Free-volume dynamics in glasses and supercooled liquids

Free volume dilatation in polymers by ortho-positronium

The possibility of positronium induced free volume cavity expansion in some polymers above the glass transition temperature was investigated using experimental positron annihilation lifetime data from the literature for polydimethylsiloxane, polyisobutylene, and polybutadiene as function of temperature. The results suggest that free volume sites can expand towards an equilibrium size, determined as the equilibrium Ps-bubble size defined earlier for low-molecular-weight liquids. The expansion can be explained by the increase of molecular mobility and hence decrease of relaxation times, which at the higher temperatures approach the o-Ps lifetimes. Nanoscale viscosities were estimated using Navier-Stokes equation and were found to be several orders of magnitude lower than the macroscopic viscosity at the same temperature.

Positron annihilation and relaxation dynamics from dielectric spectroscopy: poly(vinylmethylether)

We report on the temperature dependence of the lifetime of the ortho-positronium (o-Ps), τ(3), annihilation in amorphous polymer poly(vinylmethylether) (PVME) from positron annihilation lifetime spectroscopy (PALS). We show that the behavior of τ(3)(T) can be divided into five regions, each of them having a linear temperature dependence, and that the crossover PALS temperatures situated at T(b1)(G), 0.76T(g)(PALS), T(b1)(L) = 1.14T(g)(PALS) and T(b2)(L) = 1.37T(G)(PALS), and marking the discontinuity in the free volume microstructure are related to various dynamic features from neutron scattering (NS) and broadband dielectric spectroscopy (BDS). First, a slight change in the PALS response in the glassy PVME at T(b1)(G) is related to the onset of the excess wing in an apparent correspondence with the fast secondary β motion from NS. A further slight bend in the liquid state at T(b1)(L) is related to a high-frequency tail of the primary α process as well as to the slow secondary β relaxation from BDS. In addition, it lies also in the vicinity of the crossover temperature, T(B)(βKWW), in the spectral dispersion of the primary α process, indicating a connection of the change in the o-Ps lifetime with the variation in the width of the primary α relaxation times distribution. Finally, the τ(3) value at T(b2)(L) is close to the mean relaxation time of the primary α process, τ(α), in coincidence with the crossover in the secondary effective β process between two regimes in the liquid PVME. All these relationships point to very close connections between the PALS response and the dynamic behavior of PVME, which can be explained in terms of the temperature dependence of the probability function of the liquid-like and the solid-like domains, as obtained from the two-order parameter (TOP) model description of the liquid to glass transition in glass-formers.

Positron annihilation response and broadband dielectric spectroscopy: salol

A phenomenological analysis of the ortho-positronium (o-Ps) annihilation from positron annihilation lifetime spectroscopy (PALS) and the dynamics from broadband dielectric spectroscopy (BDS) are reported on a small molecular glass former of intermediate H-bonding and fragility: salol. The dielectric spectra extend over a very broad frequency range of about 2 × 10(-2)-3.5 × 10(11) Hz, providing information on the α-relaxation, the secondary relaxation giving rise to the excess wing, and the shallow high-frequency minimum in the micro- to milli-meter wave range. A number of empirical correlations between the o-Ps lifetime, τ(3)(T), and the various spectral and relaxation features have been observed. Thus, the phenomenological evaluation of the τ(3)(T) dependence of the PALS response of the amorphous sample reveals three characteristic PALS temperatures: T(g)(PALS), T(b1)(L) = 1.15T(g)(PALS) and T(b2)(L) = 1.25T(g)(PALS), which are discussed in relation to similar findings for some typical small molecular vdW- and H-bonded glass formers. A slighter change of the slope at T(b1)(L) appears to be related to the transition from excess wing to the primary α-process-dominated behavior, with the secondary process dominating in the deeply supercooled liquid state below T(b1)(L). The high-temperature plateau effect in the τ (3)(T) plot occurs at T(b2)(L) and agrees with the characteristic Stickel temperature, T(B)(ST), marking a qualitative change of the primary α process, but it does not follow the relation T(b2)(L) < T(α) [τ(3)(T(b2)) < τ(α)]. Both effects at T(b1)(L) and T(b2)(L) correlate with two crossovers in the spectral shape and related non-exponentiality parameter of the structural relaxation, β (KWW). Finally, the application of the two-order parameter (TOP) model to the structural relaxation as represented by the primary α relaxation times from BDS leads to the characteristic TOP temperature, T(m)(c), close to T(b1) from PALS. Within this model the phenomenological interpretation is offered based on changes in the probability of occurrence of solid-like and liquid-like domains to explain the dynamic as well as PALS responses. In summary, all the empirical correlations support further very close connections between the PALS response and the dielectric relaxation behavior in small molecule glass formers.

