Thermal variation of free-volumes size distribution in polypropylenes. Probed by positron annihilation lifetime technique

Positron annihilation lifetime measurement was applied to the study of free-volume properties in three kinds of polypropylene as a function of temperature in the range of 25–180°C at thermal equilibrium. Positron lifetime data for polypropylenes were analyzed with a Laplace inversion technique in order to obtain continuous positron annihilation lifetime (PAL) distributions. At each temperature, four distinct PAL distributions were recognized. The distribution of the longest lived component was associated with a pick-off annihilation of ortho-positronium (o-Ps) trapped in free-volume of amorphous region, which grew bigger as the temperature increased. The hole radius distributions of free-volumes were estimated from the results of o-Ps lifetime distributions. A detailed analysis showed a mean radius of free volumes was 0.34 nm at room temperature and that was 0.42 nm near the melting point for each specimen. The distributions of hole radii of free volumes were found to be broader after thermal treatments. The relaxation of free volumes was attributed to the thermal equilibrium and the evacuation of included molecules in free volumes. © 1995 John Wiley & Sons, Inc.     

Temperature dependence of the free volume in polytetrafluoroethylene studied by positron annihilation spectroscopy

The temperature dependence of the free volume holes in pure polytetrafluoroethylene (PTFE) and doped with 25% glass have been studied in the temperature range (30–250 °C) using positron annihilation lifetime spectroscopy. The data clearly revealed the glass transition temperatures for pure and doped PTFE are 130 and 110 °C, respectively. As the temperature increases, the free volume distribution becomes positioned at larger free volume hole size. A good correlation between the electrical conductivity and the o-Ps parameters was achieved.     

Detection of free volumes in polyaniline complexes with various acids by using positron lifetime spectroscopy

The positron lifetime spectroscopy (PLS), a non-destructive characterization method, utilizes positronium (Ps; an electron–positron bound state) as a probe and measures its lifetime in polymer free volumes. For the first time the free volumes have been estimated by PLS in polyaniline (PANI) complexes with various inorganic and organic acids. It was found that the o-Ps lifetime increases and the intensity decreases with increasing ionic radius of the counter-ions in PANI complexes. Obviously, larger counter anions result in enhanced mean size of the voids corresponding to the free volume in the bulk polymer.Electrical conductivity has been measured by conventional four-probe technique. The glass transition temperature and temperature of removal of the absorbed water have been determined by using differential scanning calorimetry. It was established fairly well correlation of the mentioned polymer parameters with the o-Ps lifetime and the free volume of PANI complexes, respectively. The greater free-volume results in a decrease of conductivity, glass transition temperature and temperature of removal of the absorbed water.     

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.     

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     

On the measurement of structural relaxation in polymers using positron annihilation lifetime spectroscopy

Positron annihilation lifetime spectroscopy has been identified as an effective means of characterizing the free volume content of amorphous polymers. The lifetime and intensity of the ortho-positronium (o-Ps) pick-off annihilation has been found to correlate with the average size and density of free volume sites, respectively. Recently, PALS has been used to evaluate and monitor the physical aging and structural relaxation of polymers in terms of both initial state and evolution in state with time. However, during extended PALS measurements in insulating materials, an electric field can build up due to positron-electron annihilation and can effectively reduce the probability of positronium formation. In this paper, an observed decrease in intensity associated with the o-Ps annihilation component in the glassy polymers polycarbonate and polystyrene is found to be unrelated to structural relaxation of the materials over the time periods examined as reported earlier by others, and, instead, to be more likely a result of electric charge build-up. © 1993 John Wiley & Sons, Inc.     

