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Direction-sensitive strain-mapping with carbon nanotube sensors
Composites Science and Technology 62 (2002) 147–150 www.elsevier.com/locate/compscitech
Short Communication
Direction-sensitive strain-mapping with carbon nanotube sensors Qing Zhao, Mark D. Frogley, H. Daniel Wagner* Department of Materials and Interfaces, Weizmann Institute of Science, Rehovot 76100, Israel Received 20 September 2001; accepted 23 October 2001
Abstract Single-wall carbon nanotubes (SWNTs) embedded in a polymer can be used as mechanical sensors because the position of the D* Raman band is strongly dependent on the strain transferred from the matrix to the nanotubes. The unpolarized Raman spectrum of the nanotubes has high strain sensitivity if the nanotubes are oriented along the principal strain axis in the polymer, whereas with polarized Raman, even unoriented nanotubes exhibit a strong wavenumber shift in the Raman spectrum with strain. These methods are demonstrated here by measuring the stress distribution around a circular hole in SWNT/polymer composites under uniaxial tension. In both cases the results fit the classical linear elasticity solution. # 2002 Elsevier Science Ltd. All rights reserved.
1. Introduction The disorder-induced D* Raman band of single-wall carbon nanotubes (SWNTs) reflects a breathing vibrational mode. The position of this band is strongly dependent on strain or stress applied to the nanotubes, so they can be used as mechanical sensors in Raman spectroscopy [1,2]. Embedding a small amount (0.1 wt.%) of SWNTs into a polymer enables the measurement of strain in the polymer without significantly changing its mechanical properties. The spatial resolution at which strain can be measured is around 1 mm, a limit imposed by the size of the Raman laser spot, and so mechanical measurements can be performed around microscale discontinuities in the polymer such as holes, cracks or fibers. When mapping with the Raman technique, the measured wavenumber shifts represent the mean response of all the nanotubes at the focal region of the laser [3]. Even for a simple uniaxial tensile test, Poisson’s contraction occurs perpendicular to the loading axis and so some of the nanotubes in a randomly oriented sample will be in compression while others will be in tension. To measure the individual components of the strain (or
* Corresponding author. E-mail address: [email protected] (H.D. Wagner).
stress), the Raman signal from nanotubes in a particular direction must be selected out. This can be achieved by physically orienting the nanotubes in the polymer or by using polarized Raman spectroscopy. We previously demonstrated an effective shear flow method for orientation of nanotubes in an ultraviolet (UV) curable urethane acrylate [3,4]. In general, however, limitations of the polymer processing method mean that nanotube orientation cannot always be obtained. Polarized Raman [5] spectroscopy is a more versatile technique. The polarized Raman intensity of the D* band is strongly dependent on the nanotube orientation and is highest when the optical polarization direction (for both incident and scattered light) is parallel to the tube axis [6–8]. Thus, if we use polarized Raman to measure a randomly dispersed SWNT composite, we predominantly select out those nanotubes lying along the polarization direction. Experiments with SWNTs randomly oriented in films of polyurethane acrylate (PUA) showed that the Raman wavenumber shift with strain is dependent on the optical polarization direction [4]. In this paper, we apply both the SWNT orientation and polarized Raman methods to map the stress around a circular hole in a polymer plate under uniaxial tension. The in-plane stress field for this situation has distinct components in the directions parallel and perpendicular to the applied stress [9] and we show that both Raman techniques can be used to quantify the individual stress components.
