Lanthanum-Doped Co₃O₄ Nanocubes Synthesized via Hydrothermal Method for High-Performance Supercapacitors

Abstract

The development of high-performance supercapacitor electrodes is crucial to meet the increasing demand for efficient and sustainable energy storage systems. Cobalt oxide (Co₃O₄), with its high theoretical capacitance, is a promising electrode material, but its practical application is hindered by poor conductivity limitations and structural instability during cycling. In this work, lanthanum La³⁺-doped Co₃O₄ nanocubes were synthesized via a hydrothermal approach to tailor their structural and electrochemical properties. Different doping concentrations (1, 3, and 5%) were introduced to investigate their influence systematically. X-ray diffraction confirmed the retention of the spinel phase with clear evidence of La³⁺ incorporation into the Co₃O₄ lattice. Also, Raman spectroscopy validated the structural integrity through characteristic Co-O vibrational modes. Scanning electron microscopy analysis revealed uniform cubic morphologies across all samples. The formation of the cubic spinel structure of 1% La³⁺-doped Co₃O₄ are confirmed from XPS and TEM studies. Electrochemical evaluation in a 3 M KOH electrolyte demonstrated that 1% La³⁺-doped Co₃O₄ nanocubes delivered the highest performance, achieving a specific capacitance of 1312 F g⁻¹ at 1 A g⁻¹ and maintaining a 79.8% capacitance retention and a 97.12% Coulombic efficiency over 10,000 cycles at 5 Ag⁻¹. It can be demonstrated that La³⁺ doping is an effective strategy to enhance the charge storage capability and cycling stability of Co₃O₄, offering valuable insights for the rational design of next-generation supercapacitor electrodes.

1. Introduction

The rising global demand for energy, coupled with growing environmental concerns, has placed immense pressure on the search for efficient, sustainable, and environmentally benign energy storage technologies. The depletion of fossil fuel reserves and the release of greenhouse gases are exacerbating these challenges, thereby intensifying research into alternative electrochemical systems for energy storage and conversion [1,2,3]. Among the wide range of candidates, including capacitors, batteries, and fuel cells, supercapacitors have emerged as a promising class of devices. They bridge the performance gap between traditional capacitors and batteries by offering both high power density and relatively high energy density. The performance of supercapacitors strongly depends on both material and operational factors, including the electrode–electrolyte interface, electrical contact with the current collector, operating temperature, and the applied current [4,5]. In recent decades, they have attracted considerable attention due to their advantageous features, including fast charge–discharge kinetics, high Coulombic efficiency, long cycle life, and cost-effective fabrication. Based on their charge storage mechanisms, supercapacitors are broadly categorized as: (i) electric double-layer capacitors (EDLCs), which rely on carbon-based nanostructures such as activated carbon, graphene, and carbon nanotubes, and (ii) pseudocapacitors, which utilize transition-metal oxides (TMOs) such as RuO₂, NiO, Fe₃O₄, Mn₃O₄, V₂O₅, and Co₃O₄ materials to store charge through rapid and reversible Faradaic reactions [6,7,8,9,10,11,12].

