Prussian Blue Analogue Mesoframes for Enhanced Aqueous Sodium-ion Storage

Mesostructure engineering is a potential avenue towards the property control of coordination polymers in addition to the traditional structure design on an atomic/molecular scale. Mesoframes, as a class of mesostructures, have short diffusion pathways for guest species and thus can be an ideal platform for fast storage of guest ions. We report a synthesis of Prussian Blue analogue mesoframes by top-down etching of cubic crystals. Scanning and transmission electron microscopy revealed that the surfaces of the cubic crystals were selectively removed by HCl, leaving the corners, edges, and the cores connected together. The mesoframes were used as a host for the reversible insertion of sodium ions with the help of electrochemistry. The electrochemical intercalation/de-intercalation of Na+ ions in the mesoframes was highly reversible even at a high rate (166.7 C), suggesting that the mesoframes could be a promising cathode material for aqueous sodium ion batteries with excellent rate performance and cycling stability.


Introduction
Coordination polymers, for instance, metal-organic frameworks (MOFs) or porous coordination polymers (PCPs), are molecular solids assembled by metal ions/clusters and ligands [1][2][3][4][5][6][7][8][9][10].The physical/chemical properties of coordination polymers, including the packing ordering of their component ions/molecules, are known to be determined by their structures [3,5,11,12].Therefore, the most widely used approach for the property regulation of coordination polymers is structure design via manipulation of the atomic/molecular packing by intermolecular interactions [13][14][15].Besides the great success achieved on the molecular/atomic scale, the structure design on a mesoscale (10~1000 nm) has recently been recognized as a promising choice [16][17][18][19].By downsizing of a bulk crystal, the volume ratio of the surface units to the bulk units can be increased significantly, leading to a coupling effect from the bulk structure and the surface units [17,20,21].For instance, the meso-sized coordination polymers can accommodate guest molecules still, but their phase-change type would be changed owing to the suppressing effect of the surface energy [14,[22][23][24].Downsizing can also shorten the diffusion distance when the guest molecules/ions travel inside, leading to high-rate adsorption/desorption ability.
46].In particular, Prussian Blue analogues have interstitial sites that are quite suitable for the alkali metal ions with a larger radius than that of the Li + ions and thus can be used as electrodes for a new generation of Na-ion and K-ion batteries [47][48][49][50][51][52][53][54][55][56][57].However, because of the poor electron conductivity of Prussian Blue analogues, it is necessary to make sure that Prussian Blue analogues can have a short diffusion distance for the guest ions [58][59][60][61][62][63][64].Therefore, Prussian Blue analogues mesoframes are highly needed.The most utilized strategy for the fabrication of mesoframes is selective etching, which occurs either during the synthesis or after the formation of compounds [14,22,[65][66][67][68][69][70][71][72][73].For example, when Prussian Blue crystal is crystallized in hot acid under a hydrothermal condition, the disassociation occurs during the growth process.When the disassociation rate is higher than the growth rate, etching of the crystal occurs [65].By understanding the disassociation kinetics of different parts of a crystal, post-etching becomes possible.When the location of the defects is known, a hollow cavity can be constructed inside the crystals as desired [12].In other cases, because of the spatial-dependent reactivity, for a cubic crystal of Prussian Blue analogues, the surfaces tend to be dissolved in the acidic/basic solution quicker than the corners and edges [22,74].Although in situ etching methods have been extensively utilized [75][76][77][78][79], they are not suitable for investigating the differences between solid cubes and mesoframes because of the difficulties in controlling the size/shape and composition.Alternatively, post-etching provides opportunities for comparison of the solid cubes and mesoframes with similar size/shape and composition.
Despite increased knowledge of the positive effect of mesoframes, the role of mesoframes on alkaline ion intercalation/de-intercalation in aqueous environment remains unclear.Compared to the alkaline ion intercalation/de-intercalation in organic electrodes, aqueous alkaline ion storage is safer and cheaper and thus is an indispensable solution for grid-scale energy storage [80][81][82][83][84].In this work, we fabricated Prussian Blue analogue (Na2Ni[Fe(CN)6], 1) mesoframes by post-etching the cubic crystals.The mesoframes of 1 showed improved Na + ion intercalation/de-intercalation at a high rate (166.7 C).

