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Directional phase separation of a binary polymer mixture driven by a temperature gradient
PHYSICA ELSEVIER
Physica D 84 (1995) 23-30
Directional phase separation of a binary polymer mixture driven by a temperature gradient Jin Okinaka, Qui Tran-Cong ~ Department of Polymer Science and Engineering, Kyoto Institute of Technology, Matsugasaki, Sakyo-ku, Kyoto 606, Japan
Abstract
Phase separation of the binary polymer mixtures poly(2-chlorostyrene)/poly(vinyl methyl ether) (P2CS/PVME) with a lower critical solution temperature was induced by using a temperature gradient. The critical point of the mixture was set between the two ends of the temperature profile. The interface which separates the miscible region from the thermodynamically unstable region of the samples was dragged toward the low temperature side by increasing the gradient. By using phase-contrast optical microscopy and digital image analysis, it was found that the mixture exhibits inhomogeneous structures with different characteristic length scales, indicating that the temperature gradient has affected the thermodynamic instabilities of the mixtures. The characteristic wavelengths of the structures along the gradient are smaller than those in the perpendicular direction. Toward the high temperature side, this structural anisotropy becomes less significant. These experimental results are qualitatively in agreement with the computer simulation reported recently by Furukawa [Physica A 180 (1992) 128] for the phase separation of binary mixtures under inhomogenous quenching conditions. These preliminary results suggest that polymer mixtures undergoing phase separation induced by a temperature gradient can provide a physical system to study the wavelength selection processes under conditions far from thermodynamic equilibrium.
1. Introduction
Phase separation of polymer mixtures has been extensively studied in the past decades because it is not only related to the critical p h e n o m e n a of the chemical systems with extremely slow transport process, but also directly connected to practical problems such as improvement of the physical properties of multiphase polymer materials via morphology control [1]. For these purposes, a large number of studies on phase separation kinetics in binary polymer mixtures has been carried out with an attempt to 1To whom correspondence should be addressed.
elucidate the time evolution of the structures resulting from thermodynamic instabilities [2]. However, the morphology obtained so far has been limited by the free-energy minimum of the systems because these experiments are performed under thermodynamic equilibrium. From the viewpoint of polymer materials science, it is of great importance if one can effectively manipulate the morphology of materials by using an adjustable external parameter to drive the systems far from equilibrium. In practice, the processing of multiphase polymers is often carried out in the presence of a temperature a n d / o r a pressure distribution. Therefore, in order to optimize the conditions for quality control of
0167-2789/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0167-2789(95)00004-6
24
J. Okinaka, Q. Tran-Cong / Physica D 84 (1995) 23-30
materials, it is necessary to understand the relationship between the deviation from equilibrium and the evolution of the morphology. In fundamental aspects, these problems directly relate to the pattern formation process in materials outside of equilibrium which has been extensively studied in metallic alloys and organic liquid mixtures under the widely known phenomenon of directional solidification [3]. In these experiments, a mixture of an organic liquid or a binary alloy is pulled with a constant velocity along a temperature gradient. Due to a continuous change in temperature of the sample along the moving direction, an interface between liquid and solid phase is formed and continuously propagates toward the low temperature side. The instability of the newly formed interfaces under this particular condition has been analyzed by using linear stability analysis, and is known as the Mullins-Sekerka instability [4]. This problem has been reviewed in relation to crystal growth phenomena [5] and has stimulated a large number of works in recent years [6]. For amorphous polymer mixtures, though the materials are liquids above the glass transition temperature (Tg), the interfaces induced by phase separation are not well defined due to the slow diffusion and the very large molecular weight of the polymer molecules. Therefore it is of great interest to observe the evolution of the morphology of polymer mixtures undergoing phase separation in the presence of a temperature gradient. In this article, we report a preliminary result of the phase separation of poly(2-chlorostyrene)/ poly(vinyl methyl ether) (P2CS/PVME) mixtures driven by a temperature gradient. In order to observe the morphology emerging from the instabilities triggered by different temperatures along the gradient, P2CS/PVME mixtures with the polymer weight fraction in the vicinity of the critical composition were used as samples. The thermodynamic instabilities of these mixtures are induced by using a temperature gradient with the profile covering both sides of the critical point of the mixtures. Instead of pulling the sample along
a constant temperature gradient, we change the temperature gradient to move the interface of the mixture toward the low temperature side. The morphology assot:iated with the phase separation obtained under this condition was observed by using phase-contrast optical microscopy and analyzed by digital image analysis. The results are discussed and compared to the two-dimensional computer simulation performed recently by Furukawa for the phase separation of binary mixtures under inhomogeneous quenching conditions [7].
