Hong Tao, Tang Zhengming, Zhu Huacheng
College of Electronical Information Engineering, China West Normal University, Nanchong 637002, China.
College of Electronics and Information Engineering, Sichuan University, Chengdu 610064, China.
J Chem Phys. 2016 Dec 28;145(24):244105. doi: 10.1063/1.4972863.
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.
在存在空间依赖电场的情况下，通过连续时间随机游走模型研究了具有线性反应动力学的无序反应的反常介电弛豫。通过主方程为不同的线性反应过程推导了两种修正的反应 - 亚扩散方程，包括瞬时湮灭反应和非瞬时湮灭反应。如果在每一步结束时瞬时添加或移除恒定比例的游走者，将有一个修正的反应 - 亚扩散方程，其中分数阶时间导数作用于标准扩散项和线性反应动力学项。如果在步骤间的等待时间内以恒定人均速率添加或移除游走者，将有一个标准的线性反应动力学项，但分数阶时间导数作用于反常扩散项。基于勒让德多项式分析了介电极化，并且两种反应的介电性质都可以用有效旋转扩散函数和组分浓度函数来表示，这与标准反应 - 扩散过程类似。结果表明，如果化学反应时间远长于弛豫时间，则有效介电常数可用于描述这些反应中的介电性质。
