The electrical double layer capacitor (EDLC), which is also frequently called super-capacitor or ultra-capacitor, is a potential electrochemical device for energy storage.^[1] Because there occurs no redox reaction at the interface between the electrode and the electrolyte, the electric charge or discharge processes are entirely controlled by the Coulomb electrostatic force, and thus the EDLC shows quite a high energy density. The most important technological development for EDLC is to improve not only its power density but also its lifecycle and safety. The operational temperature, potential range and conductivity are important factors of electrolyte for further developing the EDLC. In general, the electrolytes including those based on water, ionic liquids (ILs) as well as organic salt solvents are potentially good candidates for EDLCs.^[2] Although a water-based electrolyte can supply a large energy density, its operation voltage has never exceeded a value of 2.0 V.^[3–5] A high-operative voltage is probably realized for the EDLC by using organic solvents. Nowadays, the EDLC is generally based on the electrolyte which is quaternary ammonium salts dissolved in organic solvent such as liquid acetonitrile (ACN) or liquid propylene carbonate (PC).^[6] Although a higher operative voltage can be achieved using IL instead of organic solvent, the shortcomings of IL such as high viscosity and low conductivity should be overcome to improve the performance of IL-based EDLC under normal conditions.^[7] Besides, the relatively high price of IL is another issue to prevent the IL-based EDLCs from being commercialized.^[8] The above statement shows that each kind of electrolyte has its own advantages and disadvantages. Many efforts should be made to develop novel electrolytes for high-performance EDLCs in the near future.^[9] Electrochemical and physicochemical properties of novel organic salt solutions or new ILs should be explored by either experiments or simulations.

Porous carbons with various pore volumes were often employed for the EDLC electrodes. In 2006, Chimola et al.^[10] found that the capacitance of the EDLC increases abnormally when the pore size is smaller than 10 Å. Dissolution of ion in small pores might be the main reason for the anomalous enhancement of capacitance as well as energy density. The experimental work has motivated many molecular dynamics (MD) simulation investigations on the EDLCs at molecular level.^[11–14] Most of the electrolytes used in simulations are ionic liquids except for those used by Yang et al.^[11] and Feng et al.,^[12] in which tetraethylammonium tetrafluoroborate(TEA-BF₄) salts with organic solvents were employed as electrolytes. To the best of our knowledge, other quaternary ammonium salts have not been investigated using molecular simulations. One of the difficulties for quaternary ammonium simulation is a lack of parameters for force fields. However, developing new organic salts is an important step for the realization of EDLC and the molecular simulation technology can play an important role in understanding the mechanism of EDLC and also in designing the EDLC at molecular level. Therefore, it is necessary to develop and refine the force field for quaternary ammonium salts.

Recently, much attention has been paid to a new organic salt, the spiro-(1, 1)-bipyrrolidinium tetrafluoroborate (abbreviated as [SBP][BF₄]), due to its good electrochemical properties such as small ion size, high solubility and high conductivity.^[15,16] Perricone et al.^[17] obtained a methoxypropionitrile(MP)/ethylene carbonate(EC) mixture-based electrolyte of 1 M [SBP][BF₄]. The electrolyte presents high capacitor performance. Zheng et al.^[18] prepared an anode of EDLC with non-porous carbon microbeads and found that the SBP cations may enlarge the storage of capability of the negative electrode. Yu et al.^[19] and Shi et al.^[20] synthesized [SBP][BF₄] salt and measured the electrochemical performances of [SBP][BF₄] with several organic solvents. The capacitances of the binary solvent electrolyte system could reach about 117.3 F/g at 293 K and 92.3 F/g at 323 K, respectively. The EDLC based on binary solvent system has an energy of 29.6 Wh/kg and a power density of 12.5 kW/ kg. In order to investigate the EDLC behaviors of [SBP][BF₄] organic salt electrolyte, we develop a force field for [SBP][BF₄] based on the framework of AMBER force field and density functional calculation. Then the force field is employed in MD simulations to predict the physicochemical properties of a mixture of [SBP][BF₄] and ACN. The aim of this paper is to testify to the force field of [SBP][BF₄]. In general, the simulation technique can explore the microstructure properties and dynamic properties of EDLC. An accurate force field is a prerequisite for predicting the right properties of EDLC, including electrolyte density distribution, charge distributions, orientations of ions, ionic mobilities, etc. Once the force field reproduces the right physicochemical properties of bulk electrolyte, it can be used for EDLC simulations in the future. For this purpose, we compare the simulated results with existing experimental results. Moreover the detailed microstructures of the [SBP][BF₄] and ACN mixtures are explored by molecular dynamics, which are very important for developing high-efficiency EDLCs at molecular levels.