2. Experiment 2.1. Samples Poly-(2-chlorostyrene) (P2CS) was obtained by radical polymerization of 2-chlorostyrene (Tokyo Kasei, Japan) in benzene at 60°C with a,a'-azobis (isobutyronitrile) as initiator. The average molecular weight Mw and its distribution index Mw/M n are 3.0 x 105 and 2.2, respectively. Poly(vinyl methyl ether) (PVME, Aldrich) was purified by reprecipitation using methanol/nheptane mixtures prior to the experiments. Sampies with a thickness of ca. 40 Ixm and an area of 0.5cm x 7.5cm were prepared by casting the toluene solutions of these polymer mixtures, and were then sandwiched between the two glass plates after drying at 90°C in vacuo over three nights.
2.2. Apparatus and experimental procedure The apparatus used in this work is shown in Fig. 1. The mixture was set horizontally with the two ends in two brass heating blocks which were thermostated by temperatures controllers (Okura Electrics, Japan). The part of the sample outside of the heating blocks (45 mm) was covered with insulator. The interface between the stable and unstable regions of the mixture was shifted toward the low temperature side by
J. Okinaka, Q. Tran-Cong / Physica D 84 (1995) 23-30
TEMPERpROFI ATUREE T~'-...,.,...,~ /HEATINBLOCK G ~ //HEATER
----1 ..... J- -J-] I AC100V
IZ ~TH~£::ONTROLLER~
Fig. 1. The setup used to observe the phase separation behavior of P2CS/PVME mixtures under a temperature gradient.
increasing the temperature of one heating block with a constant heating rate. At first, an initial temperature gradient was applied to the sample by setting the heating block A at 60°C and the block B at 40°C. Both the temperatures are initially located in the stable (one-phase) region of the mixture. Then the temperature of the block A was increased to 210 °C with a constant heating rate of 0.5°C/min. To estimate the gradient, the temperatures at five different positions of the sample between the blocks A and B were directly measured by using micro-thermocouples. Actually, the temperature gradient is not exactly linear with the length of the sample between the two heating blocks. Under the experimental conditions of this study, the gradient was set to be linear in the region covering the interface and the phase-separating part of the mixture (ca 15mm from the block A). The temperature gradient was estimated from these temperatures and the distances between the micro-thermocouples. Under this experimental condition, the temperature gradient was 0.6°C/ mm at the initial stage and eventually reaches the final value 4.0°C/mm after 320min. In this way the quench boundary was forced to move toward the low temperature side (block B) with
25
an average velocity of 3 mm/hr. As the temperature of the hot source (block A) reaches the equilibrium value, the sample was allowed to stay in the final temperature gradient for an additional period of 30 min before quenched into the glassy region of the mixture (0 °C). This time period is necessary for the morphology in the vicinity of the interface to grow to the extent which is observable by optical microscopy. The resulting morphology was then observed by using a phase-contrast optical microscope (Nikon, Model XF-TNF-21). The optical images of the morphology observed along the direction of the temperature gradient were transferred to a digital image analyzer (Pias Co., LA525, Japan) for subsequent analysis using two-dimensional fast Fourier transform (FFT). The one-dimensional power spectra were then extracted and curve smoothing was performed with the MarchandMarmet algorithm [8]. 2.3. Results and discussion
The phase diagram of P2CS/PVME mixtures was measured by light scattering at a fixed angle (20 °) under several heating ratios 0.5, 0.2 and 0.1°C/rain. The boundary between the stable and unstable regions of the mixtures was eventually obtained by extrapolating the scattering data to zero-heating rate. This procedure is necessary because the mass diffusion is several orders of magnitude smaller than the thermal diffusivity of polymers. As shown in Fig. 2, these P2CS/ PVME mixtures possess a lower critical solution temperature (LCST), i.e. the sample undergoes phase separation upon increasing temperature. The composition dependence of the glass transition temperature (Tg) obtained by differential scanning calorimetry (Mac Science DSC-3100) with a heating rate of 5 °C/min is also illustrated in the same figure. Details of the molecular weight dependence of the miscibility of these mixtures have been published elsewhere [9]. Since the temperature gradient is set across the phase boundary, only the mixtures with the
