- Email: [email protected]
Birefringence change in epoxy glass aged under strain
Journal of Non-Crystalline Solids 352 (2006) 4956–4959 www.elsevier.com/locate/jnoncrysol
Birefringence change in epoxy glass aged under strain Hiroshi Kawakami *, Keiji Kishimoto, Yukuo Nanzai, Yoshihiro Sato Department of Mechanical Engineering, Osaka City University Sugimoto, Sumiyoshi, Osaka 558–8585, Japan Available online 1 September 2006
Abstract Structural relaxation in epoxy glass aged under strain (strain aging) was studied by means of birefringence. Two types of samples were prepared from the same epoxy precursor: one has a crosslinked structure and the other has a linear molecular structure. Epoxy glasses were uniaxially elongated and then strain aged for various aging times. Elongation was resumed at the end of strain aging. Birefringence change was measured over strain aging tests. Modified stress-optical rule, MSOR, was applied to experimental results to separate (total) stress into two stress components: glassy stress and rubbery stress. Experimental results indicated that crosslinks cause co-operation between the thermal motions of flexible polymer chains and the rotational orientation of the monomer unit around the chain axis. 2006 Elsevier B.V. All rights reserved. PACS: 83.80.Ab; 61.43.Fs; 83.85.St; 42.70.Ce; 83.80.Jx Keywords: Optical properties; Polymers and organics; Rheology; Stress relaxation; Structural relaxation
1. Introduction
2. Sample and experiment
As it has been successfully used to study the deformation mechanisms of glassy linear polymers [1–5], the birefringence technique with the Modified Stress-Optical Rule (MSOR) [1] is expected to be a powerful tool to study deformation mechanisms of polymer glass with a crosslinked structure, such as epoxy glass. In the previous study [6], the applicability of the MSOR to birefringence changes of epoxy glasses was verified. In the present study, the birefringence changes in epoxy glasses were monitored over strain aging experiments, and the effects of crosslinks on strain aging of epoxy glass are discussed. This is probably the first application of the MSOR for the investigation of strain aging phenomenon of glassy polymers.
Bisphenol–A type epoxide precursor was cured by 4, 4 0 – diaminodiphenylmethane (4,4 0 –DDM) to form a sample with a crosslinked structure (sample C). The stoichiometric ratio was set to 1. The stirred mixture of the epoxide precursor and the curing agent was cured at 343 K (70 C) for 12 h followed by a heat treatment at 433 K (160 C) for 12 h. The glass transition temperature Tg of the sample C was about 428 K (155 C), and the molecular weight between crosslinks was about 493 g/mol. The epoxide precursor was also polymerized by aniline to form an uncrosslinked structure of linear molecules (sample L). The Tg of the sample L was about 360 K (87 C), and the number average molecule weight was about 26000 g/mol. Dog bone type tensile specimens (40 mm in gage length, 10 mm in width and 2 mm in thickness) were cut from the samples. The specimens were annealed at a temperature 5 K above their glass transition temperatures for 4 h and slowly cooled down to room temperature at a cooling rate of 0.1 C.
*
Corresponding author. E-mail address: [email protected] (H. Kawakami).
