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SANS, SAXS, rheology and birefringence—strengths and weaknesses in probing phase behaviour of a diblock copolymer
ARTICLE IN PRESS
Physica B 350 (2004) e885–e888
SANS, SAXS, rheology and birefringence—strengths and weaknesses in probing phase behaviour of a diblock copolymer Martin E. Vigilda,*, Ruya . Eskimergenb, Kell Mortensenc a
Department of Chemical Engineering, Danish Polymer Centre DTU, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark b Department of Manufacturing and Management, Danish Polymer Centre DTU, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark c Danish Polymer Centre Ris^ , DK-4000 Roskilde, Denmark
Abstract Asymmetrically composed diblock copolymers exhibit multiphase behaviour and transit the lamellae, gyroid and hexagonal cylindrical phases before reaching the order–disorder temperature, TODT. During a heating experiment towards TODT we observe that birefringence measurements are more sensitive than dynamic mechanical testing and have faster data acquisition rates than SANS when used to follow transient states of the sample. However, birefringence measurements cannot alone identify the precise phase behaviour. r 2004 Published by Elsevier B.V. PACS: 61.12.Ex; 78.20.Fm; 82.35.Jk Keywords: Small-angle neutron scattering; Birefringence; Dynamical mechanical analysis; Multi-phase behaviour; Diblock copolymer
1. Introduction
2. Experimental
We study the phase behaviour of a polystyrene– polyisoprene (SI) diblock copolymer [1] using small-angle neutron scattering (SANS), small angle X-ray scattering (SAXS), birefringence, and dynamic mechanical spectroscopy (DMS). It is our aim to illustrate the complementarity of these techniques for the investigation of multiphase behaviour. Each technique has strengths and weaknesses, but none of them can be used as a complete stand-alone measurement, which will convey all information about the sample phase behaviour.
The sample (SI-29) studied here was polymerized using ‘‘living’’ anionic polymerization [2] to an overall molecular weight of Mn=29500 g/mol, a volume fraction of fPI=0.67, and a polydispersity index of Mw/Mn=1.01. DMS data was recorded using a modified Rheometrics RSA II instrument, which also facilitated simultaneous SANS or birefringence measurements. The rheometer could be fitted with a custom build birefringence set-up [1], or it could be fitted online with the SANS machine [3]. The temperature control during heating cycles was accurate within 1 C. SANS data was obtained at the SANS II instrument at SinQ, The Paul Scherrer Institute, Switzerland [4]. SAXS data was obtained at the
*Corresponding author. Fax: +45-45882161. E-mail address: [email protected] (M.E. Vigild). 0921-4526/$ - see front matter r 2004 Published by Elsevier B.V. doi:10.1016/j.physb.2004.03.229
ARTICLE IN PRESS e886
M.E. Vigild et al. / Physica B 350 (2004) e885–e888
Fig. 1. In birefringence the optical anisotropy is measured as the difference in diffractive index along the vertical and horizontal axes, Dn13. The analyzer produces linearly polarized light in the vertical direction. During the transmission the light is unevenly retarded, if the material has birefringence, and elliptically polarized light result. The analyzer only accepts light with its electrical field vector in the horizontal plane.
Fig. 2. The lamellar and gyroid phases are documented by SAXS. On the left the sample is in the lamellar state (at 90 C), and on the right the sample is in the gyroid state (at 130 C).
Stanford Synchrotron Radiation Laboratory, USA. Fig. 1 shows the principle of the birefringence measurement.
3. Results and discussion Fig. 2 shows initial 2D SAXS data from the SI sample at two different temperatures, which clearly indicates the lamellar and the gyroid phase. We want to study how phase transition evolves, as temperature is increased—and also to find out if the sample contains more than two phases. First, we show temperature-dependent data from SANS in Fig. 3, recorded during a temperature ramp of 1 C/min from 80 C to 170 C. A ring of scattering (similar to the first-order ring in Fig. 2, left) is observed on the 2D SANS detector throughout the temperature ramp. In Fig. 3 the dependence of the scattering peak position (q) is mapped as a function of temperature. It shows a monotonic increase in q, which is to be expected. Thermally increased motion of the polymer chains will result in chain end-to-end contraction which in turn will shrink the micro-phase segregated structure. There is a small, but insignificant feature at approximately 155 C. From the data no phase transitions seem evident in this temperature interval. The corresponding measurement—measuring the viscoelastic properties of the diblock—is shown in Fig. 4 (closed symbols). The elastic shear modulus G0 gives more information on the phase transition than could be extracted from Fig. 3. The
Fig. 3. The peak position (q) follows a slow increase upon heating (1 C/min) without clear features of phase transitions as measured by radially integrated SANS data.
