Diffusion-controlled Reaction Research Articles

Fluoride- and OSDA-free synthesis of ZSM-5 with controllable b-axis orientation: Insights into the role of medium alkalinity and seed induction

MFI-topology nanosheets with a b-axis-oriented structure are valuable catalysts in diffusion-controlled acid-catalyzed reactions. Therefore, b-axis-oriented ZSM-5 nanosheets were synthesized herein in a fluoride-free solution without using special additives and complex methods. The initial gel pH of mixed raw materials was adjusted to approximately 5–7 (weak acidity) to direct nanosheet structure formation. The target ZSM-5 zeolite with a b-axis-oriented structure was achieved through the synergistic effect between the involved gel pH and seed solution. The seed solution directed the formation of an MFI structure, and the low alkalinity of the gel limited crystal growth in the b plane, thereby affording b-axis-oriented thin sheets. The ratio of the lengths of the c and b axes of the obtained ZSM-5 could be effectively tuned by adjusting the pH of the initial gel. Compared with the nanosized hexagonal ZSM-5 sample synthesized in a strong-basic system, the as-synthesized b-axis-oriented ZSM-5 exhibited a lower coking rate and higher propylene yield during the considered 1-hexene cracking reaction.

A numerical study of the generalized Steklov problem in planar domains

Abstract We numerically investigate the generalized Steklov problem for the modified Helmholtz equation and focus on the relation between its spectrum and the geometric structure of the domain. We address three distinct aspects: (i) the asymptotic behavior of eigenvalues for polygonal domains; (ii) the dependence of the integrals of eigenfunctions on domain symmetries; and (iii) the localization and exponential decay of Steklov eigenfunctions away from the boundary for smooth shapes and in the presence of corners. For this purpose, we implemented two complementary numerical methods to compute the eigenvalues and eigenfunctions of the associated Dirichlet-to-Neumann operator for planar bounded domains. We also discuss applications of the obtained results in the theory of diffusion-controlled reactions and formulate conjectures with relevance in spectral geometry.

Microstructure of ternary Sn-Bi-xCu alloy on mechanical properties, current endurance and corrosion morphology via cycling corrosion test

Low melting temperature of Sn-58 wt.% Bi (SB) solders adding 0.5wt.% Cu (SB05C) and 1.7wt.% Cu (SB17C) concentrations were evaluated for the signal transmission in the 3D IC package. Microstructure combined with phase analysis and Pandat simulation were together with to explain the relationship among the mechanical property, electrical endurance and corrosion resistance. By Cu decoration, the presence Cu6Sn5 intermetallic compound (IMC) acts as heterogeneous nucleation sites to reduce surface free energy and generate fine Bi grain that resulted in higher hardness value. The power-law was used to explain the mechanism of interfacial IMC growth, both Cu6Sn5 and Cu3Sn formation were speculated to be volume diffusion control and surface reaction domination, respectively. The fracture morphology by shear testing indicates that earliest plastic deformation accompanied with brittle rupture were major factors due to the intergranular fracture and Cu6Sn5 compound induced bulk fracture. By cycling corrosion test (CCT), the lump shape of SnO2 by-product was found among solders at three cycling. After seven cycling, Sn phase has been completely corroded and Cu6Sn5 IMC began to be corroded forming circle shape of Cu2O but Bi phase still not be corroded among solders. In the electrical endurance, dense Cu6Sn5 dispersed in solder bulk and fine grain size were feasible to induce current crowding and joule heating, thus Cu deteriorated SB solders is easily failed.

Imperfect diffusion-controlled reactions for stochastic processes with memory

Many physical processes are controlled by the time that a random walker needs to reach a target. In many practical situations, such as reaction kinetics, this target is imperfect: multiple random encounters may be necessary to actually trigger a reaction. So far, most analytical approaches of imperfect reaction kinetics have been limited to Markovian (memoryless) stochastic processes. However, as soon as the random walker interacts with its environment, its motion becomes effectively non-Markovian. Here, we present a theory that provides the mean reaction time for a non-Markovian Gaussian random walker in a large confining volume in the presence of a spatially localized reaction rate or a gated target. Remarkably, in the weakly reactive regime, for strongly subdiffusive processes, our theory predicts that the deviation of the mean reaction time to the reaction controlled time displays a non-trivial scaling with the reactivity, which we identify analytically. This effect illustrates how the memory of past passages to the target influences the statistics of next-return times, to the difference of Markovian processes. The theory is developed in one and two dimensions and agrees with stochastic simulations. These results provide a refined understanding of how non-Markovian transport and local reactivity influence the kinetics of diffusion controlled reactions.

