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Pressure and molecular-weight dependences of elastic properties of polystyrene polymers studied by Brillouin spectroscopy
Current Applied Physics 17 (2017) 1396e1400
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Current Applied Physics journal homepage: www.elsevier.com/locate/cap
Pressure and molecular-weight dependences of elastic properties of polystyrene polymers studied by Brillouin spectroscopy Byoung Wan Lee a, Min-Seok Jeong a, Jong Sun Choi b, Jaehoon Park c, Young Ho Ko d, Kwang Joo Kim d, Jae-Hyeon Ko a, * a
Department of Physics, Hallym University, 1 Hallymdaehakgil, Chuncheon, Gangwondo 24252, Republic of Korea Department of Electrical, Information & Control Engineering, Hongik University, 94 Wausan-ro, Mapo-gu, 04066 Seoul, Republic of Korea Department of Electronic Engineering, Hallym University, 1 Hallymdaehakgil, Chuncheon, Gangwondo 24252, Republic of Korea d 4-2-2, Agency for Defense Development, P.O. Box 35, Yuseong, Daejeon 34186, Republic of Korea b c
a r t i c l e i n f o
a b s t r a c t
Article history: Received 23 May 2017 Received in revised form 8 July 2017 Accepted 3 August 2017 Available online 4 August 2017
Pressure and molecular-weight dependences of acoustic mode behaviors of polystyrene polymeric material were investigated by using Brillouin spectroscopy. The longitudinal, the transverse and the bulk sound velocities were measured over a wide pressure range from ambient pressure to more than 10 GPa for five polystyrene polymers whose molecular weight ranging from 3700 to 979200. The longitudinal and the bulk sound velocities displayed nearly the same pressure dependence for all polystyrenes indicating that the effective free volume is very similar in five polystyrene polymers despite the huge change in the molecular weight. The Poisson's ratio slightly increased with decreasing molecular weight. © 2017 Published by Elsevier B.V.
Keywords: Polystyrene Brillouin scattering Elastic Pressure Sound velocity
1. Introduction The microscopic nature of the glassy state and the glass transition have been studied intensively during the past decades. The transformation from the liquid state to the glassy state upon cooling is accompanied by unusual changes in many physical properties. The metastable and nonequilibrium nature of the supercooled liquid and the glassy states prevents one from applying normal theory of phase transition to the glass transition phenomena. Pressure is another important thermodynamic variable that has substantial effects on the glassy state of amorphous materials [1]. Compression by pressure reduces the free volume in the material and thus changes the density, the elastic moduli, etc. significantly [2]. The equation of state obtainable from the highpressure experiment is one of the fundamental physical data of amorphous materials including polymeric materials [3e13]. We can predict the behavior of polymers under extreme conditions, such as high pressures and high strain rates, based on the equation of state. The understanding of mechanical properties of amorphous
* Corresponding author. E-mail address: [email protected] (J.-H. Ko). http://dx.doi.org/10.1016/j.cap.2017.08.003 1567-1739/© 2017 Published by Elsevier B.V.
materials under extreme conditions is important for their applications in various fields. Polystyrene (PS, (C8H8)n) is one of the most widely-used thermoplastics in various applications. The basic structure of PS consists of main hydrocarbon chains with large side phenyl groups. Similar to other thermoplastics, PS is in a glassy state at room temperature and exhibits fluidity at high temperatures above ~100 C, which is the approximate glass transition temperature of PS. In spite of its wide application in various fields, the mechanical and elastic properties of PS, especially under extreme conditions, have not been studied in detail. Only temperature dependence of acoustic properties of PS has been reported by several groups, in particular, in the vicinity of Tg [14e19]. To the best of our knowledge, there is no report on the highpressure elastic properties of PS polymers, especially their dependence on the molecular weight. Brillouin spectroscopy is a nondestructive, noncontact method to measure elastic properties of transparent condensed matters. The characteristic frequency range of this technique is 109 ~ 1010 Hz, which is much higher than that of the conventional ultrasonic technique. The diamond anvil cell (DAC) is one of the most typical ways to apply hydrostatic pressure to the sample inside the cell [2]. We used a combination of
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a Brillouin spectrometer and the DAC to measure pressure dependences of sound velocities of five PS samples with different molecular weights ranging from 3700 to 979200, which corresponds to the change of nearly three-order of magnitude in the molecular weight. The obtained data will be discussed in terms of the free volume theory [20]. 2. Experiment Five atactic PS samples with different molecular weights (Mw) were purchased from Aldrich (average Mw ~ 3700, 35000, 192000, 350000, and 979200). These polymer samples were investigated without any pre-treatment or purification. The temperature dependence of three PS samples were investigated in our previous study [19]. A conventional six-pass tandem Fabry-Perot interferometer (TFP-1, JRS Co.) was used to measure the Brillouin spectra of five PS samples. A diode-pumped solid-state laser (Excelsior 532300, Spectra Physics) at a wavelength of 532 nm was used as an excitation source. A conventional photon-counting system combined with a multichannel analyser (1024 channels) was used to detect and average the signal. A small piece of PS was cut and inserted in a diamond anvil cell (DAC) for high-pressure measurements. Additional pressuretransmitting medium was not used in this study. A few ruby spheres were included in the DAC, which were used as a pressure marker. The fluorescence spectrum of the ruby spheres excited by the 532-nm laser light was measured by using a grating-based spectrometer (HR4000, Ocean Optics) to get the exact pressure values at each step. Pressure gradient was about 0.2 GPa at pressures below 3 GPa, but it reached more than 1.5 GPa at high pressures above 10 GPa. The existence of the pressure gradient in the DAC indicates that hydrostatic condition is not satisfied to a certain degree in the high pressure cell. However, it was clearly shown that reliable equations of state can be derived for polymeric materials measured without any pressure-transmitting medium in DAC [21]. A forward, symmetric scattering geometry with a scattering angle of approximately 60 was carried out for all five samples. The Brillouin spectrum was measured from the ambient condition to at least 10 GPa. The detailed description of the experimental setup for present Brillouin scattering experiment can be found elsewhere [22e24].
