Cooperative relaxation

Cooperative Relaxation Properties in Glass-Forming Liquids. 

G. Adam and J. H. Gibbs, On the temperature dependence of cooperative relaxation properties in glass-forming liquids. J. Chem. Phys. 43, 139-146 (1965). 

When polymer chains become sufficiently concentrated, entanglement interactions lead to cooperative relaxation phenomena that can dominate the dynamical response. The relaxation times dramatically slow down with concentration and nonlinear flow phenomena... 

Another type of kinetics pattern currently under discussion is related to the so-called Mode-Coupling Theory (MCT) developed by Gotze and Sjogren [74], In the MCT the cooperative relaxation process in supercooled liquids and amorphous solids is considered to be a critical phenomenon. The model predicts a dependence of relaxation time on temperature for such substances in the form... 

Figure 13 plots the relaxation times ratio x, / x j and the amplitude A corresponding to the macroscopic relaxation time of the decay function determined by (25). Near the percolation threshold, x, /xi exhibits a maximum and exhibits the well-known critical slowing down effect [152], The description of the mechanism of the cooperative relaxation in the percolation region will be presented in Section V.B. 

A detailed description of the relaxation mechanism associated with an excitation transfer based on a recursive (regular) fractal model was introduced earlier [47], where it was applied for the cooperative relaxation of ionic microemulsions at percolation. 

In this context, the value To should be associated with the smallest cooperative relaxation time reflecting the EW dynamics obeying the same VFT temperature law as the main relaxation times x and xmax (see Fig. 26). At the same time, the ratio x/xo is strongly dependent on concentration (Fig. 38). The increase of the ratio x/xo with increase of water content indicates that the EW of glycerol is eroded by water molecules much faster than the main relaxation process. In order to clarify such a mechanism, let us assume that the EW is the result of some fast short-range cooperative dynamics that can be associated with... 

Thus, one may summarize the physical picture of the relaxation dynamics in KTN crystal-doped with Cu+ ions in the following way In the paraelectric phase, as the ferroelectric phase transition is approached, the Nb5+ ions form dipolar clusters around the randomly distributed Cu+ impurity ions. The interaction between these clusters gives rise to a cooperative behavior according to the AG theory of glass-forming liquids. At the ferroelectric phase transition the cooperative relaxation of the Cu+ ions is effectively frozen. ... 

It is well known [54,270] that the macroscopic dielectric relaxation time of bulk water (8.27 ps at 25°C) is about 10 times greater than the microscopic relaxation time of a single water molecule, which is about one hydrogen bond lifetime [206,272-274] (about 0.7 ps). This fact follows from the associative structure of bulk water where the macroscopic relaxation time reflects the cooperative relaxation process in a cluster of water molecules. 

Of the microphase-structure dependent physical properties of ionomers, perhaps the most widely studied are glass transition temperatures, (Tg), and dynamic mechanical response. The contribution of the Coulombic forces acting at the ionic sites to the cohesive forces of a number of ionomeric materials has been treated by Eisenberg and coworkers (7). In cases in which the interionic cohesive force must be overcome in order for the cooperative relaxation to occur at Tg, this temperature varies with the magnitude of the force. For materials in which other relaxations are forced to occur at Tg, the correlation is less direct. 

Kubat, M. J., Rflia, R, Rychwalski, R. W., and Kubat, J., Stochastic approach to cooperative relaxation processes in solids, Europhys. Lett., 50, 507 (2000). 

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