J. Okinaka, Q. Tran-Cong / Physica D 84 (1995) 23-30
26
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1.0
W e i g h t Fraction of P 2 C S
Fig. 2. Phase diagram (Td) and glass transition temperatures (Tg) of P2CS/PVME mixtures observed respectivelyby light scattering and differential scanning calorimetry. critical composition P2CS/PVME (30/70) were used to avoid the interference between the nucleation and the spinodal decomposition process. The structures described hereafter are therefore the consequences of the interactions between unstable modes with different characteristic wavelengths of the spinodal decomposition process induced by different temperatures along the gradient. Figure 3a shows a series of optical micrographs taken at the four different positions illustrated in Fig. 4, after quenching the sample to 0°C. The figures show the small portion ca 0.3 mm from the macroscopic interface between the phase separated and miscible regions of the sample experienced the temperature gradient. The bright (smaller refractiveindex) and dark (larger refractive-index) regions indicate respectively PVME-rich and P2CS-rich domains which arise from the intermediate stage of the spinodal decomposition process. Several features are seen from these optical micrographs. First of all, compared to the low temperature region, the morphology is more coarsened in the
high temperature side of the gradient. This result is simply the consequence of the kinetics of the spinodal decomposition process, i.e. a larger growth rate at a higher temperature [10,11]. Because the morphology already developed into the micrometer scale and also grows with time, the bi-continuous structures shown in Figs. 3a probably correspond to the late stage (nonlinear region) of the spinodal decomposition process. There also exists the anisotropy for the structures shown in Fig. 3a, as revealed by the 2D fast Fourier transform indicated in Fig. 3b. This anisotropy gradually decreases toward the high temperature side of the gradient and finally almost disappears at the distance beyond 0.3 mm from the interface. It is worth noting that the structure in the low temperature region (beyond the position (1)) close to the interface is so small that it cannot be observed within the resolution of optical microscopy. On the other hand, the structures in the high temperature region (beyond the position (4)) are almost isotropic with the characteristic lengths which gradually increase with temperature. Eventually, droplets appear because the mixture in these locations almost reaches the phase equilibrium. In order to confirm the existence of different characteristic length scales induced by the temperature gradient, a similar experiment using a P2CS/ PVME mixture with the same critical composition (30/70) was repeated without a temperature gradient. Namely, the temperatures of the two heating blocks were increased from the same initial temperature (40°C) to 160°C with the same heating rate (0.5 °C/min). The morphology obtained from this experiment is homogeneous and isotropic. An example of such a structure is shown in Fig. 5a. As shown in Fig. 5b, the so-called "spinodal ring" obtained from the 2DFFT power spectra of this optical micrograph assures the isotropic phase morphology of the mixture. These experimental results suggest that the anisotropy seen in Fig. 3a comes from the effects of the temperature gradient on the phase separation process of the mixture. To quantify
J. Okinaka, Q. Tran-Cong / Physica D 84 (1995)2.3-30
27
Temperature Gradient High
~ Low
(a)
(4)
(3)
(2)
(1)
,
(b)
I
I
Fig. 3. (a) Morphology of a P2CS/PVME (30/70) mixture under the temperature gradient described in the text. The scale corresponds to 5 txm. The direction of the gradient is indicated by the arrow. (b) The 2D power spectra corresponding to the optical micrographs shown in (a). The scale corresponds to 5 x 104 cm ~.