Fig. 4. Synchronized rheology and birefringence data. Oscillatory shear elastic modulus (G0 , closed symbols) measured at frequency o=1 rad/s and shear amplitude g=1%, and the birefringence signal (Dn, open symbols) while heating (1 C/min).
ARTICLE IN PRESS M.E. Vigild et al. / Physica B 350 (2004) e885–e888
modulus comes down from larger values onto a plateau level of approximately 104 Pa. Between 120 C and 130oC there is a slight change of signal and at 150 C we see the onset of a long drop towards 170 C. Without the knowledge of the SAXS data in Fig. 1 it would be difficult to document multiphase behaviour. However, this data can be interpreted to support a lamellar-togyroid transition followed by a disordering (over a rather long temperature range). The birefringence signal is also mapped out in Fig. 4 (open symbols). Birefringence is much more ‘lively’. The 120–130 C interval locates a small peak, which is followed by a dip towards zero. The gyroid phase is cubic and has no birefringence. This is in fine accord with a lamellar–to–gyroid transition, but the transient peak remains unexplained. At 150 C the birefringence rises dramatically and reaches a maximum just before 160 C. Finally it drops synchronized with the rheology as the ODT temperature is approached. The latter part of the temperature interval clearly illustrates how the birefringence measurement is much more sensitive to the formation of the hexagonal phase between gyroid and disorder. This phase is not evident from the rheology alone. However, the assignment of phases in block copolymers cannot be justified in general based on only birefringence and rheology. But in this case of diblocks it can be done by reference to the relatively well-understood phase behaviour [5,6]. SANS can be a very powerful technique in identifying phases. Not in the form of the data treated in Fig. 3, but in combination with large amplitude oscillatory shear (LAOS). Fig. 5 shows such shear alignment of both the lamellar and the gyroid phase. The shear aligned data is very sensitive to thermodynamical changes that influences phase behaviour. For example the gyroid 10 spot pattern will instantly transform into a 2 spot pattern (not shown) when it is heated beyond the order–order transition temperature around 150 C. This agrees with a transformation into the hexagonal state. In this way epitaxial relations between phases can be monitored via LAOS as well as exact transition temperatures. In conclusion we would like to ask the question: Why do we need to do SANS experiments to study
e887
Fig. 5. 2D-SANS data from shear aligned samples. On the left the lamellar phase in its perpendicular orientation. On the right the gyroid phase in a characteristic alignment.
phase behaviour of mesoscopic polymer systems. Clearly the SAXS experiment offers more intensity which facilitates the observation of a second-order ring of scattering (Fig. 1 left). Both rheology and birefringence experiments are more responsive to phase changes induced by temperature. The first argument for SANS is that we can use aluminium, and thereby obtain very good thermal control of samples. The second argument is that LAOS needs a good transfer of momentum and forces between the shear plates containing the sample. To include windows (necessary for SAXS) could compromise the control of the shear field exposed to the sample. With 2D anisotropic SANS data the phase identification is also more reliable, because it takes the advantage of measuring the reciprocal space in a two-dimensional projection, which contains more structural information than the azimuthally averaged intensity scattered from an unaligned sample. The third and final argument is rather psychological. Phase transitions in diblocks can easily take between 1 and 10 h depending on sample composition and molecular weight. With neutrons this is an acceptable timeframe for the experimentalist to run a time-resolved experiment. With high flux X-ray sources a 10 h waiting (for something to happen) would be completely out of the question. Of course it could be done, but it would never happen.
Acknowledgements The authors would like to thank Nitash Balsara, Hany Eitouni and John Pople. This study was supported by the Danish Neutron Scattering
ARTICLE IN PRESS e888
M.E. Vigild et al. / Physica B 350 (2004) e885–e888
Centre (DANSCATT) provided by the Danish Natural Science Research Council (SNF), and supported by the Danish Technical Research Council (STVF) through a grant to the Danish Polymer Center. MEV acknowledges support from the Hempel Foundation.
References [1] R. Eskimergen, Ph.D. Thesis, Technical University of Denmark, Lyngby, 2003.
[2] S. Ndoni, C.M. Papadakis, K. Almdal, F.S. Bates, Rev. Sci. Instrum. 66 (1995) 1090. [3] M.E. Vigild, K. Almdal, K. Mortensen, I.W. Hamley, J.P.A. Fairclough, A.J. Ryan, Macromolecules 31 (1998) 5702. [4] P. Strunz, K. Mortensen, Physica B (2003), in press. [5] I.W. Hamley, The Physics of Block Copolymers, Oxford University Press, Oxford, 1998. . [6] F.S. Bates, M.F. Schulz, A.K. Khandpur, S. Forster, J.H. Rosedale, K. Almdal, K. Mortensen, Faraday Discussions 98 (1994) 7.
