Cooperative motion

On the other hand, the formation of the high pressure phase is preceded by the passage of the first plastic wave. Its shock front is a surface on which point, linear and two-dimensional defects, which become crystallization centers at super-critical pressures, are produced in abundance. Apparently, the phase transitions in shock waves are always similar in type to martensite transitions. The rapid transition of one type of lattice into another is facilitated by nondilTusion martensite rearrangements they are based on the cooperative motion of many atoms to small distances. ... 

While thin polymer films may be very smooth and homogeneous, the chain conformation may be largely distorted due to the influence of the interfaces. Since the size of the polymer molecules is comparable to the film thickness those effects may play a significant role with ultra-thin polymer films. Several recent theoretical treatments are available [136-144,127,128] based on Monte Carlo [137-141,127, 128], molecular dynamics [142], variable density [143], cooperative motion [144], and bond fluctuation [136] model calculations. The distortion of the chain conformation near the interface, the segment orientation distribution, end distribution etc. are calculated as a function of film thickness and distance from the surface. In the limit of two-dimensional systems chains segregate and specific power laws are predicted [136, 137]. In 2D-blends of polymers a particular microdomain morphology may be expected [139]. Experiments on polymers in this area are presently, however, not available on a molecular level. Indications of order on an... 

Figure 7. Experimental data (symbols) for TNB s viscosity [78] superimposed on the results of the fitting procedure (line) from Lubchenko and Wolynes [47] are shown. Ta is diown by a tickmark. (TNB = trinaphthyl benzene). The temperature Ter signifies a crossover from activated to collisional viscosity, dominant at the lower and higher temperatures, respectively (see text). The temperature is varied between the boiling point and the glass transition. The right-hand side panel depicts the temperature dependence of the length scales of cooperative motions in the liquid. The thick solid and dashed lines are the critical radius and the cooperativity length respectively. Taken from Ref. [47] with permission.

Point defects in solids make it possible for ions to move through the structure. Ionic conductivity represents ion transport under the influence of an external electric field. The movement of ions through a lattice can be explained by two possible mechanisms. Figure 25.3 shows their schematic representation. The first, called the vacancy mechanism, represents an ion that hops or jumps from its normal position on the lattice to a neighboring equivalent but vacant site or the movement of a vacancy in the opposite direction. The second one is an interstitial mechanism where an interstitial ion jumps or hops to an adjacent equivalent site. These simple pictures of movement in an ionic lattice, known as the hopping model, ignore more complicated cooperative motions. 

In the glassy amorphous state polymers possess insufficient free volume to permit the cooperative motion of chain segments. Thermal motion is limited to classical modes of vibration involving an atom and its nearest neighbors. In this state, the polymer behaves in a glass-like fashion. When we flex or stretch glassy amorphous polymers beyond a few percent strain they crack or break in a britde fashion. 

Lett., 80, 2338 (1998). Stringlike Cooperative Motion in a Supercooled Liquid. 

Other moves are specific for dilute solutions (or single chain simulations) and very congested systems (as melts). Some complex rules involving different chains have been developed for the equilibrium study of melts of linear chains, such as the cooperative motion algorithm [105] where beads are moved cooper-... 

Pakula et al. [155] have used the cooperative motion algorithm to study melts of stars with up to 64 units. They studied the internal bead profiles and the correlations of the star centers of mass. They observed an ordering of the systems of stars with high functionalities. 

Gauger and Pakula [191] performed an MC simulation of comb polymers on the fee lattice in dilute and dense media, using the cooperative motion algorithm. It is shown that, unlike linear chains, the EV screening does not appear in the global mean size dependence on N. However, this screening is complete for the branches in the melt, which exhibit ideal behavior. 

Pakula and Zhulina [213] have simulated dry brushes at melt densities in contact with a repulsive wall. They used the cooperative motion algorithm. Their re-... 

The molecular mobility of water in Nafion was investigated using NMR spectroscopy, by Starkweather and Chang,Boyle et al., and Bunce et al. The overall conclusion of these studies was that water possessed less mobility than that of liquid water and that there were cooperative motions among the molecules and strong interactions with the ion exchange groups. 

When this model is applied to the interpretation of spin relaxation of polymers in solution the extent of cooperation motion can he measured hy a parameter R = (W /Wb) / which is found to take on values from 1 to 50. If a bond is the smallest moving unit, then R, called the "range", corresponds approximately to the number of bonds Involved in cooperative or coupled motion ( ). Both Wg and are strongly temperature dependent and vary non-monoton-Ically with temperature which appears to complicate this simple identification of R. 

Figure 4.2 is a plot of log(cr) versus log(viscosity) constructed from dielectric data of Figure 4.1 and measurements on a dynamic rheometer. The figure shows that at a viscosity less than 1 Pas (10P), a is proportioned to l/tj because the slope of log(n) versus log( j) is approximately — 1. The gel point of the polymerization reaction occurs at 90 min based on the crossover of G and G" measured at 40rad/s. This is very close to the time at which rj achieves 100 Pas, which is also often associated with gel. The region of gel marks the onset of a much more rapid change in viscosity than with a. This is undoubtedly due to the fact that as gel occurs the viscoelastic properties of the resin involve the cooperative motion of many chains, whereas the translational diffusion of the ions continues to involve motions over much smaller molecular dimensions. 

Does the active site have to be a rigidly maintained structure Isn t it possible that the groups comprising the active site execute correlated, cooperative motion of some kind, perhaps a nonlinear oscillation that is sustained by energy pumping ... 

Dielectric relaxation study is a powerful technique for obtaining molecular dipolar relaxation as a function of temperature and frequency. By studying the relaxation spectra, the intermolecular cooperative motion and hindered dipolar rotation can be deduced. Due to the presence of an electric field, the composites undergo ionic, interfacial, and dipole polarization, and this polarization mechanism largely depends on the time scales and length scales. As a result, this technique allowed us to shed light on the dynamics of the macromolecular chains of the rubber matrix. The temperature as well as the frequency window can also be varied over a wide... 

The terminal spectrum is furnished by cooperative motions which extend beyond slow points on chain in the equivalent system. The modulus associated with the terminal relaxations is vEkT, which is smaller by a factor of two than the value from a shifted Rouse spectrum. It is consistent with a front factor g = j given by some recent theories of rubber elasticity (Part 7). The terminal spectrum for E 1 has the Rouse spacings for all practical purposes, shifted along the time axis by an undetermined multiplying factor (essentially the slow point friction coefficient). Thus, the model does not predict the terminal spectrum narrowing which is observed experimentally. 

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