Materials
Sodium hexacyanoferrate (Na4[Fe(CN)6]•10H2O), nickel chloride hexahydrate (NiCl2•6H2O), hydrochloric acid (HCl), and trisodium citrate dihydrate (C6H5Na3O7•2H2O) were purchased from Sinopharm Chemical Reagent Co. and used without further purification.The most utilized strategy for the fabrication of mesoframes is selective etching, which occurs either during the synthesis or after the formation of compounds [14,22,[65][66][67][68][69][70][71][72][73].For example, when Prussian Blue crystal is crystallized in hot acid under a hydrothermal condition, the disassociation occurs during the growth process.When the disassociation rate is higher than the growth rate, etching of the crystal occurs [65].By understanding the disassociation kinetics of different parts of a crystal, post-etching becomes possible.When the location of the defects is known, a hollow cavity can be constructed inside the crystals as desired [12].In other cases, because of the spatial-dependent reactivity, for a cubic crystal of Prussian Blue analogues, the surfaces tend to be dissolved in the acidic/basic solution quicker than the corners and edges [22,74].Although in situ etching methods have been extensively utilized [75][76][77][78][79], they are not suitable for investigating the differences between solid cubes and mesoframes because of the difficulties in controlling the size/shape and composition.Alternatively, post-etching provides opportunities for comparison of the solid cubes and mesoframes with similar size/shape and composition.

Synthesis of Cubic Crystals of 1
Despite increased knowledge of the positive effect of mesoframes, the role of mesoframes on alkaline ion intercalation/de-intercalation in aqueous environment remains unclear.Compared to the alkaline ion intercalation/de-intercalation in organic electrodes, aqueous alkaline ion storage is safer and cheaper and thus is an indispensable solution for grid-scale energy storage [80][81][82][83][84].In this work, we fabricated Prussian Blue analogue (Na 2 Ni[Fe(CN) 6 ], 1) mesoframes by post-etching the cubic crystals.The mesoframes of 1 showed improved Na + ion intercalation/de-intercalation at a high rate (166.7 C).

Synthesis of Cubic Crystals of 1
Sodium hexacyanoferrate (5 mmol, 2.425 g) was dissolved in water (250 mL) to form a clear solution (Solution A).Nickel chloride hexahydrate (2.5 mmol, 587 mg) and trisodium citrate dihydrate (12.7 mmol, 3.75 g) were dissolved in water (250 mL) to form Solution B. Solutions A and B were mixed under magnetic stirring for 5 min and then allowed to age at 25 • C for 24 h.The product was obtained after centrifugation and washed with water and ethanol several times.Finally, the cubic crystals of 1 were collected by drying at 25 • C in a vacuum oven for 24 h.

Synthesis of Mesoframes of 1
The cubic crystals of 1 (50 mg) were added to 20 mL of 0.4 M HCl.The solution was ultrasonicated for 1 h.Then, the product was obtained after centrifugation and washed with water and ethanol several times.Finally, the mesoframes were collected by drying at 25 • C in vacuum oven for 24 h.We noted that Fe(II) in the surfaces of the crystals was easily oxidized into Fe(III) during etching in atmosphere according to the FT-IR spectrum (Figure S8).The existence of Fe(III) in the framework changed the crystal structure from R-3 into Fm-3m (Figure S9).Therefore, the powder needed to be reduced electrochemically to convert the Fe(III) into Fe(II), making sure the crystals structure of the mesoframes was R-3 before further characterization.

Characterization
The morphology of the products was observed by a field emission scanning electron microscope (FESEM, Hitachi S-4800) (Hitachi, Tokyo, Japan) and a transmission electron microscope (TEM, JEOL JEM-2100 F) ((JEOL, Tokyo, Japan).The powder X-ray diffraction patterns were measured with a Rigaku RINT 2500 X diffractometer with Cu Kα radiation (35 kV, 25 mA).The Fourier transform infrared spectroscopy (FT-IR) spectra were obtained with a Thermo Nicolet i50.

Electrochemical Measurement
The electrochemical performance was measured using three-electrode cells.The working electrode was prepared as follows: the powder of 1 (70%), acetylene black (20%), and poly(vinylidene difluoride) (10%) were well mixed in N-methyl-2-pyrrolidone until a homogeneous slurry was formed.The slurry was then coated onto the carbon cloth with an area of 1 cm × 2 cm and was dried at 80 • C in a vacuum oven for 15 h.The mass loading of the active materials was around 2 mg cm -2 for each test.An Ag/AgCl electrode was used as a reference.The counter electrode contained activated carbon instead of the prepared materials, and it was also coated onto the carbon cloth.These three electrodes were immersed in the neutral solution of 1 M NaNO 3 and measured with the CHI 660E (Shanghai Chen Hua Instrument, Shanghai, China) electrochemical workstation.

