PBAs possess a distinctive open metal-organic framework, categorizing them within a subset of coordination compounds characterized by the molecular formula A_xM[M′(CN)₆]_1-y□_y ·zH₂O (0 ≤  x ≤ 2, 0 ≤  y ≤ 1). Herein, 'A' signifies an alkali metal (AM) ion (such as Na⁺, K⁺), while 'M' and 'M′' represent TM ions, including but not limited to Fe, Co, Mn, Ni, and Cu. The symbol '□' denotes vacancies within the M′(CN)₆ lattice, and 'H₂O' refers to the water of crystallization, encompassing both interstitial and coordination water. Variables 'y' and 'z,' indicating the number of vacancies and water of crystallization, respectively, are contingent upon synthetic conditions, including the liquid-phase environment and the presence of chelating agents. Conversely, 'x' is dictated by the cumulative valence of the TM ions [49]. Intriguingly, due to disparate 3D orbital splitting, the dual TM ions in PBAs manifest divergent spin states. As illustrated in Fig. 2a, coordination via C induces a more potent crystal field than coordination through N, engendering a broader partition in the M′ 3D orbitals compared to M. This differential results in M assuming a pronounced high spin (HS) state and M′ adopting a distinct low spin (LS) state [50,51,52,53].

The prevalent metal hexacyanoferrate (A_xM[Fe(CN)₆]_1-y □_y·zH₂O, denoted as MHCF) adopts a face-centered cubic (FCC) configuration anchored within a calcite-type framework. Within this FCC lattice, nitrogen and carbon atoms of the CN ligands engage with divalent or trivalent iron ions exhibiting varying spin states, thereby establishing Fe^HS-N₆ and Fe^LS-C₆ octahedra. These octahedral units are interconnected in an alternating sequence, culminating in the formation of expansive ion channels and substantial interstitial voids [38,54]. Conventionally, PBAs are synthesized via aqueous co-precipitation, a methodology that inherently induces Fe(CN)₆ vacancies and crystallization water within the structure, attributed to the unregulated, swift nature of the precipitation. To preserve electrostatic equilibrium, the structure incorporates a quarter of the Fe(CN)₆ vacancies, derived from the Fe³⁺: Fe(CN)₆ molar proportion (4:3), with a more illustrative representation of the crystal configuration presented in Fig. 2b. The omission of Fe(CN)₆ sites prompts adjacent 6 HS Fe³⁺ to attain a state of unsaturation, compelling the ingress of six coordinating water molecules within these voids to sustain the cubic framework's integrity. It warrants emphasis that these vacancies exhibit a random distribution across the entire crystalline matrix. Additionally, each unit cell encompasses eight interstitial sites, each capable of accommodating a singular water molecule, culminating in 14 water molecules per unit cell [55]. In the context of nonaqueous batteries, the pronounced hydration level inherent to the crystalline structure predisposes the system to ancillary reactions, thereby elevating the significance of water expulsion as a pivotal impediment for PBA utilization within such battery systems. Contrarily, within ASIBs and APIBs, the crystallization water in PBAs demonstrates remarkable stability throughout charge-discharge cycles. MHCF's electrochemical processes, involving both the insertion/extraction of AM ions and the redox activities of M and Fe ions, proceed concomitantly. Notably, this charge-discharge protocol is explicable with reference to a structural model devoid of vacancies, excluding any participatory role of crystalline water in the reaction mechanism:

During the charging phase, the sequential oxidation of M and Fe ions within MHCF facilitates the expulsion of AM ions from the crystalline lattice. Conversely, the discharge phase sees the reduction of M and Fe ions, concomitant with the reincorporation of AM ions. Should M represent redox-active elements such as Fe, Mn, or Co, the resulting FeHCF, MnHCF, and CoHCF display two sets of redox peaks, accommodating two AM ions and yielding a theoretical specific capacity of approximately 170 mAh g^-1. However, this often incurs pronounced structural distortion and diminished cycling stability. In instances where M signifies an inert element, ZnHCF, NiHCF, and CuHCF proffer a solitary active Fe²⁺/Fe³⁺ redox site, attributable to the electrochemical inertness of Ni²⁺ and Cu²⁺, thereby constraining the specific capacity to a maximum of 80 mAh g⁻¹, albeit typically accompanied by an exceptionally prolonged cycle life. Notably, the full activation of the Fe^LS redox reaction presents a substantial challenge due to the existence of Fe(CN)₆ vacancies, culminating in an actual capacity for MHCF that falls short of theoretical projections. Concurrently, the redox process precipitates an evolution within the crystal structure, transitioning from cubic to monoclinic, rhombic, and, ultimately, tetragonal configurations. This structural metamorphosis predominantly hinges on the crystallization of water content alongside the specific types and concentrations of AM and TM ions [56,57]. As evidenced in Fig. 2c, FeHCF and CoHCF predominantly maintain a cubic phase structure [58,59]. The insertion/extraction of AM ions typically induces a bi-phase transition, oscillating between cubic and rhombic structures [60,61]. An uptick in x within the lattice amplifies Coulombic interactions, prompting a systematic lattice expansion. Specifically, in the context of Na as the AM, the asymmetric distribution of electrons from TM ions across degenerate orbitals engenders divergent electron shielding effects in various directions for guest cations when x surpasses 1.5. This phenomenon triggers a transition from cubic to monoclinic configurations through structural distortion [61]. Subsequent diminution of crystallization water mitigates vesicular repulsion, distorting the crystal structure and facilitating the transition from monoclinic to rhombic phases [62]. Conversely, when K serves as the AM, configurations deficient in K typically exhibit a cubic structure [63], while K-enriched environments predominantly assume a monoclinic structural phase, impervious to the presence of crystallization water [64,65]. Unlike FeHCF and CoHCF, MnHCF experiences intensified distortions, a consequence of structural aberrations invoked by the Jahn-Teller effect within the MnHS-N₆ octahedral [66,67]. Consequently, MnHCF undergoes a tri-phasic transformation spanning monoclinic, cubic, and tetragonal phases (Fig. 2d). In the case of NiHCF and CuHCF, characterized by the electrochemical inertness of Ni²⁺ and Cu²⁺, the cubic lattice undergoes minimal distortion, shifting marginally toward a monoclinic form or eschewing a structural phase transition altogether (Fig. 2e) [68,69]. The repeated redox reactions always accompany the structural evolution, which leads to the dissolution of PBAs. NiHCF and CuHCF undergo minimal structural changes due to their characteristic of being zero-strain materials in long-term cycling, and their ultra-high structural stability makes TM ion dissolution more challenging. For the higher voltage plateau and dual redox centers increasing the capacity for FeHCF and CoHCF, the dissolution of TM ions becomes more accessible. Finally, the severe structural distortion caused by the Jahn-Teller effect of Mn leads to severe TM ions in MnHCF. Therefore, it is essential to comprehend the TM ion dissolution mechanism in PBAs to acquire more stable materials.

