Modelling of surface nanoparticle inclusions for nanomechanical measurements by an AFM or nanoindenter: spatial...

Finite element analysis (FEA) is used to model nanoindentation by a rigid, spherically shaped indenter, axially indenting an elastic two phase polymer system comprised of a cylindrical nanoparticle of compliant polymer set in a semi-infinite matrix of stiffer polymer. The cylindrical nanoparticle is normal to the sample surface. An axisymmetric finite element model is used to determine the reduced modulus measured as a function of the indentation depth for various nanoparticle radii and extensions below the surface. We show how the previous simple analytical equations may be extended to describe these situations with accuracy. This gives excellent agreement with the FEA and provides a clear guide to the maximum indentation depth as a function of both the nanoparticle radius and its thickness consistent with a choice of either computation from the analytical equations or direct measurement with a maximum of 10% error in the measured reduced modulus.