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Area of Science:

  • Physics
  • Materials Science
  • Computational Science

Background:

  • Percolation theory is crucial for understanding conductivity in disordered systems.
  • Curved linear objects, such as metal nanowires, are prevalent in thin-film electronics.
  • Existing models often simplify objects as straight lines, neglecting curvature effects.

Purpose of the Study:

  • To investigate the percolation threshold of objects modeled as quadratic Bézier curves.
  • To quantify the relationship between curve curviness and critical number density.
  • To analyze the conductivity exponents of these curved objects.

Main Methods:

  • Monte Carlo simulations were employed to model percolation.
  • Critical number densities were calculated for varying degrees of curve curviness.
  • Excluded area and apparent conductivity exponents were computed.

Main Results:

  • A method was developed to determine critical number density based on excluded area for any curviness.
  • Apparent conductivity exponents were found to be analogous to straight objects (sticks) in specific systems.
  • The study establishes a link between geometric properties of curves and their conductive behavior.

Conclusions:

  • The findings provide a framework for understanding percolation in systems with curved elements.
  • Results are applicable to the optoelectrical performance analysis of curved metal nanowire films.
  • This research bridges geometric modeling with physical properties relevant to materials science.