Condensed Matter Physics, 2010, vol. 13, No. 4, p. 43602:18 DOI:10.5488/CMP.13.43602 Title: Some rigorous relations for partial conductivities in ionic liquids Author(s):  I. Mryglod (Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii Str., 79011 Lviv, Ukraine; Institute of Applied Mathematics and Fundamental Sciences of Lviv Polytechnic National University, 79013 Lviv, Ukraine) ,   V. Kuporov (Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii Str., 79011 Lviv, Ukraine)  Starting with the rigorous expressions, derived previously for the generalized transport coefficients of a multicomponent fluid, we obtained several exact relations for partial conductivities of ionic chargeasymmetric mixtures. For a simpler case of a chargesymmetric binary mixture such kind of relations was discovered experimentally by Sundheim more than 50 years ago and is known as the "universal golden rule". Some more complicate models, describing in particular the cases of ternary and multicomponent mixtures, are considered. The general relation for partial ionic conductivities is derived for a multicomponent ionic fluid. It is shown that such relations can be considered in fact as an example of a more general class of rigorous expressions valid for (k,ω)dependent quantities. Key words: ionic liquids, transport coefficients, mutual diffusion coefficient, ionic conductivity, molten salt PACS: 66.10.cg, 66.10.Ed, 82.45.Gj, 47.10.g
