- Email: [email protected]
Effect of electron-irradiation on the free volume of PEEK studied by positron annihilation
Nuclear Ins~umen~ Non-Holed
and Methods in Physics Research B 91(1994) 447-449
Effect of electron-irradiation by positron annihilation
Beam Interactions with Materials&Atoms
on the free volume of PEEK studied
Y. Kobayashi a**,K. Haraya a, S. Hattori a and T. Sasuga b a National Institute of Mater& and Chemical Research, Tsukuba, Ibaraki 30.5, Japan b Takasaki Radiation Chemistry Research Establishment, Japan Atomic Energy Research Institute, Takasaki. Gunma 370-12, Japan
A good linear correlation was found between the size of a cavity where o~o-positronium (o-Ps) annihilates by the pick-off mechanism and the total free volume of mole~lar liquids and polymers. Based on the correlation, the free volume of poly(ary1 ether-ether ketone) (PEEK) was evaluated as a function of electron irradiation dose and the result was compared with that obtained from gas diffusivity measurements. It was found that the effect of irradiation on the free volume of PEEK was rather small; the free volume was decreased only by a few percent (relative value) when the samples were irradiated with a dose of 50 MGy in air.
1. Introduction The lifetime spectrum of positrons a~~lat~g in molecular substances usually contains three exponentially decaying components. The longest-lived component with a lifetime T3 and the corresponding relative intensity I3 is attributed to the annihilation of orthopositronium (o-Ps) which is the bound state between a positron and an electron with parallel spin orientation. In condensed matter, the positron in o-Ps annihilates with one of the bound electrons with opposite spin. This process is called pick-off annihilation. The pick-off annihilation lifetime is inversely proportional to the overlap of the positron and electron wave functions and hence can be related to the size of a cavity where o-Ps is located at the time of the annihilation. In the present paper, we show that there exists a good linear correlation between the cavity size estimated from the o-Ps lifetimes and the total free volume of molecular liquids and polymers. The correlation is successfully applied to determine the free volume of electron-irradiated poly(ary1 ether-ether ketone) (PEEK) samples and the result is compared with that obtained from gas diffusivity measurements.
2. Experimental
D = 12/60,
where I is the membrane
thickness.
3. Results and discussion
PEEK is a radiation resistant polymer with a high grass transition temperature of about 420 K. Semicrystalline and amorphous samples with a thickness of 0.2 * Corresponding 55 1397.
mm for positron measurements and an amorphous sample with a thickness of 25 p,rn for diffusivity measurements were irradiated in air with 2 MeV electrons from a Dyn~itron-~~ accelerator at JAERI. The dose rate was 5 kGy/s and the effect of radiation-induced oxidation was insignificant. Positron lifetime measurements were performed with the system previously described ill. The positron source was about 0.37 Msq 22Na sealed in a thin Kapton film. Samples were stacked together to make sufficient thickness and the source was sand~ched between two equivalent stacks. The positron lifetime spectra were resolved into three exponential terms by computer analysis. Gas diffusivity was determined for argon, oxygen and nitrogen by measuring time-lags for travelling through the amorphous thin film samples. Pressure measurements were carried out by a pressure transducer with a full-scale range of 10 Torr. Permeation time-lag B was measured under a pressure difference of 1 atm. The diffusion coefficient D was calculated from the relation
author. Tel. +81 298 54 4622, fax +81 298
Variations of the o-Ps lifetime and its relative intensity I3 for PEEK as a function of irradiation dose up to 50 MGy are presented in Figs. 1 and 2, respectively. Closed symbols indicate the data for semi-crystalline samples and open symbols indicate those for amorphous samples. In both cases the intensity decreases
0168-583X/~/$07.00 0 1994 - Elsevier Science B.V. All rights reserved Ss1310168-583X(94)00058-4
VI. POLYMERS
448
4
0
X Kobayashi et al. /Nucl. Instr. and Meth. in Phys. Res. B 91 (1994) 447-449
1.6 1
I.57 0
0
amorphous
n
semi-crystalline
1 10
1 20
8 30
’ 40
1o-9T
8 50
0
8 10
of o-Ps lifetime in irradiated function of dose.