these structures, the 1D power spectra in the directions parallel and perpendicular to the temperature gradient are extracted from the 2D FFT data. As an example, the 1D power spectra corresponding to the position (4) indicated in Fig. 4 are shown in Fig. 6. Obviously, the characteristic wavelength along the temperature gradient is smaller than in the perpendicular
p,-
HighTemperature
~
k
I
Low Temperature
0. Phase separated region
Miscible region
Fig. 4. Schematical presentation of the observation area on the sample corresponding to the morphology shown in Fig. 3a.
direction. For convenience, the wavenumbers (q) corresponding to the maxima of the spectra obtained in these two directions are denoted as (qmaxll) and ( q m a x ± ) , respectively. The difference in these two qmax'S, i.e. the inverse characteristic length scales, becomes significant upon approaching the phase boundary as depicted in Fig. 7. These results imply that the morphology observed under the temperature gradient is probably determined by the presence of the two different effects taking place simultaneously in the mixture. One is thermal fluctuations and the other is instabilities propagating along the temperature gradient. At a constant temperature, the thermal fluctuations at an arbitrary position of the sample grow with time and are determined by either the Cahn-Hilliard [12] or the nonlinear phase separation kinetics [13], depending upon the distance from the quench boundary. These
J. Okinaka, Q. Tran-Cong / Physica D 84 (1995) 23-30
28
! }i3 1
il~!i
I
(a)
[
(b)
Fig. 5. Morphology (a) and the corresponding 2D power spectra (b) obtained with a P 2 C S / P V M E (30/70) mixture undergoing phase separation without the temperature gradient. The scales are 5 ~m and 5 x 104 cm 4, respectively.
in the order parameter at the boundary between the already phase-separated and the newly phase-separating portion of the sample. Under this circumstance, the structural anisotropy will be determined by the interactions between the the instability directed by the gradient and the already existing thermal fluctuations. Since the
fluctuations are intrinsically isotropic and their growth rates depend on temperature. On the other hand, in the presence of a temperature gradient continuously changing with time, these fluctuations are also affected by the instabilities propagating from the high temperature region to the lower one. Namely, there exists a mismatch
at p o s i t i o n (4)
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~ 80
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q (cm -1) Fig. 6. The 1D power spectra obtained from Fig. 3b for the location (4) of the sample.
J. Okinaka, Q. Tran-Cong / Physica D 84 (1995) 23-30 5.0xtO
29
4
°°°° 4.0 °° °o o°° X °°°" 3.0 °°,
~ °°o° °°°
E 2.0
.°
°°°
°°o o° °°
°-
°° J
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o°
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I (2)
(1
Position Fig. 7. The spatial inhomogeneity of a P2CS/PVME (30/70) mixture undergoing phase separation in the presence of the temperature gradient. The interval between two successive positions is 0.1 ram. The notation for the positions on the abcissa is the same as in Fig. 4.
effects of the former are significant in the region close to the quench boundary (low temperature) and are less effective in the high temperature region, the anisotropy of the morphology becomes less significant in the area far from the interface between the phase separated and the miscible regions. The changing rate of the temperature gradient and the intrinsic growth rate of thermal fluctuations probably play an important role in the resulting morphology. It is worth noting that recently Furukawa has performed computer simulation for binary mixtures undergoing phase separation under directional quenching conditions [7]. According to these results, the morphology of the mixtures strongly depends on the velocity of the quench boundary. As the quench boundary velocity increases, the morphology changes from columnar, undulatory lamella to randomly bi-continuous structures. The last one simply results from the time delay of the phase separation at locations with different temperatures in the sample. The situation was obtained when the quench boundary moved too fast toward the side of low temperature. The Fourier power spectra of the undulatory lamella morphology obtained under an intermediate
front velocity in these simulations are quite similar to those shown in Fig. 3b.
3. Summary We have shown the preliminary experimental results of binary polymer mixtures undergoing phase separation far from thermodynamical equilibrium. The control parameter in this work is the velocity of the phase boundary driven by the time dependent temperature gradient. The anisotropic morphology seems to be the result of the interactions between the unstable modes in different parts of the sample. The experiments shown here provide not only a way to observe the mode selection processes of polymer materials under thermodynamically open conditions, but also give an insight into the strategy for morphology control of multiphase polymer materials during processing. Furthermore, polymers with improved physical properties can be obtained, in principle, by controlling these instabilities. Details such as the dependence of the morphology on the velocity of the phase boundary as well as the effects of sample thickness are
30
J. Okinaka, Q. Tran-Cong / Physica D 84 (1995) 23-30
currently u n d e r investigation
and will be re-
p o r t e d later.
