Anomalous dielectric relaxation with linear reaction dynamics in space-dependent force fields

Area of Science:

• Physics
• Physical Chemistry
• Nonlinear Dynamics

Background:

• Dielectric relaxation in disordered systems is complex.
• Linear reaction dynamics and space-dependent electric fields introduce unique challenges.
• Understanding these phenomena is crucial for materials science and condensed matter physics.

Purpose of the Study:

• To investigate anomalous dielectric relaxation in disordered reactions with linear reaction dynamics.
• To derive modified reaction-subdiffusion equations under space-dependent electric fields.
• To analyze dielectric polarization and properties using theoretical models.

Main Methods:

• Utilized the continuous time random walk (CTRW) model.
• Derived modified reaction-subdiffusion equations via the master equation for instantaneous and non-instantaneous annihilation reactions.
• Analyzed dielectric polarization using Legendre polynomials.

Main Results:

• Two types of modified reaction-subdiffusion equations were derived, featuring fractional temporal derivatives.
• Dielectric properties are described by effective rotational diffusion and component concentration functions.
• Effective permittivity accurately describes dielectric properties when reaction time exceeds relaxation time.

Conclusions:

• The study provides a theoretical framework for understanding dielectric relaxation in complex reaction systems.
• Modified reaction-subdiffusion equations capture the interplay between diffusion, reaction, and electric fields.
• The findings offer insights into the behavior of disordered materials under external fields.