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Phase transitions and nanometre-scale ordered structures of a binary system of a liquid-crystalline amphiphilic diblock copolymer, poly(ethylene oxide)- b-poly{11-[4-(4-butylphenylazo)phenoxy]undecyl methacrylate} [PEO m- b-PMA(Az) n, where m and n are the degrees of polymerization of the PEO and PMA(Az) domains, respectively], and lithium trifluoromethanesulfonate (LiCF3SO3) were investigated by differential scanning calorimetry and small-angle X-ray scattering (SAXS). PEO114- b-PMA(Az)51 formed a highly ordered hexagonally packed PEO cylinder structure in the temperature range below 393 K and transformed to a body-centred-cubic structure in the isotropic state above 393 K. The PEO114- b-PMA(Az)51/LiCF3SO3 systems with various LiCF3SO3 concentrations (molar ratio 0 < LiCF3SO3/EO = fLi < 1) formed the hexagonally packed cylinder structure at room temperature. From the effects of LiCF3SO3 concentration on the phase transitions, the size and the order of the hexagonally packed cylinder structure, it was found that PEO114- b-PMA(Az)51 and LiCF3SO3 formed a complex efficiently at a molar equivalent of three ethylene oxide repeating units per LiCF3SO3 unit. The ordering of the hexagonally packed cylinder structure decreased with increasing LiCF3SO3 concentration and the radius of the PEO cylinder evaluated by SAXS profile fitting increased from 2.7 to 8.3 nm. For the PEO114- b-PMA(Az)51/LiCF3SO3 system with fLi = 1, the hexagonally packed cylinder structure remained even in the isotropic state because the PEO volume fraction (φPEO) increased from φPEO = 0.06 ( fLi = 0) to φPEO = 0.23 ( fLi = 1) on the formation of the LiCF3SO3/PEO complex. [ABSTRACT FROM AUTHOR]