- Email: [email protected]
PEO studied by positron annihilation lifetime measurement1
1 November 1999
Physics Letters A 262 Ž1999. 195–205 www.elsevier.nlrlocaterphysleta
Compositional and temperature dependence of free volume in segmented copolymer PETrPEO studied by positron annihilation lifetime measurement 1 B. Wang b
a,)
, M. Zhang a , J.M. Zhang a , C.Q. He a , Y.Q. Dai a , S.J. Wang a , D.Z. Ma b
a Department of Physics, Wuhan UniÕersity, Wuhan 430072, China Department of Material Science and Engineering, UniÕersity of Science and Technology, Hefie 230026, China
Received 2 April 1999; received in revised form 10 August 1999; accepted 11 August 1999 Communicated by L. Sham
Abstract Positron lifetime measurements were performed for segmented copolymer polyŽethylene oxide. –polyŽethylene terephthalate. ŽPEOrPET. as a function of the hard segment content ŽPET. and the temperature, which is used to study the free volume properties, structural transition and miscibility behaviour of segmented copolymer PEOrPET. From the variation of the ortho-positronium Ž o-Ps. lifetimes with changes in the hard segment content, we find that the free volume decreases with increase of the hard segment, this fact means that the hard segment microdomains act as physical cross-links that suppress movement of the chains and that the interactions between the hard segment ŽPET. and soft segment ŽPEO. also plays an important role. On the other hand, the temperature dependence of positron lifetimes reveals the existence of two glass transition temperatures. This experimental results show that the hard segment PET is immiscibility with soft segment PEO in segmented copolymer PEOrPET ŽPEO molecular weight 4000, PET content 30 wt.%.. The maximum entropy lifetime method ŽMELT. is used to detect the distributions of the free volume holes. Large differences in width of the free volume hole distributions as a function of temperature are observed. q 1999 Elsevier Science B.V. All rights reserved. PACS: 78.70.Bj
1. Introduction Block copolymers have long sequences of one type of repeat unit joined at one or both ends to blocks of a different repeat unit. Such molecules possess physical and chemical properties that are quite different from the corresponding homopolymers. The reason is that the covalent bonding of two chemically dissimilar blocks
) 1
Corresponding author. Fax: q86-27-7812-661; e-mail: [email protected] Supported by the National Natural Science Foundation of China.
0375-9601r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 5 - 9 6 0 1 Ž 9 9 . 0 0 5 5 9 - 9
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composed of amorphous and crystalline segments results in a new material whose properties are not a simple function of the individual homopolymers. There has been considerable scientific and industrial interest in such materials, which has led to numerous studies of their structure and properties w1,2x, such as the rich variety of phase behavior, the interfacial and surfactant properties, the transition between the ordered state and the disordered state. On the other hand, copolymers are especially attractive in the fact that their molecular design may be tailored to a specific application by controlling such features as the copolymer Ži.e., diblock, triblock, or multiblock., as well as the block length of the respective blocks. A great number of techniques have been used to characterize the structure and thermal properties including differential scanning calorimetry ŽDSC. w3–5x, nuclear magnetic resonance ŽNMR. w6x, Fourier transform infrared ŽFTIR. w7–9x, small angle X-ray scattering ŽSAXS. w10–12x, dynamic mechanical analysis ŽDMA. w6x, scanning electron microscopy ŽSEM. w13x, and transmission electron microscopy ŽTEM. w14x. The utilization of copolymer polymers in industrial applications requires a basic understanding of their material properties. A key problem in this regard is relating the macroscopic properties to atomic-scale free volume hole. Although a great deal of research has been expended in the past decade towards understanding the influence of free volume on the physical properties of polymers, only limited information with regard to free volume size, concentration and shape has been forthcoming. In fact, reports of direct experimental measurement of these parameters are very scanty owing to the very small size and dynamic nature of the free volume w15x. In recent years, positron annihilation lifetime spectroscopy ŽPALS. has emerged as a unique and potent probe for detecting the free volume properties of polymers w16x. PALS is able to give direct information about the free volume at the atomic scale in polymers, which has been widely used in polymer studies w17–22x. The positron Žeq. is an antiparticle to the electron, and has properties identical to those of the electron except for the charge being positive. The positron preferentially samples regions of minimal positive charge density because of the repulsive interaction between eq and the positive nucleus. By introducing positrons from a radioactive source into a polymer sample, they diffuse at the free state or may form a bound-state positronium ŽPs. w16x after the positrons are thermalized. The typical lifetime of the free positron is in the range of 0.3–0.5 ns, whereas the lifetime of Ps atom depends on the spin state. The para-positronium Ž p-Ps. with the singlet state annihilation is in about 0.1 ns. The ortho-positronium Ž o-Ps. with the triplet state has an intrinsic lifetime of 140 ns in vacuum. However, in polymers the o-Ps atoms are preferentially localized in the atomic-scale holes and their lifetime is shortened to about 1–5 ns by the pick-off annihilation with an electron from the surrounding molecules. The o-Ps lifetime directly correlates to the free volume hole size and its intensity contains information about the free volume concentration w16x. The relationship between the o-Ps lifetime t 3 and the radius of the free volume hole R has been established by an empirical equation w23x.
t3s
1 2
1y
R
1 q
R0
2p
sin
2pR R0
y1
Ž 1.
˚ . is the fitted empirical electron layer thickness. Eq. Ž1. is obtained where R 0 s R q D R and D R Žs 1.656 A under the assumption that the hole has a spherical geometry and has an infinite potential for the Ps localizing. Further, the fractional free volume f is evaluated in terms of the o-Ps intensity I3 and the free volume hole size V s Ž4r3. p R 3 , f s CVI3 , where C is the constant. Recently, a numerical Laplace inversion technique ŽCONTIN. w24,25x and a maximum entropy method ŽMELT. w26,27x have been developed to resolve the continuous distribution of the o-Ps lifetime in polymers, which directly measure the free volume distribution w28–30x. In this paper, we report the results of the positron lifetime measurement on the segmented copolymer polyŽethylene oxide. –polyŽethylene terephthalate. ŽPEOrPET. as a function of PET content and temperature, and discuss the microstructural features and miscibility behaviour.
