A Bioinspired Membrane with Ultrahigh Li+/Na+ and Li+/K+ Separations Enables Direct Lithium Extraction from Brine.

Membranes with precise Li+/Na+ and Li+/K+ separations are imperative for lithium extraction from brine to address the lithium supply shortage. However, achieving this goal remains a daunting challenge due to the similar valence, chemical properties, and subtle atomic-scale distinctions among these monovalent cations. Herein, inspired by the strict size-sieving effect of biological ion channels, a membrane is presented based on nonporous crystalline materials featuring structurally rigid, dimensionally confined, and long-range ordered ion channels that exclusively permeate naked Li+ but block Na+ and K+. This naked-Li+-sieving behavior not only enables unprecedented Li+/Na+ and Li+/K+ selectivities up to 2707.4 and 5109.8, respectively, even surpassing the state-of-the-art membranes by at least two orders of magnitude, but also demonstrates impressive Li+/Mg2+ and Li+/Ca2+ separation capabilities. Moreover, this bioinspired membrane has to be utilized for creating a one-step lithium extraction strategy from natural brines rich in Na+, K+, and Mg2+ without utilizing chemicals or creating solid waste, and it simultaneously produces hydrogen. This research has proposed a new type of ion-sieving membrane and also provides an envisioning of the design paradigm and development of advanced membranes, ion separation, and lithium extraction.

Flexible Multicavity SERS Substrate Based on Ag Nanoparticle-Decorated Aluminum Hydrous Oxide Nanoflake Array for Highly Sensitive In Situ Detection.

Flexible surface-enhanced Raman scattering (SERS) substrates are very promising to meet the needs for real-time and on-field detection in practical applications. However, high-performance flexible SERS substrates often suffer from complexity and high cost in fabrication, limiting their widespread applications. Herein, we developed a facile method to fabricate a flexible multicavity SERS substrate composed of a silver nanoparticle (AgNP)-decorated aluminum hydrous oxide nanoflake array (NFA) grown on a polydimethylsiloxane (PDMS) membrane. Strong plasmon couplings promoted by multiple nanocavities afford high-density hotspots within such a flexible AgNPs@NFA/PDMS film, boosting high SERS sensitivity with an enhancement factor (EF) of ∼1.54 × 109, and a limit of detection (LOD) of ∼7.4 × 10-13 M for rhodamine 6G (R6G) molecules. Furthermore, benefiting from the high sensitivity, high mechanical stability, and transparency of this substrate, in situ SERS detections of trace thiram and crystal violet (CV) molecules on the surface of cherry tomatoes and fish have been realized, with LODs much lower than the maximum allowable limit in food, demonstrating the great potential of such a flexible substrate in food safety monitoring. More importantly, the preparation processes are very simple and environmentally friendly, and the techniques involved are completely compatible with well-established silicon device technologies. Therefore, large-area fabrication with low cost can be readily realized, enabling the extensive applications of SERS sensors in daily life.

Lithium Hydride in the Solid Electrolyte Interphase of Lithium-Ion Batteries as a Pulverization Accelerator of Silicon.

As a highly promising next-generation high-specific capacity anode, the industrial-scale utilization of micron silicon has been hindered by the issue of pulverization during cycling. Although numerous studies have demonstrated the effectiveness of regulating the inorganic components of the solid electrolyte interphase (SEI) in improving pulverization, the evolution of most key inorganic components in the SEI and their correlation with silicon failure mechanisms remain ambiguous. This study provides a clear and direct correlation between the lithium hydride (LiH) in the SEI and the degree of micron silicon pulverization in the battery system. The reverse lithiation behavior of LiH on micron silicon during de-lithiation exacerbates the localized stress in silicon particles and contributes to particle pulverization. This work successfully proposes a novel approach to decouple the SEI from electrochemical performance, which can be significant to decipher the evolution of critical SEI components at varied battery anode interfaces and analyze their corresponding failure mechanisms.

Deciphering the Lithium-Ion Conduction Mechanism of LiH in Solid-Electrolyte Interphase.

