title: Anomalous dielectric relaxation with linear reaction dynamics in space-dependent force fields.
abstract: The anomalous dielectric relaxation of disordered reaction with linear reaction dynamics is studied via the continuous time random walk model in the presence of space-dependent electric field. Two kinds of modified reaction-subdiffusion equations are derived for different linear reaction processes by the master equation, including the instantaneous annihilation reaction and the noninstantaneous annihilation reaction. If a constant proportion of walkers is added or removed instantaneously at the end of each step, there will be a modified reaction-subdiffusion equation with a fractional order temporal derivative operating on both the standard diffusion term and a linear reaction kinetics term. If the walkers are added or removed at a constant per capita rate during the waiting time between steps, there will be a standard linear reaction kinetics term but a fractional order temporal derivative operating on an anomalous diffusion term. The dielectric polarization is analyzed based on the Legendre polynomials and the dielectric properties of both reactions can be expressed by the effective rotational diffusion function and component concentration function, which is similar to the standard reaction-diffusion process. The results show that the effective permittivity can be used to describe the dielectric properties in these reactions if the chemical reaction time is much longer than the relaxation time.
authors.affiliation: College of Electronical Information Engineering, China West Normal University, Nanchong 637002, China.
authors.forename: Tao
authors.initials: T
authors.lastname: Hong
authors.affiliation: College of Electronical Information Engineering, China West Normal University, Nanchong 637002, China.
authors.forename: Zhengming
authors.initials: Z
authors.lastname: Tang
authors.affiliation: College of Electronics and Information Engineering, Sichuan University, Chengdu 610064, China.
authors.forename: Huacheng
authors.initials: H
authors.lastname: Zhu