The solution coprecipitation method is a low-cost, non-toxic, highly controllable, highly scalable and mass-producible method for PBAs. In the conventional coprecipitation process, the extremely high precipitation rate leads to too fast nucleation rate, and the prepared PBAs particles have the disadvantages of low crystallinity, serious particle agglomeration, and a large number of lattice vacancies and water. Chelating agents are usually added to the precursor solution to reduce the nucleation rate and improve the crystallinity of the product. The ligand of the chelator has a high complexing ability with transition metal ions, acting as a competitor for M₂ CN {{)}_6}^{4-} ions and hindering the spontaneous nucleation and precipitation of PBAs. The negatively charged ligand ions can be adsorbed on the surface of the initial nucleus at the same time, which can inhibit the growth rate of the nucleus and prevent serious grain aggregation. Nuclei tend to grow into well-shaped monodisperse grains containing fewer defects under the action of chelating agents. Citrate, oxalate, disodium ethylenediaminetetraacetate (Na₂EDTA), sodium manganese ethylenediaminetetraacetate (MnNa₂-EDTA), sodium pyrophosphate (Na₄P₂O₇) and other chelating agents have been added to the material preparation process to obtain PBAs with good crystallinity and low vacancy content^{[22,25⇓⇓⇓⇓⇓~31][32][33][34][35⇓~37]}.

Sodium citrate contains three carboxylate groups, which can complex with divalent and trivalent metal ions according to the molar ratio of 1 ∶ 1. It is a common chelating agent in the preparation of PBAs, especially for Ca²⁺, Fe²⁺ and Mn²⁺. Zuo et al. Synthesized cubic Na_1.56Mn[Fe(CN)₆]0_.86□_0.14·1.2H₂O by using sodium citrate to control the nucleation rate during the precipitation reaction^[22]. When the current density is 15 mA·g^-1, the reversible discharge specific capacity of 133 mAh·g^-1 can be provided, and the redox mechanism is revealed:

{\mathrm{Na}}_2^{+} Mn²⁺[Fe²⁺(CN)₆]↔Na⁺Mn²⁺[Fe³⁺(CN)₆]+Na⁺+e^-

Na⁺Mn²⁺[Fe³⁺(CN)₆]↔Mn³⁺[Fe³⁺(CN)₆]+Na⁺+e^-

Shen et al. Obtained the sodium-rich monoclinic phase Na_xMnFe(CN)₆ by carrying out the precipitation reaction at high temperature and adding sodium citrate into the precursor solution^[25]. The obtained product has two morphologies of small irregular particles and large cuboid particles, as shown in fig. 1. When sodium citrate was not added to the precursor solution, PBAs could be rapidly nucleated in an environment with high concentrations of Mn²⁺ and [Fe(CN)₆]^4- ions to form many small-sized and irregularly shaped particles (PW-2). After the addition of sodium citrate, some Mn²⁺ ions can be complexed by sodium citrate to form a complex, so that two kinds of Mn²⁺, free Mn²⁺ and complexed Mn²⁺, exist in the solution. During the reaction, free Mn²⁺ ions can rapidly react with [Fe(CN)₆]^4- ions to form irregular small-sized particles. In contrast, the release rate of the Mn²⁺ from the complex is lower, resulting in a slower nucleation rate and thus a larger particle size of the prepared PBAs. The Na_1.80Mn[Fe(CN)₆]_0.98·1.76H₂O(PW-1) prepared by sodium citrate-assisted coprecipitation method can provide a specific discharge capacity of 144 mAh·g^-1 at 0.1 C(1 C=150 mA·g^-1), and can still maintain 72. 7% of the initial capacity after 2100 cycles at a current density of 1 C.

In addition to the addition of sodium citrate, polyphosphate chelating agents are also commonly used in the preparation of PBAs. Xu et al. Synthesized high-performance and high-stability monoclinic Na_1.48Ni[Fe(CN)₆]_0.89·2.87H₂O(NaNiFe(CN)₆) by adding Na₄P₂O₇ to the precursor solution to reduce the coprecipitation rate^[35]. The lattice distortion in the monoclinic sample reduces the band gap (as shown in Figure 2) and promotes the redox activity of Fe, which can deliver a discharge capacity of 85.7 mAh·g^-1 at 0.1 C and no obvious capacity fading after 1200 cycles at a current density of 300 mA·g^-1.

