We assume that the main contribution to the properties of composite polymer materials with embedded high-aspect-ratio nanoparticles (CNTs, graphene, etc.) comes from the percolation cluster - a structure that forms when a critical concentration is reached, above which particles in the polymer form connected networks.

Generally, material properties depend on the characteristics of the matrix, individual particles, and the percolation cluster. For instance, when considering gas and liquid permeability through composite materials, the overall membrane permeability depends on the permeability of the matrix, the interfacial layer formed by particle-polymer interactions, and the percolation cluster itself.

The volume fraction occupied by the percolation cluster depends on particle geometry and interfacial layer thickness.

Nonlinear effects are observed not only in electrical conductivity but also in mechanical properties (Reference), transport properties (Reference), and thermal conductivity (Reference) of polymer composites with high-aspect-ratio particles.

To predict percolation thresholds and calculate cluster characteristics, we developed software that computes percolation cluster parameters for various geometric objects in finite-sized systems.

A statistical computational method for modeling random processes including particle distribution in matrices, diffusion phenomena, and percolation behavior.

We employ Monte Carlo methods to calculate percolation cluster parameters (probability, strength, volume fraction, etc.). The simulation begins by defining the computational domain size in either 2D or 3D space, followed by selecting an appropriate particle model.

After model selection, specify particle core dimensions and interfacial layer thickness. The full software version allows defining particle size distribution functions and iteration counts for statistical averaging of percolation cluster parameters.