Water rotational relaxation constant

The rotational diffusion constant in water at 25° and neutral pH as measured by electric birefringence (258) is 230 X 105 sec-1 or 0.73 X HT8 sec as a relaxation time. For a hydrodynamic ellipsoid of dimensions 66 X 22 A and a molecular weight of 14,000, the calculated relaxation tilde is 0.72 X 10-8 sec. However, the apparent asymmetry of the molecule from the X-ray structure corresponds to an axial ratio of no more than 2 1 rather than 3 1. 

Table 9 The self-diffusion constant for water and the ubiquitin molecule D p in aqueous solutions as calculated with different force fields for the water. In addition, i and T2 are rotational relaxation times for the ubiquitin molecule. Where possible, the results are compared with experimental values. All results are from ref. 36... 

Water molecules are constantly in motion, even in ice. In fact, the translational and rotational mobility of water directly determines its availability. Water mobility can be measured by a number of physical methods, including NMR, dielectric relaxation, ESR, and thermal analysis (Chinachoti, 1993). The mobility of water molecules in biological systems may play an important role in a biochemical reaction s equilibrium and kinetics, formation and preservation of chemical gradients and osmotic pressure, and macromolecular conformation. In food systems, the mobility of water may influence the engineering processes — such as freezing, drying, and concentrating chemical and microbial activities, and textural attributes (Ruan and Chen, 1998). 

Even if we consider a single solvent, e g., water, at a single temperature, say 298K, depends on the solute and in fact on the coordinate of the solute which is under consideration, and we cannot take xF as a constant. Nevertheless, in the absence of a molecular dynamics simulation for the solute motion of interest, XF for polar solvents like water is often approximated by the Debye model. In this model, the dielectric polarization of the solvent relaxes as a single exponential with a relaxation time equal to the rotational (i.e., reorientational) relaxation time of a single molecule, which is called Tp) or the Debye time [32, 347], The Debye time may be associated with the relaxation of the transverse component of the polarization field. However the solvent fluctuations and frictional relaxation occur on a faster scale given by [348,349]... 

In several previous papers, the possible existence of thermal anomalies was suggested on the basis of such properties as the density of water, specific heat, viscosity, dielectric constant, transverse proton spin relaxation time, index of refraction, infrared absorption, and others. Furthermore, based on other published data, we have suggested the existence of kinks in the properties of many aqueous solutions of both electrolytes and nonelectrolytes. Thus, solubility anomalies have been demonstrated repeatedly as have anomalies in such diverse properties as partial molal volumes of the alkali halides, in specific optical rotation for a number of reducing sugars, and in some kinetic data. Anomalies have also been demonstrated in a surface and interfacial properties of aqueous systems ranging from the surface tension of pure water to interfacial tensions (such as between n-hexane or n-decane and water) and in the surface tension and surface potentials of aqueous solutions. Further, anomalies have been observed in solid-water interface properties, such as the zeta potential and other interfacial parameters. 

The H NMRD profiles of Mn(OH2)g+ in water solution show two dispersions (Fig. 5.43). The first (at ca. 0.05 MHz, at 298 K) is attributed to the contact relaxation and the second (at ca. 7 MHz, at 298 K) to the dipolar relaxation. From the best fit procedure, the electron relaxation time, given by rso = 3.5 x 10 9 and r = 5.3 x 10 12 s, is consistent with the position of the first dispersion, the rotational correlation time xr = 3.2 x 10 11 s is consistent with the position of the second dispersion and is in accordance with the value expected for hexaaquametal(II) complexes, the water proton-metal center distance is 2.7 A and the constant of contact interaction is 0.65 MHz (see Table 5.6). The impressive increase of / 2 at high fields is due to the field dependence of the electron relaxation time and to the presence of a non-dispersive zs term in the equation for contact relaxation (see Section 3.7.2). If it were not for the finite residence time, xm, of the water molecules in the coordination sphere, the increase in Ri could continue as long as the electron relaxation time increases. 

Here 7 is the nuclear spin, is the quadrupolar coupling constant, tj is an asymmetry parameter, is the Gd- O distance, and r j is defined by Eq. 12. The difficulty of this technique is that both the quadrupolar coupling constant and the Gd - O distance can only be estimated. However, rotational correlation times obtained from longitudinal 2Q relaxation rates can provide a good comparison for similar Gd(III) complexes. One advantage is that the rotational correlation time is measured directly on the Gd(III) complex. Furthermore, the determined in this way corresponds to the rotation of the Gd(III) - coordinated water oxygen vector which is probably analogous to the rotation of the Gd(III) - coordinated water proton, which, itself determines proton relaxivity. 

A similar study has been reported on specifically deuterated pyridines in a series of aqueous solutions. (172) A rotational diffusion model is used to interpret the relaxation data. The diffusion constant for reorientation around the C2 axis of pyridine is found to increase as the viscosity of the solution increases whereas the constant for reorientation about the axis perpendicular fo the molecular plane decreases as the amount of water present in the solution increases. These observations are attributed to short range ordering due to hydrogen bond formation. 

Pal et al., 2002). To understand the different solvation timescales, we have fitted the decay curves to multiexponentials. Four different solvation timescales are identified, from ultrafast to slow components. An ultrafast component with a time constant of 40-50 fs, followed by a fast component at 0.7-1.2 ps was observed. Two slower components with time constants in the range of 6-17 and 42-88 ps were also noticed. Such different solvation timescales arise from the presence of different types of water molecules within the hydration layer (Bandyopadhyay et al., 2005). The initial ultrafast relaxation arises from the high frequency librational (hindered rotation) and intermolecular vibrational (hindered translation) motions of the "free" or bulk-like water molecules. The moderately damped rotational motions of these water molecules contribute to the fast relaxation ( 1 ps). The slowest component observed (42-88 ps) arises from those water molecules which... 

To explain the bimodal dielectric relaxation in aqueous protein solutions, Nandi and Bagchi proposed a similar dynamic exchange between the bound and the free water molecules [21]. The bound water molecules are those that are attached to the biomolecule by a strong hydrogen bond. Their rotation is coupled with that of the biomolecule. The water molecules, beyond the solvation shell of the proteins, behave as free water molecules. The free water molecules rotate freely and contribute to the dielectric relaxation process, whereas the rotation of the doubly hydrogen-bonded bound water molecules is coupled with that of the biomolecule and hence is much slower. The free and bound water molecules are in a process of constant dynamic exchange. The associated equilibrium constant, K, can be written as... 

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