Argon
0 A
Oxygen Nitrogen
’ 20
/ 30
0 40
8 50
dose/MGy
doselMGy Fig. 1. Variation
0
PEEK
as a
Fig. 3. Variation of diffusion coefficients of argon, oxygen and nitrogen through irradiated amorphous PEEK as a function of dose.
markedly with irradiation dose, while the lifetime change is relatively small. The effect of irradiation on the gas diffusion coefficients are summarized in Fig. 3. As was stated in the introduction, the o-Ps lifetime can be related to the positronium (Ps) cavity volume. Here we use a semi-empirical relation, proposed by Nakanishi et al., to determine the Ps cavity size from the pick-off annihilation lifetime. The relation is written as
ume determined from pick-off lifetimes by using the relation of Nakanishi et al. It is clearly seen that there exists a strong correlation between the two quantities. The correlation is fairly well approximated by a linear relation and can be used for quantitative analysis as shown later. According to the free volume theory of diffusion, the gas diffusion coefficient is related to the total free volume V, as
7;l=
D =A exp( -B/V,),
(2 ns-l)[l
-(R/R,)
+O.l59{sin(27~rR/R,)}],
where R is the cavity radius and R, = R + 0.166 nm [2]. The cavity volume is given as (4~/3) R3. Fig. 4 shows the plot of the total free volume of molecular liquids and polymers evaluated by the group contribution method of Bondi [3] versus Ps cavity vol-
where Haraya argon, deduce shows
A and B are constants
and Hwang measured oxygen and nitrogen the numerical values a plot of the diffusion
depending on the gas. diffusion coefficients of in various polymers to of A and B [4]. Fig. 5 coefficient of argon in
0.7 0.6
0
amorphous
n
semi-crystalline
9
0.5
*g
0.4
b 5
0.3
z ’
0.2
: G= 0.1 0.0 0.0
of o-Ps intensity in irradiated function of dose.
0.2
0.3
Ps cavity volume/nm3
dose/MGy Fig. 2. Variation
0.1
PEEK
as a
Fig. 4. Plot of Bondi’s free volume versus o-Ps cavity volume for molecular liquids and polymers.
449
Y Kobayashi et al. /Nucl. Instr. and Meth. in Phys. Res. B 91 (1994) 447-449
Table 2 Free volume contents in the amorphous region of electronirradiated semicrystalline PEEK samples determined from o-Ps lifetimes Dose
Free volume content (cm3/g)
(MGY)
o-Ps
0 10 30 50
3 5 7 9 11 13 l/o-Ps cavity volume/inverse nm3 Fig. 5. Plot of diffusion coefficient of argon, D(Ar), versus inverse o-Ps cavity volume for polymers. PDMS: poly(dimethylsiloxane); PMP: poly(4-methyl-1-pentane); PETU: poly(ether-urethane); PS: polystyrene; PC: polycarbonate; PSF: polysulfone; PES: polfiether-sulfone) polymers reported by Haraya and Hwang versus inverse Ps cavity volume determined from o-Ps lifetimes. As expected from the free volume model of diffusion and the linear correlation in Fig. 4, the logarithm of the diffusion coefficient decreases linearly with inverse cavity volume. Similar correlations were obtained for oxygen, and nitrogen as well. The quantitative free volume of the PEEK samples can be evaluated by converting first the lifetime data in Fig. 1 to the cavity volume and then to the free volume by using the equation of Nakanishi et al, and the correlation in Fig. 4. Free volume contents thus determined are given in Tables 1 and 2. Table 1 also includes free volume contents of the amorphous film samples determined from the diffusivity data in Fig. 3 #I. Both sets of data show that the effect of irradia-
various
#’ The free volume of the irradiated samples cannot be determined by the Bondi method because of the unknown chemical structure. Table 1 Free volume contents of electron-irradiated amorphous PEEK samples determined from o-Ps lifetimes and diffusion coefficients of argon, oxygen and nitrogen Dose (MGY)
Density (g/cm31
Free volume content (cm3/g) o_ps Argon Oxygen Nitrogen
0 10 30 50
1.256 1.259 1.261 1.263
0.110 0.109 0.107 0.108
0.122 0.121 0.119 0.118
0.125 0.126 0.121 0.121
0.125 0.124 0.121 0.120
0.111 0.108 0.109 0.106
