Correlated/non-correlated ion dynamics of charge-neutral ion couples : the origin of ionicity in ionic liquids

Proton/Fluoride spin-lattice ($T_1$) nuclear magnetic relaxation dispersion (NMRD) measurements of 1-butyl-3-methyl-$1H$-imidazolium hexa-fluorophosphate, [$C_4mim][PF_6]$, have been carried out using high field spectrometers and fast-field-cycling instrument at proton Larmor frequencies ranging from 10kHz to 40 MHz, at different temperatures. The NMRD profiles are interpreted by means of a simple relaxation model based on the inter- and intra-ionic dipole-dipole relaxation mechanism. Using an atomic molecular-ion dynamic simulation at 323 K the relevant spin dipole-dipole(DD) correlation functions are calculated. The results indicate the NMRD profiles can be rationalized using intra- and inter-ionic spin DD interactions, however, both are mainly modulated by ionic reorientation because of temporary correlations with cations, where modulation by translational diffusion plays a minor role. Reorientational dynamics of charge-neutral ion couples (i.e. $[C_4mim]^{...}[PF_6]$) and $[C_4mim]^{+}$ ions are in the nano-second (ns) time range whereas the reorientation of $[PF_6]{^-}$ is characterized by a reorientational correlation time in the pico-second (ps) regime. Based on the NMRD profiles we conclude the main relaxation mechanism for $[PF_6]{^-}$ is, due to fast internal reorientational motion, a partially averaged F-F intra and a F-H inter-ionic DD coupling as the anion resides in close proximity to its temporary oppositely charged cation partner. The F-$T_1$- NMRD data display a ns dispersions which is interpreted as being due to correlated reorientational modulations resultant from H-containing charge-neutral ion couple $[C_4mim]^{...}[PF_6]$. The analysis of ionicity is based on the free anion fraction, $f$ and it increase with temperature with $f$ $\rightarrow$ 1 at the highest temperatures investigated. The fraction is obtained from the H-F NMRD profiles as correlated-non-correlated dynamics of the ions. The analysis of $T_1$ relaxation rates of C, H, F and P at