- Email: [email protected]
Free-volume hole properties near the surface of polymers obtained from slow positron annihilation spectroscopy
surface ELSEVIER
science
Applied Surface Science l 16 (1997) 251-255
Free-volume hole properties near the surface of polymers obtained from slow positron annihilation spectroscopy Y.C. Jean a,*, H. Cao a, G.H. Dai a R. Suzuki b T. Ohdaira b, y. Kobayashi c K. Hirata c " Department ofChemistr3.', Unit'ersiO" of Missouri - Kansas CiO', Kansas CiO', MO 641 I0, USA b Electrotechnical l.ztboratoo', Tsukuba, lbaraki 305, Japan ~"National Institute of Materials and Chemical Research. Tsukuba, lbaraki 305, Japan
Received 2 June 1996: accepted 15 July 1996
Abstract
We have measured the positron annihilation lifetime spectra in an epoxy polymer using the electrotechnical laboratory (ETL) slow-positron facility as a function of positron energy from 0.2 to 3.0 keV. The ortho-positronlum lifetime from the bulk increases near the surface while the intensity decreases. The results are interpreted in terms of a Ps free-volume model. A larger hole size and fraction near the polymeric surface are observed. A reduction of glass transition temperature near the surface is estimated from the WLF theory, Kevwords: Free volume: Glass transition: Polymers: Epoxy: Surfaces: Slow positrons
1. Introduction
In recent years, positron annihilation lifetime (PAL) spectroscopy has been established as a useful tool in probing the microscopic properties of polymeric materials (see for example [1]). One of the great successes in this line of research is the direct determination of free-volume hole properties at an atomic scale ( 2 - 2 0 A) in polymers. It has been demonstrated that PAL is able to determine the free-volume hole size, distribution, fraction, and anisotropic structure of polymers [ 1]. The high sensitivity of PAL in probing free-volume properties arises
Corresponding author. Tel.: + 1-816-2352280: fax: + 1-8162355502: e-mail: [email protected].
from the fact that the positronium atom (Ps, an atom consisting of a positron and an electron) is preferentially trapped (localized) in atomic-scale free-volume holes. Most existing PAL studies have emphasized the bulk of polymers. Recently, there have been several reports on results using slow positrons [2-4]. By controlling the incident energy of positrons, one can probe the physical properties, particularly those of the free-volume holes, near the surface of polymeric materials. Studies of polymeric surfaces are important to many industrial applications, such as coatings, adhesives, and gas separations (see for example [5]). In this paper, we report a PAL study and free-volume hole properties in a well-studied epoxy polymer as a function of incident positron energy.
0169-4332/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved. Pll S0 I 6 9 - 4 3 3 2 ( 9 6 ) 0 1064- 1
252
Y.C. Jean et al. /Applied Surface Science 116 (1997) 251-255
2. Experiments The epoxy samples used in this study are the same as those reported in our previous studies by using fast positrons [6,7]. They are amine-cured epoxies with a chemical composition of DGEBA (diglycidylether of bisphenol-A), DDH (N,N'-dimethyl-l,6-diamino-hexane), and DAB (1,4-diaminobutane), all supplied by Imperial Chemical, Americas, at an equivalent ratio (5:3:2). A glass transition temperature (Tg) of 52°C was determined by DSC (differential scanning calorimetry) measurements. The samples were cured under a dry N 2 environment and spun at a speed of 1000 rpm on an aluminum plate during curing. The cured epoxy sample (thickness 25-35 /xm) coated on an aluminum plate was cut (1.5 cm × 1.5 cm) and then mounted in the beam line for the positron measurements. For each experiment, the sample was first heated to 130°C for 30 min and then slowly cooled down to the measurement temperature. The vacuum of the sample chamber was about 10- 6 and 10- 8 Torr at high and low temperatures, respectively. The positron annihilation lifetime (PAL) spectra were recorded at the intense slow-positron facility in the electrotechnical laboratory (ETL) [8]. The slow positrons were generated with the electron linac (75 MeV, 1 /xs, 50-100 pps) by the use of a Ta converter and a W moderator. The slow positrons generated were temporarily stored in a linear storage section and then extracted to the pulsing system as a quasi-continuous beam. The positron pulsing system consists of three stages under a magnetic field of 0.008 T: a reflection type chopper, a sub-harmonic pre-buncher, and a harmonic buncher. The final pulsed positron beam has a cross-section of 1 cm diameter with a variable energy from 100 eV to 30 keV. Monitoring of the positron lifetime began with the final pulsed signal (150 ps width) and terminated with the detection of annihilation photons by a BaF 2 scintillator. The lifetime resolution is 250 ps at a counting rate of 1000 cps (1 /zA of electron linac current). Each PAL was collected at a period of a few minutes with a total statistics of approximately 4 × 105 counts. The obtained PAL spectra were X 2 fitted into three or four lifetimes by using PATFIT programs [9]. Two series of PAL spectra were acquired-short-
gated (80 ns) and long-gated spectra (800 ns) to search for surface Ps and free Ps in vacuum, respectively. The Doppler broadening of energy spectra was measured at the National Institute of Materials and Chemical Research. Detailed methodology of the slow positrons and of the measurement of the Sparameters are described elsewhere [3].
