Interface Coordination Engineering of P-Fe3O4/Fe@C Derived from an Iron-Based Metal Organic Framework for pH-Universal Water Splitting

Abstract

Developing electrocatalysts with high energy conversion efficiency is urgently needed. In this work, P-Fe₃O₄/Fe@C electrodes with rich under-coordinated Fe atom interfaces are constructed for efficient pH-universal water splitting. The introduction of under-coordinated Fe atoms into the P-Fe₃O₄/Fe@C interface can increase the local charge density and polarize the 3d orbital lone electrons, which promotes water adsorption and activation to release more H^*, thus elevating electrocatalytic activity. As a donor-like catalyst, P-Fe₃O₄/Fe@C displays excellent electrocatalytic performance with overpotentials of 160 mV and 214 mV in acidic and alkaline electrolytes at 10 mA cm⁻², in addition to pH-universal long-term stability.

1. Introduction

Electrochemical water-splitting to produce high purity hydrogen is an effective solution owing to the low cost, high purity, and eco-friendliness. A high overpotential is necessary to impel the hydrogen evolution reaction (HER). To date, significant endeavors have been devoted to explore high-performance HER electrocatalysts with a low overpotential, including sulphide, carbide, nitride, phosphide, and so on [1,2,3,4,5]. However, they are limited due to inferior electrical conductivity, leading to sluggish reaction kinetics, low energy conversion efficiency, and poor cycling stability [6,7,8]. Therefore, developing HER electrocatalysts with high energy conversion efficiency is urgently needed for pH-universal water-splitting.

Recently, iron-based materials have received intense attention because of their relatively lower intrinsic electrical resistivity, abundant reserves, and inexpensive metallic element; therefore, iron has been widely studied as an electrocatalyst [9]. Iron phosphides show excellent electrocatalytic HER activity due to highly active hydrogenases [10,11]. However, it suffers from poor operation stability owing to the high oxygen sensitivity of iron phosphide [12]. Fortunately, Fe₃O₄ exhibits superb electrical conductivity compared with other metal oxides because of the electron transfer between Fe (III) and Fe (II) [13,14,15]. In addition, Fe₃O₄ shows a low water dissociation energy to rapidly break the H-O bond [16,17,18]. Based on the above advantages, Fe₃O₄ has shown promising potential as an electrocatalyst [19,20,21,22]. It has been reported that iron-based oxide/hydroxides show good OER activity, yet their application for HER is relatively rare.

The interface characterization of electrocatalysts is all-important for HER. Constructing a rich interface based on Fe₃O₄ is considered to be a relatively effective means, which can not only adjust the electronic structure in the upper edge of the valence band but also provide more active sites and expedite charge transfer, thus enhancing the HER activity. Owing to the bond order–length–strength (BOLS) correlation and nonbonding electron polarization (NEP) effect [23], Fe nanostructures with rich under-coordinated atoms can fascinate more electrons to facilitate the Volmer step in the HER process. Therefore, it is an attractive means to construct P-Fe₃O₄/Fe@C with rich under-coordinated atom interfaces for efficient pH-universal HER. Herein, we report an interface coordination engineering of P-Fe₃O₄/Fe@C by introducing proper under-coordinated Fe atom ratios into interfaces for acidic and alkaline HER. MIL-53(Fe) has been chosen as the precursor to synthesize the P-Fe₃O₄/Fe@C. By adjusting the pyrolysis temperature, the under-coordinated Fe atom ratios in the P-Fe₃O₄/Fe@C interfaces can be effectively controlled. It is expected that the introduction of proper under-coordinated atom ratios in the P-Fe₃O₄/Fe@C interfaces will significantly elevate their HER activity across a wide pH range. However, little attention has been paid to study the influence of interface characterization on the HER performance of P-Fe₃O₄/Fe@C. The electrocatalytic mechanism was also studied, except for the characterization of HER activity for P-Fe₃O₄/Fe@C.

2. Experimental

2.1. Synthesis of MIL-53(Fe)

Briefly, 540 mg FeCl₃·6H₂O and 344 mg 1,4-benzenedicarboxylate (H₂BDC) were dispersed into N,N-dimethylformamide (40.88 g, DMF) under magnetic stirring for 30 min. Then, the above solution was transferred to the autoclave and reacted at 150 °C for 15 h. After the reaction, the obtained precipitate (MIL-53(Fe)) was filtrated, washed three times with DMF and methanol, and dried at 80 °C for 12 h.