Fig. 1. Brillouin spectra of polystyrene with Mw ¼ 350000 at three pressures. The red lines denote the best-fitted results. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
3. Results and discussion Fig. 1 shows a few typical Brillouin spectra of the PS sample with Mw ¼ 350000. Each Brillouin spectrum consists of either one or two Brillouin doublets. Other PS polymers with different molecular weights exhibited similar pressure dependence of Brillouin spectra. The high-frequency and low-frequency component corresponds to the longitudinal acoustic (LA) and the transverse acoustic (TA) mode, respectively. The strong LA mode shifts from ~5 GHz at 0.3 GPa to more than 12 GHz at ~8.7 GPa. The TA mode appears at most pressures except for low-pressure range, the frequency of which changes as pressure increases. This result suggests that the PS samples become stiffened enough to sustain shear strains under high pressures. However, the PS sample with Mw ¼ 979200 did not show any TA mode over the whole pressure range. The measured spectra were curve-fitted by using the Lorentzian function convoluted with the Gaussian instrumental function of the Fabry-Perot interferometer. The Brillouin frequency shift (nB) of both acoustic modes could be obtained for all five PS samples over a wide pressure range. Fig. 2 shows the pressure dependences of the Brillouin shift of two acoustic modes for all PS samples. The nB of the LA mode could be measured from the ambient pressure to high pressures more
Fig. 2. Pressure dependence of the Brillouin frequency shift of the LA and TA modes of five PS samples.
than 10 GPa, but the nB of the TA mode could be measured in a limited pressure range, because the TA mode of polymeric materials is too weak in intensity or too close to the laser line to measure at low pressures. The Brillouin frequency shift of the LA mode increases smoothly from ~5 GHz at ambient pressure to ~14 GHz at the highest pressures upon compression. The increasing rate of nB with respect to pressure is large at low pressures below ~2 GPa and becomes smaller at high pressures. The change in nB of the TA mode is rather small, rising from ~3 GHz to ~6 GHz with increasing pressure. The most interesting result is that the pressure dependences of the Brillouin shift for the two acoustic modes do not exhibit noticeable molecular-weight dependence in spite of the large change in Mw ranging from 3700 to 979200, corresponding to
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the change of nearly three orders of magnitude. Fig. 2 shows that only the TA mode shows a slight molecular-weight dependence, i.e., the TA mode frequency tends to decrease slightly with decreasing Mw. The Brillouin frequency shift of the PS with Mw ¼ 3700 displays the smallest values over the whole pressure range. Sound velocities can be obtained without the need to know the refractive index if we use the present forward, symmetric scattering geometry [22]. The Brillouin frequency shift nB measured at this scattering geometry can be used to calculate the sound velocity V by using the following equation:
V¼
lnB
2 sinðq=2Þ
;
(1)
where q is the scattering angle, ~60 in the present cases and l the laser wavelength in vacuum. Fig. 3 shows the pressure dependences of the longitudinal and transverse sound velocities of the five PS samples. The sound velocity of the LA mode increases from 2500 to 3000 m/s near the ambient pressure to ~7000 m/s at the highest pressures upon compression. The change in the sound velocity of the TA mode is in the range from ~1400 to ~3200 m/s, increasing smoothly upon compression. The increasing rate of nB with respect to the pressure is large at low pressures below ~2 GPa and becomes smaller at high pressures. The sound velocities, similar to the nB, do not exhibit any significant molecular-weight dependences, except that the transverse sound velocity tends to increase with increasing molecular weight. If we combine the two sound velocities, the pressure depenqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dence of the bulk sound velocity VB ¼ V 2LA 4V 2TA =3 can be obtained, where VLA and VTA are the longitudinal and the transverse sound velocity, respectively. The pressure dependence of VB is shown in Fig. 4. The bulk velocities were calculated for all PS polymers except for PS with Mw ¼ 980000 which did not show the TA mode. It increases from ~2750 m/s to ~6400 m/s with compression over the investigated pressure range. Because of the insensitiveness of the LA and TA mode velocities to the molecular weight, the bulk velocity also does not depend substantially on the molecular weight. The pressure dependence of density r can be derived from the bulk velocities by using a well-known thermoR dynamic equation of r ¼ r0 þ ðg=VB2 Þdp, where r0 is the density at ambient pressure, g is the ratio of the isobaric and the isochoric specific heats (the integration should be carried out over the
Fig. 3. Pressure dependence of the sound velocities of the LA and TA modes of five PS samples.
