Polyaniline Hybrid Nanofibers via Green Interfacial Polymerization for All-Solid-State Symmetric Supercapacitors.

In this study, we report an enormously simple green approach for the synthesis of polyaniline hybrid (PANI-SO) nanofibers in emeraldine salt form. We have carried out the synthesis via an interfacial polymerization method using vegetable oil as an organic phase instead of the commonly used solvents like CHCl3, CCl4, etc. Characterization techniques such as Fourier transform infrared (FTIR), UV-visible, powder X-ray diffraction (PXRD), scanning electron microscopy (SEM), thermogravimetric analysis (TGA), and differential scanning calorimetry (DSC) have been used for studying the synthesized polyaniline hybrid nanofibers. An interesting observation is the crystallization of small organic molecules in the PANI matrix. PANI-SO shows a pseudocapacitance behavior with a capacitance value of 302 F g-1 at a current density of 1 A g-1. In addition, the material shows an energy density of 26.8 W h kg-1 and a maximum power density of 402.6 W kg-1. Furthermore, the PANI-SO electrode maintains about 84% of the initial capacitance after 1000 cycles. Similarly, the PANI-SO symmetric solid-state supercapacitor shows an areal capacitance of 118.7 mF cm-2 and retains a stability of 80% even after 1000 cycles. Thus, the PANI-SO electrode shows a good cyclic performance, which implies the structural stability of PANI-SO nanofibers. The electrochemical properties of PANI-SO are compared with those of PANI nanofibers synthesized by taking CHCl3 as the organic phase and keeping all other parameters identical. PANI-SO is observed to be a superior material compared to the latter one. All electrochemical analyses show that the PANI synthesized using cooking soyabean oil (PANI-SO) is an effective supercapacitor material.

Introduction

The worldwide demand for energy is accelerating at an alarming rate due to the increase in population. It is estimated that the world will need to double its energy supply by 2050.[1] The modern society cannot even imagine a day without portable electronic devices, like mobile phones, laptops, smartwatches, electric vehicles, etc., which require a high power in a short time.[2,3] Hence, the storage of energy is essential that can be used at a later time. Renewable energy and development of energy storage devices are of primary interest to many research groups all over the world. In terms of energy storage devices, there are two main electrochemical systems, namely, batteries and electrochemical capacitors (ECs).[4−7] Differing from conventional capacitors, supercapacitors are energy storage devices of greater interest due to the fact that they exhibit extremely high power density, reasonable energy density, and fairly long cycle life.[8−10] On the basis of the energy storage mechanism, supercapacitors can be classified into two categories.[11−13] One is the electrical double-layer capacitor (EDLC), where the capacitance comes from the pure electrostatic charge accumulated at the electrode/electrolyte interface. Therefore, EDLC is strongly dependent on the surface area of the electrode materials that is accessible to the electrolyte ions.[14−16] The other category is the pseudocapacitor, in which fast and reversible faradic processes take place due to electroactive species.[17−20] These two mechanisms can function simultaneously depending on the nature of the electrode materials. Recently, many advanced materials such as metal–organic frameworks (MOFs) and hybrid two-dimensional (2D) materials were used as electrode materials in electrochemical capacitors.[21−23]

Conducting polymers have attracted great interest as they show pseudocapacitive nature.[24−27] Polyaniline (PANI) is one of the most widely studied conducting polymers as it can be easily synthesized from aniline.[28−30] The low-cost PANI shows good electronic properties due to protonation, very high specific capacitance due to redox reactions, and good thermal stability.[31,32] Several synthetic methods for the synthesis of PANI have been reported in the literature.[29,31] We have introduced a small modification in the synthetic process as this is the ideal time to develop a green synthetic approach for electroactive materials that will be used in supercapacitors. Here, we report a single-step synthetic method for PANI hybrid nanofibers where we have used cooking oil as an organic phase. The synthetic method is based on the well-known interfacial polymerization of aniline.[29] Instead of using common solvents, viz., CCl4, CHCl3, hexane etc., we have used refined soybean oil (Glycine max) as an organic phase. PANI nanofibers are formed at room temperature in 3 h. An interesting observation is the crystallization of organic molecules in the polymeric PANI matrix. Another sample of PANI nanofiber (PANI-CHCl3) was synthesized using CHCl3 as an organic phase and keeping all other experimental conditions identical. The electrochemical analysis for both the materials shows that PANI-SO is a superior electrode material to PANI-CHCl3. The primary advantage of our approach is that it is a green approach of preparation and it introduces a novel method to synthesize PANI hybrid nanofibers showing enhanced electrochemical performance as supercapacitor electrodes.