Anionic COF nanosheets construct porous and charged interlayer for the preparation of high-performance desalination membranes

Polyamide (PA) membranes prepared by interfacial polymerization (IP) provide an effective solution for efficient desalination. The IP reaction, as a diffusion-controlled polymerization reaction, regulates the storage and diffusion of monomers in the IP process to achieve effective regulation of the PA membrane structure. Higher initial monomer concentration and slower monomer release rate can effectively reduce the membrane thickness and enhance the permeance of the membrane. Herein, ionic covalent organic framework (iCOF) materials with well-developed and ordered pore channels bearing high-density –SO3H groups are used to construct a porous and charged interlayer to regulate the release process of monomers during the IP process. The well-ordered pore structure of iCOF provides sufficient storage space for amine monomers and uniform monomer distribution, accelerating the closure of the incipient film. Moreover, the electrostatic interactions between the high density of negatively charged anionic groups on iCOF and the positively charged amine monomer can reduce the diffusion coefficient of the amine monomer by a factor of two. The above two effects resulted in a nearly 10-fold reduction in the thickness of the PA separation layer and an increase in water permeance up to 24.8 L m−2 h−1 bar−1, nearly three times improvement compared to unmodified PA membrane.

Tailoring a facile electronic and ionic pathway to boost the storage performance of Fe3O4 nanowires as negative electrode for supercapacitor application

Today, high-energy applications are devoted to boosting the storage performance of asymmetric supercapacitors. Importantly, boosting the storage performance of the negative electrodes is a crucial topic. Fe3O4-based active materials display a promising theoretical storage performance as a negative electrode. Thus, to get a high storage performance of Fe3O4, it must be tailored to have a higher ionic and electronic conductivity and outstanding stability. Functionalized graphite felt (GF) is an excellent candidate for tailoring Fe3O4 with a facile ionic and electronic pathway. However, the steps of the functionalization of GF are complex and time-consuming as well as the energy loss during this step. Thus, the in-situ functionalization of the GF surface throughout the synthesis of Fe3O4 active materials is proposed herein. Fe3O4 is electrodeposited at the in-situ functionalized GF surface with the crystalline nanowires-like structure as revealed from the various analyses; SEM, TEM, Mapping EDX, XPS, XRD, wettability test, and Raman analysis. Advantageously, the synthetic approach introduces full homogeneous and uniform coverage of the large surface area of the GF. Thus, Fe3O4 nanowires with high ionic and electronic conductivity are characterized by a higher storage performance. Interestingly, Fe3O4/GF possesses a high specific capacity of 1418 mC cm−2 at a potential scan rate of 10 mV s−1 and this value retained to 54% at a potential scan rate of 50 mV s−1 at an extended potential window of 1.45 V. Remarkably, the diffusion-controlled reaction is the main contributor of the storage of Fe3O4/GF electrode as revealed by the mechanistic studies.

Improved recovery of lithium from spent lithium-ion batteries by reduction roasting and NaHCO3 leaching

Lithium supply risk is increasing and driving rapid progress in lithium recovery schemes from spent lithium-ion batteries (LIBs). In this study, a facile recycling process consisting mainly of reduction roasting and NaHCO3 leaching was adopted to improve lithium recovery. The Li of spent LiNixCoyMn1−x−yO2 powder were converted to Li2CO3 and LiAlO2 with the reduction effect of C and residual Al in the roasting process. NaHCO3 leaching was utilized to selectively dissolve lithium from Li2CO3 and water-insoluble LiAlO2. The activation energy of NaHCO3 leaching was 9.31 kJ∙mol−1 and the leaching of lithium was a diffusion control reaction. More than 95.19 % lithium was leached and recovered as a Li2CO3 product with a purity of 99.80 %. Thus, this approach provides a green path to selective recovery of lithium with good economics.

