慢极化弛豫理论

Relaxation Theory of Slow Polarization

提出了凝聚态电介质中的空间电荷扩散模型，用来解释慢极化效应．对自由弛豫过程中的扩散方程，用分离变数方法求出了精确的级数解．当时间ｔ甚小于响应时间τ时，精确解给出的衰减函数为ｅｘｐ（－ｔ／τ），与经验公式一致．但当ｔ较大时精确的衰减函数过渡到指数形式，近似的理论衰减函数可表示为ｅｘｐ（－ｔ／τ＋ａｔ２／τ２）；当ｔ＜２．５τ时它的近似程度很好．理论给出ａ＝３．６１３５２．在室温下对石蜡作了仔细测量，结果和理论完全一致．当ｔ≥２．５τ时，衰减函数已减小至不超过０．６７％；

A diffusion model of space charges in condensed dielectrics is used to explain the slow polarization effect. By separation of variables the diffusion equation is solved in a series form. When the time t is much smaller than the response time, the solution leads to a decay function exp( -t/τ ), which is in agreement with the empirical formula. But for larger t ,the decay function transforms into exponential form. A theoretical decay function is given as exp(- t/τ+at 2/τ 2) for t<2 5τ with a=3 613 52. When t≥2 5τ , the decay function is smaller than 0 67%, it is hardly to detect in measurement. A careful experiment for paraffin in room temperature shows that this is an excellent approximate formula.