Co₃O₄ nanoparticles have garnered considerable research interest among metal oxide nanoparticles due to their affordability and superior electroactivity. Co₃O₄ being a transition metal oxide, can display various oxidation states (Co²⁺, Co³⁺, and Co⁴⁺), enhancing its complex redox chemistry. Co₃O₄ is a multifunctional, antiferromagnitic p-type semiconductor characterized by a spinel crystal structure. The direct optical band gaps of Co₃O₄ nanoparticles are approximately 1.48 and 2.19 eV, facilitating their applications in several domains including catalysis [13], gas detection [14], water splitting [15], and biological [16] uses. Furthermore, Co₃O₄ has arisen as a viable electrode material for electrochemical energy storage systems, especially supercapacitors, due to its significant theoretical specific capacity of approximately 3560 F g⁻¹ and the availability of numerous redox active sites that promote rapid and reversible faradaic reaction. However, its practical application is hindered by poor intrinsic conductivity, high internal resistance, and a relatively small electroactive surface area, resulting in capacitances that are far below the theoretical value [12,17,18]. To overcome these limitations, two primary strategies have been widely explored: (1) morphology engineering to expose more active sites, and (2) cation doping to improve conductivity and electrochemical activity [19,20]. An assortment of dopants such as Ni, Mn, Fe, Cu, Zn, and Cr has been integrated into the Co₃O₄ lattice to lower resistance and create more redox-active sites [21,22,23,24,25,26,27]. Additionally, Co₃O₄-based composites combined with carbon materials, conducting polymers and other metal compounds significantly improve its electrochemical performance for energy storage applications. For example, Annu et al. summarized that cobalt-based nanocomposite combined with conducting polymers such as polypyrrole (PPy) and polyaniline (PANI) exhibits superior electrochemical performance owing to the synergistic effect of cobalt oxide’s high capacitance and the polymers conductivity and pseudocapacitive behavior, making them promising for use in supercapacitors, batteries, and hybrid devices [28]. Deng et al. incorporated cadmium into porous Co₃O₄ nanosheets through a co-precipitation approach, and the optimized composition with 5% Cd delivered a specific capacitance of 737 F g⁻¹at 1 A g⁻¹, retaining 96% of its capacity after 1000 cycles [29]. Similarly, chromium-doped Co₃O₄ nanoflowers synthesized by Faisal et al. via a hydrothermal method exhibited a maximum capacitance of 1283 F g⁻¹ at 6 at.% Cr and maintained 72.86% of their initial capacitance after 1000 charge–discharge cycles [2]. Aadil et al. reported the growth of mesoporous Ag-doped Co₃O₄ nanosheets on nickel foam, which offered a large surface area (176 m² g⁻¹) and excellent electrochemical properties, including 1425 F g⁻¹at 1 A g⁻¹, 92.84% retention at 10 A g⁻¹, and stable cycling with 96.4% retention over 5000 cycles [30]. Additionally, Ce-doped Co₃O₄ nanoflakes were produced by Faisal et al. via the hydrothermal method and demonstrated an optimal performance at 5.0 at.% Ce, yielding 1309.6 F g⁻¹ at 5 mV s⁻¹, with 90.86% capacitance retention after 2000 cyclic voltammograms, and a rate capability of 82.87% at 10 A g⁻¹ [31]. Furthermore, Aslam et al. incorporated Ni, Mn, and Zn dopants into Co₃O₄ via a co-precipitation process, where Mn_0.05Co_2.95O₄ exhibited the most promising pseudocapacitive behavior with 80.8 F g⁻¹ at 1 A g⁻¹ along with excellent cycling stability [32].

More recently, rare earth metal doping (La, Nd, Gd, and Sm) has been investigated as a promising approach to further enhance the electrical conductivity and supercapacitor performance of Co₃O₄ [33]. In particular, Sm-doped Co₃O₄ electrodes exhibited excellent performance with a capacitance retention of 93.18%. The high ionic radii and strong complexation ability of rare earth ions can induce lattice distortion, resulting in smaller crystallite sizes, enhanced electrical conductivity, and reduced charge transfer resistance. Specifically, La³⁺ ions (with an ionic radius of 1.16 Å) exhibit a strong affinity for oxygen-containing functional groups, which stabilizes the surface structure and enhances electrical conductivity when incorporated into the Co₃O₄ [34]. In addition, various synthesis strategies have been explored for the fabrication of nanostructured Co₃O₄, including sol–gel, spray pyrolysis, chemical deposition, solvothermal, co-precipitation, and hydrothermal processes. Among these, the hydrothermal method stands out due to its simplicity, scalability, and precise control over morphology through reaction parameters (temperature, duration, precursor concentration) [34,35,36,37,38,39,40,41].

Therefore, in this study, La-doped Co₃O₄ nanocubes were synthesized via a facile hydrothermal method with varying La concentrations (1–5 mol%). The impact of La doping on the structural, morphological, and electrochemical properties was systematically evaluated. The results demonstrate that incorporating 1 mol% La significantly enhances the electrochemical performance, establishing La-doped Co₃O₄ as a highly promising electrode material for next-generation supercapacitor applications.

2. Materials and Methods

2.1. Chemical Materials

All chemicals and solvents used in this work were of reagent grade and employed without further purification. Cobalt (II) nitrate hexahydrate (Co(NO₃)₂·6H₂O), lanthanum (III) nitrate hexahydrate (La(NO₃)₃·6H₂O, 99.99%), and polyvinylidene fluoride (PVDF) were purchased from Sigma-Aldrich (Saint-Louis, MS, USA). Potassium hydroxide (KOH) pellets were obtained from Molychem. Additional materials included deionized (DI) water, ethanol (99.5%), activated carbon, and N-Methyl-2-pyrrolidone (NMP).

2.2. Preparation of Lanthanum-Doped Co₃O₄ Nanoparticles

Lanthanum-doped Co₃O₄ nanoparticles were synthesized via a hydrothermal method, as illustrated in Figure 1. Solution A was prepared by dissolving 1 mol L⁻¹ Co(NO₃)₂·6H₂O in 20 mL of DI water under constant stirring. Lanthanum nitrate was added in molar ratios of 1%, 3%, and 5% with respect to Co²⁺ ions, and the solution was until complete dissolution. Separately, solution B was prepared by dissolving 1 mol L⁻¹ KOH in 20 mL of DI water. The solution was subsequently added drop wise to solution A while continuously stirring to achieve a homogenous mixture, with the pH of the combined solution maintained at 9 to ensure regulated nucleation and development of the nanoparticles. The resulting solution was transferred into a 100 mL Teflon-lined stainless-steel autoclave and heated at 200 °C for 24 h. After cooling to room temperature. The precipitated was collected, washed four times with ethanol and deionized water in order to remove impurities, and afterwards dried at 80 °C for 12 h. The dried powder was then calcinated at 400 °C for 4 h, utilizing a controlled heating rate of 3 °C min⁻¹. The final products were labeled as 1%, 3%, and 5% La-Co₃O₄, reflecting the different lanthanum contents.

