Radial distribution function, ionic liquids

Figure 4.1-11 The EXAFS data and pseudo-radial distribution functions of Co(ll) in (a) basic and (b) acidic chloroaluminate ionic liquid. Reproduced from reference 46 with permission.

The ordering of the anions in bmimX ionic liquids has also been suggested by our recent large-angle x-ray scattering experiment on liquid bmimi [23]. Figure 13 shows a differential radial distribution function obtained for liquid bmimi at room temperature. Clear peaks in the radial distribution curve are... 

The first method comprises theories based on a statistical description of ionic liquids in a very rigorous way using radial distribution functions obtained from X-ray diffraction. These are theories based on the principle of corresponding states. 

Fig. 1 Diagrams depicting a a layer of a cubic sodium chloride crystal b a monoclinic 1,3-dimethylimidazolium chloride ionic-liquid crystal c two radial distribution functions (RDFs) in liquid l-dodecyl-3-methylimidazolium hexafluorophosphate. Anions and cations are depicted in red and blue. In the cases of b and c the blue circles represent the centroid of the imidazolium rings of the cations. The alternating sequences of red and blue circles in a and b as well as the two curves in phase opposition in c clearly indicate the existence and nature of the polar networks in ionic condensed phases...

Fig. 9 Pair-pair radial distribution functions of different solutes in different ionic liquid solutions. Solvents A l-butyl-3-methylimidazolium hexafluorophos-phate B l-butyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide C tri-hexyl(tetradecyl)phosphonium bis(trifluoromethanesulfonyl)imide. Solutes ...

When an ionic salt such as NaCl melts, the ionic lattice (see Figure 5.15) collapses, but some order is stiU retained. Evidence for this comes from X-ray diffraction patterns, from which radial distribution functions reveal that the average coordination number (with respect to cation-anion interactions) of each ion in liquid NaCl is 4, compared with 6 in the crystalline lattice. For cation-cation or anion-anion interactions, the coordination number is higher, although, as in the solid state, the intemuclear distances are larger than for cation-anion separations. The solid-to-liquid transition is accompanied by an increase in volume of il0-15%. The number of ions in the melt can be determined in a similar way to that described in Section 8.8 for H2SO4 systems in molten NaCl, v = 2. 

Baston et al. [60] studied the samples of ionic liquid after the anodization of uranium metal in [EMIMjCl using the U Lm-edge EXAFS to establish both the oxidation state and the speciation of uranium in the ionic liquid. This was part of an ongoing study to replace high-temperature melts, such as LiQ KQ [61], with ionic liquids. Although it was expected that, when anodized, the uranium would be in the +3 oxidation state, electrochemistry showed that the uranium is actually in a mixture of oxidation states. The EXAFS of the solution showed an edge jump at 17166.6 eV, indicating a mixture of uranium(IV) and uranium(VI). The EXAFS data and pseudo-radial distribution functions for the anodized uranium in [EMIMjCl are shown in Eig. 4.1-12. 

Atomic molten salts such as the alkali halides have been studied extensively using experimental methods such as neutron diffraction and extended X-ray absorption fine structure, enabling their structures in the liquid melt to be quantified. Investigations were pioneered by Enderby and co-workers, who began with molten NaCl [2], perhaps now the best known exanple of such structural research. Their work demonstrated clearly the charge ordering within the system and has become the standard tenplate for the liquid structure of purely ionic binary melts. The radial distribution functions (RDFs) obtained from the study for all pairs of ions in molten NaCl are shown in Figure 4.1. in which the prominent feature is the maximum in... 

NO3 anions are surrounded by four to five imidazolium cations. Chaumont, Engler and Wipff employed the same technique to examine the solvation of uranyl and strontium nitrates as well as uranyl chlorides in the same ionic liquids.As was observed in the previous study, the anions of the ionic liquids solvate the strontium and uranyl ions preferentially. Detailed radial distribution functions and coordination numbers were computed. This group has extended this work by making comparisons of computed solvation ordering with data from experimental spectroscopic studies. 

Klein et al. revealed a new catalytic mechanism of FA decomposition in the presence of IL 1,3-dimethylimidazolium ([mmim]) performing a Bom-Oppenheimer molecular dynamics (BO-MD)[200, 201] simulation at an elevated temperature of 3,000 K. It was shown that formate (HC02 ) dissociates into hydride (H ) and carbon dioxide (CO2), which was proposed to be the ratedetermining step. This decomposition pathway can be explained by the stabilization of the hydride in the strong electrostatic field (cation and anion shells) of the IL. Calculated radial distribution functions (RDF) shed light on the solvation of the formate in the ionic liquid 1,3-dimethylimidazolium formate [mmim] [HCOO] [202]. 

In addition to AIMD simulation of bulk-phase ionic liquids, scientists have extended the simulation to mixed systems. Kirchner et al. studied a one-to-one mixture of EmimSCN and EmimCl. The results showed that the coordination of the anion to the most acidic hydrogen atoms in the system correlates with its basicity. The addition of the chloride anion has an important non-ideal influence on the complete system and changes the types of interactions present. Bhargava and Balasubramanian implemented an AIMD simulation of BmimPF6-C02 system. The results implied that the solvation of CO2 in Bmim PFg is primarily facilitated by the anion, as observed from the radial and spatial distribution functions. CO2 molecules were aligned tangent to the PFg spheres and were most probably located inside the octahedral voids of the anion. 

Fig. 10 shows the radial particle densities, electrolyte solutions in nonpolar pores. Fig. 11 the corresponding data for electrolyte solutions in functionalized pores with immobile point charges on the cylinder surface. All ion density profiles in the nonpolar pores show a clear preference for the interior of the pore. The ions avoid the pore surface, a consequence of the tendency to form complete hydration shells. The ionic distribution is analogous to the one of electrolytes near planar nonpolar surfaces or near the liquid/gas interface (vide supra). 

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