2.2. Fabrication of P-Fe₃O₄/Fe@C Catalysts

Firstly, MIL-53(Fe) powder was carbonized at 600, 700, 800, and 900 °C for 2 h at a heating rate of 2 °C min⁻¹ in an Ar atmosphere. After carbonation, MIL-53(Fe) was transformed into the Fe₃O₄/Fe@C hybrids. By adjusting the pyrolysis temperature, the ratios of Fe₃O₄ and Fe can be effectively controlled. Then, 0.1 g Fe₃O₄/Fe@C hybrids and 0.7 g NaH₂PO₂·H₂O were placed into two different porcelain boats in a sealed crucible and then heated to 300 °C for 2 h. The final high purity products, which are P-Fe₃O₄/Fe@C hybrids, were washed three times with ethanol and DI water, and dried at 70 °C for 24 h. The P-Fe₃O₄/Fe@C hybrids obtained at 600, 700, 800, and 900 °C were named as FCP600, FCP700, FCP800, and FCP900, respectively.

3. Results and Discussion

3.1. Characterization

Figure 1 shows the synthetic procedure of P-Fe₃O₄/Fe@C hybrids. MIL-53(Fe) is constructed by choosing H₂BDC as the organic building block related to Fe³⁺ as the inorganic metal center. MIL-53(Fe) is connected by an FeO₄(OH)₂ octahedron and H₂BDC. After the thermal treatment in an Ar atmosphere, the Fe³⁺ in the MIL-53(Fe) is transformed into the Fe₃O₄ with a certain amount of metal Fe. At the same time, the organic building blocks are pyrolyzed to amorphous carbon to form the Fe₃O₄/Fe@C hybrids. After the in-situ pyrolysis process in the presence of sodium hypophosphite, the sodium hypophosphite is decomposed to form the PH₃ in the Ar atmosphere at 300 °C. The P atoms are doped by the reaction of PH₃ and Fe₃O₄/Fe@C hybrids to form the P-Fe₃O₄/Fe@C hybrids.

The XRD results in Figure 2a demonstrate the phase and crystal structure of MIL-53(Fe), FCP700, FCP800, and FCP900. The XRD pattern of MIL-53(Fe) is similar to the previously reported result (CIF: 690314-690316) [24,25], demonstrating that the MIL-53(Fe) is successfully prepared. MIL-53(Fe) shows strong diffraction peaks, indicating good crystallinity. The XRD pattern of FCP600 has been provided in Figure S1. The main diffraction peaks at 24.1°, 33.2°, 35.6°, 40.9°, 49.5°, 54.1°, 62.4°, and 64.0° are attributed to the (012), (104), (110), (113), (024), (116), (214), and (300) planes of Fe₂O₃ (JCPDS, No. 33-0664), respectively. The XRD patterns of FCP700, FCP800, and FCP900 display the Fe₃O₄ and Fe diffraction peaks, indicating the formation of P-Fe₃O₄/Fe@C hybrids. The main diffraction peaks at 30.1°, 35.1°, 43.1°, 56.9°, and 62.5° are attributed to the (220), (311), (400), (511), and (440) planes of Fe₃O₄ (JCPDS, No. 74-0748), respectively [13]. The diffraction peaks at 44.6° and 65.0° are ascribed to the (110) and (200) planes of the standard cubic Fe (JCPDS, No. 87-0721), respectively. However, no diffraction peaks of iron phosphide are found in the XRD patterns of FCP700, FCP800, and FCP900, demonstrating the absence of iron phosphide in P-Fe₃O₄/Fe@C hybrids.

With the increase of thermal treatment temperature, the diffraction peaks' intensity of Fe₃O₄ decreases, and then the Fe increases. The ratio of Fe to Fe₃O₄ in the interface of P-Fe₃O₄/Fe@C can be adjusted by changing the thermal treatment temperature. With the increase of thermal treatment temperature, the ratio of Fe to Fe₃O₄ in P-Fe₃O₄/Fe@C interface increases. Rich under-coordinated Fe atoms in the interface of P-Fe₃O₄/Fe@C have a tremendous influence on the electrochemical water-splitting reaction. According to the BOLS–NEP theory [23], rich under-coordinated Fe atoms can adjust the electronic structure of P-Fe₃O₄/Fe@C, leading to the core electron entrapment and 3d orbital lone electron polarization, which can increase the local charge density and raise the occupied valence states towards the Fermi level of P-Fe₃O₄/Fe@C [26]. The coupling effect of entrapment and polarization can accelerate the water adsorption and activation to release more H* in the electrochemical water-splitting reaction [27,28].

