Modeling of the percolation phenomenon of disordered two-dimensional systems

摘要

The article presents the examination method of the percolation phenomenon by modeling occurring in the metal-dielectric nanocomposites of electron tunneling phenomena. This method using the full high voltage discharge phenomenon. Nanocomposites are materials composed of two types of phases, dielectric and metallic. Metallic phase elements are random distributed on the dielectric matrix. The probability is congruous to normal distribution and nanoparticles sized are not the same. The quantum tunneling phenomenon makes possible the current flow without direct contact between neighboring nanoparticles. The point of the studied phenomenon is the step change conductivity during direct current flow. This step change depends on concentration of metallic phase is called percolation threshold. Due to this phenomenon percolation has become the subject of nanomaterials research. Due to the similarity, the incomplete high-voltage discharges phenomenon in air was used to study percolation. In the model, the air is the dielectric medium. Iron discs simulate the metallic phase. The two-dimensional matrix where he discs will be placed of a dielectric material was made. A random point generator to create coordinates where metal discs will be placed was used. The voltage increase is controlled by the created electronic system connected to a stepper motor that drives the autotransformer. The voltage rise speed is 2 kV / s. Metal disks size 3mm, 6mm, 8mm, 10mm and 14mm were used. The test consists in reading the voltage value at which the dielectric matrix is punctured for different contents of the metallic phase. The inverse of the read voltage is the conductivity value of the entire system. When the content of metal discs is low, the conductivity of the system is low. After exceeding a certain concentration value, there is a step decrease in conductivity. The point at which a step change in conductivity occurs is called the percolation threshold. To determine the percolation point, dielectric matrices were measured for different contents of the metallic phase. A series of measurements was created that differed in the concentration of metallic discs (the area of the discs in relation to the surface area between the electrodes). For each of them, the breakdown voltage value was measured and a graph of the reversal of this voltage from concentration was created. The result of the test was the direct determination of the percolation threshold value from the obtained graph.