Results and Discussion

The Fourier transform infrared (FTIR) spectra of PANI-SO and PANI-CHCl3 are shown in Figure a. For PANI-SO, the peaks at 3421 and 2919 cm–1 are due to the H–N–H and N–H stretching modes. PANI-CHCl3 also exhibits the H–N–H and N–H bands at 3407 and 2912 cm–1, respectively. The bands at 1624 and 1452 cm–1 confirm the C=C stretching vibrations of the quinoid and benzenoid rings of PANI-SO, which are similar to those of PANI synthesized by the conventional method.[33] The bands at 1260 and 1128 cm–1 are due to the C–N stretching of primary aromatic amines and the C–H bending vibrations.[34] Similarly, the bands at 1624 and 1527 cm–1 of PANI-CHCl3 are due to the C=C and C=N stretching modes. The band at 1283 cm–1 indicates the C–N stretching of aromatic amines.[35] By comparing all of the band vibrations with the literature values of PANI, it is seen that PANI-SO exhibits similar band vibrations to those of PANI-CHCl3.

Figure 1

(a) FTIR spectra, (b) UV–visible spectra, and (c) the corresponding powder X-ray diffraction (PXRD) pattern of PANI-SO and PANI-CHCl3.

The UV–visible spectra of PANI-SO and PANI-CHCl3 were recorded by dispersing the nanofiber samples in water, which is shown in Figure b. We observe two characteristic peaks of PANI for both the materials. PANI-SO and PANI-CHCl3 show a sharp peak at 348 nm, which arises from the π–π* electronic transition within the benzenoid segments.[36] The broad absorption peak at 680 nm arises from the π-polaron transition. We do not see any apparent differences between PANI-SO and PANI-CHCl3.

It is interesting to note that the powder XRD patterns of PANI-SO and PANI-CHCl3 are significantly different and are shown in Figure c. Both samples have the characteristic polyaniline emeraldine salt (PANI-ES) peaks at 2θ = 20.1 and 25.1°, respectively.[37] We have also compared the PXRD pattern with that of bulk PANI synthesized by the chemical oxidation method (Figure S1). But PANI-SO has many low-intensity crystalline peaks along with the characteristic PANI-ES peaks. These small multiple peaks may be due to the crystallization of organic molecules in the polymer matrix. Vegetable soya oil is composed of five fatty acids, viz., stearic, oleic, linoleic, linolenic, and palmitic acids.[38] The oil is also rich in vitamin E. The major components are saturated and unsaturated fatty acids. At the oil/water interface along with the monomer, the saturated and unsaturated fatty acids were also in contact with the oxidizing agent of the aqueous phase. Aniline and ammonium persulfate (APS) oxidize unsaturated fatty acids by introducing −OH groups in the chain, resulting in the water solubility of the oxidized molecules. The oxidized organic molecules get transferred to the aqueous phase due to the added hydrophilicity by the hydroxyl groups and attain supersaturation in the aqueous phase. This leads to the crystallization of the oxidized molecules due to intermolecular hydrogen bonding inside the PANI-SO nanofiber matrix. It is also observed that the oil/water interface becomes blurry after the polymerization reaction, which remains distinct in the case of the CHCl3/water interface. This also suggests the reaction of the oil component at the interface.

The morphology of PANI-SO is shown in Figure a. It is observed that uniform nanofibers of diameter 50 nm were formed. The surfaces of the nanofibers are rough and made of some granular particles. This may be due to the crystallization of oxidized organic molecules derived from the vegetable soyabean oil. Energy-dispersive X-ray analysis (EDAX) of PANI-SO (Supporting Information, Figure S2 and Table S1) also shows the weight percentage of various elements, viz., C (58.51%), N (10.91%), O (10.69%), S (7.10%), and Cl (12.79%). The EDAX clearly indicates the absence of metal content in PANI-SO. In Figure b, the fibrous morphology of PANI-CHCl3 is observed with some agglomerated fibers.