Temperature dependence of positron lifetime in ordered porous silica (SBA-3)

The temperature dependence of positron lifetime in uniform mesopores was analyzed. We used SBA-3 as the sample material, which possesses an ordered porous structure with uniform cylindrical mesopores. The positron lifetime corresponding to the annihilation in the mesopores increased gradually with a decrease in temperature down to 100 K, and its relative intensity also increased concomitantly. This result was attributed to the lower probability of the escape of the ortho-positronium (o-Ps) from the mesopores into the intergrain space at lower temperatures. An anomalous and sudden increase in the lifetime was observed at around 100 K; this result was in agreement with an increase in the positron lifetime reported in a previous study. It was revealed that the increase in the lifetime is very steep in cases of uniform mesopores, suggesting that the temperature dependence is influenced by the pore size.     

Positron age–momentum correlation studies of free volumes in polymers

Positron age–momentum correlation (AMOC) spectroscopy, which can sensitively probe momentum distributions of positrons and positronium (Ps), was conducted for studying the pick-off process of the triplet bound state ortho-Ps (o-Ps) with electrons at the walls of the free volumes in polymers. Influences of different chemical elements forming free volume were investigated. It was found that the momentum distribution of o-Ps pick-off annihilation sensitively depends on the electronic state in the free volumes. The feasibility of the chemical analysis relevant to the free volume in polymers is discussed.     

Positronium annihilation in amine-cured epoxy polymers

Positronium annihilation spectroscopy (PAS) has been used to study the microstructural properties of amine-cured epoxy polymers. We have determined the free-volume “hole” sizes in these polymers by comparing the observed ortho-positronium lifetimes with the known lifetime–free volume correlation for low-molecular-weight systems. The free volumes for four epoxies with different crosslink densities are found to vary significantly over the temperature range between ?78° and 250°C. The free-volume holes for these polymers are found to range from 0.025 to 0.220 nm³. Two important transition temperatures were found: one corresponds to the glass transition temperature T_g determined by differential scanning calorimetry (DSC), and the other occurs about 80–130°C below T_g. The sub-T_g transition temperature is interpreted tentatively as being where hole size reaches dimensions adequate for positronium trapping or else the onset temperature for local mode or side-chain motions. These two transition temperatures plus two additional onset temperatures are found to be correlated with crosslink densities calculated from stoichiometry.     

Positron annihilation in hypercrosslinked polystyrenes

Positron annihilation in hypercrosslinked polystyrene, called CPS(0.3)150E, has been studied as a function of temperature in the range from 35 to 370 K. The positron lifetime spectra were resolved into five components using the PATFIT and MELT programs. The annihilation rate constant of the longest-lived component was found to increase linearly with increasing temperature. Remarkably, the distribution of o-Ps lifetimes resolved by MELT was shown to broaden with decreasing temperature. Moreover, an effect of the oxygen pressure on the positronium characteristics was also investigated in another hypercrosslinked polystyrene, CPS(0.3)100E. The oxygen pressure varied from vacuum to 6 atm. The annihilation rate constants of the long-lived components were observed to increase linearly as a function of the oxygen pressure, which demonstrates a dependence of the kinetic of o-Ps quenching on the pore size.     

Study of the size and numerical concentration of the free volume of carbon filled HDPE composites by the positron annihilation method

In this paper, the size and numerical concentration of free volume of high density polyethylene/carbon black (HDPE/CB) composite were investigated by positron annihilation lifetime spectroscopy (PALS). The PALS were measured in two series of samples, one with various CB contents in the composites and the other with changing the temperature of HDPE/CB composite containing 25 phr CB. It was found that the important parameters of PALS show their fluctuation around the percolation threshold. The conductivity of HDPE/CB is controlled by CB contribution, and that can be reflected in o-Ps lifetime. The temperature dependence of positron lifetimes reveals that the existence of glass transition temperatures and the size of free volume holes increases when temperature increases above glass transition. The results observed from the second set of samples suggest that positive temperature coefficient is in some way related with free volume expansion. The experiment facts implied that the conductivity of HDPE/CB was related with not only the size of free volume holes but also the number of free volume holes. The Doppler-broadening of HDPE/CB was also investigated.     

