Stable Manganese-Based High-Entropy Prussian Blue for Enhanced Sodium-Ion Storage

Abstract

Prussian blue (PB) and its analogs (PBAs) are considered ideal cathode materials for sodium-ion batteries (SIBs) due to the following merits, including high redox potential, simple synthesis methods, and excellent structural stability. Herein, we synthesized a high-entropy PB cathode material, Na_1.20Mn_0.38Fe_0.15Ni_0.14Co_0.15Cu_0.16[Fe(CN)₆]_0.82□_0.18·0.38H₂O (HE-HCF), through a facile co-precipitation method. The five transition metals in HE-HCF have similar atomic sizes and electronegativity, collectively occupying the high-spin Fe-HS sites. The manganese-based system design reduces the preparation cost, and the high-entropy doping approach further decreases the content of crystalline water in the structure. Benefiting from the synergistic effects of the multiple component elements, HE-HCF demonstrates a capacity retention rate of 72.7% at 0.1 A g⁻¹. Moreover, it even maintains 85.3% of its initial capacity after 1000 cycles at 1 A g⁻¹. Electrochemical impedance spectroscopy (EIS) and galvanostatic intermittent titration technique (GITT) analyses further confirm that HE-HCF exhibits low charge transfer resistance and a small reaction activation energy.

1. Introduction

Sodium-ion batteries (SIBs) represent a next-generation energy storage technology, widely positioned as the prime substitution to lithium-ion batteries (LIBs) because of their superior crustal abundance, inherent safety advantages, and remarkable cost-effectiveness [1,2,3,4]. Among the critical factors governing the electrochemical performance of SIBs, the structural design and performance optimization of cathode materials are of pivotal importance [5]. PB and PBAs are deemed as ideal cathode materials for the commercialization of SIBs, owing to their simple preparation process, low raw material costs, and large crystal frameworks that facilitate the transport of sodium ions. The introduction of nano-scale gap interfaces has brought practical flexibility to the field of ions that facilitate the transport of sodium ions [6,7]. Among the various PBAs, manganese-based hexacyanoferrates (Na_xMn[Fe(CN)₆·nH₂O, abbreviated as Mn-HCF) stand out as the most promising candidates on account of their abundant reserves, low extraction costs, and high average voltage, making them highly suitable for the commercial application of SIBs [8,9]. However, PBAs undergo irreversible phase transitions and lattice distortions during cycling, which detrimentally affects the material’s electrochemical cycling stability. Additionally, the unavoidable formation of coordination water during the synthesis process can react with the electrolyte, leading to harmful side reactions [8]. These factors significantly hinder the practical commercialization of SIBs [10,11,12].

PBAs follow the general formula A_xM[Fe(CN)₆]_y·zH₂O, in which A denotes alkaline or multivalent cations (e.g., Na⁺, K⁺, and Mg²⁺), while M stands for transition metals (e.g., Fe, Mn, Cu, and Ni), y indicates the occupancy of [Fe(CN)₆] units (0 < y < 1), with 0 < x < 2 and z < 4 [13,14,15]. Different elements have different influences on the kinetic reactions during the charging and discharging processes [14]. Vacancies at [Fe (CN)₆] sites are commonly present, affecting both structural and electrochemical properties. The structure comprises alternating low-spin Fe-C₆ and high-spin M-N₆ octahedra cyanide-bridged into an open 3D double-perovskite architecture with abundant redox-active sites. Intrinsic [Fe (CN)₆] vacancies further tune both structural stability and electrochemical behavior [16,17].

In Mn-hexacyanoferrates (Mn-HCFs), pronounced Mn³⁺ induced Jahn-Teller distortion within Mn-N₆ octahedra triggers severe phase transition that degrades cycling reversibility and accelerates capacity decay [18]. Improving the practical viability of PBAs and tackling their inherent issues requires optimization through methods like metal substitution, surface modification, defect tuning, and forming PBA composites [19]. Raising the configurational entropy through equimolar incorporation of five or more transition-metal cations (>1.5R) has recently emerged as an effective remedy: the resulting high-entropy lattice suppresses distortion and irreversible phase change while enhancing cycling stability [13,20,21,22]. The high-entropy strategy shows great potential in improving the general electrochemical performance of materials.

