Positron free volume

The sizes and concentration of the free-volume cells in a polyimide film can be measured by PALS. The positrons injected into polymeric material combine with electrons to form positroniums. The lifetime (nanoseconds) of the trapped positronium in the film is related to the free-volume radius (few angstroms) and the free-volume fraction in the polyimide can be calculated.136 This technique allows a calculation of the dielectric constant in good agreement with the experimental value.137 An interesting correlation was found between the lifetime of the positronium and the diffusion coefficient of gas in polyimide.138,139 High permeabilities are associated with high intensities and long lifetime for positron annihilation. 

Network properties and microscopic structures of various epoxy resins cross-linked by phenolic novolacs were investigated by Suzuki et al.97 Positron annihilation spectroscopy (PAS) was utilized to characterize intermolecular spacing of networks and the results were compared to bulk polymer properties. The lifetimes (t3) and intensities (/3) of the active species (positronium ions) correspond to volume and number of holes which constitute the free volume in the network. Networks cured with flexible epoxies had more holes throughout the temperature range, and the space increased with temperature increases. Glass transition temperatures and thermal expansion coefficients (a) were calculated from plots of t3 versus temperature. The Tgs and thermal expansion coefficients obtained from PAS were lower titan those obtained from thermomechanical analysis. These differences were attributed to micro-Brownian motions determined by PAS versus macroscopic polymer properties determined by thermomechanical analysis. 

A fascinating insight into the impact that modelling can make in polymer science is provided in an article by Miiller-Plathe and co-workers [136]. They summarise work in two areas of experimental study, the first involves positron annihilation studies as a technique for the measurement of free volume in polymers, and the second is the use of MD as a tool for aiding the interpretation of NMR data. In the first example they show how the previous assumptions about spherical cavities representing free volume must be questioned. Indeed, they show that the assumptions of a spherical cavity lead to a systematic underestimate of the volume for a given lifetime, and that it is unable to account for the distribution of lifetimes observed for a given volume of cavity. The NMR example is a wonderful illustration of the impact of a simple model with the correct physics. 

Recently, the same series of six polyimides was studied by positron annihilation spectroscopy to determine die fractional free volume directly. In all three H/F analogue pairs, the increased free volume of the fluorinated polymer accounted for around 50% of the observed decrease in refractive index and dielectric constant. This result confims an astonishingly large free volume contribution predicted by our earlier estimates.Future work will investigate the generality of this result to other polymer systems. 

Positron annihilation lifetime spectroscopy (PALS) provides a method for studying changes in free volume and defect concentration in polymers and other materials [1,2]. A positron can either annihilate as a free positron with an electron in the material or capture an electron from the material and form a bound state, called a positronium atom. Pnra-positroniums (p-Ps), in which the spins of the positron and the electron are anti-parallel, have a mean lifetime of 0.125 ns. Ortho-positroniums (o-Ps), in which the spins of the two particles are parallel, have a mean lifteime of 142 ns in vacuum. In polymers find other condensed matter, the lifetime of o-Ps is shortened to 1-5 ns because of pick-off of the positron by electrons of antiparallel spin in the surrounding medium. 

An important feature of o-Ps in polymers is that these particles tire preferentially formed or trapped in holes or regions of low electron density. The annihilation rate of o-Ps is proportional to the overlap of the positron and the pick-off electron wavefunctions and therefore the lifetime of o-Ps will depend on the size of the hole. The relative number of o-Ps pick-off annihilations is related to the number of suitable free volume sites in the polymer [3]. 

Abstract. Free-volume structure in the lanthanum salt of laurinic acid in crystalline and liquid-crystalline states and an effect of dissolved Cgo molecules on the mean nanovoid radius and concentration were studied by means of the positron annihilation technique. La(Ci2H25COO)3 clathrate compound with dissolved C6o molecules was obtained, which is thermodynamically more stable than a simple mixture of components. Increased mean nanovoid radius (from 0.28 to 0.39 nm) after the inclusion of C6o molecules and concomitant decrease of the positronium annihilation rate by a factor of 2.7 indicate the decrease of the smallest nanovoid concentration. 

