Structure factor line shape model gives approximate nanoscale size of polar aggregates in pyrrolidinium-based ionic liquids

Room temperature ionic liquids (RTILs) are interesting due to their myriad uses in fields such as catalysis and electrochemistry. Their properties are intimately related to their structures, yet structural understanding is difficult to achieve. This work presents a derivation of an approximate expression for the radial distribution function, <i>g</i>(<i>r</i>). The derivation assumes a Lorentzian line shape for total structure factors, <i>S</i>(<i>Q</i>). The derived form for <i>g</i>(<i>r</i>) is used to present new equations for maxima and minima in <i>g</i>(<i>r</i>) and to define a half-length, the value of <i>r</i> where <i>g</i>(<i>r</i>) decays to one-half its maximum value. A detailed test of the model is presented using experimentally measured and calculated <i>S</i>(<i>Q</i>) for <i>N</i>-methyl-<i>N</i>-propylpyrrolidinium bis(trifluoromethylsulfonyl)imide (C1C3pyrrTFSI). Then, the model is extended to the series of RTILs with anions of increasing size, C1C3pyrrX (X^- = Cl^-, Br^-, BF₄^-, PF₆^-, OTf^-, TFSI^-). The model predicts maxima and minima in the entire series within 4.2% of those calculated directly from molecular dynamics simulations. This reinforces our previous conclusion that distances within "polar scattering domains" responsible for the charge alternation peak in <i>S</i>(<i>Q</i>) are quantitatively related to inter-ionic distances within polar aggregates in these RTILs. The half-length is found to increase approximately linearly as anion size increases. We argue that the half-length is a measure of polar aggregate size in these RTILs.