Spin probe mobility in relation to free volume and relaxation dynamics of glass‐formers: A series of spin probes in poly(isobutylene)

We present the dynamics of a series of three paramagnetic molecules of different volume, mass, and shape in amorphous glass‐forming polymer poly(isobutylene) (PIB) as investigated by means of electron spin resonance (ESR) technique. The reorientation behavior of spin probes is related to the ortho‐positronium (o‐Ps) annihilation in PIB from positron annihilation lifetime spectroscopy (PALS) and the extracted free volume information. It is also related to the dynamic data of PIB from broadband dielectric spectroscopy (BDS), neutron scattering (NS), and nuclear magnetic resonance (NMR) spectroscopy from literature. In the case of the smallest spin probe, 2,2,6,6‐tetramethyl‐1‐piperidinyloxy (TEMPO), a discontinuous course of the spectral parameter 2A_zz′ versus T dependence was observed and the subsequent phenomenological model‐free analyses of the spectral parameter, 2A_zz′ versus T, as well as of the correlation time, τ_c, versus 1/T plots provided the characteristic ESR temperatures ( , T_50G, ) and (T, T, T). These characteristic ESR temperatures were found to be consistent with the characteristic PALS temperatures: T, T = T from temperature dependences of the mean o‐Ps lifetime, τ₃, or the width of o‐Ps lifetime distribution, σ₃, respectively. In addition, the relationships between the spin probe size, V, and the free volume hole size distributions g_n(V_h) at the characteristic ESR temperatures indicate the significant influence of the free volume fluctuation at the crossover from slow to rapid regime as well as within the rapid motional regime. On the other hand, the two larger spin probes exhibit a rather continuous 2A_zz′–T plots with the respective T_50G's lying in the vicinity of T independently of their volume, mass and shape, suggesting the common origin of underlying process controlling this T_50G transition. Finally, these mutual PALS and ESR findings were compared with the known dynamic behavior of PIB which suggest that the dynamics of the TEMPO and the larger spin probes are related to free volume fluctuation associated with primary α ‐ and secondary β processes, respectively. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1058–1068, 2009     

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.     

Effect of electric field strength and exposure time on epoxy and high density polyethylene measured by positron annihilation lifetime

Using the positron annihilation lifetime technique, the annihilation parameters have been measured for epoxy and high density polyethylene (HDPE) as a function of AC electric field strength and the exposure time. The lifetime spectra have been resolved into three components, the longest component (I₃₃) is attributed to the pick-off annihilation of o-Ps in the amorphous regions. The intermediate one (I₂₂) is due to the annihilation of free positrons, while the shorter component (I₁₁) stems from self annihilation of p-Ps. In HDPE, the o-Ps parameters ₃ andI ₃ are measured as a function of electric field strengths in the range from 10 to 100 kV/cm exposed for 24 hours. A decrease inI ₃ of 8% is observed from zero to 50 kV/cm followed by an increase of the same order from 50 to 100 kV/cm. By investigating the effect of the exposure time from 2 to 24 hours at 16 and 50 kV/cm, the effect is confirmed and is attributed to the inhibition of o-Ps formation at lower field strength. In epoxy, the effect or exposure time onI ₃ at 166 and 133 kV/cm shows a similar behavior as in HDPE. At 133 kV/cmI ₃ decreases by only 2.5%. On the other hand, the changes in ₃ occur at short exposure times. Again at large times the saturation is obtained. These effects are attributed to the expansion of free volume (increase of ₃) competing at longer exposure times with other phenomena, such as liberation of free radicals, which reduce the o-Ps intensityI ₃ through the conversion to p-Ps. The reactions between o-Ps and free radicals might also lead to free positrons, which could explain the increase ofI ₂ and the decrease of ₃ at longer exposure times.     

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.     

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 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.     

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.      