Acknowledgement T h e financial support f r o m the Ministry of E d u c a t i o n , Science and Culture t h r o u g h the G r a n t - i n - A i d No. 04805093 is gratefully acknowledged. We thank Professor Hiroshi F u r u k a w a ( Y a m a g u c h i University, Japan) for m a n y helpful discussions and sending preprints prior to publication.
References [1] See, for example, D.R. Paul and L.H. Sperling, eds., Multicomponent Polymer Materials, Advances in Chemistry 211 (American Chemical Society, Washington DC., 1986). [2] See, for example, L.A. Utracki, Polymer Alloys and Blends (Hansen, Munich, Germany, 1989).
[3] See, for example, C. Godre~he, ed., Solids far from Equilibrium (Cambridge University Press, New York, 1992). [4] W.W. Mullins and R.F. Sekerka, J. Appl. Phys. 35 (1964) 444. [5] J.S. Langer, Rev. Mod. Phys. 52 (1980) 1. [6] R. Trivedi, J.A. Sekhar and J. Mazumdar, eds., Principles of Solidification and Materials Processing, Vols. 1, 2 (Trans Tech Publications, Switzerland, 1991). [7] H. Furukawa, Physica A 180 (1992) 128; Morphology Transitions in Ordering Dynamics under Static and Dynamic External Conditions, in: Formation, Dynamics, Statistics of Patterns II, K. Kawasaki, ed. (World Scientific, Singapore, 1993) p. 266. [8] P. Marchand and L. Marmet, Rev. Sci. Instrum. 54 (1983) 1034. [9] Q. Tran-Cong, H. Nakano, J. Okinaka and R. Kawakubo, Polymer 34 (1994) 1242. [10] J.D. Gunton, M. San Miguel and P.S. Sahni, in: Phase Transition and Critical Phenomena, S. Domb and J.L. Lebowitz, eds. Vol. 8, Chapter 3 (Academic Press, New York, 1983). [11] P.G. de Gennes, J. Chem. Phys. 72 (1980) 4756; P. Pincus, J. Chem. Phys. 75 (1981) 1996. [12] J.W. Cahn, J. Chem. Phys. 42 (1965) 93. [13] See, for example, H. Furukawa, Adv. Phys. 34 (1984) 703.
Physica D 84 (1995) 23-30
Directional phase separation of a binary polymer mixture driven by a temperature gradient Jin Okinaka, Qui Tran-Cong ~ Department of Polymer Science and Engineering, Kyoto Institute of Technology, Matsugasaki, Sakyo-ku, Kyoto 606, Japan
Abstract
Phase separation of the binary polymer mixtures poly(2-chlorostyrene)/poly(vinyl methyl ether) (P2CS/PVME) with a lower critical solution temperature was induced by using a temperature gradient. The critical point of the mixture was set between the two ends of the temperature profile. The interface which separates the miscible region from the thermodynamically unstable region of the samples was dragged toward the low temperature side by increasing the gradient. By using phase-contrast optical microscopy and digital image analysis, it was found that the mixture exhibits inhomogeneous structures with different characteristic length scales, indicating that the temperature gradient has affected the thermodynamic instabilities of the mixtures. The characteristic wavelengths of the structures along the gradient are smaller than those in the perpendicular direction. Toward the high temperature side, this structural anisotropy becomes less significant. These experimental results are qualitatively in agreement with the computer simulation reported recently by Furukawa [Physica A 180 (1992) 128] for the phase separation of binary mixtures under inhomogenous quenching conditions. These preliminary results suggest that polymer mixtures undergoing phase separation induced by a temperature gradient can provide a physical system to study the wavelength selection processes under conditions far from thermodynamic equilibrium.