Results
The crystals of 1 were synthesized by a weak-chelation-agent-assisted crystallization method [85].Approximately, nickel chloride was mixed with tri-sodium citrate to form a green solution at first.Then, the green solution was mixed with a sodium hexacyanoferrate solution.After aging at room temperature for 24 h, the green precipitates were harvested.Scanning electron microscopy (SEM) revealed that the obtained crystals were of a cubic shape with a size ranging from 200 to 400 nm (Figure 2a).Transmission electron microscopy confirmed that the crystals were solid (Figure 2b).The cubic crystals of 1 were immersed into an HCl solution (0.4 mol L -1 ) under continuous stirring.After 1 h, the samples were harvested by centrifugation.SEM images illustrate that the center of the surfaces of the cubic crystals was empty (Figure 2c).The corners and edges were well-retained after etching.The TEM image implies that there were solid cores inside each particle (Figure 2d).All the evidence suggests that the mesoframes of 1 were successfully obtained after post-etching the cubic crystals.To facilitate our discussion, the cubic crystals of 1 are denoted as 1 cube , while the mesoframes are designated as 1 frame .The crystal structures of 1cube and 1frame were investigated by powder X-ray diffraction (PXRD).The diffraction profiles of both samples are similar, indicating an identical crystal structure (Figure 3).The diffraction patterns can be assigned to a rhombohedral structure (R-3), which is typical for Prussian Blue analogues with the interstitial sites occupied by a rich amount of Na + ions [86].The slight broadening of the peaks of 1frame is probably due to the lattice defects induced by etching.FT-IR spectra are shown in Figure 4.For both samples, a similar peak near 2090 cm -1 was observed.This band belongs to the characteristic of stretching vibration of Fe-CN-Ni [87].Therefore, the PXRD and FT-IR investigations confirm that both 1cube and 1frame present the same crystal structure and composition, allowing us to explore the mesostructural property.The crystal structures of 1 cube and 1 frame were investigated by powder X-ray diffraction (PXRD).The diffraction profiles of both samples are similar, indicating an identical crystal structure (Figure 3).The diffraction patterns can be assigned to a rhombohedral structure (R-3), which is typical for Prussian Blue analogues with the interstitial sites occupied by a rich amount of Na + ions [86].The slight broadening of the peaks of 1 frame is probably due to the lattice defects induced by etching.FT-IR spectra are shown in Figure 4.For both samples, a similar peak near 2090 cm -1 was observed.This band belongs to the characteristic of stretching vibration of Fe-CN-Ni [87].Therefore, the PXRD and FT-IR investigations confirm that both 1 cube and 1 frame present the same crystal structure and composition, allowing us to explore the mesostructural property.The crystal structures of 1cube and 1frame were investigated by powder X-ray diffraction (PXRD).The diffraction profiles of both samples are similar, indicating an identical crystal structure (Figure 3).The diffraction patterns can be assigned to a rhombohedral structure (R-3), which is typical for Prussian Blue analogues with the interstitial sites occupied by a rich amount of Na + ions [86].The slight broadening of the peaks of 1frame is probably due to the lattice defects induced by etching.FT-IR spectra are shown in Figure 4.For both samples, a similar peak near 2090 cm -1 was observed.This band belongs to the characteristic of stretching vibration of Fe-CN-Ni [87].Therefore, the PXRD and FT-IR investigations confirm that both 1cube and 1frame present the same crystal structure and composition, allowing us to explore the mesostructural property.To investigate the role of the frame-like mesostructure, we used the powders of 1 to host Na + ions.We selected an electrochemistry-controlled method to probe the Na-ion insertion/extraction amount.The crystals of 1 were used as cathodes in a three-electrode system in an NaNO3 solution.In this aqueous battery system, a reversible insertion/extraction of Na + ions into/from the frameworks of 1 can be realized by electrochemical redox of Fe 2+ /Fe 3+ ions.For the storage/consumption of one electron, an Na + ion enters/leaves the host frameworks.Herein, we simply recorded the capacity change to understand the intercalation/de-intercalation of the Na + ion.The galvanostatic charge/discharge curves shown in Figure 5 present that 1frame can deliver a reversible specific capacity of 61 mAh .g -1 at a current density of 70 mA•g -1 between 0.001 to 1.0 V (vs.Ag/AgCl).The discharge curve contains a plateau at 0.3-0.6V (vs.Ag/AgCl), corresponding to the insertion of Na + ions.Moreover, 1cube shows similar specific capacity (60 mAh .g -1 ) at a current density of 70 mA .g -1 between 0.001 to 1.0 V (vs.Ag/AgCl).As we can see in the cyclic voltammetry (CV) curves (Figure 6), the center of the positions of redox peaks of the 1cube crystals is at around 0.4 V (vs.Ag/AgCl), and the center of the peaks of 1frame locates at around 0.36 V (vs.Ag/AgCl).The redox peaks of 1frame are much sharper corresponding to a larger quantity of the intercalated Na + ion in the frameworks of 1frame at this potential.To investigate the role of the frame-like mesostructure, we used the powders of 1 to host Na + ions.We selected an electrochemistry-controlled method to probe the Na-ion insertion/extraction amount.The crystals of 1 were used as cathodes in a three-electrode system in an NaNO 3 solution.In this aqueous battery system, a reversible insertion/extraction of Na + ions into/from the frameworks of 1 can be realized by electrochemical redox of Fe 2+ /Fe 3+ ions.For the storage/consumption of one electron, an Na + ion enters/leaves the host frameworks.Herein, we simply recorded the capacity change