Evidence for suboceanic small-scale convection from a “garnet”-bearing lherzolite xenolith from Aitutaki Island, Cook Islands

Garnet peridotite xenoliths have been rarely reported from suboceanic mantle. Petrographic and geochemical characteristics of garnet-bearing oceanic peridotite xenoliths provide precious information on dynamics of the suboceanic lithosphere and asthenosphere interaction. We examined a lherzolite xenolith included in olivine nephelinite lava from Aitutaki Island, a member of the Cook-Austral volcanic chain. The lherzolite xenolith contains reddish fine-grained (< 5 µm in size) mineral aggregates (FMAs) with size range of 0.5–6 mm, consisting of olivine, calcic and sodic plagioclases, aluminous spinel, native iron, and nepheline. Microstructural observations and chemical data corroborate that the FMA is a decomposed pyrope-rich garnet including chromian spinel grains with an irregular highly indented morphology in the center. The FMA is surrounded by pyroxene-poor and olivine-rich aureole. The spatial and morphological relationships of FMA and chromian spinel with pyroxene-depleted margin suggest a reaction of aluminous spinel + pyroxenes → pyrope-rich garnet + olivine, which requires a compression before decomposition of the garnet to FMA. An orthopyroxene grain shows slight but clear chemical zoning characterized by increase in Al, Ca, and Cr from the grain center to the rim. The zoning patterns of Al and Ca in the orthopyroxene grain can be modeled by diffusion-controlled solid-state reactions induced by pressure and temperature changes, keeping surface concentrations in equilibrium with the other coexisting mineral phases. The results indicate that the mantle, from which the lherzolite xenolith was derived, underwent isothermal decompression followed by a weak heating on a time scale of a few tenths of million years before the xenolith extraction. From the deduced compression and decompression histories, we hypothesize that the mantle beneath Aitutaki Island was once dragged down to a garnet-stable deep mantle region and brought up later by small-scale sublithospheric convection.

A clean metallurgical process for vanadium precipitation from vanadium-rich solutions

Ammonium salt vanadium precipitation process has excellent performance in industrial production, but its shortcomings such as high cost and environmental impact are not conducive to sustainable development. In this paper, ethylenediamine was selected as the precipitant, and vanadate was precipitated from acidic simulated vanadium-rich solutions by the ammonium salt precipitation process. The high purity V2O5 product was obtained after calcination. Under optimal conditions, the precipitation rate of vanadium reached 94.8 %, and the purity of vanadium was as high as 99.1 %. The vanadium precipitation product was hexamethyl ammonium, and the vanadium product was V2O5. It can be derived by the differential method that the reaction order was n = 2.4, the reaction rate equation was CV-1.4=kt+a, and the apparent activation energy was 27.8097 kJ/mol, which can be classified as the diffusion-controlled reaction. This innovative process enables a savings of 5050 yuan per ton of V2O5. On this basis, a complete V2O5 production process with zero waste discharge was designed.

A Cascade-Amplified Pyroptosis Inducer: Optimizing Oxidative Stress Microenvironment by Self-Supplying Reactive Nitrogen Species Enables Potent Cancer Immunotherapy.

Selective generation of sufficient pyroptosis inducers at the tumor site without external stimulation holds immense significance for a longer duration of immunotherapy. Here, we report a cascade-amplified pyroptosis inducer CSCCPT/SNAP that utilizes reactive nitrogen species (RNS), self-supplied from the diffusion-controlled reaction between reactive oxygen species (ROS) and nitric oxide (NO) to potentiate pyroptosis and immunotherapy, while both endogenous mitochondrial ROS stimulated by released camptothecin and released NO initiate pyroptosis. Mechanistically, cascade amplification of the antitumor immune response is prompted by the cooperation of ROS and NO and enhanced by RNS with a long lifetime, which could be used as a pyroptosis trigger to effectively compensate for the inherent drawbacks of ROS, resulting in long-lasting pyroptosis for favoring immunotherapy. Tumor growth is efficiently inhibited in mouse melanoma tumors through the facilitation of reactive oxygen/nitrogen species (RONS)-NO synergy. In summary, our therapeutic approach utilizes supramolecular engineering and nanotechnology to integrate ROS producers and NO donors of tumor-specific stimulus responses into a system that guarantees synchronous generation of these two reactive species to elicit pyroptosis-evoked immune response, while using self-supplied RNS as a pyroptosis amplifier. RONS-NO synergy achieves enhanced and sustained pyroptosis and antitumor immune responses for robust cancer immunotherapy.