The benefits are exemplified by Brezesinski’s quasi-zero-strain PBA cathode containing five transition metals [23]. These elements share the same nitrogen coordination sites in equimolar ratios, increasing the system’s configurational entropy to over 1.5R. This innovation achieved a quasi-zero-strain working mechanism. Chou et al. fabricated a disordered cubic high-entropy framework structure containing five transition metals, exhibiting an ultra-long lifespan exceeding 50,000 cycles alongside outstanding rate performance [24]. Additionally, Ting et al. discovered that the constituent elements in a high-entropy PBA (HE-PBA) cathode comprising five metals play distinct roles [25]. For instance, Cu doping effectively enhances electrical conductivity [26], while Zn doping regulates vacancy formation. Their co-doping even produces a synergistic effect, adjusting particle size distribution and specific surface area. These works highlight the synergistic “mixing effect” intrinsic to high-entropy chemistry.

Building on this concept, we synthesized a manganese-based (high-entropy hexacyanoferrate) HE-HCF using a facile one-step co-precipitation method, introducing Fe, Co, Ni and Cu—transition metals with similar ionic radii and electronegativities—into the Mn lattice. The single-phase, high-entropy structure offers multiple active redox sites, dampens the Jahn–Teller effect and lowers production cost. The material delivers 72.7% capacity retention at 0.1 A g⁻¹ and 85.3% following 1000 cycles at 1 A g⁻¹, together with eminent rate properties, underscoring the efficacy of the high-entropy strategy for Mn-based PBA cathodes.

2. Materials and Methods

2.1. Material Synthesis

2.1.1. Synthesis of FeMn-PBA

The sodium-rich monoclinic FeMn-HCF was synthesized via a facile co-precipitation maneuver. Solution A was fabricated through dispersing 4 mmol of MnCl₂·4H₂O in 150 mL of deionized water and magnetically stirring for 6 h at ambient temperature. Solution B contained 6 mmol Na₄Fe(CN)₆·10H₂O, 20 mmol C₆H₅Na₃O₇, and 20 mmol NaCl, dissolved in 150 mL deionized water. Afterwards, solution A was slowly added to solution B with continuous stirring (this step is carried out under a nitrogen atmosphere). Then the resultant mixture was allowed to age under ambient conditions for 24 h followed by triple washing with deionized water and ethanol. Finally, the precipitate was vacuum-dried at 120 °C for 12 h to yield the FeMn-HCF sample.

2.1.2. Synthesis of HE-PBA

HE-HCF (40% Mn) was prepared via an ordinary ambient-temperature co-precipitation strategy. 10 mmol of Na₄Fe(CN)₆·10H₂O, 20 mmol of C₆H₅Na₃O₇, and 20 mmol of NaCl were dissolved in 300 mL of deionized water (denoted as solution A). 2 mmol of MnCl₂·4H₂O and 3 mmol of other precursors (NiCl₂·6H₂O, FeCl₂·4H₂O, CuCl₂·2H₂O, CoCl₂·6H₂O, each 0.75 mmol) were dissolved in 300 mL of deionized water (denoted as solution B). Solution A was slowly introduced into solution B, followed by continuous magnetic stirring for 6 h (this step is carried out under a nitrogen atmosphere). The mixture aged quiescently for 24 h followed by centrifugation and triple washing with deionized water and ethanol. The precipitate was vacuum-dried at 60 °C for 12 h, mechanically pulverized, and finally annealed at 120 °C in vacuum oven for 12 h to obtain the HE-HCF sample.

