Cation motion frequencies

The variation of the cation-motion frequency with cation charge shows that the spectrum probes a force field in which Coulombic interactions are important. This leads to the conclusion that it also should vary significantly with the charge on the anionic site. 

Figure 6. Plot of X (defined in text) versus cation motion frequency for MPSSA (6.9) ionomer films.

Anotho exmnple of the use of FIR spectroscopy for investigation of the cation-anion site interactions and state of aggregation in ionomers was described by Mattera and Risen [161]. They obtained the FIR spectra of polyfstyrene sulfonic acid) (PSSA) ionomers containing alkali and alkaline earth ions. Strong broad bands the frequencies of which are cation depenctent have been observed and assigned to cation motion (Fig. 35, Table 5). Figure 36 shows plots of the cation motion frequency v vs. where Mc + is the mass... 

Fig. 36. Plots of the cation motion frequency Vo vs. (Mcn.) for different dehydrated PSSA (6.9 mole % sulfonate) ionomer films, Ret [161]...

Tlie effects of dehydration and anirealing on FIR spectra of PSSA ionomers were also discussed. It was shown that the cation motion frequency decreases and the absorption bands become more pronounced and better defined upon dehydration. This is interpreted as being due to an increased interaction between the sulfonate groups and the cation as solvent is removed. Also the vibrational bands become better defined after the samples of PSSA ionomers... 

The interpretation of the lattice vibrations for scheeUte type molybdates or tungstates with relatively light cations, Ca or Sr, has indicated that the lowest translational vibrations are produced by Mo—Mo or W—W motions respectively, while those at higher frequency are from cation-cation motions 98). This has not been found, however, in the case of the barium or lead compounds. The librational frequencies have been found to decrease hnearly with the ionic radius of the cation for AMO4 type compounds, where A = Ca, Sr, Ba, or Pb and M =Mo or W 98). 

Figure 3. Variation of cation-motion band frequency with cation (a) comparison of frequencies for cations of approximately the same mass but different charge (b) plot of frequency versus inverse square root of cation mass.

For each of the ionomer systems studies as well as for cations in zeolites, the cation-motion bands are easy to identify, because they vary in frequency approximately as M"1, where M is the mass of the cation. However, M-i 1 clearly is not the correct complete reduced mass for the vibration, since that would require the site to be of infinite mass. A better approximation to the proper reduced mass, p, can be obtained by considering at least the atoms immediately surrounding the cation. Typically, p is calculated from models in which the cation has either an octahedral surrounding (for the T mode) or a tetrahedral surrounding (for the T2 mode). With it and the band frequency, the force field element, (force constant), for the vibration can be calculated. 

In many cases the temperature dependence of the quadrupolar coupling constant is an indicator of dynamic processes, because the symmetry around the lithium cation is affected by motions which are fast on the NMR time scale. If the rate of these processes exceeds 1/x, the effective symmetry around the lithium cation increases and a decrease in x( Li) results. In Li MAS spectra, a broadening of the satellite transitions can be observed which eventually disappear completely if the rate of the dynamic process comes in the order of the quadrupole frequency. This behaviour was observed for the THF solvated dimer of bis(trimethylsilylamido)lithium, where the Li MAS spectrum at 353 K shows only the central transition and the sidebands caused by CSA and homonuclear Li- Li dipole coupling (Figure 27) . The simulation of the high-temperature spectrum yielded —20 ppm and 1300 Hz for these quantities, respectively. The dipole coupling agrees closely with the theoretical value of 1319 Hz calculated from the Li-Li distance of 2.4 A, which was determined by an X-ray study. 

Classical trajectory studies of the association reactions M+ + H20 and M+ + D20 with M = Li, Na, K (Hase et al. 1992 Hase and Feng 1981 Swamy and Hase 1982,1984), Li+(H20) + H20 (Swamy and Hase 1984), Li+ + (CH3)20 (Swamy and Hase 1984 Vande Linde and Hase 1988), and Cl- + CH3C1 (Vande Linde and Hase 1990a,b) are particularly relevant to cluster dynamics. In these studies, the occurrence of multiple inner turning points in the time dependence of the association radial coordinate was taken as the criterion for complex formation. A critical issue (Herbst 1982) is whether the collisions transfer enough energy from translation to internal motions to result in association. Comparison of association probabilities from various studies leads to the conclusion that softer and/or floppier ions and molecules that have low frequency vibrations typically recombine the most efficiently. Thus, it has been found that Li+ + (CH3)20 association is more likely than Li+ + H20 association, and similarly H20 association with Li(H20)+ is more likely than with the bare cation Li+. The authors found a nonmonotonic dependence of association probability on the assumed HaO bend frequency and also a dependence on the impact parameter, the rotational temperature, and the orientation of the H20 dipole during the collision. 

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