1. Introduction
The rising advancements in and utilization of energy emphasize the increasing importance of exploring efficient and eco-friendly sources for energy storage and conversion. In this context, several investigators have directed their attention toward batteries and supercapacitors (SC
s), alternatively called ultracapacitors or electrochemical capacitors, as primary devices for storing energy [
1,
2,
3]. These devices are primarily useful for revitalizing contemporary technological applications, including smart electronics, electronic/hybrid vehicles, and wearable and stretchable devices [
4]. In recent decades, the compact designs of these devices have been found to be applicable as an integrated power source for the automatization of vehicle windows, foldable displays for computers and mobiles, field-effect transistors, health tracking devices, etc. [
5]. The appealing characteristics of supercapacitors include energy densities that surpass conventional capacitors, extended cycle life, and enhanced power densities compared to batteries [
6]. These qualities and their safe operation make them highly prominent across various applications [
7,
8,
9]. In the twenty-first century, lightweight, portable, miniaturized, and flexible gadgets have attracted a lot of interest among the above-mentioned applications. Designing electrode materials with excellent electrical ability, eminent mechanical durability, and the longest possible span of continuous performance to fulfill the requirements of such applications is a substantial challenge at present [
10,
11,
12,
13]. Hence, researchers globally have focused on conducting thorough investigations into the development of the materials needed to meet the current demands. Commonly utilized materials for lightweight and flexible supercapacitors include conducting polymers, metal oxides/hydroxides, carbon derivatives, and various composites of these species [
12]. In addition to these, there is a predominant focus on investigating semiconductors or 2D materials like MoS
2, WS
2, V
2O
5, g-C
3N
4, SnO
2, WO
3, and WS
2, which are predominantly under investigation to develop electrodes for energy storage devices [
8,
14,
15].
Due to its impressive electrical configuration, outstanding structural stability, and environmentally friendly properties, graphitic carbon nitride (g-C
3N
4), from the affordable redox-active semiconductor family, is considered a viable option for electrode material. The two-dimensional (2D) graphite-like structure of g-C
3N
4 further enhances its potential applications in flexible electrode technology [
16,
17]. This material represents a stable structural variant within carbon nitride, featuring a hexagonal arrangement formed by σ bonds. Additionally, it exhibits an extensively dispersed π-conjugated system: a result of carbon and nitrogen’s sp
2 hybridization [
18]. The van der Waals interactions resulting from π-orbitals between individual layers contribute to the outstanding thermal and chemical stability of g-C
3N
4. Combining this with its advantageous electronic structure, with a bandgap (Eg) of about 2.7 eV, g-C
3N
4 becomes an outstanding material for a wide range of applicability. Its utilization spans catalysis, pollutant degradation, bioimaging, light-emitting diodes, photocatalytic applications, and various other applications [
19,
20,
21,
22,
23]. Additionally, this material’s layered characteristics contribute to substantial surface-to-volume ratios, further amplifying, significantly, the efficient utilization of active sites. Consequently, this results in improved electrochemical performance, leading to a reduction in the distances for both electronic and ionic transfers [
24]. This renders it notable as an electrode material in energy storage devices. However, when viewed as a possible electrode, unmodified g-C
3N
4 exhibits poor long-term stability and restricted electrochemical performance. Additionally, the Van der Waals force is responsible for g-C
3N
4 nanosheets’ tendency to agglomerate, which results in decreased specific power and energy density [
5].
Hence, it is imperative to devise and explore additional strategies aimed at enhancing the electrochemical performance of this material. In this context, a method that entails the creation of hybrid or composite electrodes utilizing this material was employed by a few researchers. This was achieved by integrating it into a conductive species or incorporating semiconductor materials. This enhances surface activity, thereby contributing to improved performance [
25]. Even though g-C
3N
4 exhibits numerous advantages as an electrode material in energy storage applications, there has been limited research focused on enhancing its electrochemical properties. Several protocols have been devised to improve the capacitive behavior of materials. This includes proton flow within nanomaterials, electron tunneling or hopping, and the spinning of electrons between the current collector (conducting substrate) and active electrode material. In this regard, the works of Y. Gao et al. [
26] and D. Ilager et al. [
27] have investigated the introduction of CTAB as a cationic surfactant, which serves as a strategic tool in overcoming the above-mentioned challenges associated with g-C
3N
4. CTAB offers a versatile platform for the controlled synthesis of two-dimensional g-C
3N
4 sheets by stimulating the surface pores. Furthermore, it impedes the clumping together of particles and increases the number of active sites, which is favorable for electrochemical energy storage purposes.