2.2. Materials Characterizations

Structural and morphological characterization employed a ZEISS Gemini-SEM 300 (15 kV, Oberkochen, Baden-Württemberg, Germany) for scanning electron microscopy while high-resolution transmission electron microscopy (HR-TEM) analyses were performed using a JEOL-2100F (200 kV, Akiruno City, Tokyo Metropolis, Japan) instrument for atomic-resolution characterization. Chemical states of constituent elements were probed via X-ray photoelectron spectroscopy (XPS) using an ESCALAB 250Xi system (Thermo Fisher Scientific, Waltham, MA, USA). Crystal structures were characterized through X-ray diffraction (XRD, Rigaku D/MAX 2200 V, Akiruno City, Tokyo Metropolis, Japan) with Cu Ka radiation, collected over a 2θ range of 10–70° at a scanning speed of 8° min⁻¹.

2.3. Electrochemical Measurements

Electrochemical evaluation of Mn-HCF and HE-HCF cathodes was employed by assembling CR2032 coin cells inside an argon-filled glove box. Electrodes contained 70:20:10 wt% active material/Ketjen Black/polyvinylidene fluoride binder (PVDF) binder, using N-methyl pyrrolidone (NMP) as dispersing solvent [27]. The active material mass loadings spanned 1.0–2.0 mg cm⁻². A glass fiber GF/D separator was used, and pure sodium metal was employed as the counter electrode. Each coin cell contained 75 μL of electrolyte, which was a solution of 1 mol L⁻¹ NaClO₄ in a 1:1 mixture of ethylene carbonate (EC) and diethylene carbonate (DEC), with 5% fluoroethylene carbonate (FEC) as an additive. The electrochemical tests were carried out on the NEWARE battery testing system.

3. Results

Employing an ordinary co-precipitation approach, the Mn-PBA framework was engineered with four equimolar transition metals (Fe, Ni, Co, Cu) to synthesize HE-HCF. The particle size of HE-HCF has reached the nanometer level, presenting an irregular cubic shape, with a particle size of approximately 100 nm (Figure 1a,b). Transmission electron microscopy (TEM) images of FeMn-HCF at a magnification of 1 μm reveal well-defined stacked cubic structures. Corresponding selected area electron diffraction (SAED) patterns unambiguously confirm its monocrystalline character (Figure S2). High-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) (Figure S3c) in conjunction with elemental mapping (Figure S3d–h) demonstrates the uniform distribution of component elements throughout the material. For HE-HCF, TEM images recorded at a scale of 200 nm show nanoscale particles with irregular morphology, consistent with a single-crystalline structure (Figure 1c). The SAED pattern (Figure 1d) exhibits distinct diffraction rings corresponding to the (200), (220), (400), (420), (440), and (620) planes. Elemental mapping further verifies the homogeneous spatial distribution of constituent metallic species across the HE-HCF particles (Figure 1f–m).