of amorphous PEEK is small; the free volume is decreased only by a few percent even if the sample was irradiated with the maximum dose of 50 MGy. The effect of the irradiation on the free volume of the semi-crystalline sample may be similar (Table 2). The decrease of the free volume may be due to intermolecular crosslinking. By taking errors involved in the measurements into account, the agreement of free volumes between the two methods is fairly good. The relative intensity of o-Ps is sometimes considered to be proportional to the number of free volume holes. However, the fact that the free volume of the amorphous PEEK samples estimated solely from the o-Ps lifetime, not from both the lifetime and the intensity, agrees with that from the gas diffusivity suggests that the change of the intensity in Fig. 2 is due to an effect other than that of free volume. Some active species formed by the irradiation may scavenge Ps precursors such as electrons, a positrons and/or hot Ps atoms, to inhibit the formation of Ps in the terminal positron spur [5].
tion on the free volume
Acknowledgement
This work was carried out as a part of nuclear cross-over research supported by the Science and Technology Agency.
References 111Y. Kobayashi, Chem. Phys. Lett. 172 (1990) 307. [2] H. Nakanishi, S.J. Wang, and Y.C. Jean, Proc. Int. Symp. on Positron Annihilation Studies of Fluids, Ed. S.C. Sharma (World Scientific, Singapore, 1987) p. 292. [3] A. Bondi, J. Phys. Chem. 68 (1964) 441. [4] K. Haraya and S.T. Hwang, J. Membrane Sci. 71 (1992) 13. [5] K. Okamoto, K. Tanaka, M. Katsube, 0. Sueoka and Y. Ito, Radiat. Phys. Chem. 41 (1993) 497.
VI. POLYMERS
and Methods in Physics Research B 91(1994) 447-449
Effect of electron-irradiation by positron annihilation
Beam Interactions with Materials&Atoms
on the free volume of PEEK studied
Y. Kobayashi a**,K. Haraya a, S. Hattori a and T. Sasuga b a National Institute of Mater& and Chemical Research, Tsukuba, Ibaraki 30.5, Japan b Takasaki Radiation Chemistry Research Establishment, Japan Atomic Energy Research Institute, Takasaki. Gunma 370-12, Japan
A good linear correlation was found between the size of a cavity where o~o-positronium (o-Ps) annihilates by the pick-off mechanism and the total free volume of mole~lar liquids and polymers. Based on the correlation, the free volume of poly(ary1 ether-ether ketone) (PEEK) was evaluated as a function of electron irradiation dose and the result was compared with that obtained from gas diffusivity measurements. It was found that the effect of irradiation on the free volume of PEEK was rather small; the free volume was decreased only by a few percent (relative value) when the samples were irradiated with a dose of 50 MGy in air.
1. Introduction The lifetime spectrum of positrons a~~lat~g in molecular substances usually contains three exponentially decaying components. The longest-lived component with a lifetime T3 and the corresponding relative intensity I3 is attributed to the annihilation of orthopositronium (o-Ps) which is the bound state between a positron and an electron with parallel spin orientation. In condensed matter, the positron in o-Ps annihilates with one of the bound electrons with opposite spin. This process is called pick-off annihilation. The pick-off annihilation lifetime is inversely proportional to the overlap of the positron and electron wave functions and hence can be related to the size of a cavity where o-Ps is located at the time of the annihilation. In the present paper, we show that there exists a good linear correlation between the cavity size estimated from the o-Ps lifetimes and the total free volume of molecular liquids and polymers. The correlation is successfully applied to determine the free volume of electron-irradiated poly(ary1 ether-ether ketone) (PEEK) samples and the result is compared with that obtained from gas diffusivity measurements.