Lithium hydride (LiH) has been widely recognized as the critical component of the solid-electrolyte interphase (SEI) in Li batteries. Although the formation mechanism and structural model of LiH in SEI have been extensively reported, the role in electro-performance of LiH in SEI is still ambiguous and has proven challenging to explored due to the complicated structure SEI and the lack of advanced in situ experimental technology. In this study, the isotopic exchange experiments combined with isotopic tracer experiments is applied to solidly illustrate the superior conductivity and Li+ conduction behavior of the LiH in natural SEI. Importantly, in situ transmission electron microscopy analysis is utilized to visualize the self-electrochemical decomposition of LiH, which is significantly distinctive from LiF and Li2O. The critical experimental evidence discovered by the work demonstrates ion transport behaviors of key components in the SEI, which is imperative for designing novel SEI and augurs a new area in optimizing the performance of lithium batteries.

Fusion Bonding Technique for Solvent-Free Fabrication of All-Solid-State Battery with Ultrathin Sulfide Electrolyte.

For preparing next-generation sulfide all-solid-state batteries (ASSBs), the solvent-free manufacturing process has huge potential for the advantages of economic, thick electrode, and avoidance of organic solvents. However, the dominating solvent-free process is based on the fibrillation of polytetrafluoroethylene, suffering from poor mechanical property and electrochemical instability. Herein, a continuously solvent-free paradigm of fusion bonding technique is developed. A percolation network of thermoplastic polyamide (TPA) binder with low viscosity in viscous state is constructed with Li6PS5Cl (LPSC) by thermocompression (≤5 MPa), facilitating the formation of ultrathin LPSC film (≤25 µm). This composite sulfide film (CSF) exhibits excellent mechanical properties, ionic conductivity (2.1 mS cm-1), and unique stress-dissipation to promote interface stabilization. Thick LiNi0.83Co0.11Mn0.06O2 cathode can be prepared by this solvent-free method and tightly adhered to CSF by interfacial fusion of TPA for integrated battery. This integrated ASSB shows high-energy-density feasibility (>2.5 mAh cm-2 after 1400 cycles of 9200 h and run for more than 10 000 h), and energy density of 390 Wh kg-1 and 1020 Wh L-1. More specially, high-voltage bipolar cell (≥8.5 V) and bulk-type pouch cell (326 Wh kg-1) are facilely assembled with good cycling performance. This work inspires commercialization of ASSBs by a solvent-free method and provides beneficial guiding for stable batteries.

Anion Binding Interaction Enhances the Robustness of Iodide for High-Performance Perovskite Solar Cells.

Owing to the ionic bond nature of the Pb-I bond, the iodide at the interface of perovskite polycrystalline films was easily lost during the preparation process, resulting in the formation of a large number of iodine vacancy defects. The presence of iodine vacancy defects can cause nonradiative recombination, provide a pathway for iodide migration, and be harmful to the power conversion efficiency (PCE) and stability of organic-inorganic hybrid perovskite solar cells (HPSCs). Here, in order to increase the robustness of iodides at the interface, a strategy to introduce anion binding effects was developed to stabilize the perovskite films. It was demonstrated that the N,N'-diphenylurea (DPU), characterized by high anionic binding constants and a Y-shaped structure, provides a relatively strong hydrogen bond donor site to effectively reduce the iodine loss during film preparation and inhibits iodide migration in the device working condition. As expected, the reduced iodine loss considerably improves the quality of the perovskite films and suppresses nonradiative recombination. The performance of the device after DPU modification was significantly increased, with the PCE rising from 23.65 to 25.01% with huge stability enhancement as well.

An Electrode-Crosstalk-Suppressing Smart Polymer Electrolyte for High Safety Lithium-Ion Batteries.

Electrode crosstalk between anode and cathode at elevated temperatures is identified as a real culprit triggering the thermal runaway of lithium-ion batteries. Herein, to address this challenge, a novel smart polymer electrolyte is prepared through in situ polymerization of methyl methacrylate and acrylic anhydride monomers within a succinonitrile-based dual-anion deep eutectic solvent. Owing to the abundant active unsaturated double bonds on the as-obtained polymer matrix end, this smart polymer electrolyte can spontaneously form a dense crosslinked polymer network under elevated temperatures, effectively slowing down the crosstalk diffusion kinetics of lithium ions and active gases. Impressively, LiCoO2/graphite pouch cells employing this smart polymer electrolyte demonstrate no thermal runaway even at the temperature up to 250 °C via accelerating rate calorimeter testing. Meanwhile, because of its abundance of functional motifs, this smart polymer electrolyte can facilitate the formation of stable and thermally robust electrode/electrolyte interface on both electrodes, ensuring the long cycle life and high safety of LIBs. In specific, this smart polymer electrolyte endows 1.1 Ah LiCoO2/graphite pouch cell with a capacity retention of 96% after 398 cycles at 0.2 C.

