A Novel Asymmetric Diffusion Path for Superior Ion Dynamic in High-Voltage Mg-Based Hybrid Batteries.

Magnesium-based batteries have garnered significant attention due to their high energy density, excellent intrinsic safety, and low cost. However, the application process has been hindered by the high Mg2+ ions diffusion barrier in solid-state structures and solid-liquid interphase. To address this issue, a hybrid battery technology based on Mg anode and Fe-based Prussian Blue Analogue cathode doped with functional transition metal ions and N═O bonds is proposed. Combined multiscale experimental characterizations with theoretical calculations, the subtle lattice distortion can create an asymmetric diffusion path for the active ions, which enables reversible extraction with significantly reduced diffusion barriers achieved by synergistic doping. The optimized cathode exhibits a working potential of 2.3 V and an initial discharge capacity of 152 mAh g-1 at 50 mA g-1. With the preferred electrolyte combined with equivalent concentration [Mg2(µ-Cl)2(DME)4][AlCl4]2 and NaTFSI salt solution, the hybrid system demonstrates superior cycling performance over 200 cycles at a high current density of 200 mA g-1, maintaining ≈100% coulombic efficiency with superior ion dynamic. The findings are expected to be marked an important step in the further application of high-voltage cathodes for Mg-based hybrid batteries.

Vanadium Molybdenum Disulfide Nanosheets Anchoring on Carbon Cloth as High-Energy Density Cathode for Magnesium-Lithium Hybrid Batteries.

Magnesium-lithium-ion hybrid batteries (MLIBs) have gained significant attention since the combination of a dendrite-free and low-cost magnesium anode with lithium-ion storage cathodes. However, the lack of high-performance cathodes has severely hindered their development, limited by the lower operating voltages of electrolytes. Herein, vanadium molybdenum disulfide nanosheets anchoring on flexible carbon cloth (VMS@CC) are constructed as high-performance cathodes for MLIBs, which inherit the electrochemical properties of high-voltage VS2 and high-capacity MoS2, simultaneously. By adjusting the V and Mo atomic ratio, the VMS@CC cathode for MLIBs delivers a record maximum energy density of 275.5 Wh kg-1 with a high working voltage of 1.07 V at 50 mA g-1. Meanwhile, under the synergistic effects of the conductive carbon cloth matrix, abundant hetero-interfaces and defects, as well as expanded interlayer spacing, the VMS@CC cathode displays superior rate capability and long-term cycling stability. Ex situ analyses demonstrate the VMS nanosheets cathode exhibits a Li+/Mg2+ co-insertion/extraction mechanism in MLIBs, following the in situ insertion of organic species in the hybrid electrolyte during the aging process. The fabricated flexible cathode herein provides a new insight into the construction of high-energy density cathodes for MLIBs.

Precisely Constructing Orbital-Coupled Fe─Co Dual-atom Sites for High-Energy-Efficiency Zn-Air/Iodide Hybrid Batteries.

Rechargeable Zn-air batteries (ZABs) are promising for energy storage and conversion. However, the high charging voltage and low energy efficiency hinder their commercialization. Herein, these challenges are addressed by employing precisely constructed multifunctional Fe-Co diatomic site catalysts (FeCo-DACs) and integrating iodide/iodate redox into ZABs to create Zinc-air/iodide hybrid batteries (ZAIHBs) with highly efficient multifunctional catalyst. The strong coupling between the 3d orbitals of Fe and Co weakens the excessively strong binding strength between active sites and intermediates, enhancing the catalytic activities for oxygen reduction/evolution reaction and iodide/iodate redox. Consequently, FeCo-DACs exhibit outstanding bifunctional oxygen catalytic activity with a small potential gap (ΔE = 0.66 V) and outstanding stability. Moreover, an outstanding catalytic performance toward iodide/iodate redox is obtained. Therefore, FeCo-DAC-based ZAIHBs exhibit high energy efficiency of up to 75% at 10 mA cm-2 and excellent cycling stability (72% after 500 h). This research offers critical insights into the rational design of DACs and paves the way for high-energy efficiency energy storage devices.

Tuning Electron Delocalization of Redox-Active Porous Aromatic Framework for Low-Temperature Aqueous Zn-K Hybrid Batteries with Air Self-Chargeability.