2. Experimental
D = 12/60,
where I is the membrane
thickness.
3. Results and discussion
PEEK is a radiation resistant polymer with a high grass transition temperature of about 420 K. Semicrystalline and amorphous samples with a thickness of 0.2 * Corresponding 55 1397.
mm for positron measurements and an amorphous sample with a thickness of 25 p,rn for diffusivity measurements were irradiated in air with 2 MeV electrons from a Dyn~itron-~~ accelerator at JAERI. The dose rate was 5 kGy/s and the effect of radiation-induced oxidation was insignificant. Positron lifetime measurements were performed with the system previously described ill. The positron source was about 0.37 Msq 22Na sealed in a thin Kapton film. Samples were stacked together to make sufficient thickness and the source was sand~ched between two equivalent stacks. The positron lifetime spectra were resolved into three exponential terms by computer analysis. Gas diffusivity was determined for argon, oxygen and nitrogen by measuring time-lags for travelling through the amorphous thin film samples. Pressure measurements were carried out by a pressure transducer with a full-scale range of 10 Torr. Permeation time-lag B was measured under a pressure difference of 1 atm. The diffusion coefficient D was calculated from the relation
author. Tel. +81 298 54 4622, fax +81 298
Variations of the o-Ps lifetime and its relative intensity I3 for PEEK as a function of irradiation dose up to 50 MGy are presented in Figs. 1 and 2, respectively. Closed symbols indicate the data for semi-crystalline samples and open symbols indicate those for amorphous samples. In both cases the intensity decreases
0168-583X/~/$07.00 0 1994 - Elsevier Science B.V. All rights reserved Ss1310168-583X(94)00058-4
VI. POLYMERS
448
4
0
X Kobayashi et al. /Nucl. Instr. and Meth. in Phys. Res. B 91 (1994) 447-449
1.6 1
I.57 0
0
amorphous
n
semi-crystalline
1 10
1 20
8 30
’ 40
1o-9T
8 50
0
8 10
of o-Ps lifetime in irradiated function of dose.
Argon
0 A
Oxygen Nitrogen
’ 20
/ 30
0 40
8 50
dose/MGy
doselMGy Fig. 1. Variation
0
PEEK
as a
Fig. 3. Variation of diffusion coefficients of argon, oxygen and nitrogen through irradiated amorphous PEEK as a function of dose.
markedly with irradiation dose, while the lifetime change is relatively small. The effect of irradiation on the gas diffusion coefficients are summarized in Fig. 3. As was stated in the introduction, the o-Ps lifetime can be related to the positronium (Ps) cavity volume. Here we use a semi-empirical relation, proposed by Nakanishi et al., to determine the Ps cavity size from the pick-off annihilation lifetime. The relation is written as
ume determined from pick-off lifetimes by using the relation of Nakanishi et al. It is clearly seen that there exists a strong correlation between the two quantities. The correlation is fairly well approximated by a linear relation and can be used for quantitative analysis as shown later. According to the free volume theory of diffusion, the gas diffusion coefficient is related to the total free volume V, as
7;l=
D =A exp( -B/V,),
(2 ns-l)[l
-(R/R,)
+O.l59{sin(27~rR/R,)}],
where R is the cavity radius and R, = R + 0.166 nm [2]. The cavity volume is given as (4~/3) R3. Fig. 4 shows the plot of the total free volume of molecular liquids and polymers evaluated by the group contribution method of Bondi [3] versus Ps cavity vol-
where Haraya argon, deduce shows
A and B are constants
and Hwang measured oxygen and nitrogen the numerical values a plot of the diffusion
depending on the gas. diffusion coefficients of in various polymers to of A and B [4]. Fig. 5 coefficient of argon in
0.7 0.6
0
amorphous
n
semi-crystalline
9
0.5
*g
0.4
b 5
0.3
z ’
0.2
: G= 0.1 0.0 0.0
of o-Ps intensity in irradiated function of dose.