Figure 2

(a) Scanning electron microscopy (SEM) image of PANI-SO, (b) SEM image of PANI-CHCl3, (c) thermogravimetric analysis (TGA) profiles of PANI-SO and PANI-CHCl3, and (d) differential scanning calorimetry (DSC) thermograms of PANI-SO and PANI-CHCl3.

TGA profiles of both PANI-SO and PANI-CHCl3 are shown in Figure c. The initial weight loss at around 110 °C is due to the evaporation of moisture from both PANI-SO and PANI-CHCl3. A significant amount of weight loss occurs for both the materials at 330 °C because of thermal decomposition of polymer chains.[39] In the case of PANI-SO, we have also noticed a significant weight loss at 252 °C, which may be due to the degradation of the organic crystals. We have also seen a weight loss between 500 and 700 °C, which is due to the further decomposition of PANI to a carbonaceous residue.[40] The degradation patterns of both the electrode materials are almost the same. At 700 °C, 90% of PANI-SO is degraded, whereas in the case of PANI-CHCl3, 75% of the initial material is degraded. Due to formation of organic crystals in PANI-SO, its degradation is more pronounced compared to PANI-CHCl3.

The DSC thermogram of PANI-SO exhibits only one endothermic peak under a nitrogen atmosphere, which is shown in Figure d. The endothermic peak observed at 156 °C may be due to melting of the organic crystals that formed due to the oxidation of fatty acids of the soyabean oil during the polymerization process in the PANI-SO nanofiber matrix, which is consistent with the TGA result. This endothermic peak is not observed in the case of PANI-CHCl3. The DSC study also confirms that there is no glass-transition temperature (Tg) and melting temperature (Tm) for the polyaniline emeraldine salt system below 200 °C.[41]

The preliminary investigation of the electrochemical behavior of the synthesized materials was performed using a three-electrode electrochemical configuration. Cyclic voltammetry (CV), galvanometric charge–discharge (GCD), and electrochemical impedance spectroscopy (EIS) techniques were used to study the capacitive behavior of the synthesized materials. For CV and GCD experiments, a 0–0.8 V potential window was used, and a 1 M H2SO4 electrolyte was used for all electrochemical experiments. CVs at different scan rates for PANI-SO and PANI-CHCl3 are shown in Figure a,b, respectively. Both the materials show the same range of redox currents, leading to an equal range of specific capacitances calculated from eq . Both the samples show two pairs of redox peaks due to leucoemeraldine ↔ emeraldine and emeraldine ↔ pernigraniline redox transformations, as shown in Scheme . Among these forms, the acid-doped form, i.e., the emeraldine form, is conducting. These reversible redox couples are responsible for the pseudocapacitance of PANI.[42,43]

Figure 3

(a, b) CV curves of PANI-SO and PANI-CHCl3 at different scan rates, respectively. (c, d) GCD curves of PANI-SO and PANI-CHCl3 at different current densities, respectively.

Scheme 1

Different Structural Transformation of PANI during Redox Reactions

The charge–discharge curves of PANI-SO and PANI-CHCl3 at different current densities in the range of 1–8 A g–1 are shown in Figure c,d, respectively. In both the cases, it is seen that the charge–discharge curves are almost symmetric, indicating capacitive like behaviors.[44] The more symmetric GCD curves of PANI-SO in comparison to PANI-CHCl3 reveal the better capacitive behavior of PANI-SO. This may be due to the organic crystals formed in the PANI-SO nanofiber matrix. We have also calculated the active surface area of both PANI-SO and PANI-CHCl3 in the potential range of 0.5–0.6 V at various scan rates of 10–100 mV s–1. Within this potential range, the faradic current on the electrode material is negligible and the current will be only due to the formation of an electrical double layer. We have plotted the current densities of both PANI-SO and PANI-CHCl3 against scan rates at a fixed potential of 0.55 V (Supporting Information, Figure S3). The plots are linear where PANI-SO gives a slope of 5.772 and PANI-CHCl3 gives the value as 3.446 (Figure S3b,d, respectively). Since the surface area will be the ratio between the capacitance from the CV and the literature value of capacitance, the material having a higher slope will have a larger surface area. By comparing both the slopes, it is clear that PANI-SO nanofibers have a larger surface area compared to PANI-CHCl3.