1. Introduction
Phase separation of polymer mixtures has been extensively studied in the past decades because it is not only related to the critical p h e n o m e n a of the chemical systems with extremely slow transport process, but also directly connected to practical problems such as improvement of the physical properties of multiphase polymer materials via morphology control [1]. For these purposes, a large number of studies on phase separation kinetics in binary polymer mixtures has been carried out with an attempt to 1To whom correspondence should be addressed.
elucidate the time evolution of the structures resulting from thermodynamic instabilities [2]. However, the morphology obtained so far has been limited by the free-energy minimum of the systems because these experiments are performed under thermodynamic equilibrium. From the viewpoint of polymer materials science, it is of great importance if one can effectively manipulate the morphology of materials by using an adjustable external parameter to drive the systems far from equilibrium. In practice, the processing of multiphase polymers is often carried out in the presence of a temperature a n d / o r a pressure distribution. Therefore, in order to optimize the conditions for quality control of
0167-2789/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0167-2789(95)00004-6
24
J. Okinaka, Q. Tran-Cong / Physica D 84 (1995) 23-30
materials, it is necessary to understand the relationship between the deviation from equilibrium and the evolution of the morphology. In fundamental aspects, these problems directly relate to the pattern formation process in materials outside of equilibrium which has been extensively studied in metallic alloys and organic liquid mixtures under the widely known phenomenon of directional solidification [3]. In these experiments, a mixture of an organic liquid or a binary alloy is pulled with a constant velocity along a temperature gradient. Due to a continuous change in temperature of the sample along the moving direction, an interface between liquid and solid phase is formed and continuously propagates toward the low temperature side. The instability of the newly formed interfaces under this particular condition has been analyzed by using linear stability analysis, and is known as the Mullins-Sekerka instability [4]. This problem has been reviewed in relation to crystal growth phenomena [5] and has stimulated a large number of works in recent years [6]. For amorphous polymer mixtures, though the materials are liquids above the glass transition temperature (Tg), the interfaces induced by phase separation are not well defined due to the slow diffusion and the very large molecular weight of the polymer molecules. Therefore it is of great interest to observe the evolution of the morphology of polymer mixtures undergoing phase separation in the presence of a temperature gradient. In this article, we report a preliminary result of the phase separation of poly(2-chlorostyrene)/ poly(vinyl methyl ether) (P2CS/PVME) mixtures driven by a temperature gradient. In order to observe the morphology emerging from the instabilities triggered by different temperatures along the gradient, P2CS/PVME mixtures with the polymer weight fraction in the vicinity of the critical composition were used as samples. The thermodynamic instabilities of these mixtures are induced by using a temperature gradient with the profile covering both sides of the critical point of the mixtures. Instead of pulling the sample along
a constant temperature gradient, we change the temperature gradient to move the interface of the mixture toward the low temperature side. The morphology assot:iated with the phase separation obtained under this condition was observed by using phase-contrast optical microscopy and analyzed by digital image analysis. The results are discussed and compared to the two-dimensional computer simulation performed recently by Furukawa for the phase separation of binary mixtures under inhomogeneous quenching conditions [7].
2. Experiment 2.1. Samples Poly-(2-chlorostyrene) (P2CS) was obtained by radical polymerization of 2-chlorostyrene (Tokyo Kasei, Japan) in benzene at 60°C with a,a'-azobis (isobutyronitrile) as initiator. The average molecular weight Mw and its distribution index Mw/M n are 3.0 x 105 and 2.2, respectively. Poly(vinyl methyl ether) (PVME, Aldrich) was purified by reprecipitation using methanol/nheptane mixtures prior to the experiments. Sampies with a thickness of ca. 40 Ixm and an area of 0.5cm x 7.5cm were prepared by casting the toluene solutions of these polymer mixtures, and were then sandwiched between the two glass plates after drying at 90°C in vacuo over three nights.
