polymeric thin films, consistent with limitations identified for comparably rigid metal and ceramic thin films. Here we employ computational simulations based on experimental parameters for compliant polyelectrolyte films, in order to separate limitations of such analysis due to the finite material thickness from those due to nonlinear constitutive relations approximating polymer deformation. We thus identify the range of strains, strain rates, and material thickness for which a modified Hertzian solution can accurately predict the elastic stiffness of polymeric films of nanoscale (< 100 nm) thickness from scanning probe microscope-enabled nanoindentation experiments.