Positronium states in the pores of silica gel

Goworek, T.; Ciesielski, K.; Jasińska, B.; Wawryszczuk, J.

doi:10.1016/s0301-0104(98)00068-8

Cited by 160 publications

(110 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…3) were useful for checking possibility to apply contemporary theoretical models, connecting EFV size and positronium lifetimes, to our experimental results. We mean here extended Tao-Eldrup (ETE) model suggested by Goworek et al [16,17] and so-called "classical regime", considering Ps atom as a classical particle in a large hole [18,19]. Analysis of our TD-data shows that the classical free path concept Distribution of the free volume holes sizes in polymeric sorbent LPS200X found from the sorption experiments.…”

Section: Concentration and Size Distribution Of Elementary Free Volumessupporting

confidence: 51%

“…Alternative approaches to the problem are illustrated on example of polyimides (temperature dependence experiments [4][5][6][7][8][9]) and on example of low-density cross-linked polymeric sorbents [10][11][12][13][14][15][16][17] (Table), TABLE PATFIT and MELT results for the lifetime spectra (first and second lines for RT and LT, correspondingly) of polymeric sorbents described in [11][12][13]. Letters ρ and S with subscripts are used to denote density (in g/cm 3 ) and specific surface of the samples (in m 2 /g) measured in two different ways [11].…”

Section: Concentration and Size Distribution Of Elementary Free Volumesmentioning

confidence: 99%

See 1 more Smart Citation

Some Aspects of Free Volume Studies in Molecular Substances Using Positron Annihilation Experiments

et al. 2005

View full text Add to dashboard Cite

Section: Concentration and Size Distribution Of Elementary Free Volumessupporting

confidence: 51%

Section: Concentration and Size Distribution Of Elementary Free Volumesmentioning

confidence: 99%

Some Aspects of Free Volume Studies in Molecular Substances Using Positron Annihilation Experiments

et al. 2005

View full text Add to dashboard Cite

“…One of attempts to improve the consistency of the model and experiment was done by Shantarovich et al [196], modifying the shape of potential well (rectangular, but deepened near the walls). More realistic approach consists in taking into account the population by Ps the energy levels in the potential well, lying higher than the ground level [197,198]. With the increase of free volume radii, besides the zero-point level, also other levels begin to appear and in favourable conditions become populated.…”

Section: The Role Of Excited Statesmentioning

confidence: 99%

“…The wavefunctions for the states with momentum l are Bessel ones j l (r). Thus, maintaining the Tao-Eldrup concept of broadened infinitely deep well and spherical geometry, we can write [198]: for several low lying levels in a spherical well assuming ∆' = ∆. As long as the spacings of Ps levels in the well are much larger than kT, the equilibrium population of the levels above the lowest one is negligible and simple Eq.…”

Section: The Role Of Excited Statesmentioning

confidence: 99%

See 1 more Smart Citation

Positronium as a probe of small free volumes in crystals, polymers and porous media

Goworek¹

2014

Annales UMCS, Chemia

View full text Add to dashboard Cite

show abstract

Positron Annihilation Spectroscopy

Dlubek

2008

Encyclopedia of Polymer Science and Technology

View full text Add to dashboard Cite

FundamentalsThe positron is the antiparticle of the electron, ie, it has the opposite charge but otherwise the same properties. In matter, a positron may be created either by the β + decay of an unstable nucleus or from a high-energy γ-photon via e + -e − pair production. If the positron encounters an electron, both particles annihilate, ie, they are transformed into photons of an energy, which is given by the famous Einstein equation, E = 2mc 2 . Here, m is the mass of the electron, c the speed of light in vacuum, and for particles at rest E = 2 × 0.511 MeV. The selection rules for the γ-photon emission are derived from the conservation laws of energy and momentum and parity considerations. Free positrons annihilate mainly into two γ-photons of energy 0.511 MeV emitted in almost collinear directions, or with much less probability into three photons of an overall energy of 1.022 MeV (16,24,25).In nonconducting materials, such as polymers, positrons can exist as free particles (e + ) or as positronium (Ps, e + e − ), which is a positron-electron bound state. Ps was experimentally discovered by DeBenedetti and Richings in 1952 (26). The "chemical" symbol Ps for positronium appears to have been introduced by McGervey and DeBenedetti in 1959 (27). Its properties and interaction with matter were reviewed in several articles (25-30). Ps is a particle of the size of a hydrogen atom, r Ps = 0.53Å, but only the mass of two electrons, and a binding energy of 6.8 eV, that is half of the ionization energy of hydrogen. The lifetime of a Ps atom depends on the relative spin orientation of positron and electron. The para-Ps (p-Ps, singlet state, spins antiparallel) decays into two photons with a mean intrinsic lifetime (self-annihilation in a vacuum) of τ pPs 0 = 0.125 ns. The ortho-Ps (o-Ps, triplet state, spins parallel) can decay only into three photons, a much slower process than two-photon emission. Therefore, o-Ps has an intrinsic lifetime of τ oPs 0 = 142 ns. The formation probabilities of the p-Ps and o-Ps states are 0.25 and 0.75 of the total Ps yield (16,25).In condensed matter studies, 22 Na is usually used as the positron source. This isotope has a half-life of 2.6 years and emits positrons with an energy distribution that has its maximum at 0.20 MeV and ranges up to 0.54 MeV (10,16). The stopping profile of positrons is a decreasing exponential function. In materials with a density of 1 g/cm 3 50%, 90%, and 99% of positrons are stopped within a thickness of 0.170, 0.60, and 1.20 mm, respectively. The energetic positrons lose their energy rapidly via ionization and excitation of electrons and finally phonons. After a few picoseconds, the positrons are in thermal equilibrium with the ambient material. In defect-free molecular crystals, positrons migrate over a mean distance of typically 100 nm before annihilating. In defected crystals and in amorphous matter, positrons may annihilate from local free volumes. The mean positron lifetimes are typically τ e+ = 200-400 ps.

show abstract

Positronium states in the pores of silica gel

Cited by 160 publications

References 23 publications

Some Aspects of Free Volume Studies in Molecular Substances Using Positron Annihilation Experiments

Some Aspects of Free Volume Studies in Molecular Substances Using Positron Annihilation Experiments

Positronium as a probe of small free volumes in crystals, polymers and porous media

Positron Annihilation Spectroscopy

Contact Info

Product

Resources

About