Microscopic relaxation

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-... 

It is apparently a general characteristic of glassy disorder, although there has been considerable debate over the relation between the stretched exponential decay and the microscopic relaxation mechanisms. 

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... 

However, Eq. (4.1) has another advantage in that it directly connects to the system-bath models used in condensed phase dynamics [38]. Here the reactive coordinates and the substrate modes comprise the relevant system and the bath, respectively. Larger molecules may provide their own bath and Eq. (4.1) can be used to calculate an ah initio system-bath Hamiltonian and microscopic relaxation and dephasing rates [33]. 

There is a close parallel between this development and the microscopic theory of condensed-phase chemical reactions. First, the questions one asks are very nearly the same. In Section III we summarized several configuration space approaches to this problem. These methods assume the validity of a diffusion or Smoluchowski equation, which is based on a continuum description of the solvent. Such theories will surely fail at the close encounter distance required for reaction to take place. In most situations of chemical interest, the solute and solvent molecules are comparable in size and the continuum description no longer applies. Yet we know that these simple approaches are often quite successful, even when applied to the small molecule case. Thus we again have a microscopic relaxation process exhibiting a strong hydrodynamic component. This hydrodynamic component again gives rise to a power law decay in the rate kernel (cf. 

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]). 

The microscopic origin of the Rosenfeld relation between D and can be understood in the following way. Let us assume k ,isa microscopic relaxation rate between two adjacent microscopic states in the phase space of the system. During the experimental time Tobs, the system makes tobs transitions and therefore visits that many microscopic states. So, we can set tobs proportional to the total number of microscopic states Q so that the states are uniformly distributed. In the next step we assume that each transition results in a displacement a of the particle. So, we have the following relation between diffusion and the rate of transitions as. 

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. 

In this chapter, we present a viscoelastic analysis of the IXS spectra collected on liquid Cs at 493 K and four pressure points, below and above the transition (Fig. 1). We show that the viscoelastic parameters are either pressure independent or smoothly dependent, except for that corresponding to the microscopic relaxation process this latter indeed doubles or even triples at the transition, while it stays... 

The description of the dynamics of the system relies then on the choice of the memory function, which accounts for the relaxation mechanisms governing the response of the liquid to an acoustic perturbation. As already said, in the case of liquid Cs at high pressures, we have already found that the best description can be obtained with a model with two relaxation mechanisms [14] the structural relaxation, represented by an exponential function of time with a characteristic time Xa, and the microscopic relaxation, represented by a Dirac s 5 function of time. The thermal relaxation was instead found to be negligible, as it is the case for all liquid alkali metals at room pressure this means that the low frequency limit... 

It seems then that the LLT in liquid Cs affects the microscopic dynamics very litde, at least as far as the high-frequency speed of sound is concerned. However, another picture appears if we look at the relaxational dynamics, that is, the relaxation time Tq, and the microscopic relaxation parameter F, as shown in Fig. 5 r describes the contribution to the broadening of the inelastic excitations coming from the microscopic relaxation. Inspecting Fig. 5b, we see that the a-relaxation time decreases on increasing pressure in the first pseudo-Brillouin zone, that is, up to q/qo = 0-5. The decrease is gradual and it is actually more important between 1 and 3.5 GPa than at higher pressures. This thus seems to be a density-dependent... 

Figure 5. The microscopic relaxation parameter F (a) and the structural relaxation time Za (b) derived from the viscoelastic fit. same symbols as in Fig. 3. While decreases gradually with pressure, P shows a discontinuous increase at the transition to more than twice of the low pressure...

The observed behavior is remarkable Why an electronic transition should affect so much the acoustic damping and more in detail the microscopic relaxation Generally speaking, we could have expected changes in the shape of the acoustic dispersion, due to changes in the electronic screening contribution to the interparticle potential. However, this is not the case, as we showed in Ref. [13] and as it appears from the data here reported. Only the acoustic damping is affected. 

The consequence is then that the microscopic relaxation, which accounts for the low-frequency intensity in the spectra and thus possibly for the pseudo-transverse modes, discontinuously changes at the LLT, as well as the damping of the acoustic modes derived using a single-excitation fitting model. 

In more complicated cases, the perturbations of equilibrium distributions over vibrational, rotational, and sometimes translational degrees of freedom must be taken into account. It must be borne in mind that the relation between macroscopic relaxation and the reaction times is far from always defining the extent of non-equilibrium. The true criterion for the reaction-induced perturbation of equilibrium distribution is formulated in terms of the microscopic relaxation and of the reaction rate constants which define the relation between the rates of changes in the population of the given quantum states of reactants caused by these two processes. For this reason, the study of elementary rates of relaxation processes is of essential kinetic interest. 

Two final remarks need to be made. First, even when the MD simulation time is short compared to the macroscopic time scale, it can still be very long when compared with the microscopic time step if a substantial energy barrier must be overcome during the microscopic relaxation. Second, the choice of the MD cell size is a delicate balance between accuracy and computational efficiency as the cell size increases, the error decreases (as for a cell of... 

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