Physica B 350 (2004) e885–e888
SANS, SAXS, rheology and birefringence—strengths and weaknesses in probing phase behaviour of a diblock copolymer Martin E. Vigilda,*, Ruya . Eskimergenb, Kell Mortensenc a
Department of Chemical Engineering, Danish Polymer Centre DTU, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark b Department of Manufacturing and Management, Danish Polymer Centre DTU, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark c Danish Polymer Centre Ris^ , DK-4000 Roskilde, Denmark
Abstract Asymmetrically composed diblock copolymers exhibit multiphase behaviour and transit the lamellae, gyroid and hexagonal cylindrical phases before reaching the order–disorder temperature, TODT. During a heating experiment towards TODT we observe that birefringence measurements are more sensitive than dynamic mechanical testing and have faster data acquisition rates than SANS when used to follow transient states of the sample. However, birefringence measurements cannot alone identify the precise phase behaviour. r 2004 Published by Elsevier B.V. PACS: 61.12.Ex; 78.20.Fm; 82.35.Jk Keywords: Small-angle neutron scattering; Birefringence; Dynamical mechanical analysis; Multi-phase behaviour; Diblock copolymer
1. Introduction
2. Experimental
We study the phase behaviour of a polystyrene– polyisoprene (SI) diblock copolymer [1] using small-angle neutron scattering (SANS), small angle X-ray scattering (SAXS), birefringence, and dynamic mechanical spectroscopy (DMS). It is our aim to illustrate the complementarity of these techniques for the investigation of multiphase behaviour. Each technique has strengths and weaknesses, but none of them can be used as a complete stand-alone measurement, which will convey all information about the sample phase behaviour.
The sample (SI-29) studied here was polymerized using ‘‘living’’ anionic polymerization [2] to an overall molecular weight of Mn=29500 g/mol, a volume fraction of fPI=0.67, and a polydispersity index of Mw/Mn=1.01. DMS data was recorded using a modified Rheometrics RSA II instrument, which also facilitated simultaneous SANS or birefringence measurements. The rheometer could be fitted with a custom build birefringence set-up [1], or it could be fitted online with the SANS machine [3]. The temperature control during heating cycles was accurate within 1 C. SANS data was obtained at the SANS II instrument at SinQ, The Paul Scherrer Institute, Switzerland [4]. SAXS data was obtained at the
*Corresponding author. Fax: +45-45882161. E-mail address: [email protected] (M.E. Vigild). 0921-4526/$ - see front matter r 2004 Published by Elsevier B.V. doi:10.1016/j.physb.2004.03.229
ARTICLE IN PRESS e886
M.E. Vigild et al. / Physica B 350 (2004) e885–e888
Fig. 1. In birefringence the optical anisotropy is measured as the difference in diffractive index along the vertical and horizontal axes, Dn13. The analyzer produces linearly polarized light in the vertical direction. During the transmission the light is unevenly retarded, if the material has birefringence, and elliptically polarized light result. The analyzer only accepts light with its electrical field vector in the horizontal plane.
Fig. 2. The lamellar and gyroid phases are documented by SAXS. On the left the sample is in the lamellar state (at 90 C), and on the right the sample is in the gyroid state (at 130 C).
Stanford Synchrotron Radiation Laboratory, USA. Fig. 1 shows the principle of the birefringence measurement.
3. Results and discussion Fig. 2 shows initial 2D SAXS data from the SI sample at two different temperatures, which clearly indicates the lamellar and the gyroid phase. We want to study how phase transition evolves, as temperature is increased—and also to find out if the sample contains more than two phases. First, we show temperature-dependent data from SANS in Fig. 3, recorded during a temperature ramp of 1 C/min from 80 C to 170 C. A ring of scattering (similar to the first-order ring in Fig. 2, left) is observed on the 2D SANS detector throughout the temperature ramp. In Fig. 3 the dependence of the scattering peak position (q) is mapped as a function of temperature. It shows a monotonic increase in q, which is to be expected. Thermally increased motion of the polymer chains will result in chain end-to-end contraction which in turn will shrink the micro-phase segregated structure. There is a small, but insignificant feature at approximately 155 C. From the data no phase transitions seem evident in this temperature interval. The corresponding measurement—measuring the viscoelastic properties of the diblock—is shown in Fig. 4 (closed symbols). The elastic shear modulus G0 gives more information on the phase transition than could be extracted from Fig. 3. The
Fig. 3. The peak position (q) follows a slow increase upon heating (1 C/min) without clear features of phase transitions as measured by radially integrated SANS data.