During charge and discharge processes, the cathode material predominantly employs TM ions as swift redox reaction centers to counterbalance the charge alterations accompanying the insertion and extraction of guest cations. The stability and electrochemical activity of TM ions critically influence the overall battery performance [70,71]. Ideally, these TM ions should remain anchored within the cathode structure throughout the repeated cycles of cation insertion and extraction [72,73]. Contrarily, in real-world scenarios, TM ions tend to dissociate from the cathode, diffuse into the electrolyte, and subsequently accumulate on the anode surface [74,75]. This phenomenon contributes not only to the diminution of active materials and the alteration of the cathode's surface structure but also significantly affects the composition and electrochemical attributes of the solid electrolyte interface on the anode surface [76]. Consequently, even minimal quantities of TM ions involved in this DMD process can precipitate a substantial decline in both the capacity and power attributes of the battery. This issue stands as a paramount challenge for PBAs and constitutes one of the most substantial hurdles for transition metal-based cathode materials [77,78].

The prevalent dissolution phenomenon is common in alkali-ion batteries (AIBs) with transition metal-based PBAs [77]. This intrinsic complication severely impairs the battery's capacity retention and cyclical stability [79]. Notably, a marked discoloration of PBA electrodes often occurs during the charge and discharge phases in aqueous solutions (Fig. 3a), attributed to the transition from insoluble to soluble forms of PBAs and exacerbated by intense water-induced dissolution of TM ions [80,81]. Additionally, the incidental seepage of TM ions into the electrolyte is an unavoidable consequence of dynamic adsorption phenomena at the electrode interface [82]. Typically, the liberation of TM ions from PBAs encompasses three stages (Fig. 3b): Initially, a majority of TM ions migrate toward the surface of the PBA electrode. These ions undergo solvation by ambient water molecules at the PBA/electrolyte interface, followed by their diffusion into the aqueous electrolyte [83,84,85]. However, this dissolution and subsequent diffusion is significantly impeded in concentrated electrolytes. The peculiar network configuration of such electrolytes curtails the mobility of water molecules, resulting in sluggish diffusion kinetics. This, in turn, effectively deters TM ion dissolution, thereby enhancing the electrodes' cyclical stability within PBAs. Furthermore, PBAs containing Jahn-Teller active TM ions exhibit a pronounced rate of metal dissolution [86,87]. Specifically, TM ions with Jahn-Teller activity experience augmented disproportionation in the presence of H⁺ in aqueous solutions. For instance, in MnHCF, higher valence Mn ions are readily reducible to Mn³⁺ or Mn²⁺ to offset Mn charge compensation. Concurrently, the renowned Jahn-Teller effect in Mn³⁺ also yields Mn²⁺ via Mn³⁺ disproportionation reactions [88]. Consequently, the Jahn-Teller effect induces a contraction of the four Mn-N bonds due to the [MnN₆]³⁺ distortion, contrary to the stable [MnN₆]²⁺, provoking unstable asymmetric contractions and expansions in PBA's octahedra throughout successive charge/discharge cycles. This instability facilitates Mn solubilization, culminating in progressive structural fracturing and severe battery capacity attrition [89]. Nevertheless, the multitude of variables inherent in PBA synthesis contributes to non-uniform defects. The crystallinity diverges post-polycrystalline assembly, complicating the straightforward quantification of dissolution kinetics. Hence, there is an urgent call for sophisticated characterization methodologies capable of accurately quantifying the dissolution of TM ions. Such advancements are pivotal for delving into the fundamental mechanisms governing the dissolution of TM ions and concomitant capacity deterioration, extending battery longevity [90].