2.3. Methods

The microstructural properties of the Co₃O₄ nanocubes were characterized by X-ray diffraction (XRD, Miniflex600, Rigaku, Tokyo, Japan) using CuK_α radiation (λ = 1.5406 Å) as X-ray source. Surface morphology was examined using a field emission scanning electron microscope (FESEM) (Carl Ziess, Jena, Germany) and a high-resolution transmission electron microscope (HR-TEM JEM-2100, JEOL, Tokyo, Japan). Raman spectroscopy (Renishaw, Wottenunder-Edge, UK) equipped with a 532 nm excitation laser (power of 50 mW) was employed to analyze the vibrational modes and to confirm the phase purity of the samples. The valance state and the elemental composition were analyzed with X-ray photoelectron spectroscopy (XPS, Kratos AXIS-Nova, Shimadzu, Tokyo, Japan).

The electrochemical performance of the prepared cobalt oxide electrodes was evaluated in a 3 mol L⁻¹ KOH aqueous electrolyte within a voltage range of 0.0 to 0.5 V at room temperature, using a CHI 608C electrochemical workstation (CH Instruments Inc., Austin, TX, USA) in a three-electrode glass cell. The working electrode was prepared by combining 80 wt.% active material, 10 wt.% PVDF, and 10 wt.% carbon black. After grinding these components for 3 h, a small amount of NMP solution was added to form a smooth slurry. Cleaned nickel foam pieces (1.5 cm²) were coated with the slurry through a drop-casting technique and dried overnight at 100 °C. For electrode preparation, commercial nickel foam sheets were cut into 1.5 cm × 1 cm pieces. Some foam pieces were immersed in 3 mol L⁻¹ hydrochloric acid and then sonicated for 15 min to remove any residual hydrocarbons on the surface. The cleaned foams were then rinsed with deionized water and ethanol in an ultrasonic bath and dried in a vacuum oven for later use. The electrode mass loading was ~2 mg cm⁻². The Ag/AgCl and a platinum strip were used as reference and counter electrodes, respectively.

3. Results and Discussion

3.1. Structure

Figure 2a presents the XRD patterns of pure and La-doped Co₃O₄ nanocubes with varying La contents (1, 3, and 5 mol%). The diffraction peaks of pristine Co₃O₄ sample are well indexed to the cubic spinel phase (JCPDS No. 00-042-1467), corresponding to the (111), (220), (311), (222), (400), (422), (511), (440), (531), (620), (533), and (622) planes. This confirms the formation of a single-phase spinel structure with a space group of Fd3m [42]. The absence of additional peaks further indicates the high phase purity of the samples. For the La-doped samples, no reflections corresponding to La-based secondary phases (e.g., La₂O₃ or LaCoO₃) were observed, suggesting successful substitution of La³⁺ into the Co₃O₄ lattice or the presence of amorphous La species below the detection limit of XRD. However, slight peak shifts, variations in relative intensities, and changes in peak broadness reveal structural modifications induced by lanthanum incorporation (Figure 2b).

At the 1 mol% La doping level, the (311) reflection exhibits slight broadening and enhanced intensity compared to the undoped sample. This is attributed to the lattice distortion and microstrain resulting from the substitution of Co³⁺ (ionic radius ~0.545 Å) with larger La³⁺ ions (ionic radius ~1.16 Å). The size mismatch introduces internal strain and crystallographic defects such as dislocations and vacancies. Increasing the La concentration to 3 mol% further broadens the peaks and decreases their intensity, implying a higher density of defects and microstrain, possibly due to excessive La incorporation that disrupts the spinel structure and limits crystallite growth. Interestingly, at 5 mol% La doping, the (311) peak becomes sharper and more intense than those of the 1% and 3% doped samples. This suggests partial recovery of crystallinity, likely due to saturation of La³⁺ solubility in the spinel lattice. At this level, La³⁺ ions may segregate toward grain boundaries or form amorphous La-rich domains undetectable by XRD, thereby relieving lattice strain and allowing coherent crystal growth, particularly along the (311) orientation.

