Evaluation of morphological representative sample sizes for nanolayered polymer blends

Summary The size of representative microstructural samples obtained from atomic force microscopy is addressed in this paper. The case of an archetypal one‐dimensional nanolayered polymer blend is considered. Image analysis is performed on micrographs obtained through atomic force microscopy, yielding statistical data concerning morphological properties of the material. The variability in terms of microstructural morphology is due to the thermomechanical processing route. The statistical data is used in order to estimate sample size representativity, based on an asymptotic relationship relating the inherent point variance of the indicator function of one material phase to the statistical, size‐dependent, ensemble variance of the same function. From the study of nanolayered material systems, the statistical approach was found to be an effective mean for discriminating and characterizing multiple scales of heterogeneity. Lay description This contribution addresses the notion of sampling in the field of materials science. The question of sampling size for microscopy is addressed, as well as its relation to the precision of measurements. Atomic force microscopy is used to image the structure of polymer composites at the nanometre scale. Based upon these images, a statistical treatment is applied, resulting in key characteristic data able to describe the structural organisation of the composite at the nano‐ and micrometre scale. Variations in this data informs us about the effect of manufacturing parameters (composition, temperature, flow rate…) on the material. From this analysis, an adequate sampling size can be predicted for a given precision. Moreover, the approach proposed in this work allowed for the separation of different scales of variability within the composite: local physical phenomena result in short‐range variability, while boundary effects due to the manufacturing process result in long‐range variations in the material. The statistical approach presented in this paper is indeed a powerful tool for understanding the interaction between manufacturing process, material structure, and functional properties of materials.