[Original] The effect of graphene interplanar spacing and carbon nanotube diameter on the capacitance of electric double layer capacitors

Abstract: As a new type of energy storage device, electric double-layer capacitors have great potential in the fields of equipment energy storage, electric vehicles and power grids due to their advantages of high power density, long service life, clean and environmental protection. Nevertheless, its low energy density has hindered its application. The energy density can be increased by increasing its capacitance. Therefore, molecular dynamics simulation (MD) is used to study the influence of graphene interplanar spacing (slit aperture) and carbon nanotube diameter (circular hole diameter) on area specific capacitance. This indirectly reflects the influence of graphene interplanar spacing and carbon nanotube diameter on energy density. By analyzing the distribution law of K+ and H2O, it is found that in the slit hole, when K+ is distributed in a single layer (the interplanar spacing is less than 0.5 nm), the capacitance increases as the interplanar spacing decreases; K+ is distributed in two layers (interplanar spacing). In the case of 0.5～0.803 nm), the opposite is true; while in a circular hole, the capacitance varies with the diameter oscillating, and due to the curvature, its area is much larger than that of a slit hole.

Keywords: supercapacitor; graphene; carbon nanotube; interplanar distance; diameter
Electric double-layer capacitors belong to a category of supercapacitors and have broad application prospects in wind power generation, electric vehicles, renewable energy and other fields. But its energy density is very low (usually not more than 20 W·h/kg, and the energy density of lithium batteries currently used in electric vehicles is about 100 to 150 W·h/kg), which greatly limits its application. In order to break this limitation and enable it to be better used in fields such as portable electronic products and new energy vehicles, it is necessary to increase its energy density. According to the energy density formula E=CV2/2 of the electric double layer capacitor, it can be seen that the energy density can be increased by increasing the capacitance.
The capacitance of a capacitor is related to the electrode material, electrode spacing, shape, and electrolyte. Chmiola et al. studied the abnormal increase in capacitance when the electrolyte is an organic solution and the slit aperture is reduced from 1 nm to 0.6 nm, breaking the view that solvated ions larger than the electrode aperture cannot contribute to capacitance. Huang et al. [5] studied the capacitance of round holes in the size of mesopores and micropores, and proposed an EDCC/EWCC model to explain the variation of capacitance with size. Feng et al. studied the relationship between the capacitance of the room temperature ionic liquid slit-hole supercapacitor and the interplanar spacing, and found that the capacitance changes when the spacing is 0.67～1.8 nm, and the abnormal increase of capacitance occurs in the interval of 0.7～1 nm. Qiu et al. studied the ionic structure and capacitance of negatively charged graphene nanochannels in NaCl aqueous solution, and concluded that when the nanopores can only accommodate ions of the opposite electrical property to the wall, the nanopores will reach the maximum capacitance and energy density. . Nicolas et al. considered the complexity of pore size dispersion and the complexity of two different solvents, and established a model to understand the capacitance of microporous carbon materials. They also observed that the surface normalized capacitance decreases with the spacing when most pores are less than 1 nm. Small but increasing result. Feng et al. studied the capacitance change of the slit holes with an interplanar spacing of 0.936～1.47 nm, and studied the distribution of K+ and H2O in the electrolyte, and explained the change of capacitance with the pore size from the perspective of configuration, and based on this The classic slit hole capacitance formula is modified to Cs=εrε0A/deff, which quantitatively explains the change of capacitance with the aperture, but this work still has certain deficiencies. First of all, according to the classic electric double layer (EDL) theory, the capacitance should decrease with the decrease of the interplanar spacing. The research of Feng et al. showed that when the aperture width is 0.936 ~ 1.47 nm, the capacitance increases abnormally, so it is smaller. Whether there will be new changes in the size has not been studied. Secondly, when the size is 0.936～1.47 nm, the experimental data points do not completely fall on the curve fitted by the formula (R2=0.926), and when the slit hole is replaced with a round hole (EWCC model), the fitted R2 is 0.921 , Which shows that the curvature should be considered in the quantitative calculation of capacitance.
In order to determine the change rule of Cs and the influence of curvature on the capacitance under small size, this paper uses the probe averaging method (PA) to study the relationship between the capacitance and spacing of the plate and the hole under the smaller size, and uses MD to study the capacitor The configuration of K+ and H2O is used to explore the microscopic mechanism of capacitance change. In order to ensure the control variables, all factors other than the size are the same as Feng et al., that is, graphene plates, K+ and H2O are selected as the simulants, while taking into account the radius of K+ (0.138 nm), there is a minimum distance between the surfaces. Select the surface spacing to be 0.4～1.203 nm. In addition, it is ensured that the diameter of the circular hole corresponds to the surface spacing of the slit hole to be equal, and while the capacitance of the circular hole changes with the diameter, the two are compared to finally obtain the effect of curvature.
1 Simulation method
First, establish two graphene planes with a charge of -0.55 C/m2, adjust the distance between the two planes to 0.936 nm, and define the interplanar distance as the distance between the center planes of the two graphene layers. Secondly, 8 and 210 K+ and H2O were filled between the two plates. Under different surface spacing, the H2O concentration was kept constant and the system remained electrically neutral, as shown in Figure 1. Under the canonical ensemble (NVT), a 1.3 ns equilibrium dynamics simulation was carried out with a time step of 1 fs. The Nose-Hoover thermostat is used to control the temperature to 300 K, the force field parameters of sp2 type carbon are used for carbon atoms, and the force field parameters of Lee etc. are used for H2O and K+. To ensure accuracy, the last 300 ps data of equilibrium kinetics was taken for research, and the data was recorded every 10 ps for result analysis. The round hole model is shown in Figure 2.