High concentration of Na⁺ in the precursor solution is an important condition for the preparation of PBAs with high Na content. The addition of excessive sodium source can not only increase the sodium ion content of the sample, but also help to stabilize the crystal structure. PBAs can be classified as Berlin green (BG), Prussian blue (PB), and Prussian white (PW) with increasing Na⁺ content in PBAs^[38].

Cui et al. Prepared Na_xMn[Mn(CN)₆](209 mAh·g^-1) with extremely high discharge capacity by using excess NaCl^[39]. To study the effect of Na⁺ concentration on the performance of PBAs, Li et al. Prepared CoHCF with high sodium content (H-CoHCF) and CoHCF with low sodium content (L-CoHCF) by controlling the NaCl content^[26]. It was found that the chemical formulas of the two products were Na_1.87Co[Fe(CN)₆]_0.98·2.2H₂O and Na_1.47Co[Fe(CN)₆]_0.90·2.3H₂O. The initial specific discharge capacity (151.1 mAh·g^-1) of H-CoHCF at a current density of 20 mA·g^-1 is significantly higher than that of L-CoHCF(128.8 mAh·g^-1). After 100 cycles, the discharge capacity retained 85.2% and 78.03% of the initial discharge capacity, respectively. It can be seen that high Na⁺ content in the solution plays an indispensable role in the preparation of high-performance PBAs.

To study the effect of Na⁺ concentration on the properties as well as the structure of PBAs in more detail, Chen et al. Synthesized Na-enriched PBAs by controlling the Na⁺ ion concentration during the synthesis process^[40]. By increasing the concentration of Na⁺ in the synthesis process, a series of PBAs were prepared by using 0 M, 1 M, 2 M, 3 M and 4 M NaCl solutions, respectively. The scanning images of PBAs are shown in Fig. 3 (a ~ d). With the increase of NaCl concentration, the morphology of PBAs changes from a cuboid with almost no visible defects to a multi-level rod-like structure, and then to a porous structure. The large specific surface area of PB-4M leads to a large area of contact between the electrode and electrolyte, and the porous structure can also promote the penetration of electrolyte and accelerate the transport of Na⁺. Electrochemical tests show that PB-4M has excellent thermal stability. The specific capacity of PB-4M at room temperature is 130 mAh·g^-1, and even at 80 ℃, it can still maintain a specific capacity of 120 mAh·g^-1. PB-4M can still deliver a reversible specific capacity of 57 mA·g^-1 after 500 charge-discharge cycles at a current density of 2 C at 80 ° C.

Element doping has been widely used in SIB materials as a basic method to adjust the capacity, lifetime, rate capability and production cost, and it is one of the most effective modification methods. Metal ions are usually doped at the M site or Na site. Transition metal ions, such as Ni²⁺, Co²⁺, Cu²⁺, Mn²⁺, Sn⁴⁺, etc., partially replace the metal at the M site^{[41⇓⇓⇓⇓⇓⇓⇓⇓⇓~51]}. K⁺ is usually doped at the Na site^[52].

Ni is often used as a doping element to improve the cycle stability of Mn[Fe(CN)₆] and Fe[Fe(CN)₆] due to the "zero strain" characteristics of Ni[Fe(CN)₆](NiHCF) during intercalation/deintercalation. Especially for Mn[Fe(CN)₆], the dismutation reaction of Mn³⁺ will occur during cycling to form Mn²⁺ and dissolve in the electrolyte, resulting in more serious capacity fading than other PBAs. However, Ni doping can significantly improve the cycle stability of Mn[Fe(CN)₆]. Oliver-Tolentino et al. Studied the effect of equimolar substitution of Ni for Mn in the open framework of the SIB electrode material hexacyanoferrate (HCF)^[41]. The results show that the substitution of Ni for Mn can increase the covalency of Mn — N bond, which can weaken the influence of electrostatic interaction on the dz² orbital during charge/discharge, thus improving the current stability. In addition, Ni doping reduces the charge density around the Mn — N bond relative to the polarizing ability of the external metal, thereby improving its rate capability. Although the cycle stability can be significantly improved after Ni doping, the entropy inevitably increases during the cycle process, and most electrode materials tend to degrade during the charge-discharge process. Recently, Xie et al. Designed a method to promote the morphological regeneration of PBAs cathode by cobalt doping^[42]. A trace amount of cobalt can slow down the crystallization process and restore the cracked region to ensure the perfect cubic structure of the PBAs cathode, and the high cycling stability is obtained based on the "electrochemically driven dissolution-recrystallization" mechanism. This self-healing during cycling provides a new strategy to improve the performance of PBAs.

