Anode Material For Lithium-ion Batteries Research Articles

Preparation of core–shell structured Bi2S3@Co1-xS nanorods with heterojunction as anode materials for lithium-ion batteries

Metal sulfides (MSs) have been extensively studied in the fields of photochemical or electrochemical energy conversion and storage. Herein, core–shell structured Bi2S3@Co1-xS nanorods with heterojunction (CSBCNs) were synthesized for the first time by a facile hydrothermal method and applied in lithium-ion batteries (LIBs). The unique nanosized core–shell structure with heterojunction enhances the surface reaction kinetics and facilitates ions and charges transfer. Moreover, it can also weaken the agglomeration of the active materials and alleviate their volume change. Compared with pure Bi2S3 nanorods, Co1-xS, and Bi2S3/Co1-xS composites, CSBCNs exhibited much better cycling performance and rate capability.

High‐Safety Anode Materials for Advanced Lithium‐Ion Batteries

Lithium‐ion batteries (LIBs) play a pivotal role in today's society, with widespread applications in portable electronics, electric vehicles, and smart grids. Commercial LIBs predominantly utilize graphite anodes due to their high energy density and cost‐effectiveness. Graphite anodes face challenges, however, in extreme safety‐demanding situations, such as airplanes and passenger ships. The lithiation of graphite can potentially form lithium dendrites at low temperatures, causing short circuits. Additionally, the dissolution of the solid‐electrolyte‐interphase on graphite surfaces at high temperatures can lead to intense reactions with the electrolyte, initiating thermal runaway. This review introduces two promising high‐safety anode materials, Li4Ti5O12 and TiNb2O7. Both materials exhibit low tendencies towards lithium dendrite formation and have high onset temperatures for reactions with the electrolyte, resulting in reduced heat generation and significantly lower probabilities of thermal runaway. Li4Ti5O12 and TiNb2O7 offer enhanced safety characteristics compared to graphite, making them suitable for applications with stringent safety requirements. This review provides a comprehensive overview of Li4Ti5O12 and TiNb2O7, focusing on their material properties and practical applicability. It aims to contribute to the understanding and development of high‐safety anode materials for advanced LIBs, addressing the challenges and opportunities associated with their implementation in real‐world applications.

High-Performance Anode Material Based on Zinc Naphthalocyanine/Graphene Composite.

Transition metal oxides are a potential anode material owing to their high theoretical capacity. Nonetheless, their large volume changes and low electrical conductivities lead to poor cycling performance and rate capabilities. In this article, an effective strategy is proposed and developed for preparing a ZnO/N-doped graphene composite (ZnNc/GO-5). The key point of this strategy is to use zinc tetra tert-butyl-naphthalocyanine (ZnNc) as a codoped source of N atoms and zinc ions, and graphene oxide (GO) which is combined with ZnNc by π-π deposition as a carbon matrix. After calcination, ZnO microcrystals coated with N-doped graphene are obtained. The unique features of the composite and synergistic effect between N-doped reduced graphene oxide and ZnO microcrystals enable good electrochemical performance by the composites when used in lithium-ion batteries. As an anode material, the as-synthesized ZnNc/GO-5 composite delivers a high first capacity of 1942.9 mAh g-1 and excellent cyclic stability of 861.4 mAh g-1 after 150 cycles at 100 mA g-1. This strategy may offer a new method of designing the anode materials of lithium-ion batteries and promote the practical use of organic molecules in next-generation lithium-ion batteries.

β12-Borophene/Graphene Heterostructure as a High-Performance Anode Material for Li-Ion Batteries.

In the world of two-dimensional (2D) materials, various Borophene allotropes have gained significant attention for their remarkable specific capacity. However, the instability of monolayers has challenged experimental investigations of innovative approaches. Due to this limitation, in this work, graphene was investigated as a sublayer with the aim of providing stability to the β12-borophene monolayer. This study delves into the potential of a novel β12-borophene/graphene (β12-B/G) van der Waals (vdW) heterostructure using Quantum Espresso software based on vdW-corrected density functional theory. Our investigation includes exploring thermal and dynamical stability, adsorption energy, open circuit voltage, specific capacity, and diffusion barrier energy properties. Impressively, the calculated specific capacity reached 907 mAh/g, outperforming other 2D materials and heterostructures. The combination of a graphene layer not only ensures dynamical stability but also provides the adsorption energy of lithiumon the β12-borophene layer, simultaneously decreasing the diffusion barrier energy in comparison with the β12-borophene monolayer. The calculated open circuit voltage falls in the range 0.08-1.09 V, rendering it suitable for an overall average commercial voltage. For the borophene layer, the computed diffusion barrier energies are approximately 0.52 and 0.78 eV. Collectively, these findings underscore the potential of theβ12-B/G heterostructure as an advanced anode material for lithium-ion batteries.