Positron annihilation in amine-cured epoxy polymers—pressure dependence

Positron annihilation spectroscopy has been used to study free volume in an arnine-cured epoxy as a function of external pressure at temperatures above and below the glass transition temperature. The observed ortho-positronium lifetime τ₃ and formation probability I₃ decreased with increasing pressure. The decrease in τ₃ is interpreted in terms of a corresponding decrease in average free-volume hole size over the range from 0.135 to 0.045 nm³. The fractional free-volume and the free-volume compressibility in the epoxy are calculated as functions of pressure at 100°C.     

Column packings for high-performance liquid chromatography and positron annihilation lifetime spectroscopy

Positron annihilation measurements as a function of temperature and the length of bonded alkyl groups have been carried out on silica gel samples. Silica gel samples were bare and bonded with alkyl group from C1 up to C18. The diameters of pores were deduced from the lifetime of trapped ortho-positronium (o-Ps), and it was found that o-Ps lifetime provides reasonable information on the pore sizes for both bare and alkyl bonded silica gels.     

Frontiers of positron and positronium chemistry in condensed media

Our work proves that positron annihilation spectroscopy is an excellent tool to follow the structural changes in chemical species. We present four examples to support the above statement. The sizes of defects in electrodeposited chromium layers were studied and estimated on the basis of positron lifetime spectra decomposed into two components. Vacancies, di-vacancies and vacancy-clusters could be identified in the electrodeposites. The changes of the size distribution of the free volume units in poly(methylmetacrylate) on the dependence of molecular weight and dispersity were described by the correlation between the lifetime ofortho-Ps and the free volume units in polymers. It was found that the free volume is affected by both the molecular weight and dispersity. The effect of dispersity was explained by the sample preparation technique, namely by the application of high pressure. The ortho-para conversion ofortho-Ps was used to follow the partial spin-crossover in [Fe(1-ethyl-1H-tetrazole)₆](BF₄)₂. The spin-crossover temperature was identified to be 105 K. A conformal structural transformation was found in [Zn(1-propyl-1H-tetrazole)₆](BF₄)₂ between 170 and 90 K by positronium lifetime measurement and the role of (BF₄)²⁻ anion, in this transformation, was proved by¹⁹F NMR spectroscopy.     

Influence of vinylidenefluoride on the physical ageing of poly(chlorotrifluoroethylene)

The influence of vinylidenefluoride (3% composition) on the physical ageing of poly(chlorotrifluoroethylene) at 70 °C has been investigated using the positron annihilation lifetime technique. Both the ortho-positronium (o-Ps) pick-off lifetime and its intensity show a systematic variation with ageing time. The o-Ps intensity exhibits non-exponential character which can be fitted with two additive exponential decay curves and the free volume is found to exhibit the Doolittle type of free volume relaxation. The relaxation times were evaluated from the structural relaxation function and the non-exponentiality parameter was estimated using the Kohlrausch-Williams-Watts (KWW) function, which indicates the deviation from exponential relaxation. Based on the relaxation times, the activation energies calculated seems to label the different kinetic units/irregularity in the chain backbone of PCTFE structure participating in the relaxation process. Physical ageing seems to yield close packing of polymer chains.     

Delayed formation and localisation of positronium in polymers at low temperatures

A theoretical model of the positron annihilation lifetime spectrum including the mechanisms of slow positronium (Ps) localisation and delayed Ps formation from a positron and a trapped electron was developed. The model was applied to two series of spectra for low-density polyethylene and high-density polyethylene (HDPE) collected at constant temperature (much below the glass temperature) as a function of measurement time. The Ps internal relaxation time and time of localisation of Ps in a free volume centre were determined. The results show that after long irradiation of the polymer a dominant fraction of positrons (unbound in Ps) annihilate from the trapped states. On the basis of parameters determined from the HDPE lifetime spectra, two S(t) curves (for sample in darkness and in light) were calculated. The predicted shapes of S(t) well agree with literature data obtained with the age–momentum correlation (AMOC) experiment. According to the new model the shapes of the para-Ps and the ortho-Ps (p-Ps) components are non-exponential. In spite of this, the multi-exponential decomposition of a polymer spectrum enables to determine correctly the value of the o-Ps lifetime, however the other parameters determined from the spectrum have no simple physical meaning.     