At present, people's research is not limited to single element doping, and two or even three elements have been used to dope PBAs. For example, Zhang et al. Successfully synthesized ternary NiCoFe-PB with good crystallinity, high Na content, low defects and crystal water by double doping of Co and Fe at the Ni site^[48]. The energy barrier and band gap of Ni-PB can be significantly reduced by double doping of Co and Fe, which is confirmed by first-principles calculations. Electrochemical measurements show that in addition to the capacity contribution of high-spin Co, Fe and low-spin Fe, Co-doping improves the electrochemical activity of low-spin Fe, and Fe-doping improves the activity of high-spin Co. After co-doping, its thermal stability has also been significantly improved. Na_1.85Ni_0.40Co_0.31Fe_0.29[Fe(CN)₆]_0.97·2.5H₂O can deliver a specific discharge capacity of 120.4 mAh·g^-1 at a current density of 20 mA·g^-1, and when the current density increases to 1 A·g^-1, it still maintains the highest theoretical capacity as well as excellent cycling performance. After 1500 cycles, NiCoFe-PB can maintain a high capacity of 68.3 mAh·g^-1, while Ni-PB, NiCo-PB and NiFe-PB only maintain discharge capacities of 23.1, 41.4 and 47.3 mAh·g^-1.

Different from the traditional doping method at the M site, doping the material with alkali metal ions K⁺ with larger radius is also an effective new modification method. Wei et al. Synthesized a novel structure-controlled sodium-site K-doped Ni[Fe(CN)₆](K-NiHCF), and obtained smaller PBAs particles after doping. Density functional theory (DFT) revealed that sodium-site K-doping could effectively stabilize the structure of NiHCF and improve the transport behavior of sodium ions and electrons^[52]. Inductively coupled plasma optical emission spectroscopy (ICP-OES) measurements of the cycled electrode slices as well as the electrolyte showed that K⁺ could not be extracted from the PBAs lattice, and that K⁺ could act as a pillar in the PBAs structure at the time of Na⁺ extraction. K⁺ doping can effectively reduce the energy barrier of Na⁺ diffusion and reduce the band gap width. Thus, the Na_1.61K_0.13Ni[Fe(CN)₆]_0.89·1.48H₂O electrode exhibited excellent sodium storage performance with an extremely high initial discharge capacity of 87.1 mAh·g^-1 at 10 mA·g^-1, retaining ∼ 86.1% of the initial capacity after 500 cycles at a current density of 500 mA·g^-1 (Fig. 4).

In order to maintain the structural stability of PBAs and inhibit the mechanical degradation, it is necessary to construct the structure at the atomic level, and the introduction of electrochemical inert ions is considered to be a feasible way^[53]. Inert ions and active ions are orderly arranged to form a core-shell structure, which not only improves the cycle stability, but also improves the interfacial compatibility.

NiHCF is often used to coat other PBAs with relatively poor cycle stability due to its ultra-high cycle stability and almost no strain during cycling. For example, the disproportionation reaction of Mn[Fe(CN)₆](MnHCF) materials during charge-discharge cycles will lead to the dissolution of Mn in the electrolyte, resulting in structural damage. Feng et al. Prepared a core-shell heterogeneous Mn[Fe(CN)₆]@Ni[Fe(CN)₆](PBM@PBN) nanomaterial by coating Ni[Fe(CN)₆](PBN) on Mn[Fe(CN)₆](PBM) through a simple solution precipitation method^[54]. The cycling stability of PBM was significantly improved after the introduction of PBN shell. Therefore, the PBN coating is able to inhibit the severe Mn ion dissolution of PBM during Na⁺ intercalation/deintercalation, thus ensuring the framework stability of PBM during long-term cycling (Fig. 5).

