Pseudo 2-dimensional nanostructures of metal oxides for high-performance supercapacitors

Abstract

Recently, high performance supercapacitors based on hollow nanostructures have been reported. The enhanced behaviours are directly attributed to the higher specific surface area of hollow particles. It is shown here that this is an oversimplified explanation. If only the surface area was driving the enhancement then other solid morphologies, with a higher specific area, should show better performance. Careful modelling and simulation studies show that hollow structures can actually be viewed as pseudo 2-dimensional (2-D) materials. This leads to performance similar to that reported in 2-dimensional materials ranging from metal oxides to MXenes. Therefore, the underlying reasons, inducing the performance enhancement, are explained for the first time. The theoretically predicted behaviour is proven experimentally by using CeO₂ hollow and solid nanostructures as the test samples. The result also establishes the importance of using hollow structures of rare-earth oxides, if they are to be used in supercapacitors. Finally, it is shown that the future direction should involve the combination of a pseudo 2-D structure with a real 2-D-carbon based electrode. The use of 2-D gC₃N₄, with a lower specific surface area than activated carbon but much higher specific capacitance, reaffirms the inferences that the role of the specific surface area is mostly over-estimated in supercapacitors.

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1. Introduction

Self-assembled hierarchical nanostructures are slowly superseding most of the conventional nanostructures for use in supercapacitor electrodes. These morphologies intrinsically show high surface area, tunable porosity and packing density, which can be easily modulated. The last decade has seen tremendous interest in 2-dimensional (2-D) nanostructures.^1–3 These can have fascinating semiconducting properties owing to modulated confinement, optical properties because of significant change in the band structures, electrical or electrochemical properties associated with their surface states and enhanced accessible active sites.^2,4–6 The interest in 2-D nanostructures was initiated by the fascinating world of graphene. Novel alternatives to graphene such as MXenes are taking the interest in 2-D nanostructures to the next level.^4,7 In terms of applicability, these materials would be useful in energy storage and harvesting devices, 5G antennas, electronics, smart textiles, EMI shielding, biomaterials, sensors, optoelectronics, environmental applications, etc.^3,8–12

The major limitations associated with most 2-D materials are low yield synthesis protocols, reproducibility, stability, and limited operating temperature range.^13,14 Hence, conventional or almost hierarchical nanostructures of metal oxides are still more preferred. For example, in energy storage devices, nano metal oxides do deliver slightly lower specific capacitance, but compensate by ensuring higher stability, cost-effectiveness and long life.¹⁵ Ideally, if 2-D structures of metal oxides can be easily produced then they would be most preferred. There have been few reports suggesting that ultrasonication-driven exfoliation of oxides like MnO₂, Mn₃O₄, NiO, and Co₃O₄ can be obtained.^16–23 But, the structural stability and phase integrity of such materials still remains questionable.

In this paper, it is shown that the fast emerging hollow nanoparticles can be viewed as pseudo-2-D nanostructures. The term pseudo is used because the materials are 3-dimensional in reality but the structures stabilize in a way that it actually simulates a layered material-like response. Using molecular dynamics and simulation, it is shown that these structures pack themselves in an arrangement that also leads to a stable channel for ion intercalation. Thus, these materials become extremely useful to energy storage devices. There have been studies in the recent past, where hollow metal oxides have been used to obtain high-performance supercapacitors and batteries. All those papers attributed the observed high performance to the higher surface area of hollow structures. Never has there been an attempt to carefully understand the origin of the higher performance in these structures. If one sees the real 2-D carbon materials, which have lower specific surface area than activated carbon, it is clear that they are able to deliver higher specific capacitance. Therefore, the role of the specific surface area of electrode materials used in supercapacitors is over estimated. It is the accessible area that plays the important role. The novel architecture of a 3-D-hollow structure is able to simultaneously fulfill both these requirements i.e. high surface area and layered like morphology. This paper opens a new dimension in the research of 2-D nanostructures.

It is now becoming clear that asymmetric or hybrid type supercapacitors would be more preferred in future applications.^24–26 Therefore, combining a 2-D metal oxide-based pseudocapacitive electrode with a 2-D carbon-based EDLC-type electrode would be the way forward.²⁷ In this paper, using pseudo-2-D CeO₂ and real 2-D gC₃N₄ electrodes, the usefulness of this strategy is unequivocally established. The use of CeO₂ in supercapacitors has been reported earlier but none of the studies have used hollow structures and hence the specific capacitance value has remained low.^27,28 To increase the value, composites of CeO₂ with graphene, etc. have been investigated by earlier workers.^29,30 But this just leads to cost escalation, without appreciable enhancement. Our studies further show that pseudo-2-D structures of rare earth oxides can also become useful and deliver high specific capacitances. The results are proven by comparing the results delivered by conventional solid nanoparticles of CeO₂. The asymmetric supercapacitors can operate up to 1.3 V, achieving a maximum specific capacitance of 60 F g⁻¹ at a current density of 1 A g⁻¹. Moreover, the fabricated hollow CeO₂‖gC₃N₄ device exhibits an excellent energy density of ∼14.33 W h kg⁻¹ with a power density of ∼703 W kg⁻¹, making it suitable for various applications.