According to the specific capacitance equation calculated from the charge–discharge curve, eq , the specific capacitance values of PANI-SO and PANI-CHCl3 at a current density of 1 A g–1 are 302 and 294 F g–1, respectively. The energy density and power density of both the electrode materials are also calculated by applying eqs and 3, respectively. PANI-SO shows an energy density of 26.8 W h kg–1 and a maximum power density of 402.6 W kg–1. Similarly, the energy and power density values calculated for PANI-CHCl3 are 26.1 W h kg–1 and 398.2 W kg–1, respectively.

The values of specific capacitance of the electrodes with both the materials are plotted against different current densities in Figure a. The capacitance of both the materials decreases with an increase in current density. The specific capacitance values of PANI-SO and PANI-CHCl3 at current densities 1, 2, and 4 A g–1 are 302, 248, and 212 F g–1 and 295, 203, and 124 F g–1, respectively. It is seen that the specific capacitance of PANI-SO is greater than that of PANI-CHCl3 at all current densities, but the difference is larger at higher current densities. It is known that the diffusion rate of an electrolyte decreases predominantly at higher current densities. This limits the penetration of ions only to the large pores of the material, leaving more surface inactive toward the charge–discharge process.[45] The organic crystals in the PANI-SO nanofibers create cracks on the nanofiber surface, leading to easier penetration of ions to a larger surface area of the material at higher current densities.

Figure 4

(a) Specific capacitance vs current densities profiles of PANI-SO and PANI-CHCl3. (b) Cyclic stability curves of PANI-SO and PANI-CHCl3 at a current density of 30 A g–1 for 1000 cycles. (c) Nyquist plot of PANI-SO and PANI-CHCl3 in the frequency range of 104–10–3 Hz; the inset shows the enlarged semicircle and corresponding equivalent electrical circuit. (d) Ragone plot of PANI-SO and PANI-CHCl3 for the three-electrode system.

The electrochemical stabilities of the synthesized materials were calculated from the GCD experiment.[46] The stability test for PANI-SO and PANI-CHCl3 was carried out at a current density of 30 A g–1 for 1000 cycles, as shown in Figure b. PANI-SO maintains about 84% of the initial capacitance after 1000 cycles. Similarly, PANI-CHCl3 electrodes are stable with 81% of the initial capacitance after completing 1000 cycles. Thus, the PANI-SO electrode shows a better cyclic performance, which implies the better structural stability of PANI-SO composite fibers.

In the impedance study, from the Nyquist plot shown in Figure c, the charge transfer resistance developed at the interface between the electrode and electrolyte can be obtained.[47] We observed almost no semicircle in the high-frequency region and an apparent straight line in the low-frequency region. The inset in Figure c shows the Nyquist plot in the high-frequency region. The internal resistance is calculated from the X-intercept in the high-frequency region in this Nyquist plot.[4] The values of internal resistance calculated for PANI-SO and PANI-CHCl3 are 20.3 and 20.1 Ω, respectively. By comparing these results, we found that PANI-SO has a higher internal resistance than PANI-CHCl3, which is due to the crystallization of small organic molecules that are insulators on the polymeric matrix, introducing more grain boundaries in the nanofibers.

We have also plotted the Ragone plot for both the electrode materials.[25,28]Figure d shows the energy density (Ed) and power density (Pd) of PANI-SO and PANI-CHCl3 at various charging rates in 1 M H2SO4. The values of energy density and power density were calculated using eqs and 3, respectively. From the Ragone plot, it is seen that both the electrode materials give similar energy density and power density at 1 A g–1.

With increasing charging rate, there is a gradual decrease in the energy density and an increase in power density occurred. PANI-SO gives a higher energy density at higher charging rates than PANI-CHCl3. At 8 A g–1, the energy density values obtained for PANI-SO and PANI-CHCl3 are 14 and 6 W h kg–1, respectively. We get a maximum power density of 3200 W kg–1 at an energy density of 14 W h kg–1 for PANI-SO. PANI-CHCl3 also gives a similar value of maximum power density, i.e., 3198 W kg–1, at an energy density of 6 W h kg–1. Careful observation shows that the crystallization of organic molecules in the polymer matrix increases the internal resistance of the material, which tends to decrease the specific capacitance of the material.

