Stiffness Gradients in Glassy Polymer Model Nanocomposites: Comparisons of Quantitative Characterization by Fluorescence Spectroscopy and Atomic Force Microscopy

The issue of how significantly and over what length scales stiffness or modulus can be modified by the presence of a substrate or nanoparticle interface is important in the design and performance of polymer nanocomposites and nanostructured polymers. Here, we provide the first comparison of stiffness gradient length scales in polymeric materials characterized by two techniques: fluorescence spectroscopy (which is sensitive to molecular caging and hence to modulus) and AFM (which, coupled with finite element analysis, provides a direct determination of modulus). After cooling samples from 140 °C at 1 °C/min, characterization is done at room temperature on model nanocomposites in which a polystyrene (PS) film is supported on both sides by glass substrates. In confined model nanocomposites, the local stiffness enhancement relative to bulk is the result of perturbations from both substrate interfaces. In a 266 nm thick PS model nanocomposite, perturbations to modulus extend ∼200 nm from each interface in a nonlinear compound effect. Both methods reveal a small (5+% by AFM) stiffness enhancement at the midpoint of a 266 nm thick model nanocomposite; the midpoint modulus increases with confinement and is 50% higher than bulk in a 60 nm thick model nanocomposite. In bulk model nanocomposites, stiffness gradients result from perturbations propagating from a single substrate interface that are damped by the bulk PS layer, and both methods indicate that stiffness gradients extend ∼80 nm from an interface. The two techniques show qualitative and quantitative agreement regarding stiffness gradient length scales and are correlated via a simple monotonic relationship between the fluorescence measurable and normalized modulus.