Age momentum correlation experiments in kapton has revealed the existence of two positron states corresponding to the trapping of positrons on the partially negatively charged O and/or N sites in the polymer chain. A young age broadening of the annihilation line shape is also observed and is attributed to the annihilation in flight of the positrons

B Van Waeyenberge

C Dauwe

J De Baerdemaeker

N Djourelov

N Laforest

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Vol. 113 (2008) ACTA PHYSICA POLONICA A No. 5
Proceedings of the 37th Polish Seminar on Positron Annihilation, La̧dek-Zdrój 2007
Is Kapton∗ Really That Simple?
C. Dauwea,†, J. De Baerdemaekera, N. Djourelova,b,
N. Laforesta,c and B. Van Waeyenbergea
aGhent University, Department of Subatomic and Radiation Physics
Proeftuinstraat 86, B-9000 Gent, Belgium
bInstitute of Nuclear Research and Nuclear Energy
72 Tzarigradsko Shoosse, 1784 Sofia, Bulgaria
c LMOPS — Université de Savoie, LMOPS — UMR 5041
Campus Scientifique, 73376 Le Bourget-du Lac, France
Age momentum correlation experiments in kapton has revealed the ex-
istence of two positron states corresponding to the trapping of positrons on
the partially negatively charged O and/or N sites in the polymer chain. A
young age broadening of the annihilation line shape is also observed and is
attributed to the annihilation in flight of the positrons.
PACS numbers: 34.80.Lx, 41.75.Fr, 36.10.Dr, 82.30.Gg
1. Introduction
Kapton occupies a very special place in the characterization of polymers with
positron annihilation spectroscopy (PAS). It is the only known amorphous polymer
that does not form positronium and thus it is the only polymer that allows us to
study states and dynamics of positrons, without being perturbed by the positron-
ium. The lifetime spectrum of kapton is reported to contain one component [1–3]
which is not dependent on temperature [4]. Kapton is also insensitive to irradi-
ation damage by the energetic positrons emitted by the 22Na sources. Brusa et
al. [5] studied the motion of positrons in kapton by observing the drift of positrons
towards the outer layer in function of an external electrical field. They found an
extremely low value for the positron diffusion constant of D+ = 2.5× 10−5 cm2/s
from which they concluded that the positrons are trapped in the negative sites
of the polymer chain, i.e. on the nitrogen and/or oxygen sites. Recent ab initio
calculations [6] have indeed found strong negative partial charges on the N and
O sites in kapton; the results are presented in Fig. 1. Because of their stronger
∗Kapton is a registered trademark of DuPont, Chemical Co.
†corresponding author; e-mail: charles.dauwe@UGent.be
(1315)
1316 C. Dauwe et al.
Fig. 1. Chemical structure for kapton, with the partial charges of the N and O sites in
eV according to Pinel et al. [6].
negative partial charges it is reasonable to consider the 2 different O sites as the
main trapping centers. Dlubek et al. have reported [7] that the lifetime spectra
of Kapton may be decomposed into two components. The shorter-lived one had a
lifetime of approximately 220 ps and intensity of 14%, and the longer-lived com-
ponent was 376 ps. As usual, this author considers the shorter-lived component to
be an artefact of a broad distribution of lifetimes due to the fact that the positron
is supposed to be trapped into the intermolecular free spaces and free volume holes
(fvh). While it is known that positronium (Ps) is efficiently trapped into these
fvh, there is no experimental evidence that this is also true for free positrons. On
the other hand, if the two lifetimes correspond to two real and distinguishable
positron states, then we may expect these states to have distinguishable values for
the S- or line shape parameters.
2. Experimental
We obtained an age momentum correlation (AMOC) relief for kapton at
the Stuttgart pelletron facility. The experimental setup, and the procedures for
AMOC experiments with the high-energy positron beam was described elsewhere
by Stoll [8]. The AMOC data set contained 2.2 × 107 counts. Summation of the
data over the energy axis generates the overall experimental lifetime spectrum
Λexp(t) and the line shape curve Sexp(t) is obtained by calculating the line shape
parameter for each time channel. In order to obtain a constant statistical quality
the energy data were grouped along the time axis, in order that each energy
spectrum contains at least 4× 105 counts.
The theoretical lifetime spectrum Λ(t) and the line shape curve S(t) can be
written as{
Λ(t) =
∑
Lj(t) with Lj(t) = Ijλj exp(−λjt),
S(t) =
∑
Sj(t)
Lj(t)
Λ(t) ,
(1)
where the index j stands for all positron states. Generally, the Sj(t) coefficients
may be function of the positron age t. However, if we assume that the trapping