0266-3538/02/$ - see front matter # 2002 Elsevier Science Ltd. All rights reserved. PII: S0266-3538(01)00187-7
148
Q. Zhao et al. / Composites Science and Technology 62 (2002) 147–150
2. Experimental 2.1. Oriented specimens The polymer matrix used was an UV curable urethane acrylate (Ebecryl 4858, Radcure). SWNTs (0.1 wt.%, Dynamic Enterprises Ltd.) were dispersed in liquid urethane acrylate by ultrasound (4 h) and then the hardener (Irgacure 651, 2 wt.%) was added and mixed mechanically. The mixture was spread on a glass slide and a doktor blade was used to shear the liquid and promote nanotube orientation. The 150 mm thick film was immediately cured by exposure to an UV source so that relaxation of the orientation is minimal. For the hole experiment, the cured film was cut into a plate of width 8 mm and a 2 mm diameter hole was cut in the center using a punch. The gauge length of the sample was 20 mm. A similar sample, without a hole, was cut from the same film for calibration of the Raman strain-shift. The oriented PUA/SWNT specimens were tested in a mini-tensile machine with the loading direction parallel to the nanotube alignment direction. Raman spectra were obtained using a Renishaw Ramascope in the 180 backscattering geometry and with a spectral resolution of 1 cm1. A HeNe laser source was used (632.8 nm, 2 mW) and the beam was focused onto the specimen surface through a 50 objective lens, forming a laser spot of approximately 2 mm in diameter. For the calibration samples, the Raman spectrum was recorded at a different position at each applied stress level. For the hole experiment, spectra were recorded at different distances from the hole edge, along the x axis as shown in Fig. 1. 2.2. Random specimens A DGEBA-based epoxy matrix (purchased from Bakelite AG) was used. SWNTs (0.1 wt.%) were dispersed in the resin (Rutapox L20) by ultrasound and then the hardener (Rutapox SL, 34 wt.%) was mixed in mechanically, followed by vacuum pumping to remove air bubbles. The mixture was spread onto a plate to make films around 180 mm thick, which were cured for 6 h at 80 C and then allowed to cool to room temperature outside the oven. Polarized Raman measurements were made with the polarization direction parallel to the direction of interest. The other parameters were the same as for the oriented samples in Section 2.1.
3. Results and discussion 3.1. Oriented SWNT/PUA with unpolarized Raman spectroscopy We recently showed that the wavenumber strain shift of the D* mode in carbon nanotubes is empirically
Fig. 1. The specimen configuration considered in the present study is a circular hole of radius a, in a thin polymer plate under unidirectional tensile stress, 0. y is the axis of applied stress and x is perpendicular to y in the plane of the plate.
proportional to the elastic strain in a PUA matrix with a constant 467 cm1/" [3]. Shifts to lower wavenumbers correspond to increases in tensile strain so that in the elastic region, the local stress is given by: ¼
o E 467
ð1Þ
where ! is the wavenumber shift, E is the Young’s modulus of the matrix and is the stress in the matrix. Fig. 2 shows the stress, (normalized to the applied stress, 0) around a hole in the matrix. The experimental points are calculated from the Raman wavenumber shift for the oriented nanotubes which was measured at positions along the x axis, starting from the hole edge (see Fig. 1) at three different levels of applied stress: 4, 6 and 8 MPa. Far away from the hole, the local stress is equal to the applied stress, and close the hole edge the stress increases to about three times the applied stress. This ‘‘stress concentration factor’’ is the same at all three applied stress levels. The solid lines in Fig. 2 are the linear elastic solution of Inglis [9] for the stress component parallel ( yy/ 0) and perpendicular ( xx/ 0) to the applied stress. The experimental data are in good
Q. Zhao et al. / Composites Science and Technology 62 (2002) 147–150
Fig. 2. Unpolarized Raman results: the normalized stress measured along the x axis from the edge of a circular hole, based on the D* peak shift of aligned SWNTs in UV cured urethane-acrylate polymer. Applied stress levels, 0, were 4, 6 and 8 MPa. The solid lines are the linear elastic solution of Inglis for normal stresses ( xx, yy) in the x and y directions [9].
agreement with the curve for yy/s0, showing that we have measured the stress component in the direction of nanotube orientation [10]. 3.2. Unoriented SWNT/epoxy with polarized Raman spectroscopy Firstly the shift of the Raman wavenumber with tensile strain was calibrated for randomly oriented SWNTs in epoxy, and the data are shown in Fig. 3. The triangle data are the combined data from several experiments with the optical polarization direction parallel to the applied stress direction. The slope of that data is 1800 cm1/" in the elastic deformation region (up to 1% strain). The large negative slope is expected because polarized Raman selects out nanotubes along the applied stress direction, and those nanotubes are in axial tension. So when the applied stress direction and the polarization direction are parallel, we can convert the wavenumber shift into stress by: ¼
o E 1800
149
Fig. 3. Polarized Raman results: calibration of the D* wavenumber shift with strain for SWNTs randomly oriented in the epoxy matrix. The square data were obtained with the polarization direction perpendicular to the applied stress direction. The triangle data were obtained with the polarization direction parallel to the applied stress direction, for which the initial slope (up to 1% strain) is 1800 cm1/".
