Decoupling subsurface inhomogeneities: a 3D finite element approach for contact nanomechanical measurements

Novel material properties can be attained when embedding three-dimensional (3D) nanoparticles (NPs) in a variety of polymeric matrices. These inhomogeneities influence the bulk mechanical response due to the local high modulus mismatch between the particles and the matrix. The degree of the mechanical mismatch that is seen near a composite surface depends on the geometry/shape and spatial location and orientation of the particle with respect to the external contact loading. Isolating each particle's contribution to the surrounding elastic field can be numerically discerned but is experimentally complex, as there are limited direct characterization approaches available at the nanoscale. Atomic force microscopy (AFM) instrumentation is one such method that can quantify subsurface particle stiffness effects on nanocomposites with a resolution of a few nanometers. This work studies the spatial and geometrical effects of subsurface silver NPs on the local composite stiffness of a polystyrene matrix using 3D finite element (FE) models to interpret contact resonance (CR) AFM measurements. The present FE-AFM findings suggest both particle shape and particle orientation have a significant role in the degree of uniformity of the stiffness distribution in the embedding matrix. The applied CR-AFM technique shows that the NP geometry can be clearly distinguished when such inhomogeneities are relatively close, 17 nm, to a free surface whereas material-interface measurements at deeper subsurfaces are obscured by experimental noise. This work demonstrates that (i) numerical solutions can assist in qualitatively elucidating nanoinstrumentation stiffness profiles in terms of particle shape and orientation and (ii) CR-AFM measurements can quantify the influence of particle geometry and orientation on the surface nanomechanics of nanocomposite materials.