Diffusion anomalies

The conditions on the phase diagram for which this anomalous behavior occurs has been termed water s structurally anomalous region. Inspection of the order map (Figure 4) reveals a dome of structural anomalies within the temperature-density plane, bounded by loci of maximum tetrahedral order (at low densities) and minimum translational order (at high densities) as shown in Figure 5. Also marked on Figure 5 are regions of diffusive anomalies,... 

The region of "Case II sorption (relaxation-controlled transport) is separated from the Fickian diffusion region by a region where both relaxation and diffusion mechanisms are operative, giving rise to diffusion anomalies time-dependent or anomalous diffusion. 

Single-Molecule Diffusion Anomalies (and Membrane Structures)... 

A survey carried out over a polymetallic ore deposit in Kyrgyzstan is described by Glebovskaya and Glebovskii (1960). The traverse shows an increase over the background CO2 concentration of 1-1.5% to a diffuse anomaly of 2-3.5% over the suboutcrop of the ore zone. There is an intense O2 anomaly, with the O2 concentration falling sharply from a consistent background of 20-20.5% O2 immediately over the mineralisation (Fig. 14-8). 

Structure-permeability relationships to clarify how diffusion anomalies are related to morphology and ionic hydration... 

Diffusion anomalies are intimately associated with the polymer s glassy/rubbery state transition. Hence, anomalous transport models have been proposed to understand penetration into polymers. 

STUDY OF NON-FICKIAN DIFFUSION ANOMALIES THROUGH TIME LAGS. I. SOME TIME-DEPENDENT ANOMALIES. 

S. Bandyopadhyay and S. Yashonath,/. Phys. Chem., 99,4286 (1995). Diffusion Anomaly in Silicalite and WI-5 from Molecular Dynamics Simulations. 

As already mentioned, three types of anomalies that are most discussed in literature with respect to the core softened fluids are diffusion anomaly, density anomaly, and structural anomaly. Here we briefly discuss these anomalies. 

If we consider a simple liquid (e.g., Lennard-Jones liquid) and trace the diffusion along an isotherm, we find that the diffusion decreases under densification. This observation is intuitively clear If density increases, the free volume decreases and the particles have less freedom to move. However, some substances have a region in density temperature plane where diffusion grows under densification. This is called anomalous diffusion region that reflects the contradiction of this behavior with the free volume picture already described. This means that diffusion anomaly involves more complex mechanisms, which will be discussed in the following. 

It is important to note that the range of densities of structural anomalies is wider than those of diffusion anomaly that is consistent with the literature data for core-softened systems. 

The breakdown of the Rosenfeld relation along isotherms can be seen from the following speculation. The regions of different anomalies do not coincide with each other. In particular, in the case of core-softened, fluids, the diffusion anomaly region is located inside the structural anomaly one. It means that there are some regions where the diffusion is still normal, while the excess entropy is already anomalous. But this kind of behavior cannot be consistent with the Rosenfeld scaling law. 

The line is defined by the set of pressures, P T), at which the liquid s diffusion coefficient reaches a maximum upon isothermal compression. The exis tence of the line in the P T plane implies that the liquid presents diffusion anomaly since at P < P (T), the diffusion coefficient increases upon isothermal compression. This is opposite to what is observed in normal liquids where D de creases upon isothermal compression (as molecules are packed closer together, the diffusivity usually decreases). 

It is important to note that although the presence of a LLCP implies that the liquid must have anomalous properties, the presence of anomalous properties in a liquid does not imply the existence of a LLCP in its phase diagram [47]. For example, systems of particles interacting via pure repulsive pair potentials can show density and diffusion anomaly, and other anomalies such as the increase of isothermal compressibility and isobaric heat capacity upon cooling (see, e.g., Ref. [52-57]). However, an LLPT has not been reported for these systems. 

Water, both in the liquid and solid (ice) phase, is very peculiar, with properties that differ from most substances. A growing list of currently 69 anomalous properties has been compiled by Chaplin [1]. For example, water is the only substance that can be found in nature in the solid, liquid, and gas phases [2]. In the solid phase, it can exist in a wide variety of crystalline phases. Water is also well known for its density anomalies (such as the liquid s density maximum at 277.13K and the solid s density minimum at 70K [3]), diffusion anomalies... 

Liquid polymorphism in one-component fluids is an example of so-called anomalous phase behavior. This term is used to emphasized the difference with respect to the normal behavior characterizing prototypical (i.e., argon like) simple liquids. Anomalous behavior includes, in addition to polymorphism in the liquid and solid phases, reentrant melting, that is, melting by compression at constant temperature, and a number of other thermodynamic, dynamic, and structural anomalies, as, for example, the density anomaly (a decrease in density upon cooling), the diffusion anomaly (an increase of diffusivity upon pressurizing), and the structural anomaly (a decrease of structural order for increasing pressure). 

Figures. Phase diagram ofthe Yoshida-Kamakura potential for a = 3.3. PandT areinreduced units. Full dots are two-phase coexistence points. Open dots are points of density maximum in the fluid phase. Diamonds and triangles denote points of —S2 maxima and D minima, respectively (D being the self-diffusion coefficient), giving the left boundary of the regions of structural and diffusion anomaly (the right boundaries, which are defined by —52 minima and D maxima, are out of the T range shown). Data are from Ref. [88].

Finally, besides polyamorphism and liquid polymorphism, this model also exhibits density and diffusion anomalies [40,41]. 

Among these models, the core-softened shoulder potential (Cho et al., 1996 de Oliveira et al., 2006a b Netz, Raymundi, Camera Barbosa, 2004) reproduces qualitatively water s structural, density and diffusion anomalies. This potential is built summing a Lennard-Jones potential and a displaced Gaussian term, as follows ... 

Fig. 3. Locating the TMD by the minimum of pressure along isochors (a) and the region of diffusion anomaly (b) for rigid dumbbells with interatomic separation A/rr = 0.50.

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. 

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. 

The obtained diffusivity anomaly for the present NS2 liquid actually also relates to the well-known transport anomalies reported for densified tetrahedral liquids [70, 127] as exemplified by the well-known example of densified water [71]. The correlation becomes obvious when we represent the oxygen diffusivity Do of NS2 (Eig. 11.21b) as a function of the system density [126], and compare the trend with corresponding results for densified silica (2500K [127]) and water (220 K [71]). 

Fig. 11.21 a Computed viscosity r)(P) as a function of pressure for T = 2000 K in the NS2 liquid. Right axis Oxygen diffusion constant red symbols) Do(P) in NS2 at 2000 K. The grey area represents an approximate delimitation of the adaptative phase, based on the window defined by the trend in q(P, 2000 K) (see Fig. 11.20a). b Oxygen diffusion constant (same as panel a) in NS2 at 2000 K but now plotted as a function of the system density, compared to diffusivity anomalies in silica blue symbols, 2500K [127]) and water black symbols, 220 K [71]... 

Finally, such structural anomalies are obviously located in pressure/composition windows where the network structure adapts to avoid the occurence of stress. This in turn leads to transport anomalies, and the well-known water-like diffusivity anomaly [71] of densified tetrahedral liquids which have been previously reported. Network adaptation or self-organization is at the core of the identified isostatic intermediate phase [28], and the present framework relating Molecular Dynamics and topological constraint counting, allows studying such phenomena in detail. 

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