Fig. 4. Pressure dependence of the bulk velocity of four PS samples. Inset is the pressure dependence of the bulk modulus of three samples.
investigated pressure range) [6]. This equation combined with the density of PS at room temperature was used to obtain the pressure dependence of density of three PS samples with Mw ¼ 35000, 192000, 350000. In more detail, the density was derived by fitting the 1=VB2 curve by using a smooth function and carrying out the integration to each experimental pressure [5,10]. The obtained density was used to calculate elastic moduli. The pressure dependence of the bulk modulus is shown in the inset of Fig. 4. Similar to the bulk velocity, the bulk modulus exhibited nearly the same pressure dependence in the range of Mw ¼ 35000e350000. The pressure dependence of the Young's modulus and the shear modulus is shown in Fig. 5, where we can know that molecular weight dependence of these moduli are also very small. A little bit larger moduli of the PS with Mw ¼ 350000 seems to be due to the slightly larger transverse sound velocity of this sample. In addition, Figs. 4 and 5 suggest that the bulk moduli are comparable to the Young's moduli in these three PS samples, indicating that C11 z2C12 z4C44 . In addition to the bulk velocity, the Poisson's ratio s can be
Fig. 5. Pressure dependence of the Young's modulus and the shear modulus of three samples.
B.W. Lee et al. / Current Applied Physics 17 (2017) 1396e1400
calculated from the two sound velocities according to the following equation,
s¼
2 2V 2 VLA TA 2 2V 2 2VLA TA
:
(2)
The Poisson's ratio denotes the ratio of the transverse strain to the axial strain and is one of the important mechanical properties of solids. The Poisson's ratio of 0.5 is the isotropic upper limit and it indicates that the condensed matter is very ductile. Fig. 6 shows the pressure dependences of the Poisson's ratio of four PS samples except for the PS with Mw ¼ 980000 which did not show the TA mode. The Poisson's ratios are in the range of 0.36e0.41, which are typical values for polymers [25]. For example, the Poisson's ratio of amorphous polyethylene terephthalate (PET) is in 0.38e0.41 [26], nearly the same as that of PS polymers. The Poisson's ratios of three PS samples (Mw ¼ 35000, 192000 350000) increase from the ambient pressure to ~4 GPa upon compression, reach maximum values and then decrease at high pressures above ~8 GPa. On the other hand, the Poisson's ratio of the PS with Mw ¼ 3700, which is in the range of 0.40e0.41, is the largest and does not show appreciable pressure dependence in the measured pressure range. The larger s values of the PS with Mw ¼ 3700 indicate that this sample is more ductile. Fig. 5 shows that the ductility seems to decrease as Mw increases. For the three samples with larger Mw, the pressure improves the ductility at low pressures, but excess pressure above ~8 GPa makes the polymer more brittle. It is difficult to discuss the microscopic structural changes induced by compression based only on the elastic data. Recent Raman scattering study on the atactic PS revealed that the overall Raman spectral features were maintained over the pressure range up to 2 GPa, that is, there was no change in the number of vibrational modes [27]. This indicates that conformational changes do not occur in the amorphous PS during the shock compression. It is consistent with previous Raman results that the conformation of atactic PS does not change upon static compression up to 8 GPa [28]. These results suggest that there would be no conformational change in the five atactic PS samples, which may maintain their amorphous state up to ~10 GPa. On the other hand, high-pressure Raman study on crystalline isotactic PS revealed significant changes in the Raman spectra, disappearing of several Raman
Fig. 6. Pressure dependence of the Poisson's ratio s of four PS samples.
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bands upon compression [28]. In this case, pressure induces disorder or irregularity in the main chain structure of the isotactic PS, which does not disappear even upon decompression. This kind of irreversibility may also affect the elastic properties substantially, which will be investigated in our next study on PS polymer systems. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Bulk velocity, VB ¼ V 2LA 4V 2TA =3, is directly related to the density, and the longitudinal sound velocity is more dominant factor in the determination of the bulk velocity, because VLA is much larger than VTA. Comparison of the bulk velocity and the longitudinal sound velocity (Figs. 3 and 4) indicates that both velocities do not exhibit any significant molecular-weight dependence. Density and the bulk velocity are sensitive to the ratio of the effective free volume among the total volume in polymers. The free volume is defined as the excess volume in the total volume over the occupied volume [20]. Free volume decreases rapidly upon compression, which is accompanied by densification, that is, rapid increase in the density. Once the free volume is collapsed at a certain pressure, the change in the density and VB may become less significant than that at lower pressures. This expectation can be seen from Figs. 3 and 4, where the increasing rates of VLA and VB with respect to pressure are larger at low pressures below ~2 or 3 GPa than those at higher pressures. It is known that the equation of state is different in these two pressure ranges, the