The Annealing Kinetics of Defects in CVD Diamond Irradiated by Xe Ions

The radiation-induced optical absorption at 1.5–5.5 eV (up to the beginning of fundamental absorption) has been analyzed in CVD diamond disks exposed to 231-MeV 132Xe ions with four fluences from 1012 to 3.8 × 1013 cm−2. The 5 mm diameter samples (thickness 0.4 mm) were prepared by Diamond Materials, Freiburg (Germany); the average grain size at growth site was around 80 μm; and the range of xenon ions was R = 11.5 μm. The intensity of several bands grows with ion fluence, thus confirming the radiation-induced origin of the defects responsible for these bands. The recovery of radiation damage has been investigated via isochronal (stepwise) thermal annealing procedure up to 650 °C, while all spectra were measured at room temperature. Based on these spectra, the annealing kinetics of several defects, in particular carbon vacancies (GR1 centers with a broad band ~2 eV) and complementary C-interstitial-related defects (~4 eV), as well as impurity-related complex defects (narrow bands around 2.5 eV) have been constructed. The experimental kinetics have also been analyzed in terms of the diffusion-controlled bimolecular reactions. The migration energies of tentatively interstitial atoms (mobile components in recombination process) are obtained, and their dependence on the irradiation fluences is discussed.

Picosecond reactions of excited radical ion super-reductants

Classical photochemistry requires nanosecond excited-state lifetimes for diffusion-controlled reactions. Excited radicals with picosecond lifetimes have been implied by numerous photoredox studies, and controversy has arisen as to whether they can actually be catalytically active. We provide direct evidence for the elusive pre-association between radical ions and substrate molecules, enabling photoinduced electron transfer beyond the diffusion limit. A strategy based on two distinct light absorbers, mimicking the natural photosystems I and II, is used to generate excited radicals, unleashing extreme reduction power and activating C(sp2)―Cl and C(sp2)―F bonds. Our findings provide a long-sought mechanistic understanding for many previous synthetically-oriented works and permit more rational future photoredox reaction development. The newly developed excitation strategy pushes the current limits of reactions based on multi-photon excitation and very short-lived but highly redox active species.

Spectral properties of the Dirichlet-to-Neumann operator for spheroids.

We study the spectral properties of the Dirichlet-to-Neumann operator and the related Steklov problem in spheroidal domains ranging from a needle to a disk. An explicit matrix representation of this operator for both interior and exterior problems is derived. We show how the anisotropy of spheroids affects the eigenvalues and eigenfunctions of the operator. As examples of physical applications, we discuss diffusion-controlled reactions on spheroidal partially reactive targets and the statistics of encounters between the diffusing particle and the spheroidal boundary.

Novel disposable screen-printed sensors based on copper oxide nanoparticles for sensitive voltammetric assay of antazoline

The fabrication and electroanalytical validation of a novel homemade screen-printed carbon electrode enriched with copper oxide nanoparticles (CuONPs/SPCEs) were demonstrated for sensitive and selective voltammetric determination antazoline (ANT) in eye drop solution and spiked serum samples. With a reported electrocatalytic activity, CuONPs catalyzed the oxidation of ANT at the electrode surface showing an irreversible anodic oxidation peak at 0.9 V under a diffusion-controlled electrode reaction. Based on the electroanalytical and molecular orbital calculation studies, oxidation of ANT molecule undergoes via oxidation of the aliphatic nitrogen atom within the ANT moiety. Linear calibration curves were illustrated covering the ANT concentration ranged from 0.01 to 3.819 µg mL−1 with and limit of detection 3 ng mL−1. The fabricated sensors enriched with CuONPs exhibited high fabrication and measurement reproducibility with a prolonged shelf lifetime (6 months). The electroanalytical approach presented adequate sensitivity and selectivity with a short analysis time, applying low-cost instrumentation and simple pretreatment protocol avoiding handling hazardous organic solvents. Trace ANT was monitored in the presence of different interfering species, degradation products, and xylometazoline hydrochloride (ZYL) in the co-formulated ophthalmic pharmaceutical samples. The CuONPs based voltammetric sensors were introduced as a reliable eco-friendly analytical tool for monitoring ANT in ophthalmic solutions and biological fluids with acceptable recovery values.