A Dual-Cation Exchange Membrane Electrolyzer for Continuous H2 Production from Seawater.

Direct seawater splitting (DSS) offers an aspirational route toward green hydrogen (H2) production but remains challenging when operating in a practically continuous manner, mainly due to the difficulty in establishing the water supply-consumption balance under the interference from impurity ions. A DSS system is reported for continuous ampere-level H2 production by coupling a dual-cation exchange membrane (CEM) three-compartment architecture with a circulatory electrolyte design. Monovalent-selective CEMs decouple the transmembrane water migration from interferences of Mg2+, Ca2+, and Cl- ions while maintaining ionic neutrality during electrolysis; the self-loop concentrated alkaline electrolyte ensures the constant gradient of water chemical potential, allowing a specific water supply-consumption balance relationship in a seawater-electrolyte-H2 sequence to be built among an expanded current range. Even paired with commercialized Ni foams, this electrolyzer (model size: 2 × 2 cm2) continuously produces H2 from flowing seawater with a rate of 7.5 mL min-1 at an industrially relevant current of 1.0 A over 100 h. More importantly, the energy consumption can be further reduced by coupling more efficient NiMo/NiFe foams (≈6.2 kWh Nm-3 H2 at 1.0 A), demonstrating the potential to further optimize the continuous DSS electrolyzer for practical applications.

Understanding the Cathode-Electrolyte Interfacial Chemistry in Rechargeable Magnesium Batteries.

Rechargeable magnesium batteries (RMBs) have garnered significant attention due to their potential to provide high energy density, utilize earth-abundant raw materials, and employ metal anode safely. Currently, the lack of applicable cathode materials has become one of the bottleneck issues for fully exploiting the technological advantages of RMBs. Recent studies on Mg cathodes reveal divergent storage performance depending on the electrolyte formulation, posing interfacial issues as a previously overlooked challenge. This minireview begins with an introduction of representative cathode-electrolyte interfacial phenomena in RMBs, elaborating on the unique solvation behavior of Mg2+, which lays the foundation for interfacial chemistries. It is followed by presenting recently developed strategies targeting the promotion of Mg2+ desolvation in the electrolyte and alternative cointercalation approaches to circumvent the desolvation step. In addition, efforts to enhance the cathode-electrolyte compatibility via electrolyte development and interfacial engineering are highlighted. Based on the abovementioned discussions, this minireview finally puts forward perspectives and challenges on the establishment of a stable interface and fast interfacial chemistry for RMBs.

Synergistic Effect of CO2 in Accelerating the Galvanic Corrosion of Lithium/Sodium Anodes in Alkali Metal-Carbon Dioxide Batteries.

Rechargeable alkali metal-CO2 batteries, which combine high theoretical energy density and environmentally friendly CO2 fixation ability, have attracted worldwide attention. Unfortunately, their electrochemical performances are usually inferior for practical applications. Aiming to reveal the underlying causes, a combinatorial usage of advanced nondestructive and postmortem characterization tools is used to intensively study the failure mechanisms of Li/Na-CO2 batteries. It is found that a porous interphase layer is formed between the separator and the Li/Na anode during the overvoltage rising and battery performance decaying process. A series of control experiments are designed to identify the underlying mechanisms dictating the observed morphological evolution of Li/Na anodes, and it is found that the CO2 synergist facilitates Li/Na chemical corrosion, the process of which is further promoted by the unwanted galvanic corrosion and the electrochemical cycling conditions. A detailed compositional analysis reveals that the as-formed interphase layers under different conditions are similar in species, with the main differences being their inconsistent quantity. Theoretical calculation results not only suggest an inherent intermolecular affinity between the CO2 and the electrolyte solvent but also provide the most thermodynamically favored CO2 reaction pathways. Based on these results, important implications for the further development of rechargeable alkali metal-CO2 batteries are discussed. The current discoveries not only fundamentally enrich our knowledge of the failure mechanisms of rechargeable alkali metal-CO2 batteries but also provide mechanistic directions for protecting metal anodes to build high-reversible alkali metal-CO2 batteries.

