Abstract The voltammetric response of one-step reversible electrochemical reactions (involving dissolved redox species) to a linear potential ramp can be modelled using the calculation method proposed in our previous work (J. Electroanal. Chem. 818 (2018) 84) provided that the mass transfer function for the species involved in the electrochemical reaction is known in closed form under one-dimensional mass transport conditions. The above approach applies in this short communication to the direct insertion reaction in thin-film planar materials under both anomalous and spatially restricted (confined) diffusion conditions. The Faradaic current is obtained first as an alternating infinite series well suited to formal analysis, and then as an integral formulation well suited to numerical computation. Finally, closed-form expressions of the voltammograms are derived at very low or very high values of the potential sweep rate, respectively. Two anomalous diffusion models taken from the electrochemical literature are investigated and compared, based on their voltammetric responses. The voltammetric peak coordinates obtained from the best model are thoroughly examined, and closed-form approximations are proposed for the voltammetric peak current and potential at very low or very high potential sweep rates. A zone diagram is plotted to illustrate the conditions for observation of those limiting situations. Finally, following a referee's request, an alternative modelling approach is proposed in Appendix, which does not require the use of scientific computation software. This approach involves both the Integral Equation method formalism and numerical inversion of Laplace transform.

中文翻译：

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从异常扩散阻抗到有限扩散条件下薄膜插入材料伏安响应的封闭形式、无限级数和积分公式。基于异常传质函数的建模贡献

摘要 一步可逆电化学反应（涉及溶解的氧化还原物质）对线性电位斜坡的伏安响应可以使用我们之前工作（J. Electroanal. Chem. 818 (2018) 84）中提出的计算方法进行建模，前提是参与电化学反应的物质的传质函数在一维传质条件下以封闭形式已知。上述方法适用于在异常和空间受限（受限）扩散条件下薄膜平面材料中的直接插入反应。法拉第电流首先作为非常适合形式分析的交替无限级数获得，然后作为非常适合数值计算的积分公式获得。最后，伏安图的闭式表达式分别在非常低或非常高的潜在扫描速率值下导出。基于它们的伏安响应，研究和比较了取自电化学文献的两个异常扩散模型。彻底检查从最佳模型获得的伏安峰值坐标，并针对非常低或非常高的电位扫描速率下的伏安峰值电流和电位提出了封闭形式的近似值。绘制区域图以说明观察这些限制情况的条件。最后，应裁判的要求，附录中提出了一种替代建模方法，该方法不需要使用科学计算软件。