Lanthanum laurates in crystalline (powder) and liquid-crystalline states, as well as after dissolution of Cgo fullerenes were studied by means of the positron annihilation technique which is extremely sensitive to the free-volume defects. 

Independent of whether or not a well-defined crossover temperature can be observed in NS data above Tg, it has been well known for a considerable time that on heating a glass from low temperatures a strong decrease of the Debye-Waller factor, respectively Mossbauer-Lamb factor, is observed close to Tg [360,361], and more recent studies have confirmed this observation [147,148,233]. Thus, in addition to contributions from harmonic dynamics, an anomalously strong delocalization of the molecules sets in around Tg due to some very fast precursor of the a-process and increases the mean square displacement. Regarding the free volume as probed by positron annihilation lifetime spectroscopy (PALS), for example, qualitatively similar results were reported [362-364]. 

The areas of inorganic and organic positron chemistry deal mainly with material characterization and industrial applications using PAS. Both chemical and electronic industries have found PAS to be a powerful method. In addition to the traditional solution chemistry of the positron and Ps [11], PAS has been developed to determine the free volume Bom-Oppenheimer approximation, such as molecular solids [14] and polymers [15]. The unique localization property of Ps in free volumes and holes has opened new hope in polymer scientific research that determination of atomic-level free volumes at the nanosecond scale of motion is possible. During the last ten years, most positron annihilation research has involved a certain amount of polymer chemistry, polymers and coatings, which will be discussed in Chapters 12 and 13. For inorganic systems, oxides are mostly studied using the positron and Ps. Silicon oxides and zeolites are the most important systems in positron and Ps chemistry. The developments in this area have on the cavity structure and chemical states of inner surfaces. Chapters 8 and 14 will discuss this subject. 

Hasegawa, M., Tabata, M., Miyamoto, T., Nagashima, Y. et al. (1995) Positron and positronium in free volume in oxides silica glass and neutron-irradiated alumina , Mater. Sci. Forum 175-178, 269. 

Positrons emitted for a radioactive source (such as 22Na) into a polymeric matrix become thermalized and may annihilate with electrons or form positronium (Ps) (a bound state of an electron and positron). The detailed mechanism and models for the formation of positronium in molecular media can be found in Chapters 4 and 5 of this book. The para-positronium (p-Ps), where the positron and electron have opposite spin, decays quickly via self-annihilation. The long-lived ortho positronium (o-Ps), where the positron and electron have parallel spin, undergo so called pick-off annihilation during collisions with molecules. The o-Ps formed in the matrix is localized in the free volume holes within the polymer. Evidence for the localization of o-Ps in the free volume holes has been found from temperature, pressure, and crystallinity-dependent properties [12-14]. In a vacuum o-Ps has a lifetime of 142.1 ns. In the polymer matrix this lifetime is reduced to between 2 - 4 ns by the so-called pick-off annihilation with electrons from the surrounding molecule. The observed lifetime of the o-Ps (zj) depends on the reciprocal of the integral of the positron (p+(rj) and electron (p.(r)) densities at the region where the annihilation takes place ... 

Alternative ways of determining the free volume fraction without using I3 have also been proposed by Dlubek et al [28], as well as, Brandzuch et al [29], Dlubek et al used the coefficient of thermal expansion of the amorphous regions and hole volume determined from positron data to determine the number density of the free volume holes. Brandzuch et. al. used the coefficient of thermal expansion just above and just below the Tg to estimate the fractional free volumes. This model is based on the assumption that the expansion of the holes of the free volume, as seen by positrons, reflects the expansion of the total volume of the material. 