The crystallite size (D) was estimated using Debye–Scherrer′s equation [43]

$$D={\displaystyle \frac{0.94\lambda }{\beta cos\theta }}$$

(1)

where λ is the X-ray wavelength (1.5406 Å for Cu K_α), β is the full width at half maximum (FWHM) in radians, and θ is the Bragg angle of the (311) planes. The dislocation density (δ) and microstrain (ε) were calculated using the relations [44,45]

$$\delta ={\displaystyle \frac{1}{D^2}},$$

(2a)

$$\epsilon ={\displaystyle \frac{\beta }{4\tan \theta }}.$$

(2b)

The calculated values are summarized in

Table 1. Crystallite size, dislocation density, and microstrain of the pristine and La-doped (1–5%) Co₃O₄ samples.

Sample	Crystallite Size (nm)	Dislocation Density (Lines/m2)	Microstrain (rd)
pristine	30.6	1.060 × 1015	0.0033
1% La-Co3O4	32.4	0.954 × 1015	0.0036
3% La-Co3O4	17.5	3.273 × 1015	0.0066
5% La-Co3O4	38.0	0.692 × 1015	0.0030

. Pristine Co₃O₄exhibits a crystallite size of 30.6 nm. At the 1% La-doping content, the size slightly increases to 32.4 nm, which may result from slight lattice expansion due to the limited La³⁺ substitution into the Co₃O₄ lattice. At the 3% La-doping level, the crystallite size decreases sharply to 17.5 nm, accompanied by a notable increase in dislocation density and microstrain, which confirms a greater degree of structural disorder. In contrast, at the 5% La-doping content, the crystallite size increases to 38.0 nm with a decrease in microstrain, consistent with a La segregation and a partial strain relaxation at high doping levels.

The Raman spectra (Figure 3) of pristine and La-doped Co₃O₄ nanocubes exhibit five Raman-active modes at 194, 478.5, 520.1, 616.5, and 684.6 cm⁻¹, corresponding to the F_2g, E_g, F_2g, F_2g, and A_1g phonon modes, respectively. These are in good agreement with the reported Raman modes of Co₃O₄. The band at 194 cm⁻¹ arises from the translational vibration of Co²⁺–O²⁻ at tetrahedral sites, while the 684.6 cm⁻¹ band corresponds to the symmetric stretching vibration of Co³⁺–O²⁻ in CoO₆octahedra. The bands at 478.5, 520.1, and 616.5 cm⁻¹ are associated with bending and stretching modes of Co–O bonds in octahedral sites. Slight shifts in peak positions with increasing La doping suggest lattice distortion and particle size effects. Notably, no Raman peaks attributed to La-based phases were detected, supporting the XRD results [46,47,48].

3.2. XPS Analysis

The surface chemical states of the 1 mol% La-doped Co₃O₄nanocubes were investigated using XPS experiments (Figure 4). The survey spectrum (Figure 4a) confirms the presence of Co 2p, O 1s, La 3d, and C 1s peaks, as well as minor Auger features, validating the successful incorporation of La into the cobalt oxide lattice. The high-resolution Co 2p spectrum (Figure 4b) displays two prominent peaks at 779.5 eV (Co 2p_3/2) and 794.6 eV (Co 2p_1/2), along with corresponding shake-up satellites. Deconvolution reveals contributions from both Co³⁺ (779.4 eV and 794.5 eV) and Co²⁺ (780.7 eV and 796.0 eV), confirming the mixed-valence state characteristic of the spinel Co₃O₄ phase. The presence of shake-up satellites further supports this coexistence [46,49]. The O 1s spectrum (Figure 4c) consists of three distinct components at 529.7 eV (lattice oxygen, O_latt), 531.2 eV (surface-adsorbed oxygen species, O_ads), and 532.4 eV (hydroxyl groups or adsorbed water molecules, O_w) [50,51]. The dominance of the O_latt contribution indicates a well-ordered crystalline structure and effective oxygen incorporation within the spinel structure. The high-resolution La 3d spectrum (Figure 4d) reveals a broad spectral profile, deconvoluted into multiple peaks centered at 833.7, 837.7, 840.6, 844.2, and 847.7 eV. These values exhibit slight deviations from the standard binding energies typically associated with La³⁺ (La 3d_5/2 at ~834 eV and La 3d_3/2 at ~851 eV) [52]. The observed shifts and broadening may result from lattice distortions due to the low La doping level, leading to modified local coordination environments around the La ions. Quantitative XPS analysis reveals a surface La atomic percentage of 0.69%, which aligns reasonably well with the intended 1 mol% doping level, considering the surface-sensitive characteristics of XPS. The calculated La/(La + Co) atomic ratio is around 2.85, indicating a slight surface enrichment, a phenomenon commonly observed in metal oxide systems upon doping [53,54]. These results collectively confirm the successful substitution of La³⁺ into the Co₃O₄ lattice, likely occupying Co³⁺ sites and preserving the spinel structure.

