Theoretical Similarity of Macro- and Nano-Interfaces

标题中的“宏观界面”是指普通电极|溶液或油|水界面，而“纳米界面”是指离子和溶剂分子之间的分子级界面。最近，我们提出了一种新的离子在油桶-水界面上的吉布斯转移能的非玻氏理论，其中离子-溶剂相互作用能由离子表面场强度的二次函数给出。这种依赖性非常类似于汞电极表面张力的电位依赖性（即，电毛细管曲线）。然后，我们建立了一个工作假设-如果宏观界面和纳米界面的界面能本质上相同，那么作为宏观界面的汞电极的表面能也将用电极表面场(E)的二次函数表示，并且二阶系数将与经验溶剂参数（如供体数（D_N），受体数（A_N）等）相关。为了验证这一工作假设，用交流阻抗法测定了汞电极在不同溶剂中的差分容量。利用容量数据，修正了扩散双层的贡献，确定了电极的界面能（γ_1）是E的函数。对于每种溶剂，γ_1都可以由E的二次函数给出，在正或负电位范围内。然后，在E < 0和E < 0时，求二阶系数a_+和a_-。在所有10种溶剂中，a_+和a_-的值与溶剂的任何性质都没有很好的相关性。然而，当排除甲酰胺和n -甲基甲酰胺两种溶剂时，a_+和a_-值与经验溶剂参数D_N （r = 0.821）和A_N （r = 0.910）具有良好的相关性，从而支持工作假设。

The "macro-interface" in the title means common electrode | solution or oil | water interfaces, whereas the "nano-interface" means molecular-level interfaces between an ion and solvent molecules. Recently, we proposed a new, non-Bornian theory of the Gibbs transfer energy of ions across the oil | water interface, in which the ion-solvent interaction energy was given by a quadratic function of the surface field strength of an ion. This dependence is very similar to the potential dependence of surface tension of a mercury electrode (I.e. , electrocapillary curves). We then established a working hypothesis―If interfacial energies of macro- and nano-interfaces are intrinsically the same, the surface energy of a mercury electrode as a macro-interface will also be expressed by a quadratic function of the surface field (E) of the electrode, and the second-order coefficient will correlate with empirical solvent parameters such as donor number (D_N), acceptor number (A_N) , etc.In order to verify this working hypothesis, the differential capacities of a mercury electrode in various solvents were measured by means of an a.c. impedance method. By using the capacity data, the interfacial energy (γ_1) of the electrode, being corrected for the contribution from the diffuse double layer, was determined as a function of E. For every solvent, γ_1 could be given by a quadratic function of E in either positive or negative potential range. The second-order coefficients, a_+ and a_-, were then evaluated for E > 0 and E < 0. Regarding all ten solvents examined, the values of a_+ and a_- did not show good correlation with any properties of the solvents. However, when excluding two solvents, formamide and N-methylformamide, the a_+ and a_- values showed good correlation with empirical solvent parameters such as D_N (r = 0.821) and A_N (r = 0.910), thus supporting the working hypothesis.