Transition and relaxation processes of polyethylene,polypropylene, and polystyrene studied by positron annihilation

Transition and relaxation processes of polyethylene (PE), polypropylene (PP), and polystyrene (PS) were studied by the positron annihilation technique. From measurements of lifetime spectra of positrons as a function of temperature, the lifetime of ortho-positronium, τ₃, and its intensity, I₃, were found to increase above 260 K for PP. This fact was attributed to a cooperative motion of large segments of molecules above the glass transition temperature, T_g. For PE, above T_g (140 K), the value of τ₃ increased, but the temperature coefficient of I₃ was negative below 230 K. From this fact, for PE, the molecular motions that cause the glass transition were associated with a rearrangement of molecules by local motions such as kink motions. The discrepancy between the results for PE and PP was attributed to the presence of methyl groups in PP and the resultant suppression of the local motions. For PS (T_g = 340 K), the molecular motions were found to start above 260 K, but those were suppressed by an interphenyl correlation. Detailed annihilation characteristics of positrons in polymers were also discussed. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 1601–1609, 1997     

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.     

Free volumes in nematic and smectic liquid-crystalline polymers probed by positron annihilation

Free volumes in thermotropic side-chain liquid-crystalline polymers were probed by positron annihilation technique. Lifetime spectra of positrons were measured in the temperature range between 130 and −60°C in cooling. For a nematic liquid-crystalline polymer (polyacrylate), the lifetime of ortho-positronium (τ₃) was decreased with decreasing temperature above the glass transition temperature (T_g, 21°C) with larger temperature coefficient than that below T_g. The intensity of ortho-positronium (I₃) was constant above T_g. These facts mean that the size of the free-volume holes decreased with the decreasing the temperature but the concentration was almost constant in nematic phase. For a smectic liquid-crystalline polymer (poly(p-methylstyrene) derivative), a discontinuous decrease in the value of τ₃ and that of I₃ were observed at 107°C, which was the transition temperature from smectic to crystalline phase. Such discontinuous changes were not observed for the polyacrylate specimen. This difference was considered to be attributed to the higher-ordered structure of the smectic phase. © 1996 John Wiley & Sons, Inc.     

Investigation of transitions and relaxation processes in polystyrene by using positron annihilation

The glass transition and relaxation processes in polystyrene resins with the number average molecular weight ranging from 7.0·10² to 9.8·10⁴ were studied with the positron annihilation technique. The pick-off annihilation lifetime of ortho-positronium (₃) and its intensity (I ₃) were measured in the temperature range from 20 to 430 K. The glass transition temperature (T _g) was determined as an onset temperature coefficient of ₃.T _g shows the molecular weight dependence in these samples. BelowT _g, local motions were detected by measurements ofI ₃. The local motions could be observed above 100 K in this experiment.I ₃ show the minimum at around 250 K and it does not show molecular weight dependence.     

Contributions of side groups to the water diffusion in cured epoxy resins (2) study on physical aging

Novolac epoxy resins cured with novolac resin, novolac acetate resin, novolac butyrate resin, and novolac phenylacetate resin named as EP, EPA, EPB, and EPP, respectively, were prepared. Their physical aging behavior at a T_g‐30 °C (30 °C below glass‐transition temperature) was examined by positron annihilation lifetime spectroscopy and differential scanning calorimetry. The ortho‐positronium annihilation lifetime τ₃ variation extent of EP is less apparent than that of the other three esterified samples during physical aging. The time dependence of ops intensity I₃ agreed with the Kohlrausch‐Williams‐Watts (KWW) equation. The relaxation time (τ₀) and nonexponential parameter were calculated. The free volume and enthalpy relaxation rate characterized by the reciprocal of τ₀ and ?ΔH/?logt, respectively, exhibit the same order—EPP > EPB > EPA > EP. These results suggest that the extend and rate of relaxation are not only related to the frozen free volume produced by quenching but also significantly influenced by segmental mobility of the network that attributed to the side‐group flexibility and their interaction with networks. This work also supports the fact that side‐group flexibility and the free‐volume fraction and distribution act in concert to control the water‐diffusion behavior in epoxy networks. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1135–1142, 2003     

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.     