Effect of cross-flow on heat and mass transfer rates at the outer surface of a spiral tube placed in a cylindrical container and possible application in heat exchanger/reactor design

This research investigates the effect of cross-flow on heat and mass transfer rates at the outer surface of a spiral tube placed in a cylindrical container and its potential application in heat exchanger/reactor design. The study evaluates various parameters such as solution velocity, spiral tube diameter, and pitch through electrochemical methods under laminar flow conditions. Results indicate that the mass transfer coefficient increases with rising solution velocity but decreases with larger spiral tube diameters and pitches. A dimensionless equation is proposed to correlate the mass transfer data for a single spiral tube, which proves valuable for designing and scaling up heat exchanger/reactor systems. The research also highlights the dual functionality of the spiral tube, with the outer surface serving as a catalyst support for an exothermic, diffusion-controlled liquid-solid reaction, while the inner surface acts as a cooler, efficiently absorbing heat generated on the outer surface. The study explores the application of this novel reactor design for heat-sensitive materials and processes requiring swift cooling, such as immobilized cell or enzyme biochemical reactions. The findings contribute to enhancing reactor productivity and achieving high selectivity and yield in electro-organic synthesis.

Liquid – Solid mass transfer characteristics of a heterogeneous reactor made of separated horizontal woven screens impinged by a submerged jet

The mass transfer characteristics of a submerged liquid jet impinging on a stack of separated screens were investigated by the electrochemical limiting current technique. The effects of changing the jet velocity, the nozzle diameter, and the screens’ porosity were studied. The present mass transfer data were found to be much higher than the data obtained by previous studies on jet impinging on flat surfaces. The mass transfer data also revealed that using the impinging jet greatly enhanced the mass transfer at screen surfaces with respect to other conventional forced convection methods used in previous studies. The mass transfer data were correlated by the equation: ShR=0.253Sc0.33ReN0.66ε0.745 for the conditions: Sc=1898, 8071 ≤ ReN≤ 33631, 0.668≤ε≤ 0.809. The importance of the above equation in the scale up and design of electrochemical and catalytic reactors suitable for diffusion-controlled reactions was highlighted. The calculated high energy utilization efficiency (kA/e) of the reactor lends support to its use in practice in preference to reactors made of flat surfaces impinged by a submerged jet. By supporting catalyst on the screens, the reactor also can replace stirred slurry reactors usually used in conducting biochemical and photochemical reactions in order to eliminate the time consuming and the costly step of separating the final product from the catalyst particles.

Paper-based sensor with electro-modified chitosan/silver nanoparticles for rapid and sensitive nitrite detection

The presence of high concentration of nitrite in natural environment and food can be harmful to water ecosystems and human health. It is of great significance to develop a reliable detection method for nitrite. In this work, a modified paper sensor (CS/AgNPs-PE) was fabricated by electrodepositing chitosan (CS) and electrochemically reducing silver nanoparticles (AgNPs) onto an oxidized graphene/cellulose/carbon fiber composite paper sensor. The successful loading of chitosan and AgNPs enhances the electrocatalytic activity of the sensor, improving the detection performance of nitrite. The electrochemical process of nitrite on the surface of the CS/AgNPs-PE was proven to be a diffusion-controlled irreversible reaction. Cyclic voltammetry and differential pulse voltammetry (DPV) were used to quantitatively analyze nitrite. A low detection limit of 7.9 × 10−7 mol L−1 can be obtained by DPV under a wide nitrite detection range of 4.0–1000 µM. CS/AgNPs-PE sensor exhibited good repeatability and selectivity, and it could be used to detect nitrite in tap water and ham samples. These results suggest that the CS/AgNPs-PE sensor is of great potential for nitrite sensing in real samples.

An experimental simulation of oxygen isotope exchange reaction between amorphous silicate dust and carbon monoxide gas in the early Solar System