Fig. 4. Synchronized rheology and birefringence data. Oscillatory shear elastic modulus (G0 , closed symbols) measured at frequency o=1 rad/s and shear amplitude g=1%, and the birefringence signal (Dn, open symbols) while heating (1 C/min).
ARTICLE IN PRESS M.E. Vigild et al. / Physica B 350 (2004) e885–e888
modulus comes down from larger values onto a plateau level of approximately 104 Pa. Between 120 C and 130oC there is a slight change of signal and at 150 C we see the onset of a long drop towards 170 C. Without the knowledge of the SAXS data in Fig. 1 it would be difficult to document multiphase behaviour. However, this data can be interpreted to support a lamellar-togyroid transition followed by a disordering (over a rather long temperature range). The birefringence signal is also mapped out in Fig. 4 (open symbols). Birefringence is much more ‘lively’. The 120–130 C interval locates a small peak, which is followed by a dip towards zero. The gyroid phase is cubic and has no birefringence. This is in fine accord with a lamellar–to–gyroid transition, but the transient peak remains unexplained. At 150 C the birefringence rises dramatically and reaches a maximum just before 160 C. Finally it drops synchronized with the rheology as the ODT temperature is approached. The latter part of the temperature interval clearly illustrates how the birefringence measurement is much more sensitive to the formation of the hexagonal phase between gyroid and disorder. This phase is not evident from the rheology alone. However, the assignment of phases in block copolymers cannot be justified in general based on only birefringence and rheology. But in this case of diblocks it can be done by reference to the relatively well-understood phase behaviour [5,6]. SANS can be a very powerful technique in identifying phases. Not in the form of the data treated in Fig. 3, but in combination with large amplitude oscillatory shear (LAOS). Fig. 5 shows such shear alignment of both the lamellar and the gyroid phase. The shear aligned data is very sensitive to thermodynamical changes that influences phase behaviour. For example the gyroid 10 spot pattern will instantly transform into a 2 spot pattern (not shown) when it is heated beyond the order–order transition temperature around 150 C. This agrees with a transformation into the hexagonal state. In this way epitaxial relations between phases can be monitored via LAOS as well as exact transition temperatures. In conclusion we would like to ask the question: Why do we need to do SANS experiments to study
e887
Fig. 5. 2D-SANS data from shear aligned samples. On the left the lamellar phase in its perpendicular orientation. On the right the gyroid phase in a characteristic alignment.
phase behaviour of mesoscopic polymer systems. Clearly the SAXS experiment offers more intensity which facilitates the observation of a second-order ring of scattering (Fig. 1 left). Both rheology and birefringence experiments are more responsive to phase changes induced by temperature. The first argument for SANS is that we can use aluminium, and thereby obtain very good thermal control of samples. The second argument is that LAOS needs a good transfer of momentum and forces between the shear plates containing the sample. To include windows (necessary for SAXS) could compromise the control of the shear field exposed to the sample. With 2D anisotropic SANS data the phase identification is also more reliable, because it takes the advantage of measuring the reciprocal space in a two-dimensional projection, which contains more structural information than the azimuthally averaged intensity scattered from an unaligned sample. The third and final argument is rather psychological. Phase transitions in diblocks can easily take between 1 and 10 h depending on sample composition and molecular weight. With neutrons this is an acceptable timeframe for the experimentalist to run a time-resolved experiment. With high flux X-ray sources a 10 h waiting (for something to happen) would be completely out of the question. Of course it could be done, but it would never happen.
Acknowledgements The authors would like to thank Nitash Balsara, Hany Eitouni and John Pople. This study was supported by the Danish Neutron Scattering
ARTICLE IN PRESS e888
M.E. Vigild et al. / Physica B 350 (2004) e885–e888
Centre (DANSCATT) provided by the Danish Natural Science Research Council (SNF), and supported by the Danish Technical Research Council (STVF) through a grant to the Danish Polymer Center. MEV acknowledges support from the Hempel Foundation.
References [1] R. Eskimergen, Ph.D. Thesis, Technical University of Denmark, Lyngby, 2003.
[2] S. Ndoni, C.M. Papadakis, K. Almdal, F.S. Bates, Rev. Sci. Instrum. 66 (1995) 1090. [3] M.E. Vigild, K. Almdal, K. Mortensen, I.W. Hamley, J.P.A. Fairclough, A.J. Ryan, Macromolecules 31 (1998) 5702. [4] P. Strunz, K. Mortensen, Physica B (2003), in press. [5] I.W. Hamley, The Physics of Block Copolymers, Oxford University Press, Oxford, 1998. . [6] F.S. Bates, M.F. Schulz, A.K. Khandpur, S. Forster, J.H. Rosedale, K. Almdal, K. Mortensen, Faraday Discussions 98 (1994) 7.