0022-3093/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2006.02.179
H. Kawakami et al. / Journal of Non-Crystalline Solids 352 (2006) 4956–4959
The test temperature was Tg – 35 K: 393 K (120 C) for specimens C and 325 K (52 C) for specimens L. The fluctuation in temperature over experiments was about ±0.2 K. The specimens were uniaxially drawn at a deformation rate of 0.25 mm/min ( about 1.6 · 104 s1 in strain rate). At a predetermined strain value, deformation was ceased being increased and the specimens were kept under the strain for various aging periods up to ta = 3.0 · 105 s, i.e. strain aged. At the end of strain aging, elongation was resumed until fracture of the specimen. Over strain aging experiments, changes in birefringence was monitored with a laboratory made Se´narmont optical system (He–Ne gas laser, wave length k = 632.8 · 109 m). Some of the annealed specimens were physically aged at the test temperature for ta = 3.0 · 105 s and then continuously elongated. The stress–strain curves and birefringence – strain curves for the physically aged specimens were the same as those of the annealed specimens, indicating that physical aging has little effect on experimental results shown in the following section. 3. Results Stress–strain curves and birefringence–strain curves for specimens C were summarized in Fig. 1. In the Fig. 1(a), the curve increasing from the origin exhibits a stress–strain
4957
relationship for an annealed specimen. The dashed curve exhibits stress relaxation behavior during strain aging under strain value of 0.07 and was plotted against aging time ta. The solid curves rising from the stress relaxation curve are stress–strain curves for strain aged specimens, and the curves are horizontally shifted according to ta. The change in stress–strain curve with aging period is qualitatively the same as that for epoxy glass aged under shear strain [7]: the stress value at the upper yield point decreased for short aging period and then increased to exceed that value of the annealed specimen. The experimental results for the specimens L (Fig. 2) were qualitatively the same as those of the specimens C, except that the specimens L strain aged more than 1.0 · 104 s exhibited brittle fracture. The MSOR states that stress r can be divided into two stress components rR and rG, and that these stress components contribute to the change in birefringence Dn as follows [5]: r ¼ rR þ rG Dn ¼ C R rR þ C G rG
ð1Þ ð2Þ
where CG and CR are materials constants designated as stress-optical coefficients. The stress component rR was ascribed to the entropic elasticity of polymer segments
True Stress [MPa]
True Stress [MPa]
50
25
0 0
0
10
2
10
104
106
100
0.3
0
Birefringence &$n
0.01
0.005 0
10
104
106
Aging time ta [s]
0.06 0.1 0.2 Nominal Strain
0.3
2
10
4
10
6
10
0.01
0.005
Aging time ta [s]
0
0
102
0.015
0.015
Birefringence &$n
25
0
Aging time ta [s]
0.07 0.1 0.2 Nominal Strain
50
0 0
0.07 0.1 0.2 Nominal Strain
0.3
Fig. 1. Experimental results for specimens C. (a) Stress–strain curves. (b) Birefringence–strain curves.
10
0
2
10
4
10
6
10
Aging time ta [s]
0.06 0.1 0.2 Nominal Strain
0.3
Fig. 2. Experimental results for specimens L. (a) Stress–strain curves. (b) Birefringence–strain curves.
4958
H. Kawakami et al. / Journal of Non-Crystalline Solids 352 (2006) 4956–4959
CG [1/Pa]
CR [1/Pa]
11
1.9 · 109 3.4 · 109
3.5 · 10 2.5 · 1011
Sample C Sample L
50
25 0
10
2
10
4
10
6
10
Aging time ta [s]
0 0
0.06
25
100
0 0
2
10
4
10
6
10
Aging time ta [s]
0.1 0.2 Nominal Strain
0.3
6
Rubbery stress σR [MPa]
0.1 0.2 Nominal Strain
0.3
2
Rubbery stressσR [MPa]
Grassy stress σG [MPa]
50
Glassy stress σG [MPa]
Table 1 Optical-stress coefficients
0
10
2
10
104
6
10
Aging time ta [s]
1
0 0
3
0.06
0.1 0.2 Nominal Strain
0.3
Fig. 4. Change in stress components with strain for specimens L. (a) rG – strain curves. (b) rR – strain curves.
4. Discussions 0
100
0
102
104
106
Aging time ta [s]
0.1 0.2 Nominal Strain
0.3
Fig. 3. Change in stress components with strain for specimens C. (a) rG – strain curves. (b) rR – strain curves.
originating from the thermal motion of flexible polymer chain, and rG was ascribed to the rotational orientation of the monomer unit around the chain axis [1,5]. The values of CG and CR for the samples are summarized in Table 1 [6]. For specimens C, relationships between the stress components and strain are shown in Fig. 3. Glassy stress decreased over stress relaxation, while rubbery stress slightly increased but was almost constant and then decreased after ta = 1.0 · 104 s. Fig. 4 shows the stress components – strain curves for specimens L. The value of rG decreased over strain aging, while rR slightly increased until about ta = 4.0 · 103 s and then suddenly decreased. Such changes in the value of stress components are similar to those of the specimens C. For strain aged specimens, the slope of rG – strain curve at the beginning of elongation increased with aging time. On the other hand the slope of rR – strain curve was almost constant independently of aging time.
