Free volume in imidazolium triflimide ([C3MIM][NTf2]) ionic liquid from positron lifetime: amorphous, crystalline, and liquid states

Positron annihilation lifetime spectroscopy (PALS) is used to study the ionic liquid 1-methyl-3-propylimidazolium bis(trifluoromethylsulfonyl)imide [C(3)MIM][NTf(2)] in the temperature range between 150 and 320 K. The positron decay spectra are analyzed using the routine LifeTime-9.0 and the size distribution of local free volumes (subnanometer-size holes) is calculated. This distribution is in good agreement with Fürth's classical hole theory of liquids when taking into account Fürth's hole coalescence hypothesis. During cooling, the liquid sample remains in a supercooled, amorphous state and shows the glass transition in the ortho-positronium (o-Ps) lifetime at 187 K. The mean hole volume varies between 70 ?(3) at 150 K and 250 ?(3) at 265-300 K. From a comparison with the macroscopic volume, the hole density is estimated to be constant at 0.20×10(21) g(-1) corresponding to 0.30 nm(-3) at 265 K. The hole free volume fraction varies from 0.023 at 185 K to 0.073 at T(m)+12 K=265 K and can be estimated to be 0.17 at 430 K. It is shown that the viscosity follows perfectly the Cohen-Turnbull free volume theory when using the free volume determined here. The heating run clearly shows crystallization at 200 K by an abrupt decrease in the mean <τ(3)> and standard deviation σ(3) of the o-Ps lifetime distribution and an increase in the o-Ps intensity I(3). The parameters of the second lifetime component <τ(2)> and σ(2) behave parallel to the o-Ps parameters, which also shows the positron's (e(+)) response to structural changes. During melting at 253 K, all lifetime parameters recover to the initial values of the liquid. An abrupt decrease in I(3) is attributed to the solvation of e(-) and e(+) particles. Different possible interpretations of the o-Ps lifetime in the crystalline state are briefly discussed.     

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.     

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     

Amorphous-amorphous transition in glassy polymers subjected to cold rolling studied by means of positron annihilation lifetime spectroscopy

In this study, polycarbonate (PC) and polystyrene (PS) are subjected to plastic deformation by means of cold rolling and the resulting variation of the free volume and its subsequent time evolution after rolling is investigated by means of positron annihilation lifetime spectroscopy (PALS). The value of the long lifetime component that is attributed to the decay of ortho-positronium (tau(o-Ps)) and its intensity (I(o-Ps)) are used to characterize, respectively, the size and the concentration of the free-volume holes. In addition to the PALS experiments, the effect of plastic deformation on the dynamic tensile modulus is investigated. The PALS results show that both for well-aged PC and PS an increase of tau(o-Ps) and a decrease of I(o-Ps) occur upon plastic deformation. During the subsequent aging, tau(o-Ps) tends to return to the value assumed before plastic deformation, while I(o-Ps) remains constant with time. These results corroborate the idea of an amorphous-amorphous transition, rather than that of a "mechanical rejuvenation" as proposed in the past to explain the ability of plastic deformation to reinitiate physical aging. Finally, a linear relation between the size of the free-volume holes and the dynamic tensile modulus is found, which suggests that the stiffness of amorphous glassy polymers is fully determined by their nanoscopic structure.     

The Spin Probe Dynamics and the Free Volume in a Series of Amorphous Polymer Glass-Formers

We report the results of a combined study of the local structure and the reorientation dynamics in a series of five amorphous polymers of different fragility: cis-trans-1,4-poly(butadiene) (c-t-1,4-PBD), cis-1,4-poly(isoprene) (cis-1,4-PIP), poly(isobutylene) (PIB), poly(vinyl methylether)(PVME) and poly (propylene glycol) (PPG) by using two different probe methods. The reorientation dynamics of the molecular spin probe 2,2,6,6-tetramethyl-1-piperidinyloxy (TEMPO) from electron spin resonance (ESR) is related to the annihilation behaviour of the atomic ortho-positronium (o-Ps) one as obtained by positron annihilation lifetime spectroscopy (PALS). It was found that a slow to fast transition in the spin probe rotation mobility at the operationally defined spectral temperature parameter, T_50G, is connected with the mean o-Ps lifetime, τ₃ (T_50G) = (2.04 ± 0.26) ns. Consequently, using the free-volume concept of the o-Ps annihilation in terms of a quantum-mechanical model of o-Ps lifetime this transition can be connected with the occurrence of the mean free volume hole, V_h (T_50G) = (102 ± 17) ų, nearly independent of the chemical composition and the basic structural relaxation parameters of the amorphous polymers investigated. Finally, the free volume hole distribution aspect of the slow to fast transition indicates the presence of a sufficient free volume fluctuation at T_50G for both typical fragile PVME and strong PIB polymer and emphasizes the essential role of free volume in the spin probe dynamics.     

