Internal mobility

As a consequence of restricted internal mobility in molecules in the crystalline state, nuclei in different conformation environments, but identical in other respects, can produce different signals in 13C cross polarization, magic angle spinning (CPMAS) solid-state NMR. This analysis is not necessarily limited to crystalline regions, since signals of different conformations are resolved if the exchange is slow with respect to the time scale of the NMR experiment. 

With concern to the high internal mobility of the molecules in the high temperature solid state phase, some parallelism to n-alkanes can be stated. In the pseudohexagonal (rotator) phase the latter are also characterized by fast molecular motions. For discrimination and according to Pfitzer 14) and Dale 13) in the following the term pseudorotator phase is used for the mobil crystalline state of cyclic molecules. 

Klemm has proposed defining internal mobility by reference to one defined ion of the system, such as the anion. In the case of pure salt, the internal transport number of the cation is then unity. In the case of a mixture, the internal mobility Uj is related to the internal transport number... 

The patterns of isotherms of the internal mobilities in binary systems consisting of two monovalent cations and a common anion could provide useful insight into the mechanism of electric conductance. The patterns may be classified into two types. In Fig. 2 the isotherms are schematically shown versus the mole fraction of the larger cation, Xj. 

Figure 2. Isotherm patterns of internal mobilities vs.mole fraction of M2X in (Mj, M2)X, where Mj and Mj are the smaller and larger cations, respectively, and X is a common anion.

Type II refers to the case in which the isotherms for both cations increase with increasing concentration of the respective cations. Such isotherms have been found for (Li, K)F,j2 (Li, K)(S04)i/2, (Na, K)OH, (Ag, Cs)Br, - (Ag, Na)I, - (Ag, K)I, - " and (Ag, CS)I. In charge asymmetric systems such as (K, Ca 2)CI, such isotherms also usually appear. A common feature of these type II systems is the particularly strong interaction of one cation with the common anion compared with that of the second cation with the anion. The strongly interacting cation will retard the internal mobility of the second cation. This is called the tranquilization effect, and will be explained in Section III.5( 70-... 

Okada et al. found that the internal mobilities of LT in molten alkali nitrates are well expressed as a function of molar volume, independent of the kind of the second cation. This finding leads to a general empirical equation ... 

Figure 6. Isotherms of the internal mobilities in 10 binary alkali nitrates. C Chemla erossing point marked only for the unelear eases. (Reprinted from M. Chemla and I. Okada, lonie Mobilities of Monovalent Cations in Molten Salt Mixtures, Electrochim. Acta 35 1761-1776, Fig. 5. Copyright 1990 with permission from Elsevier Seienee.)...

The internal mobilities of alkali halides have not yet been investigated systematically as with the alkali nitrates. However, it seems that an equation similar to Eq. (12) holds. To indicate this explicitly, the reciprocal values of the internal mobilities at 973 K in (Li, CS)CP are shown in Fig. 8. Figure 8 indicates that m" is a linear function of Vm, as Eq. (12) suggests however, the parameters A, Vo, and E are different at two different Vm... 

In such systems as (M, Mj (i/2))X (M, monovalent cation Mj, divalent cation X, common anion), the much stronger interaction of M2 with X leads to restricted internal mobility of Mi. This is called the tranquilization effect by M2 on the internal mobility of Mi. This effect is clear when Mj is a divalent or trivalent cation. However, it also occurs in binary alkali systems such as (Na, K)OH. The isotherms belong to type II (Fig. 2) % decreases with increasing concentration of Na. Since the ionic radius of OH-is as small as F", the Coulombic attraction of Na-OH is considerably stronger than that of K-OH. 

The effect of highly polarizable cations on transport properties has scarcely been studied. Since the nitrate melts of Ag and TL are stable and have high polarizabilities, as shown in Table 5, their internal mobilities in binary mixtures containing one or both of these cations have been measured frequently. The isotherms are shown for and m,., in Figs. 10 and 11,... 

Figure 10. Isotherms of internal mobilities in various binary nitrates containing Ag as one cation. (Reprinted from I. Okada and P.-H. Chou, Anomalous Behavior of Internal Mobilities for Ag(I) and T1(I) Ions in Molten Nitrates, J. Electrochem. Soc. 144 (4) 1333, 1997, Fig.2. Reproduced by permission of the Electrochemical Society, Inc.)...

When internal mobilities of Ag are plotted against the molar volume of the mixtures, Eq. (12) seems to be applicable to AgL The internal mobilities of TF are plotted against molar volume in Fig. 12 as a compari-... 

The Effeet of Highly Polarizable Cations on the Internal Mobility of the Seeond Cation in (Mi, M2)N03... 

In the alkali and alkaline earth nitrate mixtures, the internal mobilities have been systematically investigated, the isotherms being shown in Fig. 15. The internal mobilities of the alkali ions as a function of the molar volume are much smaller than expressed by an equation such as Eq. (12). This means that the internal mobilities of the alkali ions, Mju, are modified by the tranquilization effect caused by the divalent cations. The M ik is assumed to be expressed by... 

Figure 15. Isotherms of internal mobilities in alkali-alkaline earth nitrate mixtures. The mobility of the alkali ion is always greater than that of the alkaline earth ion. (Reprinted from T. Koura, H. Matsuura, and I. Okada, "A Dynamic Dissociation Model for Internal Mobilities in Molten Alkali and Alkaline Earth Nitrate Mixtures,"/ Mol. Liq. 73-75 195, Fig. 4, Copyright 1997 with permission from Elsevier Science.)...

Danek and his group have independently proposed a quite similar model, which they call the dissociation modeV - For this model Olteanu and Pavel have presented a versatile numerical method and its computing program. However, they calculated only the electrical conductivity or the molar conductivity of the mixtures, and the deviation of the internal mobilities of the constituting cations from the experimental data is consequently vague. 

Extending this to a system consisting of two kinds of cations (1 and 2) and one kind of anion, Klemm has derived equations for calculating internal cation mobihties. The internal mobility Map of an a ion with reference to a P ion is directly related to the velocity change in the relevant two ions caused by the perturbation field ... 

Internal mobilities were calculated for molten LiCl and (Li, Cs)Cl (Xcs = 0.90). The values are given in Table 8, which shows that the calculated mli is much smaller than Ucs, that is, the Chemla effect can be reproduced by MD simulation. 

Calculated Internal Mobilities of Pnre LiCl and (Li, Cs)Cl (a cs = 0.90) Compared with Experimental ... 

For (Li, Cs)Cl, the internal mobilities have been calculated from Eqs. (27) and (28), and are given in Table 8. The SEVs were calculated from the same MD runs and are plotted against the calculated internal mobilities in Fig. 17 with excellent correlation between these calculated quantities. The good correlation of the SEV with the calculated and experimental internal mobilities suggests that relatively short-range cation-anion interaction plays a role in internal mobilities and the separating motion of pairs, that is dissociation, is related to the internal mobilities. In other words, the result of the SEV supports the dynamic dissociation model. 

Figure 17. Self-exchange velocities vs. internal mobilities calculated from the same MD runs for pure LiCl and (Li, Cs)Cl mixture(xcs, = 0.90). experimental for u. (Reprinted from Ref 47 with permission of Trans Tech Publications.)...

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