contraction of the matrix. It is clear that polarized Raman can distinguish between different strain components. Fig. 4 shows the results for a random SWNT/epoxy film with a hole in the middle and with the polarization direction parallel to the loading direction. The local stress, , was measured from the hole edge along the x axis (see Fig. 1). The experimental points are the normalized matrix stress, / 0, at applied stress levels of 4, 6, 7 and 8 MPa. Once again, there is a stress concentration
ð2Þ
Since the epoxy resin has a higher Young’s modulus (about 1700 MPa) than PUA (about 1200 MPa), better strain resolution is obtained for epoxy-based system. In addition, data (solid squares in Fig. 3) were obtained with the polarization direction perpendicular to the applied stress and in that case, the D* wavenumber first shifts upwards slightly and then stays constant. This is because now the nanotubes that are perpendicular to the applied tensile stress are selected out, and they are in axial compression via Poisson’s
Fig. 4. Polarized Raman results: the normalized stress measured along the x axis from the edge of a circular hole, based on the D* peak shift of unoriented SWNTs in epoxy with polarized Raman. Applied stress levels, 0, were 4, 6, 7 and 8 MPa. The solid lines are the linear elastic solution of Inglis for normal stresses ( xx, yy) in the x and y directions [9].
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Q. Zhao et al. / Composites Science and Technology 62 (2002) 147–150
factor of three at the hole edge which agrees with Inglis’ theoretical result (the solid line yy/ 0 in the figure).
4. Conclusions Nanotube sensors may be used in polymers for quantitative stress mapping in an elastic deformation situation. This has been demonstrated by measuring the stress field in the vicinity of holes in polymer films. Two cases were studied: (a) SWNTs aligned in PUA, probed by unpolarized Raman spectroscopy, and (b) SWNTs randomly oriented in epoxy, probed by polarized Raman spectroscopy. In both cases, the experimental data are in good agreement with the classical theory of Inglis. The random dispersed case is more useful in practice because different stress components can be measured in the same sample.
Acknowledgements This project was funded by the CNT Thematic Network on ‘‘Carbon Nanotubes for Future Industrial Composites’’ (EU) and by the MINERVA foundation. H.D. Wagner is the incumbent of the Livio Norzi Professorial chair.
References [1] Wood JR, Wagner HD. Single-wall carbon nanotubes as molecular pressure sensors. Appl Phys Lett 2000;76:2883. [2] Wood JR, Zhao Q, Frogley MD, Meurs ER, Prins AD, Peijs T, et al. Carbon nanotubes: from molecular to macroscopic sensors. Phys Rev 2000;B 62:7571. [3] Wood JR, Zhao Q, Wagner HD. Orientation of carbon nanotubes in polymers and its detection by Raman spectroscopy. Composites 2001;A32:391. [4] Frogley MD, Zhao Q, Wagner HD. Polarized resonance–Raman spectroscopy of single-wall carbon nanotubes within a polymer under strain. Submitted 2001. [5] The scattered light from the sample is passed through an analyzer that selects light that has the electric vector parallel to that of the incident light. Without the analyzer we term the technique ‘‘unpolarized Raman’’ although the incident light is polarized in both cases. [6] Saito R, Takeya T, Dresselhaus G, Dresselhaus MS. Raman intensity of single-wall carbon nanotubes. Phys Rev 1998;B 57: 4145. [7] Gommans HH, Alldredge JW, Tashiro H, Park J, Magnuson J, Rinzler AG. Fibers of aligned single-wall carbon nanotubes: polarized Raman spectroscopy. J Appl Phys 2000;88:2509. [8] Duesberg GS, Loa I, Burghard M, Syassen K, Roth S. Polarized Raman spectroscopy on isolated single-wall carbon nanotubes. Phys Rev Lett 2000;85:5436. [9] Dally JW, Riley WF. Experimental stress analysis. McGraw-Hill, 1985. p. 79–80. [10] Zhao Q, Wood JR, Wagner HD. Stress fields around defects and fibers in a polymer using carbon nanotubes as sensors. Appl Phys Lett 2001;78:1748.