For both specimens C and L, the value of rG decreased over strain aging, while that of rR slightly increased for a while and decreased. Such results indicate that rotations of side groups is the primary motion of strain aging phenomenon and that the rotations of the main chain is slow and have a little effect on stress–strain curves. When the strain aged specimens L were deformed, the slope of rR is almost constant independently of aging period, while that of rG increased with aging time. Therefore the rotation of main chain is independent of a structure resulting from the rotation of side groups. On the other hand for the specimens C, the slope of rR – strain curves increased when the specimens were strain aged more that about 1.0 · 103 s. Such results presumably indicates that the rotation of main chain is constrained by the structure results from rotation of side groups, i.e. co-operativity. 5. Conclusions For polymer glasses with/without crosslinks, the rotations of side groups is the main molecular motion of strain aging phenomenon. And if crosslinks exists, the rotation of side group causes a structure which constrains rotation of main chains.
H. Kawakami et al. / Journal of Non-Crystalline Solids 352 (2006) 4956–4959
Acknowledgement The authors wish to thank Danippom Ink And Chemicals, Inc. for kindly supplying the epoxy resin used. References [1] T. Inoue, H. Okamato, K. Osaki, Macromolecules 24 (1991) 5670. [2] T. Inoue, H. Okamoto, K. Osaki, Macromolecules 25 (1992) 7069.
4959
[3] T. Inoue, E.J. Hwang, K. Osaki, Polymer 38 (1997) 1029. [4] T. Inoue, D.S. Ryu, K. Osaki, T. Takabe, J. Polym. Sci. Poly. Phys. 37 (1999) 399. [5] K. Osaki, H. Okamoto, T. Inoue, E.J. Hwang, Macromolecules 28 (1995) 3625. [6] H. Kawakami, M. Tomita, Y. Nanzai, J. Rheol. 49 (2005) 461. [7] H. Kawakami, R. Otsuki, Y. Nanzai, Polym. Eng. Sci. 45 (2005) 20.
Birefringence change in epoxy glass aged under strain Hiroshi Kawakami *, Keiji Kishimoto, Yukuo Nanzai, Yoshihiro Sato Department of Mechanical Engineering, Osaka City University Sugimoto, Sumiyoshi, Osaka 558–8585, Japan Available online 1 September 2006
Abstract Structural relaxation in epoxy glass aged under strain (strain aging) was studied by means of birefringence. Two types of samples were prepared from the same epoxy precursor: one has a crosslinked structure and the other has a linear molecular structure. Epoxy glasses were uniaxially elongated and then strain aged for various aging times. Elongation was resumed at the end of strain aging. Birefringence change was measured over strain aging tests. Modified stress-optical rule, MSOR, was applied to experimental results to separate (total) stress into two stress components: glassy stress and rubbery stress. Experimental results indicated that crosslinks cause co-operation between the thermal motions of flexible polymer chains and the rotational orientation of the monomer unit around the chain axis. 2006 Elsevier B.V. All rights reserved. PACS: 83.80.Ab; 61.43.Fs; 83.85.St; 42.70.Ce; 83.80.Jx Keywords: Optical properties; Polymers and organics; Rheology; Stress relaxation; Structural relaxation
1. Introduction
2. Sample and experiment
As it has been successfully used to study the deformation mechanisms of glassy linear polymers [1–5], the birefringence technique with the Modified Stress-Optical Rule (MSOR) [1] is expected to be a powerful tool to study deformation mechanisms of polymer glass with a crosslinked structure, such as epoxy glass. In the previous study [6], the applicability of the MSOR to birefringence changes of epoxy glasses was verified. In the present study, the birefringence changes in epoxy glasses were monitored over strain aging experiments, and the effects of crosslinks on strain aging of epoxy glass are discussed. This is probably the first application of the MSOR for the investigation of strain aging phenomenon of glassy polymers.