2. Materials and method

2.1 Material synthesis

The solid and hollow nanostructures of CeO₂ and 2-D graphite carbon nitrate were used as the positive and negative electrode materials for the study. The synthesis protocol of all the materials is given in the ESI.†

2.2 Material characterization

The morphology of the materials was analysed by scanning electron microscopy (SEM, CARL ZEISS SUPRA 40) and transmission electron microscopy (TEM, FEI-TECNAI G220S-Twin operated at 200 kV). Brunauer–Emmett–Teller (BET) surface area and porosity were measured with a Quantachrome Novatouch analyser. The phase formation of the materials was confirmed by XRD analysis, using a Rigaku Miniflex diffractometer, with Cu Kα (λ = 0.15406 nm) as the incident radiation. A Horiba Scientific SZ-100 nanoparticle analyser was used for the particle size and zeta potential measurements.

2.3 Electrochemical measurement

The electrodes were prepared by mixing 80 wt% CeO₂, 10 wt% activated carbon and 10 wt% polyvinylidene fluoride in acetone. The mixture was stirred continuously at 80 °C for 8 h, to obtain a homogeneous slurry. The slurry was coated onto a graphite sheet (1 cm × 1 cm) and dried in a vacuum oven for ∼12 h. Cyclic voltammetry (CV), galvanostatic charge–discharge (CD) and impedance spectroscopy (EIS) were performed in 3 M KOH, using a Metrohm Autolab (PGSTAT302N) potentiostat, in both three-electrode and device configurations. For the three-electrode measurements, platinum wire and Ag/AgCl/3.0 M KCl were used as counter and reference electrodes, respectively. The electrochemical analysis of the asymmetric supercapacitor device was performed using CR2032 type cells. Whatman glass fibre was used as a separator in the asymmetric device.

2.4 Simulation of the pseudo-2-D structures

Molecular dynamic simulations were performed using the LAMMPS software package. The simulation, to visualize the structures, was performed initially by considering one sphere only. The model was extended to construct the adjacent spheres and the closest approach was reduced to make the spheres just touch side-by-side. The crystal structure for the material and bond energy was fixed according to the data obtained from the XRD. A cubic simulation box (600 nm × 600 nm × 600 nm), with periodic boundaries, was considered. The system energy was minimized during the simulation. The simulation was performed at a time step of 1 millisecond.

3. Results and discussion

3.1 Structural and morphological characterization

The structure, phase and purity of the CeO₂ hollow and solid structures were determined by the X-ray diffraction analysis. The X-ray diffraction pattern of both hollow and solid CeO₂ is shown in Fig. 1(a). The formation of the crystalline and cubic phase, confirmed using JCPDS card no. (81-0792), in both types of CeO₂ nanostructures, was discernible.³¹ No impurity peak was detected in the XRD patterns. The average crystallite size was ∼5.70 nm for hollow CeO₂ and ∼5.29 nm for the solid particles. The unit cell dimensions and microstrain estimated in both the CeO₂ nanostructures are given in Fig. S1 and Table S1 (ESI†), respectively. The particle size distribution of the material is shown in Fig. S2 (ESI†). The mean particle size of the hollow and solid CeO₂ was estimated as ∼315 and 260 nm, respectively. This indicated that both the structures possess high homogeneity and narrow distribution. Fig. 1(b) depicts the Raman spectra, showing the presence of a phonon mode at 460 cm⁻¹, which is linked to the F_2g mode. This mode confirmed the cubic fluorite structure of hollow CeO₂.³² It appears due to the symmetric Ce–O stretching vibration, which is very sensitive towards defects/disorder in the structure. The peaks at 260 cm⁻¹ and 600 cm⁻¹ could be attributed to the second-order transverse acoustic (2TA) mode and defect induced (D) modes.³³

Fig. 1 (a) XRD, and (b) Raman spectra of hollow and solid CeO₂.