Air self-charging aqueous batteries promise to integrate energy harvesting technology and battery systems, potentially overcoming a heavy reliance on energy and the spatiotemporal environment. However, the exploitation of multifunctional air self-charging battery systems using promising cathode materials and suitable charge carriers remains challenging. Herein, for the first time, we developed low-temperature self-charging aqueous Zn-K hybrid ion batteries (AZKHBs) using a fully conjugated hexaazanonaphthalene (HATN)-based porous aromatic framework as the cathode material, exhibiting redox chemistry using K+ as charge carriers, and regulating Zn-ion solvation chemistry to guide uniform Zn plating/stripping. The unique AZKHBs exhibit the exceptional electrochemical properties in all-climate conditions. Most importantly, the large potential difference causes the AZKHBs discharged cathode to be oxidized using oxygen, thereby initiating a self-charging process in the absence of an external power source. Impressively, the air self-charging AZKHBs can achieve a maximum voltage of 1.15 V, an impressive discharge capacity (466.3 mAh g-1), and exceptional self-charging performance even at -40 °C. Therefore, the development of self-charging AZKHBs offers a solution to the limitations imposed by the absence of a power grid in harsh environments or remote areas.

1T-2H Mixed-Phase MoS2 Stabilized with a Hyperbranched Polyethylene Ionomer for Mg2+ /Li+ Co-Intercalation Toward High-Capacity Dual-Salt Batteries.

Dual-salt magnesium/lithium-ion batteries (MLIBs) benefit from fast lithium ion diffusion on the cathode side while providing safety due to the dendrite-free Mg2+ stripping/plating mechanism on the anode side. Bulk MoS2 (B-MoS2 ), as a cathode for magnesium-ion batteries (MIBs), suffers from low conductivity and relatively van der Waals gaps and, consequently, resists against divalent Mg2+ insertion due to the high Coulombic interactions. In MLIBs, it exhibits a Daniell-cell type mechanism with the sole accommodation of Li+ . In this paper, the synthesis of a 1T/2H mixed-phase MoS2 (MP-MoS2 ) modified with a hyperbranched polyethylene ionomer, I@MP-MoS2 , for high-capacity MLIBs with a distinct Mg2+ /Li+ co-intercalation mechanism is reported. Benefiting from the enhanced conductivity (due to 53% metallic 1T phase), expanded van der Waals gaps (79% expansion compared to B-MoS2 , 1.11 vs 0.62 nm), and enhanced interactions with THF-based electrolytes following the modification, I@MP-MoS2 shows a dramatically increased Mg2+ storage compared to its parent analogue (144 mAh g-1 vs ≈2 mAh g-1 at 20 mA g-1 ). In MLIBs, I@MP-MoS2 is demonstrated to exhibit remarkable specific capacities up to ≈270 mAh g-1 at 20 mA g-1 through a Mg2+ /Li+ co-intercalation mechanism with 87% of capacity retention over 200 cycles at 100 mA g-1 .

Flexible TiVCTx MXene film for high-performance magnesium-ion storage device.

Magnesium-based battery system has emerged as the potential candidate to beyond Li-ion battery system due to the numerous advantageous of magnesium anode, such as natural abundance, high capacity and dendrites free. However, the selection of cathode materials and the intercalation of magnesium-ions in the cathode host material remains a challenge due to the strong interaction of highly polar divalent magnesium ions with the cathode material, making the diffusion of magnesium ions relatively difficult. Herein, the flexible TiVCTx MXene film was developed via a facile and economical approach. As the cathode host material for magnesium-ion storage, the freestanding TiVCTx MXene film displays a high specific capacity of 111 and 135 mAh g-1 at a current density of 0.05 A g-1 for magnesium-ion batteries (MIB) and Mg/Li hybrid batteries (MLHB). Furthermore, a long-term cycling stability over 1000 cycles was demonstrated and a detailed investigation of the unique long activation phenomenon of MXene films during cycling. More importantly, the reaction mechanism of magnesium-ion storage was validated, i.e., the MXene interlayer spacing variation with the reversible Mg2+ diffusion behavior. This work reveals the magnesium storage mechanism of MXene materials and provides a new pathway for high-performance storage of magnesium-ion cathode materials.

Ball-in-ball NiS2@CoS2 heterojunction driven by Kirkendall effect for high-performance Mg2+/Li+ hybrid batteries.