Positron annihilation lifetime and differential scanning calorimetric study of immiscible NBR/PE blends

The temperature dependence of the mean size of nanoscale free‐volume holes, 〈V_h〉, in polymer blend system consisting of polar and nonpolar polymers has been investigated. The positron lifetime spectra were measured for a series of polymer blends between polyethylene (PE) and nitrile butadiene rubber (NBR) as a function of temperature from 100 to 300 K. The glass transition temperatures (T_g) for blends were determined from the ortho‐positronium (o‐Ps) lifetime τ₃ and the mean size of free‐volume holes 〈V_h〉 versus temperature as a function of wt % of NBR. The T_gs estimated from the PALS data agree very well with those estimated from DSC in view of different time scales involved in the two measurements. Both DSC and PALS results for the blends showed two clear T_gs of a two‐phase system. Furthermore, from the variation of thermal expansivity of the nanoscale free‐volume holes, the thermal expansion coefficients of glass and amorphous phases were estimated. Variations of the o‐Ps formation probability I₃ versus temperature for pure PE and blends with low wt % of NBR were interpreted on the basis of the spur reaction model of Ps formation with reference to the effects of localized electrons and trapping centers produced by positron irradiation. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 227–238, 2009     

Ortho‐positronium lifetime distribution analyzed with MELT and LT and free volume in poly(ε‐caprolactone) during glass transition,melting, and crystallization

Positron annihilation lifetime spectroscopy (PALS) was used to study the free volume behavior in the temperature range between 100 and 370 K in semicrystalline poly(ε‐caprolactone) (PCL). For the analysis of the spectra we used the well‐known routine MELT as well as the new program LT8.0, which allows both discrete and log‐normal distributed annihilation rates. From experiments, confirmed by the analysis of simulated spectra, we found that MELT returns too large values for the o‐Ps lifetime τ₃ associated with too small intensities I₃. This is due to the underestimation of the width of o‐Ps lifetime distribution in MELT (the spectra analyzed contained 3 million counts). The same effects were observed in the parameters obtained from the discrete term analysis. LT, however, returns, when allowing the o‐Ps lifetime to be distributed, rather accurate values for τ₃, I₃, and the width (standard deviation σ₃) of the o‐Ps lifetime distribution. The effect of the glass transition, melting, and crystallization on the annihilation parameters was observed. These results were compared with differential scanning calorimetry (DSC) and pressure–volume–temperature (PVT) experiments. From this comparison, the number density of holes and the fractional free (hole) volume have been estimated. At a “knee” temperature T_k ≈ 1.5 T_g, a leveling off of the o‐Ps lifetime τ₃ and a distinct decrease in the width, σ₃, of its distribution was observed; the latter effect was detected for the first time. Fast motional processes and/or the disappearance of the dynamic heterogeneity of the glass and the transition to a homogeneous liquid are discussed as possible reasons for these effects. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 3077–3088, 2003     

Open spaces and relaxation processes in the subsurface region of polypropylene probed by monoenergetic positron beams

Open spaces and relaxation processes in the subsurface region of isotactic polypropylene were investigated by monoenergetic positron beams. From measurements of the lifetime spectra of positrons, the size of the open spaces in the subsurface region (≤ 0.2 μm) was found to be larger than that in the bulk; their differences were estimated as 20% at 295 K and 10% at 395 K. From conventional positron annihilation experiments, the glass‐transition temperatures, T_{g (upper)}and T_g(lower) were determined as 306 K and 278 K, respectively. These transition temperatures were associated with the onset temperatures of the molecular motions under the constraint imposed by crystalline regions and those free from the constraint, respectively. In the subsurface region, although the onset temperatures of the molecular motions were close to those in the bulk, the molecular motions above T_{g (lower)} were found to be suppressed. The annihilation characteristics of positrons with different implantation energies were also discussed. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 101–107, 2000     