to understand the intercalation/de-intercalation of the Na + ion.The galvanostatic charge/discharge curves shown in Figure 5 present that 1 frame can deliver a reversible specific capacity of 61 mAh•g -1 at a current density of 70 mA•g -1 between 0.001 to 1.0 V (vs.Ag/AgCl).The discharge curve contains a plateau at 0.3-0.6V (vs.Ag/AgCl), corresponding to the insertion of Na + ions.Moreover, 1 cube shows similar specific capacity (60 mAh•g -1 ) at a current density of 70 mA•g −1 between 0.001 to 1.0 V (vs.Ag/AgCl).As we can see in the cyclic voltammetry (CV) curves (Figure 6), the center of the positions of redox peaks of the 1 cube crystals is at around 0.4 V (vs.Ag/AgCl), and the center of the peaks of 1 frame locates at around 0.36 V (vs.Ag/AgCl).The redox peaks of 1 frame are much sharper corresponding to a larger quantity of the intercalated Na + ion in the frameworks of 1 frame at this potential.To investigate the role of the frame-like mesostructure, we used the powders of 1 to host Na + ions.We selected an electrochemistry-controlled method to probe the Na-ion insertion/extraction amount.The crystals of 1 were used as cathodes in a three-electrode system in an NaNO3 solution.In this aqueous battery system, a reversible insertion/extraction of Na + ions into/from the frameworks of 1 can be realized by electrochemical redox of Fe 2+ /Fe 3+ ions.For the storage/consumption of one electron, an Na + ion enters/leaves the host frameworks.Herein, we simply recorded the capacity change to understand the intercalation/de-intercalation of the Na + ion.The galvanostatic charge/discharge curves shown in Figure 5 present that 1frame can deliver a reversible specific capacity of 61 mAh .g -1 at a current density of 70 mA•g -1 between 0.001 to 1.0 V (vs.Ag/AgCl).The discharge curve contains a plateau at 0.3-0.6V (vs.Ag/AgCl), corresponding to the insertion of Na + ions.Moreover, 1cube shows similar specific capacity (60 mAh .g -1 ) at a current density of 70 mA .g -1 between 0.001 to 1.0 V (vs.Ag/AgCl).As we can see in the cyclic voltammetry (CV) curves (Figure 6), the center of the positions of redox peaks of the 1cube crystals is at around 0.4 V (vs.Ag/AgCl), and the center of the peaks of 1frame locates at around 0.36 V (vs.Ag/AgCl).The redox peaks of 1frame are much sharper corresponding to a larger quantity of the intercalated Na + ion in the frameworks of 1frame at this potential.We investigated the rate performance of the crystals of 1. Figure 7 shows that 1frame and 1cube have similar capacities (approximately 60 mAh .g -1 ) at a low current density 70 mA•g -1 (1 C).However, with the increase in the current rate, the capacity of 1cube decreased more drastically than the 1frame.For instance, when the charge/discharge current density was as high as 10 A•g -1 (166.7 C), the capacity retention of 1frame was as high as 88%.However, the 1cube could only retain 41% of the initial capacity (Figure 7).The wonderful rate performance of 1frame suggests that this material could be suitable for long-term cycling.Figure 8 illustrated that 1frame could deliver a high capacity at a current density of 83.3 C (5 A•g -1 ).The retained capacity is 94.34% of the initial capacity after 500 cycles (Figure 8).To check the performance at higher temperature, the 1frame was measured at a different current density and cycled at 5 A•g -1 at 40 °C (Figure S1).The rate and cycling performances, compared with performances at 25 °C, were almost unchanged.This result indicated that the rate and cycling performances were not affected at 40 °C [88].We investigated the rate performance of the crystals of 1. Figure 7 shows that 1 frame and 1 cube have similar capacities (approximately 60 mAh•g -1 ) at a low current density 70 mA•g -1 (1 C).However, with the increase in the current rate, the capacity of 1 cube decreased more drastically than the 1 frame .For instance, when the charge/discharge current density was as high as 10 A•g -1 (166.7 C), the capacity retention of 1 frame was as high as 88%.However, the 1 cube could only retain 41% of the initial capacity (Figure 7).The wonderful rate performance of 1 frame suggests that this material could be suitable for long-term cycling.Figure 8 illustrated that 1 frame could deliver a high capacity at a current density of 83.3 C (5 A•g -1 ).The retained capacity is 94.34% of the initial capacity after 500 cycles (Figure 8).To check the performance at higher temperature, the 1 frame was measured at a different current density and cycled at 5 A•g −1 at 40 • C (Figure S1).The rate and cycling performances, compared with performances at 25 • C, were almost unchanged.This result indicated that the rate and cycling performances were not affected at 40 • C [88].We investigated the rate performance of the crystals of 1. Figure 7 shows that 1frame and 1cube have similar capacities (approximately 60 mAh .g -1 ) at a low current density 70 mA•g -1 (1 C).However, with the increase in the current rate, the capacity of 1cube decreased more drastically than the 1frame.For instance, when the charge/discharge current density was as high as 10 A•g -1 (166.7 C), the capacity retention of 1frame was as high as 88%.However, the 1cube could only retain 41% of the initial capacity (Figure 7).The wonderful rate performance of 1frame suggests that this material could be suitable for long-term cycling.Figure 8 illustrated that 1frame could deliver a high capacity at a current density of 83.3 C (5 A•g -1 ).The retained capacity is 94.34% of the initial capacity after 500 cycles (Figure 8).To check the performance at higher temperature, the 1frame was measured at a different current density and cycled at 5 A•g -1 at 40 °C (Figure S1).The rate and cycling performances, compared with performances at 25 °C, were almost unchanged.This result indicated that the rate and cycling performances were not affected at 40 °C [88].