On the other hand, these crystals introduce cracks on the polymeric matrix, causing a larger electrochemical surface area, which is responsible for the increase in specific capacitance of the material. The overall effect of the crystals is a slight increase in specific capacitance, higher cyclic stability, and higher specific capacitance values at higher current densities for PANI-SO in comparison to PANI-CHCl3. We have compared the specific capacitance value of PANI-SO with those of similar materials studied by other groups and found comparable results with electrochemically synthesized PANI nanofibers (Table S2 in the Supporting Information).

The photograph of an all-solid-state symmetric supercapacitor is shown in Figure a. Figure b shows the cyclic voltammograms of the PANI-SO solid-state symmetric supercapacitor at different scan rates. The CV curves show the redox peaks within the selected potential range of 0–0.8 V. The presence of redox peaks in the CV loop confirms the pseudocapacitive behavior of the PANI-SO material in the all-solid-state supercapacitor. Figure c shows the galvanostatic charge–discharge curves of the solid-state supercapacitor of PANI-SO, which are recorded at different current densities from 1 to 8 mA cm–2. PANI-SO shows nonideal triangular-shaped charge–discharge curves, which is due to the redox processes in polyaniline nanofibers. We have also calculated the areal capacitance of the PANI-SO solid-state supercapacitor by applying eq . The areal capacitance obtained for this electroactive material is 118.7 mF cm–2. The energy density and power density are also calculated for the PANI-SO solid-state symmetric capacitor. PANI-SO shows an energy density of 10.55 mW h cm–2 and a power density of 396 mW cm–2 at a current density of 1 mA cm–2.

Figure 5

(a) Snapshot of the solid-state symmetric supercapacitor of PANI-SO, (b) CVs of PANI-SO at different scan rates, (c) GCD curves of PANI-SO at different current densities, and (d) cyclic stability of PANI-SO at a current density of 30 mA cm–2 for 1000 cycles.

The stability of the PANI-SO all-solid-state supercapacitor was also examined by galvanostatic charge–discharge for 1000 cycles at a current density of 30 mA cm–2. With increasing number of cycles, the pseudocapacitance value decreases slightly. From Figure d, it is seen that PANI-SO maintains about 80% of the initial capacitance after 1000 cycles. Thus, the PANI-SO electrode material synthesized by the interfacial polymerization method shows good electrochemical stability at a higher current density in the all-solid-state symmetric supercapacitor.

Conclusions

We have synthesized PANI-SO by a one-step method, i.e., an interfacial polymerization method, which is a green approach. PANI hybrid nanofibers have been prepared using an environmentally friendly vegetable oil as a solvent. Moreover, these hybrid nanofibers show better electrochemical performances as compared to nanofibers prepared using CHCl3 as the solvent, keeping the other conditions identical. FTIR, UV–visible, PXRD, and TGA have confirmed the successful synthesis of PANI-SO. The morphology study also confirms that the PANI-SO fibers are in nanoform. PANI-SO exhibits a specific capacitance of 302 F g–1 at a current density of 1 A g–1 and a good cyclic stability of 84% up to 1000 cycles. This electroactive material also shows a good areal capacitance value of 118.7 mF cm–2. It is seen that although PANI-SO and PANI-CHCl3 show similar values of specific capacitance, power densities, and energy densities, PANI-SO clearly shows better cyclic stability and higher specific capacitance at higher current densities. For practical utilization of a material, it is essential to preserve the specific capacitance at higher current densities. Considering all aspects such as specific capacitance, energy density, power density, specific capacitance values at higher current densities and cyclic stability, it is clear that PANI-SO is a superior electrode material for electrochemical supercapacitors compared to PANI-CHCl3. Thus, PANI-SO is a new polyaniline-based hybrid nanomaterial having potential application as an electrochemical supercapacitor electrode material.

Experimental Section

Materials

Aniline, ammonium persulfate (APS), hydrochloric acid (35–38%), sulfuric acid (98%), and chloroform were purchased from Merck, India. Vegetable soybean oil (Fortune) was bought from a local grocery store. Aniline was double-distilled prior to its use, and all other chemicals were used as received. Distilled water was used to perform all experiments.