Monte Carlo calculations of hole size distributions: Simulation of positron annihilation spectroscopy

Consequences are explored of a hole size distribution in an amorphous polymer for the ortho-positronium (o-Ps) lifetime (τ₃) and intensity (I₃), determined by positron annihilation lifetime spectroscopy. The disordered lattice model, with a vacancy fraction h as a central quantity, is used to represent the equation-of-state behavior of the polymer. By means of Monte Carlo simulations, we obtain the cluster size distribution as a function of h and hence temperature. The predicted average cluster size and the cluster concentration are compared to τ₃ and I₃ data, respectively, for bisphenol-a polycarbonate. Furthermore, the influence of an o-Ps lifetime distribution on the experimental mean τ₃ is investigated. By mimicking the computational methods used in experimental analysis, agreement between experiment and theory in respect to τ₃ and to I₃ in the melt ensues. In the glass, however, the experimental I₃ becomes increasingly smaller with decreasing temperature than is computed. These deviations may result from a distortion of the equilibrium free volume. © 1992 John Wiley & Sons, Inc.     

Free volumes in polystyrene probed by positron annihilation

Free volume characteristics in three samples of monodisperse polystyrene were investigated by positron annihilation technique over a temperature range from 300 to 380 K. The number-average molecular weight of the samples ranged from 5730 to 1,524,000. The observed lifetime spectra were resolved into three components, where the longest lifetime, τ₃ was associated with the pick-off annihilation of ortho-positronium (o-Ps) trapped by free volumes. The change of the temperature coefficient of τ₃ was observed at around 350 K, at which the value of τ₃ was a constant value of 2,3 ns for all specimens with different molecular weights. There was no discrete change of τ₃ in intensity, which is corresponding to the number of free volumes. The size of free volume at glass transition was evaluated to be 0.l nm³. © 1996 John Wiley & Sons, Inc.     

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     

The effect of gamma irradiation on glass transition temperature and thermal stability of Se96Sn4 chalcogenide glass

Se₉₆Sn₄ chalcogenide glass was prepared by melt quenching technique and exposed, at room temperature, to different doses of 4, 8, 12, 24 and 33 kGy of high-energy ⁶⁰Co gamma irradiation. Differential scanning calorimeter (DSC) was used under non-isothermal condition to determine the glass transition temperature T_g, onset T_c and peak T_p temperatures of crystallization, of un-irradiated and γ-irradiated samples, at four different heating rates. The variation of T_g with heating rates was utilized to calculate the glass transition activation energy E_t for un-irradiated and γ-irradiated glass, using the methods suggested by Kissinger and Moynihan. Based on the obtained values of the characteristic temperatures T_g, T_c and T_p, thermal stability was monitored through the calculation of the S parameter and the crystallization rate factor 〈K_p〉 for irradiated and un-irradiated glass. Results reveal that, as γ-dose increases T_g increases up to 12 kGy then decreases at higher doses but remains more than that of un-irradiated glass. Meanwhile, both E_t and 〈K_p〉 attain their minimum values at the same dose of 12 kGy and the glass is thermally stable at this particular dose.     

Three-gamma annihilation of ortho-positronium in NiO/γ-Al2O3 catalysts detected by positron lifetime and coincidence Doppler broadening measurements

The pore structure of NiO/γ-Al₂O₃ catalysts is characterized by positron lifetime and Doppler broadening measurements. A very long lifetime τ₄ of 92 ns is resolved from the positron lifetime spectrum measured for pure Al₂O₃, which could be attributed to the ortho-positronium (o-Ps) lifetime in large pores. It was also found that the fitted lifetime τ₄ and its corresponding intensity I₄ obtained from the lifetime spectra both decrease with narrowing energy window of the stop channel in the fast–fast coincidence lifetime measurement system. This suggests that the ultra long lifetime is primarily due to the self annihilation of o-Ps which emits three gamma-rays. Such 3γ annihilation is further evidenced by measuring the Doppler broadening of annihilation gamma rays in coincidence with the prompt gamma rays (1.28 MeV) emitted from the ²²Na positron source. In NiO/γ-Al₂O₃ catalysts both the lifetime τ₄ and its intensity I₄ decreases with increasing NiO content (from 3 wt% to 40 wt%), which indicates decreasing of the number of 3γ events. The 3γ annihilation parameter analyzed from the coincidence Doppler broadening spectrum shows consistent decrease with increasing NiO content.     

