Final Report - Strategic Environmental Research and Development ...

5.5.4.7 Nanopore structure characterization of primer films
Bulk Free Volume
In standard PAL, one uses the well-established relationship between ortho-Positronium (o-Ps)
pick-off lifetime (τ 3 in a few ns) and spherical free-volume hole radius R (in a few Å), as defined
by the following semi-empirical equation [5.12-5.15]:
3
0.5
1
R
R
0
1 2R
sin
2
R0
1
[5.19]
where, τ 3 (o-Ps lifetime) and R (hole radius)are expressed in ns and nm units, respectively, and
R 0 =R+DR where DR is a constant for an electron layer thickness (1.66 Å).
Similarly, the free-volume hole size V h is defined as the following Eq:
V h
4
R
3
3
[5.20]
Lifetime measurements of the positron in primer films also allow the estimation of the fractional
free volume, ffv(%), by using the semi-empirical equation [5.16]:
ffv(%)
A
I3
V h
[5.21]
where I 3 is the relative intensity of the o-Ps lifetime component, V h is the free volume of the
single hole (in nm 3 ), and A is the normalization constant.
The positron lifetime spectra were analyzed using the PATFIT-88 package program. The
measured PALS spectra were well resolved into three components (τ 1 , τ 2 and τ 3 ) with their
intensities (I 1 , I 2 , and I 3 ) after the background and positron source correction was subtracted. As
discussed above, the third component τ 3 (the longest-lived component) is assigned to the pick-off
annihilation of ortho-Positronium (o-Ps) in the free volume holes within the films. Since the cast
primer films have a thickness ranging between 240 and 370 mm. Two pieces of identical primer
film samples are stacked together to assure a suitable thickness (> 300 mm) for average lifetime
measurement. The stacked film samples were oriented to have both the front faces (face-to-face)
toward the positron source. After analysis of the front face, the same sample was reoriented to
have the reverse faces towards to the positron source (back-to-back), or to have a mixed faces
(mixed faces). In addition, samples were also analyzed before and after exposure to beam
conditions, labeled as before and after vac. in the sample orientation column of the table. The
results of bulk PALS measurements are presented in Table 5.11 and Table 5.12. Only the
lifetimes and the intensities of the longest-lived component of the positron lifetime spectrum
have been summarized because they were used to calculated the free volume radius, R, free
volume size, Vh, and fractional free volume, ffv(%) values according to the Eq. [5.17-5.19].
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