Water reorientation times

As a generalization, high-frequency dielectric relaxation spectroscopy in dilute aqueous salt solutions is rather insensitive to the nature of the anion, provided it is not dipolar itself, but does respond to the cation that orients the water dipoles around it through its electric field, and affects the water reorientation times, manifested by the appearance of the so-called slow water. ... 

Spohr found a significant reduction in the dipole reorientation time for a different model of water (but using the same water/Pt potential). In that paper, the reorientation dynamics are characterized by the spectral densities for rotation around the three principal axes of the water molecule. These calculations demonstrated the hindered rotation of water molecules in the plane parallel to the surface. In addition, a reduction in the frequency of rotation about the molecular dipole for water molecules in the adsorbed... 

In order to obtain information on the electron relaxation time in copper aqua ion, measurements should not be performed in water solution, because the correlation time for proton relaxation is in that case the reorientational time, which is much smaller than T g. NMRD profiles should be actually acquired in ethylene glycol solution and at temperatures lower that room temperature, so that the reorientational time increases one two orders of magnitude (see Section II.B). In this way T e of the order of 10 s can be estimated. 

The NMRD profile of Mn(H20)g in water solution shows two dispersions (Fig. 10) in the 0.01-100 MHz range of proton Larmor frequency one, at about 0.05 MHz, due to the contact relaxation, and a second, at about 7 MHz, due to the dipolar relaxation (39). The correlation time for contact relaxation is the electron relaxation time, whereas the correlation time for dipolar relaxation is the reorientational time (ir = 3.2 x 10 , in accordance with the value expected for hexaaquametal(II) complexes). This accounts for the different positions of the two dispersions in the profile. From a best fit of longitudinal and transverse proton relaxation profiles, the electron relaxation time is described by the parameters A = 0.02-0.03 cm and... 

Chromium(III) has a ground state in pseudo-octahedral symmetry. The absence of low-lying excited states excludes fast electron relaxation, which is in fact of the order of 10 -10 ° s. The main electron relaxation mechanism is ascribed to the modulation of transient ZFS. Figure 18 shows the NMRD profiles of hexaaqua chromium(III) at different temperatures (62). The position of the first dispersion, in the 333 K profile, indicates a correlation time of 5 X 10 ° s. Since it is too long to be the reorientational time and too fast to be the water proton lifetime, it must correspond to the electron relaxation time, and such a dispersion must be due to contact relaxation. The high field dispersion is the oos dispersion due to dipolar relaxation, modulated by the reorientational correlation time = 3 x 10 s. According to the Stokes-Einstein law, increases with decreasing temperature, and... 

Alternatively, in order to take into account the effects of rotational diffusion of a water molecule around the metal-oxygen axis, a rotational correlation time for the metal-H vector was considered as an additional parameter besides the longer overall reorientational time 82). 

When the temperature is lowered and/or the viscosity of the solution is increased by using glycerol-water mixtures as solvent, the reorientational correlation time increases. Since the reorientational time is the correlation time for nuclear relaxation, the effects on the NMRD profile (Pig. 27) are (i) higher relaxivity values at low frequencies (ii) a shift toward lower... 

The NMRD profiles of V0(H20)5 at different temperatures are shown in Fig. 35 (58). As already seen in Section I.C.6, the first dispersion is ascribed to the contact relaxation, and is in accordance with an electron relaxation time of about 5 x 10 ° s, and the second to the dipolar relaxation, in accordance with a reorientational correlation time of about 5 x 10 s. A significant contribution for contact relaxation is actually expected because the unpaired electron occupies a orbital, which has the correct symmetry for directly overlapping the fully occupied water molecular orbitals of a type (87). The analysis was performed considering that the four water molecules in the equatorial plane are strongly coordinated, whereas the fifth axial water is weakly coordinated and exchanges much faster than the former. The fit indicates a distance of 2.6 A from the paramagnetic center for the protons in the equatorial plane, and of 2.9 A for those of the axial water, and a constant of contact interaction for the equatorial water molecules equal to 2.1 MHz. With increasing temperature, the measurements indicate that the electron relaxation time increases, whereas the reorientational time decreases. 

Interestingly, the reorientational time is about 2-3 times larger than expected for a hexaaqua ion. Indeed, the second sphere water molecules... 

The presence of second-sphere water molecules could be considered also for other metal aqua ions, like iron(III) and oxovanadium(IV) aqua ions, where the reorientational time is found to be longer than expected. However, in the other cases increases much less than for the chromium(III) aqua ion, thus suggesting that second-sphere water molecules are more labile, their lifetime being of the order of the reorientational time. 

As an example of behavior of a typical Gd-complex and Gd-macromolecule we discuss here the NMRD profiles of a derivative of Gd-DTPA with a built-in sulfonamide (SA) and the profile of its adduct with carbonic anhydrase (see Fig. 37) 100). Other systems are described in Chapter 4. The profile of Gd-DTPA-SA contains one dispersion only, centered at about 10 MHz, and can be easily fit as the sum of the relaxation contributions from two inner-sphere water protons and from diffusing water molecules. Both the reorientational time and the field dependent electron relaxation time contribute to the proton correlation time. The fit performed with the SBM theory, without... 

Fig. 4 Dipolar reorientational time correlation function, Cw(t) for bound water molecules in the micellar solution, and for bulk water molecules.

Fig. 8 Reorientational time correlation function of the water dipole, C (<), for water molecules in the three segments of the protein.

The NMR rotational reorientation time of liquid water at 25 °C is 2.5 10-12 sec and the dielectrid relaxation time of liquid water is 8 1(T12 sec173). 

Reorientational times T for water molecules in various adsorbates and in bulk water. 

Returning to our problem, we remark that the temperature dependences of such parameters as, for example, the Debye relaxation time td(7 ) (which determines the low-frequency dielectric spectra), or the static permittivity s are fortunately known, at least for ordinary water [17], As for the reorientation time dependence t(T), it should probably correlate with in(T), since the following relation (based on the Debye relaxation theory) was suggested in GT, p. 360, and in VIG, p. 512 ... 

Figure 26 Results of the decomposition of the measured transient spectra the peak positions (a), spectral widths (FWHM) (b), and reorientation times (c) of three prominent spectral components I—in, attributed to different local structures of water, as a function of temperature experimental points the lines are drawn as a guide for the eye.

Both transition times, reorientation of water near the ion and translation, can be calculated. The value for the reorientation time of I" is 5 2 ps this is a low value because of the weak field in the water arising from the large size of r. The hindered... 

Another problem in the quantal approach is that ions in solution are not stationary as pictured in the quantum mechanical calculations. Depending on the time scale considered, they can be seen as darting about or shuffling around. At any rate, they move and therefore the reorientation time of the water when an ion approaches is of vital concern and affects what is a solvation number (waters moving with the ion) and what is a coordination number (Fig. 2.23). However, the Clementi calculations concerned stationary models and cannot have much to do with dynamic solvation numbers. 

Halle et al. (1981) measured NMR relaxation for solutions of several proteins as a function of frequency and protein concentration. They estimated hydration by use of a two-state fast-exchange model with local anisotropy and with assumed values of the order parameter and several other variables. The hydration values ranged from 0.43 to 0.98 h for five proteins, corresponding approximately to a double layer of water about a protein. The correlation time for water reorientation was, averaged over the set of proteins, 20 psec, about eight times slower than that for bulk water. A slow correlation time of about 10 nsec was attributed to an ordering of water by protein at very high concentration. 

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