A Molecular-Sieving Interphase Towards Low-Concentrated Aqueous Sodium-Ion Batteries.

Aqueous sodium-ion batteries are known for poor rechargeability because of the competitive water decomposition reactions and the high electrode solubility. Improvements have been reported by salt-concentrated and organic-hybridized electrolyte designs, however, at the expense of cost and safety. Here, we report the prolonged cycling of ASIBs in routine dilute electrolytes by employing artificial electrode coatings consisting of NaX zeolite and NaOH-neutralized perfluorinated sulfonic polymer. The as-formed composite interphase exhibits a molecular-sieving effect jointly played by zeolite channels and size-shrunken ionic domains in the polymer matrix, which enables high rejection of hydrated Na+ ions while allowing fast dehydrated Na+ permeance. Applying this coating to electrode surfaces expands the electrochemical window of a practically feasible 2 mol kg-1 sodium trifluoromethanesulfonate aqueous electrolyte to 2.70 V and affords Na2MnFe(CN)6//NaTi2(PO4)3 full cells with an unprecedented cycling stability of 94.9% capacity retention after 200 cycles at 1 C. Combined with emerging electrolyte modifications, this molecular-sieving interphase brings amplified benefits in long-term operation of ASIBs.

A Highly-Fluorinated Lithium Borate Main Salt Empowering Stable Lithium Metal Batteries.

Traditional lithium salts are difficult to meet practical application demand of lithium metal batteries (LMBs) under high voltages and temperatures. LiPF6, as the most commonly used lithium salt, still suffers from notorious moisture sensitivity and inferior thermal stability under those conditions. Here, we synthesize a lithium salt of lithium perfluoropinacolatoborate (LiFPB) comprising highly-fluorinated and borate functional groups to address the above issues. It is demonstrated that the LiFPB shows superior thermal and electrochemical stability without any HF generation under high temperatures and voltages. In addition, the LiFPB can form a protective outer-organic and inner-inorganic rich cathode electrolyte interphase on LiCoO2 (LCO) surface. Simultaneously, the FPB- anions tend to integrate into lithium ion solvation structure to form a favorable fast-ion conductive LiBxOy based solid electrolyte interphase on lithium (Li) anode. All these fantastic features of LiFPB endow LCO (1.9 mAh cm-2)/Li metal cells excellent cycling under both high voltages and temperatures (e.g., 80 % capacity retention after 260 cycles at 60 °C and 4.45 V), and even at an extremely elevated temperature of 100 °C. This work emphasizes the important role of salt anions in determining the electrochemical performance of LMBs at both high temperature and voltage conditions.

Suppressing Element Inhomogeneity Enables 14.9% Efficiency CZTSSe Solar Cells.

Kesterites, Cu2ZnSn(SxSe1- x)4 (CZTSSe), solar cells suffer from severe open-circuit voltage (VOC) loss due to the numerous secondary phases and defects. The prevailing notion attributes this issue to Sn-loss during the selenization. However, this work unveils that, instead of Sn-loss, elemental inhomogeneity caused by Cu-directional diffusion toward Mo(S,Se)2 layer is the critical factor in the formation of secondary phases and defects. This diffusion decreases the Cu/(Zn+Sn) ratio to 53% at the bottom fine-grain layer, increasing the Sn-/Zn-related bulk defects. By suppressing the Cu-directional diffusion with a blocking layer, the crystal quality is effectively improved and the defect density is reduced, leading to a remarkable photovoltaic coversion efficiency (PCE) of 14.9% with a VOC of 576 mV and a certified efficiency of 14.6%. The findings provide insights into element inhomogeneity, holding significant potential to advance the development of CZTSSe solar cells.

Oxygen vacancy chemistry in oxide cathodes.

Secondary batteries are a core technology for clean energy storage and conversion systems, to reduce environmental pollution and alleviate the energy crisis. Oxide cathodes play a vital role in revolutionizing battery technology due to their high capacity and voltage for oxide-based batteries. However, oxygen vacancies (OVs) are an essential type of defect that exist predominantly in both the bulk and surface regions of transition metal (TM) oxide batteries, and have a crucial impact on battery performance. This paper reviews previous studies from the past few decades that have investigated the intrinsic and anionic redox-mediated OVs in the field of secondary batteries. We focus on discussing the formation and evolution of these OVs from both thermodynamic and kinetic perspectives, as well as their impact on the thermodynamic and kinetic properties of oxide cathodes. Finally, we offer insights into the utilization of OVs to enhance the energy density and lifespan of batteries. We expect that this review will advance our understanding of the role of OVs and subsequently boost the development of high-performance electrode materials for next-generation energy storage devices.