X-ray diffraction (XRD) analysis reveals that FeMn-HCF exhibits typical monoclinic phase characteristics, with noticeable splitting of characteristic peaks at (220), (420), (440), and (620) planes (Figure 2a). In contrast, HE-HCF shows no such peak splitting. The peak splitting in FeMn-HCF is attributed to its high sodium content [28]. The single-phase structure of HE-HCF indicates that all five transition metal elements are well-incorporated without forming other impurity phases. The Rietveld refined XRD patterns of both samples reveal the complete phase purity and crystal structure integrity of FeMn-HCF and HE-PBA (Figure 2c,f). The crystallographic parameters from the refined XRD patterns are summarized in Tables S1 and S2. It can be seen that FeMn-HCF and HE-HCF belong to the monoclinic phases with P21/n space group. It can be observed that the unit cell parameters and lattice volume of HE-HCF are slightly smaller than those of FeMn-HCF due to the introduction of other cationic ions, which can well explain the redshift of its Raman peaks. Additionally, from Table S2, it can be seen that in HE-HCF, Fe occupies the 2a (Fe1, high-spin state, Fe-HS) and 2d (Fe2, low-spin state, Fe-LS) sites. The other four transition metal elements occupy the same site as Fe1, indicating that they are codoped. In PB and PBAs, the adsorbed water and interstitial water are relatively easy to remove, while the crystalline water tends to form strong coordination chemical bonds within the crystals and is difficult to remove by common drying and heat treatment methods [29]. Thermogravimetric analysis (TGA) shows that HE-HCF experiences a mass loss of 9.53% before 180 °C, attributed to desorption of adsorbed and interstitial water. Between 180 °C and 210 °C, there is a 4.77% mass loss, associated with the elimination of coordinated water occupying vacancy sites [12]. For FeMn-HCF, a mass loss of 1.93% occurs up to 180 °C, and between 180 °C and 270 °C, a 10.57% mass loss is observed, corresponding to the removal of coordinated water. These TGA results suggest that high-entropy doping with transition metals can reduce the coordinated water content in the crystal structure. The subsequent mass loss beyond 270 °C for FeMn-HCF and beyond 210 °C for HE-HCF is due to the collapse and decomposition of their crystal structures under high-temperature conditions (Figure 2b). Raman spectroscopy indicates that the peak at 2117 cm⁻¹ in HE-HCF is attributed to the stretching vibration of Fe²⁺-CN-M²⁺(M²⁺ = Fe²⁺, Mn²⁺, Ni²⁺, Co²⁺, Cu²⁺) bonds, while the feature at 2143 cm⁻¹ assigns the stretching vibration of Fe²⁺-CN-M³⁺ bonds (Figure 2d). Compared to FeMn-HCF, both peaks in HE-HCF exhibit a red shift, suggesting that the stretching vibration of Fe²⁺-CN-M²⁺ is stronger than that of Fe²⁺-CN-Mn²⁺. This implies that the interatomic distances between M²⁺ ions and coordinated C and N atoms are shorter than those between Mn²⁺ ions and coordination atoms, leading to slight distortions in the crystal structure due to changes in lattice parameters. In addition to TGA, Fourier-transform infrared spectroscopy (FTIR) further confirms the crystalline water incorporation. Within the wavenumber range of 500 to 4000 cm⁻¹, distinct stretching vibration peaks are located at 595 cm⁻¹ (Fe-CN), 1619 cm⁻¹ (H-O-H), 2080 cm⁻¹ (-C≡N), and 3461 cm⁻¹ (O-H) (Figure 2e). Notably, compared to FeMn-HCF [5,30], the peaks associated with O-H and H-O-H functional groups in HE-HCF are significantly reduced, nearly disappearing. This indicates a substantial reduction in coordinated water within the sample material, which is beneficial for structural stability during electrochemical cycling. The decrease in the Fe-CN peak intensity is attributed to the substitution of high-spin Fe²⁺ (Fe-HS) by other doping atoms. Both TGA and FTIR results demonstrate that HE-HCF contains less coordinated water than FeMn-HCF, suggesting that high-entropy doping is an effective method for reducing coordinated water content in the crystal. Typically, high-spin Fe-HS sites may be occupied by vacancies or coordinated water; however, during the doping process with five transition metal elements, a competitive relationship forms, wherein these metals vie with coordinated water for Fe-HS sites, thereby reducing the coordinated water content within the crystal.

Inductively Coupled Plasma Optical Emission Spectroscopy (ICP-OES) analysis (Table S3) indicates that the chemical formula of HE-HCF is Na_1.20Mn_0.38Fe_0.15Ni_0.14Co_0.15Cu_0.16[Fe(CN)₆]_0.82□_0.18 (□denotes vacancies within the lattice), with elemental molar ratios closely aligning with the intended stoichiometric ratios. Additionally, the chemical formula for FeMn-HCF is determined to be Na_1.74Mn [Fe(CN)₆]_0.82□_0.18·1.77 H₂O, indicating a sodium-rich monoclinic phase, in good accordance with the XRD characterization data. Utilizing the configurational entropy formula:

$${∆S}_{conf}=-{\displaystyle \sum _{i=1}^n}{x}_{i}ln{x}_i$$

(1)

where ${∆S}_{conf}$ represents the configurational entropy, and xi denotes the molar fraction. The calculated ∆S_conf value for HE-HCF is 1.5R, confirming that the synthesized HE-HCF is a high-entropy material.

