Coupling of Caged Molecule Dynamics to JG β-Relaxation II: Polymers

Abstract

At temperatures below the nominal glass transition temperature Tgα, the structural α-relaxation and the Johari-Goldstein (JG) β-relaxation are too slow to contribute to susceptibility measured at frequencies higher than 1 GHz. This is particularly clear in the neighborhood of the secondary glass transition temperature Tgβ, which can be obtained directly by positronium annihilation lifetime spectroscopy (PALS) and adiabatic calorimetry, or deduced from the temperature at which the JG β-relaxation time τβ reaches 1000 s. The fast process at such high frequencies comes from the vibrations and caged molecules dynamics manifested as the nearly constant loss (NCL) in susceptibility measurements, elastic scattering intensity, I(Q, T), or the mean-square-displacement, ⟨u(2)(T)⟩, in quasielastic neutron scattering experiment. Remarkably, we find for many different glass-formers that the NCL, I, or ⟨u(2)⟩ measured in the glassy state changes its temperature dependence at temperature THF near Tgβ. In paper I (Capaccioli, S.; et al. J. Phys. Chem. B 2015, 119 (28), 8800-8808) we have made known this property in the case of the polyalcohols and a pharmaceutical glass former, flufenamic acid studied by THz dielectric spectroscopy, and explained it by the coupling of the NCL to the JG β-relaxation, and the density dependence of these processes. In this paper II, we extend the consideration of the high frequency response to broader range from 100 MHz to THz in the glassy state of many polymers observed by quasielastic light scattering, Brillouin scattering, quasielastic neutron scattering, and GHz-THz dielectric relaxation. In all cases, the NCL changes its T-dependence at some temperature, THF, below Tgα, which is approximately the same as Tgβ. The latter is independently determined by PALS, or adiabatic calorimetry, or low frequency dielectric and mechanical spectroscopy. The property, THF ≈ Tgβ, had not been pointed out before by others or in any of the quasielastic neutron and light scattering studies of various amorphous polymers and van der Waals small molecular glass-formers over the past three decades. The generality and fundamental importance of this novel property revitalize the data from these previous publications, making it necessary to be reckoned with in any attempt to solve the glass transition problem. In our rationalization, the property arises first from the fact that the JG β-relaxation and the caged dynamics both depends on density and entropy. Second, the JG β-relaxation is the terminator of the caged dynamics, and hence the two processes are inseparable or effectively coupled. Consequently, the occurrence of the secondary glass transition at Tgβ necessarily is accompanied by corresponding change in the temperature dependence of the NCL, I, or ⟨u(2)⟩ of the fast caged dynamics at THF ≈ Tgβ.

The significance of the amorphous potential energy landscape for dictating glassy dynamics and driving solid-state crystallisation

“…1 also contains results from BLS, 36 neutronscattering mean-squared-displacement (MSD), 37 and deuteron nuclear magnetic resonance ( 2 H-NMR) spin-lattice relaxation 38 measurements on ortho-terphenyl (OTP), and neutron-scattering MSD, 39 positron spectroscopy (PS), 40,41 quasi-elastic light scattering (QELS), 39 and dielectric spectroscopy 42 for polymethyl methacrylate (PMMA), which exhibit the same temperature-dependent behaviour as described for sorbitol, although with different values for T ga and T gb . It is important to comment that as noted previously, 18,19 these data represent the detection of T ga and T gb across timescales spanning over 15 orders of magnitude, indicating that a fundamental link between the processes must exist.…”

“…Additionally, the absolute values of T g are known to be slightly dependent on the heating/cooling rate as well as the thermal history of the sample, 35 however in the case of this study these relatively minor temperature shifts were minimised by using very slow cooling rates as well as the lack of significance on the overall aim of this work, which is related to the universality of the observed phenomena. Furthermore, to highlight that the results presented in this work are not simply confined to small-molecule or hydrogen bonded systems like sorbitol, and as originally suggested based on previous reports, 18,19 Fig. 1 also contains results from BLS, 36 neutronscattering mean-squared-displacement (MSD), 37 and deuteron nuclear magnetic resonance ( 2 H-NMR) spin-lattice relaxation 38 measurements on ortho-terphenyl (OTP), and neutron-scattering MSD, 39 positron spectroscopy (PS), 40,41 quasi-elastic light scattering (QELS), 39 and dielectric spectroscopy 42 for polymethyl methacrylate (PMMA), which exhibit the same temperature-dependent behaviour as described for sorbitol, although with different values for T ga and T gb .…”

“…There have been attempts to reconcile these observations within the context of the coupling model, 45 which argues that spectral changes observed at terahertz frequencies are coupled to their fundamental relaxations via a so-called 'fast process', typically referred to as 'cage-rattling' motion. [17][18][19]21 However,…”

“…T ga and T gb ), which are loosely defined as the slowing of the corresponding dielectric relaxation processes beyond time scales that are readily detected by experiment (E100 s). 17 It is important to clarify that T gb has only recently been explored in-depth, 14,18,19 and it represents the vitrification of the b-relaxation process as originally described by Johari and Goldstein. 20 There have been attempts to link the experimental observations at frequencies exceeding the dielectric relaxations (such as mid-infrared, Raman or terahertz spectroscopies) to the fundamental process of collective translational and (hindered) rotational motions by means of a coupling process.…”

Terahertz response of organic amorphous systems: experimental concerns and perspectives

“…A further examination of these results and other high-frequency data on amorphous systems clearly revealed that the vitrification of JG-beta relaxation is a universal process observed across a wide size and chemistry of glass-forming systems, and that the sensitivity of the high-frequency techniques to this effect is linked to the associated changes in the caged dynamics [2,7,8].…”