In a classical molecular simulation, the accurate prediction of physicochemical properties requires a reliable and stable force field. In the present study, a twenty-five-site model for [SBP]⁺ is adopted, and the structure of [SBP][BF₄] was calculated by density functional of Perdew, Burke and Ernzerhof^[21] implemented in Dmol³ package.^[22,23] We chose the double numerical basis set with a polarization function (DNP). It was validated that the DNP basis set is comparable to 6–31 G** basis set of Gaussian basis set and Slater type orbitals, but more numerically efficient.^[24,25] The geometric structure and charge distribution were calculated. Several configurations of pair ions were calculated, and the results were the same. The optimized geometries are demonstrated in Fig. 1 and the atomic charges determined by the Mulliken analysis^[26,27] are given in Table 1.

The AMBER force field^[28] has been successfully utilized to predict the thermodynamic properties of protein and DNA solutions^[29] as well as organic compounds and ILs.^[30] In this study, the AMBER force field was selected. In the AMBER force field, the potential energy E of a system can be expressed as

The force field parameters of [SBP][BF₄] were mainly taken from the AMBER and Andrade et al.^[31] The model of ACN was completely cited from Ref. [32] by Wu et al. The charges and LJ parameters of the force field are given in Table 1, in addition, the optimized bond lengths, angles, as well as dihedrals, are also listed in Table 1.

Fig. 1.

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	Fig. 1. Equilibrium geometries of simulated [SBP][BF4] and ACN molecules.

Table 1.

Table 1.

Table 1. Charges and force fields for [SPB][BF4] and ACN molecules. . Molecule Atom Chargea/e Source SBP C −0.220 3.3997 0.4577 this workaAMBERb C −0.056 3.3997 0.4577 this worka AMBERb N −0.378 3.2500 0.7113 this worka AMBERb H 0.140 2.4714 0.0657 this worka AMBERb H 0.165 2.4714 0.0657 this worka AMBERb BF4 B 0.766 3.5814 0.3975 this worka AMBERb F −0.431 3.1181 0.2552 this worka AMBERb ACN N −0.532 3.2500 0.7113 this worka AMBERb C1 0.480 3.3997 0.3598 this worka AMBERb C2 −0.479 3.3997 0.4577 this worka AMBERb H 0.177 2.4714 0.0657 this worka AMBERb Bond Source SBP C–C 1.55 1297.04 this worka AMBERb N–C 1.47 1410.01 this worka AMBERb C–H 1.07 1610.80 this worka AMBERb BF4 B–F 1.39 1213.36 Ref. [31] ACN N–C 1.15 2510.40 Ref. [32] C–C 1.46 1673.60 Ref. [32] C–H 1.09 1422.60 Ref. [32] Angle Source SBP N–C1,4,5,8 – C2,3,6,7 104.71 209.20 this worka AMBERb C4,5–N–C1,8 105.29 209.20 this worka AMBERb C1,2,5,6–C2,3,6,7–C3,4,7,8 103.05 292.60 this worka AMBERb C1,4–N–C5,8 111.04 292.60 this worka AMBERb N–C1,4,5,8–H 109.50 230.00 this worka AMBERb C–C–H 109.50 155.00 this worka AMBERb H–C–H 109.50 146.00 this worka AMBERb BF4 F–B–F 109.50 209.20 this worka AMBERb ACN C2–C1–N 180.00 334.72 Ref. [32] C1–C2–H 109.50 146.44 Ref. [32] H–C2–H 109.50 127.61 this worka AMBERb Dihedral Vn/kJ·mol−1 na γ / a Source SBP C1,5–C2,6–C3,7–C4,8 0.67 3 180.0 AMBER C2,6–C3,7–C4,8–N 0.00 1 180.0 AMBER C2,3–C1,4–N–C4,1 0.84 2 180.0 AMBER C3,7–C4,8–N–C5,1 0.00 1 180.0 AMBER H–X–X–H 0.00 2 0.0 AMBER ACN N–C1–C2–H 0.00 1 0.0 Ref. [32] a from this work b from the AMBER force field.

Table 1. Charges and force fields for [SPB][BF4] and ACN molecules. .

All-atoms molecular dynamic (MD) simulations in this work were carried out with the MD simulator LAMMPS.^[33] MD simulations were first carried out at a constant temperature of 298 K and a pressure of 0.1 MPa. After equilibrium, the constant temperature and constant volume dynamics simulations were performed 10 ns for ensemble average. The Nose–Hoover thermostat was employed to control the temperature of simulating system.^[34,35] The initial configurations are generated by a Monte–Carlo algorithm and ions can distribute evenly in electrolyte solution. The time-step was taken to be 1.0 fs. The ordinary three-dimensional periodic boundary conditions were used. The cutoff distance of simulated system was taken to be 15 Å. The particle–particle particle mesh (PPPM) algorithm was employed for the long-range Coulomb force calculations and the grid distance of fast Fourier transform (FFT) was 1.9 Å. The configurations of the system were saved every 100 time-steps in the simulations for further analyses. The concentrations of solution range from x_salt = 0.05 (0.9 M) to x_salt = 0.142 (2.2 M). The interval covers the working concentration range of organic salt electrolytes for realizing the EDLCs.^[10,14,20] The details of the simulated systems and main simulated results of mixtures are shown in Table 2. The equilibrium configurations of the simulation box are displayed in Fig. 2.^[36]

Fig. 2.