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.     

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.     

Free volume evolution in polyoxymethylene studied by positron annihilation spectroscopy

The free volume hole and its distribution in polyoxymethylene have been studied over the temperature range (5–90 °C) by positron annihilation lifetime spectroscopy. At a certain temperature (20 °C) the variation of ortho-positronium lifetime shows a distinct increase in its slope. The hole volume shows a small linear increase with temperature below glass transition temperatue and a steeper increase above it. A linear relation between ln(σT^0.5) and 1/V_h was observed and the critical hole volume was estimated.     

A study of time dependence of ortho-positronium annihilation in a poly(butadiene) at different temperatures: a meaning of I3 parameter

Positron annihilation measurements as a function of temperature and time have been carried out on a poly(butadiene). The measurements were performed at several temperature points from 14 to 225 K. The measurement time was several hours to four days. The analysis of data shows the following features:

(i) the value of τ₃ does not depend on the rate of cooling or time,

(ii) the value of I₃ depends on the rate of cooling and the history of thermal treatment,

(iii) the dependence of I₃ on time can be described by Debye function. But the rise in I₃ is observed at very low temperatures,

(iv) the I₃ decays to value of I₃ observed during very slow cooling.

Permeability,permselectivity, and penetrant‐induced plasticization in fluorinated polyimides studied by positron lifetime measurements

The ortho‐positronium (o‐Ps) lifetime τ₃ and its intensity I₃ in various fluorinated polyimides were determined by the positron annihilation technique and were studied with the spin–lattice relaxation time T₁ and the propylene permeability, solubility, diffusivity, and permselectivity for propylene/propane in them. τ₃, I₃, and the distribution of τ₃ changed when the bulky moieties in the polyimides were changed. The polyimides, having both large τ₃ and I₃ values, exhibited a short T₁ and a high permeability with a low permselectivity. The propylene permeability and diffusivity were exponentially correlated with the product of I₃ and the average free‐volume hole size estimated from τ₃. In highly plasticized states induced by the sorption of propylene, the permeability increased with the propylene pressure in excellent agreement with the change in the free‐volume hole properties probed by o‐Ps. The large and broad distribution of the free‐volume holes and increased local chain mobility for the 2,2‐bis(3,4‐decarboxyphenyl) hexafluoropropane dianhydride‐based polyimides are thought to be important physical properties for promoting penetrant‐induced plasticization. These results suggest that o‐Ps is a powerful probe of not only the free‐volume holes but also the corresponding permeation mechanism and penetrant‐induced plasticization phenomenon. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 308–318, 2003     

A study on free‐volume properties of styrene‐acrylic ester type copolymers

The positron annihilation lifetime measurements have been performed on a number of amorphous styrene–methyl acrylate copolymers and styrene–butyl methacrylate copolymers. The densities of copolymers were obtained with immersion method by using a capillary pycnometer and the average molecular weights were determined by gel chromatography. The lifetime τ₃ of ortho‐positronium (o‐Ps) pick‐off annihilation have been found to correlate with side group volume and polarity of macromolecular chains in the copolymers, and relative intensity I₃ is attributed mainly to the electron‐attracting groups trapping the spur electrons and positrons. The experimental results have been discussed on the basis of the structural variation of macromolecular chains. In addition, the PALS measurement as a function of time for polystyrene and several styrene–methyl acrylate copolymers has also been performed. The result shows that an electric field is built in polymers during extended positron annihilation spectroscopy measurement, and the field effect is a main factor which causes the decrease in I₃ with time. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2476–2485, 1999