Positron annihilation spectroscopy study of moisture absorption in protective epoxy coatings

Position annihilation spectroscopy (PAS) was used to measure the relative free-volume fraction of protective epoxy coatings before and after exposure to liquid water at room temperature. The relative free volume fraction determined before water exposure was compared to the equilibrium water uptake of each coating and a correlation was found. The relative free-volume fraction of the epoxy coatings decreased slightly after water exposure. This decrease is contrary to the free volume theory of plasticization, but is consistent with the antiplasticization process. Larger decreases in the relative free volume fraction were sought by repeating the water uptake experiments with nitrobenzene which in the bulk, liquid form quenches ortho-positronium (o-Ps). Since the o-Ps lifetime remained approximately constant and the o-Ps intensity decreased after nitrobenzene absorption, nitrcbenzene is believed to be inhibiting the formation of o-Ps in the epoxy free volume cavities. Larger decreases in the relative free volume fractions were found after nitrobenzene exposure than after water exposure. These larger decreases are due to the fact that nitrobenzene is a better inhibitor of o-Ps formation than water in the epoxy free volume cavities. Larger volume fractions of nitrobenzene were absorbed by the coatings than water and were interpreted to be due to interactions between nitrobenzene and the epoxies. © 1993 John Wiley & Sons, Inc.     

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     

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.     

Kit development for labelling erythrocytes or leukocytes with technetium-99m in vitro

Positron lifetime spectroscopy has been applied to estimate the free-volume hole size distribution in glassy polycarbonate (PC) and polystyrene (PS) as well as in plastically deformed and undeformed, semi-crystalline polyethylene (HDPE). The hole radius density distribution is determined from the ortho-positronium lifetime distribution which is obtained via a Laplace-inversion of the positron lifetime spectrum. The hole volume density distribution and the number density distribution of holes is estimated from the hole radius density distribution. In PC and in PS all of the distributions may be well approximated by a single Gaussian. The hole radius and the hole number density distributions have centres <r> and <v _n > at 0.29 nm and 0.1 nm³ in PC, and at 0.28 nm and 0.09 nm³ in PS. The FWHM of the corresponding distributions are 0.042 nm and 0.040 nm³ (PC), and 0.039 nm and 0.34 nm³ (PS), respectively. Both, the shape and the width of the distributions correlate well with the free volume theory of BUECHE. In PE the lifetime spectra consist of four components. The o-Ps lifetime distribution is bimodal and may be attributed to o-Ps annihilation in the crystalline and in the amorphous phase of the polymer. The corresponding hole size distributions show definite changes of their position and width following plastic deformation which we attribute to homogeneous crystal lattice dilatation and/or a local disorder in the crystals and to an increase in the eccentricity of holes in the amorphous phase.     

Nitroxide spin probe study of probe size,hydrogen bonding and polymer matrix rigidity effects on poly(acrylic acid)/poly(ethylene oxide) complexes

An electron spin resonance (ESR) spin probe study was performed on 1 : 1 by weight poly(acrylic acid) (PAA)/poly(ethylene oxide) (PEO) complex over the 100–450 K temperature range with a series of tetramethylpiperidyloxy‐based spin probes. Measurements of the parameters T_5mT, Ta and Td demonstrated the effects of probe size and the strength of hydrogen bonding. The probes in the series Tempone, Tempo, Tempol and Tamine (respectively 4‐oxo‐, unsubstituted, 4‐hydroxy‐ and 4‐amino‐2,2,6,6,‐tetramethylpiperidine ‐1‐oxyl) displayed noticeable increases in the hydrogen‐bonding effect, as indicated by Ta and Td. These increases correlated with increasing hydrogen bond acceptor strength. On the other hand, as the probe size became larger, T_5mT gradually increased due to the free volume decrease. These effects were analyzed using the established theoretical relationship of T_5mT to probe volume expressed by f. Meanwhile, in order to investigate the effect of polymer matrix rigidity, a similar study was performed with a nitroxide spin probe, 2,2,6,6‐tetramethyl‐1‐piperidine‐1‐oxyl (Tempo), on PAA/PEO complexes of different weight compositions. The quantitative fast motion fraction in the composite ESR spectrum was calculated. The influence of changes in the composition of PAA on the molecular mobility was characterized by changes of the spectral parameters and τ_c. The molecular mobility was shown to diminish with increasing content of PAA in PAA/PEO blends duo to the restriction of the polymer matrix rigidity increase. Copyright © 2003 John Wiley & Sons, Ltd.     