Synthesis of PANI-SO Nanofibers

PANI-SO samples were prepared by interfacial polymerization reported by Richard Kaner’s group with required modifications.[29] In our study, aniline (3.2 mmol) was dissolved in soybean oil (10 mL) to form the organic phase. The aqueous phase was formed by dissolving the oxidizing agent APS (0.8 mmol) in 1 M HCl (10 mL) solution. Upon mixing, a clear interface is formed between the aqueous and organic components with the organic layer on top of the aqueous layer as the density of soya oil is less than that of water. After a few minutes, green PANI-SO nanofibers were visible at the oil–water interface and due to the hydrophilic nature of the nanofibers, they diffused to the aqueous phase forming a good dispersion. The reaction was kept undisturbed to continue at room temperature for 3 h. The nanofibers were collected from the aqueous phase by filtration and washing with distilled water and ethanol, followed by drying at room temperature. The formation of PANI-SO at the biphasic interface at different time intervals is shown in Figure .

Figure 6

Snapshots of interfacial polymerization of aniline in the soyabean oil–H2O system. The top layer is aniline dissolved in the organic phase and the bottom layer is an aqueous solution of APS in 1 M HCl. The reaction times for a, b, c and d are 15 s, 48 s, 1 min, and 3 min, respectively.

Synthesis of PANI-CHCl3 Nanofibers

For comparison of properties of PANI-SO and to perform control electrochemical experiments, we have synthesized PANI-CHCl3 nanofibers by employing exactly identical experimental conditions but using CHCl3 as the organic phase instead of vegetable oil. For washing and drying, the same procedure was adopted as that used for PANI-SO. For comparison, synthesis of bulk PANI is given in Supporting Information S1.

Structural and Electrochemical Characterization

The morphologies of PANI-SO and PANI-CHCl3 were studied by field emission SEM (FESEM) (LEO 1430 VP). For structural characterization, UV–vis spectroscopy (1800 SHIMADZU), FTIR spectroscopy (IR-Infinity 1, SHIMADZU), and powder X-ray diffraction (Rigaku Ultima IV) techniques were used. The thermal stability of the synthesized materials was investigated by thermogravimetric analysis (TGA, TGA/DSC1, STARe System). Differential scanning calorimetry (DSC) was also done with a DSC 8000. All electrochemical experiments were performed on a CHI-660D electrochemical workstation. For three-electrode systems, slurry was prepared by dispersing PANI nanofibers and acetylene black (9:1) in a 3:1 water–isopropanol mixture through sonication for 15 min. Then, 10 μL of the dispersed material was deposited on a finely polished glassy carbon electrode and 1% Nafion solution was used as a binder. The mass loadings of PANI-SO and PANI-CHCl3 are 3.652 × 10–5 and 1.025 × 104–5 g, respectively. Platinum foil and Ag/AgCl electrodes were used as the counter and reference electrodes, respectively.[48] The following equations were used for the calculation of specific capacitance, Cs (F g–1), energy density, Ed (W h kg–1), and power density, Pd (kW kg–1).[49,50]where I is the constant current in A applied in the charge–discharge process, Δt is the discharge time in s, m is the mass of the active material deposited on the glassy carbon electrode in g, and ΔV is the potential range in charge–discharge experiments in V. Stabilities of the electrodes were investigated by performing 1000 charge–discharge cycles in 1 M H2SO4 solution at a high current density of 30 A g–1.

Moreover, electrochemical impedance spectroscopy (EIS) is another useful tool that was used for the conductivity study of the active electrode materials, PANI-SO and PANI-CHCl3. The impedance studies for both the electrodes were carried out in 1 M H2SO4 in the frequency range of 104–10–3 Hz.

A symmetric solid-state capacitor was constructed by depositing a paste of PANI-SO on graphite paper (resistivity of <13 m Ω cm2). The paste was made by mixing the active material, conducting carbon (acetylene black), and poly(vinylidene fluoride) (PVDF) as the binder in the ratio 8:1:1 and a 3:1 water/isopropanol mixture as the solvent. Equal amounts of paste were deposited on two carbon papers on an area of 1 cm2. A gel was prepared by dissolving poly(vinyl alcohol) in 1 M H2SO4, which was used as the solid electrolyte and separator in the two-electrode solid-state symmetric supercapacitor.[51] In the two-electrode system, the average mass loading in the electrode was 1.5 mg cm–2. The areal capacitance of the solid-state capacitor was calculated by applying the following equationwhere I represents the discharge current in mA, t denotes the discharge time in s, ΔV is the potential drop during the discharge in V, and S represents the surface area of the active material in the device in cm2.