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2. Experiment 2.1. Sample preparation The series of polyŽethylene terephthalate. –polyŽethylene oxide. ŽPEOrPET. segmented copolymers with different lengths of soft segments ŽPEO. and different hard segments ŽPET. have been synthesized using a two-step reaction method according to the route as follows
Further details of the synthetic scheme were published elsewhere w6x. The PET content and length of hard segment determined by NMR, and the intrinsic viscosity values wh x were presented in Ref. w6x. They are listed in Table 1. 2.2. Positron lifetime measurement A 30 mCi 22 Na positron source sealed between two sheets of aluminum foil Ž1 mgrcm2 . was sandwiched between two pieces of the same samples. Positron lifetime measurements were carried out using a conventional
Table 1 Parameters of segmented copolymer PEOrPET Samples
PEOrPET-25 PEOrPET-30 PEOrPET-35 PEOrPET-40 PEOrPET-45 PEOrPET-30
PEO ŽM w . 2000 2000 2000 2000 2000 4000
Hard segment content
Length of hard segment
Theory
NMR
Theory
NMR
25 30 35 40 45 30
26.9 31.0 35.3 42.0 47.0 32.0
3.5 4.5 5.6 6.9 8.5 8.9
3.9 4.7 5.7 7.5 9.2 9.8
wh x ŽdL gy1 .
0.58 0.60 0.67 0.73 0.62 0.76
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fast–fast coincident spectrometer on samples of different hard segment content PET Žwt.%. ŽPEO molecular weight is 2000. at ambient temperature and on sample ŽPEO molecular weight 4000, PET content 30%. in the temperature range from 130 to 360 K respectively. Each spectrum contained approximately 10 6 counts for PATFIT w31x and 6 = 10 6 counts for MELT respectively.
3. Resuls and discussion 3.1. Composition dependence of the free Õolume The measured positron lifetime spectra of different hard content samples were best resolved into three components using POSITRONFIT after the background and the positron source correction were subtracted. Variances of fits Ž x 2 . were smaller than 1.2. The time resolution of the system was found to be a sum of two Gaussians with ŽFWHM.1 s 260 ps, Ž93%., and ŽFWHM. 2 s 340 ps, Ž7%.. Since the emphasis in this work is on the o-Ps annihilation characteristic, we do not discuss the first and second components. The compositional dependence of the o-Ps annihilation parameters are shown in Figs. 1–3 respectively. From Fig. 1, it is clear that the o-Ps lifetime shows no systematic variation with increase of the hard segment content and that it can be considered as a constant. This fact means that the size of the free volume hole does not vary with respect to the hard segment content. However, the o-Ps intensity decreases continuously with increasing hard segment content as shown in Fig. 2, which indicates that the concentration of the free volume hole diminishes as the PET content increases because the o-Ps intensity is assumed to be directly proportion to the number density of the free volume holes w16x. On the other hand, the change in the fractional free volume as a function of length of the hard segment content is the same as the change in the o-Ps intensity. As mentioned above, we can see that the greater the hard segment content, the less the free volume. The decreases of the
Fig. 1. o-Ps lifetime as a function of hard content ŽPET wt.%. for segmented copolymer PEOrPET.
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Fig. 2. o-Ps intensity as a function of hard content ŽPET wt.%. for segmented copolymer PEOrPET.
concentration of the free volume and the fractional free volume perhaps result from the two facts as follows. The one is that the hard segment microdomains act as thermally physical cross-linking w4x, which can suppress the movements of the chains; the other reason is that the interactions between the hard segment PET and soft
Fig. 3. Fractional free volume as a function of length of hard content for segmented copolymer PEOrPET.
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segment PEO can also limit the segmental motion. From Fig. 2, it is evident that the change in the o-Ps intensity is non-linear with linear increase of PET content, it doesn’t satisfy the addition rule as follows I3 Ž copolymer PEOrPET. s Ž 1 y x . I3 Ž PET . q xI3 Ž PET .
Ž 2.
where x is the weight fraction of PET Žwt.%., which suggests that the interactions among chains generated in copolymer PEOrPET affect the formation of free volume. Perhaps this fact means that the terephthalate groups of hard segment PET are influence on the formation of the positronium. 3.2. Temperature dependence of free Õolume 3.2.1. Structural transition and miscibility behaÕior The most important property of polymers is the glass transition because the macroscopic properties strongly depend on temperature. The glass transition temperature Tg represents the temperature at which there is a dramatic change of the properties of polymers, such as the specific volume, the specific heat, the viscoelastic and rheological properties, and the segmental motion, etc. It is well known, many physical properties can be described based on the free volume theory by an empirical equation — the Williams–Landel–Ferry ŽWLF. equation in which Tg is an important parameter. One of the most useful approaches to analyze the glass transition is to use the concept of free volume. It is envisaged that the free volume will be sensitive to the change in temperature. Positron spectroscopy is a useful tool to probe the atomic scale free volume. The plots of the o-Ps lifetime and fractional free volume as a function of temperature in the range 120–360 K are shown in Figs. 4 and 5a respectively. From Fig. 4, it is interesting that we observe three inflection points at 205, 270 and 310 K respectively. At the lowest temperatures up to 205 K, the o-Ps lifetimes are nearly constant with a slight rise in t 3 with increasing
Fig. 4. o-Ps lifetime as a function of temperature for segmented copolymer PEOrPET.
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Fig. 5. Fractional free volume as a temperature for segmented copolymer PEOrPET ŽPEO molecular weight 4000, PET content 30 wt.%..
temperature, which means that the size of the free volume is nearly unchanged. This is due to all motions including molecules and chains being completely frozen. Nevertheless, the change in the o-Ps lifetime is very marked between 205 K and 270 K, which indicates that the motions of partial main chains are activated owing to the thermal expansion of the free volume. It is noteworthy that the glass transition of pure PET occurs near 340 K Žsee below., hence, PET is still in glassy state in the temperature range 205–270 K, for this reason, the inflection point should be assigned to the PEO as the glass transition temperature Tg1 . It is necessary to point out the complex behaviour at inflection point 310 K. According to our previous work, T s 310 K may represent the liquid–liquid transition temperature Te for PEO, t 3 remains almost constant w16x above Te . If we took T s 310 K for Te , we should observe the constant of t 3 . In reality, t 3 increases rapidly with increasing temperature as shown in Fig. 4. It is appropriate that the inflection point at 310 K is identified as the glass transition Tg2 related to the PET. The glass transition temperature of PET in segmented copolymer is lower than that in pure PET Žsee later. because the PEO becomes viscoelastic state above 310 K and provides considerably the free volume to the migrations of molecules for PET, which makes the chains of PET migrate more easily. Similar results have been reported in previous literature w32x. Generally, the Tg determined by PALS is often a few Kelvins lower than Tg measured by DSC w33x inasmuch as the measured time for PALS is much longer than measured time for DSC, as shown in Table 2. The long-time relaxation process may affect significantly the molecular structure of polymer, and in particular the relaxation of molecular chains. Comparing the Tg1 with Tg2 , it is distinct that the
Table 2 Comparison of transition temperatures determined by PALS and DSC for segmented copolymer PEOrPET
Glass transition temperature Tg1 ŽK. Glass transition temperature Tg2 ŽK. b-transition temperature ŽK.
