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.

Effect of free volume and temperature on the structural relaxation in polymethylphenylsiloxane: A positron lifetime and pressure-volume-temperature study

The microstructure of the free volume and its temperature dependence in polymethylphenylsiloxane (PMPS) have been examined using positron annihilation lifetime spectroscopy (PALS) and pressure-volume-temperature experiments. The hole-free volume fraction h and the specific hole-free and occupied volumes, Vf=hV and Vocc=(1-h)V, were estimated employing the Simha-Somcynsky (SS) lattice-hole theory. From the PALS spectra analyzed with the new routine LT9.0 the hole size distribution, its mean, <nuh>, and mean dispersion, sigmah, were calculated. A comparison of <nuh> with V and Vf delivered a constant specific hole number Nh'. Using a fluctuation approach the temperature dependency of the volume of the smallest representative freely fluctuating subsystem, <VSV>, is estimated to vary from approximately 8.5 nm3 at Tg to approximately 3 nm3 at T/Tg>or=1.15. Unlike other polymers, the segmental relaxation from dielectric spectroscopy of PMPS follows the Cohen-Turnbull free volume theory almost perfectly in the temperature and pressure ranges between 243 and 279 K and 0 and approximately 100 MPa. This behavior correlates with the small mass of the SS lattice mer which indicates the high flexibility of the PMPS chain. Above 293 K and approximately 150 MPa, the free volume prediction gives relaxation times that are too small, which indicates that effects of thermal energy must be included in the analysis. To quantify the degree to which volume and thermal energy govern the structural dynamics the ratio of the activation enthalpies, Ei=R[(d ln taudT1)]i (tau-relaxation time of alpha relaxation), at constant volume V and constant pressure P, EV/EP, is frequently determined. The authors present arguments for necessity to substitute EV with EVf, the activation enthalpy at constant (hole) free volume, and show that EVf/EP changes as expected: increasing with increasing free volume, i.e., with increasing temperature and decreasing pressure. EVf/EP (=0.04-0.1) exhibits remarkably smaller values than EV/EP (=0.44-0.53), which leads to the inference that the free volume plays a distinctly larger role in dynamics than traditionally concluded from EV/EP. This conclusion is in agreement with the results of our more direct Cohen-Turnbull free volume analysis.