Mg2+/Li+ hybrid batteries (MLHBs), which support the rapid insertion and removal of Mg2+/Li+ bimetallic ions, are promising energy storage systems. Inspired by the Kirkendall effect, ball-in-ball bimetallic sulfides with heterostructures were prepared as cathode materials for the MLHBs. First, a nickel-cobalt precursor (NiCo-X precursor) with three-dimensional (3D) nanosheets on its surface was prepared using a solvothermal method based on the association reaction between alkoxide molecules. Subsequently, the NiCo-X precursor was vulcanized at high temperature using the potential energy difference as the driving force to successfully prepare NiS2@CoS2 core-shell hollow spheres. When used as the positive electrode material for the MLHBs, the NiS2@CoS2 hollow spheres exhibited excellent Mg2+/Li+ ion storage capacity, high specific capacity, good rate performance, and stable cyclic stability owing to their tough hierarchical structure. At a current density of 500 mA g-1, a specific capacity of 536 mAh g-1 was maintained after 200 cycles. By explaining the transformation mechanism of Mg2+/Li+ in bimetallic sulfides, it was proven that Mg2+ and Li+ worked cooperatively. This study provides a new approach for developing MLHBs with good electrochemical properties.

Hetero-Solvation-Diluted Strongly-Coordinated Zn2+ -Cosolvent Pairs Downshifting Zn Electrode Potential for High-Voltage Hybrid Batteries.

Mild aqueous Zn batteries (AZBs) generally suffer a low-voltage/energy dilemma, which compromises their competitiveness for large-scale energy storage. Pushing Zn anode potential downshift is an admissible yet underappreciated approach for high-voltage/energy AZBs. Herein, with a mild hybrid electrolyte containing in situ-derived diluted strongly-coordinated Zn2+ -cosolvent pairs, a considerable Zn anode potential downshift is initially achieved for high-voltage Zn-based hybrid batteries. The chosen butylpyridine cosolvent not only strongly coordinates Zn2+ ions but also acts as a hydrogen-bond end-capping agent to inhibit hydrogen evolution reaction (HER). The electrolyte environment with hetero-solvation-diluted strongly-coordinated Zn2+ -cosolvent pairs remarkably lowers Zn2+ activity, responsible for the Zn electrode potential downshift (-0.330 V vs Zn), confirming to modified Nernst law (ΔE = R T n F $\frac{{RT}}{{nF}}$ ln[a(Zn2 + )/a(coordinated solvent)]). With the diluted Zn2+ -containing hybrid electrolyte, the Zn//Zn symmetric cell in the hybrid electrolyte shows a long lifespan over 1270 h at a stripping/plating capacity of 0.4 mA h cm-2 . Compared with in common hybrid electrolytes, the as-assembled Zn-MnO2 hybrid battery delivers a ca. 0.278 V enhanced voltage plateau (1.57 V) and a long-term cyclability of over 736 cycles. This work opens a new avenue toward Zn anode potential downshift for high-voltage AZBs, which can extend to other mild metal batteries.

Completely Activated and Phase-Transformed KFeMnHCF for Zn/K Hybrid Batteries with 14 500 Cycles by an OH-Rich Hydrogel Electrolyte.

Metal hexacyanoferrates are recognized as superior cathode materials for zinc and zinc hybrid batteries, particularly the Prussian blue analog (PBA). However, PBA development is hindered by several limitations, including small capacities (<70 mAh g-1 ) and short lifespans (<1000 cycles). These limitations generally arise due to incomplete activation of redox sites and structure collapse during intercalation/deintercalation of metal ions in PBAs. According to this study, the adoption of a hydroxyl-rich (OH-rich) hydrogel electrolyte with extended electrochemical stability windows (ESWs) can effectively activate the redox site of low-spin Fe of the Kx Fey Mn1-y [Fe(CN)6 ]w ·zH2 O (KFeMnHCF) cathode while tuning its structure. Additionally, the strong adhesion of the hydrogel electrolyte inhibits KFeMnHCF particles from falling off the cathode and dissolving. The easy desolvation of metal ions in the developed OH-rich hydrogel electrolytes can lead to a fast and reversible intercalation/deintercalation of metal ions in the PBA cathode. As a result, the Zn||KFeMnHCF hybrid batteries achieve the unprecedented characteristics of 14 500 cycles, a 1.7 V discharge plateau, and a 100 mAh g-1 discharge capacity. The results of this study provide a new understanding of the development of zinc hybrid batteries with PBA cathode materials and present a promising new electrolyte material for this application.