Synthesis of nanosheet-like α-Ni(OH)2/g-C3N4 hybrid anode material with enhanced lithium storage performance

Nickel hydroxide (Ni(OH)2) has been recognized as a promising anode material for lithium-ion batteries (LIBs) because of its high theoretical capacity, cost-effectiveness, and simple synthesis method. However, the application of Ni(OH)2 is hampered by its volume effect and poor electrical conductivity. To address these challenges, herein, a α-Ni(OH)2/g-C3N4 composite is prepared by a hydrothermal approach. The composite possesses a hierarchical nanosheet-like morphology with fibrous nanostructures on the surface. Due to the unique hybrid nanostructure and the synergistic effect of α-Ni(OH)2 and g-C3N4 components, the α-Ni(OH)2/g-C3N4 composite exhibits significantly enhanced lithium storage performance in terms of electrochemical activity, cyclability, and kinetics than the bare α-Ni(OH)2 counterpart. Specifically, the α-Ni(OH)2/g-C3N4 achieves a remarkable capacity of 696 mA h g−1 after 400 cycles at 0.5 A g−1, far larger than the corresponding value (96 mA h g−1) of pure α-Ni(OH)2. CV and GITT analysis demonstrate the α-Ni(OH)2/g-C3N4 composite has an obvious pseudocapacitance behavior and a much smaller polarization effect than the bare α-Ni(OH)2 during cycling. This work could provide clues for the structural design and performance improvement of nickel hydroxide-based anode materials for LIBs.

Encapsulating Si particles in multiple carbon shells with pore-rich for constructing free-standing anodes of lithium storage

Silicon based (Si-based) materials are considered to be the most promising anode materials for lithium-ion batteries (LIBs) due to their high specific capacity. However, the issues of poor electrical conductivity and volume expansion during cycling have not been effectively addressed. The optimum remedy is to select specific materials to establish an exceptional conductive and volume buffer structure to assist the Si materials to develop its excellent lithium storage properties. Here, Si particles were encapsulated into porous carbon fibers containing ultrafine Co particles (CP) to obtained Si-x@CP-y film. Among them, the addition of Si particles and the void structure was precisely regulated to achieve a superior electrode with a high specific capacity. Subsequently, the two-dimensional conductive material reduced graphene oxide (rGO) nanosheets were further incorporated to obtain Si-2@CP-2@rGO films with core@multi-shell structure. The final electrode was equipped with one-, two-, and three-dimensional electronic pathways to allow rapid electron transport, and featured with multi-layer buffer structure and reserved pores that could effectively mitigate volume changes. As expected, the free-standing Si-2@CP-2@rGO electrode delivered a high specific capacity of 1221.2 mAh/g after 100 cycles at 0.1 A/g in a half cell, and the assembled full cell showed 249.0 mAh/g after 200 cycles at 0.2 A/g, which fulfilled the lightweight requirement for new energy storage devices.

Mo-doping modulated cationic vacancy in Zn3V2O8 with enhanced electrochemical performance for lithium-ion batteries

Given diverse redox reactions and abundant raw materials, Zn3V2O8 with high specific capacity is considered as a potential anode material for lithium-ion batteries. Same as other transition metal oxides, Zn3V2O8 suffers from infertile conductivity, sluggish ion diffusion and fast capacity loss derived from volume expansion during discharge/charge process, further hindering its application. In this work, a novel Mo doped Zn3V2O8 (Zn3V2-xMo5x/6O8) anode material with cationic vacancy (V vacancy) has been designed through a facile sol-gel method. It is found that a small Mo-doping amount has nearly no influence on the crystal structure, morphology and element valence states of Zn3V2O8. Mo doped Zn3V2O8 samples possess smaller charge transfer resistance and higher lithium ion diffusion coefficient. The results of electrochemical performance illustrate that Mo doped Zn3V2O8 can deliver higher reversible specific capacities and better rate capability compared with Zn3V2O8, which can be ascribed to the introduction of V vacancy. In particular, when Mo-doping amount is set as 0.03, the obtained Zn3V1.97Mo0.025O8 exhibits a reversible capacity of 481.1 mAh g−1 after 600 cycles at 1 A g−1. It is believed that this work could provide an effective and feasible strategy to construct high performance transition metal vanadate anode materials for lithium-ion batteries.