Discussion
On the basis of the relationship between the transferred electrons and the amount of the intercalated Na + ions, ∆Ne = ∆NNa+, we converted the electrochemical data into the intercalation-deintercalation curves for Na + ions against the potential (vs.Ag/AgCl) (Figures 9 and 10).Apparently, both 1cube and 1frame can accommodate the same amount of Na + ions at a lower uptake rate, indicating that both samples have a similar capacity for the Na + ions (Figure 9).However, the uptake of Na + ions by 1cube is much lower than that by 1frame at a higher uptake rate (Figure 10).The uptake by 1frame did not decrease too much, while 50% the uptake by 1cube was lost.Apparently, the interstitial sites in 1frame could be utilized almost completely at a high rate, while the number of the accessed interstitial sites in 1cube was significantly reduced.
There are three factors that may be affected by the meso-structure: (1) the contact between the crystal and the electrolyte; (2) the crystal structure and meso-structure change during the intercalation process; (3) the diffusion distance inside the frameworks.For Factor 1, we firstly measured the specific surface area of 1frame and 1cube by the Brunauer-Emmett-Teller (BET) method (Figure S2).The specific surface area of 1frame (59.6 m 2 •g -1 ) is close to that of 1cube (49.2 m 2 •g -1 ).Such a small difference can be ignored by considering that the crystals have to be well mixed with the conductors and electrolytes during the electrode preparation.Therefore, Factor 1 can be ignored.For Factor 2, we need to understand the structure change during the intercalation process.The ex situ PXRD analysis was carried out.For both crystals, a similar phase change between the R-3 and Fm-3m structures was recorded as shown in Figures S3 and S4.The structure change is due to the accommodation and release of Na + ions.The shape of the two samples was also checked by SEM after 500 cycles.We noted that the meso-structures of both samples were retained (Figure S5).It should be noted that the small particles are conductive carbons that are not crystals of 1.This result suggests that Factor 2, for the mesoframes, is not different from the cube and thus should not be considered as the reason.
Regarding Factor 3, the 1frame obviously has a shorter diffusion pathway for the Na + ions than that of 1cube since various parts of the crystals have been removed.For the intercalation of Na + ions into Prussian Blue analogues, the solvated Na + ions need to first be de-solvated.Then, the de-solvated Na + ions can enter the frameworks of the host.The entered Na + ions may be partially re-solvated by the mobile water molecules in the crystals during the next diffusion stage.Because re-solvation can enlarge the radius of the Na + ions, the diffusion of the re-solvated Na + ions is slower than the desolvated Na + ions.Shortening the diffusion distance can likely minimize the diffusion of the resolvated Na + ions and accelerate the intercalation process, leading to the utilization of the interstitial sites adequately.To confirm this point, we measured the diffusion coefficient for both samples.The diffusion coefficient of Na + ions can be calculated with the Randles-Sevcik equation [89]: Ip = 2.69 × 10 5 n 3/2 SCNaDNa 1/2 ν 1/2 , where Ip is the peak current (A), n is the number of electrons transferred per molecule during the intercalation/deintercalation procedure (n = 1 for Fe 2+ /Fe 3+ redox pair), S is the