boundary being the specific pressure at which the free volume collapses completely [6]. It indicates that free volume is collapsed at around 2e3 GPa in polystyrene polymers. Nearly the same pressure dependences of VLA and VB of five PS samples with different molecular weights indicate that the free volume conditions e volume ratio, shapes, etc. e are very similar in these polymers without showing any significant molecular-weight dependence. White and Lipson suggest that total free volume consists of “vibrational free volume” and excess free volume in polymeric materials [20]. The vibrational free volume denotes the space where solid-like segmental motions are allowed, while the excess free volume is the rest, additional free volume existing in the melt associated with imperfect packing. Since all the PS samples at ambient temperature are in the glassy state, the ratio of the excess free volume is expected to be smaller than the vibrational free volume [20]. In addition, the high-frequency elastic property probed by Brillouin scattering in the GHz range may be more relevant to the vibrational free volume. However, we noted our experimental result that the estimated density increased by ~20% during the initial compression up to ~2 GPa, and this change in density became moderate upon further compression. We thus thought that the initial changes in the elastic properties might be related to the reduction and removal of the void space, that is, the excess free volume in the bulk of PS. In this context, the relatively rapid changes in sound velocities at low pressures may reflect the complete collapse of the excess free volume together while the smooth changes at high pressures are associated with the diminishing vibrational free volume. It will be interesting to compare the present result with highpressure elastic data of other representative polymers. The basic structure of PS is hydrocarbon long chains on which randomlydistributed phenyl groups are attached. These side groups may afford enough free volume at ambient pressure. In the case of poly(methyl methacrylate) (PMMA), two side groups, CH3 and C2H3O2 are attached to the backbone chain. These side groups and their random positions may afford enough free volume in the material, in which segmental relaxational motions are allowed to some degree. Compression by pressure will reduce the free volume and make it collapse at a certain pressure, which is accompanied by rapid increase in density, longitudinal and bulk velocities. Interestingly, the pressure dependence of the longitudinal sound
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B.W. Lee et al. / Current Applied Physics 17 (2017) 1396e1400
velocity of PMMA is nearly the same as that of PS over a wide pressure range [8]. On the other hand, PET consists of repeating ethylene terephthalate without any side group. PET tends to exhibit semi-crystallinity, and its glass transition temperature is much higher than those of PMMA and PS. The lack of side groups does not afford enough free volume, and thus the density of PET is much larger than those of PMMA and PS at ambient conditions. Accordingly, the longitudinal sound velocity of PET is nearly doubled as compared to those of PMMA and PS over a wide pressure range [9,26]. The origin of the dependence of the Poisson's ratio on Mw is not clear at the moment, that is, the reason why the Poisson's ratio of the PS with Mw ¼ 3700 is the largest needs to be investigated. It seems to be caused by the slight molecular-weight dependence of the transverse sound velocity. The TA mode is related to the shear deformation in polymers. The glass transition temperature Tg of PS is weakly dependent on the molecular weight and becomes lower for the low-molecular weight PS [16]. Therefore, the more ductile behavior of PS with Mw ¼ 3700 may be attributed to its lower Tg compared to other PS samples with higher molecular weights. However, the difference in the Poisson's ratio for four PS samples is not large, and thus it can be suggested that mechanical (elastic) properties of PS polymers are nearly the same under high pressures up to more than 10 GPa.
4. Conclusion Pressure dependences of longitudinal, transverse and bulk sound velocities of five PS polymers, whose molecular weight varying between 3700 and 979200, were investigated over a wide pressure range from ambient pressure to more than 10 GPa. The pressure dependences of the longitudinal and bulk sound velocities are nearly the same for five PS samples. This suggests that the free volume conditions, such as volume ratio and shapes of free volume, are very similar in these polymers without showing any significant molecular-weight dependence. The transverse sound velocity weakly depends on the molecular weight, which affects the pressure dependence of the Poisson's ratio. The observed behaviors of PS polymers under high pressures are fundamental mechanical properties of these amorphous materials and are expected to be useful for their applications under extreme conditions.
Acknowledgment This work was supported by the Defense Research Laboratory Program of the Defense Acquisition Program Administration and the Agency for Defense Development of Republic of Korea and by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIP) (NRF-2016R1A2B4012646).
