Microscopic relaxation time

It is well known [54,270] that the macroscopic dielectric relaxation time of bulk water (8.27 ps at 25°C) is about 10 times greater than the microscopic relaxation time of a single water molecule, which is about one hydrogen bond lifetime [206,272-274] (about 0.7 ps). This fact follows from the associative structure of bulk water where the macroscopic relaxation time reflects the cooperative relaxation process in a cluster of water molecules. 

In the context of the model presented above, the microscopic relaxation time of a water molecule is equal to the cutoff time of the scaling in time domain To-For the most hydrophilic polymer, PVA, the strong interaction between the polymer and the water molecule results in the greatest value of microscopic relaxation time To, only 10% less than the macroscopic relaxation time of the bulk water. The most hydrophobic polymer, PVP, has the smallest value of a single water molecule microscopic relaxation time, which is almost equal to the microscopic relaxation time of bulk water (see Table III). Therefore, weakening the hydrophilic properties (or intensifying the hydrophobic properties) results in a decreasing of interaction between the water and the polymer and consequently in the decrease of To-... 

The time evolution of the reactive flux is given by projected dynamics [28] but in simulations we may replace projected dynamics by ordinary dynamics and insert absorbing states in the reactant and product regions to yield well defined plateau values. Such a procedure will be accurate provided there is a sufficient time scale separation between the relaxation time for reactive events and other microscopic relaxation times in the system. 

Elliott (1987, 1988 and 1989) approached the relaxation problem differently. In his diffusion controlled relaxation (DCR) model, Elliott, like Charles (1961) considers ionic motion to occur by an interstitialcy mechanism. There is a local motion of cations (for example Li ion in a silicate glass) among equivalent positions located around a NBO ion. Motions of cations among these positions causes the primary relaxational event and it occurs with a characteristic microscopic relaxation time t. The process gives rise to a polarization current. However, when another Li ion hops into one of the nearby equivalent positions with a probability P(/), a double occupancy results around the anion and this makes the relaxation instantaneous. Since the latter process involves the diffusion of a Li ion, the process as a whole involves both polarization and diffusion currents. Thus the relaxation function can be written as [l-P(/)]exp(-t/r). [1-P(0] is a function of the jump distance and the diffusion constant. Making use of the Glarum-Bordewijk relation (Glarum, 1960 Bordewijk, 1975) for [1-/ (/)] Elliott (1987) has shown that... 

So the average moment in the direction of the field is given by Eq. (28) which can define the microscopic relaxation time that depends on the resistive force experienced by the individual molecules (for more details, see MacConnell [32]). 

Tjn 10 s. Thus, we have found the typical microscopic relaxation time for a low molecular weight liquid. ... 

For the volume fractions presented in Figs. (3-6) the shear modulus is on the order of lOdyn/cm and the sound velocity V(= /s/p) = l-5cm/s. The microscopic relaxation time T(-rj/E) 1-10 ms, and the attenuation length A.[= (ImK) =2F/0 t1 1-10cm. For frequencies below IkHz the dissipation is small and the shear waves are propagating. The dimensions of the measuring cell encourage the formation of standing waves. 

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