In addressing the enhancement of energy density in ASIBs and APIBs, a critical obstacle remains the control of TM ion dissolution, necessitating a strategic focus on electrolyte engineering [91]. During the dissolution process, water molecules in the electrolyte are distinguished as either free or solvated water. Free water, exhibiting weak H-O bonds, is highly prone to deprotonation and hydrolysis, leading to spontaneous hydrolysis and subsequent by-product formation. Additionally, this reactive free water initiates the deterioration of the active material, resulting in substantial cathodic TM ion dissolution. Thus, the refinement of electrolyte engineering adheres to two central principles: the diminution of free water and the stabilization of dissolution equilibrium [92]. The water-in-salt electrolytes (WiSE) approach represents a paradigm for mitigating free water content, whereby various anions embed within the solvated structure and upon the electrode surface, impeding direct water-electrode material interaction. Nevertheless, when juxtaposed with nonaqueous cells, the constrained voltage window of aqueous electrolytes (~ 1.23 V) significantly curtails the potential output voltage and energy density of both ASIBs and APIBs. Okada et al. explored the ramifications of elevated electrolyte concentration on the operational voltage of ASIBs, employing Na₂MnFe(CN)₆ as the cathode and NaTi₂(PO₄)₃ as the anode, with the objective of enhancing discharge voltage [93]. Cyclic voltammetry (CV) revealed that the electrochemical window with a high-concentration electrolyte (17 mol kg^-1 NaCl) extended from 1.9 to 2.8 V, contrasting with its low-concentration (1 mol kg^-1 NaCl) counterpart. The latter exhibited pronounced capacity decay following the initial cycle, attributed primarily to the anodic dissolution of TM ions provoked by the electrolytic reduction of water, yielding H₂ and alkalinizing the electrolyte solution. Conversely, utilizing the extended stabilizing potential window of 17 mol kg^-1 NaClO₄, a discharge capacity of 117 mAh g^-1 was achieved during the first cycle, alongside robust rate performance and cycling stability. Further examinations replaced 17 mol kg^-1 NaClO₄ with 9 mol kg^-1 NaTFSI [30]. As NaF dissolves in saturated yet under-concentrated 9 mol kg^-1 solution, the influx of OH^- and F^- ions from NaF compromises the structural integrity of PBAs, precipitating instability within alkaline solutions. Given the explosive and hygroscopic properties inherent to NaClO₄, the exploration for more benign and stable salts is imperative. Subsequent studies by Ji et al. introduced a 30 M potassium acetate (KAc) electrolyte, achieving a broad 3.2-V electrochemical stabilization window and facilitating the reversible activity of anodic KTi₂(PO₄)₃ in APIBs [94]. In a similar vein, Passerini et al. leveraged the high solubility of KAc, formulating a high-concentration cationic electrolyte with NaAc and pioneering the use of Al foil as the cathodic current collector in an aqueous milieu [95].

Despite the wide voltage window exhibited by KAc-based WiSE, its alkalinity (pH = 9) poses compatibility issues with PBAs. Hu et al. introduced a comprehensive APIB system featuring Fe-substituted PBA (KFeMnHCF-3565) cathode, 3,4,9,10-perylenetetracarboxylic diimide (PTCDI) anode, and 22 M KCF₃SO₃ WiSE electrolyte [31]. The X-ray diffraction (XRD) pattern and refinement results for KFeMnHCF-3565, depicted in Fig. 5a, confirm a monoclinic phase with a P21/n space group, complemented by a scanning electron microscope (SEM) inset displaying cubic structures measuring 200-800 nm per particle. Figure 5b illustrates a schematic of the quintessential open-framework crystal structure. Differing electrochemical behaviors under varying conditions are presented in Fig. 5c-f. The KMnHCF electrode, as revealed in Fig. 5c, underwent pronounced Fe and Mn dissolution during cycling in the electrolyte. A comparative assessment between Fig. 5c and d demonstrates that elevating the KMnHCF electrode's electrolyte concentration from 1 to 22 M enhanced capacity retention from 23 to 60%, marking a considerable improvement in cycling performance, yet it continued to experience capacity and voltage decline. In contrast, the KFeMnHCF-3565 electrode, characterized by partial Mn substitution with Fe, inhibited the dissolution of Fe and Mn to some extent, as evidenced in Fig. 5e and f, leading to enhanced capacity and cycling stability. Notably, the employment of 22 M KCF₃SO₃ concentrated electrolyte negated dissolution, capacity, or voltage degradation. In subsequent innovations, a unique WiSE for ASIBs was formulated by incorporating tetraethylammonium triflate (TEAOTF) salt (9 mol kg^-1 NaOTF + 22 mol kg^-1 TEAOTF), diminishing transition metal dissolution in the NaMnHCF cathode and markedly bolstering cycling performance [96]. Figure 5g underscores that 9 mol kg^-1 NaOTF + 22 mol kg^-1 TEAOTF offers an expanded electrochemical window (3.3 V), with the inset highlighting the electrolyte’s merits, including reduced viscosity and diminished electrode dissolution. The NaMnHCF cathode, delineated in Fig. 5h, manifested two voltage plateaus (0.7 and 1.0 V vs. Ag/AgCl). Remarkably, as Fig. 5i illustrates, the NaMnHCF electrode in 9 mol kg^-1 NaOTF + 22 mol kg^-1 TEAOTF electrolyte exhibited superior cycling stability, minimal capacity loss, and augmented average coulombic efficiency relative to the 9 mol kg^-1 NaOTF electrolyte. Figure 5j reveals a substantial reduction in Fe and Mn dissolution in the 9 mol kg^-1 NaOTF + 22 mol kg^-1 TEAOTF electrolyte compared to its 9 mol kg^-1 NaOTF counterpart. The Raman peak's broadening and diminution near 3487 cm^-1 suggest that the mitigation of dissolution is attributed to the electrolyte's free water content, and the elevated electrolyte concentration impedes the free water’s corrosive effect on the electrode.

