用昂萨格唯象关系估算嵌入型电极材料中锂离子表观扩散系数

Evaluation of Apparent Lithium Ion Diffusion Coefficient in Insertion Electrode Materials by the Onsager Phenomenological Relation

锂离子嵌入型电极材料中锂离子和电子会在二者电化学位梯度的推动下流动,锂离子的＂嵌入＂和＂脱出＂涉及锂离子和电子在电极材料中的扩散过程。导出了用著名的昂萨格唯象关系估算的等温条件下锂离子表观扩散系数和电子表观电导率的计算通式,并给出在磷酸铁锂（LixFe-PO4）正极中锂离子表观扩散系数D＊1的估算实例。计算结果表明：D＊1随嵌入度x的变化,主要是由于系统内部电场对浓度场的影响所造成的,而与离子流和电子流之间的相互作用关系不大。在x很小、电极材料组成接近FePO4相时D＊1值很大,如在x=0.01处D＊1的计算值为10-12cm^2.s^-1,但随着x的增加D＊1值急剧下降;在x=0.1-1.0之间,D＊1值下降趋缓,约为10-13-10^-14cm2.s^-1,其均值约为8×10-14cm2.s^-1;当x=1.0且电极材料组成为LiFePO4相时,D＊1值最低,约为2×10^-14cm2.s^-1。

Lithium ion flow and electron flow within lithium insertion electrode materials are driven by electrochemical potential gradients of both lithium ion and electron.Lithium ion insertion or extraction process is coupled with the diffusion of lithium ions as well as the diffusion of electrons.According to the Onsager phenomenological relation,general formulae to calculate the apparent diffusion coefficient D＊1 of lithium ion and the apparent conductivity σ＊1 of electron were deduced under isothermal condition.Furthermore,the values of D＊1 for LixFePO4 positive electrode materials were evaluated as examples.The calculation results show that the change of D＊1 with lithium content x is mainly caused by the influence of internal electrical field on the internal concentration field within the electrode material,but slightly related to the interaction between the ion flow and the electron flow.The value of D＊1 is very high at low x close to FePO4 phase,for instance,D＊1 is about 10^-12 cm2·s^-1 at x=0.01.However,D＊1 sharply drops with the increase of x,and then shows a gradual decline from 10-13 cm2·s-1 to 10-14 cm2·s^-1 with a mean value of about 8×10^-14 cm2·s-1 in the range of x=0.1~1.0.As x=1.0 for LiFePO4 phase,D＊1 reaches to the minimum of about 2×10-14 cm2·s-1.