3. Results and discussion All PAL spectra were first fitted into four lifetimes without any constraint. The longest lifetime (~'4) and the corresponding intensity (14) vary with the incident energy, as previously reported [2]. In order to obtain information about polymeric properties, we then analyzed all data into four components by constraining '7"1 0.12 ns and z4 6-142 ns (as determined from the unconstrained results). ~-~ and ~'4 are attributed to p-Ps annihilation and o-Ps emitted from the surface. Two intermediate lifetimes, ~'z --- 0.35-0.45 ns and "r3 1.0-4.0 ns, are attributed to the positron and to the o-Ps annihilation in the bulk a n d / o r near the surface of polymers, respectively. We also measured the PAL on the same sample using the conventional fast positron (22Na source) technique; the results are: rj = 0.145 + 0.09 ns, I I = 20.0 ___0.5%, r e = 0.382 __+0.09 ns, 12 = 56 ___2%, ~'3 = 1.60 _ 0.02 ns, and 13 = 24.0 ___0.2%. These are referred to as the bulk lifetimes in epoxy polymers. Fig. 1 shows the variations of ~'3 and 13 with respect to the positron incident energy. As shown in Fig. 1, 13 increases but "/'3 decreases as the energy increases. The increase of 13 is due to the increase of positronium formation in the bulk. The decrease of ~'3 is related to structural changes in free-volume holes, as a function of positron implantation depth from the surface. The mean implantation depth of the positron is normally expressed by the formula [10]: =
=
=
z ( E ) = ( 4 0 0 / p ) E ~'6
(1)
where z is expressed in ,~, p is the density in g / c m 3, and E is the incident energy in keV. For example, at the very low energy° E = 0.2 keV, the positron penetrates only about 27 A from the surface.
E C. Jean et al./Applied Surface Science 116 (1997) 251-255
Epoxy at 25°C 2.1
rable to but smaller than those reported by Xie et al. in different types of polymers. The decrease of ~'3 with respect to incident energy is very interesting because 73 is directly correlated to the radius of free-volume holes ( R f ) by the following equation [1]:
T
2.0 1.9 1.8
[
1.7
73 = 0.5 1
1.6 1.5 1.4 0
1
2
253
+
3
gf
+ 1.66
l(
,. t]-
sin 2~ Rf + 1.66
(3)
where ~'3 and g f are expressed in ns and ,~ respectively. A longer ~'3 at low incident positron energy indicates that the free-volume hole size is larger near the surface than in the bulk. The variation of freevolume radius (Rf) with respect to the mean depth (z) is plotted in Fig. 2. The hole size decreases from
Positron Energy (keV) 25
21
16 3.0 12 2.8
8 0
1
2
3
T
2.6 OO
v
2.4
Positron Energy (keV) Fig. 1. 7-3 and 13 versus positron incident energy in epoxy. 7-3 and 13 are o-Ps lifetime and intensity in the bulk of the polymer. The curve of I 3 is fitted to Eq. (2).