Co-Solvent Electrolyte Design to Inhibit Phase Transition toward High Performance K+ /Zn2+ Hybrid Battery.

Manganese hexacyanoferrate (MnHCF) is one of the most promising cathode materials for aqueous battery because of its non-toxicity, high energy density, and low cost. But the phase transition from MnHCF to Zinc hexacyanoferrate (ZnHCF) and the larger Stokes radius of Zn2+ cause rapid capacity decay and poor rate performance in aqueous Zn battery. Hence, to overcome this challenge, a solvation structure of propylene carbonate (PC)-trifluoromethanesulfonate (Otf)-H2 O is designed and constructed. A K+ /Zn2+ hybrid battery is prepared using MnHCF as cathode, zinc metal as anode, KOTf/Zn(OTf)2 as the electrolyte, and PC as the co-solvent. It is revealed that the addition of PC inhabits the phase transition from MnHCF to ZnHCF, broaden the electrochemical stability window, and inhibits the dendrite growth of zinc metal. Hence, the MnHCF/Zn hybrid co-solvent battery exhibits a reversible capacity of 118 mAh g-1 and high cycling performance, with a capacity retention of 65.6% after 1000 cycles with condition of 1 A g-1 . This work highlights the significance of rationally designing the solvation structure of the electrolyte and promotes the development of high-energy-density of aqueous hybrid ion batteries.

Electrochemically Activated Expanded Graphite with Tailor-Made Pores for Magnesium-Organocation Hybrid Batteries.

Persisting limitations of lithium-ion batteries (LIBs) in terms of safety, energy and power density, natural resources, and the price call for expeditious research to develop the "beyond Li-ion" technologies. In this regard, magnesium-organocation hybrid batteries (MOHB) hold the potential to address the above issues associated with LIBs by utilizing abundant and inexpensive elements of magnesium and carbon for the anode and cathode, respectively. Moreover, magnesium metal anode is highly energy-dense yet less susceptible to the dendrite formation, enabling safer operation compared to lithium metal anodes. In this study, we targeted to increase the capacity and rate capability of porous carbon cathode of MOHB by generating tailor-made pores, which were provided by the interlayer accommodation of solvated organic cations with controlled sizes during the electrochemical activation of expanded graphite. Our electrochemically activated expanded graphite can be used as an efficient cathode in MOHB with enhanced kinetics, specific capacitance, and cycle life.

Origin of Excellent Charge Storage Properties of Defective Tin Disulphide in Magnesium/Lithium-Ion Hybrid Batteries.

Lithium-ion batteries (LIBs) are excellent electrochemical energy sources, albeit with existing challenges, including high costs and safety concerns. Magnesium-ion batteries (MIBs) are one of the potential alternatives. However, the performance of MIBs is poor due to their sluggish solid-state Mg2+ diffusion kinetics and severe electrode polarizability. Rechargeable magnesium-ion/lithium-ion (Mg2+/Li+) hybrid batteries (MLHBs) with Mg2+ and Li+ as the charge carriers create a synergy between LIBs and MIBs with significantly improved charge transport kinetics and reliable safety features. However, MLHBs are yet to reach a reasonable electrochemical performance as expected. This work reports a composite electrode material with highly defective two-dimensional (2D) tin sulphide nanosheets (SnSx) encapsulated in three-dimensional (3D) holey graphene foams (HGF) (SnSx/HGF), which exhibits a specific capacity as high as 600 mAh g-1 at 50 mA g-1 and a compelling specific energy density of ~ 330 Wh kg-1. The excellent electrochemical performance surpasses previously reported hybrid battery systems based on intercalation-type cathode materials under comparable conditions. The role played by the defects in the SnSx/HGF composite is studied to understand the origin of the observed excellent electrochemical performance. It is found that it is closely related to the defect structure in SnSx, which offers percolation pathways for efficient ion transport and increased internal surface area assessable to the charge carriers. The defective sites also absorb structural stress caused by Mg2+ and Li+ insertion. This work is an important step towards realizing high-capacity cathode materials with fast charge transport kinetics for hybrid batteries.