PALS
DSC
205 310 270
218 325 –
202
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slope of curve in the temperature range 270–360 K is more abrupt than the slope of curve in the temperature range 205–270 K. This fact can be explained as follows. First, the higher the temperature, the larger the expansion of the free volume. Secondly, as mentioned above, the motion of chains of PET can’t affect the motion of chains of PEO because PET maintains the glassy state below 270 K, but the motion of molecules and chains of rubbery state PEO can influence significantly the glass transition of PET, which means that the glass transition of PET in segmented copolymer gets easier than that in pure PET. This is why the value of Tg2 in segmented copolymer is lower than that in homopolymer PET.The temperature dependence of o-Ps intensity I3 is shown in Fig. 6 in the temperature range 120–360 K, we observe the increase of I3 with increase of temperature except for the narrow range near Tg1 and three inflection points. In addition, the variation of the fractional free volume as a function of temperature shows the similar three inflection points as shown in Fig. 5. When T - Tg1 , the matrix is in glassy state, the motions of all chains are frozen, thus to good approximation it can be assumed that the fractional free volume is nearly a constant, this is consistent with the free volume theory. When T ) Tg1 , the fractional free volume increases continuously with increasing temperature. It is surprising that the inflection point at 270 K is observed as shown in Figs. 4 and 5. In order to confirm what this point represents, the measurements of the positron annihilation parameters were performed for homopolymer PET as shown in Fig. 7. We find that there is a transition point near 265 K for PET and that the o-Ps lifetime displays a broad change. This is in good agreement with the result reported by Takayanagi Žfound in measurement of loss modulus E as a function of temperature at 138 Hz for PET samples of differing degrees of crystallinity. w34x. On the other hand, we didn’t observe the structural transition point at 270 K in previously studied for PEO w35x. According to Takayanagi’s report and our experimental results, we think that perhaps the inflection point at 270 K represents secondary relaxation, i.e., b transition. From Table 2, we can see that the sensitivity of probing the structural transitions by PALS is higher than those observed by DSC, because we didn’t observe the b transition point in the measurements of DSC. Now, we discuss the miscibility behavior of segmented copolymer PEOrPET by virtue of Figs. 4 and 5. Generally, the use of Tg in determination of polymer miscibilities based on the judgement that the observation
Fig. 6. o-Ps intensity as a function of temperature for segmented copolymer PEOrPET ŽPEO molecular weight 4000, PET content 30 wt.%..
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Fig. 7. o-Ps lifetime as a function of temperature for pure PET.
of a single Tg between those of pure components is taken as the evidence of miscibility. Tg can be determined by the empirical Fox equation Žfor example, see w36x. 1 Ws Wh s q Ž 3. Tg Tgs Tgh where Ws and Wh are the weight fraction of the soft segment and hard segment respectively in copolymer, Tgs and Tgh are the glass transition temperatures of the soft segment and the hard segment homopolymers respectively. Since a miscibility copolymer will exhibit a singe glass transition between the Tgs of the components with a sharpness of the transition similar to that of the component, therefore, the existences of two glass transition temperatures in the segmented copolymer PEOrPET shows that the hard segment PET and soft segment PEO are immiscibility to each other. This experimental result means that the phase separation occurs. Comparing the variation of the positron annihilation parameters as a function of temperature between the temperature range 270–310 K and above 310 K, it is evident that the slope of former is larger than that of later as shown in Figs. 4 and 5. Why so? The possible reason why the slope declines is that the PEO becomes quasi-liquid state above 310 K, which makes the o-Ps lifetime is temperature independence as experimentally observed due to the formation of the bubble w16x and makes slow the increase of the o-Ps lifetime. Under the circumstances, the increase of the o-Ps lifetime stems from only the contribution of hard segment of PET. 3.2.2. Free Õolume hole distribution In order to study the physical properties of free volume in segmented copolymer PEOrPET, the MELT program is used to determine the distributions of the free volume hole as a function of the temperature. Since the free volume hole exists in a distribution, the o-Ps lifetime is expressed more correctly as a distribution rather than as discrete values. In addition to the PATFIT analysis, the lifetime spectra were analyzed with the MELT program. Due to the heterogeneity of local molecular structure in a polymer and the existence of different positron state, it has been proposed that the experimental spectrum should contain an integral of continuous decay function w37x ` f Žt . yt y Ž t . s N0 R Ž t . ) exp dt q B Ž 4. t t 0 where y Ž t . is the experimentally measured spectrum, RŽ t . is the resolution function, ) denotes the convolution, f Žt . is the continuous positron lifetime probability distribution function ŽPDF., N0 is the number of counts, and
H
ž /
204
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Fig. 8. Free volume hole size distributions at different temperature for segmented copolymer PEOrPET ŽPEO molecular weight 4000, PET content 30 wt.%..
B is the noise and number of background counts. Recently, Shukla and co-workers w26,27x have developed a program named the maximum entropy lifetime method ŽMELT., in which the maximum entropy method of solution is applied. It has been shown that MELT is a promising method for finding a reliable o-Ps lifetime distribution in polymers w38x. Fig. 8 shows the free volume hole radius distribution at different temperatures. From Fig. 8, we can see that the higher the temperature, the larger the radius of the free volume hole, this is due to the thermal expansion of the free volume. Comparing the distributions of the free volume holes for different temperature, we find that the value of peak of distribution shifts toward higher value and the distribution becomes extremely broad with a rise in temperature. Simultaneously, the low temperature peak is quite narrow, which means that the change in the free volume hole radius is very small because the matrix is in glassy state. However, the middle peak Žat 270 K. is very broad and has not only two tails stretching out toward smaller and larger radius respectively but also unsymmetric distribution. Small holes and larger holes result from the contribution of the glassy state PET and the rubbery state PEO respectively. Perhaps this fact suggests that the microphase separation occurs in this segmented copolymer, further studies on this observation is needed.
