Application of fractional calculus in modeling transient currents in polymers
DOI:
https://doi.org/10.29105/ingenierias27.96-948Keywords:
Transient currents, Caputo derivative, fractional calculus, Mittag-Leffler, polymerAbstract
This article reviews the limitations of the mathematical models commonly used across the literature for the general description of the phenomenon of transient currents in polymeric materials through a power law or a negative exponential function, and proposes the application of fractional calculus. Among the limitations of the traditional approaches stand out their failure in the association of this distinctive electrical behavior with physical parameters. The causes of these stem from the complexity of electrical behavior in polymers. This phenomenon occurs through the relaxation of electric charge as a function of time, where the viscoelasticity of the polymer widely influences the movement of electric dipoles and the conduction of electric charge carriers. Typically, the phenomenon of transient currents is described using RC (resistor-capacitor) circuits, where a resistor and a capacitor represent the ability of a polymer to dissipate and store electrical charge. The mathematical model herein constructed through the application of fractional calculus provides with a physical interpretation of its parameters, which describe complex behaviors in polymers.
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Copyright (c) 2024 Jesús Gabino Puente-Córdova, Karla Louisse Segura-Méndez, Flor Yanhira Rentería-Baltiérrez, Isaac Yair Miranda-Valdez
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