A positron lifetime and Doppler-broadening study of positron states and free volume in polyethylene

Positron lifetime (LT) and Doppler-broadening (DB) studies of polyethylene have been performed simultaneously in the temperature range between 80 and 300 K. The LT spectra have been analysed assuming four exponential components. Two long-lived components appear, which were attributed too-Ps pick-off annihilation in crystalline regions (₃ = 0.9 to 1.2 ns) and at free-volume holes in the amorphous phase ( to 2.8), The variation in ₄ correponds to an increase of the mean hole size from 0.053 nm³ at 80 K to 0.188 nm³ at 300 K. From the data the glass transition temperature (T _g=195 K), the coefficient of thermal expansion of holes in the glassy and rubbery phase ( _{h, g} = 14.5 · 10^–4 K^–1 and _{h, r} = 189 · 10^–4 K^–1) and the fractional free volume (2.8% to 10.4%) were estimated. The DB curves were fitted by a sum of three Gaussians, the narrowest of which is assumed to represent the self-annihilation ofp-Ps localised at holes. The intensity of the narrow component,I _n, varies between 0 and 7.3% in a similar way as the LT intensityI _4/3 varies. From this it was concluded that other Ps reactions beside pick-off are not important. Further, it was shown that the average positron lifetime is dominated by theo-Ps component,T _{4 g}, while the behaviour of the DB peak height is mainly affected by thep-Ps narrow componentI _n .     

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.     

Studies of crystallization of SiO2-glass by positron annihilation

The crystallization of silica glass has been studied by positron lifetime spectroscopy and accompanying investigations using X-ray diffraction and nuclear magnetic resonance (NMR). To this end isothermal and isochronal heat treatments were performed in the range from 700 °C up to 1600 °C. The lifetime spectra are analyzed by two lifetime components. The decrease of the short lifetime (200 ps) is attributed to the increasing volume fraction of the crystalline phase. The long lifetime (1000 ps) is related with the pick-off annihilation of theo-Ps states in cavities.With starting formation of crystallization nuclei the long lifetime increases which is explained by expanding cavities at the interface between crystalline phase and amorphous matrix.     

Effect of cyclic stress on structural changes in polycarbonate as probed by positron annihilation lifetime spectroscopy

Positron annihilation lifetime spectroscopy (PALS) is used to probe structural changes in glassy polycarbonate in terms of changes in the hole volume and the number density of holes during fatigue (cyclic stress) aging. The ortho-positronium (o-Ps) pickoff annihilation lifetime τ₃, as well as the intensity I₃, were measured as a function of cyclic stresses and various previous thermophysical aging histories. It is found that τ₃, the longest of the three lifetime components resolved in the PALS of glassy polycarbonate, increases when a cyclic stress is applied. These results indicate that there is a structural change during fatigue aging. The “holes” where o-Ps can localize become larger upon fatigue aging. These results also suggest that a significant distinction exists between structural changes induced by thermophysical aging and fatigue aging. The o-Ps annihilation intensity, which is a relative measure of the hole density in a material, showed a continuous decrease upon fatigue aging, indicating the possibility of hole coalescence, which could be a precursor of crazing. The interaction between thermophysical aging and fatigue aging corresponds very well with the enthalpy relaxation behavior as reported previously, viz., a well-aged sample is much more sensitive to cyclic stress. More importantly, it is hypothesized that fatigue failure initiation is probably closely related to hole size and density fluctuation.