Secondary relaxation dynamics

Gilmanshin R., Williams S., Callender R. H., Woodruff W. H. and Dyer R. B. Fast events in protein folding relaxation dynamics of secondary and tertiary structure in native apomyoglobin. Proc. Natl. Acad. Sci., USA (1997) 94(8) 3709-3713. 

At low temperature the material is in the glassy state and only small ampU-tude motions hke vibrations, short range rotations or secondary relaxations are possible. Below the glass transition temperature Tg the secondary /J-re-laxation as observed by dielectric spectroscopy and the methyl group rotations maybe observed. In addition, at high frequencies the vibrational dynamics, in particular the so called Boson peak, characterizes the dynamic behaviour of amorphous polyisoprene. The secondary relaxations cause the first small step in the dynamic modulus of such a polymer system. 

Chapter 4 deals with the local dynamics of polymer melts and the glass transition. NSE results on the self- and the pair correlation function relating to the primary and secondary relaxation will be discussed. We will show that the macroscopic flow manifests itself on the nearest neighbour scale and relate the secondary relaxations to intrachain dynamics. The question of the spatial heterogeneity of the a-process will be another important issue. NSE observations demonstrate a subhnear diffusion regime underlying the atomic motions during the structural a-relaxation. 

Below Tg, in the glassy state the main dynamic process is the secondary relaxation or the )0-process, also called Johari-Goldstein relaxation [116]. Again, this process has been well known for many years in polymer physics [111], and its features have been estabhshed from studies using relaxation techniques. This relaxation occurs independently of the existence of side groups in the polymer. It has traditionally been attributed to local relaxation of flexible parts (e.g. side groups) and, in main chain polymers, to twisting or crankshaft motion in the main chain [116]. Two well-estabhshed features characterize the secondary relaxation. 

A more realistic model for the secondary relaxation needs to consider motions of a molecular group (considered as a rigid object) between two levels. The group may contain N atoms with the scattering length h, at positions r (i=lj ). The associated motion may consist of a rotation aroimd an arbitrary axis, e.g. through the centre of mass depicted by a rotational matrix Q and a displacement by a translational vector . In order to evaluate the coherent dynamic structure factor, scattering amphtudes of the initial (1) and final (2) states have to be calculated ... 

For this polymer the influence of the secondary relaxation on the dynamic structure factor seems to be much weaker than in the case of PB. Figure 4.31b... 

Finally, solute radical ions can be generated by light-induced, one-photon or multiphoton ionization of their parent compounds (Chaps. 5 and 16). This approach is particularly useful in the ultrafast studies of short-lived, unstable radical ions that aim to unravel their solvation, recombination, reaction, and vibrational relaxation dynamics of the primary charges (see, e.g., Chap. 10). Whereas the time scale of radiolytic production of secondary ions is always limited by the rate with which the primary species reacts with the dispersed parent molecules, light-induced charge separation can occur in <100 fsec. There are many studies on photoionization of solute molecules in liquid solutions we do not intend to review these works. 

By combining the results of several methods (dynamic mechanical, dielectric, NMR, etc.), it is usually possible to determine quite reliably the structural units whose motions give rise to secondary relaxations. If dynamic mechanical measurements alone are employed, the usual procedure is that the chemical constitution is systematically altered and correlated with the dynamic mechanical response spectra, i.e. with the temperature-dependence of the G" and G moduli. If the presence of a certain group in polymers is marked by the formation of a loss peak characterized by a certain temperature position, size and shape etc., then the conclusion may be drawn that the motional units responsible for the secondary relaxation are identical or related with that group. Naturally, the relations obtained in this way are empirical and qualitative. 

Of the diluents known to affect the dynamic relaxation behavior of polymers in the glassy state, water has so far received the greatest attention. Many polymers, which in the dry state are lacking any secondary relaxation process at temperatures from 77 to 273 K, e.g. poly(methyl methacrylate)135, polymethacrylamide136, cellulose and its derivatives137, collagen138, polysulfones139, poly(2,6-dimethylphenylene oxide)139, and others,... 

Various experimental techniques (dielectric relaxation, dynamic mechanical analysis, 1H, 2H and 13C solid-state NMR) have been used for investigating the secondary transitions of BPA-PC, and the block copolymers of BPA and TMBPA carbonates as well as compatible blends of BPA-PC and TMBPA-PC. They have provided lots of information on the motions of methyl, phenyl ring and carbonate units in bulk BPA-PC. The effect of intermolecular packing has also been clearly evidenced. 

Although molecular mobility is severely restricted below the glass transition temperature, the dynamic glass transition temperature (main transition or, conventionally -relaxation) in polymers as it have been described above, is usually accompanied by subglass secondary relaxations labeled as p, y, S, relaxations. The glass transition at low temperatures is assumed to be caused by the cooperative motion of many particles, while the secondary relaxations have a more localized molecular... 

Extensive dynamic mechanical property studies have been carried out on hydrogen-bonded (81) and nonhydrogen-bonded (60,82) polyurethanes. Several secondary relaxations were found in addition to the major hard- and soft-segment transitions. Molecular mechanisms could... 

In order to compare primary dynamics with secondary relaxation steps, we depict on the left-hand side of Fig. 15 the anisotropic spectra (a-c), which consist mainly of spectral components with the same linear polarization as directly induced by the pump pulse. On the right-hand side of the figure the corresponding isotropic spectra (d-f) are shown. In the latter spectral components can notably contribute that result from a relaxation process, where the initially orientation of the OH transition dipole is (partially) lost. 

Figure 1. A sketch of the temperature evolution of the susceptibility spectra of simple molecular liquids upon passing from low-density fluid (a) to the glass (d). We anticipate two distinguishable temperature regimes for the evolution of glassy dynamics, namely, a high-temperature regime (b) and a low-temperature regime (c), the latter characterized by the emergence of slow secondary relaxation processes.

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