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”是指离子与溶剂分子之间的分子级界面。最近，我们提出了一种新的关于离子在油/水界面上的Gibbs转移能的非玻尔理论，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。这种依赖关系非常类似于汞电极表面张力的电势依赖关系(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，汞电极作为宏观界面的表面能也将由电极表面场(E)的二次函数表示，二阶系数将与经验溶剂参数相关，如施主数目(D_N)、受主数目(A_N)等。为了验证这一工作假设，用交流电流法测量了汞电极在不同溶剂中的微分电容。阻抗法。根据电容数据，经扩散双电层贡献修正后的电极界面能(γ_1)为E的函数。对于每种溶剂，γ_1均可由E在正负电势范围内的二次函数给出。然后评估了E&gt；0和E&lt；0的二阶系数a_和a_-。在所考察的10种溶剂中，a_和a_-值与溶剂的任何性质都没有显示出很好的相关性。在排除甲酰胺和N-甲基甲酰胺两种溶剂时，a_n和a_-值与D_N(r=0.821)和A_N(r=0.910)等经验溶剂参数有很好的相关性，从而支持了工作假说。

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.