The NiHCF layer is not only beneficial to improving the performance of the MnHCF material, but also plays an important role in improving the cycle stability of the (Fe[Fe(CN)]₆)FeHCF. Sun et al. Successfully introduced NaNi[Fe(CN)₆](NNFCN) into the outer layer of NaFe[Fe(CN)₆](NFFCN) by ion exchange method to improve the structural stability by applying compressive stress through the formation of NNFCN shell^[55]. The improved stability of NNFCN @ NFFCN (NNFFCN) benefits from the almost negligible volume expansion of NNFCN, so that the strain generated in the core during Na⁺ intercalation can be partially suppressed, weakening the destruction of the NFFCN core. Two kinds of core-shell PBAs, NNFFCN-0.002M NiCl₂ and NNFFCN-0.005M NiCl₂, were prepared by varying the NiCl₂ concentration (0.02 M and 0.05 M) in the precursor solution. At a current density of 500 mA·g^-1, the NNFFCN-0.002M NiCl₂ exhibited a high specific discharge capacity of 82.9 mAh·g^-1 and excellent rate capability, which was 3.5 times higher than that of the Original NFFCN (NFFCN-original) at 1000 mA·g^-1, and the full cell with NNFCN @ NFFCN as the cathode showed remarkable cycling stability at 500 mA·g^-1 for 3000 cycles. At the same time, the constructed core-shell heterostructure has a built-in electric field, and the NNFCN @ NFFCN has fast Na⁺ migration characteristics, and the Na⁺ diffusion coefficient is significantly improved (1×10^-10cm²·s^-1) compared with the diffusion coefficient (4×10^-11cm²·s^-1) of the original NFFCN (Fig. 6).

In addition to NiHCF, Cu[Fe(CN)₆](CuHCF) can also serve as a good coating shell. Wang et al. Prepared FeHCF @ CuHCF composite with porous structure by hydrothermal method, which has excellent cycling stability^[56]. 80.6% of the initial specific capacity can be retained after 1000 cycles at a current density of 50 mA·g^-1. Although the design of core-shell structure has played an important role in improving the electrochemical performance of PBAs, the complicated preparation process and strict lattice matching requirements have limited the development of core-shell PBAs. Recently, Zuo et al. Synthesized core-shell PBAs (MnFeHCF @ MnFeHCF) by one-step synthesis method for the first time, which showed excellent rate performance^[57]. It has a high capacity of 131 mAh·g^-1 at a current density of 50 mA·g^-1 and exhibits an appreciable discharge capacity of about 100 mAh·g^-1 even at 1600 mA·g^-1. The performance improvement of the material is mainly due to two aspects, the first aspect is that the substitution of Mn helps to improve the conductivity of the material, and the other aspect is that the core-shell structure with matched lattice parameters is more conducive to improving the diffusion coefficient of sodium ions. In addition, the structural transformation of MnFeHCF @ MnFeHCF upon extraction/insertion of sodium ions helps to release the internal stress and effectively maintain the integrity of the crystal structure (Fig. 7).

Poor electronic conductivity is one of the intrinsic factors that limit the high rate and high capacity of PBAs. In view of the poor electronic conductivity of PBAs, the introduction of conductive materials into PBAs has become an effective way to improve their rate performance and capacity. However, due to the low decomposition temperature of PBAs, the conventional high-temperature coating process is not technically feasible^[58]. Therefore, a new technique for introducing conductive materials into PBAs by solution method has been widely studied. This is mainly using conductive carbon materials such as reduced graphene oxide (RGO), graphene oxide (GO), graphene (GR), carbon nanotubes (CNT) to composite with PBAs in liquid phase environment^{[59,60][61][62][63,64]}.