2.2 2.0
i
0
500
,
i
1000
,
i
1500
,
i
2000
OO
z (A)
Therefore, a very low fraction ( < 10%) of o-Ps annihilation in the bulk is observed for E < 0.2 keV. As the positron energy increases, the o-Ps annihilation in the bulk increases. When E > 2 keV, the PAL spectrum is identical to that obtained from the fast positron method. The variation o f 13 with respect to E is similar to an exponential function as reported by Xie et al. [4]. We then fit the 13 with E by an equation of the form
I3(E ) = I 3 ( ~ )
- [ I 3 ( ~ ) - I3(0)]e -E/E°
(2)
13(0) are the o-Ps bulk lifetime at E = zc and E = 0, respectively. I3(oo) is taken from the fast positron result, i.e., 24%. 13(0) and E o are two fitting parameters. The results are: I3(0)= 5% and E o = 0.73 + 0.01 keV. These results are compaw h e r e 13(oo) a n d
5.0
4.0
II
3.0
2.0
t .0
i
0
500
i
1000
,i
1500
i
2000
co
z (A)
Fig. 2. Frce-volumc hole radius (Rf) and fraction (fv) versus the mean implantation distance z from the surfacc of an epoxy polymer.
254
E C. Jean et a l . / Applied Surface Science 116 (1997) 251-255
2.9 ~, near the surface to 2.4 ,~ in the bulk. The formation mechanism of Ps in polymers is unknown. Xie et al. interpreted it in terms of a recombination process between positrons and electrons in a radiation track [4], while Kobayashi et al. used the Ore (hot) model [3]. Here we have applied the simple free-volume model originally proposed by Brandt et al. [11]; i.e., Ps is formed in the free volume of molecular, substrates. Thus o-Ps intensity is related to the number of free-volume holes and the freevolume hole fraction in the bulk, f v , can be calculated from an empirical equation [1]: f v = 0.0018 • 4
(4)
3
where f v and /~(~) are expressed in ~3 and % respectively. In Fig. 2, we also plot the variation of free-volume fraction, f v , with respect to the implantation distance z. f v increases as the distance nears the surface and reaches the bulk value as z > 1000 The increase of free-volume hole fraction near the surface is rather interesting. According to the Williams-Landel-Ferry (WLF) free-volume theory [12], the free volume fraction f v is directly related to the glass transition temperature by a semi-empirical equation [13]: f v =.fo + ( T -
T~)ol
(5)
where c~ is the difference in the thermal expansion coefficients above and below Tg and f0 is the reference free-volume fraction at Tg. In the epoxy poly-
80
60
I J
C
0
, 0
i 500
,
~ 1000
,
r 1500
,
i
Epoxy
at 25
°C
0.54
0.53
[]
[2]
[]
[]
0.52 Ca.
d,
0.52 [
0
2
4
6
8
10
Positron Energy (keV) Fig. 4. Variation of S-parameter versus positron incident energy in an epoxy polymer.
mer studied here, a = 4.0 × 10 -4 K - I . An increase of f v leads to a reduction of Tg. In Fig. 3, we plot the variation of Tg as estimated according to Eq. (5) and f v calculated from Eqs. (3) and (4) as a function of implantation distance (z). Near the surface, a lower ~ is obtained. The reduction of Tg near the surface has been predicted from theoretical calculations [14,15]. Recently, a Brillouin light scattering measurement in a freely standing polystyrene film showed a significant reduction of Tg near the surface [16]. That is contrary to the thermal expansion result by using X-ray reflectivity in a polystyrene film supported on silicon substrates [17]. The current PAL result supports the theoretical prediction of ~ reduction near the surface. The variation of o-Ps pick-off annihilation in the bulk can be monitored by measuring the S-parameter of the Doppler shift in the annihilation energy near 511 keV. Fig. 4 shows the variation of S with respect to the positron energy. The increase of S is due to the increase of o-Ps pick-off annihilation in the bulk. The variation of S is similar to that of 13 shown in Fig. 1. This is a further confirmation of the PAL results presented above.
2000
z (A) Fig. 3. Variation of glass transition temperature (T~) versus the mean. implantation distance z from the surface of an epoxy polymer. T~ is estimated from Eq. (5) and fv is calculated from Eqs. (3) and (4).
