Internal mobility , effect

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-... 

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,... 

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... 

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. 

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We may thus remark that the conformational results for aziridine acyl derivatives retain the undoubtedly positive aspect of evidencing the ensemble of effects causing the internal mobility of these molecules nevertheless more efforts seem necessary to achieve more precise definition of the conformer... 

Effect of Internal Mobility (Flexibility). It seems that the internal mobility or flexibility of the plasticizer molecule plays an important, if not the most important, role in determining plasticizer efficiency. This appears to be true irrespective of the polymer which is being plasticized, unless there are overriding physical factors involved, such as polymer crystallinity. In general, the lowering of T0 will be proportional to the temperature difference between (Tg)polymer and (Tg)plasticizer- This is illustrated in Table XIV. This table also shows that if the polymer itself is quite flexible, such as polychloroprene (Neoprene), the plasticizer efficiency is quite small, and may even result in negative AT values. 

Table IX is a collection of new data on mass effects of mobilities in salts. (See Reference 29 for earlier data.) In Table IX it can be seen that for the series of the chlorides and the nitrates of the alkali metals the internal mass effect /x+ decreases with increasing mass of the cation. This kind of behavior has been observed in many earlier examples and is qualitatively consistent with almost any model of ion transport including even the ionic gas model mentioned earlier in this article.

The external mass effects deal with mobilities with respect to the container of the salt. They are related to the internal mass effects by external transport numbers... 

It has been demonstrated by numerical simulations [9] that, with this definition, eq. 2 provides a reasonable order-of-magnitude estimate of the effectiveness factor also in the case of single-file diffusion. While in the case of ordinary diffnsion the intracrystalline mean life time may be easily correlated with the crystal size and the internal mobility [11], similar analytical expressions for single-file diffusion have not been established. The rule-of-thumb given in Ref. [10] on the basis of a few first numerical simulations turned out to be of rather limited validity in recent more refined considerations [12]. 

Side chains (even when modeled as single-interaction spheres) should have some conformational freedom that reflects their internal mobility in real proteins. Pairwise interaction potentials should be as specific as possible, and in the absence of explicit solvent, a burial potential that reflects the hydrophobic effect may be necessary... 

A corrugation at the solid surface can be achieved by using potentials for die solid phase based on the atomic and molecular constitution. This is almost compulsory for studies on systems having a large internal mobility (biomolecules are the outstanding example), but it is also used for more compact solid surfaces, such as metals. In the last quoted example the discreteness of the potential is not exploited to address corrugation effects but rather to introduce mobility (i.e., vibrations, or phonons) in the solid part of the system, in parallel to the mobility explicitly considered by the models for the liquid phase. 

If, however, we desire the ends of the chain to be at some other distance apart, e.g. a distance r, when r < r ax, this can be effected in a number of different ways indeed, because of the internal mobility of the chain, we may arrange the individual links in many different ways and still have the two terminal C atoms separated by the distance r. If we imagine a large number—say, 1000—of such chains scattered at random on the floor, and then measure the distances between the ends for every chain and draw up statistics, it is very unlikely on grounds of probability that the maximum distance will be found frequently, since it can be obtained only in one way any shorter distance can be obtained by a large number of configurations and will, consequently, be found much more frequently in actual conditions. 

The first two sections of this discussion have given an outline of the present knowledge of nuclear framework and internal motions in molecules it will now be necessary to amplify and to differentiate the information by a survey of the intra- and inter-molecular forces and to explain how conclusions may be drawn from atomic distances, valence angles, vibrations and rotations, regarding the primary valence forces which hold a molecule together. Although forces must be given prominence as causes, the path of research has been in the reverse direction. The causes have been inferred from the effects of primary valences, i.e. from the existence, form and internal mobility of the molecule. It seems reasonable, therefore, to follow the inductive way here. 

In the present chapter, which has been devoted essentially to the discussion of intra- and inter-molecular forces, reference has repeatedly been made in describing the latter, to the behavior of substances in the condensed phases, i.c. in the liquid and solid phase, in order to obtain criteria it is now time to proceed to a comprehensive discussion of the structure of solids and liquids, in which our knowledge of the magnitude, form and internal mobility of molecules and the forces uniting them will find very effective application. 

It should be pointed out that, here again, an effect is present which is of less importance in the treatment of systems composed of small molecules. In that case the interchangeability of the single independent particles of the mixture is the main point the two components can replace one another, they can occupy, to the order of magnitude, the same space and also possess the same internal mobility. The entropy gain on mixing is due merely to the fact that, in the mixture, more places are available to each of the participants. 

If, however, one part of the mixture consists of very large molecules with high internal mobility and the other of normal molecules, which may reasonably be regarded as rigid spheres, the conditions of simple replace-ability no longer hold and we obtain the above mentioned additional entropy effect. 

In principle, this solution means an application of internal molecular statistics to the problem in the presence of considerable internal mobility, the effective length of the thread-like molecules need not be identified with their maximum length rather the effective length is actually proportional to the square root of the total length. 

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