# Boron-Decorated Pillared Graphene as the Basic Element for Supercapacitors: An Ab Initio Study
## 1 Introduction  
Currently, the rapid development of electronics requires energy-intensive, safe, and efficient energy storage sources for portable and stationary applications. Lithium-ion batteries (LIBs) are usually used if high energy density and long-term operations are required. Supercapacitors (SCs) are applied when high power density with a short exposure time should be obtained [1]. The operation principles of these two sources are different: LIBs work on electrochemical Faraday processes, while SCs use an electrostatic charge storage process. Faraday processes are slower than electrostatic processes. This limits the maximum power density of batteries and their discharge/charge currents. SCs have a huge power density due to electrostatic interactions, but the energy density is much lower. Modern lithium batteries have a limited life span of tens of thousands of cycles and require sophisticated tracking systems to safely charge and discharge them [2, 3]. In turn, the lifetime of SCs exceeds one million cycles, the charging method is quite simple and safe, and full discharge does not lead to degradation of the electrodes [4, 5, 6]. Thus, in terms of lifetime and ease of use, SCs have obvious advantages over batteries, but low-energy density is still the main limiting factor to their widespread application. The energy of a SC is contained in its capacitance of the double electric layer, which is formed at the media boundary and depends on the effective area of the electrodes [7]. In addition to the double-layer capacitance, there is also a quantum capacitance that directly affects the total electrode capacitance:  
\[\frac{1}{C_{Total}}=\frac{1}{C_{D}}+\frac{1}{C_{Q}} \tag{1}\]  
Quantum capacitance, first investigated in [8], is directly related to the density of states (DOS), so for materials with a low DOS near the Fermi level, the quantum capacitance will also be a low value. For metal electrodes (for example, electrodes of a classical dielectric capacitor) in which the DOS is high, the quantum capacitance will also be high. Here, the quantum capacitance \(C_{Q}\) and the double-layer capacitance \(C_{D}\) contribute to the total capacitance \(C_{Total}\), according to the law of addition of capacitors connected inseries. From the expression above, it can be concluded that for increasing the efficiency of SCs, it is necessary to simultaneously increase both \(C_{Q}\) and \(C_{D}\). SCs are divided into two types of devices: EDLC and hybrid. In EDLC, both electrodes have the same structure and electrostatic mechanism of charge accumulation. In hybrid ones, electrostatic charge accumulation occurs on one of the electrodes, and the Faraday process occurs on the other [9]. Hereinafter, according to the SC, we denote the EDLC. To increase \(C_{D}\), the electrode material must have a sufficiently large effective area. Carbon materials, for example, widely used activated carbon, are suitable for this role [10, 11, 12]. Due to the developed surface, the electrolyte penetrates into the pores of the activated carbon and thereby creates a double-layer capacitance. The disadvantages of the activated carbon electrode are its low mechanical strength and electrical conductivity due to the amorphous structure and the gaps between the layers [13]. In addition, researchers [14, 15] revealed a pattern of reduction in the total capacitance of carbon materials due to the low value of \(C_{Q}\). It is possible to increase the \(C_{Q}\) value of carbon materials by adsorption of various compounds on their surfaces, as shown in theoretical [16, 17, 18, 19] and experimental works [20, 21]. Boron compounds are actively used for modification of such carbon structures as single-walled carbon nanotubes (SWCNTs) and graphene. The total capacitance of the synthesized SC in this case ranges from 32.2 F to 1544 F/g [22, 23, 24, 25].