Incorporating ZIF-8-derived ZnSe into hollow carbon nanospheres as anodes for lithium-ion batteries

Transition metal selenides (TMSs) show great potential as anode materials for lithium-ion batteries (LIBs), boasting a high theoretical capacity. Nevertheless, their practical utility faces challenges, mainly stemming from significant volume changes that lead to rapid capacity decay during charge and discharge cycles. To overcome this challenge, we present a systematic approach involving the growth of uniformly dispersed ultrafine ZnSe nanoparticles derived from ZIF-8 on the surface of hollow carbon nanospheres (ZnSe@N-HCS/700). When utilized as an anode material for LIBs, the ZnSe@N-HCS/700 electrode demonstrates exceptional electrochemical performance. Specifically, it achieves a capacity of 1299 mAh g−1 after 100 cycles at a current density of 100 mA g−1 and maintains a capacity of 614 mAh g−1 even after 1800 cycles at 2500 mA g−1. The hollow structure of the composite alleviates the volume variation of ZnSe nanoparticles during charge and discharge processes, and provides a large reactive surface area, thereby significantly enhancing lithium storage capacity. In conclusion, our strategy presents an innovative approach to synthesize negative electrode materials with unique structures for LIBs.

Deciphering the storage mechanism of biochar anchored with different morphology Mn3O4 as advanced anode material for lithium-ion batteries

Biochar is regarded as a promising lithium-ion batteries anode material, owing to its high cost-effectiveness. However, the poor specific capacity and cycling stability have limited its practical applications. A straightforward and cost-efficient solvothermal method is presented for synthesizing Mn3O4/biochar composites in this study. By adjusting solvothermal temperatures, Mn3O4 with different morphology is prepared and anchored on the biochar surface (MKAC-T) to improve the electrochemical performance. Due to the morphological effect of nanospherical Mn3O4 on the biochar surface, the MKAC-180 anode material demonstrates outstanding reversible capacity (992.5 mAh/g at 0.2 A/g), significant initial coulombic efficiency (61.1 %), stable cycling life (605.3 mAh/g at 1.0 A/g after 1000 cycles), and excellent rate performance (385.8 mAh/g at 1.6 A/g). Moreover, electro-kinetic analysis and ex-situ physicochemical characterizations are employed to illustrate the charge storage mechanisms of MKAC-180 anode. This study provides valuable insights into the “structure–activity relationship” between Mn3O4 microstructure and electrochemical performance for the Mn3O4/biochar composites, illuminating the industrial utilization of biomass carbon anode materials.

Synergistic Engineering of CoO/MnO Heterostructures Integrated with Nitrogen-Doped Carbon Nanofibers for Lithium-Ion Batteries.

The integration of heterostructures within electrode materials is pivotal for enhancing electron and Li-ion diffusion kinetics. In this study, we synthesized CoO/MnO heterostructures to enhance the electrochemical performance of MnO using a straightforward electrostatic spinning technique followed by a meticulously controlled carbonization process, which results in embedding heterostructured CoO/MnO nanoparticles within porous nitrogen-doped carbon nanofibers (CoO/MnO/NC). As confirmed by density functional theory calculations and experimental results, CoO/MnO heterostructures play a significant role in promoting Li+ ion and charge transfer, improving electronic conductivity, and reducing the adsorption energy. The accelerated electron and Li-ion diffusion kinetics, coupled with the porous nitrogen-doped carbon nanofiber structure, contribute to the exceptional electrochemical performance of the CoO/MnO/NC electrode. Specifically, the as-prepared CoO/MnO/NC exhibits a high reversible specific capacity of 936 mA h g-1 at 0.1 A g-1 after 200 cycles and an excellent high-rate capacity of 560 mA h g-1 at 5 A g-1, positioning it as a competitive anode material for lithium-ion batteries. This study underscores the critical role of electronic and Li-ion regulation facilitated by heterostructures, offering a promising pathway for designing transition metal oxide-based anode materials with high performances for lithium-ion batteries.

