Tunneling-percolation model of multicomponent nanocomposites

Abstract

Using a mixture of different types of fillers has been experimentally shown to improve the electrical conductivity of polymer nanocomposites beyond the weighted average due to synergistic effects. In this study, we develop a critical path analysis-based tunneling-percolation model for multicomponent systems of nanocomposites with ellipsoidal fillers. The nature of the interaction between different filler components is controlled by a key modeling parameter capturing the tunneling interactions between fillers. This generalization allows us to examine scenarios where the nature of a given type of filler can be varied continuously from an insulating-type to a conductive-type. The percolation behavior of two-component systems with a combination of prolate, oblate, and spherical fillers is investigated using Monte Carlo simulations for different relative volume fractions and nature of interactions while keeping the total volume fraction fixed. The simulation results are shown to be in semi-quantitative agreement with predictions made by the second-virial-approximation-based theories. Our results suggest that for multicomponent systems with well-dispersed fillers, the synergistic effects are linked directly with the nature of interactions between different filler types. Moreover, addition of prolate fillers to oblate or spherical fillers should generally improve the electrical conductivity of multicomponent nanocomposites.

Electromechanical Properties of PVDF-Based Polymers Reinforced with Nanocarbonaceous Fillers for Pressure Sensing Applications

“…The percolation threshold is reported to occur when the first conductive paths spanning all the nanocomposite are formed due to the proximity of the conductive fillers embedded in the isolating matrix. This phenomenon has been explained by different theoretical models [19,20,21].…”

Percolation networks inside 3D model of the mineralized collagen fibril

“… To determine percolation paths in the equatorial plane, we select the clusters from step (a) with vertices of the platelets that are outside a circumference of diameter equal to 90% of the MCF diameter. For each selected cluster we determine the minimum (w min ) and maximum (w max ) coordinates of the vertices along W direction and compute the distance d W : In order to take into account the cylindrical geometry of the simulation domain, in W direction we assume that the clusters are percolating if their length d W is greater or equal to the chord length W percolation : In post processing analysis, we observed that a bistable behaviour 40 , 60 is developed when considering clusters composed by more than four platelets. Thus, we identified a minimum chord length of 50 nm and 120 nm for the MCF diameter of 50 nm and 200 nm respectively, for which a well-defined sigmoidal trend for the percolation probability is achieved.…”

“…Thus, we identified a minimum chord length of 50 nm and 120 nm for the MCF diameter of 50 nm and 200 nm respectively, for which a well-defined sigmoidal trend for the percolation probability is achieved. For each selected cluster we identified the minimum (t min ) and maximum (t max ) coordinates of the vertices along T direction and compute the distance d T : Analogously to the analysis performed for spanning clusters in W direction, we consider that clusters are percolating in T direction if the following relation is valid: In post-processing analysis, we observed that the system has a percolation-like behaviour 40 , 60 when the minimum chord length T percolation is equal to 25 nm and 50 nm for the MCF diameter of 50 nm and 200 nm, respectively. For percolation paths in the longitudinal direction, we selected the clusters from step (a) with coordinates of vertices along L direction that are outside a cylinder of length equal to 950 nm, i.e.…”

Electromechanical Properties of PVDF-Based Polymers Reinforced with Nanocarbonaceous Fillers for Pressure Sensing Applications

“…The percolation threshold is reported to occur when the first conductive paths spanning all the nanocomposite are formed due to the 3 proximity of the conductive fillers embedded in the isolating matrix. This phenomenon has been explained by different theoretical models [19][20][21].…”