The temperature dependence of the local free volume in polyethylene and polytetrafluoroethylene: A positron lifetime study

Positron lifetime measurements, performed in the temperature range 80–300 K, are reported for polyethylene (PE) and polytetrafluoroethylene (PTFE). The lifetime spectra have been analyzed using the data processing routines LIFSPECFIT and MELT. Two long-lived components appear, which are attributed to pick-off annihilation of ortho-positronium in crystalline regions and at holes in the amorphous phase. The ortho-positronium lifetimes, τ₃ and τ₄, are used to estimate the crystalline packing density and the size of local free volumes in the crystalline and amorphous phases. The interstitial free volume in the crystals exhibits a weak linear increase with the temperature which is attributed to thermal expansion of the crystal unit cell. In the amorphous phase, the hole volume varies between 0.053 and 0.188 nm³ (PE) and between 0.152 and 0.372 nm³ (PTFE). Its temperature variation may be fitted by two straight lines, the intersection of which is used to estimate a glass transition temperature of T_g = 195 K for both PE and PTFE. The slopes of the free volume in the glassy and crystalline phases with the temperature correlate well with each other. The coefficients of thermal expansion of the hole volume are compared with the macroscopic volume change below and above the glass transition. From this comparison a fractional hole volume at T_g of 4.5 (PE) and 5.7% (PTFE) and a number of 0.73 (PE) and 0.36 (PTFE) × 10²⁷ holes/m³ is estimated. Finally, it is found that the intensity of o-Ps annihilation in crystals shows a different temperature dependence to that in the amorphous phase. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1513–1528, 1998     

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, , and mean dispersion, sigmah, were calculated. A comparison of 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, , 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.     

Temperature dependence of free volume of polyacrylamide gels studied by positron lifetime measurements

Changes of positronium (Ps) cavity radii in polyacrylamide and poly(N-isopropylacrylamide) gels were studied from 120 to 300 K by positron lifetime technique and it has been shown that the Ps cavity radius in the hydrogels changes by three or four stages. Temperature dependence of the Ps cavity radius exhibits variations similar to common polymers around the glass transition temperature. Hydrophilicity of the polymer chains significantly affects the Ps cavity radius just below 273 K. These results suggest an important role of free volume on the state of water in hydrogels.     

Radiation induced nano-scale free volume modifications in amorphous polymeric material: a study using positron annihilation lifetime spectroscopy

Radiation exposure modifies the nano scale free volume of the polymers which has direct correlation to certain properties of polymeric materials. CR-39 (DOP) polycarbonate polymeric films were exposed to gamma radiation at different doses for the study of nano scale free volume as well as structural and optical properties. An overall increase in the number of free volume holes at all doses was observed. UV–visible studies showed an improvement in the optical properties due to decrease in direct band gap energy. X-ray diffraction spectra of the polymer samples showed the increased amorphous nature of the polymer.     

The size and number of local free volumes in polypropylenes: A positron lifetime and PVT study

The temperature dependence of the mean size of local free volumes in an amorphous atactic (aPP) and a semicrystalline syndiotactic polypropylene (sPP), and an amorphous ethylene‐propylene copolymer (E‐co‐P48) has been studied. Pressure‐volume‐temperature (PVT) experiments were performed for aPP, from which the hole fraction h of the Simha‐Somcynsky theory and the number density of holes were estimated. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 3089–3093, 2003     

Experimental free volume aspects of the polymer rheology as obtained by positron annihilation lifetime spectroscopy

The ortho‐positronium (o‐Ps) annihilation parameters, i.e. the mean o‐Ps lifetime, τ₃, and the o‐Ps relative intensity, I₃, in cis‐1,4‐polybutadiene (cis‐1,4‐PBD) and polyisobutylene (PIB) over a wide temperature range including the glass‐liquid transition have been measured by means of positron annihilation lifetime Spectroscopy (PALS). From them the free volume microstructural characteristics, i.e. the mean free volume hole size, V_h, and the free volume hole fraction, f_h, have been determined via a semiempirical quantum‐mechanical model of o‐Ps in a spherical hole or a phenomenological model of volumetric and free volume hole properties, respectively. Consequently, the literature rheological data for both the above‐mentioned polymers have been related to the free volume hole fractions via the WLF‐Doolittle type equation. It has been found that i) in the case of PIB this equation holds over 130K above the glass transition temperature T_g and ii) in the case of cis‐PBD the WLF‐Doolitle equation is valid in the temperature range over 60K above 1.3T_g, but below 1.3T_g down to T_g the modified WLF‐Doolittle‐Macedo‐Litovitz equation with the additional activation‐energy term describes the shift factor data better.     