Characteristics and properties of anode materials for lithium-ion batteries

Lithium-ion secondary batteries (LIBs) are battery systems with high energy densities. They are essential components of todays information-rich, mobile societys portable, entertainment, computing, and telecommunications technology. After 1981, most of the research on anode materials mainly focused on the anode containing Li, such as LiAl alloy, LiC alloy, etc. These materials have high prices, unstable cycling performance, and are difficult to be commercialized. The successful commercialization of LIBs began in 1991 with SONYs manufacturing of petroleum coke-based anode materials. Among them, anode plays a crucial role in LIBs. Anode materials that have been commercialized include carbon, alloys, and lithium titanate. Lithium-ion batteries using carbon anode materials and lithium titanate anode materials can meet the needs of electric vehicles (EVs) and large-scale energy storage applications to a certain extent, and alloy anode materials can promote the energy density of LIBs. The properties of the commercialized anode materials are covered in this paper. Next generation anode materials such as silicon anode materials are also introduced.

Synergistic boost in Fe3O4 anode performance for li-ion batteries via Zn and Cu double doping and multi-walled carbon nanotube composite integration

In this study, a novel nanocomposite material comprising pure Fe3O4 (FO), doped Zn0.5Cu0.5Fe2O4-3 (ZCFO-3), and Zn0.5Cu0.5Fe2O4-3@ Multi-walled carbon nanotube (ZCFO-3@MWCNT) nanocomposite material is carefully prepared using a simple one-step hydrothermal process. Comprehensive surface and morphological analysis are conducted using X-ray diffraction (XRD), Field emission scanning electron microscopy (FESEM), and High-resolution transmission electron microscopy (HRTEM), while compositional studies are investigated through Raman spectroscopy and X-ray photoelectron spectroscopy (XPS). The electrochemical performance is fully analyzed through Cyclic voltammetry (CV), Electrochemical impedance spectroscopy (EIS), rate capability tests, discharge/charge capacity, and cyclic stability evaluations. Among these three nanomaterials, ZCFO-3@MWCNT nanocomposite at 100 mA g−1 current density reveals the best performance, with a discharge capacity of 1974 mAh g–1, ZCFO-3 and FO reveal 1340 mAh g–1 and 1317 mAh g–1 respectively. After 800 cycles at 500 mA g−1 current density, ZCFO-3@MWCNT stays strong with a discharge capacity of 646 mAh g–1, while ZCFO-3 manages only 362 mAh g–1 and FO only 111 mAh g–1. After 1200 cycles at 500 mA g−1, the nanocomposite still delivers 518 mAh g–1. This study suggests that ZCFO-3@MWCNT could be a promising anode material for lithium-ion batteries.

Imidazole-Intercalated Cobalt Hydroxide Enabling the Li+ Desolvation/Diffusion Reaction and Flame Retardant Catalytic Dynamics for Lithium Ion Batteries.

Lithium-ion batteries have found extensive applications due to their high energy density and low self-discharge rates, spanning from compact consumer electronics to large-scale energy storage facilities. Despite their widespread use, challenges such as inherent capacity degradation and the potential for thermal runaway hinder sustainable development. In this study, we introduce a unique approach to synthesize anode materials for lithium-ion batteries, specifically imidazole-intercalated cobalt hydroxide. This innovative material significantly enhances the Li+ desolvation/diffusion reaction and flame-retardant dynamics through complexing and catalytic synergetic effects. The lithium-ion batteries incorporating these materials demonstrate exceptional performance, boasting an impressive capacity retention of 997.91 mAh g-1 after 500 cycles. This achievement can be attributed to the optimization of the solid electrolyte interphase (SEI) interface engineering, effectively mitigating anode degradation and minimizing electrolyte consumption. Experimental and theoretical calculations validate these improvements. Importantly, imidazole intercalated Co(OH)2 (MI-Co(OH)2) exhibits a remarkable catalytic effect on electrolyte carbonization and the conversion of CO to CO2. This dual action suppresses smoke and reduces toxicity significantly. The presented work introduces a novel approach to realizing high-performance and safe lithium-ion batteries, addressing key challenges in the pursuit of sustainable energy solutions.

