Doppler broadening of positron annihilation radiation as a probe for the anisotropy of free‐volume‐holes in polymers

Abstract

PACS 71.60.+z, 78.70.Bj Doppler broadening of annihilation radiation (DBAR) measurements have been performed in uniaxially hot-drawn poly(methylmethacrylate) (PMMA) samples. The DBAR spectra were deconvoluted into three Gaussians. The full width at half-maximum of the narrow component which is due to para-Positronium (pPs) self-annihilation is under discussion. An anisotropy of the free volume holes (FVHs) has been detected by measuring the deformed samples at the stretching and transverse directions. The sample deformed at 280% was also measured as a function of the orientation angle (0 • -90 • ) with respect to the stretching direction. The momentum distribution of p-Ps, which is considered as a structureless particle confined in FVH of ellipsoidal or cuboid shape, was calculated as a function of the potential well size and depth and compared with experiment.1 Introduction Positron annihilation lifetime spectroscopy (PALS) has been proven to be a very sensitive technique to study free-volume holes (FVHs) in polymers [1,2]. When a positron (e + ) enters condensed matter, after thermalization and diffusion, it eventually annihilates with an electron (e − ) of the medium, mostly by two 511 keV gamma quanta. Before the annihilation, the e + exists as a "free" positron (it annihilates directly with an e − with a lifetime (τ ) of ∼ 0.3-0.5 ns), or forms a positronium (Ps). In condensed matter, the ortho-positronium (o-Ps) lifetime (τ o−P s ), which is 142 ns in vacuum, is quenched to some nanoseconds as e + of the o-Ps atom annihilates with e − from the surrounding molecules (the socalled pick-off process). There is a well-known correlation between the radius (R) of spherical FVH and τ o−P s derived from the Tao-Eldrup model [3].The second most frequently used technique to detect open volume defects and to study their properties is the Doppler broadening of annihilation radiation (DBAR). In DBAR the interest is focussed on the 511 keV line, which is Doppler-broadened due to the momentum component P z of the e + − e − pair, where z is the detection direction. The peak is a superposition of a narrow (approximately a Gaussian) component due to the self-annihilation of para-positronium (p-Ps) and broader Gaussian-like distributions due to free e + and o-Ps pick-off annihilation [2,3]. The narrow component reflects the localization momentum of the p-Ps inside FVH and according to the Heisenberg uncertainty principle, it is sensitive to the FVH size.In a simple quantum-mechanical model, it is assumed that the Ps is confined in a spherically shaped potential well of infinite depth and radius R with a spatial overlap of the Ps wave function with molecules within a layer δR of the potential wall. The relationship between θ 1

Positron Annihilation Spectroscopy

“…The p-Ps annihilation leads to a "narrow" component on the annihilation line. Its width mirrors the kinetic momentum of the p-Ps and, since localized at a hole the dimension of the hole (60)(61)(62)(63).…”

“…The angles ξ and ϕ have typical values of 10 mrad. Two position-sensitive detectors (larger area scintillation detectors or wire chambers) separated by 10 m or more and operating in coincidence are used to measure the angular correlation of annihilation radiation (ACAR) (60)(61)(62)(63)(64)(65)(66). The counting rate of annihilation photons coming from the same annihilation event is determined as a function of the angles between both 511 keV photons.…”

“…This method has a very good resolution but requires extremely strong positron sources (∼10 9 Bq) and measuring periods of many days. For polymers, it is not frequently used, though it can be applied to measure the anisotropic hole size in the case that the holes are aligned (60)(61)(62)(63)(64)(65). This anisotropy can be concluded from the anisotropy of the kinetic momentum of the p-Ps localized at a hole via the relation r h | ξ,ϕ = 1.66/FWHM| ξ,ϕ − δr, where FWHM| ξ,ϕ is the full half width (in mrad) of the ACAR curve determined in the direction (ξ,ϕ) and δr = 0.166 nm.…”