The XPS profiles of both the hollow and solid CeO₂ are given in Fig. S3(a and b) (ESI†), respectively. Fig. S3(c and d) (ESI†) show the FTIR spectroscopy results of both the CeO₂ nanostructures. The absorption bands at 3663 cm⁻¹ and 1554–1624 cm⁻¹ could be attributed to the stretching and bending mode, respectively. The CO₂ absorption on the surface of the material was observed at 2364 cm⁻¹. The stretching bond of O–C–O was found at 1376 cm⁻¹. The formation of the CeO₂ was confirmed by the bending mode of Ce–O–Ce, appearing below the 650 cm⁻¹ regions.³⁴ The peak at around 431 cm⁻¹ was attributed to the vibration related stretching mode of O–Ce–O.¹⁴ Fig. S4(a and c) (ESI†) depict the nitrogen adsorption–desorption type IV isotherm of the hollow and solid CeO₂ nanostructures, showing the capillary condensation at high relative pressure. The BET specific surface area of the hollow CeO₂ nanostructure was ∼154 m² g⁻¹ and that for the solid structure was ∼107 m² g⁻¹. The pore size distribution indicated microporous nature, with an average pore diameter of ∼1.51 and 1.68 nm, for the solid and hollow structures, respectively, as shown in Fig. S4(b and d) (ESI†). The zeta potential revealing the average surface charge of solid and hollow CeO₂ is shown in Fig. S5(ESI†).

The enhancement in the electrochemical properties of the transition metal oxides is directly related to their particle morphology.³⁵ To obtain the morphology related information of the synthesized materials, SEM and TEM measurements were performed and the corresponding micrographs are shown in Fig. 2(a)–(d). The results suggested the formation of hollow nanospheres, as well as solid nanoparticles. Along with the morphology of the material, the following information could be obtained from the SEM and TEM results: (a) size of the hollow nanospheres, (b) inner dimension of the cavity, (c) width of the nanospheres, and (d) homogeneity. The SEM result clearly suggested that smaller grains were wrapped along the boundary, leading to the hollow nanospheres. The size of the hollow nanospheres was in the range of 120–200 nm. The diameter of the cavity was ∼60–80 nm. The wall thickness of the nanospheres was ∼30 nm. The size of the solid CeO₂ nanoparticles was found to be in the range of 15–25 nm, as calculated from SEM pictures. The presence of Ce and O atoms in both hollow and solid nanostructures is confirmed by elemental mapping analysis, as shown in Fig. S6 and S7 (ESI†), respectively. The TEM micrograph confirmed that a low precursor concentration helps in the growth of hollow morphologies. The cavity was suppressed with increasing concentration of precursor, leading to porous morphologies at higher concentrations.³⁶ TEM micrographs also indicated the uniform distribution of spherical grains in the boundary of the hollow structures. These small grains were around ∼5–10 nm in size. For solid nanoparticles, the size of each of the small particles was around 5–12 nm. The selected area energy diffraction (SAED) patterns of both types of CeO₂ structures confirmed the polycrystalline nature, as shown in Fig. S8 (ESI†). All the rings of the SAED patterns corroborated the XRD data. The EDX result, confirming the presence of elements Ce and O, is given in Fig. S9 (ESI†).

Fig. 2 (a and c) SEM and (b and d) TEM micrographs of hollow and solid CeO₂, respectively.

3.2 Hollow particles as a pseudo 2-D nanostructure

Until now, most studies have suggested the hollow or cage frame type structures as better performing materials because they have higher surface area. As discussed earlier, it is now becoming clear that the role of the surface area of metal oxide particles used in supercapacitors is slightly overestimated. It has been reported that a surface area increase of 75 to 100% in solid to hollow structures can lead to 75 to 100% increase in the specific capacitance.³⁷ But a similar increase in surface area of a given metal oxide, with a different solid morphology, does not lead to such enhancement in specific capacitance.³⁸ Therefore, there must be additional underlying reasons that drive this increased electrochemical performance. The result discussed below shows that the hollow structure can behave like a pseudo-2-D structure, which leads to their higher performance. The formation of the hollow structures, as an extended form of layered structure, can be explained by using molecular dynamics. The details of coding and energy minimization procedure used during the assembling of hollow particles are described in the ESI.†Scheme 1(a)–(d) show the simulated structures of the hollow CeO₂. Scheme 1(e) shows the hollow structure with one side opening and Scheme 1(f) shows the hollow structures with two side openings, simulated by LAMMPS. During the simulation, the lattice parameters obtained from XRD analysis were utilized to construct the building blocks. Here the lattice parameters for the nanosphere were a = b = c = 5.425 Å.

Scheme 1 (a) Half sphere is constructed, (b) 3-D view of Scheme 1(a), (c) two halves of the sphere, (d) a whole spherical structure of CeO₂, (e) sphere with one side opening, and (f) CeO₂ sphere with two side opening.

