Percolation Effects in Mixed Matrix Membranes with Embedded Carbon Nanotubes

Polymeric membranes with embedded nanoparticles, e.g., nanotubes, show a significant increase in permeability of the target component while maintaining selectivity. However, the question of the reasons for this behavior of the composite membrane has not been unequivocally answered to date. In the present work, based on experimental data on the permeability of polymer membranes based on Poly(vinyl trimethylsilane) (PVTMS) with embedded CNTs, an approach to explain the abnormal behavior of such composite membranes is proposed. The presented model considered the mass transfer of gases and liquids through polymeric membranes with embedded CNTs as a parallel transport of gases through the polymeric matrix and a "percolation" cluster-bound regions around the embedded CNTs. The proposed algorithm for modeling parameters of a percolation cluster of embedded tubular particles takes into account an agglomeration and makes it possible to describe the threshold increase and subsequent decrease permeability with increasing concentration of embedded particles. The numerical simulation of such structures showed: an increase in the particle length leads to a decrease in the percolation concentration in a matrix of finite size, the power of the percolation cluster decreases significantly, but the combination of these effects leads to a decrease in the influence of the introduced particles on the properties of the matrix in the vicinity of the percolation threshold; an increase in the concentration of embedded particles leads to an increase in the probability of the formation of agglomerates and the characteristic size of the elements that make up the percolation cluster, the influence of individual particles decreases and the characteristics of the percolation transition determine the ratio of the sizes of agglomerates and matrix; and an increase in the lateral linear dimensions of the matrix leads to a nonlinear decrease in the proportion of the matrix, which is affected by the introduced particles, and the transport characteristics of such MMMs deteriorate.