XPS was performed to determine the functional group and valence information of P-Fe₃O₄/Fe@C (FCP800). As shown in Figure S2, all elements (P, C, O and Fe) can be found in the XPS survey spectrum, relating to the presence of P-Fe₃O₄/Fe@C. The Fe 2p XPS spectrum (Figure 2b) has four peaks at 710.6, 718.7, 724.0, and 730.5 eV, which are attributed to the Fe 2p_3/2, Fe 2p_3/2 sat, Fe 2p_1/2, and Fe 2p_1/2 sat, respectively, demonstrating the existence of Fe₃O₄ [18,29]. The satellite peaks at 710.6 and 724.0 eV may correspond to either the γ-Fe₂O₃ or Fe₃O₄ phase, because the Fe 2p_3/2 and Fe 2p_1/2 peaks are close for both phases. The peak at 718.7 corresponds to the γ-Fe₂O₃. The peak at 730.5 eV corresponds to the binding energy of Fe²⁺. The peak at 706.6 eV corresponds to the Fe 2p_3/2 peak of the metallic Fe [16,30]. In the C 1s XPS spectrum for Figure 2c, the peaks at 283.4 and 284.8 eV correspond to C-C and C-O, respectively [31,32,33,34,35]. The peaks at 128.4 and 129.2 eV are attributed to P-Fe in the P 2p spectrum (Figure 2d) [16]. The broad peak at 132.5 eV corresponds to the oxidation product of P [36]. Results indicate that the P is successfully doped into the Fe₃O₄/Fe@C, and the prepared sample is P-Fe₃O₄/Fe@C.

Figure 3 shows the FESEM and HRTEM images of FCP700, FCP800, and FCP900. The morphology of FCP600 (not shown here) is similar to that of FCP700, FCP800, and FCP900. P-Fe₃O₄/Fe@C has nanolayered structures with the embedding of nanoparticles (Figure 3a–c). The size of nanoparticles and nanosheets are about 30 nm and 2 μm. FCP700, FCP800, and FCP900 display similar morphology, demonstrating that the thermal treatment temperature has no effect on the morphology of P-Fe₃O₄/Fe@C. The nanolayered structures with the embedding of nanoparticles are also found in the HRTEM of P-Fe₃O₄/Fe@C, which can provide high specific surface area and ion transport interface to improve the electrocatalytic activity. As shown in Figure 3d–f, the carbon support shows a layered structure, and the embedded nanoparticles are Fe and Fe₃O₄. The lattice fringe spacing in Figure 3e,f are 0.20 and 0.25 nm, corresponding to the (110) plane of Fe (JCPDS, No. 87-0721) and (311) plane of Fe₃O₄ (JCPDS, No. 74-0748), respectively.

The nitrogen adsorption–desorption isotherms of P-Fe₃O₄/Fe@C in Figure 4 display the Type IV curves with an H₃ hysteresis loop, demonstrating the presence of mesoporous structures. The specific surface areas, pore volume, and average pore size of FCP600, FCP700, FCP800, and FCP900 are summarized in Table 1. The average pore diameters of FCP600, FCP700, FCP800, and FCP900 have no obvious effect on the electrocatalytic reaction process. The porosity plays a crucial role in electrocatalysis by enhancing the accessibility of reactants to active sites, facilitating the mass transport of reactants and products, increasing the specific surface area to provide more active sites, and improving charge transfer. Therefore, the largest specific surface area and mesoporous structure for FCP800 can provide a transport channel and more reaction-active sites, thus lowering the overpotential at a low current density, which represents the conditions of a relatively small driving force [37].

