This paper proposes a novel exponential rational function method, a modification of the well-known exp-function method, to find exact solutions of the time fractional Cahn-Allen equation and the time fractional Phi-4 equation. The solution procedure is reduced to solve a system of algebraic equations, which is then solved by Wu?s method. The results show that the present method is effective, and can be applied to other fractional differential equations.

Fractional Fokas equation is studied, its exact solution is obtained by the direct algebraic method. The solution process is elucidated step by step, and the fractional complex transform and the characteristic set algorithm are emphasized.

Lithium metal batteries (LMBs) are promising next-generation battery technologies with high energy densities. However, lithium dendrite growth during charge/discharge results in severe safety issues and poor cycling performance, which hinders their wide applications. The rational design and application of functional polymer materials in LMBs are of crucial importance to boost their electrochemical performances, especially the cycling stability. In this review, recent advances of advanced polymer materials are examined for boosting the stability and cycle life of LMBs as different components including artificial solid electrolyte interface (SEI) and functional interlayers between the separator and lithium metal anode. Thereafter, the research progress in the design of advanced polymer electrolytes will be analyzed for LMBs. At last, the major challenges and key perspectives will be discussed for the future development of functional polymers in LMBs.

Epoxy resins have widespread applications across various industries, such as anticorrosive coatings, owing to their exceptional attributes. However, there is a constant demand for enhancements to their mechanical characteristics to cater to the requirements of unique and specialized conditions. In this work, graphene oxide modified by 4,4′-Oxydianiline (MGO) was prepared using a covalent grafting reaction. The MGO in epoxy resin composites exhibited a rougher morphology and thin layers with a superior tensile strength (38 MPa), elastic modulus (358 MPa), flexural strength (85 MPa), flexural modulus (957 MPa), and hardness (62 HD). The results indicated that the mechanical properties of epoxy resin are significantly improved by MGO and the improved mechanical properties of epoxy resin composites are due to the strong interfacial bonding between MGO and epoxy.

Lithium-metal batteries have attracted extensive research attention because of their high energy densities. Developing appropriate electrolytes compatible with lithium-metal anodes is of great significance to facilitate their practical application. Currently used electrolytes still face challenges of high production costs and unsatisfactory Coulombic efficiencies of lithium plating/stripping. In this research, we have developed a diluted electrolyte which is compatible with both lithium-metal anode and sulfurized polyacrylonitrile cathode. It presents a very high Li plating/stripping Coulombic efficiency of 99.3% over prolonged cycling, and the as-assembled anode-free Li-S battery maintains 71.5% of the initial specific capacity after 200 cycles at 0.1 A g⁻¹. This work could shed light on designing a low-cost and high-performance liquid electrolyte for next-generation high-energy batteries.

In the critical situation of energy shortage and environmental problems, Si has been regarded as one of the most potential anode materials for next-generation lithium-ion batteries as a result of the relatively low delithiation potential and the eminent specific capacity. However, a Si anode is subjected to the huge volume expansion–contraction in the charging–discharging process, which can touch off pulverization of the bulk particles and worsens the cycle life. Herein, to reduce the volume change and improve the electrochemical performance, a novel Si@SiO_x/C anode with a core–shell structure is designed by spray and pyrolysis methods. The SiO_x/C shell not only ensures the structure stability and proves the high electrical conductivity but also prevents the penetration of electrolytes, so as to avoid the repetitive decomposition of electrolytes on the surface of Si particle. As expected, Si@SiO_x/C anode maintains the excellent discharge capacity of 1,333 mAh g⁻¹ after 100 cycles at a current density of 100 mA g⁻¹. Even if the current density reaches up to 2,000 mA g⁻¹, the capacity can still be maintained at 1,173 mAh g⁻¹. This work paves an effective way to develop Si-based anodes for high-energy density lithium-ion batteries.