4. C o n c l u s i o n
We present free-volume hole properties as a function of distance from the surface to the bulk of an
Y.C. Jean et a l . / Applied SurJhce Science 116 (1997) 251-255
epoxy by using the PAL method. An increase of free-volume hole size and fraction near the surface is observed. A reduction of T~ near the surface has been estimated according to WFL theory.
Acknowledgements We are especially thankful to Dr. T.C. Sandreczki for preparing the thin-film samples of epoxy polymers for this experiment. This research has been supported by the National Science Foundation of the United States, by the University of Missouri Research Board, and by the Science and Technology Agency of Japan.
References [1] Y.C. Jean, in: Positron Spectroscopy of Solids, Eds. A. Dupasquier and A.P. Mills, Jr. (IOS Press, Amsterdam. 1995) p. 503. [2] Y.C. Jean, G.H, Dai, H. Shi, R. Suzuki and Y. Kobayashi, in: API Proc., Eds. E. Ottewitte and A.H. Weiss, Vol. 303 (1994) p. 129.
255
[3] Y. Kobayashi, I. Kojima, S. Hishita, T. Suzuki. E. Asari and M. Kitajima, Phys, Rev. B 52 (1995) 823. [4] L. Xie, G.B. DeMaggio, W.E. Frieze, J. DeVries. D.W. Gidley, H.A. Hristov and A.F. Yee, Phys. Rev. Left. 74 ( t 995) 4947. [5] W.J. Feast, H.S. Munro and R.W. Richards. Eds., Polymer Surfaces and Interfaces (John Wiley and Sons. New York, 1993). [6] Y.C. Jean, T.C. Sandreczki and D.P. Ames, J. Polym. Sci. B 24 (1986) 1247. [7] Q. Deng, F. Zandiehnadem and Y.C. Jean, Macromolecules 25 (1992) 1090. [8] R. Suzuki, Y. Kobayashi, T. Mikado, H. Ohgaki, M. Chiwaki, T. Yamazaki and T. Tomimasu, Jpn. J. Appl. Phys. 30 (1991) L532. [9] PATFIT-88 package, purchased from Ris,a National Laboratory, Denmark (1989). [10] P.J. Schultz and K.G. Lynn, Rev. Mod. Phys. 60 (1988) 701. [11] W. Brandt. S. Berko and W.W. Walker. Phys. Rex. 12 (1960) 1289. [12] M.L. Williams, R.F. Landel and J.D. Ferry. J, Am. Chem. Soc. 77 (1955) 3701. [13] J.D. Ferry, Viscoelastic Properties of Polymers, 3rd ed. (John Wiley and Sons, New York. 1980). [14] A.M. Mayes, Macromolecules 27 (1994) 3114. [15] K.F. Mansfield and D.N. Theodoroce. Macromolecules 24 (1991) 6283, [16] J.A. Forrest, K. Dalnoki-Veress. J.R. Stevens and J.R. Dutcher, Phys. Rev. Lett. 77 (1996) 2002. [17] W.E. Wallace, J.H. van Zanten and W.L. Wu. Phys. Rev. E 52 (1995) R3331.
science
Applied Surface Science l 16 (1997) 251-255
Free-volume hole properties near the surface of polymers obtained from slow positron annihilation spectroscopy Y.C. Jean a,*, H. Cao a, G.H. Dai a R. Suzuki b T. Ohdaira b, y. Kobayashi c K. Hirata c " Department ofChemistr3.', Unit'ersiO" of Missouri - Kansas CiO', Kansas CiO', MO 641 I0, USA b Electrotechnical l.ztboratoo', Tsukuba, lbaraki 305, Japan ~"National Institute of Materials and Chemical Research. Tsukuba, lbaraki 305, Japan
Received 2 June 1996: accepted 15 July 1996
Abstract
We have measured the positron annihilation lifetime spectra in an epoxy polymer using the electrotechnical laboratory (ETL) slow-positron facility as a function of positron energy from 0.2 to 3.0 keV. The ortho-positronlum lifetime from the bulk increases near the surface while the intensity decreases. The results are interpreted in terms of a Ps free-volume model. A larger hole size and fraction near the polymeric surface are observed. A reduction of glass transition temperature near the surface is estimated from the WLF theory, Kevwords: Free volume: Glass transition: Polymers: Epoxy: Surfaces: Slow positrons
1. Introduction
In recent years, positron annihilation lifetime (PAL) spectroscopy has been established as a useful tool in probing the microscopic properties of polymeric materials (see for example [1]). One of the great successes in this line of research is the direct determination of free-volume hole properties at an atomic scale ( 2 - 2 0 A) in polymers. It has been demonstrated that PAL is able to determine the free-volume hole size, distribution, fraction, and anisotropic structure of polymers [ 1]. The high sensitivity of PAL in probing free-volume properties arises
Corresponding author. Tel.: + 1-816-2352280: fax: + 1-8162355502: e-mail: [email protected].