Short Communication
Direction-sensitive strain-mapping with carbon nanotube sensors Qing Zhao, Mark D. Frogley, H. Daniel Wagner* Department of Materials and Interfaces, Weizmann Institute of Science, Rehovot 76100, Israel Received 20 September 2001; accepted 23 October 2001
Abstract Single-wall carbon nanotubes (SWNTs) embedded in a polymer can be used as mechanical sensors because the position of the D* Raman band is strongly dependent on the strain transferred from the matrix to the nanotubes. The unpolarized Raman spectrum of the nanotubes has high strain sensitivity if the nanotubes are oriented along the principal strain axis in the polymer, whereas with polarized Raman, even unoriented nanotubes exhibit a strong wavenumber shift in the Raman spectrum with strain. These methods are demonstrated here by measuring the stress distribution around a circular hole in SWNT/polymer composites under uniaxial tension. In both cases the results fit the classical linear elasticity solution. # 2002 Elsevier Science Ltd. All rights reserved.
1. Introduction The disorder-induced D* Raman band of single-wall carbon nanotubes (SWNTs) reflects a breathing vibrational mode. The position of this band is strongly dependent on strain or stress applied to the nanotubes, so they can be used as mechanical sensors in Raman spectroscopy [1,2]. Embedding a small amount (0.1 wt.%) of SWNTs into a polymer enables the measurement of strain in the polymer without significantly changing its mechanical properties. The spatial resolution at which strain can be measured is around 1 mm, a limit imposed by the size of the Raman laser spot, and so mechanical measurements can be performed around microscale discontinuities in the polymer such as holes, cracks or fibers. When mapping with the Raman technique, the measured wavenumber shifts represent the mean response of all the nanotubes at the focal region of the laser [3]. Even for a simple uniaxial tensile test, Poisson’s contraction occurs perpendicular to the loading axis and so some of the nanotubes in a randomly oriented sample will be in compression while others will be in tension. To measure the individual components of the strain (or
* Corresponding author. E-mail address: [email protected] (H.D. Wagner).
stress), the Raman signal from nanotubes in a particular direction must be selected out. This can be achieved by physically orienting the nanotubes in the polymer or by using polarized Raman spectroscopy. We previously demonstrated an effective shear flow method for orientation of nanotubes in an ultraviolet (UV) curable urethane acrylate [3,4]. In general, however, limitations of the polymer processing method mean that nanotube orientation cannot always be obtained. Polarized Raman [5] spectroscopy is a more versatile technique. The polarized Raman intensity of the D* band is strongly dependent on the nanotube orientation and is highest when the optical polarization direction (for both incident and scattered light) is parallel to the tube axis [6–8]. Thus, if we use polarized Raman to measure a randomly dispersed SWNT composite, we predominantly select out those nanotubes lying along the polarization direction. Experiments with SWNTs randomly oriented in films of polyurethane acrylate (PUA) showed that the Raman wavenumber shift with strain is dependent on the optical polarization direction [4]. In this paper, we apply both the SWNT orientation and polarized Raman methods to map the stress around a circular hole in a polymer plate under uniaxial tension. The in-plane stress field for this situation has distinct components in the directions parallel and perpendicular to the applied stress [9] and we show that both Raman techniques can be used to quantify the individual stress components.