Therefore, through this research work, we aimed to thoroughly analyze the electrochemical performance of graphitic carbon nitride (g-C3N4) prepared with and without the incorporation of the cationic surfactant, CTAB. The ensuing discussion will unveil the noteworthy influence of CTAB interaction in customized g-C3N4 sheets on supercapacitive performance. This will provide insights into heightened capacity, a detailed understanding of the charge–storage mechanism, and prolonged cycling stability. We observed that the specific capacitance of g-C3N4 with CTAB increases by about 28% when compared with g-C3N4 prepared without CTAB. This electrode also dominates in terms of cycling stability by retaining 75.1% of capacitance after 5000 charge–discharge cycles, which was 69.8% for electrode material without CTAB.
3. Results and Discussion
Figure 1a represents the X-ray diffraction patterns for graphitic carbon nitride (g-C
3N
4) prepared through the thermal condensation process. The black color diffraction pattern was assigned to g-C
3N
4 without CTAB, and for CTAB-integrated g-C
3N
4 it was illustrated by the red color. Diffraction patterns of both samples were indexed as per JCPDF card number 087-1526 and indicate hexagonal crystallinity with space group
. The crystal planes noted at 2θ angles of 12.84° (001) and 27.68° (002), through thermal condensation of melamine without CTAB, effectively confirm the formation of graphitic carbon nitride [
29]. These planes reflect the in-plane ordering of units of the tri-s-triazine and layer-to-layer distance, respectively [
30]. Although the recurrence of this diffraction pattern was noted during the thermal condensation of melamine integrated with CTAB, therein lies a very small difference. This difference lies in the 2θ positions of those crystal planes. Here, the incorporation of a minimal quantity of cationic surfactant caused a displacement of the characteristic peaks of g-C
3N
4 to a lower 2θ angle. The negative shift, i.e., shifting towards a lower 2θ angle, can be visualized through
Figure 1b for the (002) crystal plane. The negative shift in the XRD diffraction peak is assigned to lattice expansion or an increase in the interlayer distance of g-C
3N
4. Furthermore, alterations in the Full Width at Half Maximum (FWHM) serve as reliable indicators to validate the influence of CTAB on crystallinity [
29,
31].
X-ray photoelectron spectroscopy (XPS) assessment was undertaken to learn more about the chemical composition of nitrogen and carbon within the fabricated g-C
3N
4 without and with CTAB. Survey spectra illustrated in
Figure 2a for both samples of the g-C
3N
4 (black color line without CTAB, red color line with CTAB) revealed the detection of only three elements: carbon (C), nitrogen (N), and oxygen (O). Carbon and nitrogen are the prime elements of g-C
3N
4 samples, while the oxygen peak comes from the handling of the samples.
Figure 2b,c display a high-resolution C 1s spectrum of the g-C
3N
4 sample without and with CTAB, respectively. These C 1s spectrums can be accurately represented by fitting three distinctive peaks integrated within them using Gaussian–Lorentzian profiles. These three peaks are associated with the distinct carbon species in the graphitic carbon nitride [
32]. Interestingly, for both samples of g-C
3N
4, i.e., without CTAB, when cationic CTAB propagated through the 2D sheets the binding energy position of these peaks carbon species remained unchanged. In both cases, these peaks were located at 284.6, 288.0, and 288.9 eV, respectively. One of the carbon species integrated within the C 1s spectrum can be identified as pure sp
2 carbon (C–C) or a C=C bond, reminiscent of the free/impure carbon species. The corresponding peak for this species is positioned at a lower binding energy, specifically at 284.6 eV [
8,
33,
34]. A sharp central peak identifies the tri-s-triazine unit, as does the pyridine-like structure inside the aromatic ring system. In particular, this peak is associated with sp
2 carbon–nitrogen (N–C–N) bonds. The binding energy position of this peak is 288.0 eV. The peak with higher binding energy, at 288.9 eV, is designated for covalent bonding in the C–N network of tertiary (3°) carbon with the three nitrogen atoms. This peak is an indication of a graphitic-like nitrogen structure [
35]. Similar to the C 1s spectrum, the three distinctive peaks are incorporated within the high-resolution nitrogen (N 1s) spectrum and this scenario is for both samples of g-C
3N
4, as illustrated in
Figure 2d,e for samples without and with CTAB, respectively. As illustrated, one tall peak and two other broad peaks inside the N 1s spectrum reflect that nitrogen species were located at binding energies of 398.5, 399.4, and 401.0 eV, respectively. The prime intensive peak at the lowest binding energy, 398.5 eV, identifies the sp
2-bonded nitrogen with graphitic carbon (–C=NH) present in the triazine rings. The broad peak next to this peak is positioned at a higher binding energy, i.e., 399.4 eV is associated with nitrogen atoms adopting a sp
2-configuration and being bonded to two carbon atoms [
30,
36]. The third peak is located at a higher binding energy of 401.0 eV, designated for nitrogen atoms trigonally bonded to all sp
2 carbons [
37].
