Deconvolution of Stress Interaction Effects from Atomic Force Spectroscopy Data across Polymer-Particle Interfaces

Atomic force microscopy (AFM) is a powerful technique for imaging polymer nanocomposites as well as other systems with heterogeneous material properties on the nanoscale. However, the quantitative measurement of modulus is highly susceptible to convoluting structural effects due to the finite tip radius and stress field interactions with particles and substrates which are often termed the "substrate effect" or "thin film effect". We present an empirical master curve that can model the change in measured modulus (E_MC) due to structural effects in an AFM indentation on a soft material near a stiff filler, using N121 and N660 carbon black-styrene-butadiene rubber nanocomposites as examples. Finite element analysis is combined with experimental AFM data across an interface at increasing indentation depths to create a robust method for confirming or rejecting the presence of an interphase layer in AFM. From the raw data, which is initially inconclusive, we reasonably estimate the width of the loosely bound layer (ζ_int) surrounding each (strongly interacting) N121 particle to be 50-60 nm after deconvolving the substrate effect. In comparison, we found no significant loosely bound layer around the (weakly interacting) N660 particles. While we have demonstrated this technique for polymer nanocomposites, we believe the strategy is broadly applicable to multiphase soft materials.