It can be seen that a part of the surface on the hollow structure can be taken as the 2-D structure, as depicted in Scheme 2(a). By considering the thickness of the sphere to be small, these structures can be considered as a pseudo-2-D structure. With the curvature of the spherical surface tending towards zero, these structures can also be taken as a planar 2-D structure. From the outside, it looks like a solid sphere but, from inside, it will be a curved 2-D structure, and hence it can be called a pseudo-2-D structure. The term pseudo is used because the structure is closed from the outer side and is not a real 2-D structure. Mathematically, it is already known that hollow surfaces, with thin boundaries, simulate a 2-D layered structure.

Scheme 2 (a) Visualizing the hollow structure with LAMMPS, (b) the molecular contribution towards electrochemical performance in solid, hollow and planar CeO₂, and (c) interparticle channel formed by three hollow structures.

Duan et al. proposed that the triangular channel among three hollow spheres is important for transportation and diffusion.³⁹ On simulating hollow spherical particles and bringing them together to obtain a dense material, an interesting feature manifested itself. This was the stabilization of the channels between the particles. Scheme 2(c) shows the three-particle attachment forming a channel for ion diffusion. Such stable channels are quite useful for electrolyte or fluid flow.

The cross-sectional area of these channels was calculated, by considering homogeneous particle size and distribution:

Area of the channel = blank triangular area – area of the spherical sections.

Part of the sphere = 3 × Area of each part circle = half of a sphere.

Here, we have considered that all the particles have the same size, i.e.

where S is the area of the channel (shaded in black), and d is the outer diameter of the hollow sphere (taking the radius as 200 nm from the TEM image). The calculated channel area = 1620 nm². This would facilitate faster and higher ion diffusion. This can be proven by further calculations and estimating the diffusion coefficient in the hollow structure and comparing the value with that obtained using solid structures.

3.2 (a) Diffusion parameter calculation

According to the Randles–Sevcik equation, the CV peak current (I_p) is directly proportional to the analyte concentration C, as described by the following simplified equation:⁴⁰
where n, F, A, D, ν, R, and T denote the number of electrons involved in the reaction of the redox couple, Faraday's constant (96 485 C mol⁻¹), the active surface area of the electrode, diffusion coefficient, scan rate, the universal gas constant (8.314 J mol⁻¹ K) and the absolute temperature (K), respectively. From the slope of the I_pvs. ν^1/2 graphs shown in Fig. S10(a and b) (ESI†), the diffusion coefficients of the hollow and solid CeO₂ electrodes were calculated in 3 M KOH electrolyte. The estimated diffusion coefficients were 1.17 × 10⁻¹¹ and 0.24 × 10⁻¹¹ cm² s⁻¹ for hollow and solid CeO₂ nanostructures, respectively. It is clear that the hollow particle-based material had ∼5 fold increment in the diffusion coefficient value as shown in Fig. S11(a and b) (ESI†). Higher diffusion also ensures higher charge storage. These results were corroborated by the zeta potential data shown in Fig. S5 (ESI†). The zeta potential values were estimated as −3.81 and 1.97 mV, for hollow and solid CeO₂, respectively.

The higher performance can also be correlated with the accessible number of atoms/particles, which take part in the redox activities. Calculating the number of atoms on the surface will further prove the importance of these pseudo 2-D structures as they may have similar numbers of atoms taking part in the redox activity as they are in a similar sized 2-D structure. Considering a sphere of radius 6 nm, the number of atoms associated with the structures would be 33 401 and 8896 in solid and hollow structures, respectively. The calculation details are given in the ESI.† Among these atoms, the number of Ce atoms present could be estimated. The number of Ce atoms present would be 11 133 and 2965 in solid and hollow structures, respectively. But, effectively, the number of atoms taking part in redox activity would be 2931 and [A(2931) + B(2615)] = 5546, in solid and hollow spheres, respectively. This means that the hollow particle would not only be lighter but also ensure more number of atoms taking part in the redox activity. Additionally, one can ask: what is the effective ratio of the atoms participating in an electrochemical reaction in these particles? Normal electrodes are made of 1 mg cm⁻² mass loading. From this, if we calculate the number of atoms, we can see that the 6 nm hollow CeO₂ particle has 4 times higher Ce atoms in the electrode. This is shown in Scheme 2(b). The ratio will increase if the sphere size increases.