Field Emission Scanning Electron Microscopy (FE-SEM) was utilized to examine the microscopic characteristics of the 2D g-C
3N
4 without and with CTAB.
Figure 3a–f yield comparable morphological views for g-C
3N
4 samples without and with CTAB at different magnifications (500 nm, 2 μm, and 5 μm). Several smaller particles contribute to generating irregularly shaped big lumps in both samples with or without CTAB (
Figure 3a,d). Maximum irregular lump formation was observed in samples lacking CTAB, which can be noticed through lower magnification images, as in
Figure 3b and
Figure 3c. Nevertheless, the introduction of CTAB results in the formation of a stacked arrangement of multiple wrinkled layers with small particles, thus, the g-C
3N
4 structure takes on a sheet-like appearance. The formation of stacked layers of sheets can be easily noticed in
Figure 3e,f for the CTAB integrated sample. Moreover, these stacked layers were spongy, as seen in
Figure 3f, which makes intercalation/deintercaltion electrolytic ions with easy way. The Energy Dispersive Spectroscopy (EDS) examination identifies signals corresponding to C and N only as illustrated in
Figure 4a,b, respectively. This affirmed the presence of composed elements in both samples and revealed impurity-free development of g-C
3N
4, irrespective of whether CTAB was included or not. The table insight of the EDS spectrum gives weight (%) and atomic percentage of the carbon and nitrogen species. The formation of g-C
3N
4 takes place with a ratio of 1:1.32 between carbon and nitrogen for the sample without CTAB, while it tends to be 1:1.39 with the inclusion of CTAB.
TEM was further used to highlight the in-depth morphology of the g-C
3N
4 samples without and with CTAB. TEM, HR-TEM images, and SAED patterns of the g-C
3N
4 samples without CTAB are represented in
Figure 5a–d while
Figure 5e–h illustrates the g-C
3N
4 integrated with CTAB. TEM and HR-TEM confirm wrinkled 2D sheet-like features for both samples, however, the sheets of the g-C
3N
4 sample without CTAB are slightly aggregated and thicker than the sample with CTAB integration. SAED confirms that both samples are amorphous.
In this work, the g-C
3N
4 samples were prepared using the thermal treatment of melamine which was conducted at 550 °C. This temperature is higher than that of the decomposition temperature of the CTAB, which is 300 °C. Through the literature, it was found that even when the decomposition of the CTAB takes place it is beneficial due to the creation of a large number of uniform pores and enhancing of the surface area. Because of the gases released (O
2, CO
2, H
2O) during the decomposition of CTAB, pores are created that are in equal dimensions to those of surfactant [
38]. Therefore, to analyze the effect of CTAB integration on the surface area and pore size distribution of g-C
3N
4, nitrogen adsorption-desorption isotherms were measured. N
2 isotherms for g-C
3N
4 without CTAB and with CTAB are represented in
Figure 6a,b, respectively, and the pore size distribution is represented in the figure inset. Isotherms of both samples display classical type IV patterns with proper H3 hysteresis curves. CTAB-integrated g-C
3N
4 was found to be richer in the surface area, exhibiting 17.19 m
2/g, whereas that of the g-C
3N
4 sample without CTAB exhibited a surface area of 12.82 m
2/g when measured using the Brunauer–Emmett–Teller (BET) method. Furthermore, the pore size distribution inset, derived based on the Barret–Joyner–Halender (BJH) method, illustrates a broad range of pore sizes. The curve reflects the average pore width of 25 nm for CTAB-integrated g-C
3N
4 and 30 nm for that without CTAB. Increased surface through CTAB integration is useful for boosting the overall electrochemical performance of the g-C
3N
4.