3.3. Morphology

The surface morphology of La-doped Co₃O₄ samples was analyzed via field-emission scanning electron microscopy, as shown in Figure 5. All samples exhibit a well-defined cubic-like morphology, typical of spinel Co₃O₄ nanostructures. However, the La doping concentration significantly influences the uniformity and surface texture of the resulting particles. At a low doping level of 1 mol% La (Figure 5a), the particles appear as highly uniform nanocubes with smooth surfaces and sharply defined edges. This morphology suggests a high degree of crystallinity and minimal structural distortion, both of which are beneficial for enhanced electrochemical performance due to increased surface area and improved charge transport pathways. Increasing the La content to 3 mol% (Figure 5b) largely retains the cubic morphology, but noticeable surface roughness and particle aggregation begin to emerge.

This result suggests a partial distortion of the crystal growth process, probably resulting from an excessive La incorporation, which may cause lattice strain or substitutional defects. The morphology of the 5 mol% La-Co₃O₄ sample (Figure 5c) exhibits a trend towards greater irregularity, characterized by less-defined cube structures and rough surfaces. The agglomeration of particles is more pronounced, and the uniformity of the nanostructures is significantly reduced. Such morphological deterioration may hinder electrochemical performance due to reduced active surface area and impaired ion/electron diffusion. These observations suggest that a low level of La doping (1 mol%) is optimal for maintaining a desirable nanocubic morphology and maximizing electrochemical performance. In contrast, higher La concentrations negatively affect particle uniformity and crystallinity, likely due to disruption of the spinel lattice during growth.

The elemental composition of the synthesized 1 mol% La-doped Co₃O₄ sample was analyzed with energy dispersive X-ray spectroscopy (EDS). The EDS spectrum is given as supplementary data in Figure S1 (Supplementary Materials). The presence of cobalt, oxygen, and lanthanum at their respective binding energies confirm a stoichiometric ratio consistent with the spinel Co₃O₄ phase with cobalt (26.59 at.%), oxygen (71.45 at.%) and lanthanum (1.96 at%) present in a stoichiometric ratio consistent with the spinel cobalt oxide (Co₃O₄) phase. The elemental mapping also confirms the uniform distribution of cobalt and oxygen throughout the scanning area of the nanocubes.

High-resolution transmission electron microscopy (HR-TEM) was utilized to examine the nanostructural properties of 1% La-doped Co₃O₄ nanocubes. Figure 6a illustrates a TEM picture that distinctly reveals a well-defined cubic morphology with sharp edges, thereby verifying the successful synthesis of homogeneous nanocubes. The particle size distribution obtained from many TEM images (Figure 6b) reveals an average particle size of approximately 131 nm. The lattice fringes in the HR-TEM image (Figure 6c) display an interplanar spacing of 0.249 nm, corresponding to the (311) plane of 1% La-Co₃O₄. The FFT pattern depicted in Figure 6c further substantiates the crystallinity of the nanocubes and the existence of distinctly resolved lattice planes. The minor increase in interplanar spacing relative to pure Co₃O₄ is due to the integration of bigger La³⁺ ions into the spinel lattice, resulting in localized lattice strain and minor distortions while preserving the overall cubic symmetry. The selected area electron diffraction (SAED) pattern (Figure 6d) exhibits bright spots accompanied by somewhat diffused rings, signifying the well-formed crystalline character of the nanocubes with a preferential orientation along the specific crystallographic axes. The integrated HR-TEM and SAED findings align remarkably with XRD investigations, validating that La doping marginally enlarges the lattice, maintains crystallinity, and does not alter the distinctive cubic shape of Co₃O₄. These structural alterations are anticipated to improve electrochemical characteristics by increasing active sites and enhancing ion transport channels within the nanocubes.

3.4. Electrochemical Properties

The electrochemical properties of La-doped Co₃O₄ electrodes were systematically studied using electrochemical impedance spectroscopy (EIS), cyclic voltammetry (CV), and galvanostatic charge–discharge (GCD) in a three-electrode configuration. The working electrodes consisted of La-doped Co₃O₄ composites with 1%, 3%, and 5% La content, while Ag/AgCl and Pt foil were used as the reference and counter electrodes, respectively. All measurements were carried out in a 3 mol L⁻¹ KOH aqueous electrolyte.