3.3 Electrochemical characterization of CeO₂

The electrochemical performance of hollow CeO₂ nanospheres, which could be considered as a pseudo-2-D structure, and solid CeO₂ nanoparticles is discussed below. Initially, the three electrode measurements were performed in 3 M KOH electrolyte, within a stable potential window of 0.6 V (from −0.3 to 0.3 V). The electrochemical performance of hollow and solid CeO₂ was also investigated in acidic electrolyte, i.e. 1 M H₂SO₄. The corresponding results are given in the ESI† (Fig. S26). The active mass of the materials was kept at ∼1 mg cm⁻², in both cases. Fig. 3(a) and (b) depict the CV profiles, as a function of scan rate. The redox peaks were visible in the CV curves, confirming the pseudocapacitive nature of CeO₂. The charge storage mechanism of CeO₂ based nanostructures in aqueous KOH depends on two mechanisms: (i) surface adsorption/desorption of K⁺ ions and (ii) intercalation/de-intercalation of K⁺ ions on the surface of the hollow CeO₂ structure. It can be represented as:⁴¹

Non-faradaic: (CeO₂)_Surface + K⁺ ↔ (CeO₂K⁺)_Surface

Faradaic: CeO₂ +e⁻ + H₂O → Ce³⁺OOH + OH⁻

Ce³⁺OOH +e⁻ + OH⁻ → CeO₂ + H₂O

Fig. 3 (a and b) CV profiles, (c) charge accumulated and (d) specific capacitance variation with the scan rate in CeO₂ hollow nanospheres and CeO₂ solid nanoparticles.

The K⁺ ions have a smaller solvation radius and higher mobility in the electrolyte solution. Therefore, it gives better insertion/de-insertion capability. The shape of the CV curves for both the hollow and solid CeO₂ based electrodes, measured at different scan rates, indicated the pseudocapacitance nature. In the electrolyte solution, the hollow and solid CeO₂ electrodes received K⁺ electrolyte ions on their surface leading to oxidation. The formula used to determine the specific capacitance from the CV profiles is given in Fig. S12 (ESI†). The estimated specific capacitance, using CV measurement, is given in Fig. 3(d). The maximum specific capacitances of the hollow and solid CeO₂ at 5 mV s⁻¹ scan rate were 58 and 19 F g⁻¹, respectively. The specific capacitance values decreased with increasing scan rate, as shown in Fig. 3(d). The much higher specific capacitance in hollow CeO₂ contributed to all the inferences that were mentioned earlier. The high performance hollow CeO₂ would be useful as it would provide a higher number of redox active atoms to take part in the reaction, improved electrolyte diffusion, formation of an enhanced number of double layers, and higher surface charge.

From the Randles–Sevcik equation, the redox peak current was calculated and its linear relationship with the square root of the scan rate is shown in Fig. S10 (ESI†) for both the electrode materials. The linear relationship suggests that the electrode surface reactions, at all scan rates, were diffusion-controlled. The redox peaks involved K⁺ ion diffusion from the electrolyte to the electrode surface during the reduction and oxidation processes. The active sites of the material perform a crucial role in the determination of the voltammetric charge. Again, the active site directly depends on the surface area of the coated material. The voltammetric charge (q*) was calculated using the following equation:⁴²

where, s, I, V and A denote the scan rate, voltammetric current (mA), potential (mV) and geometric area of the electrode (cm²), respectively. Additionally, q* can be expressed as:

q* = q₀ + s^−1/2

where, q₀ is the charge measured by the double layer and s is the scan rate. Fig. 3(c) depicts the q* vs. s^−1/2 curve for hollow CeO₂. The curve indicated that the adsorbed charges on the surface of the electrode were decreasing with increasing scan rate. This type of curve has also been observed in other metal oxides, showing pseudocapacitive behaviour, such as RuO₂, IrO₂, etc.⁴³ The enhancement in the adsorption of charges on the electrode surface leads to a higher number of ions interacting with active sites of the electrode material. This result was a convoluted picture of the contribution from double-layer capacitance and pseudocapacitance. In this case, the adsorbed charge was ∼46 mC cm⁻² and ∼15 mC cm⁻² for hollow and solid CeO₂, respectively, at 5 mV s⁻¹ scan rate. This once again indicated that the hollow CeO₂ electrode has a high number of active sites, which increases the surface adsorption capacity, leading to enhanced electrochemical performance. The galvanostatic charge–discharge curves of hollow and solid CeO₂ electrodes at different current densities are shown in Fig. 4(a) and (b). The maximum specific capacitances of hollow and solid CeO₂ were estimated to be 166 and 63 F g⁻¹, respectively, at 1 A g⁻¹ current density. The formula to calculate the specific capacitance from the CD profiles is given in the ESI.† The variation of specific capacitance value with increasing current density is shown in Fig. 4(c). The contribution of surface and diffusion capacitance for both CeO₂ using Dunn's method is shown in Fig. S13(a)–(e) (ESI†).

