Figure 1 . (a) Schematic diagram of microporous TiC-CDC electrode with specific PSD obtained from ref. 12 . (b) Illustration of ion desolvation caused by geometrical confinement of nanoslit. (c) A representative nanoslit in the positively charged electrode.
Figure 1 (b) displays the schematic graph of ion desolvation in confined liquid, in which the anion is encircled by solvent molecules due to the static electronic attraction. Here, acetonitrile (MeCN) solvent is considered in order to perform a faithful comparison with experiments. MeCN is a typical linear polar fluid and it can be modeled as a linear molecule containing three parts42 : the methyl group (blue sphere), the carbon group (grey sphere), and the nitrogen group (yellow sphere). The solvent structure of MeCN surrounding the solute ion is described by the local density distribution of MeCN molecules, , which depends on both the spatial position, , and the Euler angle, , of MeCN molecule in space.
The spatial orientation of a MeCN molecule can be alternatively characterized by the included angle between the linear MeCN molecule and the vector connecting the solute ion to the carbon group of MeCN, designated as . In this work, the cosine value of , i.e .,, is employed to describe the spatial orientation of MeCN, which can be converted from the Euler angle through a rotation matrix operation.43In nanopores, the interfacial interaction and the geometrical confinement effect may destroy the solvation structure of ion, leading to the rearrangement of local density distribution of MeCN, and this feature becomes more pronounced as the pore size decreases down to several molecule sizes, resulting in a significant decrease of the MeCN number within the first solvation shell. When further decreasing the pore size, the solvation diameter of ion will decrease until the occurrence of a bare ion.
Since not all solvent molecules within the first solvation shell contribute to the solvation diameter of ions,44-45the spatial orientation distribution of MeCN can be additionally introduced to distinguish the contributing molecules. This idea has been applied to evaluate the ion hydration size in confined liquid water by using the MDFT, in which of the contributing water molecules in the first solvation shell was determined as [-1.0, -0.44] for cation and [0.48, 1.0] for anion.36 In this work, we adopt the same concept to calculate the solvation diameter of ions in confined MeCN:
, (1)