Figure 7a shows the Nyquist plots of the La-doped Co₃O₄ electrodes. Each spectrum features a high-frequency intercept on the real axis, a depressed semicircle in the medium-frequency region, and an inclined line in the low-frequency region. The intercept corresponds to the solution resistance (R_s = 0.24 Ω), which reflects the combined effects of electrolyte, electrode, and contact resistances. The diameter of the semicircle represents the charge-transfer resistance (R_ct) at the electrode/electrolyte interface. At the same time, the inclined line is associated with Warburg impedance, arising from ion diffusion processes within the porous electrode [55]. Among the samples, the 1% La-doped Co₃O₄ electrode shows the smallest semicircle diameter, indicating the lowest R_ct (2.2 Ω) and the most efficient charge-transfer kinetics. This improvement arises from enhanced conductivity and better electronic interactions at low La doping. However, higher doping levels (3% and 5%) increase R_ct, likely due to structural distortions or blockage of electroactive sites caused by excess La incorporation. The inset equivalent circuit model (R_s, R_ct, a constant phase element Q for double-layer capacitance, and a Warburg element W) fits the experimental data well, supporting this interpretation. Overall, the EIS results confirm that 1% La doping achieves the best balance between conductivity and charge transfer, whereas higher doping concentrations degrade the electrochemical pathways. Figure 7b displays the CV profiles of the La-doped Co₃O₄ electrodes recorded at the scan rate of 10 mVs⁻¹ within the potential window of 0 to 0.5 V (vs. Ag/AgCl). All electrodes show pronounced and nearly symmetric anodic and cathodic peaks, corresponding to the reversible Faradaic redox transitions of Co²⁺/Co³⁺ in an alkaline electrolyte according the following relationships [56,57]

$${\mathrm{C}\mathrm{o}}_3{\mathrm{O}}_4+{\mathrm{O}\mathrm{H}}^{-}+{\mathrm{H}}_2\mathrm{O}\leftrightarrow 3\mathrm{C}\mathrm{o}\mathrm{O}\mathrm{O}\mathrm{H}+{\mathrm{e}}^{-},$$

(3)

$$\mathrm{C}\mathrm{o}\mathrm{O}\mathrm{O}\mathrm{H}+{\mathrm{O}\mathrm{H}}^{-}\leftrightarrow {\mathrm{C}\mathrm{o}\mathrm{O}}_2+{\mathrm{H}}_2\mathrm{O}+{\mathrm{e}}^{-}.$$

(4)

The 1% La-doped Co₃O₄ electrode delivers the highest peak currents and integrated CV area, indicating superior redox activity and faster kinetics compared with the 3% and 5% La-doped samples. At higher doping levels (3% La), partial blocking of electroactive sites and lattice distortions hinder the redox processes. Figure 7c–e presents the CV responses of the 1%, 3%, and 5% La-doped Co₃O₄ electrodes at scan rates in the range 1–50 mV s⁻¹. As the scan rate increases, anodic peak potentials shift positively (from 0.26 to 0.35 V for 1% La; 0.30 to 0.39 V for 3% La; and 0.31 to 0.38 V for 5% La), while cathodic peaks shift negatively (from 0.19 to 0.13 V for 1% La, and 0.25 to 0.20 V for 3% and 5% La), consistent with polarization effects and internal resistance contributions [22,58]. Notably, the peak shapes remain well-preserved, indicating rapid electron/ion transport, as well as excellent reversibility. The specific capacitance (C_s) was calculated from the CV curves using the relation [59,60]:

$$C_s=\frac{{\int }_{V_a}^{V_c}I\left(V\right)dV}{mv\Delta V}$$

(5)

where ${\int }_{V_a}^{V_c}I\left(V\right)dV$ is the CV integral area, m is the active mass, v is the scan rate, and ΔV represents the potential window. Results are given in

Table 2. Specific capacitance of La doped Co₃O₄ samples at various scan rates.

Scan Rate (mV s−1)	Specific Capacitance (F g−1)
	1% La-Co3O4	3% La-Co3O4	5% La-Co3O4
1	1355	1011	511
3	985	763	400
5	903	656	372
7	832	602	349
10	732	540	320
30	459	379	233
50	375	308	191

. As shown in Figure 7f and Table 2, the 1% La-doped Co₃O₄ electrode delivers the highest specific capacitance across all scan rates, followed by 3% and 5% La-doped Co₃O₄. A decrease in capacitance is observed with increasing scan rate for all electrodes, attributed to limited ion diffusion into the electrode’s deeper active sites at higher sweep rates [61]. These findings confirm that moderate La doping (approximately 1%) enhances electrochemical performance by promoting conductivity and redox kinetics, while excessive doping limits ion accessibility and compromises structural stability.

The charge–storage mechanism was further analyzed using the power–law relationship [55,62,63]:

$$i_p=a{v}^b,$$

(6)

$${\log i}_p=\mathrm{l}\mathrm{o}\mathrm{g}a+b\log v,$$

(7)

where i_p is the peak current, v is the scan rate, and b reflects the dominant mechanism (0.5—diffusion-controlled; 1.0—capacitive-controlled). The calculated b-values were 0.65 (1% La-Co₃O₄), 0.61 (3% La-Co₃O₄), and 0.75 (5% La-Co₃O₄) (Figure 8a–c), suggesting mixed capacitive- and diffusion-controlled processes in all samples. The contribution percentages are listed in Table S1 (Supplementary Materials file).

