Dielectric permittivity of interfaces in polymer nanocomposites from electrostatic force microscopy

Abstract

The addition of nanofillers can lead to a significant change in the dielectric properties of polymer nanocomposites. The cause for the change has been identified as the presence of an interfacial layer of polymer surrounding the nanoparticle, which has properties different from the bulk matrix polymer. Controlling the properties of the nanocomposite requires an understanding of the interfacial region between the nanoparticle and the matrix polymer. The nanometer-scale dimension of the interfacial region falls below the spatial resolution of many experimental measurement techniques. This makes the quantitative characterization of their properties a challenge. Electrostatic Force Microscopy (EFM), an AFM-derived method, is a promising technique to characterize interfacial regions owing to its ability to probe the local capacitive response of the sample. However, due to the probe geometry and the long-range nature of electrostatic forces, the actual probed region of the specimen becomes too complex to be defined, and EFM signals get easily misinterpreted. This thesis work presents a methodology to reliably extract interfacial permittivity combining machine learning, numerical simulations, and experimental EFM measurements. We first demonstrate the efficacy of machine learning (ML) models to extract interface permittivity using a data set of synthetic EFM force gradient scans generated by finite element simulations. We show that both support vector regression (SVR) and random forest (RF) algorithms can ‘invert’ the force gradient scan to predict the permittivity with high accuracy. We investigate a two-unknown case where particle depth inside the surface and interphase dielectric constant are unknown, but the interphase thickness is assumed to be known. From a modest database of 200 finite-element simulations, we show that ML models can predict interphase permittivity with a typical accuracy of 0.24 (mean absolute error). We then investigate a case where interphase thickness is also assumed unknown and demonstrate that the models continue to achieve an impressive accuracy of 0.45 for the extracted interphase permittivity. Feature reduction by principal component analysis (PCA) improves the model’s performance and reveals force gradient contrast to be the most important feature in permittivity detection. These ML models perform better than analytical approaches by capturing significant geometric complexity of EFM measurements. We then performed EFM measurements on the tailored nanocomposite systems to test ML performance on the experimental data. Interfacial measurements were carried for two different grafted silica nanoparticles dispersed in PMMA. For a grafted brush of high dielectric constant, signal contrast at the interfacial region was observed in EFM images. The dielectric permittivity and thickness of the interfacial region were quantified using the ML model with high accuracy. The predicted interface parameters match with the parameters of grafted brush estimated from other experiments. For PMMA-grafted brushes, an intrinsic interfacial region of higher permittivity than the matrix was predicted. The results of interfacial permittivity obtained from the EFM measurements were also verified by referring to bulk material characterization. It is anticipated that the present method, opening new possibilities in understanding the matrix/particle interfacial region, may help with the judicious design and engineering of high-performance polymer nanodielectrics. In addition, nanocomposites samples with varying surface chemistry and filler loading were prepared and characterized by TEM, dielectric spectroscopy, and breakdown strength measurements. The impact of filler loading, surface chemistry, and dispersion on the dielectric property was quantified using tools available in Nanomine (a polymer nanocomposite repository). Our collaborators used the experimental data to validate simulation models and build a design strategy for nanodielectrics.