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A radically new percolation model for describing the extremal dependence of the degree of rein forcement of polymer/carbon nanotube nanocomposites on the nanofiller content has been proposed. It has been shown that, for this nanofiller, the percolation threshold almost coincides with the aggregation threshold on the concentration scale. From the structural point of view, the extremum of this dependence is caused by the change in the type of the reinforcing component (from interphase regions to the skeleton of carbon nan otubes). From the mathematical point of view, the behavior of the degree of reinforcement is described by the general percolation relationship with replacement of the critical exponents near the percolation threshold. Neither the functionalization of the nanofiller nor the preliminary ultrasound treatment qualitatively change the dependence under study.

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