0266-3538/02/$ - see front matter # 2002 Elsevier Science Ltd. All rights reserved. PII: S0266-3538(01)00187-7
148
Q. Zhao et al. / Composites Science and Technology 62 (2002) 147–150
2. Experimental 2.1. Oriented specimens The polymer matrix used was an UV curable urethane acrylate (Ebecryl 4858, Radcure). SWNTs (0.1 wt.%, Dynamic Enterprises Ltd.) were dispersed in liquid urethane acrylate by ultrasound (4 h) and then the hardener (Irgacure 651, 2 wt.%) was added and mixed mechanically. The mixture was spread on a glass slide and a doktor blade was used to shear the liquid and promote nanotube orientation. The 150 mm thick film was immediately cured by exposure to an UV source so that relaxation of the orientation is minimal. For the hole experiment, the cured film was cut into a plate of width 8 mm and a 2 mm diameter hole was cut in the center using a punch. The gauge length of the sample was 20 mm. A similar sample, without a hole, was cut from the same film for calibration of the Raman strain-shift. The oriented PUA/SWNT specimens were tested in a mini-tensile machine with the loading direction parallel to the nanotube alignment direction. Raman spectra were obtained using a Renishaw Ramascope in the 180 backscattering geometry and with a spectral resolution of 1 cm1. A HeNe laser source was used (632.8 nm, 2 mW) and the beam was focused onto the specimen surface through a 50 objective lens, forming a laser spot of approximately 2 mm in diameter. For the calibration samples, the Raman spectrum was recorded at a different position at each applied stress level. For the hole experiment, spectra were recorded at different distances from the hole edge, along the x axis as shown in Fig. 1. 2.2. Random specimens A DGEBA-based epoxy matrix (purchased from Bakelite AG) was used. SWNTs (0.1 wt.%) were dispersed in the resin (Rutapox L20) by ultrasound and then the hardener (Rutapox SL, 34 wt.%) was mixed in mechanically, followed by vacuum pumping to remove air bubbles. The mixture was spread onto a plate to make films around 180 mm thick, which were cured for 6 h at 80 C and then allowed to cool to room temperature outside the oven. Polarized Raman measurements were made with the polarization direction parallel to the direction of interest. The other parameters were the same as for the oriented samples in Section 2.1.
3. Results and discussion 3.1. Oriented SWNT/PUA with unpolarized Raman spectroscopy We recently showed that the wavenumber strain shift of the D* mode in carbon nanotubes is empirically
Fig. 1. The specimen configuration considered in the present study is a circular hole of radius a, in a thin polymer plate under unidirectional tensile stress, 0. y is the axis of applied stress and x is perpendicular to y in the plane of the plate.
proportional to the elastic strain in a PUA matrix with a constant 467 cm1/" [3]. Shifts to lower wavenumbers correspond to increases in tensile strain so that in the elastic region, the local stress is given by: ¼
o E 467
ð1Þ
where ! is the wavenumber shift, E is the Young’s modulus of the matrix and is the stress in the matrix. Fig. 2 shows the stress, (normalized to the applied stress, 0) around a hole in the matrix. The experimental points are calculated from the Raman wavenumber shift for the oriented nanotubes which was measured at positions along the x axis, starting from the hole edge (see Fig. 1) at three different levels of applied stress: 4, 6 and 8 MPa. Far away from the hole, the local stress is equal to the applied stress, and close the hole edge the stress increases to about three times the applied stress. This ‘‘stress concentration factor’’ is the same at all three applied stress levels. The solid lines in Fig. 2 are the linear elastic solution of Inglis [9] for the stress component parallel ( yy/ 0) and perpendicular ( xx/ 0) to the applied stress. The experimental data are in good
Q. Zhao et al. / Composites Science and Technology 62 (2002) 147–150
Fig. 2. Unpolarized Raman results: the normalized stress measured along the x axis from the edge of a circular hole, based on the D* peak shift of aligned SWNTs in UV cured urethane-acrylate polymer. Applied stress levels, 0, were 4, 6 and 8 MPa. The solid lines are the linear elastic solution of Inglis for normal stresses ( xx, yy) in the x and y directions [9].
agreement with the curve for yy/s0, showing that we have measured the stress component in the direction of nanotube orientation [10]. 3.2. Unoriented SWNT/epoxy with polarized Raman spectroscopy Firstly the shift of the Raman wavenumber with tensile strain was calibrated for randomly oriented SWNTs in epoxy, and the data are shown in Fig. 3. The triangle data are the combined data from several experiments with the optical polarization direction parallel to the applied stress direction. The slope of that data is 1800 cm1/" in the elastic deformation region (up to 1% strain). The large negative slope is expected because polarized Raman selects out nanotubes along the applied stress direction, and those nanotubes are in axial tension. So when the applied stress direction and the polarization direction are parallel, we can convert the wavenumber shift into stress by: ¼
o E 1800
149
Fig. 3. Polarized Raman results: calibration of the D* wavenumber shift with strain for SWNTs randomly oriented in the epoxy matrix. The square data were obtained with the polarization direction perpendicular to the applied stress direction. The triangle data were obtained with the polarization direction parallel to the applied stress direction, for which the initial slope (up to 1% strain) is 1800 cm1/".