References [1] G. Floudas, M. Paluch, A. Grzybowski, K.L. Ngai, Molecular Dynamics of GlassForming Systems, Springer, Heidelberg, 2011 chapters 4 ~ 5. [2] M.I. Eremets, High Pressure Experimental Methods, Oxford Univ. Press, Oxford, 1996. [3] L.L. Stevens, C.J. Eckhardt, J. Chem. Phys. 122 (2005) 174701. [4] J.J. Haycraft, L.L. Stevens, C.J. Eckhardt, J. Chem. Phys. 124 (2006) 024712. [5] L.L. Stevens, E.B. Orler, D.M. Dattelbaum, M. Ahart, R.J. Hemley, J. Chem. Phys. 127 (2007) 104906. [6] A.S. Benjamin, M. Ahart, S.A. Gramsch, L.L. Stevens, E.B. Orler, D.M. Dattelbaum, R.J. Hemley, J. Chem. Phys. 137 (2012) 014514. [7] M.-S. Jeong, J.H. Kim, J.-H. Ko, Y.H. Ko, K.J. Kim, Curr. Appl. Phys. 13 (2013) 1774. [8] M.-S. Jeong, J.-H. Ko, Y.H. Ko, K.J. Kim, Curr. Appl. Phys. 15 (2015) 943. [9] Y.H. Ko, K.J. Kim, B.W. Lee, M.-S. Jeong, J.-H. Ko, J. Korean Phys. Soc. 66 (2015) 1120. [10] Y.H. Ko, J. Min, J. Song, Curr. Appl. Phys. 16 (2016) 311. [11] J. Wang, X. Zhao, E.B. Berda, C. Chen, K. Wang, S. Chen, B. Zou, B. Liu, Q. Zhou, F. Li, D. Chao, Polymer 90 (2016) 1. [12] B.W. Lee, J. Ryeom, J.-H. Ko, D.W. Kim, C.H. Park, J. Park, Y.H. Ko, K.J. Kim, J. Korean Phys. Soc. 69 (2016) 213. [13] J. Wang, Q. Zhou, D. Chao, F. Li, T. Cui, RSC Adv. 7 (2017) 8670. [14] Y. Wada, K. Yamamoto, J. Phys. Soc. Jpn. 11 (1956) 887. [15] R. Kono, J. Phys. Soc. Jpn. 15 (1960) 718. [16] D.M. Smith, T.A. Wiggins, Appl. Opt. 11 (1972) 2680. [17] E.M. Brody, C.J. Lubell, C.L. Beatty, J. Polym. Sci. Polym. Phys. Ed. 13 (1975) 295. [18] J.A. Forrest, K. Dalnoki-Veress, J.R. Dutcher, A.C. Rowat, J.R. Stevens, Mat. Res. Soc. Symp. Proc. 407 (1996) 131. [19] S.H. Oh, B.W. Lee, J.-H. Ko, H. Lee, J. Park, Y.H. Ko, K.J. Kim, J. Korean Phys. Soc. 69 (2017) 791. [20] R.P. White, J.E.G. Lipson, Macromolecules 49 (2016) 3987. [21] B.W. Lee, S. Shin, M.-S. Jeong, J.-H. Ko, Y.H. Ko, K.J. Kim, Curr. Appl. Phys. 16 (2016) 1571. [22] J.-H. Ko, M.-S. Jeong, B.W. Lee, J.H. Kim, Y.H. Ko, K.J. Kim, T.H. Kim, S. Kojima, M. Ahart, Korean J. Opt. Phot. 24 (2013) 279. [23] S.H. Oh, B.J. Cho, M.S. Jeong, J.-H. Ko, J. Inf. Disp. 17 (2016) 87. [24] M.S. Jeong, J.-H. Ko, T.H. Kim, Y.H. Ko, K.J. Kim, S. Kojima, New Phys. Sae Mulli 66 (2016) 1375. [25] G.N. Greaves, A.L. Greer, R.S. Lakes, T. Rouxel, Nat. Mater. 10 (2011) 823. [26] Y.-H. Ko, M. Ahart, J.-H. Ko, J. Song, J. Korean Phys. Soc. 70 (2017) 382. [27] V. Rastogi, S. Chaurasia, U. Rao, C.D. Sijoy, V. Mishra, M. Kumar, M.N. Deo, S. Chaturvedi, S.M. Sharma, J. Raman Spectrosc. 48 (2017) 458. [28] Y. Furushima, K. Tazaki, H. Fujimoto, Solid State Commun. 140 (2006) 240.
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Current Applied Physics journal homepage: www.elsevier.com/locate/cap
Pressure and molecular-weight dependences of elastic properties of polystyrene polymers studied by Brillouin spectroscopy Byoung Wan Lee a, Min-Seok Jeong a, Jong Sun Choi b, Jaehoon Park c, Young Ho Ko d, Kwang Joo Kim d, Jae-Hyeon Ko a, * a
Department of Physics, Hallym University, 1 Hallymdaehakgil, Chuncheon, Gangwondo 24252, Republic of Korea Department of Electrical, Information & Control Engineering, Hongik University, 94 Wausan-ro, Mapo-gu, 04066 Seoul, Republic of Korea Department of Electronic Engineering, Hallym University, 1 Hallymdaehakgil, Chuncheon, Gangwondo 24252, Republic of Korea d 4-2-2, Agency for Defense Development, P.O. Box 35, Yuseong, Daejeon 34186, Republic of Korea b c
a r t i c l e i n f o
a b s t r a c t
Article history: Received 23 May 2017 Received in revised form 8 July 2017 Accepted 3 August 2017 Available online 4 August 2017
Pressure and molecular-weight dependences of acoustic mode behaviors of polystyrene polymeric material were investigated by using Brillouin spectroscopy. The longitudinal, the transverse and the bulk sound velocities were measured over a wide pressure range from ambient pressure to more than 10 GPa for five polystyrene polymers whose molecular weight ranging from 3700 to 979200. The longitudinal and the bulk sound velocities displayed nearly the same pressure dependence for all polystyrenes indicating that the effective free volume is very similar in five polystyrene polymers despite the huge change in the molecular weight. The Poisson's ratio slightly increased with decreasing molecular weight. © 2017 Published by Elsevier B.V.
Keywords: Polystyrene Brillouin scattering Elastic Pressure Sound velocity
1. Introduction The microscopic nature of the glassy state and the glass transition have been studied intensively during the past decades. The transformation from the liquid state to the glassy state upon cooling is accompanied by unusual changes in many physical properties. The metastable and nonequilibrium nature of the supercooled liquid and the glassy states prevents one from applying normal theory of phase transition to the glass transition phenomena. Pressure is another important thermodynamic variable that has substantial effects on the glassy state of amorphous materials [1]. Compression by pressure reduces the free volume in the material and thus changes the density, the elastic moduli, etc. significantly [2]. The equation of state obtainable from the highpressure experiment is one of the fundamental physical data of amorphous materials including polymeric materials [3e13]. We can predict the behavior of polymers under extreme conditions, such as high pressures and high strain rates, based on the equation of state. The understanding of mechanical properties of amorphous
* Corresponding author. E-mail address: [email protected] (J.-H. Ko). http://dx.doi.org/10.1016/j.cap.2017.08.003 1567-1739/© 2017 Published by Elsevier B.V.
