We explain a new approach to the representation theory of the partition category based on a reformulation of the definition of the Jucys-Murphy elements introduced originally by Halverson and Ram and developed further by Enyang. Our reformulation involves a new graphical monoidal category, the affine partition category, which is defined here as a certain monoidal subcategory of Khovanov's Heisenberg category. We use the Jucys-Murphy elements to construct some special projective functors, then apply these functors to give self-contained proofs of results of Comes and Ostrik on blocks of Deligne's category ReppS t q., . . . of Jucys-Murphy elements in these partition algebras, which were studied further by Enyang [E1, E2]. Enyang worked out a recursive definition for the Jucys-Murphy elements and used them to construct an analog of Young's orthogonal form for the irreducible P n ptq-modules. His definition involves a complicated five term recurrence relation, making the Jucys-Murphy elements for partition algebras considerably harder to work with than the classical Jucys-Murphy elements of the symmetric groups. Recently, Creedon [Cr] has revisited Enyang's work,

This work focuses on the synthesis of LiFePO4–PANI hybrid materials and studies their electrochemical properties (capacity, cyclability and rate capability) for use in lithium ion batteries. PANI synthesis and optimization was carried out by chemical oxidation (self-assembly process), using ammonium persulfate (APS) and H3PO4, obtaining a material with a high degree of crystallinity. For the synthesis of the LiFePO4–PANI hybrid, a thermal treatment of LiFePO4 particles was carried out in a furnace with polyaniline (PANI) and lithium acetate (AcOLi)-coated particles, using Ar/H2 atmosphere. The pristine and synthetized powders were characterized by XRD, SEM, IR and TGA. The electrochemical characterizations were carried out by using CV, EIS and galvanostatic methods, obtaining a capacity of 95 mAhg−1 for PANI, 120 mAhg−1 for LiFePO4 and 145 mAhg−1 for LiFePO4–PANI, at a charge/discharge rate of 0.1 C. At a charge/discharge rate of 2 C, the capacities were 70 mAhg−1 for LiFePO4 and 100 mAhg−1 for LiFePO4–PANI, showing that the PANI also had a favorable effect on the rate capability.

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