Fiber Aggregation in Nanocomposites: Aggregation Degree and Its Linear Relation with the Percolation Threshold

Fiber aggregation in nanocomposites has an important effect on macroscopic electrical performance. To quantitatively evaluate its effect, an index to characterize the degree of aggregation is imperative and, ideally, it should have three features simultaneously, i.e., (1) single-parametric, dimensionless, and physically meaningful, (2) applicable to different aggregation topologies, and (3) one-to-one, corresponding to material electrical properties. However, these features remain largely unexplored. Here, we propose a new aggregation degree that is defined as the average increment of the fiber number connecting with each one when fibers aggregate from a uniform distribution state. This index is applicable to different aggregation topologies, from lump-like to network-like aggregating clusters. By geometric probability analysis and numerical validations, we demonstrate the index can be concisely expressed by the characteristic parameters of the aggregating cluster since it only depends on the local features. Interestingly, a one-to-one linear relation between the aggregation degree and the percolation threshold is found, which is independent of the distribution law of the fibers. This work may provide a guide to the property characterization, performance prediction, and material design of nanocomposites, and give physical insight into the understanding of systems with similar non-uniform distributions.