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4 - Network Structure and Geometric Parameters
Catalin R. Picu, Rensselaer Polytechnic Institute, New York
Book:

Network Materials

Published online:

15 September 2022

Print publication:

22 September 2022, pp 95-127
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Summary

The structure of network materials is stochastic. This chapter introduces the minimum set of geometric parameters required to describe the network structure. This set includes the fiber and crosslink densities, the mean segment length, a measure of preferential fiber orientation, and the connectivity index. The relation between the mean segment length and the fiber density is established for two- and three-dimensional networks with cellular and fibrous architectures. The effect of fiber tortuosity, fiber preferential alignment, and excluded volume interactions on the mean segment length are outlined. The statistics of pore sizes in networks of fibrous and cellular types is discussed in terms of the geometric network parameters. The percolation threshold, at which the first connected path forms across the network domain, is discussed for specific methods used to generate the network.