Enabling Reversible MnO2/Mn2+ Transformation by Al3+ Addition for Aqueous Zn-MnO2 Hybrid Batteries.

Aqueous rechargeable Zn-manganese dioxide (Zn-MnO2) hybrid batteries based on dissolution-deposition mechanisms exhibit ultrahigh capacities and energy densities due to the two-electron transformation between MnO2/Mn2+. However, the reported Zn-MnO2 hybrid batteries usually use strongly acidic and/or alkaline electrolytes, which may lead to environmental hazards and corrosion issues of the Zn anodes. Herein, we propose a new Zn-MnO2 hybrid battery by adding Al3+ into the sulfate-based electrolyte. The hybrid battery undergoes reversible MnO2/Mn2+ transformation and exhibits good electrochemical performances, such as a high discharge capacity of 564.7 mAh g-1 with a discharge plateau of 1.65 V, an energy density of 520.8 Wh kg-1, and good cycle life without capacity decay upon 2000 cycles. Experimental results and theoretical calculation suggest that the aquo Al3+ with Brønsted weak acid nature can act as the proton-donor reservoir to maintain the electrolyte acidity near the electrode surface and prevent the formation of Zn4(OH)6(SO4)·0.5H2O during discharging. In addition, Al3+ doping during charging introduces oxygen vacancies in the oxide structure and weakens the Mn-O bond, which facilitates the dissolution reaction during discharge. The mechanistic investigation discloses the important role of Al3+ in the electrolyte, providing a new fundamental understanding of the promising aqueous Zn-MnO2 batteries.

Flexible Ti3C2Tx/Nanocellulose Hybrid Film as a Stable Zn-free Anode for Aqueous Hybrid Zn-Li Batteries.

Aqueous zinc-based batteries are a very promising technology in the post-lithium era. However, excess zinc metals are often used, which results in not only making a waste but also lowering the actual energy density. Herein, a Ti3C2Tx/nanocellulose (derived from soybean stalks) hybrid film is prepared by a facile solution casting method and employed as the zinc-free anode for aqueous hybrid Zn-Li batteries. Benefiting from the ultra-low diameter and rich hydroxyl groups of nanocellulose, the hybrid film exhibits better mechanical properties, superior electrolyte wettability, and more importantly, significantly improved zinc plating/stripping reversibility compared to the pure Ti3C2Tx film. The hybrid film also dramatically overwhelms the stainless steel as the electrode for reversible zinc deposition. Further analysis shows that the hybrid film can lower the zinc deposition overpotential and promote the desolvation process of hydrated Zn2+ ions. In addition, it is found that hexagonal Zn thin flakes are horizontally deposited onto the hybrid film owing to the low lattice mismatch between the Ti3C2Tx surface and the (002) facet of Zn. Consequently, zinc dendritic growth and accompanied harmful side reactions can be considerably inhibited by the hybrid film, and the assembled Zn-Li hybrid batteries exhibit excellent electrochemical performances. This work might inspire future work on zinc-based batteries.

A high-performance rechargeable Mg2+/Li+ hybrid battery using CNT@TiO2 nanocables as the cathode.

Porous CNT@TiO2 nanocables are prepared via an impregnation method combined with calcination, which not only display the illusive capacity of 233.5 mAh g-1 but also possess outstanding rate performance (144.9 mAh g-1 at 500 mA g-1). Compared with TiO2 nanoparticles and nanotubes, CNT@TiO2 exhibits the excellent electrochemical performance on account of the unique coaxial nanocable feature (short ion diffusion path, large contact surface area, supernal conductivity, and favorable structure stability), which simultaneously overcomes the aggregation of TiO2 particles and the collapse of TiO2 nanotubes. Importantly, there are no significant changes in the morphology and phase after long cycling, meaning that CNT@TiO2 has a highly structural stability and reversibility. Therefore, CNT@TiO2 can be applied as a promising cathode material for Mg2+/Li+ hybrid batteries.

Dual-Carbon Batteries: Materials and Mechanism.

Various carbon nanomaterials are being widely studied for applications in supercapacitors and Li-ion batteries as well as hybrid energy storage devices. Dual-carbon batteries (DCBs), in which both electrodes are composed of functionalized carbon materials, are capable of delivering high energy/power and stable cycles when they are rationally designed. This Review focuses on the electrochemical reaction mechanisms and energy storage properties of various carbon electrode materials in DCBs, including graphite, graphene, hard and soft carbon, activated carbon, and their derivatives. The interfacial chemistry between carbon electrodes and electrolyte is also discussed. The perspective for further development of DCBs is presented at the end.