The utilization of economical electrolyte additives presents a more pragmatic and feasible approach compared to the high salt requisites of WiSE. Qian et al. have demonstrated that the introduction of the surfactant sodium dodecyl sulfate (SDS) into the aqueous medium effectively mitigates hydrogen or oxygen evolution at the electrode interface, thereby extending the electrochemical stability window of the electrolyte to approximately 2.5 V [97]. In this context, SDS molecules adhere to the electrode surface via electrostatic interactions, effectively precluding the precipitation of hydrogen or oxygen. Employing Na₂MnFe(CN)₆ as the cathode and zinc sheets as the anode, the resulting aqueous rechargeable hybrid ion battery manifests an energy density peaking at 170 Wh kg^-1, maintaining capacity retention of 75% across 2000 cycles within an operational voltage of 2.0 V. Energy density computations, grounded in density flooding theory, underscore the pivotal role of SDS in curbing water splitting, manganese dissolution, and anode degradation, thereby enhancing cyclic durability and rate capacity. Empirical evidence suggests that the incorporation of surfactants into aqueous electrolytes augments the electrochemical stability window to 2.5 V. Adjusting the electrolyte composition to match the TM ions of the cathode alters dissolution equilibria, curbing continuous active material attrition, and the incorporation of TM ions within the cathode serves to fortify the structural integrity. Furthering this approach, Li et al. succeeded in bolstering the structural stability of Na₂CoFe(CN)₆ through the integration of specific electrolyte additives (1 wt% CoSO₄) within an aqueous 1 M Na₂SO₄ electrolyte [60]. The structural alterations of the electrode skeleton throughout the cyclic process have been examined via XRD, Fourier transform infrared spectroscopy (FTIR), and inductively coupled plasma atomic emission spectroscopy (ICP-AES). These analyses have elucidated that the presence of Co²⁺ ions in the electrolyte effectively precludes both the disintegration of the CoHCF skeletal framework and the solubilization of TM ions within the structure during cycling. Similarly, Lu et al. instigated an in situ electrochemical cation substitution in the KMnF cathode by incorporating 0.2 M Fe(CF₃SO₃)₃ into a 21 M KCF₃SO₃ electrolyte [32]. This innovative approach to surface modification markedly curtailed manganese dissolution, thereby enhancing both structural and surface chemical stabilities of the electrode. Investigations involving scanning transmission electron microscopy (STEM) electron energy loss spectroscopy line scans and elemental mapping were executed on the cross-sectional regions of both original and altered electrodes. Figure 6a and b displays intensity contour plots and elemental compositions, demonstrating a uniform presence of Fe and Mn in both initial and modified electrodes. Notably, the surface of the altered electrode showed a substantial relative increase in Fe in contrast with Mn, solidifying the conclusion that Fe³⁺ is integrated into the electrode framework during cycling in the amended electrolyte. Comprehensive characterizations indicated that Fe present in the modified electrolyte compensates for the Mn vacancies generated in situ within the KMnF structure. Consequently, the KMnF electrode revealed exceptionally prolonged cyclical stability, sustaining a capacity of roughly 120 mAh g^-1 following 130,000 cycles at 2500 mA g^-1 without notable capacity attrition per cycle (Fig. 6c). In a more nuanced approach, Wang and associates ingeniously incorporated Na₄Fe(CN)₆ as a supplemental salt in the concentrated aqueous NaClO₄-based electrolyte solution, aiming to occupy the Mn vacancies emergent on the surface [98]. Addressing the lattice expansion ensuing from Na⁺ extraction, the [Fe(CN)₆]⁴⁻ anion was employed to engage with dislocated or displaced Mn, thereby rectifying Mn vacancies in situ and fortifying the surface's chemical stability. Post 300 cycles utilizing diverse electrolytes, Fig. 6d illustrated pronounced Mn accumulation within individual particles when subjected to the standard electrolyte. Conversely, Mn distribution remained uniform across particles in the presence of the modified electrolyte (Fig. 6e), denoting the efficacious curtailment of Mn dissolution. Subsequent analyses employed electron energy-loss spectroscopy (EELS) on the particles' cross-sections harvested from the cycling electrode (Fig. 6f and g). Within the unmodified electrolyte system, the Mn L₃/L₂ intensity ratio surged markedly from 4.02 (point A) to 5.18 (point B). This alteration in ratio underscored the Mn's inhomogeneous valence state within discrete particles and the persistence of an elevated valence state, potentially linked to amorphous compounds emanating from structural degradation. In stark contrast, the Mn L₃/L₂ intensity ratio within the modified electrolyte system exhibited negligible fluctuation, signifying a consistent valence state of Mn across the particles. As delineated in Fig. 6c, the capacity retention of the PTCDI||NaFeMnF stood at 73.4% following 15,000 cycles at 2 A g^-1, with the specific capacity sustained at 47.5 mAh g^-1, and the coulombic efficiency approached a near-perfect 100%.

WiSE, the highly concentrated electrolytes, has been proven effective in expanding the electrochemical stabilization window of aqueous electrolytes and improving low-temperature performance through increased salt concentration. However, its practical applications could be limited for its high viscosity, low conductivity, and high cost. In particular, their increased cost and viscosity do not offer enough benefits. The incorporation of organic solvents, such as dimethyl carbonate and acetonitrile, can effectively decrease the viscosity of WiSE while also decreasing salt content and preventing water proton activity [99]. However, due to their toxicity and flammability, organic additives are unsuitable for use as electrolyte additives in aqueous solutions.

By effective strategies incorporating electrolyte additives and WiSE, electrolyte engineering has aroused great concern and demonstrates the ability to mitigate TM ion dissolution. Ultra-high salt concentrations decrease active water content and increase viscosity, thereby hindering the dissolution and diffusion of substances on electrode surfaces. Heightened viscosity and slower interfacial processes contribute to reducing overall rate performance. However, the cost implications of salt concentration cannot be ignored as high-energy density and long cycle life are undoubtedly the most critical features for a large-scale energy storage device. Additionally, incorporating cation trapping agents into the electrolyte enables in situ repair of surface defects formed during charging and discharging, improves dissolution equilibrium, and further enhances cycling stability.

The process of TM doping/substitution involves the replacement of certain or all sites within the original matrix with alternative ions or groups, representing a paramount strategy in the material optimization studies of PBAs. This technique engenders structural vacancies, occupies voids, or meticulously adjusts lattice parameters, contributing to the enhancement of structure and inherent properties. PBAs, predicated on redox behavior, are categorized into two primary types: dual-electron transfer PBAs (DE-PBAs, with M and M′ encompassing elements such as Mn, Fe, and Co) and single-electron transfer PBAs (SE-PBAs, where M includes Cu, Ni and M′ involves Fe, Co, and Mn). DE-PBAs, despite possessing a superior theoretical capacity, often undergo substantial structural degradation due to significant deformation experienced during charge and discharge cycles. Conversely, SE-PBAs exhibit commendable cycling stability and elevated electrical conductivity but are constrained by a lower capacity attributable to the presence of a single active redox component. Consequently, the role of doping/substitution becomes indispensable in augmenting their electrochemical attributes, encompassing aspects such as specific capacity, rate capability, and operational potential.