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 volume‐size dependence on temperature and average molecular‐weight in poly(ethylene oxide) determined by positron annihilation lifetime spectroscopy

Positron lifetime measurements were carried out in a series of poly(ethylene oxide)—PEO—of different average molecular weights (M _w): 1000, 1500, 6000, 10,000, 300,000, and 4 M. The mean radius (R ) and the mean free volume size (V_f) values were determined using a semiempirical equation that correlates the ortho‐positronium (o‐Ps) lifetime (τ₃) and size of holes existing in the amorphous phases. The hole mean radius values determined at room temperature from lifetime spectra were found to be between 2.68 and 2.97 Å, and the hole volumes between 80 and 110 ų. Free volume size evolution was studied with temperature variation until the melting temperature of the PEO samples. The degree of crystallinity and the melting temperatures were determined by Differential Scanning Calorimetry. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 219–226, 1999     

Sorption of CO2 in polymers observed by positron annihilation technique

Positron annihilation lifetimes were measured for several polymers in the atmosphere of high pressure CO₂ gas. At low CO₂ pressured both ₃ andI ₃ decreased due to the Langmuir-type sorption, and at higher pressures their values recovered because the Henry-type sorption takes over. The amount of sorbed CO₂ and dilation of the bulk volume were measured simultaneously, and the free volume fraction was determined at each CO₂ pressure. The free volume fraction became smaller (for polyimide and polycarbonate) or slightly larger (for polyethylene) with the progress of sorption. However, the size of the o-Ps hole estimated from the ₃ value increased regardless of the change of the free volume fraction. It appears that o-Ps is selectively looking at larger holes or expanding the holes in which it is accommodated. For polycarbonate, which remains to be glassy even at the largest CO₂ sorption attained in the experiment, the o-Ps hole size became larger than that before sorption. This implies that, even if the polymer is glassy as bulk, the sorption site is strongly prone to molecular displacement by the pressure of the penetrating Ps. Cautious consideration is evoked about directly correlating the o-Ps lifetime and intensity with the free volume in general.     

Free volume microstructure of amorphous polymers at glass transition temperatures from positron annihilation spectroscopy data

The analysis of annihilation characteristics of ortho-positronium at conventional calorimetric glass transition temperatures for a series of amorphous polymers reveals empirical correlations of average lifetime of o-Ps , and of its product with a relative intensityI _3g with appropriateT _g ^DSC values. These trends in terms of free volume mean that both the average size of free volume hole entityv _hg and the fractional free volume grow with increasingT _g ^DSC . The results are discussed considering the chemical microstructure as well as possible mechanisms acting in glass transition. A relation is indicated between geometric and flexibility characteristics of chains and thev _hg andf _g parameters of free volume microstructure on the one side and potential motional processes responsible for solidification of the amorphous system on the other side.     

Diffusivity enhancement of water vapor in poly(vinyl alcohol)–fumed silica nano-composite membranes: Correlation with polymer crystallinity and free-volume properties

The diffusion coefficients of water vapor in poly(vinyl alcohol)–fumed silica (PVA–FS) nano-composite membranes were determined using the gravimetric method. Water vapor was observed to diffuse more rapidly in membranes with increased FS content. The vapor diffusion coefficient was determined as 1.2 × 10⁻¹³ m²/s in pure PVA and was observed to increase to 3.0 × 10⁻¹³ m²/s in PVA composites containing 30% FS nano-particles. The free-volumes of PVA–FS membranes were characterized using positron annihilation lifetime (PAL) spectroscopy. PAL results showed that both the ortho-positronium (o-Ps) lifetime and intensity increased with the addition of FS. The intensity (I₃) was found to be higher than the estimated value determined from the linear combination of the data from pristine PVA and FS, and correlated excellently with the polymer amorphous content. The PAL results indicate that a higher FS content in PVA increases the free-volume hole size (a volume increase from 40 to 55 Å³) and free-volume hole density (an I₃ increase from 23 to 28%), resulting in a higher fractional free-volume in the nano-composites. The increase in the relative polymer free-volume with higher FS content was associated with a decrease in the PVA crystallinity, as determined from differential scanning calorimetry measurements. It is postulated that the incorporated FS nano-particles interrupt polymeric chain packing and retard crystallization during membrane formation. More crystalline segments were transformed into amorphous regimes in the nano-composites containing more FS. A correlation between water diffusivity and the fractional free-volume was obtained, and the water diffusivity was successfully expressed by the free-volume theory.     