However, when the current density increases to the visible industry-relevant levels, the relationship between porosity and overpotential can change. The mass transport limitation becomes more prominent as the current density increases. At the visible industry-relevant current density, deep pores are blocked or inaccessible due to the slow mass transport inside, which can result in reactant depletion near the catalyst surface and hinder the efficient access of reactants to the active sites, thus increasing the overpotential [38]. Therefore, the general effect of porosity on a certain activity of electrocatalyst is very complex and non-linear. The reaction conditions, such as the nature of the reactants, electrolyte composition, temperature, and current density, are crucial for interpreting the relationship between porosity and electrochemical performance accurately.

3.2. Electrocatalytic Activity of HER

The electrocatalytic activity of P-Fe₃O₄/Fe@C was evaluated in 1.0 M KOH and 0.5 M H₂SO₄ electrolytes using a standard three-electrode system. The HER activities of Pt/C and the Fe₃O₄/Fe@C electrocatalyst were also tested for comparison, as shown in Figure S3. The Fe₃O₄/Fe@C shows a low overpotential with 218 and 280 mV and Tafel slope with 65.5 and 176.26 mV dec⁻¹ in the acidic and alkaline electrolytes. Figure 5a shows the linear sweep voltammetry (LSV) curves of Pt/C and P-Fe₃O₄/Fe@C in the 0.5 M H₂SO₄ electrolyte. P-Fe₃O₄/Fe@C shows good HER electrocatalytic activity. The thermal treatment temperature has an impact on the HER performance of P-Fe₃O₄/Fe@C. With the increase of thermal treatment temperature, the HER performance of P-Fe₃O₄/Fe@C increases and then decreases. For Figure 5b, FCP800 shows the best HER activity with the lowest overpotential (η) of 160 mV at 10 mA cm⁻², compared to those of FCP600 (228 mV), FCP700 (171 mV), and FCP900 (196 mV). It is worth mentioning that P-Fe₃O₄/Fe@C (FCP800) shows outstanding electrocatalytic activity, even under the high current density of 50 mA cm⁻² at overpotentials of 242 mV in the acidic medium. The HER-specific activity of FCP600, FCP700, FCP800, and FCP900 are 2.50, 5.13, 7.56, and 3.92 mA cm⁻² at the overpotential of 150 mV in 0.5 M H₂SO₄ electrolyte, respectively (Figure S4a). The HER mass activity of FCP600, FCP700, FCP800, and FCP900 are 2.81, 4.29, 4.47, and 2.08 A mg⁻¹ at the overpotential of 150 mV in 0.5 M H₂SO₄ electrolyte, respectively (Figure S4b). The electrocatalytic reaction kinetics of P-Fe₃O₄/Fe@C was studied by means of the Tafel plots constructed from the LSV curves (Figure 5c). The Tafel slope values for FCP600, FCP700, FCP800, and FCP900 are 100.55, 68.84, 55.78, and 76.87 mV dec⁻¹, respectively. The relatively smaller Tafel slope for FCP800 demonstrates the fast HER reaction kinetics. The double-layer capacitance (C_dl) was evaluated by the CV curves with different scan rates (Figures S5 and S6). For Figure 5d, the C_dl values for FCP600, FCP700, FCP800, and FCP900 are 5.5, 12.2, 15.9, and 15.2 mF cm⁻², respectively. The Tafel plots and C_dl results are consistent with the electrocatalytic activity. The electrochemical active surface area (ECSA) values of FCP600, FCP700, FCP800, and FCP900 are 137.5, 305.0, 397.5, and 380.0 in the acidic electrolyte, respectively.