from the fact that the positronium atom (Ps, an atom consisting of a positron and an electron) is preferentially trapped (localized) in atomic-scale free-volume holes. Most existing PAL studies have emphasized the bulk of polymers. Recently, there have been several reports on results using slow positrons [2-4]. By controlling the incident energy of positrons, one can probe the physical properties, particularly those of the free-volume holes, near the surface of polymeric materials. Studies of polymeric surfaces are important to many industrial applications, such as coatings, adhesives, and gas separations (see for example [5]). In this paper, we report a PAL study and free-volume hole properties in a well-studied epoxy polymer as a function of incident positron energy.
0169-4332/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved. Pll S0 I 6 9 - 4 3 3 2 ( 9 6 ) 0 1064- 1
252
Y.C. Jean et al. /Applied Surface Science 116 (1997) 251-255
2. Experiments The epoxy samples used in this study are the same as those reported in our previous studies by using fast positrons [6,7]. They are amine-cured epoxies with a chemical composition of DGEBA (diglycidylether of bisphenol-A), DDH (N,N'-dimethyl-l,6-diamino-hexane), and DAB (1,4-diaminobutane), all supplied by Imperial Chemical, Americas, at an equivalent ratio (5:3:2). A glass transition temperature (Tg) of 52°C was determined by DSC (differential scanning calorimetry) measurements. The samples were cured under a dry N 2 environment and spun at a speed of 1000 rpm on an aluminum plate during curing. The cured epoxy sample (thickness 25-35 /xm) coated on an aluminum plate was cut (1.5 cm × 1.5 cm) and then mounted in the beam line for the positron measurements. For each experiment, the sample was first heated to 130°C for 30 min and then slowly cooled down to the measurement temperature. The vacuum of the sample chamber was about 10- 6 and 10- 8 Torr at high and low temperatures, respectively. The positron annihilation lifetime (PAL) spectra were recorded at the intense slow-positron facility in the electrotechnical laboratory (ETL) [8]. The slow positrons were generated with the electron linac (75 MeV, 1 /xs, 50-100 pps) by the use of a Ta converter and a W moderator. The slow positrons generated were temporarily stored in a linear storage section and then extracted to the pulsing system as a quasi-continuous beam. The positron pulsing system consists of three stages under a magnetic field of 0.008 T: a reflection type chopper, a sub-harmonic pre-buncher, and a harmonic buncher. The final pulsed positron beam has a cross-section of 1 cm diameter with a variable energy from 100 eV to 30 keV. Monitoring of the positron lifetime began with the final pulsed signal (150 ps width) and terminated with the detection of annihilation photons by a BaF 2 scintillator. The lifetime resolution is 250 ps at a counting rate of 1000 cps (1 /zA of electron linac current). Each PAL was collected at a period of a few minutes with a total statistics of approximately 4 × 105 counts. The obtained PAL spectra were X 2 fitted into three or four lifetimes by using PATFIT programs [9]. Two series of PAL spectra were acquired-short-
gated (80 ns) and long-gated spectra (800 ns) to search for surface Ps and free Ps in vacuum, respectively. The Doppler broadening of energy spectra was measured at the National Institute of Materials and Chemical Research. Detailed methodology of the slow positrons and of the measurement of the Sparameters are described elsewhere [3].