materials under extreme conditions is important for their applications in various fields. Polystyrene (PS, (C8H8)n) is one of the most widely-used thermoplastics in various applications. The basic structure of PS consists of main hydrocarbon chains with large side phenyl groups. Similar to other thermoplastics, PS is in a glassy state at room temperature and exhibits fluidity at high temperatures above ~100 C, which is the approximate glass transition temperature of PS. In spite of its wide application in various fields, the mechanical and elastic properties of PS, especially under extreme conditions, have not been studied in detail. Only temperature dependence of acoustic properties of PS has been reported by several groups, in particular, in the vicinity of Tg [14e19]. To the best of our knowledge, there is no report on the highpressure elastic properties of PS polymers, especially their dependence on the molecular weight. Brillouin spectroscopy is a nondestructive, noncontact method to measure elastic properties of transparent condensed matters. The characteristic frequency range of this technique is 109 ~ 1010 Hz, which is much higher than that of the conventional ultrasonic technique. The diamond anvil cell (DAC) is one of the most typical ways to apply hydrostatic pressure to the sample inside the cell [2]. We used a combination of
B.W. Lee et al. / Current Applied Physics 17 (2017) 1396e1400
1397
a Brillouin spectrometer and the DAC to measure pressure dependences of sound velocities of five PS samples with different molecular weights ranging from 3700 to 979200, which corresponds to the change of nearly three-order of magnitude in the molecular weight. The obtained data will be discussed in terms of the free volume theory [20]. 2. Experiment Five atactic PS samples with different molecular weights (Mw) were purchased from Aldrich (average Mw ~ 3700, 35000, 192000, 350000, and 979200). These polymer samples were investigated without any pre-treatment or purification. The temperature dependence of three PS samples were investigated in our previous study [19]. A conventional six-pass tandem Fabry-Perot interferometer (TFP-1, JRS Co.) was used to measure the Brillouin spectra of five PS samples. A diode-pumped solid-state laser (Excelsior 532300, Spectra Physics) at a wavelength of 532 nm was used as an excitation source. A conventional photon-counting system combined with a multichannel analyser (1024 channels) was used to detect and average the signal. A small piece of PS was cut and inserted in a diamond anvil cell (DAC) for high-pressure measurements. Additional pressuretransmitting medium was not used in this study. A few ruby spheres were included in the DAC, which were used as a pressure marker. The fluorescence spectrum of the ruby spheres excited by the 532-nm laser light was measured by using a grating-based spectrometer (HR4000, Ocean Optics) to get the exact pressure values at each step. Pressure gradient was about 0.2 GPa at pressures below 3 GPa, but it reached more than 1.5 GPa at high pressures above 10 GPa. The existence of the pressure gradient in the DAC indicates that hydrostatic condition is not satisfied to a certain degree in the high pressure cell. However, it was clearly shown that reliable equations of state can be derived for polymeric materials measured without any pressure-transmitting medium in DAC [21]. A forward, symmetric scattering geometry with a scattering angle of approximately 60 was carried out for all five samples. The Brillouin spectrum was measured from the ambient condition to at least 10 GPa. The detailed description of the experimental setup for present Brillouin scattering experiment can be found elsewhere [22e24].
Fig. 1. Brillouin spectra of polystyrene with Mw ¼ 350000 at three pressures. The red lines denote the best-fitted results. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
3. Results and discussion Fig. 1 shows a few typical Brillouin spectra of the PS sample with Mw ¼ 350000. Each Brillouin spectrum consists of either one or two Brillouin doublets. Other PS polymers with different molecular weights exhibited similar pressure dependence of Brillouin spectra. The high-frequency and low-frequency component corresponds to the longitudinal acoustic (LA) and the transverse acoustic (TA) mode, respectively. The strong LA mode shifts from ~5 GHz at 0.3 GPa to more than 12 GHz at ~8.7 GPa. The TA mode appears at most pressures except for low-pressure range, the frequency of which changes as pressure increases. This result suggests that the PS samples become stiffened enough to sustain shear strains under high pressures. However, the PS sample with Mw ¼ 979200 did not show any TA mode over the whole pressure range. The measured spectra were curve-fitted by using the Lorentzian function convoluted with the Gaussian instrumental function of the Fabry-Perot interferometer. The Brillouin frequency shift (nB) of both acoustic modes could be obtained for all five PS samples over a wide pressure range. Fig. 2 shows the pressure dependences of the Brillouin shift of two acoustic modes for all PS samples. The nB of the LA mode could be measured from the ambient pressure to high pressures more
Fig. 2. Pressure dependence of the Brillouin frequency shift of the LA and TA modes of five PS samples.
