Glass Transition and Secondary Relaxations in Molecular Liquids and Crystals

Abstract

Annals New York Academy of Sciences 0.05 17.2 mole % Chlorobenrene -c&-Decalin 0.01 tan 6 0.005 0.001 80 90 100 110 120 130 140 150 T /OK t FIGURE 1. The dielectric loss factor, tan 6 , of 17.2 mole% chlorobenzene/cis-decalin mixture at 1 k H z plotted against temperature, showing the temperature of the a and /3 relaxation peaks.quency. One maximum occurred at a temperature above the glass transition and the other, which was 1-2 orders of magnitude lower, occurred at several tens of degrees below the glass transition temperature Tg. A typical plot showing the two maxima is given in FIGURE 1, where tan 6 of 17.2 mole% solution of chlorobenzene in cis-decalin is plotted logarithmically against temperature at 1 kHz. Dilute solutions of halogen-substituted benzenes and naphthalenes in nonpolar solvent, cis-decalin,2 approximately 40 mole% mixtures of toluene, substituted benzenes and naphthalenes in pyridine2 and in tetrahydrofuran, pure liquids, e.g., isopropylbenzene,2 o-terphenyl,2 methyl-substituted h e p t a n o l~,~ dialkyl p h t h a l a t e~,~ insulating calcium nitrate tetrahydrate, and glucose-water mixtures of several compositions: all showed similar peaks in tan &temperature plots.The peak a t temperatures below Tg could not be detected in a few substances, namely in a mixture of chloronaphthalene in tetrahydrofuran,2 propylene carbonate,2 i~o -b u t a n o l ,~ I ,2-pr0panediol,~ 45 mole% Ca(NO3),KNO3,* and in glycerol,6 but the secondary relaxation could be clearly seen in a plot of tan 6 against the logarithm of frequency at temperatures below Tg in the chloronaphthalene-tetrahydrofuran mixture.2 The secondary relaxation could be clearly observed also in glycerol on the application of a few kilobam6 In other substances J o h a r i et al.: Molecular Liquids and Crystals 119 \ I / \ -/ \ / \ , / , I , \it can probably be either detected at high pressures or resolved (although less convincingly) bv a suitable analytical method as in ice.7 Without implying a similarity in their molecular mechanisms to the loss peaks seen in amorphous polymers, the relaxation observed above Tg is referred t o here as a relaxation and that observed immediately below Tg as p relaxation.The spectral features of the two relaxations were quite apparent. In the majority of substances, the plots of t " against the logarithm of frequency for a relaxation were asymmetric and had a half-width of 2-3 decades of frequency, which is many times higher than 1.40 decades for a single relaxation time. The frequency of 12 1 0 8 -w 6 PI1 4) 4 2 0 4 3 t W U 4) 2 I 0 17.2 molr % chlorobmronrcia-drcalln d ,' \ \ FIGURE 2. The dielectric loss c'' of 17.2 mole "/, chlorobenzenelcis-decalin mixture plotted logarithmically against frequency at 139.9"K ( 0 ) and 122.1"K ( 0 ) . The top curve is the (Y relaxation and the bottom curve the p relaxation region. The dashed curves are for a Debye-type single relaxation time. Johari et al.: Molecular Liquids and Crystals 34 mole % I-CHLORONAPHTHALENE-121 73 83 93 103 113 123 133 143 153 TEMPERATURE / O K FIGU...

Nature and properties of the Johari–Goldstein β-relaxation in the equilibrium liquid state of a class of glass-formers

“…These trends of the J-G ␤-peak in the Class A glass-formers are the same as that shown by the ␤-relaxation in Class B glass-formers such as toluene, 58 3-fluoraniline, 58 sorbitol, 59 and polybutadiene, 60 and can be considered as additional evidence that the ␤-relaxation of glycerol, PC, and PG we have resolved from their dielectric spectra are indeed the J-G ␤-relaxation. Thus the results of this work confirms the belief 7,8 that the J-G relaxation is an intrinsic feature of the glass transition of all glass-formers. Only its relaxation strength and the separation between its relaxation time and the ␣-relaxation time may vary from one glass-former to another.…”

“…7 Based on these results, it was proposed that the occurrence of these so-called Johari-Goldstein ͑J-G͒ ␤-relaxations is an inherent property of the supercooled state. 7,8 However, the microscopic origin of these ␤-relaxations is still a matter of controversy ͑see, e.g., Ref.…”

A robust comparison of dynamical scenarios in a glass-forming liquid

“…The aim of this exercise is to elucidate whether, in addition to the expected translational diffusion of the molecular centre of mass, all molecules are subjected to: either two additional (and distinct) relaxation processes affecting the entire ensemble (HG); or if some molecules are moving faster than others giving rise to the so-called islands of mobility (HT). 38,39 Mathematically the HG can be described by a multiplicative ansatz of dynamical processes in the time domain and, as such, it affects all molecules on the time scale of the a-relaxation. The HT, on the other hand, is based on the arithmetic sum of two processes, each one affecting a certain percentage of molecules at a-relaxation time scales.…”

Source of non-Arrhenius average relaxation time in glass-forming liquids

“…There is a general tendency that fragile liquids have broader distributions of relaxation times than strong liquids [27,28]. This rule, however, is not without exceptions [29,30].…”