Free volume from positron lifetime and pressure-volume-temperature experiments in relation to structural relaxation of van der Waals molecular glass-forming liquids

Positron annihilation lifetime spectroscopy (PALS) is employed to characterize the temperature dependence of the free volume in two van der Waals liquids: 1, 1'-bis(p-methoxyphenyl)cyclohexane (BMPC) and 1, 1'-di(4-methoxy-5-methylphenyl)cyclohexane (BMMPC). From the PALS spectra analysed with the routine LifeTime9.0, the size (volume) distribution of local free volumes (subnanometer size holes), its mean, [v(h)], and mean dispersion, σ(h), were calculated. A comparison with the macroscopic volume from pressure-volume-temperature (PV T) experiments delivered the hole density and the specific hole free volume and a complete characterization of the free volume microstructure in that sense. These data are used in correlation with structural (α) relaxation data from broad-band dielectric spectroscopy (BDS) in terms of the Cohen-Grest and Cohen-Turnbull free volume models. An extension of the latter model allows us to quantify deviations between experiments and theory and an attempt to systematize these in terms of T(g) or of the fragility. The experimental data for several fragile and less fragile glass formers are involved in the final discussion. It was concluded that, for large differences in the fragility of different glass formers, the positron lifetime mirrors clearly the different character of these materials. For small differences in the fragility, additional properties like the character of bonds and chemical structure of the material may affect size, distribution and thermal behaviour of the free volume.

Temperature dependence of the free volume from positron lifetime experiments and its relation to structural dynamics: phenylphthalein-dimethylether

Positron annihilation lifetime spectroscopy (PALS) was used to study the microstructure of the free volume in the temperature range between 103 K and 393 K in phenylphthalein-dimethylether (PDE), a low-molecular-weight glass former. Using the routine LIFETIME9.0, the ortho-positronium (o-Ps) lifetime distribution was analyzed, and from this, the volume distribution gn(vh) of subnanometer-size holes was calculated. From a comparison of PALS and specific volume data, the number density and the volume fraction of holes were estimated. These free-volume data, as a function of temperature, were used to test the validity of the Cohen-Turnbull (CT) free-volume theory. It was found that the structural relaxation from dielectric spectroscopy can be described by the CT theory after introducing a corrected free volume (Vf-DeltaV), where DeltaV=0.014 cm3/g. The extended free-volume theory of Cohen and Grest can be fitted to the dielectric-relaxation and free-volume data, but the parameters of both fits are not consistent. PDE shows some peculiar features. The "knee" in the o -Ps lifetime expansion and crossover in temperature dependence of the frequency of the primary dielectric relaxation process occur at different temperatures. In addition, the change in the Vogel-Fulcher-Tammann parameters at TB/Tg=1.1 has no observable effect on the mean free volume vh (or Vf). The size of the smallest representative freely fluctuating subsystem, VSV estimated from the standard deviation sigmah of gn(vh), decreases from 4.1 nm3 to 2.6 nm3 when the temperature increases from T/Tg=1.0 to 1.15. Correspondingly, the length of dynamic heterogeneity, xi=VVS1/3, decreases from 1.6 nm to 1.4 nm. It is concluded that at T/Tg approximately 1.10=TB/Tg the system transforms from a heterogeneous to a homogeneous (true) liquid.

Characteristic temperatures of glassy behaviour in a simple liquid

A model for the metastable liquid in terms of holes present in the amorphous structure is considered using the classical density functional theory (DFT). For a one component Lennard-Jones liquid we obtain the temperature dependence of the free volume v(f) in the metastable state. A temperature T(0), similar to that of the characteristic transition of the free volume theory, is identified by extrapolating v(f)(T) to zero. The Kauzmann temperature T(K) is also obtained here by extrapolating the entropy difference between the supercooled state and that of the crystal to zero. We compare the temperatures T(0) and T(K) obtained in our model with other two characteristic temperatures for glassy behaviour, namely (a) the dynamic transition temperature T(c) of the mode coupling theory (MCT) and (b) the glass transition temperature T(g) which was obtained by Leonardo et al (2000 Phys. Rev. Lett. 84 6054) from studying the violation of the fluctuation-dissipation theorem. All the four temperatures, obtained from independent routes, are located with respect to the melting temperature T(m) in a manner which is in agreement with experiments.