To further investigate the elemental composition and oxidation states of FeMn-HCF and HE-HCF, X-ray photoelectron spectroscopy (XPS) analyses were carried out. The survey spectrum of FeMn-HCF confirms the presence of Na, Fe, and Mn in the sample (Figure 3a). In contrast, the survey spectrum of HE-HCF demonstrates that, in addition to these three elements, Ni, Co, and Cu are also successfully incorporated (Figure 3b). The Na 1s and Fe 2p peaks in FeMn-HCF (Figure S4a,b) show no significant differences compared to those in HE-HCF (Figure 3c,d). Judging from the peak position, it is Fe²⁺ [31]. However, the satellite peak at 646.28 eV observed in the Mn 2p spectrum of HE-HCF is not present in the FeMn-HCF, indicating that Mn exists solely in the Mn³⁺ oxidation state in FeMn-HCF (Figure S4c) [30]. For HE-HCF, the Na 1s spectrum exhibits a solitary peak at 1071.9 eV (Figure 3c). Meanwhile, the Fe 2p peaks appear at 708.6 eV (Fe 2p₃/₂) and 721.5 eV (Fe 2p₁/₂), with a spin–orbit splitting energy of 12.9 eV, indicating the presence of Fe²⁺ (Figure 3d) [32,33,34]. In the Mn 2p spectrum, peaks at 642.2 eV and 654.1 eV are assigned to Mn²⁺ 2p_3/2 and Mn²⁺ 2p_1/2, respectively (Figure 3e) [35]. The Ni 2p spectrum exhibits characteristic Ni²⁺ signatures including a spin–orbit doublet at 856.5 eV (2p_3/2) and 874.0 eV (2p_1/2), accompanied by satellite features at higher binding energies (Figure 3f) [5]. Additionally, small peaks at 858.6 eV and 876.2 eV are attributed to Ni³⁺. Similarly, the Co 2p and Cu 2p spectra display satellite peaks at 786.2 eV and 802.4 eV, as well as at 944.3 eV and 964.7 eV, respectively, confirming the presence of Co²⁺ [36] and Cu²⁺ (Figure 3g,h) [33,34]. Moreover, the Cu 2p spectrum displays characteristic Cu⁺ signatures at 933.0 eV (2p_3/2) and 952.9 eV (2p_1/2) [37,38,39]. This observation indicates the occurrence of an internal redox reaction during the synthesis process, leading to the reduction of Cu²⁺ to Cu⁺, accompanied by partial oxidation of Ni²⁺ to Ni³⁺. The existence of Cu⁺ can decrease the distortion, contributing to ameliorated structural integrity and suppressed irreversible phase transformation [39]. Furthermore, the average chemical state of Fe coordinated with carbon (Fe1) and metal ions coordinated with nitrogen (Fe2, Mn, Ni, Co, and Cu) is determined to be +2.