Discussion
On the basis of the relationship between the transferred electrons and the amount of the intercalated Na + ions, ∆N e = ∆N Na+ , we converted the electrochemical data into the intercalation-deintercalation curves for Na + ions against the potential (vs.Ag/AgCl) (Figures 9 and 10).Apparently, both 1 cube and 1 frame can accommodate the same amount of Na + ions at a lower uptake rate, indicating that both samples have a similar capacity for the Na + ions (Figure 9).However, the uptake of Na + ions by 1 cube is much lower than that by 1 frame at a higher uptake rate (Figure 10).The uptake by 1 frame did not decrease too much, while 50% of the uptake by 1 cube was lost.Apparently, the interstitial sites in 1 frame could be utilized almost completely at a high rate, while the number of the accessed interstitial sites in 1 cube was significantly reduced.
There are three factors that may be affected by the meso-structure: (1) the contact between the crystal and the electrolyte; (2) the crystal structure and meso-structure change during the intercalation process; (3) the diffusion distance inside the frameworks.For Factor 1, we firstly measured the specific surface area of 1 frame and 1 cube by the Brunauer-Emmett-Teller (BET) method (Figure S2).The specific surface area of 1 frame (59.6 m 2 •g −1 ) is close to that of 1 cube (49.2 m 2 •g −1 ).Such a small difference can be ignored by considering that the crystals have to be well mixed with the conductors and electrolytes during the electrode preparation.Therefore, Factor 1 can be ignored.For Factor 2, we need to understand the structure change during the intercalation process.The ex situ PXRD analysis was carried out.For both crystals, a similar phase change between the R-3 and Fm-3m structures was recorded as shown in Figures S3 and S4.The structure change is due to the accommodation and release of Na + ions.The shape of the two samples was also checked by SEM after 500 cycles.We noted that the meso-structures of both samples were retained (Figure S5).It should be noted that the small particles are conductive carbons that are not crystals of 1.This result suggests that Factor 2, for the mesoframes, is not different from the cube and thus should not be considered as the reason.
Regarding Factor 3, the 1 frame obviously has a shorter diffusion pathway for the Na + ions than that of 1 cube since various parts of the crystals have been removed.For the intercalation of Na + ions into Prussian Blue analogues, the solvated Na + ions need to first be de-solvated.Then, the de-solvated Na + ions can enter the frameworks of the host.The entered Na + ions may be partially re-solvated by the mobile water molecules in the crystals during the next diffusion stage.Because re-solvation can enlarge the radius of the Na + ions, the diffusion of the re-solvated Na + ions is slower than the de-solvated Na + ions.Shortening the diffusion distance can likely minimize the diffusion of the re-solvated Na + ions and accelerate the intercalation process, leading to the utilization of the interstitial sites adequately.To confirm this point, we measured the diffusion coefficient for both samples.The diffusion coefficient of Na + ions can be calculated with the Randles-Sevcik equation [89]: I p = 2.69 × 10 5 n 3/2 SC Na D Na 1/2 ν 1/2 , where I p is the peak current (A), n is the number of electrons transferred per molecule during the intercalation/deintercalation procedure (n = 1 for Fe 2+ /Fe 3+ redox pair), S is the effective contact area between the electrode and electrolyte (here the area of the electrode = 1 cm 2 ), C Na is the molar concentration of Na + ions (1.3 × 10 -3 mol•cm -3 ) [90], D Na is the diffusion coefficient of Na + ions (cm 2 •s -1 ), and ν is the scan rate (V•s -1 ).We carried out CV scans at various scan rates from 0.2 to 1 mV s -1 (Figures S6a and S7a).The peak current correlates linearly to the square root of the scan rate for both samples.On the basis of the slopes received from the plots of the anodic I p versus ν 1/2 (Figures S6b and S7b), the calculated D Na is 7.35 × 10 -9 cm 2 •s -1 for 1 cube , and 14.0 × 10 -9 cm 2 •s -1 for 1 frame , respectively.Apparently, the diffusion coefficient for Na + in 1 frame is significantly larger than in 1 cube .The diffusion coefficient strongly relates to the moving of the Na + ions, including the transfer from the electrolytes to the interstitial sites and the movement among the interstitial sites.In general, the transfer part is fast, while the moving part is slow.Because the transfer part for both samples is similar owing to their close specific surface areas, the less contribution there is from the moving part, the larger the diffusion coefficient can be.The moving step in 1 frame is shorter than in 1 cube because of the shape of the mesoframe, indicating less contribution to the diffusion coefficient from the moving step in 1 frame .Therefore, the diffusion coefficient for 1 frame is larger than for 1 cube .The larger diffusion coefficient means that Na + ions can move fast and thus utilize the interstitial sites at a high current rate, leading to a larger capacity at a high current density.Therefore, we can say the short diffusion distance in 1 frame enlarges the D Na and is thus the apparent reason for the better rate performance of the mesoframe structure.