of e+ on the negative potential sites is immediate, then each contribution has a
characteristic constant Sj value. The combined variance χ2τ,S = 0.5(χ
2
τ + χ
2
S) of
the fit is calculated from the residues both in the lifetime (LT) and the line shape
(S) spectra
Is Kapton Really That Simple? 1317
χ2τ,S =
1
2νt
∑ [Λ(ti)− Λexp(ti)]2
Λexp(ti)
+
1
2νs
∑ [S(ti)− Sexp(ti)]2
σ2s (ti)
, (2)
where νt and νs are the number of degrees of freedom in te LT- and the S-fitting
and σs(ti) is the standard deviation of the experimental S-value at ti. A non-linear
least squares computer program was written to fit Eq. (1) to the experimental data.
The non-linear fitting parameters are the decay constants λj ; the linear parameters
are Ij and Sj .
3. Results and discussion
The experimental line shape versus positron age data Sexp(t) are shown in
Fig. 2. We see that these data are not compatible with a single-state system. There
must be at least two states and the positron state with the shorter lifetime has the
lower S-value. Therefore we first fitted Eq. (1) with two components. The result
of this fitting is [τi] = [153, 372] ps, [Ii] = [7.0, 93.0]% and [Si] = [0.4589, 0.4910].
The variances of the fit are [χ2τ,S , χ
2
τ , χ
2
S ] = [1.31, 1.36, 1.26]. The resulting fitted
S(t) curve is shown as the dashed line in Fig. 2. Both variances χ2τ , χ
2
S indicate that
the two-component model is not acceptable. Also the S-value of the shorter-lived
component is very small with respect to the one for the longer component. N and
O have very similar electronic structure and positrons localized on either of them
are expected to have barely distinguishable line shapes, and a small difference in
their S-parameters. The experimental data around zero age also seem to indicate
the existence of a juvenile broadening of the line shape. Juvenile broadening has
been observed exclusively in materials which form positronium and it would be due
to the finite thermalization time of the newly formed Ps. In the non-Ps material
kapton the juvenile broadening must be due to some alternative process.
Within the limited energy range of an S-parameter analysis, the in-flight an-
nihilation of the injected positrons yields an approximately constant contribution.
The S parameter of a constant contribution is simply Sflight = NC/NT , where
NC and NT are the number of channels for the central and the total summation
in the determination of the experimental S-values. Recently, do Nascimento et
al. [9] found a 0.066% contribution of in-flight annihilation in a source based 2D
Doppler experiment in aluminium. A new model with 3 contributions was fitted
to our AMOC data. The first contribution was a “prompt” curve i.e. with τ1 = 0
and S1 = 0.35 which constitutes the in-flight annihilation, and the other 2 have
free fitting parameters. The result of this fitting is shown on the S(t) curve as
the solid line in Fig. 2. The obtained model parameters are [τi] = [0, 229, 378] ps,
[Ii] = [0.6, 12.0, 87.4]% and [Si] = [0.35, 0.4818, 0.4908]. The variances of the fit
are [χ2τ,S , χ
2
τ , χ
2
S ] = [0.98, 1.15, 0.81].
The results for the lifetimes τ2 and τ3 and their intensities are now in very
good agreement with the ones found by Dlubek et al. [7]. It is also clear now that
S2 is only slightly smaller than S3 which could correspond to the 2 different O
sites. The intensity of the in-flight contribution is 0.6%. The total probability for
1318 C. Dauwe et al.
Fig. 2. Experimental and fitted line shape curves for kapton. The dashed line is the two-
component fit, the solid line corresponds to the two-component plus in-flight annihilation
model.
in-flight annihilation, Pflight(E+, Z) is a function of the positron energy and the
atomic number of the material, and was calculated by Azuelos and Kitching [10].
For low-Z material this probability is ≈ 0.5% at the energy of 200 keV which is
the mean positron energy from a 22Na source. This means that do Nascimento
observed approximately 10% of all in-flight events. At 3.5 MeV, the energy of
the positrons in our experiment, the total in-flight probability increased to ≈ 8%.
Because of the improper geometry for observing the 511 keV peak, this observed
in-flight annihilation fraction will be much lower than 8%. Thus we also observed
10% of the in-flight annihilations.
4. Acknowledgments
We thank H. Stoll and the MPI, Stuttgart, for the use of their AMOC ap-
paratus. This research is part of the Interuniversity Poles of Attraction Program,
(IUAP 5/1). It was furthermore supported by Fonds voor Wetenschappelijk On-
derzoek, Vlaanderen (FWO) and the research fund of the Ghent University.
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Is Kapton * Really That Simple?

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Is Kapton * Really That Simple?

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