Graphene oxide is often used to prepare composites because of its high specific surface area, abundant functional groups on the surface, and good conductivity. Wang et al. Prepared a NaMn[Fe(CN)₆]/RGO(NMHCF/RGO) composite with high Na content by a simple precipitation method^[59]. Immobilizing NMHCF on RGO, the presence of RGO not only improves the electronic conductivity, but also helps to eliminate the interstitial water. The interstitial water content of NMHCF(Na_1.89Mn[Fe(CN)₆]_0.98□_0.02·0.16H₂O) encapsulated with RGO was significantly lower than that of NMHCF(Na_1.67Mn[Fe(CN)₆]_0.9□_0.1·11.47H₂O) without RGO, as verified by ICP analysis. The discharge capacity of NMHCF/RGO is obviously improved, and the specific discharge capacity is 161 mAh·g^-1 at a current density of 20 mA·g^-1. Even at a current density of 1000 mA·g^-1, NMHCF/RGO can still provide a specific discharge capacity of 90 mAh·g^-1 (Fig. 8).

Carbon nanotubes can be seen as curled graphene, so they also have excellent conductive properties. You et al. Formed a robust Na_xFeFe(CN)₆/CNT(PB/CNT) composite by nucleating Na_xFeFe(CN)₆ cubic nanoparticles on CNTs, and PB particles nucleated on carbon nanotube fibers to form a continuous conductive network^[63]. The CNT network can facilitate the entry of PB nanoparticles into the liquid electrolyte and good contact with the current collector to improve its electrochemical performance at low temperature. The intercalated carbon nanotubes significantly improve the electron transport ability of the composite, resulting in a room temperature electronic conductivity of PB/CNT that is four orders of magnitude higher than that of bare PB. In addition, due to the "metallic character" of carbon nanotubes, the conductivity of PB/CNT is further increased by 47.6% when cooled to -25 ° C, which holds great potential for building low-temperature batteries. At − 25 ° C and a current of 0.1 C, PB/CNT can still deliver a specific capacity of 142 mAh·g^-1 and a specific energy of 408 Wh·kg^-1, with a capacity retention of 86% after 1000 cycles at a current density of 2.4 C.

In addition to the introduction of conductive carbon materials, composite conductive polymers are also an effective way to improve the electrochemical performance of PBAs, and the use of conductive polymers can effectively reduce the occurrence of side reactions. At present, polyaniline (PANI), sodium vanadium fluorophosphate (NVOPF), poly (3,4-ethylenedioxythiophene) (PEDOT), poly (3,4-ethylenedioxythiophene) ∶ poly (4-styrenesulfonate) (PEDOT ∶ PSS) composite PBAs have been developed^{[65,66][67][68][69]}.

Polyaniline is a special conductive polymer, and its conductivity comes from the conjugated structure of p electrons in the molecular chain. The coating of polyaniline can significantly improve the poor conductivity of PBAs. Zhang et al. Prepared Prussian blue nanocubes with high crystallinity and good dispersion by a single iron source precipitation method, and then coated a layer of uniform conductive polyaniline on their surface through the polymerization of aniline with the assistance of polyvinylpyrrolidone (PVP) to form a core-shell structure^[65]. PANI inhomogeneously coated PB (PB @ PANI-NP) was obtained without the addition of PVP. PB @ PANI has an initial specific discharge capacity of 108.3 mAh·g^-1 at a current of 100 mA·g^-1 and exhibits excellent rate capability as well as cycling stability. At 5 A·g^-1, this electrode material has a capacity of 63.3 mAh·g^-1 with 93.4% capacity retention after 500 cycles at a current density of 100 mA·g^-1 (Fig. 9). Different from the two-step preparation of PANI-coated PBAs, Yu et al. Adopted an in situ PANI coating strategy^[66]. The precursor of PB was rapidly precipitated after ball milling, and then aniline was added into the electrolyte and polymerized under electrochemical conditions, that is, the PANI was uniformly coated on the PBAs material by charge-discharge activation at a current density of 5 C and a voltage window of 3. 4 V ~ 4.2 V. The uniform coating of PANI greatly improves the ionic conductivity and electronic conductivity of the material. PB @ PANI has a specific discharge capacity of 149.9 mAh·g^-1 at a current density of 1 C. The polyaniline-coated electrode material exhibited a high specific capacity retention of 62.7% after 500 cycles. This is significantly higher than that of the uncoated sample (40.1%). The uniform conductive polymer coating can significantly improve the conductivity of the PBAs electrode and effectively inhibit the dissolution of transition metals in the electrolyte during long-term cycling.