4. Conclusion The positron annihilation lifetime measurements as a function of composition and temperature were made for the segmented copolymer PETrPEO. The compositional dependence of the o-Ps lifetime indicates that the hard segment content play an important role. The greater the hard segment content, the stronger the physical cross-linking and the interaction between the soft and hard segments, which brings about the decrease of the free volume. From the variations of the o-Ps annihilation parameters as a function of temperature, we observe two glass transition temperatures for sample ŽPEO molecular weight 4000, PET content 30 wt.%., which suggests that the PEO is immiscibility with PET in segmented copolymer PEOrPET.
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5. Further reading The reader may be interested in the following references: w39,40x.
References w1x I. Goodman ŽEd.., Development in Block Copolymers, Applied Science, New York, 1982. w2x M.J. Folks ŽEd.., Processing, Structure and Properties of Block Copolymers, Elsevier, New York, 1985. w3x L. Hager, T.B. MacCvury, R.M. Gerkin, F.E. Critchfield, Urethane Chemistry and Applications, ACS Symposium Serves 172, ACS, Washington, DC, 1981. w4x T.K. Chew, J.Y. Chui, T.S. Shieh, Macromolecules 30 Ž1997. 5068. w5x T.K. Chen, T.S. Shieh, J.Y. Chui, Macromolecules 31 Ž1998. 1312. w6x X.L. Luo, X.U. Zhang, M.T. Wang, D.Z. Mar, Chem. J. Chinese Univ. 18 Ž1997. 642. w7x W.P. Yang, C.W. Macosko, Makromol. Chem., Macromol. Symp. 25 Ž1989. 33. w8x T.J. Hsu, L.J. Lee, Polym. Eng. Sci. 28 Ž1998. 955. w9x H. Ishida, C. Scott, J. Polym. Eng. 6 Ž1986. 201. w10x M.J. Elwell, S. Mortinmer, A.J. Ryan, Macromolecules 27 Ž1994. 94. w11x W. Bcas, G.E. DErbyshire, D. Bogg, J. Cooke, M.J. Elwell et al., Science 267 Ž1995. 996. w12x A.J. Ryan, W.R. Willkoman, T.B. Bergstran, C.W. Mbcosko et al., Macromolecules 24 Ž1991. 2883. w13x N. Lou, D.N. Wang, S.K. Ying, J. Polym. Sci. B: Polym. Phys. 35 Ž1997. 865. w14x B.G. Risch, D.E. Rodrigons, K.R. Lyan, J.E. McGrath, G.L. Wilkest, Polymer 37 Ž1996. 1229. w15x J.D. Ferry, Viscoelastic Properties of Polymers, 3rd edn., John Wiley and Sons, New York, 25, 1987, 2511. w16x Y.C. Jean, Microchem. J. 42 Ž1990. 72. w17x B. Wang, S.Q. Li, S.J. Wang, Phys. Rev. B 56 Ž1997. 503. w18x B. Wang, C.Q. He, J.M. Zhang, S.Q. Li, S.J. Wang et al., Phys. Lett. A 235 Ž1997. 557. w19x C.L. Wang, S.J. Wang, Z.N. Qi, J. Polym. Sci. B: Polym. Phys. 34 Ž1996. 193. w20x C.L. Wang, S.J. Wang, Polymer 38 Ž1997. 173. ˇ ˇ Macromolecules 30 Ž1997. 6909. w21x J. Bartos, O. Sausa, ˇ P. Bandzuch, ˇ w22x J. Liu, Y.C. Jean, Macromolecules 28 Ž1995. 5774. w23x H. Nakanishi, S.J. Wang, Y.C. Jean, in: S.C. Sharma ŽEd.., Positron Annihilation Studies of Fluid, vol. 292, World Scientific, Singapore, 1988. w24x R.B. Gregor, Y. Zhu, Nucl. Instr. Methods A 302 Ž1991. 496. w25x R.B. Gregor, Y. Zhu, Nucl. Instr. Methods A 290 Ž1990. 172. w26x L. Hoffmann, A. Shukla, M. Peter et al., Nucl. Instr. Methods A 355 Ž1993. 276. w27x A. Shukla, M. Peter, L. Hoffmann, Nucl. Instr. Methods A 355 Ž1993. 310. w28x C.L. Wang, H.J. Frans, Macromolecules 29 Ž1996. 8249. w29x G. Dluek, C.H. Hubner, S. Echler, Nucl. Instr. Methods B 142 Ž1998. 191. ¨ w30x C.L. Wang, T. Hirade, F.H.J. Maurer, J. Chem. Phys. 108 Ž1998. 4654. w31x P. Kirkegaard, M. Eldrup, O. Mogensen, J. Peterson, Comput. Phys. Commun. 23 Ž1981. 307. w32x D.C. Pan, Q.D. Bao, T.Y. Yu, Mechanical Properties of Polymers and Blend Polymers, Shanghai Sci. and Tech. press, 1988, p. 250 Žin chinese.. w33x D. Lin, S.J. Wang, J. Phys. Condens. Matter 4 Ž1992. 3331. w34x I.M. Ward, Mechanical Properties of Solid Polymers, 2nd edn., John Wiley and Sons, New York, 1983. w35x B. Wang, Z.L. Peng, Y.Q. Dai, S.J. Wang et al., J. Phys. IV 3 Ž1993. 257. w36x M.M.A. Najjar, S.H. Hamid, E.Z. Hamad, Polym. Eng. Sci. 36 Ž1996. 2083. w37x D.M. Scharader, S.G. Usmar, in: S.C. Sharma ŽEd.., Positron Annihilation Studied on Fluids, World Scientific Publishing, Singpore, 1988, p. 215. w38x C. Wastlund, F.H.J. Maurer, Nucl. Instr. Methods B 117 Ž1996. 467. ˇ w39x M. Eldrup, D. Lightbody, J.N. Sherwood, Chem. Phys. 63 Ž1981. 51. w40x S.J. Tao, J. Phys. Chem. 56 Ž1972. 5499.
