纳米多孔超级电容器充电次数与存储性能的关系
Relation between charging times and storage properties of nanoporous supercapacitors
摘要：
研究纳米多孔电极的动态和静态存储性能之间的相关性有利于基于超级电容器技术的进一步发展。虽然经典的密度泛函理论（c-DFT）很好地描述了电容对孔尺寸的依赖性，但是在文献中已经注意到缺乏能够正确估计充电时间的动态c-DFT扩展。在这里，我们开发了一个基于c-DFT的纳米孔内电解质的动态模型，并真实地描述了随时间变化的充电过程和最大静态电容。我们的计算表明，充电开始与时间的总电荷的平方根依赖性，然后遵循两个随后的指数趋势与显着不同的时间尺度，同意与发表的模拟。我们证明了完全充电时间对应于取决于孔隙大小的第一或第二指数趋势的时间尺度。此外，我们发现解析表达式，以适应广泛的参数的时间尺度。导出的相关性提供了充电时间与孔隙尺寸、施加电压和孔隙内最终离子密度的关系，使得这些表达式对于设计具有功率和能量特性的最佳组合的超级电容器是有用的。
英文摘要：
Investigating the correlations between dynamic and static storage properties of nanoporous electrodes is beneficial for further progress of supercapacitors-based technologies. While the dependence of the capacitance on the pores' sizes is well described by classical Density Functional Theory (c-DFT), the lack of dynamic c-DFT extension capable for correct estimation of the charging time has been noted in the literature. Here, we develop a dynamic model of the electrolyte inside nanopores based on c-DFT and realistically describing both the time-dependent charging process and maximum static capacitance. Our calculations show that the charging starts with a square-root dependency of the total charge on time and then follows two subsequent exponential trends with significantly different time scales that agree with published simulations. We demonstrate that the full charging time corresponds to the timescale of either the first or the second exponential trend depending on the pores' size. Also, we find analytical expressions to fit the timescales for a wide range of parameters. Derived correlations provide the relation of charging time to pores' size, applied voltage, and final ions' densities inside the pore, making these expressions useful to design supercapacitors with an optimal combination of power and energy characteristics.
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