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Fig. 2. Equilibrium results (the ACN and H atoms of SBP are ignored for clarity.) at xsalt = 0.051 (a), 0.090 (b), 0.101 (c), 0.119 (d), 0.130 (e), and 0.142 (f), with the colours of blue, cyan, green and white representing the atoms of N, C, B, and F*, respectively. For black–white graph, black, dark gray (big ball), light gray (small ball), and white represent the atoms of of N, C, B, and F, respectively.

Table 2.

Table 2.

Table 2. Simulation results of [SBP][BF4] + ACN mixtures in this work. . System Particle number Mole fraction Self-diffusion coefficient/10−11 m2·s−1 ρ/g· cm−3 η/mPa·s κ/S·m−1 [SBP][BF4] ACN xsalt D+ D− D2 D 0 0 1331 0.000 – – 399.4 399.4 0.781 0.52 – 1 144 2662 0.051 131.3 132.9 272.3 275.9 0.886 0.75 7.68 2 264 2662 0.090 88.7 88.1 191.4 182.1 0.975 1.14 8.60 3 150 1331 0.101 76.9 78.5 165.5 156.6 1.001 1.32 8.51 4 180 1331 0.119 59.4 58.2 117.5 110.4 1.022 1.67 7.45 5 200 1331 0.130 52.13 54.31 111.7 104.1 1.036 1.95 6.85 6 220 1331 0.142 44.0 45.6 104 96.6 1.047 2.14 6.28

Table 2. Simulation results of [SBP][BF4] + ACN mixtures in this work. .

In the table, D₊, D₋, D₂, D are the diffusion coefficients of cations, anions, ACN molecules and the solutions.

Table 3.

Table 3.

Table 3. Experimental results of [SBP][BF4] + ACN mixtures in this work. . Experiment Mole fraction xsalt ρ/g·cm−3 η/mPa·s κ/S·m−1 0 0.777 – – 1 0.051 0.886 0.734 5.65 2 0.091 0.986 1.191 6.82 3 0.119 1.016 1.67 6.87 4 0.127 1.037 1.79 6.91 5 0.141 1.048 2.11 6.56

Table 3. Experimental results of [SBP][BF4] + ACN mixtures in this work. .

The development of electrical double layer capacitors requires an in depth understanding of the interactions between the molecules. Molecular simulations provide a powerful tool at molecular level to meet this requirement for EDLC development. In this work, a force field for an organic salt solution is developed and the MD simulations are performed to predict the densities, self-diffusion coefficients, viscosities, and conductivities of [SBP][BF₄] + ACN binary solution under different conditions. The MD simulations reproduce the densities for the binary mixture of [SBP][BF₄] + ACN very well. Based on the self-diffusion coefficients sampled from the trajectories of simulated systems, the viscosities of the mixtures are predicted by the Stokes–Einstein equation, which match the experimental results well. Through RDF analysis, the interactions of cation–solvent and solvent–solvent become stronger with the increase of concentration. In addition, as the mole fraction x_salt is increased, the change tendency of conductivity of mixtures is in agreement with that from the experiment.

In summary, based on the framework of AMBER and quantum mechanics calculations, the force field is developed in the present study and has been successfully applied to the binary mixtures of [SBP][BF₄] and ACN. The predicted properties agree well with the corresponding experimental data. The EDLCs have higher power density than rechargeable batteries in that the electrical charge is stored in the electrical double layer formed at the electrode/electrolyte interface, which could rapidly adsorb–desorb without faradic reactions. So, the electrolytes used in EDLCs demand high electrical conductivity and low viscosity to enable the high mobilities of the electrolyte ions between the two electrodes. In other words, the electrolytes with low electrical conductivity and high viscosity supply low mobility and high electrolyte solution resistance, which is improperly used in high-power performance application. For realizing the EDLCs, new electrolytes, which have high conductivities and low viscosities, should be developed and tested. To choose and testify the electrolytes requires a large amount of experimental work. With the help of molecular dynamics simulation, based on the force field developing method presented here, it is easy to predict the viscosities and conductivities of a novel electrolyte under different conditions. Simulations will reduce the experimental jobs and save time in developing electrolytes. In conclusion, this work provides a good way to understand and estimate the macroscopic properties of the organic salt solutions that have promise to be used in the electrical double layer capacitors.