Relaxation modes/processes

Berezhkovskii A M and Zitserman V Yu 1992 Multidimensional activated rate processes with slowly relaxing mode Physica A 187 519-50... 

The stress—relaxation process is governed by a number of different molecular motions. To resolve them, the thermally stimulated creep (TSCr) method was developed, which consists of the following steps. (/) The specimen is subjected to a given stress at a temperature T for a time /, both chosen to allow complete orientation of the mobile units that one wishes to consider. (2) The temperature is then lowered to Tq T, where any molecular motion is completely hindered then the stress is removed. (3) The specimen is subsequendy heated at a controlled rate. The mobile units reorient according to the available relaxation modes. The strain, its time derivative, and the temperature are recorded versus time. By mnning a series of experiments at different orientation temperatures and plotting the time derivative of the strain rate observed on heating versus the temperature, various relaxational processes are revealed as peaks (243). 

For paramagnetic spin systems, there are two major processes of relaxation (55). One relaxation mode involves spin-flipping accompanied by lattice phonon creation and/or annihilation (spin-lattice relaxation), and the other mode is due to the mutual flipping of neighboring spins such that equilibrium between the spins is maintained (spin-spin relaxation). For the former mode of relaxation, th decreases with increasing temperature, and the latter relaxation mode, while in certain cases temperature dependent, becomes more important (th decreases) as the concentration of spins increases. 

For a few polyatomic molecules, where there is a large difference between Vj and v2, the rate of the complex process (c) is much slower, and the condition P2 > P12 > Pi applies. This gives rise to a double relaxation phenomenon. Process (b) is again too slow to play any role, but process (a) is now faster than process (c). The vibrational energy of mode 2 (and any upper modes) relaxes... 

Recently it has been found that besides the above two broad bands one relaxation mode appears as a central ctxnponent below 50 cm. 0d7-I92V This relaxation mode is due to the creation and annihilation process of hydrogen bond among water clusters. From the change of this specoal profile as well as the two broad bands in water and aqueous solutions we can obtain tte dynamical aspect of water. 

Anomalous rotational diffusion in a potential may be treated by using the fractional equivalent of the diffusion equation in a potential [7], This diffusion equation allows one to include explicitly in Frohlich s model as generalized to fractional dynamics (i) the influence of the dissipative coupling to the heat bath on the Arrhenius (overbarrier) process and (ii) the influence of the fast (high-frequency) intrawell relaxation modes on the relaxation process. The fractional translational diffusion in a potential is discussed in detail in Refs. 7 and 31. Here, just as the fractional translational diffusion treated in Refs. 7 and 31, we consider fractional rotational subdiffusion (0rotation about fixed axis in a potential Vo(< >)- We suppose that a uniform field Fi (having been applied to the assembly of dipoles at a time t = oo so that equilibrium conditions prevail by the time t = 0) is switched off at t = 0. In addition, we suppose that the field is weak (i.e., pFj linear response condition). 

The decay rate of the fast mode rfeff is proportional to tf and hence an effective fast diffusion coefficient = rfeff(/ 2 may be defined. The decay rate of the slow process exhibits deviation from -dependence, and the experimental data shows approximately a -dependence characteristic either of internal relaxation modes or of the diffusion of labile tenuous clusters. 

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