Free-volume dynamics in glasses and supercooled liquids

Abstract

A free-volume theory is developed based on the defect diffusion model (DDM). In addition, positronium annihilation lifetime spectroscopy (PALS) ortho-positronium free-volume and intensity data are presented for poly(propylene glycol) with a molecular weight of 4000 (PPG 4000) in both the glassy and liquid states and dielectric relaxation and electrical conductivity data are reported for PPG 4000 in the liquid state. The DDM is used to interpret all of the data for PPG 4000 and previously reported PALS and dielectric relaxation data for glycerol. It is shown that while the PPG 4000 data exhibit a preference for the three-halves power law, the data for glycerol favor the first power (standard Vogel-Fulcher-Tammann) law. Good agreement between the DDM and the experimental results is found for all of the electrical data and the PALS free-volume data. While reasonable agreement is also found for the PALS intensity data for PPG 4000, a discrepancy exists between the experimental PALS intensity data and theory for glycerol. For the electrical conductivity for PPG 4000, a transition is observed at the same temperature (about 1.4 T(g) where T(g) is the glass transition temperature) where the PALS free volume changes from steeply rising with temperature to approximately independent of temperature. The same behavior is observed at about 1.5 T(g) for previously reported dielectric relaxation and PALS data for glycerol. Model parameters are presented that show the dominance of mobile single defects above (1.4-1.5) T(g) and the dominance of immobile clustered single defects below T(g) . Finally, a coherent picture of glasses and glass-forming liquids is presented based on the theory and results of the experiments.

Orientation polarization from faster motions in the ultraviscous and glassy diethyl phthalate and its entropy

“…3 in Ref. 21 whose size increases with the temperature, and the plot of the hole volume against T of different polymers and molecular materials show a qualitatively similar elbow shaped, [20][21][22][23][24][25] as the plot of ⌬⑀ ␤ observed here. These issues need to be resolved before interpreting the NMR studies of ␤ relaxation in terms of small-angle motions of all molecules in the structure.…”

“…More recently the same elbow shape has been observed in the corresponding plot of the hole volume measured by positron annihilation lifetime spectroscopy ͑PALS͒. [20][21][22][23][24][25] The plot of ␣ ␤ against the temperature in Fig. 3͑B͒ shows a shallow minimum at T immediately above T g in the 180-187 K range.…”

“…5 One of the characteristic features of the ␤ relaxation is that its relaxation strength increases with increase in the temperature T. 4,5,18 This means that as the number of molecules contributing to the availability of distinct configurations increases with increase in T, C p,exc and S exc and any contribution to volume should increase, and hence one would expect that the increase in the ␤-relaxation strength may be at least qualitatively related to C p,exc and S exc and possibly to free volume. Bartoš and co-workers [19][20][21][22][23][24][25] have studied a series of glasses, both molecular and polymeric and have found that as T is increased, the hole volume V h in the structures of the glass and ultraviscous liquid also increases slowly. It increases slowly in the glassy state and increases rapidly in the ultraviscous liquid or rubber state at T Ͼ T g , thus showing an elbowlike feature in its plot against T. Thus, two more quantities, namely, ͑d⌬⑀ ␤ / dT͒ p ͓see Ref.…”

Positron annihilation and relaxation dynamics from dielectric spectroscopy and nuclear magnetic resonance: Cis–trans-1,4-poly(butadiene)

“…Recent instrumental and spectral analytical advances in BDS [29][30][31] enable to reveal further connections between the various features of the PALS response and the glassy dynamics. 26,[32][33][34][35][36][37][38][39][40] Two empirical T b2 and T L b1 rules establish the specific relationships between the o-Ps lifetime, τ 3 , and the primary α relaxation time, τ α , namely, τ α (T b2 )∼ 10 −9 s or τ α (T b1 ) ∼ 10 −6±1 s, respectively. 26,32 In the former case, for many glass-formers at the onset of the plateau or quasi-plateau effect in the PALS response the relation τ 3 ∼ = τ α has been often found.…”

Free volume dilatation in polymers by ortho-positronium

“…[14][15][16][17][18][19][20][21][22] A major increase of slope at low temperatures reflects the transition of the polymer from a glassy to a rubbery state (at the glass transition temperature T g ) and is accompanied by an increase of the expansion coefficient of the macroscopic volume. At temperatures above approximately 1.2-1.6 × T g , a clear decrease in slope may be observed.…”