Fig. 4 (a and b) CD profiles, (c) specific capacitance from the CD profile and (d) cycling data of CeO₂ hollow and solid nanoparticles.

The conductivity of both nanostructures was measured using a two-probe approach. As shown in Fig. S14 (ESI†), the conductivity of the hollow CeO₂ was observed to be ∼3.31 × 10⁻³ Ω⁻¹ cm⁻¹, while the solid structure had a conductivity of ∼2.82 × 10⁻³ Ω⁻¹ cm⁻¹. The higher surface area and porosity of hollow CeO₂ could be related to its higher specific capacitance.⁴⁴ The high surface area and microporous structure of the hollow nanospheres would generate more active sites in the electrode material, allowing more K⁺ ions to diffuse through the electrode–electrolyte interface.⁴⁵

Another important parameter of any charge storage device for practical application is its cycling stability. Fig. 4(d) shows the cycling performance of both CeO₂ based nanostructures. The materials were subjected to repetitive charging and discharging at a constant current density of 2 A g⁻¹ in the potential range of −0.3 to 0.3 V for 3000 cycles. Primarily, capacitance degradation was observed after 2000 cycles. After 3000 cycles, the specific capacitance value was ∼91% for the hollow structure and ∼86% for the solid material.

The Coulombic efficiency was calculated by using the equation:

where η is the Coulombic efficiency (%), and t_d and t_c are the discharging and charging time, respectively. The nearly triangular charge–discharge profiles were found to give a Coulombic efficiency of ∼88% and ∼76% for hollow and solid structures, respectively, at 5 A g⁻¹ current density, as shown in Fig. S15 (ESI†). The Coulombic efficiency at other current densities is given in Table S7 (ESI†).

3.3. (a) Mechanism behind the enhancement of capacitance in pseudo 2-D-hollow nanostructures

The major reasons leading to higher performance in pseudo 2-D-nanostructures are mentioned below:

(a) The high surface area of hollow CeO₂ would lead to higher redox activity.

(b) The opening of the cavity makes the inner surface of the particle accessible to the incoming ions, which increases the net charge collection at the electrodes.

(c) Hollow CeO₂ spheres provide a lower diffusion coefficient, which reduces hindrance to the incoming solvated ions for accessing the interior surface of the core.

(d) The cavity of the hollow spheres also provides a high volume for ion adsorption, which ensures good cycling efficiency to these materials, as reported in some recent reports.

(f) Hollow structures will be able to compensate for volume charges as a function of internal heating during cycling.

These are schematically shown in Scheme 3. For solid structures, the surface facing the electrolyte will only accommodate the charges to collect near its surface. When these solid structures are converted to hollow structures, then the interior of the hollow structures, as well as some part of the exterior, will store charges.

Scheme 3 Charge storage mechanism of the (a) bulk material, (b) 2-D material and (c) hollow material (porous 2-D).

3.4. Combining real 2-D structures with pseudo 2-D nanostructures

It is clear that hollow CeO₂ can deliver performance as a 2-D structure. As mentioned earlier, hybrid type supercapacitors are able to deliver high specific capacitance, energy and power density. Therefore, using a carbon-based counter electrode would be the way forward. Generally, activated carbon-based electrodes are used, as these particles have much higher specific capacitance. Over the last few decades, ever since the discovery of graphene or graphitic carbon-based layered structures, their use as a counter electrode has gained immense popularity. Even though these 2-D structures may have lower surface area than activated carbon, improved channels and electrolyte intercalation leads to high redox activity, which ensures higher specific capacitance. Combining pseudo 2-D metal oxides with real 2-D carbon structures would be interesting. Therefore, we chose a fast emerging 2-D carbon based material, i.e. graphitic carbon nitride (gC₃N₄). A preliminary study showed that gC₃N₄ has much higher performance than activated carbon, as given in the ESI.† The electrochemical measurement showed that gC₃N₄ had a specific capacitance of 32 F g⁻¹, while activated carbon achieved 22 F g⁻¹ at the same scan rate of 10 mV s⁻¹ in 3 M KOH, as shown in Table 1. The pseudocapacitance behaviour of 2-D-gC₃N₄ could be attributed to the tris-triazine unit connected with planar amino groups in each layer. The weak van der Waals force of the amino group acts between the layers, which enhances the specific capacitance.⁴⁶

Table 1 Comparison table of 2-D-gC₃N₄ and activated carbon

Material	Specific surface area (m^2 g^−1)	Specific capacitance (F g^−1)
		Scan rate (10 mV s^−1)	Current density (1 A g^−1)
Activated Carbon	71	22	35
2-D-gC3N4	20.15	32	46

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The formation of a 2-D-layered structure of graphitic carbon nitride is discernible from the formation of the tris-triazine structure, confirmed by the XRD data shown in Fig. S16(a) (ESI†). The formation of particles with a layered structure could be easily inferred by examining the AFM, SEM and TEM pictures, respectively, shown in Fig. S16(b)–(d) (ESI†). The FTIR result is shown in Fig. S17 (ESI†). The C and N element present in the 2-D graphite carbon nitrate structure was confirmed by EDX analysis, as shown in Fig. S18 (ESI†).