than 10 GPa, but the nB of the TA mode could be measured in a limited pressure range, because the TA mode of polymeric materials is too weak in intensity or too close to the laser line to measure at low pressures. The Brillouin frequency shift of the LA mode increases smoothly from ~5 GHz at ambient pressure to ~14 GHz at the highest pressures upon compression. The increasing rate of nB with respect to pressure is large at low pressures below ~2 GPa and becomes smaller at high pressures. The change in nB of the TA mode is rather small, rising from ~3 GHz to ~6 GHz with increasing pressure. The most interesting result is that the pressure dependences of the Brillouin shift for the two acoustic modes do not exhibit noticeable molecular-weight dependence in spite of the large change in Mw ranging from 3700 to 979200, corresponding to
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the change of nearly three orders of magnitude. Fig. 2 shows that only the TA mode shows a slight molecular-weight dependence, i.e., the TA mode frequency tends to decrease slightly with decreasing Mw. The Brillouin frequency shift of the PS with Mw ¼ 3700 displays the smallest values over the whole pressure range. Sound velocities can be obtained without the need to know the refractive index if we use the present forward, symmetric scattering geometry [22]. The Brillouin frequency shift nB measured at this scattering geometry can be used to calculate the sound velocity V by using the following equation:
V¼
lnB
2 sinðq=2Þ
;
(1)
where q is the scattering angle, ~60 in the present cases and l the laser wavelength in vacuum. Fig. 3 shows the pressure dependences of the longitudinal and transverse sound velocities of the five PS samples. The sound velocity of the LA mode increases from 2500 to 3000 m/s near the ambient pressure to ~7000 m/s at the highest pressures upon compression. The change in the sound velocity of the TA mode is in the range from ~1400 to ~3200 m/s, increasing smoothly upon compression. The increasing rate of nB with respect to the pressure is large at low pressures below ~2 GPa and becomes smaller at high pressures. The sound velocities, similar to the nB, do not exhibit any significant molecular-weight dependences, except that the transverse sound velocity tends to increase with increasing molecular weight. If we combine the two sound velocities, the pressure depenqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dence of the bulk sound velocity VB ¼ V 2LA 4V 2TA =3 can be obtained, where VLA and VTA are the longitudinal and the transverse sound velocity, respectively. The pressure dependence of VB is shown in Fig. 4. The bulk velocities were calculated for all PS polymers except for PS with Mw ¼ 980000 which did not show the TA mode. It increases from ~2750 m/s to ~6400 m/s with compression over the investigated pressure range. Because of the insensitiveness of the LA and TA mode velocities to the molecular weight, the bulk velocity also does not depend substantially on the molecular weight. The pressure dependence of density r can be derived from the bulk velocities by using a well-known thermoR dynamic equation of r ¼ r0 þ ðg=VB2 Þdp, where r0 is the density at ambient pressure, g is the ratio of the isobaric and the isochoric specific heats (the integration should be carried out over the
Fig. 3. Pressure dependence of the sound velocities of the LA and TA modes of five PS samples.
Fig. 4. Pressure dependence of the bulk velocity of four PS samples. Inset is the pressure dependence of the bulk modulus of three samples.
investigated pressure range) [6]. This equation combined with the density of PS at room temperature was used to obtain the pressure dependence of density of three PS samples with Mw ¼ 35000, 192000, 350000. In more detail, the density was derived by fitting the 1=VB2 curve by using a smooth function and carrying out the integration to each experimental pressure [5,10]. The obtained density was used to calculate elastic moduli. The pressure dependence of the bulk modulus is shown in the inset of Fig. 4. Similar to the bulk velocity, the bulk modulus exhibited nearly the same pressure dependence in the range of Mw ¼ 35000e350000. The pressure dependence of the Young's modulus and the shear modulus is shown in Fig. 5, where we can know that molecular weight dependence of these moduli are also very small. A little bit larger moduli of the PS with Mw ¼ 350000 seems to be due to the slightly larger transverse sound velocity of this sample. In addition, Figs. 4 and 5 suggest that the bulk moduli are comparable to the Young's moduli in these three PS samples, indicating that C11 z2C12 z4C44 . In addition to the bulk velocity, the Poisson's ratio s can be
Fig. 5. Pressure dependence of the Young's modulus and the shear modulus of three samples.
B.W. Lee et al. / Current Applied Physics 17 (2017) 1396e1400
calculated from the two sound velocities according to the following equation,
s¼
2 2V 2 VLA TA 2 2V 2 2VLA TA
:
(2)
The Poisson's ratio denotes the ratio of the transverse strain to the axial strain and is one of the important mechanical properties of solids. The Poisson's ratio of 0.5 is the isotropic upper limit and it indicates that the condensed matter is very ductile. Fig. 6 shows the pressure dependences of the Poisson's ratio of four PS samples except for the PS with Mw ¼ 980000 which did not show the TA mode. The Poisson's ratios are in the range of 0.36e0.41, which are typical values for polymers [25]. For example, the Poisson's ratio of amorphous polyethylene terephthalate (PET) is in 0.38e0.41 [26], nearly the same as that of PS polymers. The Poisson's ratios of three PS samples (Mw ¼ 35000, 192000 350000) increase from the ambient pressure to ~4 GPa upon compression, reach maximum values and then decrease at high pressures above ~8 GPa. On the other hand, the Poisson's ratio of the PS with Mw ¼ 3700, which is in the range of 0.40e0.41, is the largest and does not show appreciable pressure dependence in the measured pressure range. The larger s values of the PS with Mw ¼ 3700 indicate that this sample is more ductile. Fig. 5 shows that the ductility seems to decrease as Mw increases. For the three samples with larger Mw, the pressure improves the ductility at low pressures, but excess pressure above ~8 GPa makes the polymer more brittle. It is difficult to discuss the microscopic structural changes induced by compression based only on the elastic data. Recent Raman scattering study on the atactic PS revealed that the overall Raman spectral features were maintained over the pressure range up to 2 GPa, that is, there was no change in the number of vibrational modes [27]. This indicates that conformational changes do not occur in the amorphous PS during the shock compression. It is consistent with previous Raman results that the conformation of atactic PS does not change upon static compression up to 8 GPa [28]. These results suggest that there would be no conformational change in the five atactic PS samples, which may maintain their amorphous state up to ~10 GPa. On the other hand, high-pressure Raman study on crystalline isotactic PS revealed significant changes in the Raman spectra, disappearing of several Raman
Fig. 6. Pressure dependence of the Poisson's ratio s of four PS samples.