Bifunctional effects of nitrogen-doped carbon quantum dots on CoS2/mesoporous carbon composites for high-performance lithium-ion batteries

Cobalt disulfide (CoS2) stands as a promising candidate for anode materials in lithium-ion batteries due to its high theoretical capacity, but it faces challenges associated with the shuttle effect of lithium polysulfide during cycling. To address these issues, zeolitic imidazolate framework (ZIF)-derived composites have been extensively explored because of distinct advantages such as the formation of nano-sized particles, heteroatom doping, and highly porous structures. However, ZIF-derived carbon supports primarily consist of ultra-micropores that can impede lithium-ion diffusion. Herein, we aimed to enhance cycling stability by introducing a nitrogen-doped carbon quantum dot (NCQD) solution derived from N-methyl-2-pyrrolidone into cobalt-based ZIF-67 to modify the porosity and dope heteroatoms of CoS2 nanoparticle-embedded heteroatom-doped carbon composites (CoS2/NSC). The mildly acidic NCQD solution resulted in the partial etching of the ZIF-67 structure, along with the deposition of NCQDs as a nitrogen source. Notably, the pore sizes could be adjusted by varying the concentration of the NCQD solution, while retaining the nitrogen functional groups during carbonization. The electrode using CoS2/NSC with the 2.8 mL NCQD pre-treatment exhibited enhanced C-rate capability with the capacity of 392 mAh/g at 2.0 A/g. Moreover, the cycling stability was improved, with a capacity retention of 77 % after 100 cycles.

A fast-charging/discharging and long-term stable artificial electrode enabled by space charge storage mechanism

Lithium‐ion batteries with fast-charging/discharging properties are urgently needed for the mass adoption of electric vehicles. Here, we show that fast charging/discharging, long-term stable and high energy charge-storage properties can be realized in an artificial electrode made from a mixed electronic/ionic conductor material (Fe/LixM, where M = O, F, S, N) enabled by a space charge principle. Particularly, the Fe/Li2O electrode is able to be charged/discharged to 126 mAh g−1 in 6 s at a high current density of up to 50 A g−1, and it also shows stable cycling performance for 30,000 cycles at a current density of 10 A g−1, with a mass-loading of ~2.5 mg cm−2 of the electrode materials. This study demonstrates the critical role of the space charge storage mechanism in advancing electrochemical energy storage and provides an unconventional perspective for designing high-performance anode materials for lithium-ion batteries.

Study of binder effect on the lithium storage kinetics of copper phosphide nanotube anode

Copper phosphide (CP) stands out as a promising anode material for lithium-ion batteries due to its high theoretical capacity (1281 mAh g−1). However, the fast capacity decay of copper phosphide poses a significant challenge due to its huge volume change. Optimization of binder selection presents an effective way to harness the high lithium storage capacity of copper phosphide. In this study, copper phosphide nanotubes were synthesized using a hard template transformation method. The following investigation delved into the impact of different binders on the electrode structure and the lithium-ion storage performance of copper phosphide. Notably, employing polyacrylic acid (PAA) as a binder resulted in a stable capacity of 526.8 mAh g−1 over 400 cycles at 100 mA g−1 for the copper phosphide electrode. The remarkable lithium-ion storage property of the CP-PAA electrode is ascribed to the robust interaction between PAA and the P–O bond on the copper phosphide surface. This interaction not only mitigated volume expansion but also enhanced the kinetics of electrochemical reactions.

MnO@Mn2O3 nanocrystals embedded in biochar networks for sustainable anode of lithium-ion batteries

MnO is an alternative for commercial graphite as anode material for lithium-ion batteries (LIBs), if the issue of unstable performance caused by volume changes, poor conductivity, and changes in valence state of Mn is addressed. In this study, a series of nano MnO/biochar-containing composite materials were prepared with Mn(NO3)2, urea and pomelo peel as raw materials, via simple hydrothermal treatment and calcination, as anode materials for LIBs, where the biochar was used as inexpensive conductive medium and volume buffer. The electrochemical performance of the composite materials shows complicated correlation with the biochar contents, which associate with different carbonization temperatures. Elaborate characterizations with XRD, SEM, TEM, and Mn 2p, Mn 3s XPS spectra were conducted and jointly analyzed, which revealed that the surface of MnO nanocrystals undergoes different degrees of oxidation. The thickness of the surface amorphous Mn2O3 layer on the MnO nanocrystals influences the long-term electrochemical stability more significantly than the circumstances of biochar encapsulation, which was proved through cyclic voltammetry (CV) measurements. A composite material with moderate biochar content and thin layer of Mn2O3 coating on MnO nanocrystals will show more stable electrochemical performance. Based on this principle, one regulated composite material (MnOx/BC-650) gives an ultra-stable capacity of 446.9 mAh∙g−1 at 500 mA∙g−1 after 200 cycles. This study provides new insight for both revealing the true structure of manganese oxides and developing long-term stable MnO-containing anode materials for LIBs.

