Relaxation times Johari-Goldstein

In the previous section, at temperatures above 7g, the Johari-Goldstein relaxation time has been shown to correspond well to the primitive relaxation time, and both are related to the structural a-relaxation time by Eq. (10). This equation should continue to hold at temperatures below T,. However, testing this relation in the glassy state is difficult because of either the scarcity or the unspecified thermal history of the data on the a-relaxation time xa. In fact, a reliable characterization of the structural relaxation can be acquired only at equilibrium, and such condition is rarely satisfied below Tg. Glassy systems are nonergodic, and their properties can depend on aging time and thermal history. Anyway, for glasses in isostructural state with a constant Active temperature Tf, both ra and To as well as Xjg should have Arrhenius dependences with activation enthalpies Ea, Eq, and Ejg respectively. Eq. (10) leads us to the relation... 

Although glass transition is conventionally defined by the thermodynamics and kinetic properties of the structural a-relaxation, a fundamental role is played by its precursor, the Johari-Goldstein (JG) secondary relaxation. The JG relaxation time, xjg, like the dispersion of the a-relaxation, is invariant to changes in the temperature and pressure combinations while keeping xa constant in the equilibrium liquid state of a glass-former. For any fixed xa, the ratio, T/G/Ta, is exclusively determined by the dispersion of the a-relaxation or by the fractional exponent, 1 — n, of the Kohlrausch function that fits the dispersion. There is remarkable similarity in properties between the JG relaxation time and the a-relaxation time. Conventional theories and models of glass transition do not account for these nontrivial connections between the JG relaxation and the a-relaxation. For completeness, these theories and models have to be extended to address the JG relaxation and its remarkable properties. 

Abstract The present study demonstrates, by means of broadband dielectric measurements, that the primary a- and the secondary Johari-Goldstein (JG) /3-processes are strongly correlated, in contrast with the widespread opinion of statistical independence of these processes. This occurs for different glassforming systems, over a wide temperature and pressure range. In fact, we found that the ratio of the a- and P- relaxation times is invariant when calculated at different combinations of P and T that maintain either the primary or the JG relaxation times constant. The a-P interdependence is quantitatively confirmed by the clear dynamic scenario of two master curves (one for a-, one for P-relaxation) obtained when different isothermal and isobaric data are plotted together versus the reduced variable Tg(P)/T, where Tg is the glass transition temperature. Additionally, the a-P mutual dependence is confirmed by the overall superposition of spectra measured at different T-P combinations but with an invariant a-relaxation time. 

Xoa primitive relaxation time of the Coupling Model Johari-Goldstein secondary relaxation time Xoj primitive relaxation time of the network junction Xaf segmental relaxation time of the fast component in binary poly-... 

Johari-Goldstein Relaxation Time with Crosslink Density... 

While all relaxation times depend on temperature and pressure, only the global motions (viscosity, terminal relaxation time, steady state recoverable compliance) are functions of Mw (and to a lesser extent MWD). An example of the various dynamics of 1,4-polyisoprene are illustrated in Fig. 10. At frequencies beyond the local segmental relaxation, or at temperatures below Tg, secondary relaxation processes can be observed, especially in dielectric spectra. In polymers, many of these secondary processes involve motion of pendant groups. However, the slowest secondary relaxation, referred to as the Johari-Goldstein process, involves all atoms in the repeat unit (or the entire molecule for low M materials). This Johari-Goldstein relaxation serves as the precursor to the prominent glass transition. 

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