effective contact area between the electrode and electrolyte (here the area of the electrode = 1 cm 2 ), CNa is the molar concentration of Na + ions (1.3 × 10 -3 mol•cm -3 ) [90], DNa is the diffusion coefficient of Na + ions (cm 2 •s -1 ), and ν is the scan rate (V•s -1 ).We carried out CV scans at various scan rates from 0.2 to 1 mV s -1 (Figures S6a and S7a).The peak current correlates linearly to the square root of the scan rate for both samples.On the basis of the slopes received from the plots of the anodic Ip versus ν 1/2 (Figures S6b and S7b), the calculated DNa is 7.35 × 10 -9 cm 2 •s -1 for 1cube, and 14.0 × 10 -9 cm 2 •s -1 for 1frame, respectively.Apparently, the diffusion coefficient for Na + in 1frame is significantly larger than in 1cube.
The diffusion coefficient strongly relates to the moving of the Na + ions, including the transfer from the electrolytes to the interstitial sites and the movement among the interstitial sites.In general, the transfer part is fast, while the moving part is slow.Because the transfer part for both samples is similar owing to their close specific surface areas, the less contribution there is from the moving part, the larger the diffusion coefficient can be.The moving step in 1frame is shorter than in 1cube because of the shape of the mesoframe, indicating less contribution to the diffusion coefficient from the moving step in 1frame.Therefore, the diffusion coefficient for 1frame is larger than for 1cube.The larger diffusion coefficient means that the Na + ions can move fast and thus utilize the interstitial sites at a high current rate, leading to a larger capacity at a high current density.Therefore, we can say the short diffusion distance in 1frame enlarges the DNa and is thus the apparent reason for the better rate performance of the mesoframe structure.The above discussion suggests that the difference in Na-ion insertion/extraction at high rates for both samples can be explained as follows.At a low rate, the Na + ions can be inserted/extracted almost fully in/from both of the cubes and mesoframes.When the rate becomes high (for example, higher than 70 mA•g -1 ), Na + ions may be hard to access to the center part of the cubes during the insertion process, while a large percentage of the interstitial site of the mesoframes can be accessed.Therefore, effective contact area between the electrode and electrolyte (here the area of the electrode = 1 cm 2 ), CNa is the molar concentration of Na + ions (1.3 × 10 -3 mol•cm -3 ) [90], DNa is the diffusion coefficient of Na + ions (cm 2 •s -1 ), and ν is the scan rate (V•s -1 ).We carried out CV scans at various scan rates from 0.2 to 1 mV s -1 (Figures S6a and S7a).The peak current correlates linearly to the square root of the scan rate for both samples.On the basis of the slopes received from the plots of the anodic Ip versus ν 1/2 (Figures S6b and S7b), the calculated DNa is 7.35 × 10 -9 cm 2 •s -1 for 1cube, and 14.0 × 10 -9 cm 2 •s -1 for 1frame, respectively.Apparently, the diffusion coefficient for Na + in 1frame is significantly larger than in 1cube.
The diffusion coefficient strongly relates to the moving of the Na + ions, including the transfer from the electrolytes to the interstitial sites and the movement among the interstitial sites.In general, the transfer part is fast, while the moving part is slow.Because the transfer part for both samples is similar owing to their close specific surface areas, the less contribution there is from the moving part, the larger the diffusion coefficient can be.The moving step in 1frame is shorter than in 1cube because of the shape of the mesoframe, indicating less contribution to the diffusion coefficient from the moving step in 1frame.Therefore, the diffusion coefficient for 1frame is larger than for 1cube.The larger diffusion coefficient means that the Na + ions can move fast and thus utilize the interstitial sites at a high current rate, leading to a larger capacity at a high current density.Therefore, we can say the short diffusion distance in 1frame enlarges the DNa and is thus the apparent reason for the better rate performance of the mesoframe structure.The above discussion suggests that the difference in Na-ion insertion/extraction at high rates for both samples can be explained as follows.At a low rate, the Na + ions can be inserted/extracted almost fully in/from both of the cubes and mesoframes.When the rate becomes high (for example, higher than 70 mA•g -1 ), Na + ions may be hard to access to the center part of the cubes during the insertion process, while a large percentage of the interstitial site of the mesoframes can be accessed.Therefore, The above discussion suggests that the difference in Na-ion insertion/extraction at high rates for both samples can be explained as follows.At a low rate, the Na + ions can be inserted/extracted almost fully in/from both of the cubes and mesoframes.When the rate becomes high (for example, higher than 70 mA•g -1 ), Na + ions may be hard to access to the center part of the cubes during the insertion process, while a large percentage of the interstitial site of the mesoframes can be accessed.Therefore, the mesoframes can have a much larger specific capacity, especially at a high current rate (higher than 0.07 A•g -1 ), representing an excellent rate performance.In addition, as our cycling test was performed at a high current rate, the cycling stability of the mesoframes of course should be superior compared to the cubes as well.