Lithiation kinetics and performance of Nb18Mo16O93 anode materials based on tetragonal tungsten-bronze structures

In lithium-ion batteries (LIBs) anode materials, Nb2O5 has a higher specific capacity and working potential than graphite, but its low conductivity and the problem of asynchronous phase transition in the reaction limit the specific capacity as well as the cycling performance of the material. In this study, Nb18Mo16O93 LIBs anode materials with tetragonal tungsten bronze (TTB) structure were successfully synthesized by combining ball milling and calcination method, using MoO3 and Nb2O5 as raw materials. The introduction of Mo atoms has led to the formation of a new material that solves the problem of low electrical conductivity of Nb2O5. Meanwhile, the Nb18Mo16O93 material forms three kinds of channels to promote Li+ transport, namely pentagonal, square channel and triangular, due to its special TTB structure. In addition, the rod-like morphology of the Nb18Mo16O93 material provides a larger contact area between the electrolyte and the electrode material, which improves the adsorption and diffusion efficiency of lithium ions. Nb18Mo16O93 as an anode material maintained a specific capacity of 692 mAh g−1 after 300 cycles at 0.1 A g−1 and 75.5 mAh g−1 after 3000 cycles at a high current of 5 A g−1. The preparation of Nb18Mo16O93 provides a new direction to solve the shortcomings of Nb2O5.

Triblock Polymer/Acetylene Black Dual‐Assisted Preparation of Ge/C Nanocomposites with Superior Lithium Storage Performance

AbstractAnode materials based on IV main group elements like Si, Ge, and Sn show great potential for lithium‐ion batteries (LIBs) due to their high specific capacity and low working potential. However, issues such as volume expansion and lattice pulverization hinder their practical usage. To address these issues for Ge, a novel F127 triblock polymer/acetylene black dual‐assisted strategy is proposed to achieve uniform dispersion of polycrystalline Ge, enabling the preparation of Ge@C nanocomposites via hydrogen reduction. The introduced F127 triblock polymer and acetylene black serves a dual purpose to enhance electrical conductivity and prevent Ge nanoparticles from agglomeration. When tested as anode material for LIBs, the Ge@C nanocomposites exhibit exceptional electrochemical performances, demonstrating a sustained specific discharge capacity of 780 mA h g−1 at 0.2 A g−1 after 100 cycles. Moreover, the capacity remains at 767 mA h g−1 even after 300 cycles at a higher current density of 0.5 A g−1. These enhanced lithium storage performances are attributed to the combined effects of well‐dispersed tiny Ge nanoparticles, uniform carbon coating, and an abundance of defects. These factors effectively mitigate the volume expansion and lattice pulverization of Ge nanoparticles and concurrently enhance their conductivity, leading to improved overall performance in LIBs.

Mathematical Model for a Lithium-Ion Battery with a SiO/Graphite Blended Electrode Based on a Reduced Order Model Derived Using Perturbation Theory

Silicon oxide (SiO) is a promising anode material for high-energy lithium-ion batteries, as it is made from low-cost precursors, has a potential close to that of Li, and has high theoretical specific capacity. However, the applications of SiO are limited by the intrinsic low electrical conductivity, large volume change, and low coulombic efficiency, which often lead to poor cycling performance. A common strategy to address these shortcomings is to blend SiO with graphite active materials to form a composite anode for better capacity retention. In this work, we derive a reduced order model (ROM1) using perturbation theory. We employ the multi-site, multi-reaction (MSMR) framework of a composite porous electrode blend consisting of two lithium-host materials, SiO and graphite. The ROM1 model employs a single-particle model (SPM) approach as the leading-order solution and involves the numerical analysis of a single, nonlinear partial differential equation for each host material that describes diffusion by means of irreversible thermodynamics, wherein chemical-potential gradients are the driving forces for the diffusion. The first-order correction treats losses other than that of the SPM.