Free volume of an epoxy resin and its relation to structural relaxation: evidence from positron lifetime and pressure-volume-temperature experiments

The microstructure of the free volume and its temperature dependence in the epoxy resin diglycidyl ether of bisphenol-A (DGEBA) have been examined using positron annihilation lifetime spectroscopy (PALS, 80-350K, 10(-5) Pa) and pressure-volume-temperature (PVT, 293-470 K, 0.1-200MPa) experiments. Employing the Simha-Somcynsky lattice-hole theory (S-S eos), the excess (hole) free volume fraction h and the specific free and occupied volumes, Vf=hV and Vocc=(1-h)V, were estimated. From the PALS spectra analyzed with the new routine LT9.0 the hole size distribution, its mean, <Vh>, and mean dispersion, sigma h, were calculated. <Vh> varies from 35 130 A3. From a comparison of <Vh>with V and Vf, the specific hole number N'h was estimated to be independent of the temperature [Nh(300 K)=N'h/V=0.65 nm-3]. From comparison with reported dielectric and viscosity measurements, we found that the structural relaxation slows down faster than the shrinkage of the hole free volume Vf would predict on the basis of the free volume theory. Our results indicate that the structural relaxation in DGEBA operates via the free-volume mechanism only when liquidlike clusters of cells of the S-S lattice appear which contain a local free volume of approximately 1.5 or more empty S-S cells. The same conclusion follows from the pressure dependency of the structural relaxation and Vf. It is shown that PALS mirrors thermal volume fluctuations on a subnanometer scale via the dispersion in the ortho-positronium lifetimes. Using a fluctuation approach, the temperature dependency of the characteristic length of dynamic heterogeneity, xi, is estimated to vary from xi=1.9 nm at Tg to 1.0 nm at T/Tg>1.2. A model was proposed which relates the spatial structure of the free volume as concluded from PALS to the known mobility pattern of the dynamic glass transition at low (cooperative alpha-relaxation) and high (alpha-relaxation) temperatures. We discuss possible reasons for the differences between the results of our method and the conclusion from dynamic heat capacity.

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

Dielectric spectra of the beta relaxation in glassy and ultraviscous liquid diethyl phthalate show that its relaxation strength Delta epsilon(beta), the distribution of times, and the relaxation rate are more sensitive to temperature T in the ultraviscous liquid than in the glassy state. The Delta epsilon(beta) against temperature plot has an elbow-shaped break near T(g) of approximately 181 K, which is remarkably similar to that observed in the entropy, enthalpy, and volume against temperature plots, and in the plot of Delta epsilon(beta) against the liquid's entropy minus its 0 K value. The ratio of Delta epsilon(beta) to diethyl phthalate's entropy, after subtracting the 0 K value, is 1.08 x 10(-3) mol K/J in the glassy state at 120.4 K, which decreases slowly to 0.81 x 10(-3) mol K/J at 176 K near T(g) and thereafter rapidly increases to 1.57 x 10(-3) mol K/J at 190 K. Variation in Delta epsilon(beta) parallels the variation of the entropy. A change in the activation energy of the beta process at T>T(g) indicates that its rate is also determined by the structure of the ultraviscous liquid. Features of beta relaxation are consistent with localized motions of molecules and may not involve small-angle motions of all molecules.

Activation Energy−Activation Volume Master Plots for Ion Transport Behavior in Polymer Electrolytes and Supercooled Molten Salts

We demonstrate the use of activation energy versus activation volume "master plots" to explore ion transport in typical fragile glass forming systems exhibiting non-Arrhenius behavior. These systems include solvent-free salt complexes in poly(ethylene oxide) (PEO) and low molecular weight poly(propylene oxide) (PPO) and molten 2Ca(NO3)2.3KNO3 (CKN). Plots showing variations in apparent activation energy EA versus apparent activation volume VA are straight lines with slopes given by M = DeltaEA/DeltaVA. A simple ion transport mechanism is described where the rate determining step involves a dilatation (expressed as VA) around microscopic cavities and a corresponding work of expansion (EA). The slopes of the master plots M are equated to internal elastic moduli, which vary from 1.1 GPa for liquid PPO to 5.0 GPa for molten CKN on account of differing intermolecular forces in these materials.