Phenomenon of the percolation in composite materials based on a polymer binder with a dispersed filler phase

Sulaberidze, V. Sh.; Скорнякова, Е. А.

doi:10.1088/1757-899x/919/2/022009

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“…The phenomenon of percolation, research of which has been rapidly gaining momentum since the 1950s, is used in the description of various systems and phenomena [1][2][3][4][5][6][7][8][9]. It is a critical phenomenon describing phase transitions of the second type, the general idea of which is that in any medium made of two phases, elements of one phase that are independent due to random factors create a more complicated structure, which results in a change in the macroscopic properties of the entire medium because of a change in the concentration of the dispersed phase [10].…”

Section: Introductionmentioning

confidence: 99%

Monte Carlo Simulation of Percolation Phenomena for Direct Current in Large Square Matrices

Zukowski,

Okal,

Kierczynski

et al. 2023

Energies

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In this study, an in-depth analysis of the percolation phenomenon for square matrices with dimensions from L = 50 to 600 for a sample number of 5 × 104 was performed using Monte Carlo computer simulations. The percolation threshold value was defined as the number of conductive nodes remaining in the matrix before drawing the node interrupting the last percolation channel, in connection with the overall count of nodes within the matrix. The distributions of percolation threshold values were found to be normal distributions. The dependencies of the expected value (mean) of the percolation threshold and the standard deviation of the dimensions of the matrix were determined. It was established that the standard deviation decreased with the increase in matrix dimensions, ranging from 0.0262253 for a matrix with L = 50 to 0.0044160 for L = 600, which is almost six-fold lower. The mean value of the percolation threshold was practically constant and amounted to approximately 0.5927. The analysis involved not only the spatial distributions of nodes interrupting the percolation channels but also the overall patterns of node interruption in the matrix. The distributions revealed an edge phenomenon within the matrices, characterized by the maximum concentration of nodes interrupting the final percolation channel occurring at the center of the matrix. As they approached the edge of the matrix, their concentration decreased. It was established that increasing the dimensions of the matrix slowed down the rate of decrease in the number of nodes towards the edge. In doing so, the area in which values close to the maximum occurred was expanded. Based on the approximation of the experimental results, formulas were determined describing the spatial distributions of the nodes interrupting the last percolation channel and the values of the standard deviation from the matrix dimensions. The relationships obtained showed that with increasing matrix dimensions, the edge phenomenon should gradually disappear, and the percolation threshold standard deviation values caused by it will tend towards zero.

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