Covalently Cross-Linked Chemistry of a Three-Dimensional Network Binder at Limited Dosage Enables Practical Si/C Composite Electrode Applications.

Currently, Si (or SiOx, 1 < x < 2) and graphite composite (Si/C) electrodes (e.g., Si/C450 and Si/C600 with specific capacities of 450 and 600 mAh g-1 at 0.1 C, respectively) have become the most promising alternative to traditional graphite anodes toward high-energy lithium-ion battery (LIB) applications by virtue of their higher specific capacity compared to graphite ones and improved cycle performance compared to Si (or SiOx) ones. However, such composite electrodes remain challenging to practical for implementation owing to electrode structure disintegration and interfacial instability caused by a large volume change of inner Si-based particles. Herein, we develop a covalent-bond cross-linking network binder for Si/C450 and Si/C600 electrodes via reversible addition-fragmentation chain transfer (RAFT) polymerization. The as-developed binder with a 3 mol % cross-linker of other monomers [termed P(SH-BA3%)] achieves improved mechanical and adhesive properties and decreased Si/C anode volume expansion, compared to the linear binder counterpart. Impressively, the P(SH-BA3%) binder at only 3 wt % dosage enables 83.56% capacity retention after 600 cycles at 0.5 C in Si/C450 anode based half-cells and retains 86.42% capacity retention at 0.3 C after 200 cycles and 80.95% capacity retention at 0.5 C after 300 cycles in LiNi0.8Co0.1Mn0.1O2 cathode (15 mg cm-2) based homemade soft package full cells. This work provides insight into binder cross-linking chemistry under limited dosage and enlightens cross-linking binder design toward practical Si/C electrode applications.

Interphase Regulation by Multifunctional Additive Empowering High Energy Lithium-Ion Batteries with Enhanced Cycle Life and Thermal Safety.

High energy density lithium-ion batteries (LIBs) adopting high-nickel layered oxide cathodes and silicon-based composite anodes always suffer from unsatisfied cycle life and poor safety performance, especially at elevated temperatures. Electrode /electrolyte interphase regulation by functional additives is one of the most economic and efficacious strategies to overcome this shortcoming. Herein, cyano-groups (-CN) are introduced into lithium fluorinated phosphate to synthesize a novel multifunctional additive of lithium tetrafluoro (1,2-dihydroxyethane-1,1,2,2-tetracarbonitrile) phosphate (LiTFTCP), which endows high nickel LiNi0.8 Co0.1 Mn0.1 O2 /SiOx -graphite composite full cell with an ultrahigh cycle life and superior safety characteristics, by adding only 0.5 wt % LiTFTCP into a LiPF6 -carbonate baseline electrolyte. It is revealed that LiTFTCP additive effectively suppresses the HF generation and facilitates the formation of a robust and heat-resistant cyano-enriched CEI layer as well as a stable LiF-enriched SEI layer. The favorable SEI/CEI layers greatly lessen the electrode degradation, electrolyte consumption, thermal-induced gassing and total heat-releasing. This work illuminates the importance of additive molecular engineering and interphase regulation in simultaneously promoting the cycling and thermal safety of LIBs with high-nickel NCMxyz cathode and silicon-based composite anode.

A Perspective on Uniform Plating Behavior of Mg Metal Anode: Diffusion Limited Theory versus Nucleation Theory.

Utilizing metal anode is the most attractive way to meet the urgent demand for rechargeable batteries with high energy density. Unfortunately, the formation of dendrites, which is caused by uneven plating behavior, always threaten the safety of the batteries. To explore the origin of different plating behavior and predict the plating morphology of anode under a variety of operating conditions, multifarious models have been developed. However, abuse of models has led to conflictive views. In this perspective, to clarify the controversial reports on magnesium (Mg) metal plating behavior, the previously proposed models are elaborated that govern the plating process. Through linking various models and clarifying their boundary conditions, a scheme is drawn to illustrate the strategy for achieving the most dense and uniform plating morphology, which also explains the seemingly contradictory of diffusion limited theory and nucleation theory on uniform plating. This perspective will undoubtedly enhance the understanding on the metal anode plating process and provide meaningful guidance for the development of metal anode batteries.