Fast Capacitive Energy Storage and Long Cycle Life in a Deintercalation-Intercalation Cathode Material.

Ni-rich Li-ion cathode materials promise high energy density, but are limited in power density and cycle life, resulting from their poor dynamic characteristics and quick degradation. On the other hand, capacitor electrode materials promise high power density and long cycle life but limited capacities. A joint energy storage mechanism of these two kinds is performed in the material-compositional level in this paper. A valence coupling between carbon π-electrons and O2- is identified in the as-prepared composite material, using a tracking X-ray photoelectron spectroscopy strategy. Besides delivering capacity simultaneously from its LiNi0.8 Co0.1 Mn0.1 O2 and capacitive carbon components with impressive amount and speed, this material shows robust cycling stability by preventing oxygen emission and phase transformation via the discovered valence coupling effect. Structural evolution of the composite shows a more flattened path compared to that of the pure LiNi0.8 Co0.1 Mn0.1 O2 , revealed by the in situ X-ray diffraction strategy. Without obvious phase transformation and losing active contents in this composite material, long cycling can be achieved.

Can Hybrid Na-Air Batteries Outperform Nonaqueous Na-O2 Batteries?

In recent years, there has been an upsurge in the study of novel and alternative energy storage devices beyond lithium-based systems due to the exponential increase in price of lithium. Sodium (Na) metal-based batteries can be a possible alternative to lithium-based batteries due to the similar electrochemical voltage of Na and Li together with the thousand times higher natural abundance of Na compared to Li. Though two different kinds of Na-O2 batteries have been studied specifically based on electrolytes until now, very recently, a hybrid Na-air cell has shown distinctive advantage over nonaqueous cell systems. Hybrid Na-air batteries provide a fundamental advantage due to the formation of highly soluble discharge product (sodium hydroxide) which leads to low overpotentials for charge and discharge processes, high electrical energy efficiency, and good cyclic stability. Herein, the current status and challenges associated with hybrid Na-air batteries are reported. Also, a brief description of nonaqueous Na-O2 batteries and its close competition with hybrid Na-air batteries are provided.

High-Voltage Operation of a V2O5 Cathode in a Concentrated Gel Polymer Electrolyte for High-Energy Aqueous Zinc Batteries.

Gel-type polymer electrolytes are very promising to replace liquid electrolytes, addressing the leakage concerns in batteries. In this work, we report a concentrated gel polymer electrolyte for aqueous zinc-metal batteries, which manifests superior Zn stripping/plating reversibility and electrolyte stability, combined with a promising electrochemical stability window and robust water-retention ability. Quasi-solid-state Zn/V2O5 batteries employing such an electrolyte reach a specific energy of 326 W h kg-1 at 20 mA g-1 based on the cathode mass and a capacity retention of 93% over 600 cycles at 500 mA g-1. Moreover, the cell performs well in the 0-40 °C temperature range without significant capacity loss. These results represent important steps toward the development of high-energy aqueous zinc batteries.

Nonaqueous Hybrid Lithium-Ion and Sodium-Ion Capacitors.

Hybrid metal-ion capacitors (MICs) (M stands for Li or Na) are designed to deliver high energy density, rapid energy delivery, and long lifespan. The devices are composed of a battery anode and a supercapacitor cathode, and thus become a tradeoff between batteries and supercapacitors. In the past two decades, tremendous efforts have been put into the search for suitable electrode materials to overcome the kinetic imbalance between the battery-type anode and the capacitor-type cathode. Recently, some transition-metal compounds have been found to show pseudocapacitive characteristics in a nonaqueous electrolyte, which makes them interesting high-rate candidates for hybrid MIC anodes. Here, the material design strategies in Li-ion and Na-ion capacitors are summarized, with a focus on pseudocapacitive oxide anodes (Nb2 O5 , MoO3 , etc.), which provide a new opportunity to obtain a higher power density of the hybrid devices. The application of Mxene as an anode material of MICs is also discussed. A perspective to the future research of MICs toward practical applications is proposed to close.