Conclusions
In summary, we synthesized monocrystalline NiFe(II) Prussian Blue analogue mesoframes by a chemical etching method.This morphology significantly reduced the diffusion pathway for Na + ions inside the crystal, leading to fast guest ion intercalation/de-intercalation, which is hard to achieve in solid crystals.The fast guest ion accommodation ability of the crystals could be used in aqueous Na-ion batteries.Based on the mesoframes, cathodes suitable for a high-rate charging/discharging (166 C) aqueous Na-ion batteries were fabricated, and it was demonstrated that the mesoframe is a promising meso-architecture for an enhancement in the performance of coordination polymers.In addition, the impressive cycling performance of the mesoframes may be useful for grid-scale energy storage.

Figure 2 .
Figure 2. (a) SEM image of cubic crystals.(b) TEM image of cubic crystals.(c) SEM image of the product from etching of the cubic crystals.Inset is an enlarged image of a particle.(d) TEM image of the product from etching of the cubic crystals.

Figure 2 .
Figure 2. (a) SEM image of cubic crystals.(b) TEM image of cubic crystals.(c) SEM image of the product from etching of the cubic crystals.Inset is an enlarged image of a particle.(d) TEM image of the product from etching of the cubic crystals.

Figure 2 .
Figure 2. (a) SEM image of cubic crystals.(b) TEM image of cubic crystals.(c) SEM image of the product from etching of the cubic crystals.Inset is an enlarged image of a particle.(d) TEM image of the product from etching of the cubic crystals.

Figure 6 .
Figure 6.CV curves of 1 crystals at a scanning rate of 1 mV•s -1 .

Figure 7 .
Figure 7. Rate performance of the 1 crystals.

Figure 6 .
Figure 6.CV curves of 1 crystals at a scanning rate of 1 mV•s −1 .

Figure 6 .
Figure 6.CV curves of 1 crystals at a scanning rate of 1 mV•s -1 .

Figure 7 .
Figure 7. Rate performance of the 1 crystals.Figure 7. Rate performance of the 1 crystals.

Figure 7 .
Figure 7. Rate performance of the 1 crystals.Figure 7. Rate performance of the 1 crystals.

Figure 8 .
Figure 8. Cycling performance of the 1 crystals at a current density of 5 A•g -1 .

Figure 8 .
Figure 8. Cycling performance of the 1 crystals at a current density of 5 A•g -1 .

Figure 10 .
Figure 10.Uptake of Na + ions by 1 crystals at different uptake rates.

Figure 10 .
Figure 10.Uptake of Na + ions by 1 crystals at different uptake rates.

Figure 10 .
Figure 10.Uptake of Na + ions by 1 crystals at different uptake rates.

Figure S1 :
Rate performance (a) and cycling performance (b) of 1 frame at different temperatures; Figure S2: N 2 adsorption-desorption isotherms of 1 crystals; Figure S3: Ex situ PXRD patterns of the electrochemically active cubic crystals at charge/discharge during the first cycle at a current density of 0.07A•g −1 ; Figure S4: Ex situ PXRD patterns of the electrochemically active mesoframes at charge/discharge during the first cycle at a current density of 0.07A•g −1 ; Figure S5: (a) SEM of cubic crystals after cycling.(b) SEM of mesoframes after cycling for 500 cycles; Figure S6: (a) Cyclic voltammetry curves of 1 cube at various scanning rates.(b) The anodic and cathodic peak currents as functions of the square root of scanning rates; Figure S7: (a) Cyclic voltammetry curves of 1 frame at various scanning rates.(b) The anodic and cathodic peak currents as functions of the square root of scanning rates; Figure S8: FT-IR spectrum of mesoframes before electrochemical activation; Figure S9: PXRD patterns of mesoframes before electrochemical activation.