The electrochemical performance of 2-D-gC₃N₄ was investigated in the potential range from 0.0 to −1.0 V (vs. Ag/AgCl) at different scan rates and current densities, in 3 M KOH. The corresponding findings are shown in Fig. S19(a) and (b) (ESI†), respectively. The specific capacitance was calculated from the CV and CD curves, and their variation with the scan rate and current density is shown in Fig. S19(c) and (d) (ESI†). The detailed discussion regarding the electrochemical performance of 2-D-gC₃N₄ is given in the ESI.†

Asymmetric supercapacitors were fabricated with CeO₂ nanostructure as the positive electrode and 2-D graphite carbon nitride as the negative electrode. Before fabricating the device, the required weight ratio of the materials was calculated, which would ensure the essential charge balanced condition. The desired mass ratio was calculated using the following mass-balance relations:

q₊ = C₊ × V₊ × m₊

q₋ = C₋ × V₋ × m₋

where, q₊ and q₋ are the charge stored, m₊ and m₋ are the mass, and C₊ and C₋ are the capacitance value of the positive and negative electrodes at the same scan rate. V₊ and V₋ denote the potential window of the positive and negative electrode material, respectively. For the present case, the required mass ratio of the positive and negative electrode was obtained as ∼1.2. The fabricated asymmetric device was found to achieve a stable potential window of 1.3 V, as shown in Fig. 5(a) and (b). The electrochemical results of the asymmetric device of solid CeO₂‖gC₃N₄ are depicted in Fig. S24(a) and (b) (ESI†). The electrochemical performance of the hollow CeO₂‖gC₃N₄ device was analysed using CV curves within the above-mentioned potential window, at scan rates ranging from 10 to 100 mV s⁻¹. The device showed nearly rectangular CV profiles, with the expected redox peaks, as shown in Fig. 5(c). This indicated a synergistic combination of pseudocapacitance and EDLC behaviour. The shape of the CV curves did not change with increasing cell voltage or by increasing scan rates. It was clear that there was no O₂ or H₂ evolution within this optimized potential window. The device was also characterized using CD measurements. The obtained specific capacitance using CV data analysis is given in Table S6 (ESI†). The specific capacitance calculated for the asymmetric device using a hollow and solid CeO₂‖gC₃N₄ combination, from CV analysis, is listed in Table S6 (ESI†). Fig. 5(d) depicts the charge–discharge profiles of the device at different current densities. The variation of specific capacitance with both scan rate and current density is shown in Fig. 6(a) and (b), respectively. The specific capacitances from CD for the asymmetric devices using solid and hollow structures are given in Table 2. The asymmetric devices fabricated using 1 M H₂SO₄ were also electrochemically investigated and they showed a stable potential window of 1.5 V, as shown in Fig. S27 (ESI†). The corresponding CD profiles and Ragone plots are given in Fig. S28 (ESI†).

Fig. 5 (a) Window comparison at fixed scan rate, (b) window optimization, (c) CV and (d) CD profiles of the hollow CeO₂‖gC₃N₄ asymmetric device.

Fig. 6 Specific capacitance from (a) CV and (b) CD, (c) Nyquist plot and (d) Ragone plot of hollow CeO₂‖gC₃N₄ and solid CeO₂‖gC₃N₄ devices.

Table 2 Specific capacitance of the hollow and solid CeO₂‖gC₃N₄ device from CD

Current density (A g^−1)	Specific capacitance (F g^−1)
	Hollow CeO2‖gC3N4	Solid CeO2‖gC3N4
1	60	28
2	52	26
3	45	15
5	33	10
7.5	24	07

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The equivalent series resistance (ESR) was calculated using the following formula:^47,48

where V is the voltage drop at the start of the discharge cycle and I is the corresponding current in ampere. The calculated equivalent series resistance was found to be ∼0.4 Ω cm⁻², at 1 A g⁻¹ current density, for hollow CeO₂‖gC₃N₄, as shown in Fig. S24(d) (ESI†). The Nyquist plot of the hollow and solid CeO₂‖gC₃N₄ device is shown in Fig. 6(c). The Nyquist plot consisted of two distinct regions, separated with a semi-circular region (high frequency) and straight-line along with an imaginary axis region (low frequency). The semicircle represents the charge transfer resistance (R_ct), which was estimated as ∼2.3 and 8.5 Ω for the hollow and solid CeO₂‖gC₃N₄ devices, respectively. The lower charge transfer resistance could be attributed to the enhanced diffusive resistance of negative ions at the porous electrode. The straight line (low-frequency region) was more towards the imaginary axis, indicating good capacitive behaviour in the hollow CeO₂‖gC₃N₄ device. The corresponding Bode plots of both the devices are shown in Fig. S29 (ESI†).