3. Results and discussion All PAL spectra were first fitted into four lifetimes without any constraint. The longest lifetime (~'4) and the corresponding intensity (14) vary with the incident energy, as previously reported [2]. In order to obtain information about polymeric properties, we then analyzed all data into four components by constraining '7"1 0.12 ns and z4 6-142 ns (as determined from the unconstrained results). ~-~ and ~'4 are attributed to p-Ps annihilation and o-Ps emitted from the surface. Two intermediate lifetimes, ~'z --- 0.35-0.45 ns and "r3 1.0-4.0 ns, are attributed to the positron and to the o-Ps annihilation in the bulk a n d / o r near the surface of polymers, respectively. We also measured the PAL on the same sample using the conventional fast positron (22Na source) technique; the results are: rj = 0.145 + 0.09 ns, I I = 20.0 ___0.5%, r e = 0.382 __+0.09 ns, 12 = 56 ___2%, ~'3 = 1.60 _ 0.02 ns, and 13 = 24.0 ___0.2%. These are referred to as the bulk lifetimes in epoxy polymers. Fig. 1 shows the variations of ~'3 and 13 with respect to the positron incident energy. As shown in Fig. 1, 13 increases but "/'3 decreases as the energy increases. The increase of 13 is due to the increase of positronium formation in the bulk. The decrease of ~'3 is related to structural changes in free-volume holes, as a function of positron implantation depth from the surface. The mean implantation depth of the positron is normally expressed by the formula [10]: =
=
=
z ( E ) = ( 4 0 0 / p ) E ~'6
(1)
where z is expressed in ,~, p is the density in g / c m 3, and E is the incident energy in keV. For example, at the very low energy° E = 0.2 keV, the positron penetrates only about 27 A from the surface.
E C. Jean et al./Applied Surface Science 116 (1997) 251-255
Epoxy at 25°C 2.1
rable to but smaller than those reported by Xie et al. in different types of polymers. The decrease of ~'3 with respect to incident energy is very interesting because 73 is directly correlated to the radius of free-volume holes ( R f ) by the following equation [1]:
T
2.0 1.9 1.8
[
1.7
73 = 0.5 1
1.6 1.5 1.4 0
1
2
253
+
3
gf
+ 1.66
l(
,. t]-
sin 2~ Rf + 1.66
(3)
where ~'3 and g f are expressed in ns and ,~ respectively. A longer ~'3 at low incident positron energy indicates that the free-volume hole size is larger near the surface than in the bulk. The variation of freevolume radius (Rf) with respect to the mean depth (z) is plotted in Fig. 2. The hole size decreases from
Positron Energy (keV) 25
21
16 3.0 12 2.8
8 0
1
2
3
T
2.6 OO
v
2.4
Positron Energy (keV) Fig. 1. 7-3 and 13 versus positron incident energy in epoxy. 7-3 and 13 are o-Ps lifetime and intensity in the bulk of the polymer. The curve of I 3 is fitted to Eq. (2).
2.2 2.0
i
0
500
,
i
1000
,
i
1500
,
i
2000
OO
z (A)
Therefore, a very low fraction ( < 10%) of o-Ps annihilation in the bulk is observed for E < 0.2 keV. As the positron energy increases, the o-Ps annihilation in the bulk increases. When E > 2 keV, the PAL spectrum is identical to that obtained from the fast positron method. The variation o f 13 with respect to E is similar to an exponential function as reported by Xie et al. [4]. We then fit the 13 with E by an equation of the form
I3(E ) = I 3 ( ~ )
- [ I 3 ( ~ ) - I3(0)]e -E/E°
(2)
13(0) are the o-Ps bulk lifetime at E = zc and E = 0, respectively. I3(oo) is taken from the fast positron result, i.e., 24%. 13(0) and E o are two fitting parameters. The results are: I3(0)= 5% and E o = 0.73 + 0.01 keV. These results are compaw h e r e 13(oo) a n d
5.0
4.0
II
3.0
2.0
t .0
i
0
500
i
1000
,i
1500
i
2000
co
z (A)
Fig. 2. Frce-volumc hole radius (Rf) and fraction (fv) versus the mean implantation distance z from the surfacc of an epoxy polymer.