4. Discussion

Figure 4a,b presents the initial three cycles of charge–discharge curves of FeMn-HCF at 0.1 A g⁻¹ and 1.0 A g⁻¹, respectively. Two distinct electron-transfer processes in FeMn-HCF are resolved by CV measurement, closely related to high-spin Mn²⁺/Mn³⁺ redox at 3.72/3.52 V and low-spin Fe²⁺/Fe³⁺ couple at 3.50/3.08 V (Figure S5) [40]. The CV curves of HE-HCF show a single redox couple at 3.53 V/3.14 V (Figure 4c). This is due to the high-entropy doping, which makes the five transition metal elements in Fe-HS sites have a similar coordination environment, resulting in the normalization of the charge–discharge voltage platform. This cooperative redox behavior manifests as a singular redox couple in the CV curve, which is also called the “cocktail” effect [41]. Furthermore, the overlapping CV curves of HE-HCF across three cycles demonstrate better reversibility and a more stable structure. Figure 4d,e shows the charge–discharge profiles of FeMn-HCF at varying current densities. In contrast, the specific capacity of HE-HCF remained relatively stable over the first three cycles. Moreover, HE-PBA exhibits a much higher specific capacity than FeMn-HCF when the current density is larger than 0.2 A g⁻¹, and the specific capacity loss upon returning to the initial current is relatively small (Figure 4f). At 0.1 A g⁻¹, FeMn-HCF delivers a discharge capacity of 122.4 m Ah g⁻¹ at the initial cycle versus 97.6 m Ah g⁻¹ for HE-HCF. However, after 13 cycles, the capacity of FeMn-HCF begins to decline sharply, dropping to 47.9 m Ah g⁻¹ after cycling 300 times (39.1% retention). In striking contrast, HE-HCF maintains 71.0 m Ah g⁻¹ after 300 cycles, retaining 72.7% of its initial discharge capacity. HE-PBA exhibits a much higher specific capacity than FeMn-HCF under various discharge current densities, and the specific capacity loss upon returning to the initial current is relatively small. At 1 A g⁻¹, HE-HCF exhibits an initial discharge capacity of 72.3 m Ah g⁻¹, which decreases to 61.7 m Ah g⁻¹ after 1000 cycles, maintaining an impressive capacity retention of 85.3%, significantly outperforming FeMn-HCF in cycling stability (Figure 4h). The pronounced degradation of FeMn-HCF is primarily attributed to the Jahn-Teller effect inherent in manganese-based PBAs, where Mn²⁺ dissolution from the lattice structure during cycling leads to severe lattice collapse and structural degradation. However, through the high-entropy doping strategy of transition metals, the electrochemical cycling stability of HE-HCF is significantly enhanced, effectively suppressing Mn²⁺ dissolution, mitigating lattice distortion, and reducing internal stress.

EIS measurements were conducted at different temperatures to investigate the impedance characteristics of FeMn-HCF and HE-HCF in depth. By fitting and analyzing the EIS data, the activation energy ($Ea$) values of FeMn-HCF and HE-HCF were further derived. The Nyquist plots feature a high-frequency semicircular arc and low-frequency linear region, representing the charge transfer resistance (R_ct) of Na⁺ diffusion and Warburg impedance, respectively. EIS measurements were performed at different temperatures for both FeMn-HCF and HE-HCF. As shown in Figure 5a, the Rct values of HE-HCF at these temperatures are 147.8, 93.7, 75.0, 62.3, and 46.6 Ω. In contrast, the R_ct values of FeMn-HCF (Figure S6) are significantly higher across all temperatures, indicating a greater internal charge transfer resistance, which is detrimental to Na⁺ transport. Conversely, HE-HCF exhibits enhanced Na⁺ diffusion capability and lower lattice diffusion resistance. Furthermore, both FeMn-HCF and HE-HCF show a decreasing trend in R_ct values as the temperature increases, suggesting that elevated temperatures facilitate Na⁺ transport and enhance the Na⁺ diffusion rate. The Arrhenius equation quantitatively governs the exponential correlation between thermal energy and reaction kinetics, serving as the fundamental framework for analyzing temperature-dependent behavior. The Arrhenius equation can be expressed as:

$$k=A·e^{-EaRT}$$

(2)

in which k denotes the reaction rate constant, while A stands for the pre-exponential factor, manifesting the reaction occurrences per second under ideal conditions. Additionally, $Ea$ is the activation energy, which denotes the minimum energy required to overcome reaction barriers, R represents the ideal gas constant, and T refers to the absolute temperature (in Kelvin). This equation shows that the reaction rate constant k increases as temperature rises. By fitting the linear relationship between the ionic conductivity ln(100σT) (S K cm⁻¹) and 1000/T (K⁻¹), the calculated slope values for FeMn-HCF and HE-HCF are −6.555 and −2.475, respectively (Figure 5b). Consequently, based on the Arrhenius equation, the activation energy $Ea$ of FeMn-HCF is determined to be 0.56 eV, whereas that of HE-HCF is only 0.21 eV (Figure 5c). This significant reduction in $Ea$ due to the high-entropy doping effect indicates a substantial decrease in the reaction energy barrier, which further facilitates the kinetic processes.