As mentioned earlier, cycling stability is one of the important parameters for practical application of supercapacitors. The cycling stability of both the fabricated devices was measured up to 3000 cycles at 2 A g⁻¹ current density and the results are given in Fig. S20(c) (ESI†). The capacitance retention after 3000 cycles was ∼96.15% for the hollow CeO₂‖gC₃N₄ device and ∼88.4% for the solid CeO₂‖gC₃N₄ device, indicating excellent cycling stability. The corresponding physicochemical characterization of the electrode after the cycling stability test is shown in Fig. S25 (ESI†).

It is now well-known that supercapacitor devices are popular because of their good balance between energy and power density. The energy density and the power density of the solid and hollow CeO₂‖gC₃N₄ devices were calculated using the following equations:

where E is the energy density (W h kg⁻¹); C is the specific capacitance (F g⁻¹); V is the voltage window (V) and P is the power density (W kg⁻¹). The fabricated hollow CeO₂‖gC₃N₄ device exhibited an excellent energy density of ∼14.33 W h kg⁻¹ along with a power density of ∼700 W kg⁻¹, whereas the solid CeO₂‖gC₃N₄ device showed an energy density of ∼6.67 W h kg⁻¹ along with a power density of ∼505 W kg⁻¹ at 1 A g⁻¹ current density, as shown in Fig. 6(d). The high energy density obtained at the higher current density is reported for the first time for a hollow CeO₂ based supercapacitor, as shown in Table 3. The excellent performance of this device could therefore be directly linked to the use of the hollow nanostructure.

Table 3 Comparison of supercapacitor performance of different CeO₂-based nanostructures

Material (current collector)	Specific capacitance (F g^−1)	Electrolyte	Device	Energy density (W h kg^−1)	Power density (kW kg^−1)	Ref.
CeO2 nanorod (Ni Foam)	154	2 M KOH	CeO2‖AC	5.83	0.75	49
CeO2 nanoparticle/graphene composite (Ni Foam)	208	3 M KOH	—	—	18	29
Nano CeO2/AC composite (carbon paper)	162	1 M HCl	CeO2/AC‖AC	4.86	3.5	50
CeO2 nanoparticle (Ni foam)	78.5	6 M KOH	—	—	—	51
Hollow CeO2-MWCNT (Ni foam)	450	6 M KOH	Hollow CeO2-MWCNT‖AC	26.2	10.6
Porous CeO2 (Ni foam)	135	1 M KOH	—	—	—	52
CeO2 nanoparticle (Ni foam)	98	3 M KOH	—	—	—	53
CeO2 nanorod (Ni foam)	162
CeO2 nanocube (Ni foam)	149
Hollow CeO2 (graphite sheet)	166	3 M KOH	Hollow CeO2‖2-D-gC3N4	14.33	0.70	Present work

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4. Conclusions

It is clearly shown that hollow particles can actually be considered as pseudo 2-D type structures. It is not only their higher specific area that leads to higher electrochemical performance. In reality, the improvement is driven by additional factors that involve stabilization of layered type characteristics but with stable channels for ion diffusion. This improves ion interaction with the solid and induces improvement in both EDLC and pseudocapacitance. Contrary to most results, it is shown that rare earth element-based oxides can also become useful for energy storage devices, provided their particles with hollow morphologies are used. Consistent explanations are based on corroborating theory and experimentally obtained results. The importance of combining pseudo 2-D nanostructures of metal oxides with real 2-D carbon-based materials to develop hybrid supercapacitors is unequivocally established. The fabricated asymmetric supercapacitors using hollow CeO₂ and gC₃N₄ as positive and negative electrodes, would deliver maximum specific capacitance of ∼60 F g⁻¹ at 1 A g⁻¹ current density, with an excellent energy density of ∼14.20 W h kg⁻¹ and power density of 700 W kg⁻¹.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The authors acknowledge the funding received from DST (India) under its MES scheme for the project entitled, “Hierarchically nanostructured energy materials for next-generation Na-ion based energy storage technologies and their use in renewable energy systems” (Grant No. DST/TMD/MES/2k16/77).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d2ma00366j

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