The capacitive and diffusion contributions were quantified using:

$$i\left(V\right)=k_{1}v+k_2{v}^{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}},$$

(8)

$$i\left(V\right)v^{{\displaystyle \raisebox{1ex}{$-1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}=k_1{v}^{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}+k_2.$$

(9)

where k₁ν and k₂ν^1/2 represent the capacitive and diffusion-controlled contributions, respectively [59,63]. The capacitive and diffusion-controlled contributions in the electrodes at various scan rates were presented in Figure 8a(ii)–c(ii). This analysis reveals that the overall electrochemical performance of the La-doped Co₃O₄ electrodes is a result of the combined effects of both surface-controlled and diffusion-controlled processes. The relative dominance of these mechanisms varies with scan rate, as illustrated by the contribution plots in Figure 8a(iii)–c(iii). With increasing scan rate, a slight decrease in diffusion-controlled behavior is observed, indicating that surface-controlled redox reactions become more dominant under rapid charge–discharge conditions. The trend suggests that, at higher scan rates, ion intercalation into the bulk electrode is partially restricted due to the limited diffusion time, thereby favoring electrochemical reactions that occur at or near the electrode surface. At 50 mV s⁻¹ scan rate, the capacitive contributions were calculated as 47.44% (1% La-Co₃O₄), 36.67% (3% La-Co₃O₄), and 63.58% (5% La-Co₃O₄). The 1% La-Co₃O₄ electrode demonstrates the most balanced contributions, enabling both rapid surface reflections and efficient ion intercalation.

The potential versus time plots at constant applied currents (GCD curves) were utilized to measure the specific capacitance, rate capability, and cycling stability of the electrodes. Figure 9a–c shows the GCD plots of the 1% La-Co₃O₄, 3% La-Co₃O₄, and 5% La-Co₃O₄ electrodes at current densities ranging from 1 to 5 A g⁻¹ in the potential window of 0 to 0.4 V. The shape of the charge and discharge profiles confirms the high reversible electrochemical behavior. Based on the discharge time (from 0.4 to 0 V), the specific capacitances of the electrodes were calculated by using the following equation [57,60]:

$$C_S={\displaystyle \frac{I∆t}{m∆V}},$$

(10)

where I represents the applied current, Δt denotes the discharge time, m is the active mass of the electrode, and ΔV refers to the potential window. The calculated specific capacitances of the electrode at corresponding current densities are presented in Figure 9d.

Among all electrodes, 1% La-Co₃O₄ exhibited the highest specific capacitances at all current densities, i.e., 1312, 1124, 915, and 804 F g⁻¹ at current densities of 1, 2, 3, and 4 A g⁻¹, respectively. Likewise, 3% La-Co₃O₄ delivered 984, 842, 579, and 420 F g⁻¹, while 5% La-Co₃O₄ shows 474, 379, 308, and 253 F g⁻¹ at the same current densities, respectively. The specific capacitance of all electrodes decreases with increasing applied current densities due to the limitation on the interaction between electrolyte ions and the electrode material at higher current densities. In addition, the cycling stability behavior of the high specific capacitance delivered sample (1%La-doped Co₃O₄) was recorded at 5 A g⁻¹ for 10,000 cycles, as shown in Figure 10. It demonstrates a Coulombic efficiency of 97.12% along with 79.8% capacitance retention even after 10,000 cycles.

The electrochemical properties of the La-doped Co₃O₄ electrodes compare well with those of pristine Co₃O₄ (see Figures S2 and S3 showing CV, GCD, long-term cycling and EIS results).