To gain deeper insights into the Na⁺ diffusion kinetics during electrochemical cycling, Galvanostatic Intermittent Titration Technique (GITT) measurements were performed on FeMn-HCF and HE-HCF. The Na⁺ diffusion coefficient (D_Na⁺) is derived from transient voltage relaxation profiles using the following equation [42]:

$$D_{{Na}^{+}}={\displaystyle \frac{4}{\pi \tau }}{\left({\displaystyle \frac{m_B{V}_M}{M_{B}A}}\right)}^2{\left({\displaystyle \frac{{\mathit{\Delta }E}_S}{{\mathit{\Delta }E}_{\tau }}}\right)}^2$$

(3)

where m_B, M_B, and V_M represent the mass, molar mass, and molar volume of the active material, respectively. Since V_M remains constant throughout the electrochemical process, and A denotes the electrode area, the voltage-time profiles of FeMn-HCF and HE-HCF are used to extract the required parameters (Figure S7a,b). Based on the calculations, the D_Na+ value for FeMn-HCF and HE-HCF are 3.421 × 10⁻¹¹ cm² s⁻¹ and 2.047 × 10⁻¹⁰ cm² s^−1, respectively (Figure S7c,d). The D_Na⁺ value of HE-HCF is approximately six times higher than that of FeMn-HCF, aligning with its superior rate properties and lower impedance values. This enhancement is primarily attributed to the smaller particle size of HE-HCF, which effectively shortens the Na⁺ diffusion path and accelerates ionic transport within the electrode.

To elucidate the charge storage mechanism of the HE-HCF electrode, cyclic voltammetry (CV) tests were conducted at varying scan rates (0.1, 0.2, 0.4, 0.6, and 0.8 mV s⁻¹). As shown in Figure 5d, the CV curves at different scan rates display well-defined and consistent redox peaks, although a gradual increase in polarization is observed with increasing scan rate. The contribution from capacitive processes was quantified by analyzing the linear relationship between the peak current (i) and the square root of the scan rate (ν), based on the equation.

$$i={av}^b$$

(4)

The b-value, reflecting the dominant charge storage mechanism, was derived through fitting the linear relationship between ln(v) and ln(i). CV analysis of HE-HCF (Figure 5e) yielded Tafel slopes of 0.667 and 0.644 for oxidation (O1) and reduction (R1) peaks, respectively. These b-values suggest that the charge storage behavior is mainly diffusion-controlled. To further quantify the capacitive contribution at each scan rate, the following equation was applied [43]:

$$i\left(V\right)=k_1\nu +k_2{\nu }^{1/2}$$

(5)

capacitive (k₁ν) and diffusion-controlled (k₂ν¹/²) contributions were quantified [44]. The constants k₁ and k₂ were determined via analysis of the linear relationship between ν^1/2 and i/ν^1/2 (Figure S8). The capacitive contribution ratio, calculated at different scan rates, indicates that the proportion of capacitive contribution increases progressively as the scan rate rises. Specifically, the capacitive contribution in the HE-HCF electrode accounts for 19% at 0.1 mV s⁻¹. When the scan rate increases to 0.8 mV s⁻¹, this proportion rises to 40% (Figure 5f).

5. Conclusions

In summary, a manganese-based high-entropy Prussian blue cathode material, Na_1.20Mn_0.38Fe_0.15Ni_0.14Co_0.15Cu_0.16[Fe(CN)₆]_0.82□_0.18·0.38H₂O (HE-HCF), was successfully synthesized via a co-precipitation method under a N₂ atmosphere. The HE-HCF exhibits a nanoscale irregular particle morphology, with five transition metal elements uniformly distributed within the structure. The choice of a manganese-based system effectively reduces the material’s synthesis cost. The high-entropy doping strategy decreases the crystallized water content in the material and suppresses the Jahn–Teller effect associated with Mn²⁺ dissolution. Benefiting from the incorporation of five transition metals, HE-HCF demonstrates prominent crystal stability and rate properties in contrast to FeMn-HCF. Specifically, even after cycling 1000 times at 1 A g⁻¹, the HE-HCF can still maintain 85.3% of its initial capacity, whereas FeMn-HCF retains only 72.7%. These results collectively demonstrate that HE-HCF possesses superior electrochemical performance and reaction kinetics.