Water dielectric relaxation time

The state of an adsorbate is often described as mobile or localized, usually in connection with adsorption models and analyses of adsorption entropies (see Section XVII-3C). A more direct criterion is, in analogy to that of the fluidity of a bulk phase, the degree of mobility as reflected by the surface diffusion coefficient. This may be estimated from the dielectric relaxation time Resing [115] gives values of the diffusion coefficient for adsorbed water ranging from near bulk liquids values (lO cm /sec) to as low as 10 cm /sec. 

It takes 10-u s, the normal dielectric relaxation time for water, to form the hydrated electron, and -10-9 s for the electron to disappear by reacting with the water molecule (the former is an overestimate, the latter an underestimate). 

Notwithstanding Platzman s theory, most calculations of radiation-chemical yields in water and aqueous solutions were performed using the free-radical model (see Magee, 1953 Samuel and Magee, 1953 Ganguly and Magee, 1956). The hypothesis was that the recapture time of the electron would be shorter than the dielectric relaxation time. Therefore, recombination would outcompete solvation. 

Migus et al. s (1987) delineation of the formation of a primary species absorbing in the IR, which develops in -110 fs and which transforms to the well-known spectrum of the hydrated electron in -240 fs, which is consistent with the longitudinal dielectric relaxation time of water (Mozumder, 1969a, b). 

Figure 5. Median jump frequencies (Sr ) 1 for water adsorbed on NaX to saturation, for water on charcoal at saturation, and that expected for bulk water (from NMR relaxation times) dashed curve marked diff diffusion coefficients by magnetic field gradient technique normalized to (Sr) 1 by choice of jump distance of 2.7 A + dielectric relaxation times of Jansen...

Dielectric relaxation measurements for the adsorbed water have been reported by Jansen (44) the dielectric relaxation time is essentially 3r where r is the rotational jump time of the water molecule. From Figure 5 it can be seen that the dielectric and NMR mobility estimates agree rather well. All is not quite in order, however, for Jensen estimates from relaxation strength that he sees only one-third of the water molecules. 

The best evidence so far for the glassy nature of HDA was provided (1) by measurements of the dielectric relaxation time under pressure at 140 K [206, 251], (2) by the direct vitrification of a pressurized liquid water emulsion to HDA [252], and (3) by a high-pressure study of the glass >liquid transition using differential thermal analysis (DTA) [253], We note here that these studies probe structurally relaxed HDA (eHDA) rather than unrelaxed HDA. It is possible that structurally relaxed HDA behaves glass like, whereas structurally uHDA shows a distinct behavior. Thus, more studies are needed in the future, which directly compare structurally relaxed and unrelaxed HDA. 

In order to understand the influence of alcohol on the zeolitization process, it is useful to summarize the structural aspects of alcohol-water mixtures. Considerable work has been done in this area. It is well-recognized that at low alcohol concentrations the viscosity, reciprocal self-diffusion coefficient, the dielectric relaxation time and NMR relaxation times of the water molecules are all greater than that of pure water.(21-241 These observations indicate that addition of alcohol to water at low levels leads to an increased structure of water.(25) This concept is also supported by X-ray diffraction studies(26) and is commonly referred to as hydrophobic hydration.(27) On a molecular level, this effect... 

The hydrogen bonds in liquid water have an average lifetime of less than 10"10 second as measured by dielectric relaxation times (4). But the hydrogen bonds between water and a polymer could exist for longer than 10"7 seconds. Such a structure would appear permanent at the frequencies used in the ultrasonic impedometer (107 cycles/sec. range), and should demonstrate a measurable shear stiffness at these frequencies. 

Figure 48. Temperature dependence of dielectric relaxation time for water confined in sample C. The data were measured under different conditions and contain a different amount of water Unfilled circles correspond to the data presented early in Fig. 46 filled circles represent the experiment with reduced water content [78]. Full line is the best fit according to (133) In To = —17.8 0.5, ), = 39 1 kJmol 1, 7) = 124 7K, D — 10 2, C = 9 x 105 3 x 10s. The dashed line was simulated from (133) for the same In To, ), 7), and D, but with C divided by a factor 1.8 (explanation in the text). (Reproduced with permission from Ref. 78. Copyright 2004, The American Physical Society.)...

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. 

Much information can be obtained from the study of dielectric relaxation times in liquids, for example, the extent to which the waters are netted together (Table 4.22). 

Fig. 26. Temperature dependence of various properties of myoglobin crystals , frequency of the O-D band maximum (IR) —, dielectric relaxation time of water (schematic) ---—, Lamb-Mossbauer factor,/o, after subtracting the harmonic mode (sche-...

Among collective dynamical properties, some turn out more sensitive than others to potential models. It can be noticed from Table 4 that, e.g., dielectric relaxation times Tq and thermal conductivity, A, coefficient agree satisfactorily with experiments both at 300 and 255 K, while shear viscosity, r], is largely underestimated, especially in the supercooled region. Longitudinal viscosity, is also underestimated, but to a lesser extent. We recall that the defect of a too fast dynamics, compared with supercooled real water, is shared by the TIP4P model [164]. 

D. Bertolini, M. Cassettari and G. Salvetti, The dielectric relaxation time of supercooled water, J. Chem. Phys., 76 (1982) 3285-3290. 

Figure 1 shows the dielectric relaxation properties of the Tween microemulsions plotted on the complex permittivity plane (from Foster et al ( 1). The mean relaxation frequency (corresponding to the peak of each semicircle) decreases gradually from 20 GHz for pure water at 25°C to ca. 2 GHz for a concentrated microemulsion containing 20% water. Since the permittivity of the suspended oil/ emulsifier is 6 or less at frequencies above 1 GHz, this relaxation principally arises from the dipolar relaxation of the water in the system. Therefore, the data shown in Figure 1 clearly show that the dielectric relaxation times of the water in the microemulsions are slower on the average than those of the pure liquid. The depressed semicircles indicate a distribution of relaxation times (9), and were analyzed assuming the presence of two water components (free and hydration) in our previous studies. 

This is, however, a macroscopic explanation of changes that occur on a molecular level, and is rather superficial. There is clearly a distribution of dielectric relaxation times in the microemulsion. The timescale of the dielectric relaxation measurement (tens of picoseconds) is too short for the phenomenon of fast exchange. It would appear, therefore, that the motional restriction of the water must vary throughout the microemulsion. 

Ice grown from the vapor phase is expected to have many lattice imperfections such as vacancies and inclusion of gas. This hypothesis can explain previous reports on snow, hoarfrost, and polar ice samples, which were considered to have a low impurity concentration, yet exhibited dielectric relaxation times shorter than those of samples that had been melted and refrozen and samples of ordinary ice. There is a possibility that these imperfections introduce differences in dielectric relaxation process between samples of ice grown from vapor-phase and liquid-phase water. Further study of other evidence is needed to elucidate such differences, for example, via a rigorous investigation of good-quality bulk hoarfrost samples. 

Figure 12. Temperature dependence of the dielectric relaxation time (open symbols) and Tjq (corresponding closed symbols) of mixtures of 35 wt.% of water with various ethylene glycol oligomers as indicated. Circles for 6EG. Squares for 5EG. Downward-pointing triangles for 4EG. Diamond for 3EG. Upward-pointing triangles for 2EG. Some of the data of Tjq (closed symbols) overlap and cannot be easily resolved. For this reason, we use the dashed lines to indicate the Arrhenius temperature dependences assumed by Tjq of the mixtures starting approximately at temperatures below Tg of the mixtures defined by zJT =l(f s located by the vertical arrows drawn. There is change of temperature dependence of Tjq at Tg.

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