A size-asymmetric mean-field theory with ionic interactions is developed for the electric double layer of room temperature ionic liquid (IL) electrolytes, based on the previous work on non-interacting ions (Y. Han et al., J. Phys.: Condens. Matter, 2014, 26, 284103). By solving the modified Poisson-Boltzmann equation with some simplified assumptions following a recent work (Z. A. H. Goodwin et al., Electrochim. Acta, 2017, 225, 190-197), an analytical expression of differential capacitance can be derived, with a scaled electrode potential due to the ionic interactions. Compared with non-interacting ions, the main effect of ionic interactions is the insufficient screening of the electrode potential, and this depresses the differential capacitance compared with the non-interactive case.

Buckingham expansion is important for understanding molecular multipoles and (hyper)polarizabilities. In this study, we give a complete derivation of Buckingham expansion in the traced form using successive Taylor series. Based on such derivation, a general Buckingham expansion in the traced form is proposed, and from which numerical calculations with finite field method of high accuracy can be achieved. The transformations from the traced multipoles and multipole-multipole polarizabilities to the corresponding traceless counterparts are realized with an auxiliary traced electric field gradient. The applications of the finite field method in this study show good agreements with previous theoretical calculations and experimental measurements.

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In the presented research, we prepared dysprosium(Ⅲ)/europium(Ⅲ) doped SrLaGa3O7 phosphors via the calcinations at 1400 °C for 3 h and researched their characteristics using X-ray diffraction and fluorescence spectrophotometer. The dysprosium (III) → europium(III) energy transfers were surveyed and the mechanisms were discussed. The reducing dysprosium(III) luminescence and lifetimes following the enhancements of europium(III) concentration confirm the existence of dysprosium(III) → europium(III) energy transfer. In this process, the quadrupole-quadrupole interaction plays the key role. Exciting at 365 nm, dysprosium(III)/europium(III) codoped SrLaGa3O7 phosphors provide tunable luminescence by reason of the energy transfer process.

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