Electrolyte Engineering Toward High Performance High Nickel (Ni ≥ 80%) Lithium-Ion Batteries.

High nickel (Ni ≥ 80%) lithium-ion batteries (LIBs) with high specific energy are one of the most important technical routes to resolve the growing endurance anxieties. However, because of their extremely aggressive chemistries, high-Ni (Ni ≥ 80%) LIBs suffer from poor cycle life and safety performance, which hinder their large-scale commercial applications. Among varied strategies, electrolyte engineering is very powerful to simultaneously enhance the cycle life and safety of high-Ni (Ni ≥ 80%) LIBs. In this review, the pivotal challenges faced by high-Ni oxide cathodes and conventional LiPF6 -carbonate-based electrolytes are comprehensively summarized. Then, the functional additives design guidelines for LiPF6 -carbonate -based electrolytes and the design principles of high voltage resistance/high safety novel electrolytes are systematically elaborated to resolve these pivotal challenges. Moreover, the proposed thermal runaway mechanisms of high-Ni (Ni ≥ 80%) LIBs are also reviewed to provide useful perspectives for the design of high-safety electrolytes. Finally, the potential research directions of electrolyte engineering toward high-performance high-Ni (Ni ≥ 80%) LIBs are provided. This review will have an important impact on electrolyte innovation as well as the commercial evolution of high-Ni (Ni ≥ 80%) LIBs, and also will be significant to breakthrough the energy density ceiling of LIBs.

Regulating Hetero-Nucleation Enabling Over 14% Efficient Kesterite Solar Cells.

Developing well-crystallized light-absorbing layers remains a formidable challenge in the progression of kesterite Cu2ZnSn(S,Se)4 (CZTSSe) solar cells. A critical aspect of optimizing CZTSSe lies in accurately governing the high-temperature selenization reaction. This process is intricate and demanding, with underlying mechanisms requiring further comprehension. This study introduces a precursor microstructure-guided hetero-nucleation regulation strategy for high-quality CZTSSe absorbers and well-performing solar cells. The alcoholysis of 2-methoxyethanol (MOE) and the generation of high gas-producing micelles by adding hydrogen chloride (HCl) as a proton additive into the precursor solution are successfully suppressed. This tailored modification of solution components reduces the emission of volatiles during baking, yielding a compact and dense precursor microstructure. The reduced-roughness surface nurtures the formation of larger CZTSSe nuclei, accelerating the ensuing Ostwald ripening process. Ultimately, CZTSSe absorbers with enhanced crystallinity and diminished defects are fabricated, attaining an impressive 14.01% active-area power conversion efficiency. The findings elucidate the influence of precursor microstructure on the selenization reaction process, paving a route for fabricating high-quality kesterite CZTSSe films and high-efficiency solar cells.

Enhanced Quasi-Fermi Level Splitting of Perovskite Solar Cells by Universal Dual-Functional Polymer.

Perovskite solar cells (PSCs) have attracted extensive attention due to their higher power conversion efficiency (PCE) and simple fabrication process. However, the open-circuit voltage (VOC) loss remains a significant impediment to enhance device performance. Here, a facile strategy to boost the VOC to 95.5% of the Shockley-Queisser (S-Q) limit through the introduction of a universal multifunctional polymer additive is demonstrated. This additive effectively passivates the cation and anion defects simultaneously, thereby leading to the transformation from the strong n-type to weak n-type of perovskite films. Benefitting from the energy level alignment and the suppression of bulk non-radiative recombination, the quasi-Fermi level splitting (QFLS) is enhanced.  Consequently, the champion devices with 1.59 eV-based perovskite reach the highest VOC value of 1.24 V and a PCE of 23.86%. Furthermore, this strategy boosts the VOC by at least 0.07 V across five different perovskite systems, a PCE of 25.04% is achieved for 1.57 eV-based PSCs, and the corresponding module (14 cm2) also obtained a high PCE of 21.95%. This work provides an effective and universal strategy to promote the VOC approach to the detailed balance theoretical limit.