0.2
0.3
Ps cavity volume/nm3
dose/MGy Fig. 2. Variation
0.1
PEEK
as a
Fig. 4. Plot of Bondi’s free volume versus o-Ps cavity volume for molecular liquids and polymers.
449
Y Kobayashi et al. /Nucl. Instr. and Meth. in Phys. Res. B 91 (1994) 447-449
Table 2 Free volume contents in the amorphous region of electronirradiated semicrystalline PEEK samples determined from o-Ps lifetimes Dose
Free volume content (cm3/g)
(MGY)
o-Ps
0 10 30 50
3 5 7 9 11 13 l/o-Ps cavity volume/inverse nm3 Fig. 5. Plot of diffusion coefficient of argon, D(Ar), versus inverse o-Ps cavity volume for polymers. PDMS: poly(dimethylsiloxane); PMP: poly(4-methyl-1-pentane); PETU: poly(ether-urethane); PS: polystyrene; PC: polycarbonate; PSF: polysulfone; PES: polfiether-sulfone) polymers reported by Haraya and Hwang versus inverse Ps cavity volume determined from o-Ps lifetimes. As expected from the free volume model of diffusion and the linear correlation in Fig. 4, the logarithm of the diffusion coefficient decreases linearly with inverse cavity volume. Similar correlations were obtained for oxygen, and nitrogen as well. The quantitative free volume of the PEEK samples can be evaluated by converting first the lifetime data in Fig. 1 to the cavity volume and then to the free volume by using the equation of Nakanishi et al, and the correlation in Fig. 4. Free volume contents thus determined are given in Tables 1 and 2. Table 1 also includes free volume contents of the amorphous film samples determined from the diffusivity data in Fig. 3 #I. Both sets of data show that the effect of irradia-
various
#’ The free volume of the irradiated samples cannot be determined by the Bondi method because of the unknown chemical structure. Table 1 Free volume contents of electron-irradiated amorphous PEEK samples determined from o-Ps lifetimes and diffusion coefficients of argon, oxygen and nitrogen Dose (MGY)
Density (g/cm31
Free volume content (cm3/g) o_ps Argon Oxygen Nitrogen
0 10 30 50
1.256 1.259 1.261 1.263
0.110 0.109 0.107 0.108
0.122 0.121 0.119 0.118
0.125 0.126 0.121 0.121
0.125 0.124 0.121 0.120
0.111 0.108 0.109 0.106
of amorphous PEEK is small; the free volume is decreased only by a few percent even if the sample was irradiated with the maximum dose of 50 MGy. The effect of the irradiation on the free volume of the semi-crystalline sample may be similar (Table 2). The decrease of the free volume may be due to intermolecular crosslinking. By taking errors involved in the measurements into account, the agreement of free volumes between the two methods is fairly good. The relative intensity of o-Ps is sometimes considered to be proportional to the number of free volume holes. However, the fact that the free volume of the amorphous PEEK samples estimated solely from the o-Ps lifetime, not from both the lifetime and the intensity, agrees with that from the gas diffusivity suggests that the change of the intensity in Fig. 2 is due to an effect other than that of free volume. Some active species formed by the irradiation may scavenge Ps precursors such as electrons, a positrons and/or hot Ps atoms, to inhibit the formation of Ps in the terminal positron spur [5].
tion on the free volume
Acknowledgement
This work was carried out as a part of nuclear cross-over research supported by the Science and Technology Agency.
References 111Y. Kobayashi, Chem. Phys. Lett. 172 (1990) 307. [2] H. Nakanishi, S.J. Wang, and Y.C. Jean, Proc. Int. Symp. on Positron Annihilation Studies of Fluids, Ed. S.C. Sharma (World Scientific, Singapore, 1987) p. 292. [3] A. Bondi, J. Phys. Chem. 68 (1964) 441. [4] K. Haraya and S.T. Hwang, J. Membrane Sci. 71 (1992) 13. [5] K. Okamoto, K. Tanaka, M. Katsube, 0. Sueoka and Y. Ito, Radiat. Phys. Chem. 41 (1993) 497.
VI. POLYMERS