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bands upon compression [28]. In this case, pressure induces disorder or irregularity in the main chain structure of the isotactic PS, which does not disappear even upon decompression. This kind of irreversibility may also affect the elastic properties substantially, which will be investigated in our next study on PS polymer systems. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Bulk velocity, VB ¼ V 2LA 4V 2TA =3, is directly related to the density, and the longitudinal sound velocity is more dominant factor in the determination of the bulk velocity, because VLA is much larger than VTA. Comparison of the bulk velocity and the longitudinal sound velocity (Figs. 3 and 4) indicates that both velocities do not exhibit any significant molecular-weight dependence. Density and the bulk velocity are sensitive to the ratio of the effective free volume among the total volume in polymers. The free volume is defined as the excess volume in the total volume over the occupied volume [20]. Free volume decreases rapidly upon compression, which is accompanied by densification, that is, rapid increase in the density. Once the free volume is collapsed at a certain pressure, the change in the density and VB may become less significant than that at lower pressures. This expectation can be seen from Figs. 3 and 4, where the increasing rates of VLA and VB with respect to pressure are larger at low pressures below ~2 or 3 GPa than those at higher pressures. It is known that the equation of state is different in these two pressure ranges, the boundary being the specific pressure at which the free volume collapses completely [6]. It indicates that free volume is collapsed at around 2e3 GPa in polystyrene polymers. Nearly the same pressure dependences of VLA and VB of five PS samples with different molecular weights indicate that the free volume conditions e volume ratio, shapes, etc. e are very similar in these polymers without showing any significant molecular-weight dependence. White and Lipson suggest that total free volume consists of “vibrational free volume” and excess free volume in polymeric materials [20]. The vibrational free volume denotes the space where solid-like segmental motions are allowed, while the excess free volume is the rest, additional free volume existing in the melt associated with imperfect packing. Since all the PS samples at ambient temperature are in the glassy state, the ratio of the excess free volume is expected to be smaller than the vibrational free volume [20]. In addition, the high-frequency elastic property probed by Brillouin scattering in the GHz range may be more relevant to the vibrational free volume. However, we noted our experimental result that the estimated density increased by ~20% during the initial compression up to ~2 GPa, and this change in density became moderate upon further compression. We thus thought that the initial changes in the elastic properties might be related to the reduction and removal of the void space, that is, the excess free volume in the bulk of PS. In this context, the relatively rapid changes in sound velocities at low pressures may reflect the complete collapse of the excess free volume together while the smooth changes at high pressures are associated with the diminishing vibrational free volume. It will be interesting to compare the present result with highpressure elastic data of other representative polymers. The basic structure of PS is hydrocarbon long chains on which randomlydistributed phenyl groups are attached. These side groups may afford enough free volume at ambient pressure. In the case of poly(methyl methacrylate) (PMMA), two side groups, CH3 and C2H3O2 are attached to the backbone chain. These side groups and their random positions may afford enough free volume in the material, in which segmental relaxational motions are allowed to some degree. Compression by pressure will reduce the free volume and make it collapse at a certain pressure, which is accompanied by rapid increase in density, longitudinal and bulk velocities. Interestingly, the pressure dependence of the longitudinal sound
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velocity of PMMA is nearly the same as that of PS over a wide pressure range [8]. On the other hand, PET consists of repeating ethylene terephthalate without any side group. PET tends to exhibit semi-crystallinity, and its glass transition temperature is much higher than those of PMMA and PS. The lack of side groups does not afford enough free volume, and thus the density of PET is much larger than those of PMMA and PS at ambient conditions. Accordingly, the longitudinal sound velocity of PET is nearly doubled as compared to those of PMMA and PS over a wide pressure range [9,26]. The origin of the dependence of the Poisson's ratio on Mw is not clear at the moment, that is, the reason why the Poisson's ratio of the PS with Mw ¼ 3700 is the largest needs to be investigated. It seems to be caused by the slight molecular-weight dependence of the transverse sound velocity. The TA mode is related to the shear deformation in polymers. The glass transition temperature Tg of PS is weakly dependent on the molecular weight and becomes lower for the low-molecular weight PS [16]. Therefore, the more ductile behavior of PS with Mw ¼ 3700 may be attributed to its lower Tg compared to other PS samples with higher molecular weights. However, the difference in the Poisson's ratio for four PS samples is not large, and thus it can be suggested that mechanical (elastic) properties of PS polymers are nearly the same under high pressures up to more than 10 GPa.
4. Conclusion Pressure dependences of longitudinal, transverse and bulk sound velocities of five PS polymers, whose molecular weight varying between 3700 and 979200, were investigated over a wide pressure range from ambient pressure to more than 10 GPa. The pressure dependences of the longitudinal and bulk sound velocities are nearly the same for five PS samples. This suggests that the free volume conditions, such as volume ratio and shapes of free volume, are very similar in these polymers without showing any significant molecular-weight dependence. The transverse sound velocity weakly depends on the molecular weight, which affects the pressure dependence of the Poisson's ratio. The observed behaviors of PS polymers under high pressures are fundamental mechanical properties of these amorphous materials and are expected to be useful for their applications under extreme conditions.
Acknowledgment This work was supported by the Defense Research Laboratory Program of the Defense Acquisition Program Administration and the Agency for Defense Development of Republic of Korea and by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIP) (NRF-2016R1A2B4012646).
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