Temperature dependence of positron annihilation lifetime spectra for polyethylene: positron irradiation effects

Lifetime spectra for linear and branched polyethylene have been measured as a function of temperature. The longest lifetime, τ₃, and its intensity, I₃, are traced over a temperature range of 105–370 K. The lifetime decreases with decreasing temperature, and upon reheating the plot is retraced. I₃ has a minimum near 265 K with considerable hysteresis in the cooling/heating cycle. At the lower temperatures the increase in I₃ is attributed to source irradiation.     

A positron annihilation lifetime study of isotactic polypropylene

Positron lifetime studies were performed on well-characterized annealed and quenched samples of isotactic polypropylene. The positron experiments were conducted from ?20 to 110°C as a function of both heating and cooling. Of the three decaying exponential components resolved from the lifetime spectra, only the long-lifetime ortho-positronium (o-Ps) pickoff component was affected by the changes in temperature. The behavior of both the lifetime and intensity of the o-Ps component was interpreted with the aid of x-ray diffraction, densitometry, and optical microscopy examinations and results from previously reported investigations of the thermal transition behavior of polypropylene. The present experiments demonstrate that o-Ps lifetimes were similar for both the annealed and quenched samples, independent of thermal cycling, while the o-Ps component intensity was significantly larger for the quenched material during heating, with both sample types exhibiting a significant hysteresis upon cooling. These results suggest that the mean free-volume cavity size is independent of prior thermal treatment, while the density of free-volume sites is a sensitive function of structure and prior thermal history. The variations of lifetime and of intensity with temperature have provided insight into polypropylene's glass transition phenomena.     

Study of free volume parameters of polystyrenes of different molecular architecture by positron annihilation lifetime measurement

Differences of size, content and size distribution of free volumes in linear branched and three-armed polystyrenes, synthesized by radical and anionic processes, were observed by positron annihilation lifetime measurements. The temperature dependence of an average free volume radius was quite similar among polystyrenes of different architectures and molecular weight distributions. The free volume radius increased with temperature, from 0.27 nm (T:60 K) to 0.29 nm (T:260 K) and 0.30 nm (T _g:363 K), then to 0.35 nm (423 K), showing turning at and transition temperature. The free volume content decreased from 60 K to 220 K to 300 K showing peculiar minimum at 220 K to 300 K depending on the molecular shape, increased above 320 K, upto 340 to 360 K. The free volume contents decreased with an increase of molecular weight and by an addition of oligomer or plasticiser, suggesting differences in relaxation time or molecular motion between the edge and middle portions of molecular chain and filling effect of smaller molecules in free volumes, respectively. The apparent free volume fraction showed clear variations atT andT _g. Size distribution of free volumes suggested more complicated behavior of free volume upon the molecular relaxations and filling effect.     

Temperature and pressure dependence of the free volume in the perfluorinated polymer glass CYTOP: A positron lifetime and pressure‐volume‐temperature study

The microstructure of the free volume was studied for an amorphous perfluorinated polymer (T_g = 378 K). To this aim we employed pressure–volume–temperature experiments (PVT) and positron annihilation lifetime spectroscopy (PALS). Using the Simha‐Somcynsky equation of state the hole free volume fraction h and the specific free and occupied volumes, V_f = hV and V_occ = (1 ? h)V, were determined. Their expansivities and compressibilities were calculated from fits of the Tait equation to the volume data. It was found that in the glass V_occ has a particular high compressibility, while the compressibility of V_f is rather low, although h (300 K) = 0.108 is large. In the rubbery state the free volume dominates the total compressibility. From the PALS spectra the hole size distribution, its mean, 〈v_h〉, and mean dispersion, σ_h, were calculated. From a comparison of 〈v_h〉 with V_f a constant hole density of N_h′ = 0.25 × 10²¹ g^?1 was estimated. The volume of the smallest representative freely fluctuating subsystem, 〈V_SV〉 ∝ 1/σ_h², is unusually small. This was explained by an inherent topologic disorder of this polymer. 〈v_h〉 and σ_h show an exponential‐like decrease with increasing pressure P at 298 K. The hole density, calculated from N_h′ = V_f/〈v_h〉, seems to show an increase with P which is unexpected. This was explained by the compression of holes in the glass in two, rather than three, dimensions. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2519–2534, 2007     

On the relation between positron annihilation lifetime spectroscopy and lattice‐hole‐theory free volume

A coincidence between the temperature‐dependent hole (free volume) fraction h above the glass transition temperature, derived from lattice‐hole theory, and the corresponding function h_Ps obtained from positronium lifetime spectroscopy has been previously observed for four polystyrene fractions ranging from 4000 to 400,000 in molar mass. This result was based on the assumed proportionality of h_Ps and the product of the orthopositronium intensity I₃ and the mean cavity volume, the proportionality constant C being molar mass dependent. However, a recent analysis of the data based on volume arguments by Olson and Jamieson revealed systematic departures between the two sets of free volume functions. We reexamine the situation by departing from the customary assumption of spherical cavities, and allowing for nonspherical geometries represented by prismatic or cylindrical disks. Agreement between spectroscopic and thermodynamic functions ensues with fixed, temperature‐independent asymmetry factors decreasing with increasing molar mass. These tentative findings suggest that systematic studies of melts with varying chain flexibility and molar mass should be attempted. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2225–2229, 2005     

Positron annihilation lifetime studies of free volume in gelatin

The variations of size, intensity, and size distribution of free volumes generated in the network of molecular chains of gelatin at the sol-gel transition were studied by means of the positron annihilation lifetime technique. Although variation in average free-volume radius was not recognized, a variation of free-volume content was observed at the sol-gel transition point of gelatin with an addition of saccharose.     

