On determining the Poisson's ratio of viscoelastic polymer microparticles using a flat punch test

Microscopic spherical polymer particles are increasingly used in a wide range of areas, including pharmacy, physics and microelectronics. For most of the applications a precise knowledge of the mechanical properties is crucial. Nanomechanical indentation, often using flat-punch geometry, allows determining the deformation and fracture properties of individual particles. Measurements of the lateral expansion as function of axial compression in the flat-punch test can under certain conditions be used to extract the Poisson's ratio of the particle material. Here, we demonstrate that the models based on linear elasticity break down even at moderate strain values in micron-sized polymer (resorcinol-formaldehyde) particles in flat-punch tests monitored with optical microscopy. Finite element analysis was used to solve the standard linear solid model of viscoelasticity, giving excellent agreement with the experimental data and pin-pointing the short-comings of linear elastic models. We finally present a parameterized equation for the sphere deformation, relating the long-term Poisson's ratio nu to the Young's modulus E and the dimensionless viscoelastic Prony parameters g(1) and tau(1).