A Study on Sampling Sufficiency for Morphological Properties of Polyurethane Foams

This study investigates the sampling sufficiency required for accurately characterizing the morphological properties of rigid polyurethane foams across three distinct regions: core, crown, and lateral edge. A total of 200 individual cells were analyzed from 30 SEM micrographs, enabling the quantification of cell length, cell width, anisotropy index, linear cell density, and shape index. Average cell length ranged from 715 to 763 μm, while cell width varied between 386 and 531 μm depending on the region. The anisotropy index increased from 0.186 in the core to 0.289 in the lateral edge, indicating progressively more elongated cells. Linear cell density showed a marked decrease from 0.062 in the core to 0.001 in the crown, reflecting differences in cellular packing. Shape index values remained relatively stable, confirming its lower sensitivity to structural variations. Monte Carlo simulations were employed to evaluate sampling sufficiency for sample sizes ranging from 2 to 30. Results demonstrated that optimal sample sizes varied with foam region and parameter: 16 cells were sufficient for core and lateral regions, whereas up to 22 cells were required for the crown to capture higher structural heterogeneity. For anisotropy and shape indices, sufficient sampling ranged between 13 and 20 cells depending on the region. The results confirm that the core exhibits lower variability (CoV for cell length: 29.1%) compared to the crown (36.4%) and lateral edge (34.9%), supporting its more homogeneous structure. However, exclusive sampling from the core may lead to biased characterization, as crown and lateral regions display significantly higher variability in both geometry and orientation. These findings establish quantitative guidelines for sampling strategies in polyurethane foam morphology, contributing to improved reproducibility and reliability in structure–property investigations of cellular materials.