For DBES data three main factors contribute to the S parameter in polymers (1) free-volume content, (2) free-volume size, and (3) chemical composition. First, larger free-volume content contributes to a larger S value. DBES measures radiation near 511 keV where a major contribution comes from p-Ps. This p-Ps contribution is only 1/3 the o-Ps intensity as that in I3 of PAL data. Second, when p-Ps is localized in a defect with a dimension fix, the momentum Ap has a dispersion according to the Heisenburg uncertainty principle AxAp > h/4n. The S parameter from DBES spectra is a direct measure of the quantity of momentum dispersion. In a larger size hole where Ps is localized, there will be a larger S parameter due to smaller momentum uncertainty. Therefore, in a system with defects or voids, such as polymers, the S parameter is a qualitative measure of the defect size and defect concentration. The value of the S parameter also depends on the momentum of the valence electrons, which annihilate with the positrons. The absolute value of the S parameter therefore, may differ from polymer to polymer. Third, the S parameter depends on the electron momentum of the elements. As the atomic number of the elements increases, the electron momentum increases, and thus the S parameter decreases. Fortunately, in chemicals of... 

After losing their kinetic energy the penetrated positrons may either directly annihilate with surrounding electrons into two gamma rays, or combine with an electron to form a Ps atom. Although both positrons and Ps are known to localize within the free volumes, a certain fraction of them may diffuse back to the surface and escape to the vacuum. The probability of positrons and Ps annihilating in the polymer depends on their diffusion coefficients. 

Since both positrons and Ps could, be localized in free-volume holes, the data of positron lifetime (t2) and o-Ps bulk lifetime (t3) provide information about the size and distribution of free-volume size as a function of the depth near the surface. Figure 11.6 shows the variation of positron lifetime and o-Ps bulk lifetime vs the depth. A significant increase of lifetimes near the surface shows a larger size of free volumes near the surface than in the bulk. Similar variations vs the positron energy indicates that both positrons and Ps are localized in free volumes and holes. Figure 11.7 shows the distributions of hole size in the polymer from the data of o-Ps lifetime distribution. Near the surface, not only the size is larger than the bulk, the distribution is significantly wider [10]. 

For subnanometer free volumes, the Tao-Eldrup model [33] is conventionally used to relate positron lifetime to free-volume size. For nanometer pores as studied here, Gidley s model [23, 24] was used to relate the positron lifetimes to pore sizes. The 47-ns lifetime for the F88 copolymer-generated porous film yields a diameter pore size of 3.7 nm if the pores are assumed to be a closed sphere, while the 54-ns lifetime for the PI03 copolymer-generated film corresponds to a diameter pore size of 4.3 nm. It is pointed out that future work is needed to relate positronium lifetimes and pore sizes, especially for uncapped films, since positronium lifetimes of those samples include contributions from both closed and open pores. 

Kluin, J.E., Vleeshouwers, S., McGervey, J.D., Jamieson, A.M., Simha, R. (1992) Temperature and time dependence of free volume in bisphenol-A polycarbonate studied by positron lifetime spectroscopy . Macromolecules. 25, 5089. 

Okamoto, K., Tanaka, K., Katsube, M., Kita, H., Ito, Y. (1993) Free volume holes of rubbery polymers probed by positron annihilation . Bull. Chem. Soc. 66, 61. 

Kristiak, J., Bartos, J., Fristiakova, K., Sausa, O., Bandzuch, P. (1994) Free-volume microstructure of amorphous polycarbonate at low temperatures determined by positron-annihilation-lifetime spectrospcopy . Phys. Rev.B. 49(10), 6601. 

Peng, Z.L., Wang, B., Li, S.Q., Wang, S.J. (1994) Free volume and ionic conductivity of poly(ether urethane)-LiC104 polymeric electrolyte studied by positron annihilation . J. Appl. Phys. 76(12), 1. 

Uedono, A., Sadamonto, R., Kaqano, T., Tanigawa, S., Uryu, T. (1995) "Free volumes in liquid-crystalline main-chain polymer probed by positron annihilation . J. Poly. Sci. B Poly. Phys. 33, 891. 

Abdel-Hady, E.E., El-Sayed, A.M.A. (1995) Free volume home distributions of polymers via the positron lifetime techniques . Polymer degradation and stability. 47, 369. 

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