Debye relaxation rotational dynamics

In contrast to the stretched exponential relaxation time, the Debye relaxation time T2 does not vary with hydration and stays around t2 = 4.7 0.4 ps and 2.5 0.6 ps for Fi and F2, respectively (Fig. 120). These values are noticeably larger than the bulk values for the same water model (2.5 and 0.9 ps [648]). The parameter a in equation (31) reflects the fraction of these weakly bound water molecules with Debye rotational dynamics. The amplitude a increases with hydration level, as it is shown in Fig. 121. At low hydrations, a is negligibly small and therefore cannot be estimated from the fits with a reasonable accuracy. At the surface of a rigid lysozyme, we have detected the appearance of the water molecules with Debye-like rotational dynamics only when Ny, > 300. On... 

Classic Brownian motion has been widely applied in the past to the interpretation of experiments sensitive to rotational dynamics. ESR and NMR measurements of T and Tj for small paramagnetic probes have been interpreted on the basis of a simple Debye model, in which the rotating solute is considered a rigid Brownian rotator, sueh that the time scale of the rotational motion is much slower than that of the angular momentum relaxation and of any other degree of freedom in the liquid system. It is usually accepted that a fairly accurate description of the molecular dynamics is given by a Smoluchowski equation (or the equivalent Langevin equation), that can be solved analytically in the absence of external mean potentials. 

Table L8 Re-orientadon times of water molecules for various processes involving the dynamics of the hydrogen bonding collective Debye relaxation time Tei, individual Debye relaxation time Te2, OH vector rotational re-orientation time (in parenthesis for D2O) r, , and mean hydrogen bond life time Thb...

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]... 

Equation (31) assumes an existence of two kinds of molecules showing quite different reorientational dynamics in the considered time interval. The water molecules with strong retardation of rotational motion and with broad distribution of relaxation times (low value of P) should be considered strongly bound. Such kind of water molecules with similar low values of the stretching exponent were observed in neutron-scattering experiment for combined rotational-translational motion of water in hydrated myoglobin (P 0.3) [643] and in simulations of water near mica surface (P k 0.25) [652]. Those water molecules, which show simple one-term exponential relaxation, like in the bulk, should be considered as weakly bound. Fractions of these two kinds of molecules ((1 - a) and a, respectively) should depend on the hydration level. Note, that weakly bound water molecules with Debye rotational relaxation were not distinguished in other simulation studies [610, 644]. 

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