Liquid-like motion

This notion of occasional ion hops, apparently at random, forms the basis of random walk theory which is widely used to provide a semi-quantitative analysis or description of ionic conductivity (Goodenough, 1983 see Chapter 3 for a more detailed treatment of conduction). There is very little evidence in most solid electrolytes that the ions are instead able to move around without thermal activation in a true liquid-like motion. Nor is there much evidence of a free-ion state in which a particular ion can be activated to a state in which it is completely free to move, i.e. there appears to be no ionic equivalent of free or nearly free electron motion. 

Investigation of the dynamics of included molecules shows that small molecules such as ethanol (two per cage) are undergoing rapid liquid-like motion, even at low temperature in the solid state. On the... 

Fig. 33 depicts 2D 2H NMR spectra of 2-picoline-d7/tri-styrene for different temperatures.189 The spectra at high temperatures, i.e., at 227 K and 216 K, can be understood within the dynamical scenario discussed in Section 3.4.1, namely a broad distribution of correlation times characterizing the liquid-like motion. In the spectrum at 130 K, the intensity is essentially restricted to the diagonal, although the /Mike process lies right in the time window of the experiment, cf. Fig. 32d. Similar behavior was found for neat glass formers (see Section 2.1). It indicates that...

The two high-temperature spectra clearly Indicate the motion of the spin label itself. Compared to the 5-DXSA films the motion is considerably more excited. In an attempt to understand the dynamics in terms of liquid-like motion, the increase of the rotational constants should lead to a shift of the whole structure at the high- and low-field extrema toward the isotropic values. 

As the temperature is further cooled, the molecules begin to segregate into planes giving rise to a smectic A or smectic C phase. In addition to the orientational order that the nematic phase shows, the smectic A and C phases exhibit a one-dimensional translational order, and can therefore form layered structures. There is a liquid-like motion of the rods in each layer and no correlation of the molecular positions from one layer to the next. In each layer, the mass centers of the molecules are randomly distributed as... 

The fatty acids used in these experiments were carefully purified, so that it can be asserted confidently that the protons in liquid-like motion, which contribute to the narrow line, are not mainly in impurity molecules. We have, however, suggested (, 9) that the liquid-like motion in the fatty acids centers about, and with increasing temperature grows out from, impurity centers or lattice defect centers in the crystal. An attempt has been made in the work reported here to obtain evidence that this liquid-like... 

Figure 2. Percent of protons in liquid-like motion as a function of temperature for pure and impure stearic acid samples...

Although one may be able to attribute the liquid-like motion appearing in the NMR spectra to expected equilibrium amounts of liquid present in a two-component system above a eutectic temperature, this does not account for the 0-1% liquid character present at temperatures below 54° or 56°C., the eutectic temperature. We believe that this must be attributed to liquid-like motion of a few molecules centered about impurity and structural defects in the crystal lattice, or alternatively (12) to motion of molecules in defects on the surface of the crystals. 

Segmental mobility (at 37°C), that is, liquid-like motion of units and side groups... 

Compared to natively folded proteins, compact denatured states ( MGs ) experience a modest increase in the number of water molecules in the hydration layer, and a slightly smaller perturbation of hydration water dynamics. Soluble protein-water dynamical coupling has been elucidated by simultaneous examination of transitions in protein and water dynamics as a function of temperature. Hydrated proteins at room temperature exhibit liquid-like motion on the subnanosecond timescale and behave like glasses at low temperature. The dynamical (or glass) transition between the low-temperature glassy state and room-temperature liquid-like state plays an important role in energy flow processes in proteins (see Ref [86] and Chapters 7 and 11). 

With the two Li ions in as widely separated positions as the simulation box allows, the dynamics were initiated and equilibrated for the same thermodynamic conditions as in pristine PAc. By artificially constraining the diffusive motion of polymer chains, the motion of Li ions was monitored through the radial distribution function g(r) [Eq. (28)]. The gcxiC ) 9h,u( ) were found to describe a liquid-like motion for Li ions, while Qu,u( ) was almost featureless except for a very small range of dopant separations. This indicates that in agreement with the results of the static lattice calculations (Section 5.3), the motion of the ions was rapid along the chain directions, but correlated by the dominant interionic Coulomb repulsions, so that they maintained (on average) the maximum distance apart permitted by the simulation box. 

A further virtue of the Gaussian function is that it is frequentfy found to be a solution to problems involving random processes. The behavior of the flexible chain undergoing violent liquid>like motions is one such random process. 

An ideal robber consists of flexible cross-linked polymer chains undergoing violent liquid-like motions. No matter what the type of cross-linking, physical or chemical, the elastomers all have this in common the macromolecules between cross-links undergo extremely rapid molecular movement. 

The microhardness of glassy polymers decreases with increasing temperature because of thermal expansion (9). At the glass-transition temperature Tg, the onset of liquid-like motions takes place. The motions of long segments above Tg require more free volume and lead to a fast decrease of microhardness with temperature. The microhardness of several glassy polymers, measured at room temperature, has been shown to be directly proportional to its glass-transition temperature (10). 

A liquid-like motion, as for instance in alpha silver iodide... 

Three years later, quasielastic neutronscattering spectra taken on single-crystalline a-AgI were reproduced (including their anisotropy) by a model that approximated the actual liquid-like motion of the silver ions by a spatial convolution of two processes [6]. One of them was a fast diffusive motion in a local cage of about 0.1 nm radius, while the other was a random hopping via tetrahedral positions. 

With a rapidly tumbling molecule, all possible orientations of the ellipsoid are sampled, causing the orientation-dependent term to average to zero and leaving only the isotropic component of the chemical shift, crisoF which is observed in liquid-state NMR spectra. Imposing a random, liquid-like motion on a solid-state sample is, however, mechanically impractical since it would require motion around... 

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