Water molecules, reorientational times

The B-coefficients obtained from viscosity and NMR signal relaxation rates pertain to dilute solutions (they are the limiting slopes towards infinite dilution). However, an equation of the form of Eq. (3.6) for NMR spin-lattice relaxation rates holds up to fairly large concentrations. Chizhik (1997) reported values of relative water molecule reorientation times Tri/Trw at 22 °C, being <1 for Br , I, NH4+, NOs, and Ns , 1.0 for K+, and >1 for Li+, Na+, Mg +, Ca +, Sr +, Ba +, F , CH, H3O+, S04 , and COs, in more or less agreement with the signs of the Bnmr in dilute solutions. Table 3.1. 

Dynamics of Reorientation. The approach of Impey, Madden and McDonald is used to consider the dynamics of reorientation for water molecules. The time autocorrelation function of the second Legrendre polynomial P2 of the angle subtended by the intramolecular H-H bond vector at time t with respect to its position at time t = 0 is calculated ... 

This is one distinguishing feature between hydrates and ice water molecules diffuse two orders of magnitude slower in hydrates than in ice. As shown in Table 2.8, ice water molecules diffuse almost an order of magnitude faster than they reorient about a fixed position in the crystal structure. In direct contrast, hydrate water molecules reorient 20 times faster than they diffuse. As for all... 

However the precise sequence of coordinate participation in the reaction path is solvent dependent. For the case just discussed, the water solvent is rapid, largely because of the small moment of inertia involved in the water molecule reorientations underlying the change of the electrical polarization. Dimethyl formamide (DMF) solvent is less rapid, and the resulting coordinate sequence on the way to the TS [3] is again in the order of decreasing slowness, but now the solvent coordinate is the slowest of the three, followed by the bend angle and finally the C - Cl bond stretch. The reaction path depends on the solvent time scale. 

Neutron-scattering and dielectric relaxation studies [23] both indicate that the water molecules solvating monovalent exchangeable cations on montmorillonite are a little less mobile, in respect to translational and reorientational motion, than are water molecules in the bulk liquid. For example, as with vermiculite, neutron-scattering data show that no water molecule is stationary on the neutron-scattering time scale. In the one-layer hydrate of Li-montmorillonite, the residence time of a water molecules is about six times longer than in the bulk liquid, with a diffusive jump distance of about 0.35 nm, and a water molecules reorients its dipole axis about half... 

Mobility of water in cellulose has been studied by solid-state and high-resolution NMR as a function of moisture content within the unfreezable moisture range (0-19% dry basis).Measurements of relative mobilities were based on relative intensities, transverse and longitudinal relaxation times and line shape analysis. At 2-16% moisture content (dry basis), water molecules reoriented anisotropically, suggesting an interaction with cellulose fibers. At moisture content below the monolayer value (2.8%, dry basis), 90% of the protons were immobile and no liquid deuterium signal was detected. A sharp increase in liquid or mobile intensity (accompanied by a decreased LW) and increases in NMR Ti and T2 relaxation times were observed as moisture increased above 9% (dry basis). 

Another important dynamic propaty to consider is the water molecule s reorientation. Given a vector u that is fixed in the molecular frame of reference, one is interested in the time-dependent quantities... 

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... 

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). 

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... 

In Eqs. (4)-(7) S is the electron spin quantum number, jh the proton nuclear magnetogyric ratio, g and p the electronic g factor and Bohr magneton, respectively. r//is the distance between the metal ion and the protons of the coordinated water molecules, (Oh and cos the proton and electron Larmor frequencies, respectively, and Xr is the reorientational correlation time. The longitudinal and transverse electron spin relaxation times, Tig and T2g, are frequency dependent according to Eqs. (6) and (7), and characterized by the correlation time of the modulation of the zero-field splitting (x ) and the mean-square zero-field-splitting energy (A. The limits and the approximations inherent to the equations above are discussed in detail in the previous two chapters. 

The importance of the magnetic coupling is easily seen in Fig. 17 which shows two water proton MRD profiles for serum albumin solutions at the same composition (89). The approximately Lorentzian dispersion is obtained for the solution, and reports the effective rotational correlation time for the protein. The magnetic coupling between the protein and the water protons carries the information on the slow reorientation of the protein to the water spins by chemical exchange of the water molecules and protons between the protein and the bulk solution. When the protein is cross-linked with itself at the same total concentration of protein, the rotational motion of the protein... 

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

An important signature of the dynamics of water molecules is the reorientation of its dipole vector that can be probed by dielectric and NMR measurements. We have calculated the single molecule dipole-dipole time correlation function (TCF), defined as,... 

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

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

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