Zhao et al. reported the synthesis of potassium-rich mesoporous K₂NiFe(CN)₆·1.2H₂O, utilizing Ni in lieu of FeHCF, serving as the cathode for ultrafast APIBs [69]. This innovative substitution strategy propelled APIBs to reach a groundbreaking rate capability of up to 500 C (8214 W kg^-1), completing a single charge/discharge cycle in a mere 4.1 s. In a distinct approach, Yan et al. replaced the Ni site in NiHCF with a [Ni(en)₂]²⁺ moiety, culminating in an entirely novel structure, [Ni(en)₂]₃[Fe(CN)₆]₂ (NienHCF), which was employed for the first time as a cathode material in ASIBs and APIBs [100]. The APIBs exhibited robust cycling stability, maintaining 77.2% of their initial capacity after 1000 cycles at 0.5 A g^-1, in conjunction with an activated carbon anode. In another development, Chen et al. detailed that Cr-substituted CrCr-PBA displayed enhanced performance in ASIBs [101]. The incorporation of Cr contributed two redox pairs at potentials of 0.62/0.65 V and 0.73/0.77 V, respectively, coordinating at two different sites mediated by C and N.

Chung et al. introduced V-doped V/Fe-PBAs materials, noting a substantial enhancement in electrochemical performance compared to Cu/Fe-PBAs and Ni/Fe-PBAs, ascribed to the structural robustness of V/Fe-PBAs electrodes and minimal lattice alterations during cycling [102]. However, ICP analyses revealed a progressive dissolution of V and Fe ions during cycling, initiating a capacity reduction at the cycle's outset. Conversely, Zhang et al. employed selective Co doping in minimal concentrations into CoFeHCF to counteract the PBAs framework's incremental degradation due to electrochemical cycling [103]. The ‘electrochemically driven dissolution-recrystallization’ self-healing mechanism endowed CoFeHCF with an increasingly organized structure, preserving an impeccable cubic morphology over numerous cycles. The morphological evolution of the CoFeHCF electrode through charge-discharge sequences under electric field influence is depicted in Fig. 7a. X-ray photoelectron spectroscopy (XPS) analyses indicated the attenuation of Fe²⁺ characteristic peaks in CoFeHCF in its deprotonated state, strengthening in the potassium form throughout the cycles (Fig. 7b). Furthermore, ex situ XRD patterns (Fig. 7c and d) documented the crystal structure's evolution during the electric field's influence, evidencing a solid solution mechanism devoid of phase transitions, accompanied by negligible lattice distortion and volume dynamics (Fig. 7e). This reversible cycle contributes significantly to the sustenance of structural integrity and electrochemical resilience. Experimental validations, allied with multiphysics simulations (MD) and density functional theory (DFT) analyses, postulate that Co incorporation within the PBA matrix could thwart Fe migration on the crystal facade, particularly in deteriorated areas, thereby recuperating crystallographic contours. The inherent ‘electrochemically driven dissolution-recrystallization’ underscores the pivotal role of the electric field in mediating reversible crystal growth. Co-integration optimally modulates the electrical reactivity of FeLS-C octahedra, fostering the self-healing attribute. Additionally, the enhanced conductivity and K-ion mobility attributable to Co doping amplify the cycling proficiency of CoFeHCF electrodes in dilute electrolytes, demonstrated over 4000 cycles (Fig. 7g). In a related study, Wang et al. incorporated Fe into CoHCF, synthesizing K_1.66Fe_0.25Co_0.75[Fe(CN)₆]·0.83H₂O (KFCHCF) for APIBs [104]. This novel cell employing a KFCHCF cathode sustained 74.35% of its discharge capacity post 10,000 cycles at 1 A g^-1. Furthermore, Reguera et al. mitigated structural perturbations by substituting MnHCF with high polarizability Co, modulating the electronic environment around Fe (LS) via cyanide connectors within the Mn-NC-Fe-CN-Co sequence [105]. This Co and Mn interaction in Co_0.55Mn_0.45HCF facilitated through the cyanide bridge fortified the redox constancy of the discharge voltage and overall electrochemical behavior, achieving 80% capacity preservation post 100 cycles.

In the domain of battery materials, the incorporation of a single TM often falls short of achieving desirable electrochemical attributes. Recent insights have underscored the potency of high-entropy compounds—comprising five or more elements—in augmenting the capacity and cycling robustness of electrode materials. These improvements are attributable to the entropic stability, lattice distortion, retarded ion diffusion, and cocktail effects inherent in these compounds [106,107]. For instance, Xing et al. integrated Mn, Co, Ni, Cu, and Fe into the PBAs for aqueous series zinc-ion batteries. This incorporation of multiple transition metals at the active sites markedly curtailed PBA dissolution, thereby enhancing cycling stability [108]. Similarly, Huang et al. employed a high-entropy approach to craft high-entropy PBA (HEPBA; M5HCF) for use as a cathode material in ASIBs [109]. Evident in Fig. 7h, M5HCF exhibited an elevated redox potential within the 0-1 V range, coupled with a negligible redox peak potential discrepancy, underpinning its commendable reversibility. The absence of conspicuous H₂ and O₂ evolution underscored the reversibility of the Na⁺ insertion/extraction reaction. Remarkably, the cocktail effect induced the convergence of M5HCF's redox peaks into a single, broadened peak, with a redox peak potential difference of a mere 0.002 V, bolstering high reversibility and cycle durability. Electrochemical impedance spectroscopy (EIS) and distribution of relaxation times (DRT) analyses confirmed that M5HCF possessed minimal charge transfer and diffusion resistance, a characteristic pivotal for superior electrochemical behavior (Fig. 7i). DFT calculations revealed that high-entropy doping substantially constricted the band gap, simplifying electron excitation into the conduction band, and bolstering electron mobility. The reduction potential (E_c) of the conduction band edge and the oxidation potential (E_v) of the valence band edge is displayed in Fig. 7k. It is worth noting that the electron excitation and leaps are favored by the narrow band edge width of M5HCF. Furthermore, the total density of states (DOS) and partial density of state (PDOS) of M5HCF and medium-entropy PBAs are calculated in Fig. 7l. Those calculations confirm that doping with high entropy can enhance the electron density and conductivity of PBAs, also have a great influence on electrochemical performance at high rates.

