Comments to the paper “The need to reconsider tradional free volume theory for polymer electrolytes”

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.

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

From positron annihilation lifetime spectroscopy analyzed with the new routine LT9.0 and pressure-volume-temperature experiments analyzed employing the equation of state (EOS) Simha-Somcynsky lattice-hole theory (SS EOS) the microstructure of the free volume and its temperature dependence of an oligomeric epoxy resin (ER6, M(n) approximately 1750 g/mol , T(g)=332 K ) of diglycidyl ether of bisphenol-A (DGEBA) have been examined and characterized by the hole free-volume fraction h, the specific free and occupied volumes V(f)=hV and V(occ)=(1-h)V, and the size distribution (mean, <nu(h)>, and mean dispersion, sigma(h)) and the mean density N(h)'=V(f)/<nu(h)>, of subnanometer-size holes. The results are compared with those from a previous work [G. Dlubek, Phys. Rev. E 73, 031803 (2006)] on a monomeric liquid of the same resin (ER1, M(n) approximately 380 g/mol, T(g)=255 K ). In the glassy state ER6 shows the same hole sizes as ER1 but a higher V(f) and N(h)'. In the liquid V(f), <nu(h)>, dV(f)/dT, and dV(f)/dP are smaller for ER6. The reported dielectric alpha relaxation time tau shows certain deviations from the free-volume model which are larger for ER6 than for ER1. This behavior correlates with the SS EOS, which shows that the unit of the SS lattice is more heavy and bulky and therefore the chain is less flexible for ER6 than for ER1. The free-volume fraction h in the liquid can be described by the Schottky equation h proportional to exp(-H(h)/k(B)T) , where H(h)=7.8 - 6.4 kJ/mol is the vacancy formation enthalpy, which opens a different way for the extrapolation of the equilibrium part of the free volume. The extrapolated h decreases gradually below T(g) and becomes zero only when 0 K is reached. This behavior means that no singularity would appear in the relaxation time at temperatures above 0 K. To quantify the degree to which volume and thermal energy govern the structural dynamics, the ratio of the activation enthalpies E(i)=R[(d ln tau/dT(-1))]i, at constant volume V and constant pressure P(E(V)/E(P)), is frequently determined. We present arguments for necessity to substitute E(V) by E(Vf), the activation enthalpy at constant (hole) free volume, and show that E(Vf)/E(P) changes as expected: it increases with increasing free volume, i.e., with increasing temperature, decreasing pressure, and decreasing molecular weight. E(Vf)/E(P) exhibits smaller values than E(V)/E(P), which leads to the general inference that the free volume plays a larger role in dynamics than concluded from E(V)/E(P). The same conclusion is obtained when scaling tau to T(-1)V(f)(-gamma) instead of to T(-1)V(-gamma), where both gamma's are material constants.

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.

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.