Electrophoretic measurement of water charge density and ion hydration

Water exchange between bulk water and water-ion complexes will be at equilibrium when the charge density of the complex surface equals the charge density of bulk water, producing a constant radius water-ion complex. This complex will migrate in an electric field at a velocity proportional to the complex radius. CE velocity is the sum of the complex charge-dependent velocity and the buffer electro-osmotic flow. Simultaneous use of both a base (1.07 mM imidazole) and an acid (1.5 mM MOPS) buffer negates EOF at pH 7.4. Electric fields below 300 V/cm (potassium, calcium) and 400 V/cm (magnesium) yield migration velocities with no dehydration of the water-ion complexes. The number of waters per complex increase with the ion charge density: K⁺ 1.90, Ca⁺⁺ 5.90, Mg⁺⁺ 6.59 waters/ion. The charge densities of the complexes are similar: K⁺ 1.24, Ca⁺⁺ 1.43, Mg⁺⁺ 1.21 e/nm², for an average bulk water charge density of 1.29 ± 0.11 (SD) e/nm². The addition of 0.1% Triton increases the number of waters for Mg⁺⁺ to 25.33 and lowers the charge density to 0.497 e/nm². High electric field dehydration shows that calcium will be fully dehydrated at 638.3 V/cm and magnesium fully dehydrated at 925.5 V/cm, which occur at 6.15 and 5.78 nm from the membrane. Dehydrated magnesium will then bind to calcium channels leading to decreased smooth muscle activation.     

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.     

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 .     

Crystallinity dependence of free-volume size and its distribution of ethylene-vinyl alcohol copolymer evaluated by positronium lifetime measurement

The size distribution of free-volume (<~0.1 nm³) of ethylene-vinyl alcohol copolymer with various crystalline degrees was estimated by positronium lifetime measurement. With increasing degree of crystallinity, the size distribution significantly narrowed and the intensity of positronium decreased. This indicates that the inhomogeneity reduces with the increase of the degree of crystallinity. It is found that the free-volume fraction estimated is reflected by the fraction of the amorphous region.     

Study of multiblock polyamide-6/Poly-(isoprene) copolymers by positron annihilation spectroscopy

Positron annihilation lifetime spectroscopy (PALS) has been used to determine the free volume in multiblock polyamide-6/poly-(isoprene) copolymers (PA-6/PI), synthesized via activated anionic bulk copolymerization. The diisocyanate functionalized telechelic PI, blocked with caprolactam (CL) has been used as a commoner and an activator at the same time. The elastic PI block incorporated into the main chain of PA-6 affects the amorphous and crystal phase of the copolymer leading to changing in degree of crystallinity. The positron annihilation lifetime spectroscopy (PAL) and Doppler broadening of annihilation line (DBAL) technique in a set of pure PA-6 and PA-6/PI copolymers with two different compositions have been applied and evaluation of the size of free-volume holes (pores), localized mainly in the disordered regions of the PA-6/PI copolymer by measuring the o-Ps lifetime (τ₃) and o-Ps intensity (I₃) has been performed.      

Hole transport of trans-1,2-biscarbazolylcyclobutane-doped poly(bisphenol A carbonate) film

The hole transport of trans-1,2-biscarbazolylcyclobutane (CB) doped poly(bisphenol A carbonate) (PC) film has been investigated in the CB concentration range of 3.8 × 10^?4 mol cm^?3 (12 wt%) to 1.6 × 10^?3 mol cm^?3 (51 wt%). The hole mobility increased drastically with increasing CB concentration. The hole mobility was analyzed by a random hopping model. The localization radius ρ₀ of the CB/PC system was 1.9 Å, which is larger than that obtained for the N-isopropyl-carbazole-doped PC system. This suggests that the larger localization radius of the CB/PC system is related to the larger spatial extent of the CB molecule. The highest hole mobility of 2.9 × 10^?6 cm² V^?1 s^?1 was obtained when the CB concentration was 1.6 × 10^?3 mol cm^?3 (51 wt%) at E = 1.6 × 10⁵ V cm^?1 and T = 298 K. This mobility is about 10 times higher than that of poly(N-vinylcarbazole) (PVCz). The activation energy of hole mobility for the CB/PC system decreased with increasing CB concentration and was 0.31 eV at 51 wt% of CB, which is lower than the 0.45 eV for PVCz. The low activation energy for the CB/PC system is ascribed to the absence of an excimer-forming site that works as a multiple-trapping site for hole carriers.     