This section delineates the functional attributes of g-C
3N
4 and examines the influence of incorporating a cationic surfactant on these properties. In this regard, the electrochemical characteristics (CV, GCD, and EIS) were investigated with a three-electrode setup using active electrodes on Ni foam prepared using g-C
3N
4 without and with CTAB.
Figure 7a illustrates a comparative analysis of the electrochemical performance between pristine g-C
3N
4 and g-C
3N
4 integrated with CTAB. The testing was conducted in a 2 mol/L aqueous KOH solution, and the recorded cyclic voltammetry (CV) curves were obtained at a scan rate of 10 mV s
−1 and voltage window of −0.1 to 0.6 V. The reversible Faradaic redox features confirm the two distinct asymmetrical redox peaks and suggest that the electrochemical activity of g-C
3N
4 is associated with pseudocapacitivity. Both electrodes have the same features, however, conversely, the electrode fabricated through integrating CTAB is accompanied by an enhanced current response/high area under the CV curve. Reversible redox peaks in the CV profile are an indication of interaction between electrodes and electrolytes; this process of interaction can be articulated as follows [
8].
Figure 7b illustrates the comparative Galvanostatic Charge–Discharge (GCD) curves at 0.5 mA cm
−2. The GCD curves of both g-C
3N
4 electrodes exhibited symmetric curves portraying exceptional charge–discharge characteristics, with impressive coulombic efficiency and minimal polarization. Moreover, the alignment of the GCD curve with CV analysis is notable, especially in the context of the CTAB-integrated g-C
3N
4 electrode. GCD gives a crucial parameter required for assessing the capacitive performance of the electrode material, which is nothing but discharging duration. Herein, the CTAB-integrated electrode outperforms the electrode material without CTAB. At the same current density of 0.5 mA cm
−2, the electrode of g-C
3N
4 with CTAB renders 254 s of discharging time and that of the electrode without CTAB can give 169 s. This enables a specific (areal) capacitance of 162.8 F g
−1 (211.7 mF cm
−2) for the CTAB-integrated electrode, which is 117.3 F g
−1 (140.8 mF cm
−2) in the case of g-C
3N
4 without CTAB.
To shed light on the charge–transfer dynamics, diffusion coefficient, and formal oxidation and reduction capabilities of the active material, we further conducted a scan rate dependence analysis of the cyclic voltammetry (CV) for each electrode.
Figure 8a,b illustrate the scan rate dependence CV profile for g-C
3N
4 without CTAB and upon integrating CTAB, respectively. The consistency of the CV curves in the case of both electrodes persists as the scan rate varies from a lower limit of 5 to a higher 100 mV s
−1. CV profiles of both electrodes reflect analogous patterns, with no notable variations even when subjected to elevated scanning speeds. This proves that g-C
3N
4-based electrodes have good reversible charge–transfer dynamics and rate capability [
39,
40]. As anticipated, a dual set of Faradaic redox peaks is set to appear when the reversible redox scanning takes place from a low scan rate to a high scan rate in both electrodes. This unveils that g-C
3N
4 electrodes are equipped with battery-like characteristics owing to intercalation and de-intercalation of electrons/ions within interlayers of the nanosheets [
41]. Slight displacement of anodic and cathodic peaks around higher and lower potentials occur, respectively, when the scan rate is changed from low to high, which elucidates an inadequate diffusion rate of ions. This phenomenon hinders the attainment of oxidation–reduction reactions, commonly referred to as electrode polarization [
42]. The peak current (reduction–oxidation peaks) of CV at each scan rate was estimated and plotted with the square root of the scan rate and fitted linearly as illustrated in
Figure 8c. The determination of the slope from the linear fitting of this graph was employed to evaluate the diffusion of K
+ ions in both electrodes, in accordance with the Randle–Sevcík equation [
43].