The electrocatalytic activity of P-Fe₃O₄/Fe@C was also studied in 1.0 M KOH electrolyte using a standard three-electrode system (Figure 6). Similar electrocatalytic activity results in Figure 6a can be found in alkaline media. As shown in Figure 6b, FCP800 shows the lowest η of 214 mV at 10 mA cm⁻², compared to those of FCP600 (288 mV), FCP700 (251 mV), and FCP900 (275 mV). Notably, P-Fe₃O₄/Fe@C (FCP800) achieves a current density of 50 mA cm⁻² at an overpotential of 341 mV in the alkaline medium. The HER-specific activity of FCP600, FCP700, FCP800, and FCP900 are 0.08, 3.56, 7.89, and 2.34 mA cm⁻² at the overpotential of 150 mV in 1.0 M KOH electrolyte, respectively (Figure S4a). The HER mass activity of FCP600, FCP700, FCP800, and FCP900 are 1.62, 2.4, 5.57, and 0.13 A mg⁻¹ at the overpotential of 150 mV in 1.0 M KOH electrolyte, respectively (Figure S4b). The Tafel slope value of FCP800 is 75.59 mV dec⁻¹, which is much smaller than those of FCP600 (111.05 mV dec⁻¹) and FCP900 (89.95 mV dec⁻¹), indicating its superior HER reaction kinetics (Figure 6c). As shown in Figure 6d, FCP800 exhibits the highest C_dl of 14.5 mF cm⁻², followed by FCP600 (5.7 mF cm⁻²), FCP700 (11.1 mF cm⁻²), and FCP900 (5.9 mF cm⁻²). The electrochemical active surface area (ECSA) values of FCP600, FCP700, FCP800, and FCP900 are 142.5, 147.5, 362.5, and 277.5 in an alkaline electrolyte, respectively. Electrochemical impedance spectroscopy (EIS) was used to investigate the electron transfer mechanism. Figure 7a displays the Nyquist plots of FCP600, FCP700, FCP800, and FCP900 electrodes. The values of R_s, R_ct, and CPE are fitted and listed in Table S1. The small semicircle diameter in the high frequency region of the Nyquist plot indicates a low charge transfer resistance (R_ct) at the electrode–electrolyte interface, which suggests a faster charge transfer kinetics and reaction rate. With the increase of Fe content in P-Fe₃O₄/Fe@C interface, the R_ct decreases and then increases. The R_ct value of the FCP800 electrodes is lowest, demonstrating a favorable charge transfer due to their excellent electronic conductivity. Therefore, P-Fe₃O₄/Fe@C shows excellent electrocatalytic HER activity and mass activity compared to previously reported Fe-based electrocatalysts in the literature, as shown in Figure 7b,c.

The electrocatalytic stability of electrocatalysts is very important in practical application. In particular, MOF materials are prone to destruction under acidic media. The electrocatalytic stability of P-Fe₃O₄/Fe@C (FCP800) was studied by a CV test. The corresponding LSV curves both before and after 500 cycles are shown in Figure 8. It can be unambiguously found that the LSV curves of FCP800 before and after 500 cycles vary very little in acidic and alkaline electrolytes, demonstrating the good electrocatalytic stability of P-Fe₃O₄/Fe@C. The XRD patterns of P-Fe₃O₄/Fe@C (FCP800) after 500 cycles in 1.0 M KOH and 0.5 M H₂SO₄ electrolytes have been provided, as shown in Figure S7. Results indicate that P-Fe₃O₄/Fe@C shows good structural stability and durability under the tested conditions, making it a promising material for various electrochemical applications.

FCP800 shows superior electrocatalytic activity with a relatively low overpotential and Tafel slope as well as remarkable stability due to the rich under-coordinated Fe atoms in the P-Fe₃O₄/Fe@C interfaces. The reasons for the enhancement of electrocatalytic activity for FCP800 are as follows: (i) rich under-coordinated Fe atoms can result in core electron entrapment and 3d orbital lone electron polarization, which can increase the local charge density and raise the occupied valence states towards the Fermi level of P-Fe₃O₄/Fe@C. The coupling effect of entrapment and polarization can promote the water adsorption and activation to release more H* in the electrochemical water-splitting reaction; (ii) an appropriate under-coordinated Fe atom proportion in the Fe₃O₄/Fe@C interfaces can increase the specific surface area and pore volume, which can provide more reaction active sites and transport channels for water molecular adsorption and electron/ion transfer, thus lowering the overpotential to a low current density; (iii) an appropriate under-coordinated Fe atom proportion can improve the electronic conductivity and reduce the charge transfer impedance of Fe₃O₄/Fe@C, which facilitate efficient electron transfer, allowing for faster electrocatalytic reaction kinetics. Meanwhile, the carbon support can also improve the electron transfer efficiency in the electrocatalytic reaction process [39,40].