Self-assembly of PBAs is an important method for the formation of complex morphologies. In recent years, materials with various special morphologies have attracted much attention. The hollow nanosphere structure has a high specific surface area, and the hollow structure can effectively reduce the volume change of the electrode material during the charge-discharge process. The preparation of hollow spheres generally requires a spherical template. For example, Tang et al. Used a simple hydrothermal method and annealing to prepare reduced Fe^ⅡOx hollow nanospheres as a self-sacrificial template to grow Na_1.58Fe[Fe(CN)₆]_0.92 hollow nanospheres under the protection of ascorbic and N₂ atmosphere^[70]. Similar to hollow nanospheres, hollow nanorods also have the advantage of hollow structure. Feng et al. Used manganese dioxide nanosheets as a self-sacrificial template to synthesize hierarchical hollow rod-like Mn-doped Prussian blue, and prepared PB (R-PB) with low vacancy content, low coordinated water content and high sodium content under solvothermal conditions^[71]. The hollow rod-like structure can effectively slow down the volume change caused by the intercalation/deintercalation process of Na⁺. The hollow rod-like structure also increases the contact area between the electrode material and the electrolyte, which improves the ion diffusion coefficient of r-PB and is beneficial to the electrochemical performance at high current density. Ren et al. Prepared Prussian white hierarchical nanotubes (PW-HN) as SIB cathode material by self-template Ostwald ripening strategy^[72]. In the initial stage of the reaction, part of the [Fe(CN)₆]^4- slowly decomposes into Fe²⁺ in an acidic environment. As the reaction proceeds, the oxidation of Fe²⁺ in the air is effectively inhibited with the help of a reducing agent (ascorbic acid), so that only a small amount of Fe³⁺ is produced. Subsequently, Fe²⁺/Fe³⁺ reacts with undecomposed [Fe(CN)₆]^4- at a slow reaction rate to form "insoluble ”Fe₄[Fe(CN)₆]₃ nuclei and give Prussian white framework with high Na content.". The morphology of the sample changes from short nanotubes to nanorods to layered nanotubes with increasing reaction time, as shown in Fig. 10 (e ~ G). PW-HN has higher specific capacity and lower polarizability than pristine PB. PW-HN has a specific discharge capacity of 115 mAh·g^-1 at a current density of 2 C as well as outstanding rate capability (specific discharge capacity of 83 mA h·g^-1 at 50 C) and excellent cycling stability (capacity retention of 65% after 10 000 cycles at a current of 10 C).

It is well known that both N₂ atmosphere protection and reducing agent can effectively inhibit the oxidation of Fe²⁺/Fe³⁺, thus enabling the preparation of PBAs with higher sodium content. Wang et al. Prepared rhombohedral Na₂Fe[Fe(CN)₆] by introducing N₂^[30]. Peng et al. Prepared highly crystalline sodium-rich Na₂Mn[Fe(CN)₆] in the presence of ascorbic acid and chelating agents^[34]. Tan et al. Used NaBH₄ as a reducing agent to prepare PW by the reduction reaction of PB^[73]. The obtained PW exhibits excellent electrochemical performance due to the extremely high sodium content, low vacancy and low water content. In addition to the prevention of transition metal oxidation during preparation, Na⁺ loss and Fe²⁺ oxidation also occur during the removal of impurities by water washing. Wang et al. Prepared PBAs with high sodium content and low vacancy content by replacing water with an aqueous solution of sodium ascorbate during the washing process to suppress the loss of Na⁺ and the oxidation of Fe^2+[74]. The material exhibited a specific capacity of 140 mAh·g^-1 at a current density of 0.1 C and good cycling stability.

The low precipitation rate has an indispensable role in reducing the defect of PBAs. In addition to the addition of chelating agents, Peng et al. First developed a facile "ice-assisted" strategy to prepare highly crystalline PBAs without any additives^[75]. The improved properties of these materials benefit from the slow precipitation rate achieved by slowly melting the raw materials, resulting in well-crystallized PBAs nanoparticles. It exhibits excellent sodium storage properties due to its highly reversible structure, sufficient Na⁺storage sites, and low defect concentration. More importantly, the elimination of defects also plays an important role in enhancing the thermal stability of this class of materials, making them suitable as cathode materials for SIBs (-10 ° C to 60 ° C).