Bisphenol–A type epoxide precursor was cured by 4, 4 0 – diaminodiphenylmethane (4,4 0 –DDM) to form a sample with a crosslinked structure (sample C). The stoichiometric ratio was set to 1. The stirred mixture of the epoxide precursor and the curing agent was cured at 343 K (70 C) for 12 h followed by a heat treatment at 433 K (160 C) for 12 h. The glass transition temperature Tg of the sample C was about 428 K (155 C), and the molecular weight between crosslinks was about 493 g/mol. The epoxide precursor was also polymerized by aniline to form an uncrosslinked structure of linear molecules (sample L). The Tg of the sample L was about 360 K (87 C), and the number average molecule weight was about 26000 g/mol. Dog bone type tensile specimens (40 mm in gage length, 10 mm in width and 2 mm in thickness) were cut from the samples. The specimens were annealed at a temperature 5 K above their glass transition temperatures for 4 h and slowly cooled down to room temperature at a cooling rate of 0.1 C.
*
Corresponding author. E-mail address: [email protected] (H. Kawakami).
0022-3093/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2006.02.179
H. Kawakami et al. / Journal of Non-Crystalline Solids 352 (2006) 4956–4959
The test temperature was Tg – 35 K: 393 K (120 C) for specimens C and 325 K (52 C) for specimens L. The fluctuation in temperature over experiments was about ±0.2 K. The specimens were uniaxially drawn at a deformation rate of 0.25 mm/min ( about 1.6 · 104 s1 in strain rate). At a predetermined strain value, deformation was ceased being increased and the specimens were kept under the strain for various aging periods up to ta = 3.0 · 105 s, i.e. strain aged. At the end of strain aging, elongation was resumed until fracture of the specimen. Over strain aging experiments, changes in birefringence was monitored with a laboratory made Se´narmont optical system (He–Ne gas laser, wave length k = 632.8 · 109 m). Some of the annealed specimens were physically aged at the test temperature for ta = 3.0 · 105 s and then continuously elongated. The stress–strain curves and birefringence – strain curves for the physically aged specimens were the same as those of the annealed specimens, indicating that physical aging has little effect on experimental results shown in the following section. 3. Results Stress–strain curves and birefringence–strain curves for specimens C were summarized in Fig. 1. In the Fig. 1(a), the curve increasing from the origin exhibits a stress–strain
4957
relationship for an annealed specimen. The dashed curve exhibits stress relaxation behavior during strain aging under strain value of 0.07 and was plotted against aging time ta. The solid curves rising from the stress relaxation curve are stress–strain curves for strain aged specimens, and the curves are horizontally shifted according to ta. The change in stress–strain curve with aging period is qualitatively the same as that for epoxy glass aged under shear strain [7]: the stress value at the upper yield point decreased for short aging period and then increased to exceed that value of the annealed specimen. The experimental results for the specimens L (Fig. 2) were qualitatively the same as those of the specimens C, except that the specimens L strain aged more than 1.0 · 104 s exhibited brittle fracture. The MSOR states that stress r can be divided into two stress components rR and rG, and that these stress components contribute to the change in birefringence Dn as follows [5]: r ¼ rR þ rG Dn ¼ C R rR þ C G rG
ð1Þ ð2Þ
where CG and CR are materials constants designated as stress-optical coefficients. The stress component rR was ascribed to the entropic elasticity of polymer segments
True Stress [MPa]
True Stress [MPa]
50
25
0 0
0
10
2
10
104
106
100
0.3
0
Birefringence &$n
0.01
0.005 0
10
104
106
Aging time ta [s]
0.06 0.1 0.2 Nominal Strain
0.3
2
10
4
10
6
10
0.01
0.005
Aging time ta [s]
0
0
102
0.015
0.015
Birefringence &$n
25
0
Aging time ta [s]
0.07 0.1 0.2 Nominal Strain
50
0 0
0.07 0.1 0.2 Nominal Strain
0.3
Fig. 1. Experimental results for specimens C. (a) Stress–strain curves. (b) Birefringence–strain curves.
10
0
2
10
4
10
6
10
Aging time ta [s]
0.06 0.1 0.2 Nominal Strain
0.3
Fig. 2. Experimental results for specimens L. (a) Stress–strain curves. (b) Birefringence–strain curves.
