Dynamic anomalies

Experimentally observed thresholds with composition in glassy chalcogenides are actually correlated with diffusivity anomalies in the liquid state. We calculate the mean square displacement following (11.6), and then apply the Einstein relationship to obtain diffusion constants in the long-time limit (See Fig. 11.6). Here, we follow the behaviour of the diffusion constant Dj with composition along an isotherm for different systems. 

In Ge-Se, we find that the diffusion actually maximizes for the composition having 20% Ge (Fig. 11.17), in a manner similar to that obtained in As-Se for which a maximum of Dse=0.72 x 10 cm /s occurs at 35 % As [51]. Furthermore, when represented as a function of inverse temperature, both Das and Dse exhibit an 

Arrhenius behavior, with an activation energy that is represented in Fig. 11.17 as a function of composition. Both quantities exhibit a minimum at 30-35% As (0.29 and 0.34 eV for Se and As, respectively), that is found in the region where the diffusivity anomaly is obtained. 

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Figure 5 Relationship among loci of structural, dynamic, and thermodynamic anomalies in SPC/E water. The structurally anomalous region is bounded by the loci of q maxima (upward-pointing triangles) and t minima (downward-pointing triangles). Inside of this region, water becomes more disordered when compressed. The loci of diffusivity minima (circles) and maxima (diamonds) define the region of dynamic anomalies, where self-diffusivity increases with density. Inside of the thermodynamically anomalous region (squares), the density increases when water is heated at constant pressure. Reprinted with permission from Ref. 29.

It helps if we eategorize the anomalies discussed above into three different types (1) thermodynamie anomalies (for example, in density, Cp, Kt and Up), (2) dynamic anomalies (relaxation time or diffusion, dynamic crossover), and (3) stmctural anomalies (in translational and orientational order). 

This interesting figure shows that the region of thermodynamic anomalies is bounded inside the region of dynamic anomalies which in turn is bounded inside the region of structural anomalies. Thus, as a preliminary guess, it can be inferred that thermodynamic and dynamic anomahes can be understood in terms of stmctural anomalies [5]. 

The range of dynamic anomalies shown by liquid water at room temperature and pressure is truly amazing. It is not just the extended hydrogen-bond network that is responsible for this but also the small lifetime of an HB that allows large-scale fluctuations in liquid water (as discussed in Chapter 1). 

In a series of recent experimental studies, it has been found that for water-methanol, water-ethanol, and water-TBA binary mixtures, striking dynamic anomalies occur at a low solute concentration range. The anomalies can be captured by spectroscopic techniques. It has been observed that the rotational anisotropy in such systems has a fast component which becomes faster and a slow component which becomes slower with increasing solute concentration. Temperature dependence of the concentration fluctuations was observed for water-TBA... 

S. Roy, S. Banegee, N. Biyani, B. Jana, and B. Bagchi, Theoretical and computational analysis of static and dynamic anomalies in water-DMSO binary mixture at low DMSO concentrations. J. Phys. Chem. B, 115 (2011), 685-692 S. Banegee, S. Roy, and B. Bagchi, Enhanced pair hydrophobicity in the water-dimediylsulfoxide (DMSO) binary mixture at low DMSO concentrations. J. Phys. Chem. B, 114 (2010), 12875-12882. 

The phases coherence which accompanies any wave scattering, doubled by the correlation of the dynamic localization, leads in corpuscular understanding of the photonic asymmetric transfer. Therefore, the dynamic asymmetry corresponds to the dynamic anomaly in the absorption language, having its bases in the dynamic localization. 

The above discussion is consistent with the possible existence of two well-defined classes of liquids simple and water like. The formers interact via spherically symmetric nonsoftened potentials and do not exhibit thermodynamic or dynamic anomalies. One can calculate translational and orientational order parameters t and ( ), and project equilibrium state points onto the (f, q) plane thereby generating what is termed the Errington Debenedetti (ED) order map [24]. In water like liquids, interactions are orientation dependent these liquids exhibit dynamic and thermodynamic anomalies, and their ED order map is in general two dimensional but becomes linear (or quasi linear) when the liquid exhibits structural, dynamic, or thermodynamic anomalies. 

Hemmer and Stell [55] showed that in fluids interacting via pairwise-additive, spherically symmetric potentials consisting of a hard core plus an attractive tail, softening of the repulsive core can produce additional phase transitions. This pioneering study elicited a considerable body of work on so called core-softened potentials that can generate water-like anomalies [58,63 67]. This important finding implies that strong orientational interactions, such as those that exist in water and silica, are not a necessary condition for a liquid to have thermodynamic and dynamic anomalies. 

COMPUTER SIMULATIONS OF LIQUID SILICA WATER-LIKE THERMODYNAMIC AND DYNAMIC ANOMALIES, AND THE EVIDENCE FOR POLYAMORPHISM... 

Thus, the distinct evidence for the dynamic anomalies of both opposite kinds have been obtained by many authors however, the experimental results depended to some extent on a method used and details of the experiments [52],... 

Fig. 22 Activation energy of segmental motion within glass transition vs temperature plots, illustrating schematically the possible dynamic anomalies in different complex polymer systems (see text) [128,129]. The transition widths are indicated above...

Kumar, R, Buldyrev, S. V., Sciortino, E, Zaccarelli, E. Stanley, H. E. (2005). Static and dynamic anomalies in a repulsive spherical ramp liquid Theory and simulation, Phys. Rev. E 71-. 021501. 

Netz, P. A., Buldyrev, S., Barbosa, M. C. Stanley, H. E. (2006). Thermodynamic and dynamic anomalies for dumbbell molecules interacting with a repulsive ramplike potential. Physical Review E 73 061504. 

Netz, P. A., Raymundi, J. R, Camera, A. S. Barbosa, M. C. (2004). Dynamic anomalies of fluids with isotropic doubled-ranged potential, Physica A 342 48. 

C. Rocchi, A. R. Bizzarri, S. Cannistraro, Water dynamical anomalies evidences by molecular djmamics simulations at the solvent-protein interface, Phys. Rev. E 57 (1998) 3315-3325. 

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