The structural study shows considerable differences in crystallite size, dislocation density, and microstrain between pristine and La-Co₃O₄ composites. The 3% La-Co₃O₄ sample has the smallest crystallite size (17.5 nm), excellent dislocation density (3.27 × 10¹⁵ lines m⁻²), and maximum microstrain (0.0066 rd). Such structural distortions and lattice defects have been shown to produce extra active sites and increase electrolyte ion accessibility by forming high-energy grain boundaries and defect-mediated diffusion channels [64]. Electrochemical experiments reveal that the 1% La-Co₃O₄ electrode exhibits the maximum capacitance (1355 F g⁻¹ at 1 mV s⁻¹), outperforming both the 3% and 5% La-Co₃O₄ electrodes. This better performance is due to the optimal balance of crystallite size and lattice imperfections. Excessive defects, such as those found in the 3% La-Co₃O₄ sample, can hinder long-range crystallinity and reduce electrical conductivity, lowering overall capacitance [65]. However, the moderate microstrain and dislocation density increase the number of electroactive sites and promote the number of electroactive sites and fast Faradaic reactions. The 5% La-Co₃O₄ sample has the highest crystallite size (38.0 nm) and lowest dislocation density (0.692 × 10¹⁵ lines/m²), but has a lower capacitance (511 F g⁻¹ at 1 mV s⁻¹). This trend indicates that crystallite overgrowth and low defect density limit the number of accessible electroactive sites, thereby reducing ion/electron transport efficiency [66]. Furthermore, the capacitance of all electrodes decreases as the scan rate increases owing to diffusion restrictions and reduced ion penetration into the deeper porous networks. The tendency is particularly prominent in the 3% La-Co₃O₄ sample, corresponding with its significant microstrain, which may generate localized lattice distortions but inhibit effective electron transport under rapid charge–discharge circumstances. The 1% La-Co₃O₄ electrode preserves greater capacitance at higher scan rates, indicating that an intermediate defect density and moderate crystallite size offer a better balance of structural integrity, conductivity, and electrochemical activity. In conclusion, the correlation between microstructural characteristics and electrochemical performance highlights that controlled La incorporation into Co₃O₄ enables defect engineering, where moderate strain and dislocation density enhance electrochemical kinetics. In contrast, excessive or insufficient defect concentrations impact capacitive behavior.

Furthermore, the specific capacitance and cycling stability of the as-prepared La-doped electrode were compared with those of previously reported earth-rare-doped cobalt oxide electrodes, as presented in

Table 3. Comparison of the electrochemical performance of the as-prepared La-doped Co₃O₄ electrode with other rare earth metal-doped (La, Nd, Gd, Sm, Ce, Pr, and Eu) cobalt oxides. Cycle numbers are marked in parenthesis.

Doping	Synthesis	Specific Capacitance	Stability	Ref.
Sm3+ (5.71 at%)	combustion	1016 F g−1 @ 5 mV s−1	93% (5000)	[34]
Gd3+ (5.46 at%)	combustion	764 F g−1 @ 5 mV s−1	-	[34]
La3+ (6.12 at%)	combustion	518 F g−1 @ 5 mV s−1	-	[34]
Nd3+ (5 mol%)	hydrothermal	1398 F g−1 @ 1 A g−1	95% (1000)	[67]
Pr3+ (2.79 at.%)	hydrothermal	99 F g−1@ 1 A g−1	88% (5000)	[68]
Ce3+	cation exchange	1288 F g−1 @ 2.5 A g−1	96.7% (6000)	[69]
La3+ (0.92 mol%)	precipitation	471 F g−1 @ 2 A g−1	93.3% (10,000)	[70]
Nd3+ (1.81 mol%)	precipitation	662 F g−1 @ 2 A g−1	93.5% (10,000	[70]
Eu3+ (3.71 mol%)	precipitation	1021 F g−1 @ 2 A g−1	91.8% (10,000)	[70]
Ce3+ (5 at%)	hydrothermal	1309 F g−1 @ 1 A g−1	90% (2000)	[31]
La3+ (1 mol%)	hydrothermal	1312 F g−1 @ 1 A g−1	79.8% @ 5 A g−1 (10,000)	this work

. The results demonstrate its superior electrochemical performance in a three-electrode system compared to the earlier cobalt oxide electrodes.

4. Conclusions

In summary, La-doped Co₃O₄ nanocubes were synthesized via a facile hydrothermal method, and the effects of La incorporation on their structural, morphological, and electrochemical properties were systematically studied. Structural analyses (XRD, Raman, and XPS) confirmed the successful substitution of La³⁺ into the Co₃O₄ lattice, introducing lattice strain, dislocations, and oxygen vacancies that modify the crystallinity and defect density of the spinel framework. Morphological observations revealed that low-level doping (1 mol%) preserved the nanocubic architecture, characterized by smooth surfaces and uniform particle distribution. In contrast, higher La concentrations (3–5 mol%) disrupted the growth process, leading to aggregation, surface roughening, and reduced structural order. Electrochemical investigations demonstrated that these structural differences strongly influence redox kinetics, conductivity, and charge storage. The 1% La-Co₃O₄ electrode achieved the highest specific capacitance (1312 Fg⁻¹ at 1 Ag⁻¹), fast ion/electron transport, as evidenced by a low charge transfer resistance, and remarkable durability, with 79.8% capacitance retention and 97.12% Coulombic efficiency over 10,000 cycles at 5 Ag⁻¹. These results concluded that low La doping effectively balances crystallinity, defect engineering, and morphology control to maximize electrochemical activity, whereas excessive doping compromises structural integrity and hinders charge transport. Therefore, this study not only identifies 1% La-Co₃O₄ as an optimal electrode material for high-performance supercapacitors but also provides valuable insights into the role of controlled doping strategies in tailoring spinel-type oxides for next-generation energy storage systems.