Physics Letters A 262 Ž1999. 195–205 www.elsevier.nlrlocaterphysleta
Compositional and temperature dependence of free volume in segmented copolymer PETrPEO studied by positron annihilation lifetime measurement 1 B. Wang b
a,)
, M. Zhang a , J.M. Zhang a , C.Q. He a , Y.Q. Dai a , S.J. Wang a , D.Z. Ma b
a Department of Physics, Wuhan UniÕersity, Wuhan 430072, China Department of Material Science and Engineering, UniÕersity of Science and Technology, Hefie 230026, China
Received 2 April 1999; received in revised form 10 August 1999; accepted 11 August 1999 Communicated by L. Sham
Abstract Positron lifetime measurements were performed for segmented copolymer polyŽethylene oxide. –polyŽethylene terephthalate. ŽPEOrPET. as a function of the hard segment content ŽPET. and the temperature, which is used to study the free volume properties, structural transition and miscibility behaviour of segmented copolymer PEOrPET. From the variation of the ortho-positronium Ž o-Ps. lifetimes with changes in the hard segment content, we find that the free volume decreases with increase of the hard segment, this fact means that the hard segment microdomains act as physical cross-links that suppress movement of the chains and that the interactions between the hard segment ŽPET. and soft segment ŽPEO. also plays an important role. On the other hand, the temperature dependence of positron lifetimes reveals the existence of two glass transition temperatures. This experimental results show that the hard segment PET is immiscibility with soft segment PEO in segmented copolymer PEOrPET ŽPEO molecular weight 4000, PET content 30 wt.%.. The maximum entropy lifetime method ŽMELT. is used to detect the distributions of the free volume holes. Large differences in width of the free volume hole distributions as a function of temperature are observed. q 1999 Elsevier Science B.V. All rights reserved. PACS: 78.70.Bj
1. Introduction Block copolymers have long sequences of one type of repeat unit joined at one or both ends to blocks of a different repeat unit. Such molecules possess physical and chemical properties that are quite different from the corresponding homopolymers. The reason is that the covalent bonding of two chemically dissimilar blocks
) 1
Corresponding author. Fax: q86-27-7812-661; e-mail: [email protected] Supported by the National Natural Science Foundation of China.
0375-9601r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 5 - 9 6 0 1 Ž 9 9 . 0 0 5 5 9 - 9
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composed of amorphous and crystalline segments results in a new material whose properties are not a simple function of the individual homopolymers. There has been considerable scientific and industrial interest in such materials, which has led to numerous studies of their structure and properties w1,2x, such as the rich variety of phase behavior, the interfacial and surfactant properties, the transition between the ordered state and the disordered state. On the other hand, copolymers are especially attractive in the fact that their molecular design may be tailored to a specific application by controlling such features as the copolymer Ži.e., diblock, triblock, or multiblock., as well as the block length of the respective blocks. A great number of techniques have been used to characterize the structure and thermal properties including differential scanning calorimetry ŽDSC. w3–5x, nuclear magnetic resonance ŽNMR. w6x, Fourier transform infrared ŽFTIR. w7–9x, small angle X-ray scattering ŽSAXS. w10–12x, dynamic mechanical analysis ŽDMA. w6x, scanning electron microscopy ŽSEM. w13x, and transmission electron microscopy ŽTEM. w14x. The utilization of copolymer polymers in industrial applications requires a basic understanding of their material properties. A key problem in this regard is relating the macroscopic properties to atomic-scale free volume hole. Although a great deal of research has been expended in the past decade towards understanding the influence of free volume on the physical properties of polymers, only limited information with regard to free volume size, concentration and shape has been forthcoming. In fact, reports of direct experimental measurement of these parameters are very scanty owing to the very small size and dynamic nature of the free volume w15x. In recent years, positron annihilation lifetime spectroscopy ŽPALS. has emerged as a unique and potent probe for detecting the free volume properties of polymers w16x. PALS is able to give direct information about the free volume at the atomic scale in polymers, which has been widely used in polymer studies w17–22x. The positron Žeq. is an antiparticle to the electron, and has properties identical to those of the electron except for the charge being positive. The positron preferentially samples regions of minimal positive charge density because of the repulsive interaction between eq and the positive nucleus. By introducing positrons from a radioactive source into a polymer sample, they diffuse at the free state or may form a bound-state positronium ŽPs. w16x after the positrons are thermalized. The typical lifetime of the free positron is in the range of 0.3–0.5 ns, whereas the lifetime of Ps atom depends on the spin state. The para-positronium Ž p-Ps. with the singlet state annihilation is in about 0.1 ns. The ortho-positronium Ž o-Ps. with the triplet state has an intrinsic lifetime of 140 ns in vacuum. However, in polymers the o-Ps atoms are preferentially localized in the atomic-scale holes and their lifetime is shortened to about 1–5 ns by the pick-off annihilation with an electron from the surrounding molecules. The o-Ps lifetime directly correlates to the free volume hole size and its intensity contains information about the free volume concentration w16x. The relationship between the o-Ps lifetime t 3 and the radius of the free volume hole R has been established by an empirical equation w23x.
t3s
1 2
1y
R
1 q
R0
2p
sin
2pR R0
y1
Ž 1.
˚ . is the fitted empirical electron layer thickness. Eq. Ž1. is obtained where R 0 s R q D R and D R Žs 1.656 A under the assumption that the hole has a spherical geometry and has an infinite potential for the Ps localizing. Further, the fractional free volume f is evaluated in terms of the o-Ps intensity I3 and the free volume hole size V s Ž4r3. p R 3 , f s CVI3 , where C is the constant. Recently, a numerical Laplace inversion technique ŽCONTIN. w24,25x and a maximum entropy method ŽMELT. w26,27x have been developed to resolve the continuous distribution of the o-Ps lifetime in polymers, which directly measure the free volume distribution w28–30x. In this paper, we report the results of the positron lifetime measurement on the segmented copolymer polyŽethylene oxide. –polyŽethylene terephthalate. ŽPEOrPET. as a function of PET content and temperature, and discuss the microstructural features and miscibility behaviour.