4958
H. Kawakami et al. / Journal of Non-Crystalline Solids 352 (2006) 4956–4959
CG [1/Pa]
CR [1/Pa]
11
1.9 · 109 3.4 · 109
3.5 · 10 2.5 · 1011
Sample C Sample L
50
25 0
10
2
10
4
10
6
10
Aging time ta [s]
0 0
0.06
25
100
0 0
2
10
4
10
6
10
Aging time ta [s]
0.1 0.2 Nominal Strain
0.3
6
Rubbery stress σR [MPa]
0.1 0.2 Nominal Strain
0.3
2
Rubbery stressσR [MPa]
Grassy stress σG [MPa]
50
Glassy stress σG [MPa]
Table 1 Optical-stress coefficients
0
10
2
10
104
6
10
Aging time ta [s]
1
0 0
3
0.06
0.1 0.2 Nominal Strain
0.3
Fig. 4. Change in stress components with strain for specimens L. (a) rG – strain curves. (b) rR – strain curves.
4. Discussions 0
100
0
102
104
106
Aging time ta [s]
0.1 0.2 Nominal Strain
0.3
Fig. 3. Change in stress components with strain for specimens C. (a) rG – strain curves. (b) rR – strain curves.
originating from the thermal motion of flexible polymer chain, and rG was ascribed to the rotational orientation of the monomer unit around the chain axis [1,5]. The values of CG and CR for the samples are summarized in Table 1 [6]. For specimens C, relationships between the stress components and strain are shown in Fig. 3. Glassy stress decreased over stress relaxation, while rubbery stress slightly increased but was almost constant and then decreased after ta = 1.0 · 104 s. Fig. 4 shows the stress components – strain curves for specimens L. The value of rG decreased over strain aging, while rR slightly increased until about ta = 4.0 · 103 s and then suddenly decreased. Such changes in the value of stress components are similar to those of the specimens C. For strain aged specimens, the slope of rG – strain curve at the beginning of elongation increased with aging time. On the other hand the slope of rR – strain curve was almost constant independently of aging time.
For both specimens C and L, the value of rG decreased over strain aging, while that of rR slightly increased for a while and decreased. Such results indicate that rotations of side groups is the primary motion of strain aging phenomenon and that the rotations of the main chain is slow and have a little effect on stress–strain curves. When the strain aged specimens L were deformed, the slope of rR is almost constant independently of aging period, while that of rG increased with aging time. Therefore the rotation of main chain is independent of a structure resulting from the rotation of side groups. On the other hand for the specimens C, the slope of rR – strain curves increased when the specimens were strain aged more that about 1.0 · 103 s. Such results presumably indicates that the rotation of main chain is constrained by the structure results from rotation of side groups, i.e. co-operativity. 5. Conclusions For polymer glasses with/without crosslinks, the rotations of side groups is the main molecular motion of strain aging phenomenon. And if crosslinks exists, the rotation of side group causes a structure which constrains rotation of main chains.
H. Kawakami et al. / Journal of Non-Crystalline Solids 352 (2006) 4956–4959
Acknowledgement The authors wish to thank Danippom Ink And Chemicals, Inc. for kindly supplying the epoxy resin used. References [1] T. Inoue, H. Okamato, K. Osaki, Macromolecules 24 (1991) 5670. [2] T. Inoue, H. Okamoto, K. Osaki, Macromolecules 25 (1992) 7069.
4959
[3] T. Inoue, E.J. Hwang, K. Osaki, Polymer 38 (1997) 1029. [4] T. Inoue, D.S. Ryu, K. Osaki, T. Takabe, J. Polym. Sci. Poly. Phys. 37 (1999) 399. [5] K. Osaki, H. Okamoto, T. Inoue, E.J. Hwang, Macromolecules 28 (1995) 3625. [6] H. Kawakami, M. Tomita, Y. Nanzai, J. Rheol. 49 (2005) 461. [7] H. Kawakami, R. Otsuki, Y. Nanzai, Polym. Eng. Sci. 45 (2005) 20.