4. Conclusions

In summary, P-Fe₃O₄/Fe@C has been synthesized by an hydrothermal method and pyrolysis for pH-universal water splitting. The proper under-coordinated Fe atoms in the P-Fe₃O₄/Fe@C interfaces can effectively enhance the electrocatalytic HER activity. Rich under-coordinated Fe atoms lead to an increased local charge density, core electron entrapment, and lone electron polarization, which can accelerate water adsorption and release more H* in the electrochemical water-splitting reaction. As a donor-like catalyst, P-Fe₃O₄/Fe@C has low overpotentials of 160 mV in acidic media and 214 mV in alkaline media at 10 mA cm⁻² and shows an excellent pH-universal electrocatalytic stability.

Author Contributions

Conceptualization, Methodology, Investigation, Data curation, Writing—original draft, M.F.; Validation, Formal analysis, P.L.; Methodology, Formal analysis, Investigation, Data curation, B.L.; Formal analysis, Visualization, Y.G.; Software, Formal analysis, C.L. and K.Y.; Conceptualization, Formal analysis, Writing—review and editing, Supervision, X.L.; Formal analysis, Writing—review and editing, J.F.; Conceptualization, Writing—review and editing, Supervision, Funding acquisition, Y.X. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

Data will be made available on request.

Conflicts of Interest

The authors declare no conflict of interest.

Footnotes

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Figures and Table

Figure 1. Synthesis process diagram of P-Fe3O4/Fe@C hybrids.

Figure 2. (a) XRD patterns of MIL-53(Fe), FCP700, FCP800, and FCP900; high-resolution XPS spectra of (b) Fe 2p, (c) C 1 s, and (d) P 2p of FCP800.

Figure 3. FESEM of (a) FCP700, (b) FCP800, and (c) FCP900; (d–f) HRTEM of FCP800.

Figure 4. Nitrogen adsorption-desorption isotherms for FCP600, FCP700, FCP800, and FCP900.

Figure 5. HER electrocatalytic activity in 0.5 M H2SO4 electrolyte: (a) LSV curves, (b) corresponding η, (c) Tafel plots, and (d) Cdl of Pt/C and P-Fe3O4/Fe@C.

Figure 6. HER electrocatalytic activity in 1.0 M KOH electrolyte: (a) LSV curves, (b) corresponding η, (c) Tafel plots, and (d) Cdl of Pt/C and P-Fe3O4/Fe@C.

Figure 7. (a) Nyquist plots of FCP600, FCP700, FCP800, and FCP900 electrodes; comparison of (b) electrocatalytic activity of Fe-based electrocatalysts in 1.0 M KOH electrolyte and (c) mass activity of HER electrocatalysts in 1.0 M KOH electrolyte.

Figure 8. LSV curves before and after 500 cycles of P-Fe3O4/Fe@C (FCP800) in (a) 1.0 M KOH and (b) 0.5 M H2SO4 electrolytes.

Table 1

Specific surface areas, pore volumes, and average pore diameters for FCP600, FCP700, FCP800, and FCP900.

Sample	Specific Surface Areas (m2 g−1)	Pore Volume (cm3 g−1)	Average Pore Diameters (nm)
FCP600	322.073	0.5141	3.911
FCP700	302.940	0.4521	3.915
FCP800	363.318	0.5427	3.913
FCP900	87.306	0.146	3.911

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/nano13131909/s1. Figure S1: XRD pattern of P-Fe₃O₄/Fe@C (FCP600). Figure S2: XPS survey spectrum of P-Fe₃O₄/Fe@C (FCP800). Figure S3: HER electrocatalytic activity in (a,b) 0.5 M H₂SO₄ and (c,d) 1.0 M KOH electrolytes: (a–c) LSV curves and (b–d) Tafel plots of Fe₃O₄/Fe@C and FCP800. Figure S4: (a) HER-specific activity and (b) mass activity of FCP600, FCP700, FCP800, and FCP900 in the 0.5 M H₂SO₄ and KOH electrolytes. Figure S5: CV curves of (a) FCP600, (b) FCP700, (c) FC800, and (d) FCP900 electrodes at different scan rates in 0.5 M H₂SO₄ solution. Figure S6: CV curves of (a) FCP600, (b) FCP700, (c) FC800, and (d) FCP900 electrodes at different scan rates in 1.0 M KOH solution. Figure S7: XRD patterns of P-Fe₃O₄/Fe@C (FCP800) after 500 cycles in 1.0 M KOH and 0.5 M H₂SO₄ electrolytes. Table S1: The fitted R_s and R_ct for FCP600, FCP700, FCP800, and FCP900.

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