Modeling Percolation in Polymer Nanocomposites by Stochastic Microstructuring

Abstract

A methodology was developed for the prediction of the electrical properties of carbon nanotube-polymer nanocomposites via Monte Carlo computational simulations. A two-dimensional microstructure that takes into account waviness, fiber length and diameter distributions is used as a representative volume element. Fiber interactions in the microstructure are identified and then modeled as an equivalent electrical circuit, assuming one-third metallic and two-thirds semiconductor nanotubes. Tunneling paths in the microstructure are also modeled as electrical resistors, and crossing fibers are accounted for by assuming a contact resistance associated with them. The equivalent resistor network is then converted into a set of linear equations using nodal voltage analysis, which is then solved by means of the Gauss–Jordan elimination method. Nodal voltages are obtained for the microstructure, from which the percolation probability, equivalent resistance and conductivity are calculated. Percolation probability curves and electrical conductivity values are compared to those found in the literature.

Modeling Electrical Percolation to optimize the Electromechanical Properties of CNT/Polymer Composites in Highly Stretchable Fiber Strain Sensors

“…CNTs are considered to have the average radius of 25 nm, with the average length of 5 μm and the conductivity was assumed to be 1.0 × 10 4 S/m. As part of our study, a random number generator is used for the length and the radius of CNTs that follows Weibull and log-normal probability distribution functions, respectively 13,35 . The Van der Waals distance d vdw and the cut-off distance d cutoff between the outermost wall of two adjacent CNTs are considered to be 3.4 Å and 10.0 Å, respectively, in our simulation.…”

Modeling of Nonlinear Optical Phenomena in Host-Guest Systems Using Bond Fluctuation Monte Carlo Model: A Review

“…Monte Carlo method uses random numbers to estimate parameters of a probe sampled from a general population. Metropolis Monte Carlo approach [146] was successfully used in polymer science [10,147]; other implementations in polymer science are also used [12,148,149].…”

Photoinduced Mass Transport in Azo-Polymers in 2D: Monte Carlo Study of Polarization Effects

“…The concept of Monte Carlo method comes down to using random numbers to estimate parameters of a probe sampled from a general population. In statistical physics, the widely used Metropolis Monte Carlo algorithm [ 50 ] was successfully implemented in polymer science [ 51 , 52 ]; other implementations are also used [ 53 , 54 , 55 ].…”