Evaluation of morphological representative sample sizes for nanolayered polymer blends

Abstract

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.

Nanorheology with a Conventional Rheometer: Probing the Interfacial Properties in Compatibilized Multinanolayer Polymer Films

“…The average experimental thicknesses of PE−PEgMA layers x PE−PEgMA and their standard deviation std PE−PEgMA were calculated from the measurement of at least 10% of the total number of layers. 29 They are reported in Table 1 and are in reasonable agreement with their respective theoretical thickness x thPE−PEgMA . std PE−PEgMA appears slightly higher than for other multilayer systems, 29 which may be due to the relatively high viscosity ratios between polymers (Table S1, Supporting Information).…”

From equilibrium lamellae to out-of-equilibrium cylinders in triblock copolymer nanolayers obtained via multilayer coextrusion

“…This small deviation between mean experimental and theoretical layer thickness may either be due to slight changes in the extruders throughput during extrusion (which will modify the film composition) and/or to the sampling size (i.e. the number of layers measured in the sample compared to the total number of layers) used to determine the mean, as discussed in a previous study [60]. Still, there is a satisfactory agreement between the (targeted) MAM theoretical layer thickness and the mean experimental one for all the samples studied.…”

Existence of a Critical Layer Thickness in PS/PMMA Nanolayered Films

“…a few pixels in terms of AFM imaging, it is critical to analyze all possible sources of error. These sources of error were studied extensively in a previous article, 56 Based on statistical parameters (K a constant and γ the scaling-law exponent) determined from a…”

“…representative-volume-element study for PS layers, 56 and knowing the nominal value h nom , the number of performed AFM images, and the size of the images, it was possible to determine the relative uncertainty rel of the thickness measurement due to sampling for each film. Calculations have shown that the sampling uncertainty varied between 5% and 30%.…”