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2. Experiment 2.1. Sample preparation The series of polyŽethylene terephthalate. –polyŽethylene oxide. ŽPEOrPET. segmented copolymers with different lengths of soft segments ŽPEO. and different hard segments ŽPET. have been synthesized using a two-step reaction method according to the route as follows
Further details of the synthetic scheme were published elsewhere w6x. The PET content and length of hard segment determined by NMR, and the intrinsic viscosity values wh x were presented in Ref. w6x. They are listed in Table 1. 2.2. Positron lifetime measurement A 30 mCi 22 Na positron source sealed between two sheets of aluminum foil Ž1 mgrcm2 . was sandwiched between two pieces of the same samples. Positron lifetime measurements were carried out using a conventional
Table 1 Parameters of segmented copolymer PEOrPET Samples
PEOrPET-25 PEOrPET-30 PEOrPET-35 PEOrPET-40 PEOrPET-45 PEOrPET-30
PEO ŽM w . 2000 2000 2000 2000 2000 4000
Hard segment content
Length of hard segment
Theory
NMR
Theory
NMR
25 30 35 40 45 30
26.9 31.0 35.3 42.0 47.0 32.0
3.5 4.5 5.6 6.9 8.5 8.9
3.9 4.7 5.7 7.5 9.2 9.8
wh x ŽdL gy1 .
0.58 0.60 0.67 0.73 0.62 0.76
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fast–fast coincident spectrometer on samples of different hard segment content PET Žwt.%. ŽPEO molecular weight is 2000. at ambient temperature and on sample ŽPEO molecular weight 4000, PET content 30%. in the temperature range from 130 to 360 K respectively. Each spectrum contained approximately 10 6 counts for PATFIT w31x and 6 = 10 6 counts for MELT respectively.
3. Resuls and discussion 3.1. Composition dependence of the free Õolume The measured positron lifetime spectra of different hard content samples were best resolved into three components using POSITRONFIT after the background and the positron source correction were subtracted. Variances of fits Ž x 2 . were smaller than 1.2. The time resolution of the system was found to be a sum of two Gaussians with ŽFWHM.1 s 260 ps, Ž93%., and ŽFWHM. 2 s 340 ps, Ž7%.. Since the emphasis in this work is on the o-Ps annihilation characteristic, we do not discuss the first and second components. The compositional dependence of the o-Ps annihilation parameters are shown in Figs. 1–3 respectively. From Fig. 1, it is clear that the o-Ps lifetime shows no systematic variation with increase of the hard segment content and that it can be considered as a constant. This fact means that the size of the free volume hole does not vary with respect to the hard segment content. However, the o-Ps intensity decreases continuously with increasing hard segment content as shown in Fig. 2, which indicates that the concentration of the free volume hole diminishes as the PET content increases because the o-Ps intensity is assumed to be directly proportion to the number density of the free volume holes w16x. On the other hand, the change in the fractional free volume as a function of length of the hard segment content is the same as the change in the o-Ps intensity. As mentioned above, we can see that the greater the hard segment content, the less the free volume. The decreases of the
Fig. 1. o-Ps lifetime as a function of hard content ŽPET wt.%. for segmented copolymer PEOrPET.
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Fig. 2. o-Ps intensity as a function of hard content ŽPET wt.%. for segmented copolymer PEOrPET.
concentration of the free volume and the fractional free volume perhaps result from the two facts as follows. The one is that the hard segment microdomains act as thermally physical cross-linking w4x, which can suppress the movements of the chains; the other reason is that the interactions between the hard segment PET and soft
Fig. 3. Fractional free volume as a function of length of hard content for segmented copolymer PEOrPET.
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segment PEO can also limit the segmental motion. From Fig. 2, it is evident that the change in the o-Ps intensity is non-linear with linear increase of PET content, it doesn’t satisfy the addition rule as follows I3 Ž copolymer PEOrPET. s Ž 1 y x . I3 Ž PET . q xI3 Ž PET .
Ž 2.
where x is the weight fraction of PET Žwt.%., which suggests that the interactions among chains generated in copolymer PEOrPET affect the formation of free volume. Perhaps this fact means that the terephthalate groups of hard segment PET are influence on the formation of the positronium. 3.2. Temperature dependence of free Õolume 3.2.1. Structural transition and miscibility behaÕior The most important property of polymers is the glass transition because the macroscopic properties strongly depend on temperature. The glass transition temperature Tg represents the temperature at which there is a dramatic change of the properties of polymers, such as the specific volume, the specific heat, the viscoelastic and rheological properties, and the segmental motion, etc. It is well known, many physical properties can be described based on the free volume theory by an empirical equation — the Williams–Landel–Ferry ŽWLF. equation in which Tg is an important parameter. One of the most useful approaches to analyze the glass transition is to use the concept of free volume. It is envisaged that the free volume will be sensitive to the change in temperature. Positron spectroscopy is a useful tool to probe the atomic scale free volume. The plots of the o-Ps lifetime and fractional free volume as a function of temperature in the range 120–360 K are shown in Figs. 4 and 5a respectively. From Fig. 4, it is interesting that we observe three inflection points at 205, 270 and 310 K respectively. At the lowest temperatures up to 205 K, the o-Ps lifetimes are nearly constant with a slight rise in t 3 with increasing
Fig. 4. o-Ps lifetime as a function of temperature for segmented copolymer PEOrPET.
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Fig. 5. Fractional free volume as a temperature for segmented copolymer PEOrPET ŽPEO molecular weight 4000, PET content 30 wt.%..
temperature, which means that the size of the free volume is nearly unchanged. This is due to all motions including molecules and chains being completely frozen. Nevertheless, the change in the o-Ps lifetime is very marked between 205 K and 270 K, which indicates that the motions of partial main chains are activated owing to the thermal expansion of the free volume. It is noteworthy that the glass transition of pure PET occurs near 340 K Žsee below., hence, PET is still in glassy state in the temperature range 205–270 K, for this reason, the inflection point should be assigned to the PEO as the glass transition temperature Tg1 . It is necessary to point out the complex behaviour at inflection point 310 K. According to our previous work, T s 310 K may represent the liquid–liquid transition temperature Te for PEO, t 3 remains almost constant w16x above Te . If we took T s 310 K for Te , we should observe the constant of t 3 . In reality, t 3 increases rapidly with increasing temperature as shown in Fig. 4. It is appropriate that the inflection point at 310 K is identified as the glass transition Tg2 related to the PET. The glass transition temperature of PET in segmented copolymer is lower than that in pure PET Žsee later. because the PEO becomes viscoelastic state above 310 K and provides considerably the free volume to the migrations of molecules for PET, which makes the chains of PET migrate more easily. Similar results have been reported in previous literature w32x. Generally, the Tg determined by PALS is often a few Kelvins lower than Tg measured by DSC w33x inasmuch as the measured time for PALS is much longer than measured time for DSC, as shown in Table 2. The long-time relaxation process may affect significantly the molecular structure of polymer, and in particular the relaxation of molecular chains. Comparing the Tg1 with Tg2 , it is distinct that the
Table 2 Comparison of transition temperatures determined by PALS and DSC for segmented copolymer PEOrPET
Glass transition temperature Tg1 ŽK. Glass transition temperature Tg2 ŽK. b-transition temperature ŽK.