A positron annihilation lifetime study of isothermal structural relaxation in bisphenol-A polycarbonate

Positron annihilation lifetime spectroscopy has been used to study the isothermal relaxation response of compression molded bisphenol-A polycarbonate at temperatures of 263, 273, and 303 K. The temperature dependence of both the lifetime and intensity of the ortho-Positronium (o-Ps) pickoff component is discussed in terms of ductile-to-brittle transition behavior and free volume theory. An additive exponential model and the Williams–Watt model were used to analyze the relaxation as a function of temperature and provided results consistent with the anticipated molecular mobility of polycarbonate at sub-T_g temperatures.     

Positron annihilation lifetime studies of free volume in ovalbumin gels

The dependence upon concentration of sodium chloride of free volume in ovalbumin gels, a main component of an egg white, is studied by the positron annihilation lifetime technique. The average free-volume radius in ovalbumin gels was about 0.27 nm at 298 K, smaller than those of organic polymers such as low-density polyethylene (0.34 nm at 300 K) and polystyrene (0.29 nm at 300 K). These differences suggest that the positronium annihilates in free volumes located close to hydrogen bonds, thus decreasing average free-volume radius. Free-volume content decreased with the increase of NaCl concentration up to 30 mM. At lower concentrations of NaCl, it seems that a correlation exists between microscopic free volume and macroscopic hardness of the ovalbumin.     

A positron lifetime study of the electron-beam-induced polymerization of 1,6-hexanediol diacrylate

Positron lifetime measurements have been used to characterize the electron-beam-induced polymerization of 1,6-hexanediol diacrylate (HDODA). Lifetimes were measured as a function of radiation dose over a range of 0.5–7.0 Mrad and analyzed into three components. All three components exhibited some variation with radiation dose. Variations in the longest lifetime component have been interpreted in terms of changes in free volume. These data have been compared with polymer fraction data for electron-irradiated HDODA obtained by gel extraction and by NMR measurements. The positron lifetime parameter that correlates most closely with polymerization as measured by those techniques is the intensity of the longest lived component.     

Variation of free volume parameters of polyalkylmethacrylate derivatives in the range from 15 to 300 K probed by positron annihilation lifetime measurement

Positron annihilation lifetime measurements of PMMA, PEMA, PiPMA, PnPMA and PnBMA were performed in the temperature range between 15 and 300 K, where , and relaxational transitions occur for these polyalkylmethacrylates. The variations of free volume size and content calculated from the longest lifetime component against temperature are correlated to the results obtained by dielectric, viscoelastic and dynamic mechanical relaxation data of the polymers. The variations of free volume sizes and contents, apparent free volume fraction and size distribution of the polyalkylmethacrylates are well correlated with the rotational transitions of side chains. The location of free volumes, in which positronium annihilates can be estimated near the vicinity of alkyl groups bound to oxygen atom of side ester chains.     

A positron annihilation lifetime measurement system with an intense positron microbeam

An intense positron microbeam was formed using an electron linear accelerator. The beam is pulsed to apply positron lifetime spectroscopy to very small samples and to obtain positron lifetime images by scanning it. Positron lifetimes are measured with time resolution of <300 ps and with lateral spatial resolution of 30–100 μm. A counting rate of the γ-ray to measure positron lifetime is about 10³ s⁻¹ which is 10 times higher than that achieved by the radioisotope based microbeam.     

Free volume in C60 modified PPO polymer membranes by positron annihilation lifetime spectroscopy

PPO (poly(2,6-dimethyl-1,4-phenylene oxide)) is a well-known membrane material showing good gas separation properties. The incorporation of nanoparticles can enhance or deteriorate the performance of composite membranes, sometimes depending only on the way of the composite preparation. We have modified the PPO polymer with C60 fullerenes up to a content of 2 wt %. Previous investigations showed a strong dependence of permeability on whether the C60 is simply dispersed in the polymer or chemically bonded to the polymer chains. Free volume effects were suggested as an explanation but not experimentally confirmed. Here, we present free volume studies by positron annihilation lifetime spectroscopy. An additional long positron lifetime shows the increased free volume of composite samples, while the high electron affinity of C60 helps to indicate the homogeneity of the samples. Combining the presented results with permeability measurements refines the understanding of this promising membrane material.