where variables are
n (number of electrons involved in the reaction),
F (Faraday constant),
A (active electrode area),
C (concentration of the electrolyte),
D (reactant diffusion factor),
R (gas constant),
T (temperature),
v (scan rate of CV measurement). Considering the constant parameters and variables from voltammetric experiments, Equation (4) can be rewritten as:
Therefore, by analyzing the slope from
Figure 8c, we estimated the diffusion coefficients for the g-C
3N
4 without and with CTAB. In contrast to the g-C
3N
4 without CTAB, the diffusion coefficient for the CTAB-integrated electrode material exhibited a noteworthy increase. The values of the diffusion parameter for g-C
3N
4 without CTAB remain 2.61 × 10
−3 cm
3 s
−1 and 2.14 × 10
−3 cm
3 s
−1 during the reversible reduction and oxidation processes, respectively. These values shift to 3.33 × 10
−3 cm
3 s
−1 and 2.35 × 10
−3 cm
3 s
−1 for g-C
3N
4 with CTAB inclusion. CTAB integration enhances the diffusion coefficient, which may be attributed to its spongy stacked-layered structure of 2D sheets (as noticed in FE-SEM). This structure provides enormous diffusion sites, boosting the diffusion process capability.
The electrodes of supercapacitors belong to a distinctive category, utilizing both electrostatic and electrochemical phenomena for charge storage. The charge storage functioning of supercapacitor electrodes can be retrieved in terms of two different approaches: capacitive and diffusion-controlled. To comprehend the charge storage mechanism within g-C
3N
4 electrodes without and with the inclusion of CTAB, we analyzed the correlation between the scan rate (
v) and redox peak current (
ip) derived from cyclic voltammograms and measured at different scan rates. Therefore, based on the power law, the linear curves of log(
i) vs. log(
v) were utilized to explore the kinetics of the charge storage mechanism within the manufactured electrodes. These log(
i) vs. log(
v) curves are illustrated in
Figure 8d,e for gC
3N
4 electrodes without CTAB and with CTAB, respectively. In general, this power law is commonly known as b-value assessment and can be expressed as follows [
44]:
The “
b-value” in this equation is nothing but a slope of the linear fitting of those curves represented in
Figure 8d,e. This value serves as a determinant for either surface-controlled or diffusion-controlled charge storage mechanisms in the electrode material. Typically, a capacitive-controlled charge storage kinetic scenario is characterized by a value of
b = 1, while a diffusive-controlled scenario is associated with a value of
b = 0.5. As represented in
Figure 8d,e, the b-values for the g-C
3N
4 electrodes without CTAB and with integrated CTAB are 0.60 and 0.62, respectively. These values manifest a biased nature in the K
+ charge storage kinetics of our electrodes, with the diffusion-controlled (Faradaic) mechanism surpassing the surface-controlled (non-Faradaic) mechanism. To assess the diffusion-controlled and surface-controlled current in our electrodes, an analysis that depends on scan rate (
v) and utilizes the current response (
i) at a constant voltage is conducted using the following equation [
45]:
The
k1 and
k2 represent the charge storage kinetics originating from surface-controlled and diffusion-controlled scenarios, respectively.
Figure 8f,g illustrates the capacitive and diffusion contribution across different scan rates of the g-C
3N
4 electrode without and with CTAB, respectively. As seen through these figures, the contribution of the diffusion mechanism is superior at lower scan rates and surface-controlled capacitance shows a progressive rise as scan rates increase. This increase indicates an intensified dependence on the scanning rate of the surface-controlled mechanism [
46]. Quantification rectifies surface-controlled mechanism progress from 22.5% at 5 mV s
−1 to 56.5% at 100 mV s
−1 for g-C
3N
4 prepared without CTAB. Additionally, with the incorporation of CTAB, the g-C
3N
4 electrode exhibits a gradual shift toward the surface-controlled mechanism. Specifically, at a scan rate of 5 mV s
−1, this mechanism contributes 25.3% to the current, and as the scan rate increases to 100 mV s
−1, its contribution rises to 60.2%. The CV curves depicted in
Figure 8h,i, obtained at a scan rate of 5 mV s
−1, illustrate the electrochemical behavior of electrodes of g-C
3N
4 without and with CTAB, respectively. These curves signify the integrated area, encompassing the current contributions from both diffusion-controlled and surface-controlled processes.