PALS
DSC
205 310 270
218 325 –
202
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slope of curve in the temperature range 270–360 K is more abrupt than the slope of curve in the temperature range 205–270 K. This fact can be explained as follows. First, the higher the temperature, the larger the expansion of the free volume. Secondly, as mentioned above, the motion of chains of PET can’t affect the motion of chains of PEO because PET maintains the glassy state below 270 K, but the motion of molecules and chains of rubbery state PEO can influence significantly the glass transition of PET, which means that the glass transition of PET in segmented copolymer gets easier than that in pure PET. This is why the value of Tg2 in segmented copolymer is lower than that in homopolymer PET.The temperature dependence of o-Ps intensity I3 is shown in Fig. 6 in the temperature range 120–360 K, we observe the increase of I3 with increase of temperature except for the narrow range near Tg1 and three inflection points. In addition, the variation of the fractional free volume as a function of temperature shows the similar three inflection points as shown in Fig. 5. When T - Tg1 , the matrix is in glassy state, the motions of all chains are frozen, thus to good approximation it can be assumed that the fractional free volume is nearly a constant, this is consistent with the free volume theory. When T ) Tg1 , the fractional free volume increases continuously with increasing temperature. It is surprising that the inflection point at 270 K is observed as shown in Figs. 4 and 5. In order to confirm what this point represents, the measurements of the positron annihilation parameters were performed for homopolymer PET as shown in Fig. 7. We find that there is a transition point near 265 K for PET and that the o-Ps lifetime displays a broad change. This is in good agreement with the result reported by Takayanagi Žfound in measurement of loss modulus E as a function of temperature at 138 Hz for PET samples of differing degrees of crystallinity. w34x. On the other hand, we didn’t observe the structural transition point at 270 K in previously studied for PEO w35x. According to Takayanagi’s report and our experimental results, we think that perhaps the inflection point at 270 K represents secondary relaxation, i.e., b transition. From Table 2, we can see that the sensitivity of probing the structural transitions by PALS is higher than those observed by DSC, because we didn’t observe the b transition point in the measurements of DSC. Now, we discuss the miscibility behavior of segmented copolymer PEOrPET by virtue of Figs. 4 and 5. Generally, the use of Tg in determination of polymer miscibilities based on the judgement that the observation
Fig. 6. o-Ps intensity as a function of temperature for segmented copolymer PEOrPET ŽPEO molecular weight 4000, PET content 30 wt.%..
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Fig. 7. o-Ps lifetime as a function of temperature for pure PET.
of a single Tg between those of pure components is taken as the evidence of miscibility. Tg can be determined by the empirical Fox equation Žfor example, see w36x. 1 Ws Wh s q Ž 3. Tg Tgs Tgh where Ws and Wh are the weight fraction of the soft segment and hard segment respectively in copolymer, Tgs and Tgh are the glass transition temperatures of the soft segment and the hard segment homopolymers respectively. Since a miscibility copolymer will exhibit a singe glass transition between the Tgs of the components with a sharpness of the transition similar to that of the component, therefore, the existences of two glass transition temperatures in the segmented copolymer PEOrPET shows that the hard segment PET and soft segment PEO are immiscibility to each other. This experimental result means that the phase separation occurs. Comparing the variation of the positron annihilation parameters as a function of temperature between the temperature range 270–310 K and above 310 K, it is evident that the slope of former is larger than that of later as shown in Figs. 4 and 5. Why so? The possible reason why the slope declines is that the PEO becomes quasi-liquid state above 310 K, which makes the o-Ps lifetime is temperature independence as experimentally observed due to the formation of the bubble w16x and makes slow the increase of the o-Ps lifetime. Under the circumstances, the increase of the o-Ps lifetime stems from only the contribution of hard segment of PET. 3.2.2. Free Õolume hole distribution In order to study the physical properties of free volume in segmented copolymer PEOrPET, the MELT program is used to determine the distributions of the free volume hole as a function of the temperature. Since the free volume hole exists in a distribution, the o-Ps lifetime is expressed more correctly as a distribution rather than as discrete values. In addition to the PATFIT analysis, the lifetime spectra were analyzed with the MELT program. Due to the heterogeneity of local molecular structure in a polymer and the existence of different positron state, it has been proposed that the experimental spectrum should contain an integral of continuous decay function w37x ` f Žt . yt y Ž t . s N0 R Ž t . ) exp dt q B Ž 4. t t 0 where y Ž t . is the experimentally measured spectrum, RŽ t . is the resolution function, ) denotes the convolution, f Žt . is the continuous positron lifetime probability distribution function ŽPDF., N0 is the number of counts, and
H
ž /
204
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Fig. 8. Free volume hole size distributions at different temperature for segmented copolymer PEOrPET ŽPEO molecular weight 4000, PET content 30 wt.%..
B is the noise and number of background counts. Recently, Shukla and co-workers w26,27x have developed a program named the maximum entropy lifetime method ŽMELT., in which the maximum entropy method of solution is applied. It has been shown that MELT is a promising method for finding a reliable o-Ps lifetime distribution in polymers w38x. Fig. 8 shows the free volume hole radius distribution at different temperatures. From Fig. 8, we can see that the higher the temperature, the larger the radius of the free volume hole, this is due to the thermal expansion of the free volume. Comparing the distributions of the free volume holes for different temperature, we find that the value of peak of distribution shifts toward higher value and the distribution becomes extremely broad with a rise in temperature. Simultaneously, the low temperature peak is quite narrow, which means that the change in the free volume hole radius is very small because the matrix is in glassy state. However, the middle peak Žat 270 K. is very broad and has not only two tails stretching out toward smaller and larger radius respectively but also unsymmetric distribution. Small holes and larger holes result from the contribution of the glassy state PET and the rubbery state PEO respectively. Perhaps this fact suggests that the microphase separation occurs in this segmented copolymer, further studies on this observation is needed.
