Synthesis and ionic conductivity measurement of a new PEO-based K+ ion conducting solid polymer electrolytes (SPEs): (1-x) PEO: x KCl, where 0≤x≤50 in wt%., are reported. The present SPEs have been prepared by hot-press technique. Ionic conductivity measurements have been carried out with the help of LCR meter. The activation energy of newly synthesized SPE has also been calculated with the help of Arrhenius plot. Materials characterizations have been carried out with the help of DSC analysis. Ionic nature of the present SPE has been explained with the help of ionic transference number (tion) measurement.
Q-systems first appeared in the analysis of the Bethe equations for the XXX model and generalized Heisenberg spin chains (Kirillov and Reshetikhin 1987 Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Steklov. 160 211-21, 301). Such systems are known to exist for any simple Lie algebra and many other Kac-Moody algebras. We formulate the Q-system associated with any simple, simply-laced Lie algebras g in the language of cluster algebras (Fomin and Zelevinsky 2002 J. Am. Math. Soc. 15 497-529), and discuss the relation of the polynomiality property of the solutions of the Q-system in the initial variables, which follows from the representation-theoretical interpretation, to the Laurent phenomenon in cluster algebras (Fomin and Zelevinsky 2002 Adv. Appl. Math. 28 119-44).
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