The comparative analysis of both electrodes validates that the incorporation of the cationic surfactant enhances the electrochemical performance of graphitic carbon nitride. To delve deeper into the effect of alteration in current densities on the specific (areal) capacitance, rate capability Galvanostatic charge–discharge (GCD) curves were recorded within the range of 0.5 to 5 mA cm⁻
2.
Figure 9a,b illustrate the GCD profile of g-C
3N
4 without CTAB and with CTAB, respectively. The GCD curves here are quite symmetric even at increasing current density. The prominent characteristics of the charge–discharge profile signify a pseudocapacitive nature, arising from the reversible electrochemical reactions occurring at the interface (electrode–electrolyte) [
41]. The deductions made from the GCD profile align with the redox characteristics observed in the cyclic voltammetry (CV) of each electrode. Specific capacitance estimated as per equations (1) and (2) are illustrated in
Figure 9c, wherein the CTAB-integrated electrode clearly surpasses the non-CTAB-integrated electrode at each current density. The comparative perspective of the g-C3N4-based electrodes was summarized in
Table S2. The rate capability performance of the g-C
3N
4 without the CTAB electrode slightly exceeds that of g-C
3N
4 with the CTAB electrode when the current density is increased by 10 times. This electrode exhibits 54.5% capacitance retention and the CTAB-integrated electrode can retain 51.6% of capacitance at initial current density, which is as illustrated in
Figure 9d.
Figure 10a,b illustrate the enduring cycling stability of the g-C
3N
4 electrodes without CTAB and with CTAB, respectively. After undergoing 5000 charge/discharge cycles at 10 mA cm
−2, the CTAB-integrated electrode retained a higher capacitance of 74.9% of its initial capacity, maintaining a high coulombic efficiency of 108%. On the other hand, the g-C
3N
4 electrode without CTAB can retain 70.8% with a coulombic efficiency of 106%. The specific capacitance was further measured by using GCD before and after stability at 3 mA cm
−2, as shown in
Figure 10c,d for electrodes without and with CTAB, respectively. This analysis indicates that an electrode without CTAB at 3 mA cm
−2 gives a specific capacitance of 57.2 F g
−1 after stability, which is 80.6 F g
−1 before stability. In the case of the electrode integrated with CTAB, the specific capacitance is 74.4 F g
−1 after stability and 102.3 F g
−1 before stability. Stacked sheets were still noticed for the CTAB-integrated g-C
3N
4 while the sheet-like structure is somewhat disturbed in the case of the g-C
3N
4 without CTAB. This was confirmed through the measurement of FE-SEM after stability analysis as represented in
Figure S1a–f in the Supplementary Materials for g-C
3N
4 without and with CTAB, respectively. The optimum performance sample (with CTAB g-C
3N
4) was further analyzed using XPS to confirm the chemical composition after a prolonged stability test.
Figure S2a represents the survey XPS spectrum of the Ni-foam-loaded CTAB-integrated g-C
3N
4 after stability, which confirms the presence of carbon (C), nitrogen (N), oxygen (O), nickel (Ni), and potassium (K). The presence of Ni is attributed to the current collector (Ni foam) used to deposit the g-C
3N
4, while the K peak is due to prolonged insertion–desertion of the KOH electrolyte in the g-C
3N
4. Even after the cyclic stability, the existence of carbon and nitrogen species was confirmed through the deconvolution of the C 1s and N 1s spectrum, which is as before stability. The only change was noticed in the C 1s spectrum which shows an additional peak, indicating the influence of oxygen atoms. This oxygen may result from the longer cycling test. Deconvoluted C 1s and N 1s spectrums are represented in
Figure S2b,c, respectively. The electrochemical impedance spectroscopy (EIS) spectra, presented in
Figure 10e–h, depict the characteristics of the g-C
3N
4 electrode without a CTAB and with CTAB, respectively, both before and after the stability test. EIS spectra of both electrodes reflect negligible changes in all regions. The EIS spectrums were fitted using ZMAN software version 2.3.2, and an equivalent circuit of fitting is illustrated in
Figure 10i. This includes the intersection at the
x-axis, mid-frequency semicircular region, and low-frequency straight line region connected in series. The intersection region gives Equivalent Series Resistance (ESR) and it is nearly constant even after stability, indicating minimal ohmic loss. The confirmation of diffusion resistance is also supported by the slope parallel to the imaginary axis in the low-frequency region called the Warburg diffusion element. Values of each element after fitting are illustrated in
Table S1.