4. Conclusion The positron annihilation lifetime measurements as a function of composition and temperature were made for the segmented copolymer PETrPEO. The compositional dependence of the o-Ps lifetime indicates that the hard segment content play an important role. The greater the hard segment content, the stronger the physical cross-linking and the interaction between the soft and hard segments, which brings about the decrease of the free volume. From the variations of the o-Ps annihilation parameters as a function of temperature, we observe two glass transition temperatures for sample ŽPEO molecular weight 4000, PET content 30 wt.%., which suggests that the PEO is immiscibility with PET in segmented copolymer PEOrPET.
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5. Further reading The reader may be interested in the following references: w39,40x.
References w1x I. Goodman ŽEd.., Development in Block Copolymers, Applied Science, New York, 1982. w2x M.J. Folks ŽEd.., Processing, Structure and Properties of Block Copolymers, Elsevier, New York, 1985. w3x L. Hager, T.B. MacCvury, R.M. Gerkin, F.E. Critchfield, Urethane Chemistry and Applications, ACS Symposium Serves 172, ACS, Washington, DC, 1981. w4x T.K. Chew, J.Y. Chui, T.S. Shieh, Macromolecules 30 Ž1997. 5068. w5x T.K. Chen, T.S. Shieh, J.Y. Chui, Macromolecules 31 Ž1998. 1312. w6x X.L. Luo, X.U. Zhang, M.T. Wang, D.Z. Mar, Chem. J. Chinese Univ. 18 Ž1997. 642. w7x W.P. Yang, C.W. Macosko, Makromol. Chem., Macromol. Symp. 25 Ž1989. 33. w8x T.J. Hsu, L.J. Lee, Polym. Eng. Sci. 28 Ž1998. 955. w9x H. Ishida, C. Scott, J. Polym. Eng. 6 Ž1986. 201. w10x M.J. Elwell, S. Mortinmer, A.J. Ryan, Macromolecules 27 Ž1994. 94. w11x W. Bcas, G.E. DErbyshire, D. Bogg, J. Cooke, M.J. Elwell et al., Science 267 Ž1995. 996. w12x A.J. Ryan, W.R. Willkoman, T.B. Bergstran, C.W. Mbcosko et al., Macromolecules 24 Ž1991. 2883. w13x N. Lou, D.N. Wang, S.K. Ying, J. Polym. Sci. B: Polym. Phys. 35 Ž1997. 865. w14x B.G. Risch, D.E. Rodrigons, K.R. Lyan, J.E. McGrath, G.L. Wilkest, Polymer 37 Ž1996. 1229. w15x J.D. Ferry, Viscoelastic Properties of Polymers, 3rd edn., John Wiley and Sons, New York, 25, 1987, 2511. w16x Y.C. Jean, Microchem. J. 42 Ž1990. 72. w17x B. Wang, S.Q. Li, S.J. Wang, Phys. Rev. B 56 Ž1997. 503. w18x B. Wang, C.Q. He, J.M. Zhang, S.Q. Li, S.J. Wang et al., Phys. Lett. A 235 Ž1997. 557. w19x C.L. Wang, S.J. Wang, Z.N. Qi, J. Polym. Sci. B: Polym. Phys. 34 Ž1996. 193. w20x C.L. Wang, S.J. Wang, Polymer 38 Ž1997. 173. ˇ ˇ Macromolecules 30 Ž1997. 6909. w21x J. Bartos, O. Sausa, ˇ P. Bandzuch, ˇ w22x J. Liu, Y.C. Jean, Macromolecules 28 Ž1995. 5774. w23x H. Nakanishi, S.J. Wang, Y.C. Jean, in: S.C. Sharma ŽEd.., Positron Annihilation Studies of Fluid, vol. 292, World Scientific, Singapore, 1988. w24x R.B. Gregor, Y. Zhu, Nucl. Instr. Methods A 302 Ž1991. 496. w25x R.B. Gregor, Y. Zhu, Nucl. Instr. Methods A 290 Ž1990. 172. w26x L. Hoffmann, A. Shukla, M. Peter et al., Nucl. Instr. Methods A 355 Ž1993. 276. w27x A. Shukla, M. Peter, L. Hoffmann, Nucl. Instr. Methods A 355 Ž1993. 310. w28x C.L. Wang, H.J. Frans, Macromolecules 29 Ž1996. 8249. w29x G. Dluek, C.H. Hubner, S. Echler, Nucl. Instr. Methods B 142 Ž1998. 191. ¨ w30x C.L. Wang, T. Hirade, F.H.J. Maurer, J. Chem. Phys. 108 Ž1998. 4654. w31x P. Kirkegaard, M. Eldrup, O. Mogensen, J. Peterson, Comput. Phys. Commun. 23 Ž1981. 307. w32x D.C. Pan, Q.D. Bao, T.Y. Yu, Mechanical Properties of Polymers and Blend Polymers, Shanghai Sci. and Tech. press, 1988, p. 250 Žin chinese.. w33x D. Lin, S.J. Wang, J. Phys. Condens. Matter 4 Ž1992. 3331. w34x I.M. Ward, Mechanical Properties of Solid Polymers, 2nd edn., John Wiley and Sons, New York, 1983. w35x B. Wang, Z.L. Peng, Y.Q. Dai, S.J. Wang et al., J. Phys. IV 3 Ž1993. 257. w36x M.M.A. Najjar, S.H. Hamid, E.Z. Hamad, Polym. Eng. Sci. 36 Ž1996. 2083. w37x D.M. Scharader, S.G. Usmar, in: S.C. Sharma ŽEd.., Positron Annihilation Studied on Fluids, World Scientific Publishing, Singpore, 1988, p. 215. w38x C. Wastlund, F.H.J. Maurer, Nucl. Instr. Methods B 117 Ž1996. 467. ˇ w39x M. Eldrup, D. Lightbody, J.N. Sherwood, Chem. Phys. 63 Ž1981. 51. w40x S.J. Tao, J. Phys. Chem. 56 Ž1972. 5499.