Spatial Patterns in Fibrous Materials: A Metrological Framework for Pores and Junctions

Several materials widely used in scientific research and industrial applications, including nano-filters and neuromorphic circuits, consist of fiber structures. Despite the fundamental structural similarity, the key feature that should be considered depends on the specific application. In the case of membranes and filters, the main concern has been on the pores among fibers, whereas in neuromorphic networks the main functionality is performed through the junctions of nanowires simulating neuron synapses for information dissemination. Precise metrological characterization of these structural features, along with methods for their effective control and replication, is essential for optimizing performance across various applications. This paper presents a comprehensive metrological framework for characterizing the spatial point patterns formed by pores or junctions within fibrous materials. The aim is to probe the influence of fiber randomness on both the point patterns of intersections (ppi) and pores (ppp). Our findings indicate a strong tendency of ppi toward aggregation, contrasting with a tendency of ppp toward periodicity and consequent pore uniformity. Both patterns are characterized by peculiarities related to collinearity effects on neighboring points that cannot be captured by the conventional anisotropy analysis of point patterns. To characterize local collinearity, we develop a method that counts the number of collinear triplets of nearest neighbor points in a pattern and designs an appropriate parameter to quantify them, also applied to scanning electron microscopy (SEM) images of membranes, demonstrating consistency with simulated data.