contraction of the matrix. It is clear that polarized Raman can distinguish between different strain components. Fig. 4 shows the results for a random SWNT/epoxy film with a hole in the middle and with the polarization direction parallel to the loading direction. The local stress, , was measured from the hole edge along the x axis (see Fig. 1). The experimental points are the normalized matrix stress, / 0, at applied stress levels of 4, 6, 7 and 8 MPa. Once again, there is a stress concentration
ð2Þ
Since the epoxy resin has a higher Young’s modulus (about 1700 MPa) than PUA (about 1200 MPa), better strain resolution is obtained for epoxy-based system. In addition, data (solid squares in Fig. 3) were obtained with the polarization direction perpendicular to the applied stress and in that case, the D* wavenumber first shifts upwards slightly and then stays constant. This is because now the nanotubes that are perpendicular to the applied tensile stress are selected out, and they are in axial compression via Poisson’s
Fig. 4. Polarized Raman results: the normalized stress measured along the x axis from the edge of a circular hole, based on the D* peak shift of unoriented SWNTs in epoxy with polarized Raman. Applied stress levels, 0, were 4, 6, 7 and 8 MPa. The solid lines are the linear elastic solution of Inglis for normal stresses ( xx, yy) in the x and y directions [9].
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Q. Zhao et al. / Composites Science and Technology 62 (2002) 147–150
factor of three at the hole edge which agrees with Inglis’ theoretical result (the solid line yy/ 0 in the figure).
4. Conclusions Nanotube sensors may be used in polymers for quantitative stress mapping in an elastic deformation situation. This has been demonstrated by measuring the stress field in the vicinity of holes in polymer films. Two cases were studied: (a) SWNTs aligned in PUA, probed by unpolarized Raman spectroscopy, and (b) SWNTs randomly oriented in epoxy, probed by polarized Raman spectroscopy. In both cases, the experimental data are in good agreement with the classical theory of Inglis. The random dispersed case is more useful in practice because different stress components can be measured in the same sample.
Acknowledgements This project was funded by the CNT Thematic Network on ‘‘Carbon Nanotubes for Future Industrial Composites’’ (EU) and by the MINERVA foundation. H.D. Wagner is the incumbent of the Livio Norzi Professorial chair.
References [1] Wood JR, Wagner HD. Single-wall carbon nanotubes as molecular pressure sensors. Appl Phys Lett 2000;76:2883. [2] Wood JR, Zhao Q, Frogley MD, Meurs ER, Prins AD, Peijs T, et al. Carbon nanotubes: from molecular to macroscopic sensors. Phys Rev 2000;B 62:7571. [3] Wood JR, Zhao Q, Wagner HD. Orientation of carbon nanotubes in polymers and its detection by Raman spectroscopy. Composites 2001;A32:391. [4] Frogley MD, Zhao Q, Wagner HD. Polarized resonance–Raman spectroscopy of single-wall carbon nanotubes within a polymer under strain. Submitted 2001. [5] The scattered light from the sample is passed through an analyzer that selects light that has the electric vector parallel to that of the incident light. Without the analyzer we term the technique ‘‘unpolarized Raman’’ although the incident light is polarized in both cases. [6] Saito R, Takeya T, Dresselhaus G, Dresselhaus MS. Raman intensity of single-wall carbon nanotubes. Phys Rev 1998;B 57: 4145. [7] Gommans HH, Alldredge JW, Tashiro H, Park J, Magnuson J, Rinzler AG. Fibers of aligned single-wall carbon nanotubes: polarized Raman spectroscopy. J Appl Phys 2000;88:2509. [8] Duesberg GS, Loa I, Burghard M, Syassen K, Roth S. Polarized Raman spectroscopy on isolated single-wall carbon nanotubes. Phys Rev Lett 2000;85:5436. [9] Dally JW, Riley WF. Experimental stress analysis. McGraw-Hill, 1985. p. 79–80. [10] Zhao Q, Wood JR, Wagner HD. Stress fields around defects and fibers in a polymer using carbon nanotubes as sensors. Appl Phys Lett 2001;78:1748.