TM doping or substitution methods used in elemental adjustments can regulate interatomic interactions, ultimately impacting the inherent stability of materials. In particular, the substitution of manganese with iron, nickel, or cobalt in Mn-based PBAs can minimize cathode degradation caused by disproportionation reactions and the Jahn-Teller distortion. Present advances in high-entropy doping help decrease the water affinity of PBAs and regulate their electronic spin states, thus boosting their electrochemical properties. Nonetheless, substituting Mn with inactive TM results in lost energy density and significantly higher costs of metal salts such as Ni and Co compared to Mn. More importantly, due to its promising adaptability, it is worthwhile to balance the relationship between energy density, cycle life, and manufacturing cost by utilizing TM doping or substitution, in various application environments.

The enhancement of structural stability in electrode materials is often linked to high crystallinity, which is evident in various systems such as chalcogenides, conducting polymers, and organic superconductors [110,111,112]. To address the issue of TM ion dissolution and thereby bolster both structural and cyclic resilience, it is imperative to engineer PBA materials of superior crystallinity. Present synthesis methodologies for PBAs predominantly encompass the self-decomposition of an exclusive iron source and co-precipitation in water. The self-decomposition approach, albeit slower in reaction kinetics, permits facile control over particle morphology and size; however, it is restrictive, allowing the synthesis of only FeHCF. Conversely, the prevalent technique involves the aqueous co-precipitation of a TM solution with a cyanide anion solution. Despite its advantages—low cost, scalability, and versatility in obtaining PBAs of varied chemical compositions—this method is not without shortcomings. The minuscule solubility product constants of PBAs in water necessitate exceedingly rapid crystal nucleation and growth, consequently leading to substantial crystal defects and vacancies in Fe(CN)₆, coordinated by lattice water. These inherent imperfections significantly undermine the stability of PBAs, facilitating the accelerated dissolution of TM ions. Given these dynamics, the strategic synthesis of ultra-low-defect PBAs becomes paramount in mitigating the challenges posed by TM ion dissolution. It is essential to refine existing methodologies or innovate new synthetic strategies to enhance the precision and control of crystal growth, thereby improving the performance metrics of PBA-based electrode materials.

Wang et al. reported the synthesis of K₂Fe^II[Fe^II(CN)₆]·2H₂O nanocubes, characterized by an open backbone structure, via a low-temperature solvothermal method employing ethylene glycol as the solvent [113]. This transition from water to ethylene glycol leveraged the solvent's reductive properties to prevent the oxidation of Fe²⁺. The resultant K₂Fe^II[Fe^II(CN)₆]·2H₂O manifested as homogeneous nanocubes, each with an approximate side length of 200 nm (Fig. 8a). Subsequent Rietveld-refined X-ray diffraction analysis revealed the crystal structure identifying it as an orthorhombic symmetric formation within the Pmn21 space group (Fig. 8b). The refined structural model, displayed in Fig. 8c, demonstrated an octahedral framework, wherein two additional Fe atoms were alternately coordinated with carbon and nitrogen. Further electrochemical investigations, depicted in Fig. 8d, highlighted the material's expedited electrochemical kinetics and minimal polarization in an aqueous electrolyte, as evidenced by multi-sweep cyclic voltammetry. The endurance test underscored the compound's robust reversibility, maintaining performance over 500 cycles at varying current densities of 500, 2000, and 3000 mA g^-1 (Fig. 8e).

Yang et al. delineated the fabrication of defect-free Na₂CoFe(CN)₆ nanocubes using a citrate chelator and explored their electrochemical characteristics in ASIBs [61]. In the co-precipitation phase, citrate ions selectively chelate Co²⁺, creating cobalt-citrate complexes, thereby moderating the rapid precipitation dynamics to facilitate the formation of uniform nanocubes. SEM images (Fig. 8f and g) confirmed that the synthesized NaCoHCF particles comprised well-defined, discrete nanocubes measuring 300-600 nm in size. The charge/discharge assay of the assembled NaCoHCF||NaTi₂(PO₄)₃ full cell, illustrated in Fig. 8h, demonstrated superior rate capability and cyclic durability (Fig. 8i). Subsequent application of Na₂CoFe(CN)₆ within organic SIB frameworks retained commendable sodium storage efficacy [114]. In a separate study, Cai et al. scrutinized the crystallinity of PB cathodes in influencing the electrochemical attributes of ASIBs [115]. High-crystallinity PB, attributed to its immaculate lattice structure and distinct nanocubic morphology, exhibited elevated discharge potential and enhanced cycle life. Concurrently, Xue et al. crafted PBAs under varying crystallinity by manipulating the acidic milieu, assessing their impact on APIBs [116]. Notably, KFe(1.0) (K_1.93Fe[Fe(CN)₆]_0.97·1.82H₂O) with pronounced crystallinity, composed of 50-nm microcrystals, registered the pinnacle of reversible capacity and performance diversity. Ex situ XRD analyses discerned negligible crystallographic alterations during K⁺ intercalation, with only marginal lattice parameter fluctuations, corroborating the structural integrity of the high-crystallinity KFe(1.0) (Fig. 7j).

