Perturbation solutions for the nonlinear Poisson–Boltzmann equation with a high-order-accuracy Debye–Hückel approximation
Perturbation solutions for the nonlinear Poisson–Boltzmann equation with a high-order-accuracy Debye–Hückel approximation
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DOI：
10.1007/s00033-020-01367-9
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发表时间：
2020-08
期刊：
影响因子：
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通讯作者：
Cunlu Zhao;Qiuwan Wang;M. Zeng
中科院分区：
文献类型：
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作者：
Cunlu Zhao;Qiuwan Wang;M. Zeng
泊松-玻尔兹曼（P-B）方程对于理解存在于许多领域的固液电解质界面具有重要意义。由于P-B方程的非线性，通常很难求出精确的显式解。本文报道了非线性P-B方程在直角坐标系和球坐标系下的几个摄动解。新的解包含一个来自双曲正弦函数的高阶精度近似的扰动参数，因此可以适用于高zeta势条件。将微扰解与传统的debye - h<s:1> ckel解和全数值解进行比较，验证了微扰解的鲁棒性和准确性。微扰解是显式的和解析的，可用于快速计算EDL势和相互作用能。
The Poisson–Boltzmann (P–B) equation is of fundamental importance in understanding solid–liquid electrolyte interfaces that are present in many fields. Due to the nonlinearity, it is usually challenging to find the explicit exact solutions of the P–B equation. The present work reports several perturbation solutions for the nonlinear P–B equation in the Cartesian and spherical coordinates. The new solutions contain a perturbation parameter from the high-order-accuracy approximation of the hyperbolic sine function and thus can apply to high zeta potential conditions. The comparison of the perturbation solutions with the traditional Debye–Hückel solutions and the full numerical solutions validates the robustness and accuracy of the perturbation solutions. The perturbation solutions are explicit and analytical and then can be used for a fast calculation of the EDL potential and interaction energy in versatile applications.