Polymer nanomechanics: Separating the size effect from the substrate effect in nanoindentation

While the moduli of thin polymer films are known to deviate dramatically from their bulk values, there is not a consensus regarding the nature of this size effect. In particular, indenting experiments appear to contradict results from both buckling experiments and molecular dynamics calculations. In this letter, we present a combined computational and experimental method for measuring the modulus of nanoindented soft films on rigid substrates that reconciles this discrepancy. Through extensive finite element simulation, we determine a correction to the Hertzian contact model that separates the substrate effect from the thickness-dependent modulus of the film. Interestingly, this correction only depends upon a dimensionless film thickness and the Poisson ratio of the film. To experimentally test this approach, we prepared poly(methyl methacrylate), polystyrene, and parylene films with thicknesses ranging from 20 to 300 nm and studied these films using atomic force microscope-based nanoindenting. Strikingly, when experiments were interpreted using the computationally derived substrate correction, sub-70 nm films were found to be softer than bulk, in agreement with buckling experiments and molecular dynamics studies. This correction can serve as a general method for unambiguously determining the size effect of thin polymer films and ultimately lead to the ability to quantitatively image the mechanical properties of heterogeneous materials such as composites.