Water rotational diffusion

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). 

Fig. 3. Schematic representation of the topological space of hydration water in silica fine-particle cluster (45). The processes responsible for the water spin-lattice relaxation behavior are restricted rotational diffusion about an axis normal to the local surface (y process), reorientations mediated by translational displacements on the length scale of a monomer (P process), reorientations mediated by translational displacements in the length scale of the clusters (a process), and exchange with free water as a cutoff limit.

Rotational diffusion constant Density extrapolated to 20°C, water Density... 

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. 

The second explanation for the solvent isotope effect arises from the dynamic medium effect . At 25 °C the rotational and translational diffusion of DjO molecules in D20 is some 20% slower than H20 molecules in H20 (Albery, 1975a) the viscosity of D20 is also 20% greater than H20. Hence any reaction which is diffusion controlled will be 20% slower in D20 than in H20. This effect would certainly apply to transition state D in Fig. 3 where in the transition state the leaving group is diffusing away. A similar effect may also apply to the classical SN1 and SN2 transition states, if the rotational diffusion of water molecules to form the solvation shell is part of the motion along the reaction co-ordinate in the transition state. Robertson (Laughton and Robertson, 1959 Heppolette and Robertson, 1961) has indeed correlated solvent isotope effects for both SN1 and SN2 reactions with the relative fluidities of H20 and D20. However, while the correlation shows that this is a possible explanation, it may also be that the temperature variation of the solvent isotope effect and of the relative fluidities just happen to be very similar (see below). 

While these models match experimental data reasonably well at lower fields, recent experiments at higher magnetic fields of 3.4 and 9.2 T show enhancement values that are much higher than predicted with the currently employed theory.41,72,79 At these higher fields, the timescale of molecular interactions that give rise to Overhauser DNP effects is much shorter (sub-picoseconds to picoseconds) and thus should be more sensitive to the rotational diffusion dynamics of water, closely related to the atomistic details of the radical and solvent, instead of translational diffusion dynamics. These atomistic details are not accurately represented in the FFHS or rotational models (Equations (13) and (15)), implying that further work needs to be done to develop more accurate models. 

The concept of measuring such rates is not new, particularly in the pharmaceutical field. Van de Waterbeemd [14] measured rates of transfer of various drugs from octanol to water and empirically related these rates to the partition coefficient. Similarly Brodin [15], using a different experimental method, obtained rates of transfer for another series of compounds between cyclohexane and water. The rotating diffusion cell has been introduced for similar purposes [16-18]. It is necessary to look into the broader background of liquid-liquid interfacial kinetics, in order to illustrate aspects of the issues under consideration. The subject has been reviewed in part by Noble [19]. 

These thermodynamic approaches to hydrophobic effects are complemented by spectroscopic studies. Tanabe (1993) has studied the Raman spectra manifested during the rotational diffusion of cyclohexane in water. The values of the diffusion coefficients are approximately half those expected from data for other solvents of the same viscosity, and the interpretations made are in terms of hindered rotation arising from the icebergs presumably formed (c/. Frank and Evans) around the cyclohexane. 

Part, and perhaps most, of hydration water has mobility close to bulk water. Rotational motion is 1/10-1/100 that of bulk solvent, and diffusion constant, 1/5. Few, if any, hydration water has Troution >10 sec. 

The most important information obtainable pertains to (i) the number and lattice potential of the hydrogen positions present in the structure (Sects. 4.2.1 and 4.2.2), (ii) the extent of distortion of the water molecules (Sect. 4.2.2), (iii) the strength and arrangement of H-bonds and other intermolecular interactions (Sects. 3.2, 4.2.3, 4.2.4, 4.2.6), (iv) the distinction between true hydrates and pseudohydrates (Sects. 3.1, 4.3), (v) the possible orientational disorder of water molecules and dynamic processes, such as rotational diffusion, involved therein (Sects. 2.2, 2.5, 3.3, 4.2.5, 4.4), and (vi) the phase transitions and other structural changes upon heating or cooling (Sect. 4.8). 

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. 

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