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     

Solvent and temperature effects on positronium annihilation parameters and on its quenching reactions with the free radical HTEMPO

Positron annihilation lifetime spectroscopy (LS) and the Doppler broadening of the annihilation radiation lineshape (DBARL) technique have been used in conjunction to study solvent and temperature effects on both the positronium (Ps) quenching reactions with the free-radical HTEMPO (4-hydroxy-2,2,6,6-tetramethylpiperidine-1-oxyl) and the annihilation parameters. A change in the nature of the quenching reaction is observed from spin conversion in benzene (Bz),N,N-dimethylacetamide (NDMA), andN-methylformamide (NMFA) to Ps oxidation inmeta cresol (m-C); it is attributed to a modification of the electron density distribution in the quenching molecule due to hydrogen bonding with them-C molecules. The data also indicate that the full-width at half-maximum of the momentum distribution associated to para-positronium (p-Ps) resulting from the spin conversion reaction is smaller by a factor of 2 than that forp-Ps directly formed in the positron spur. The ortho-positronium (o-Ps) pickoff lifetime and momentum distribution are shown to give access to physicochemical and structural properties of the solvents.     

Isotope effect in gas transport. II. Effect of the glass transition on the size of the free volume element

A diffusive gas-transport isotope effect is used to estimate the size of the free volume element above and below the glass transition for poly(ethyl methacrylate) and poly(vinyl fluoride). The cavity size, as measured by the hydrogen probe molecule, is apparently larger in the glassy region for both polymers than it is above T_g. It is postulated that the number of free volume elements essentially decreases below T_g, so that the total free volume, which is the sum of all such elements, is smaller below the glass transition, in accord with density measurements on bulk polymers.     

Mobility of anionic spin probes in water-containing nylon 6 film

The rotational mobility of anionic spin probes in water-containing nylon 6 film was investigated by means of electron spin resonance (ESR) measurements for comparison with the results for nonionic spin probes reported previously. The extrema separation of the ESR spectra, 2Az′ increased with time owing to the evaporation of water. In the higher temperature region, 2Az′ increased steeply with time at first, and then more slowly, whereas for the nonionic spin probes, 2Az′ increased gradually and monotonically with time. This fact suggests that the anionic probe molecules are more strongly affected by water than the nonionic ones, i.e., the former probes are located in hydrophilic regions and the latter in hydrophobic regions. T_50G, which can be empirically correlated with the glass transition temperature of the polymer T_g decreased with increasing water content. The decreasing tendency for the anionic spin probes was stronger than that for the nonionic ones. This fact also indicates that the local environment around the probe molecules varies from probe to probe. The rotational correlation time τ_R decreased markedly with an increase in water content. The Arrhenius plots of τ_R showed two crossover points. The crossover points in the higher temperature region T_n decreased greatly with increasing water content. The difference in T_n between dried and water-containing films was larger than that for T_50G. The activation energy for rotation, E, also decreased with increasing water content. It is suggested that water concentrates around the anionic spin probes and makes their rotation much easier.     

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 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.     

The effect of crystallinity on chain mobility and free volume in the amorphous regions of a miscible polycarbonate/polyester blend

Homopolymers and blends of polycarbonate/ThermX have been investigated by differential scanning calorimetry, dynamic mechanical analysis, density measurements, and positron annihilation lifetime spectroscopy. The study focuses on the chain mobility and free volume in the amorphous miscible regions of the blends and how this mobility and free volume are affected by increasing crystallinity. It is proposed that judicious annealing, which results in increasing crystallinity (while avoiding ageing or transesterification), induces a constraint on the amorphous region leading to an increase in T_g and coalescence of free volume sites. © 1994 John Wiley & Sons, Inc.     

Macrochain configuration, stucture of free volume and transport properties of poly(1-trimethylsilyl-1-propyne) and poly(1-trimethylgermyl-1-propyne)

The relationship between poly(1-trimethylsilyl-1-propyne) (PTMSP) and poly(1-trimethylgermyl-1-propyne) (PTMGP) microstructure, gas permeability and structure of free volume is reported. n-Butane/methane mixed-gas permeation properties of PTMSP and PTMGP membranes with different cis-/trans-composition have been investigated. The n-butane/methane selectivities for mixed gas are by an order higher than the selectivities calculated from pure gas measurements (the mixed-gas n-butane/methane selectivities are 20?C40 for PTMSP and 22?C35 for PTMGP). Gas permeability and n-butane/methane selectivity essentially differ in polymers with different cis-/trans-composition. Positron annihilation lifetime spectroscopy investigation of PTMSP and PTMGP with different microstructure has determined distinctions in total amount and structure of free volume, i.e. distribution of free volume elements. The correlation between total amount of free volume and gas transport parameters is established: PTMSP and PTMGP with bigger free volume exhibit higher n-butane permeability and mixed-gas n-butane/methane selectivity. Such behavior is discussed in relation to the submolecular structure of polymers with different microstructure and sorption of n-butane in polymers with different free volume.