The fabrication of single-crystal cathodes, characterized by micrometer-sized individual particles devoid of grain boundaries, has been advocated to enhance stability and dependability. This strategy has recently garnered significant interest, underscoring the imperative for a synthesis technique tailored to PBAs. By minimizing grain boundaries, single-crystal particles curtail side reactions, deter TM ion dissolution, and mitigate voltage degradation. Hu et al. pioneered the creation of inverse opal single-crystal PBAs, exploiting the solubility properties of PBAs in volatile HCl environments and subsequent crystallization within a template [117]. These single-crystal constructs augment the contact surface, interfacing the structural matrix with the external conductive network or electrolyte, markedly abbreviating the ion diffusion path from the surface to the internal matrix. Notably, within the cohort of APIBs, these single-crystal PBAs manifest exemplary electrochemical prowess, sustaining nearly intact capacity retention approaching 100% post 1000 cyclic repetitions under a load of 20 A g^-1.

Furthermore, it is worth noting that not all defects have adverse effects. A rational structural design can be made in PBAs by incorporating controllable defects or vacancy engineering, which enhancing structural stability, improving dissolution, and offering novel ideas in further explorison [37,117,118]. Mai et al. discovered that they could impede the movement of Fe-C bonds by intentionally introducing Fe^III vacancies in PBAs. In addition, it effectively mitigated the lattice distortion of Fe-C octahedra, thus leading to improvements in PBAs' reversibility and cyclic stability [119]. In a similar study, Yang et al. utilized strong chelation to introduce manganese vacancies, V_Mn, on the surface of MnHCF [66]. For this V_Mn, it can impede Mn-N bond movement, thus preventing Jahn-Teller distortion of the Mn-N₆ octahedra, causing a reversible phase shift in the structure from monoclinic, cubic, and orthorhombic phases and improving electrochemical stability.

Particularly, the defects inherent in the structure of PBAs increase their susceptibility to solubilization, not only hindering ion storage and transport but also impairing crystallinity and structural robustness. Meanwhile, this can expedite the rapid dissolution of TM ions. With the use of low-cost aqueous co-precipitation synthesis, it is feasible to work out a promising approach of reducing harmful structural defects in designing rational structures incorporating low-cost chelating agents. However, further research is required on the precise conformational relationships of PBAs, given the complex influencing factors in the synthesis process.

The strategy of engineering composites grounded in PBAs presents a promising pathway to curtail TM ion migration efficaciously. Among various transition metal ions, the leaching of Mn ions into the electrolyte exhibits pronounced severity, necessitating a targeted approach for its mitigation. Liao et al. enhanced the electrochemical attributes of Na₂Mn[Fe(CN)₆] (PBM) through a meticulous solution-precipitation technique, encapsulating it with Na₃(VOPO₄)₂F (NVOPF) [120]. This NVOPF encapsulation served to thwart the ancillary reactions between PBM and the electrolyte, concomitantly stalling the dissolution of Mn ions, thereby bolstering electrochemical efficacy. Subsequently, an advanced composite, PBM@PBN, was synthesized by overlaying PBM with Na₂Ni[Fe(CN)₆] (PBN) [121]. The PBN stratum not only impeded PBM's peripheral reactions with the electrolyte but also forestalled the seepage of Mn²⁺ ions therein, culminating in augmented multifaceted performance and extended battery longevity. As depicted in Fig. 9a, ICP analyses post-extended cycling sessions revealed a marked curtailment in electrolytic Mn. Initial dissolution rates of Mn from both PBM and PBM@PBN electrodes were akin. Nonetheless, after 200 cycles, PBM witnessed a quadrupled Mn dissolution rate relative to PBM@PBN, underscoring the inhibitory role of the PBN coating. Furthermore, energy-dispersive X-ray spectroscopy (EDS) mapping affirmed a higher residual Mn content on the PBM-separated membrane compared to its PBM@PBN counterpart (Fig. 9b and c). Hu et al. unveiled a simplistic aqueous phase coating technique, devising a comprehensive CoχB layer upon the MnHCF surface [122]. Owing to the all-encompassing nature and buffer capacity of the nanoscale CoχB layer, the tailored MnHCF hindered Mn ion dissolution, minimized intraparticle fissuring, and, thus, demonstrated endurance through thousands of cycles. Figure 9d vividly captures the CoχB's ameliorative impact on MnHCF's structural frailties and Mn ion dissolution throughout the cycling process. Ex situ XRD analyses revealed the MnHCF-5% CoχB electrode undergoing reversible phase modulations from rhombohedral to tetrahedral configurations amid Na⁺ intercalation/de-intercalation (Fig. 9e), validating the CoχB coating's efficiency in negating cubic particle deformation.

The development of composites based on PBAs presents a strategy for enhancing electrochemical attributes in ASIBs. For instance, Feng et al. enhanced the specific capacity and rate performance of Na_1.88Fe[Fe(CN)₆]·0.7H₂O by integrating Ketjenblack through a ball milling process [123]. Similarly, Zarbin et al. synthesized carbon nanotube composite PBAs, where the formation of PB on individual CNTs facilitated slower Fe diffusion, thereby improving reversibility and stability in APIBSs [124]. This structural modification also conferred enhanced electronic conductivity, ameliorating charge transport limitations within the PBs. In another study, Coronado et al. developed PB/MoS₂ nanocomposites, with MoS₂ promoting uniform PB nucleation, which expanded the material's specific surface area [125]. This increased optimized PB-matrix contact, enhancing electron transport and structural resilience, reflected in superior cathodic properties for ASIBs and APIBs. Performance metrics indicated a discharge capacity of 177 mAh g^-1 and a specific capacitance of 354 F g^-1 at 1 A g^-1 for ASIBs, with APIBs demonstrating improved values of 215 mAh g^-1 and 489 F g^-1 under identical conditions. Addressing PBM's electrical conductivity deficits, Li et al. incorporated GO and rGO to form GO/PBM and rGO/PBM composites, as depicted in Fig. 9f [126]. Spectroscopic analysis revealed an elevated G-band intensity for rGO/PBM relative to GO/PBM, suggesting augmented sp²-hybridized carbon concentration post-reduction, thereby bolstering rGO/PBM conductivity (Fig. 9g). Concurrently, diminished water content in both composites implied defect diminution (Fig. 9h). This structural refinement facilitated commendable cycling stability, retaining approximately 91% and 89% capacity over 200 cycles for GO/PBM and rGO/PBM, respectively (Fig. 9i). Notably, rGO inclusion substantially enhanced the active material's electrical conductivity, expediting Na⁺ intercalation/deintercalation and markedly boosting rate performance (Fig. 9j).

