Electrostatic interactions make a large contribution to solvation free energy in ionic fluids such as electrolytes and colloidal dispersions. The electrostatic contribution to solvation free energy has been ascribed to the self-energy of a charged particle. Here we apply a variational field theory based on lower bound inequality to the inhomogeneous fluids of one-component charged hard-spheres, thereby verifying that the self-energy is given by the difference between the total correlation function and direct correlation function. Based on the knowledge of the liquid state theory, the self-energy specified in this study not only relates a direct correlation function to the Gaussian smearing of each charged sphere, but also provides the electrostatic contribution to solvation free energy that shows good agreement with simulation results. Furthermore, the Ornstein-Zernike equation leads to a set of generalized Debye-Hückel equations reflecting the Gaussian distributed charges.

中文翻译：

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静电对胶体溶剂化的贡献（自能量修饰的玻耳兹曼分布）。

静电相互作用对离子液体（例如电解质和胶体分散体）中的溶剂化自由能做出了很大贡献。静电对溶剂化自由能的贡献已归因于带电粒子的自能。在这里，我们将基于下界不等式的变分场理论应用于单组分带电硬球的非均匀流体，从而验证了总相关函数与直接相关函数之间的差给出了自能量。基于液态理论的知识，本研究中指定的自能不仅将直接相关函数与每个带电球体的高斯拖尾相关，而且还提供了对溶剂化自由能的静电作用，与模拟结果显示出良好的一致性结果。此外，