Analysis of a polydisperse system using small-angle X-ray scattering

The small-angle X-ray data from a polydisperse solution of sodium silicate have been measured in the concentration range 3.6–169 mg/cm³ using aKratky camera. The following values of the particle parameters were obtained: the average radius of gyration =7.5 nm, the average particle weight =900 000, the average volume =671 nm³, and the average particle surface area =717 nm².From the above parameters and the apparent specific volume, analysed to be 0.422 cm³/g, the water content of the silicate particles was determined to be 3% (by weight).From small-angle X-ray measurements, performed on solutions exposed to a hydrodynamic field, it is indicated that at least the larger particles in the solution have a relatively symmetric shape. Based on this observation it was assumed that the particles in solution are spherical, and particle size distribution functions were calculated using a least-squares program. It was found that the distribution cannot be described by a simple function, such as aGaussian function; instead, the distribution follows a histogram with three local maxima.Dedicated to Prof. Dr. Dr.Otto Kratky, Graz, on the occasion of his 80th birthday.     

Positron annihilation lifetime measurements in collagen biopolymer

Lifetime measurement in Positron Annihilation Spectroscopy (PAS) is applied to the study of free-volume collagen characteristics as a function of concentration. The lifetimes of positrons were measured by a conventional fast-fast coincidence system. All lifetime data are fitted in three components by using the computer program POSITRON-FIT and resolved. For each concentration, lifetime distributions were analyzed in order to obtain the different components, thus we have observed three components of which one long component τ₃. This long lived component can be associated with a pick-off annihilation of ortho-positronium (o-Ps) trapped in free volumes of amorphous region. This investigation shows the potential of positron annihilation spectroscopy in the study of biopolymer microstructures.     

Free‐volume variation in polyethylenes of different crystallinities: Positron lifetime,density, and X‐ray studies

High‐quality positron lifetime measurements (70 million total counts) are reported for polyethylenes (PEs) of different crystallinities (X_c = 3–82%). The specific volumes of the crystalline and amorphous phases (V_c and V_a, respectively) were estimated from density and wide‐angle X‐ray scattering (WAXS) experiments. Some samples (those with low values of X_c) were branched PEs, and those with high values of X_c were linear PEs for which X_c was varied with changes in the crystallization temperature. Both V_c and V_a increase with decreasing X_c in the range 0% ≤ X_c ≤ 56% (the branched PEs) but are constant for X_c ≥ 56% (the linear PEs). The lifetime spectra were analyzed with the MELT and LIFSPECFIT routines. Artifacts that can appear in the spectrum analysis were checked via an analysis of computer‐generated spectra. Four lifetime components appeared in all of the PEs; the two long‐lived ones are attributed to pick‐off annihilation of ortho‐positronium (o‐Ps) in crystalline regions (τ₃) and in holes of the amorphous phase (τ₄). With increasing X_c, τ₃ decreases from about 1.2 to 1 ns, τ₄ decreases from 3.0 to 2.5 ns, and the intensity I₄ decreases from 29 to 0%. An increase in I₃ from 6 to 12% was observed. A comparison with simulations shows that the true I₃ value approaches 0 for X_c → 0%. The decrease in I₄ is weaker than the increase in X_c; this leads to the conclusion that the apparent specific o‐Ps yield in the amorphous phase I₄^Xc increases with X_c. Possible reasons for this surprising results are discussed. The fractional free hole volume [h = (V_a ? V_occ)/V_a, where V_occ is the crystalline occupied volume] was estimated from density and WAXS results. Between X_c = 0 and 56%, h decreases from 0.151 to 0.090, but it does not change further above X_c = 56%. The mean size (v) of the local free volumes (holes) estimated from τ₄ decreases from 200 to 150 ų. The number density of holes (N_h) calculated from these values (N_h = h/v) also decreases from 0.8 to 0.6 nm^?3 in the range 0% ≤ X_c ≤ 56%. The values of V_a, V_c, h, and N_h increase with an increasing degree of branching but do not vary for linear PEs. The possible influence of a crystalline–amorphous interfacial phase (three‐phase model) on the observed lifetime parameters is also discussed. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 40: 65–81, 2002     

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.