Combining the conductive material and PBA can create a protective layer on the surface of the electrode material, reducing the impact of reactive water on the PBA and minimizing lattice damage during charging and discharging cycles. This method addresses the issue of inadequate intrinsic conductivity in PBA, prevents material dissolution caused by structural collapse, and enhances the overall stability of the composite electrode. Since PBAs' poor intrinsic thermal stability decomposes at 350 °C, the limited selection of composite strategies is largely available. Thus, further research can be focused on identifying stable candidate materials in both electrode material and electrolyte to expand the options for stable composite formation with PBAs at lower temperatures.

Electrolyte design aims to reduce free water and control the dissolution equilibrium, requiring an analysis of parameters such as salt anions’ hydrophobicity, salt concentration, and salt solubility in aqueous solutions. For PBAs, they encounter restricted voltage windows and significant problems with TM ion dissolution during cycling in low salt concentration conventional electrolytes. Therefore, the importance of developing electrolytes that broaden voltage windows and hinder TM ion dissolution cannot be overstated. High salt concentrations are the most effective and efficient strategy for high-energy, stable aqueous batteries, though the cost may hinder larger-scale use. Additionally, non-flammable electrolytes with high WiSE concentrations can expand the electrochemical stability window and curb material dissolution. The high viscosity and slow interfacial processes impede electrode kinetics and ion transport, hindering high rate performance. Nonetheless, energy storage devices prioritize cycle stability and energy density over other metrics. Specifically, in situ surface modification and repair of PBA materials can be accomplished by introducing a cation trapping agent into the electrolyte to inhibit TM ion dissolution. Synergizing the WiSE technique with an in situ surface modification strategy can potentially optimize energy density and cycle stability, making it a promising avenue of research. Additionally, developing new ‘dilute’ high-concentration electrolyte systems could enhance competitiveness by reducing costs and improving both rate performance and cycle stability.

In general, defects in the synthesis process can lead to structural breakdown during subsequent cycles for PBA cathodes. Therefore, it is necessary to improve synthesis methods aiming to minimize these harmful defects. In addition, aqueous co-precipitation synthesis and appropriate chelating agents are crucial for low cost, large-scale synthesis. Moreover, the electrochemical framework can be designed and adjusted through doping/substitution strategies using TM. Particularly, MnHCF is advantageous due to its low cost and high-energy density. However, the dissolution of Mn has received great attention, especially the dissolution partially replacing Mn with inactive TM, which can be reduced. Structural distortion from the Jahn-Teller effect can also be reduced. In addition, it is of significant interest on the incorporation of trace Co doping for self-repair and the emergence of high-entropy PBAs. Furthermore, combining PBAs with highly conductive materials boosts conductivity, prevents material dissolution from structural collapse, and enhances composite electrode stability. The overall rate performance and cycling stability can be significantly improved by synergizing these strategies. Notably, there is a lack of comprehensive research on anode material modification strategies, specifically on TM deposition on SEI. This topic desperately requires the attention of professionals and academics.

The integration of advanced in situ characterization methodologies with theoretical computations serves as a pivotal auxiliary instrument, deepening the comprehension of electrochemical processes in PBAs for ASIBs and APIBs. Delving into the dissolution phenomena of TM ions mandates the utilization of refined in situ characterization techniques, including in situ XRD, TEM, XPS, Raman, and STEM, fostering an intricate understanding of the underpinning principles of TM ion dissolution. In parallel, molecular dynamics simulations prove instrumental in dissecting interfacial interactions between electrodes and electrolytes, thereby elucidating critical parameters within the TM ion dissolution trajectory. Additionally, first-principles calculations, particularly those concerning the density of states and ion diffusion barriers within PBA electrodes, are indispensable in uncovering inherent reaction pathways and crystallographic transformations during charge-discharge cycles. For the application of these advanced characterizations and computational tools, there is a deeper understanding of the TM dissolution mechanism that helps to overcome the electrochemical performance degradation caused by TM dissolution-migration-deposition.

In the strategic enhancement of battery design and management, cognizance of the aging mechanism and subsequent implications of battery degradation is paramount. Battery cycle life is subject to an array of influences. Notably, the cathode undergoes recurrent alterations in its material constitution throughout the charge/discharge cycles, culminating over time in structural disintegration, TM ion dissolution, and consequent capacity attrition. The attrition of electrolyte volume markedly impinges on the comprehensive battery lifespan, a scenario pronounced particularly in button and soft-pack batteries. Marginal electrolyte diminution marginally impacts battery functionality, whereas substantial electrolyte depletion precipitates an abrupt capacity regression. Furthermore, issues stemming from alkali metal deposition and solid electrolyte interphase formation contribute to expedited capacity deterioration, engendering safety concerns. Addressing battery degradation necessitates expanded research, with a substantial body of inquiry concentrating on the capacity degradation attributable to individual determinants. Unraveling the inherent correlation among the rates of cathode capacity decay, capacity decay, and electrolyte utilization is crucial for achieving equilibrium control at the battery's operational limit.

Conflict of interest The authors declare no interest conflict. They have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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