The reaction mechanism and kinetics of oxygen isotope exchange between tens of nanometer-sized amorphous silicate grains with forsterite composition (amorphous forsterite) and low-pressure carbon monoxide (CO) gas (PCO) of 0.05–1 Pa at 643–883 K were examined to investigate oxygen isotopic evolution in the protosolar disk that led to the mass-independent oxygen isotopic variation of planetary materials. Both CO gas supply- and diffusion-controlled isotope exchange reactions were observed. At 753–883 K and PCO of 0.05–1 Pa, the supply of CO gas controls the isotope exchange reaction, and its rate is 2–3 orders of magnitude smaller than that of the H2O supply-controlled isotope exchange reaction. The diffusion-controlled isotope exchange occurred at 643–703 K and PCO of 0.3 Pa, and the reaction rate of D (m2/s) = (3.1 ± 2.3) × 10−23 exp[−41.7 ± 9.6 (kJ mol−1) R−1 (1/T − 1/1200)] was obtained.We found that the oxygen isotope exchange rates of amorphous forsterite with CO and H2O gases are larger than those of gaseous isotope exchange between CO and H2O gases at a wide range of temperatures, wherein amorphous forsterite crystallization does not precede the isotope exchange reaction of amorphous forsterite with these gases. The most sluggish isotope exchange rate between H2O and CO in the gas phase suggests that amorphous forsterite would play a role in accelerating gaseous isotopic equilibrium through the isotope exchange of amorphous forsterite with both CO and H2O. We found that the oxygen isotopic equilibrium between 0.1 μm-sized amorphous forsterite, CO, and H2O would be accomplished through the isotope exchange of amorphous forsterite at temperatures as low as ∼600–700 K in the dynamically accreting protosolar disk, which is significantly lower than expected for the case of gaseous isotope exchange (>∼800 K).

Reaction kinetics of Li4SiO4 and Li4Ti5O12 in biphasic breeder ceramics after lithium burn-up

Advanced ceramic breeder (ACB) pebbles consisting of the two phases Li4SiO4 and Li2TiO3 serve as the EU reference tritium breeding material. In the present study, the phase stability with regard to a lithium-burn-up is investigated. The loss of lithium due to its transmutation will lead to a compositional change of the breeder material. Li4SiO4 and Li2TiO3 will partly be transformed to the lithium-poorer phases Li2SiO3 and Li4Ti5O12, respectively. However, from the phase diagram it is anticipated that only Li2SiO3 will occur as a third phase after a lithium burn-up as the generated Li4Ti5O12 is expected to further react with Li4SiO4 to form again Li2TiO3 and more Li2SiO3. Therefore, the reaction between Li4SiO4 and Li4Ti5O12 and its temperature dependence were investigated in detail and its reaction kinetics were determined. It was found that this diffusion-controlled reaction with an activation energy of 75 kJ/mol (0.78 eV) will slow down at low irradiation temperatures and may not take place at very low temperatures.

Low-crystallinity conductive multivalence iron sulfide-embedded S-doped anode and high-surface area O-doped cathode of 3D porous N-rich graphitic carbon frameworks for high-performance sodium-ion hybrid energy storages

Sodium-ion hybrid energy storages (SIHESs) are promising electrochemical energy storages for many applications, but their low energy and power densities are yet to be overcome. Herein, we report a strategy to realize ultrahigh-energy density and fast-rechargeable SIHESs. Ultrafine iron sulfide-embedded S-doped carbon/graphene (FS/C/G) anode materials are synthesized from iron-based metal-organic framework (MOF)/graphene oxide heterostructures via graphitic carbon formation and sulfidation. Operando and ex-situ analyses reveal that cycled iron sulfides are rescaled into low-crystallinity conductive fragments with Fe vacancies and multivalence Fe2+/Fe3+ states. Size reduction to fragments inside a 3D porous S-doped N-rich graphitic carbon framework induces high-capacity/high-rate FS/C/G performance. Moreover, 3D porous O-doped carbon cathode materials are synthesized from zeolitic imidazolate frameworks (ZIFs) via pyrolysis-assisted micropore and KOH-assisted mesopore formations. This ZIF-derived porous carbon (ZDPC) has a ∼20-fold higher surface area (3972 m2/g) than conventional ZDCs, O-induced micropores/N-rich sites for high capacity, heteroatom-induced ion-accessible defects/mesopores, and N-rich conductive graphitic carbon networks. Additionally, FS/C/G//ZDPC SHHES benefits from diffusion-controlled and capacitive reactions, as demonstrated by its hitherto highest energy density of 247 Wh kg-1 outperforming state-of-the-art SIHESs, fast-rechargeable power density (up to 34,748 W kg-1) exceeding battery-type reactions by more than 100 folds, and cycle stability with ∼100 % Coulombic efficiency over 5000 charge-discharge cycles.