254
E C. Jean et a l . / Applied Surface Science 116 (1997) 251-255
2.9 ~, near the surface to 2.4 ,~ in the bulk. The formation mechanism of Ps in polymers is unknown. Xie et al. interpreted it in terms of a recombination process between positrons and electrons in a radiation track [4], while Kobayashi et al. used the Ore (hot) model [3]. Here we have applied the simple free-volume model originally proposed by Brandt et al. [11]; i.e., Ps is formed in the free volume of molecular, substrates. Thus o-Ps intensity is related to the number of free-volume holes and the freevolume hole fraction in the bulk, f v , can be calculated from an empirical equation [1]: f v = 0.0018 • 4
(4)
3
where f v and /~(~) are expressed in ~3 and % respectively. In Fig. 2, we also plot the variation of free-volume fraction, f v , with respect to the implantation distance z. f v increases as the distance nears the surface and reaches the bulk value as z > 1000 The increase of free-volume hole fraction near the surface is rather interesting. According to the Williams-Landel-Ferry (WLF) free-volume theory [12], the free volume fraction f v is directly related to the glass transition temperature by a semi-empirical equation [13]: f v =.fo + ( T -
T~)ol
(5)
where c~ is the difference in the thermal expansion coefficients above and below Tg and f0 is the reference free-volume fraction at Tg. In the epoxy poly-
80
60
I J
C
0
, 0
i 500
,
~ 1000
,
r 1500
,
i
Epoxy
at 25
°C
0.54
0.53
[]
[2]
[]
[]
0.52 Ca.
d,
0.52 [
0
2
4
6
8
10
Positron Energy (keV) Fig. 4. Variation of S-parameter versus positron incident energy in an epoxy polymer.
mer studied here, a = 4.0 × 10 -4 K - I . An increase of f v leads to a reduction of Tg. In Fig. 3, we plot the variation of Tg as estimated according to Eq. (5) and f v calculated from Eqs. (3) and (4) as a function of implantation distance (z). Near the surface, a lower ~ is obtained. The reduction of Tg near the surface has been predicted from theoretical calculations [14,15]. Recently, a Brillouin light scattering measurement in a freely standing polystyrene film showed a significant reduction of Tg near the surface [16]. That is contrary to the thermal expansion result by using X-ray reflectivity in a polystyrene film supported on silicon substrates [17]. The current PAL result supports the theoretical prediction of ~ reduction near the surface. The variation of o-Ps pick-off annihilation in the bulk can be monitored by measuring the S-parameter of the Doppler shift in the annihilation energy near 511 keV. Fig. 4 shows the variation of S with respect to the positron energy. The increase of S is due to the increase of o-Ps pick-off annihilation in the bulk. The variation of S is similar to that of 13 shown in Fig. 1. This is a further confirmation of the PAL results presented above.
2000
z (A) Fig. 3. Variation of glass transition temperature (T~) versus the mean. implantation distance z from the surface of an epoxy polymer. T~ is estimated from Eq. (5) and fv is calculated from Eqs. (3) and (4).
4. C o n c l u s i o n
We present free-volume hole properties as a function of distance from the surface to the bulk of an
Y.C. Jean et a l . / Applied SurJhce Science 116 (1997) 251-255
epoxy by using the PAL method. An increase of free-volume hole size and fraction near the surface is observed. A reduction of T~ near the surface has been estimated according to WFL theory.
Acknowledgements We are especially thankful to Dr. T.C. Sandreczki for preparing the thin-film samples of epoxy polymers for this experiment. This research has been supported by the National Science Foundation of the United States, by the University of Missouri Research Board, and by the Science and Technology Agency of Japan.
References [1] Y.C. Jean, in: Positron Spectroscopy of Solids, Eds. A. Dupasquier and A.P. Mills, Jr. (IOS Press, Amsterdam. 1995) p. 503. [2] Y.C. Jean, G.H, Dai, H. Shi, R. Suzuki and Y. Kobayashi, in: API Proc., Eds. E. Ottewitte and A.H. Weiss, Vol. 303 (1994) p. 129.
255
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