Fig. 7.

a) Cross-correlation 〈M_D(0) · J(t)〉 of ${\text{EMIM}}^{+}{\text{CF}}_3{\text{SO}}_3^{-}$/water mixture with x_H2O = 0.974 [black line] and x_H2O = 0.643 [orange line]. The solid lines represent the correlation of the total collective rotational dipole moment M_D (t) with the current J(t) whereas the dashed lines stand for the correlation of the ionic collective rotational dipole moment $M_D^{+}(t)+M_D^{-}(t)$ with the current J(t). b) Fit of 〈M_D(0) · J(t)〉 of ${\text{EMIM}}^{+}{\text{CF}}_3{\text{SO}}_3^{-}$/water 2 at x_H2O = 0.643 according to $f(t)=\underset{2}{\overset{k}{{{\displaystyle \sum }}^{\text{}}}}{A}_k{t}^{{\gamma }_k-1}{e}^{-t/{\tau }_k}$ with the parameters given in Table VI. The orange line are the same data as a), the black dotted line and dashed line represent k = 1 and k = 2 contribution of f(t), respectively. The sum of both contributions is displayed as dash-dotted line. c) Contribution of the above mentioned cross-correlation 〈M_D (0) · J(t〉 to the dielectric spectrum of ϵ(ω). Please note that this contribution is part of ϑ₀(ω) additionally.