Abstract Semi-analytical modelling of transient experiments at cylindrical wire or fiber electrodes is hindered by the unavailability of numerical procedures for calculating special functions arising in the models. A theory is developed, of the chronoamperometric Faradaic current for a reversible charge transfer reaction at a cylindrical electrode. Arbitrary potential steps and unequal diffusion coefficients (δ = DO/DR ≠ 1) are assumed. Two procedures (written in C++) are designed, for computing a special function occurring in the theory. One procedure is computationally inexpensive, but has a low accuracy (relative error moduli close to 2% in the worst case, when −0.5 ≤ log (δ) ≤ 0.5). The second is more expensive, but highly accurate (relative error moduli close to 4 × 10−14 in the worst case, when −3 ≤ log (δ) ≤ 3). Numerical experiments demonstrate that the effect of δ ≠ 1 on the current is not negligible, even for δ not much different from unity. Therefore, the theory presented should be taken into account in experimental investigations. The code for the procedures is freely available.

中文翻译：

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圆柱线电极可逆电荷转移的计时电流法：DO ≠ DR 的理论，以及电流的高精度计算

摘要 圆柱线电极或纤维电极瞬态实验的半解析建模由于无法计算模型中出现的特殊函数的数值程序而受到阻碍。提出了一种关于在圆柱形电极上进行可逆电荷转移反应的计时电流法法拉第电流的理论。假定任意电位阶跃和不等扩散系数 (δ = DO/DR ≠ 1)。设计了两个程序（用 C++ 编写），用于计算理论中出现的特殊函数。一种程序计算成本低，但精度低（在最坏情况下，当 -0.5 ≤ log (δ) ≤ 0.5 时，相对误差模数接近 2%）。第二种更昂贵，但精度很高（在最坏的情况下，当 -3 ≤ log (δ) ≤ 3 时，相对误差模数接近 4 × 10−14）。数值实验表明，δ≠1对电流的影响是不可忽略的，即使对于δ与unity相差不大。因此，在实验研究中应考虑所提出的理论。程序的代码是免费提供的。