2.2. Apparatus and experimental procedure The apparatus used in this work is shown in Fig. 1. The mixture was set horizontally with the two ends in two brass heating blocks which were thermostated by temperatures controllers (Okura Electrics, Japan). The part of the sample outside of the heating blocks (45 mm) was covered with insulator. The interface between the stable and unstable regions of the mixture was shifted toward the low temperature side by
J. Okinaka, Q. Tran-Cong / Physica D 84 (1995) 23-30
TEMPERpROFI ATUREE T~'-...,.,...,~ /HEATINBLOCK G ~ //HEATER
----1 ..... J- -J-] I AC100V
IZ ~TH~£::ONTROLLER~
Fig. 1. The setup used to observe the phase separation behavior of P2CS/PVME mixtures under a temperature gradient.
increasing the temperature of one heating block with a constant heating rate. At first, an initial temperature gradient was applied to the sample by setting the heating block A at 60°C and the block B at 40°C. Both the temperatures are initially located in the stable (one-phase) region of the mixture. Then the temperature of the block A was increased to 210 °C with a constant heating rate of 0.5°C/min. To estimate the gradient, the temperatures at five different positions of the sample between the blocks A and B were directly measured by using micro-thermocouples. Actually, the temperature gradient is not exactly linear with the length of the sample between the two heating blocks. Under the experimental conditions of this study, the gradient was set to be linear in the region covering the interface and the phase-separating part of the mixture (ca 15mm from the block A). The temperature gradient was estimated from these temperatures and the distances between the micro-thermocouples. Under this experimental condition, the temperature gradient was 0.6°C/ mm at the initial stage and eventually reaches the final value 4.0°C/mm after 320min. In this way the quench boundary was forced to move toward the low temperature side (block B) with
25
an average velocity of 3 mm/hr. As the temperature of the hot source (block A) reaches the equilibrium value, the sample was allowed to stay in the final temperature gradient for an additional period of 30 min before quenched into the glassy region of the mixture (0 °C). This time period is necessary for the morphology in the vicinity of the interface to grow to the extent which is observable by optical microscopy. The resulting morphology was then observed by using a phase-contrast optical microscope (Nikon, Model XF-TNF-21). The optical images of the morphology observed along the direction of the temperature gradient were transferred to a digital image analyzer (Pias Co., LA525, Japan) for subsequent analysis using two-dimensional fast Fourier transform (FFT). The one-dimensional power spectra were then extracted and curve smoothing was performed with the MarchandMarmet algorithm [8]. 2.3. Results and discussion
The phase diagram of P2CS/PVME mixtures was measured by light scattering at a fixed angle (20 °) under several heating ratios 0.5, 0.2 and 0.1°C/rain. The boundary between the stable and unstable regions of the mixtures was eventually obtained by extrapolating the scattering data to zero-heating rate. This procedure is necessary because the mass diffusion is several orders of magnitude smaller than the thermal diffusivity of polymers. As shown in Fig. 2, these P2CS/ PVME mixtures possess a lower critical solution temperature (LCST), i.e. the sample undergoes phase separation upon increasing temperature. The composition dependence of the glass transition temperature (Tg) obtained by differential scanning calorimetry (Mac Science DSC-3100) with a heating rate of 5 °C/min is also illustrated in the same figure. Details of the molecular weight dependence of the miscibility of these mixtures have been published elsewhere [9]. Since the temperature gradient is set across the phase boundary, only the mixtures with the
J. Okinaka, Q. Tran-Cong / Physica D 84 (1995) 23-30
26
200 - -
7-
-
I
I
I
~
I--7
i] i
150
~'
10o
) P2CS/PVME(30/70)
& [.-,
]
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-50 t 0.0
i
I
0.1
0.2
L 0.3
I 0.4
0.5
i
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0.6
0.7
0.8
0.9
1.0
W e i g h t Fraction of P 2 C S
Fig. 2. Phase diagram (Td) and glass transition temperatures (Tg) of P2CS/PVME mixtures observed respectivelyby light scattering and differential scanning calorimetry. critical composition P2CS/PVME (30/70) were used to avoid the interference between the nucleation and the spinodal decomposition process. The structures described hereafter are therefore the consequences of the interactions between unstable modes with different characteristic wavelengths of the spinodal decomposition process induced by different temperatures along the gradient. Figure 3a shows a series of optical micrographs taken at the four different positions illustrated in Fig. 4, after quenching the sample to 0°C. The figures show the small portion ca 0.3 mm from the macroscopic interface between the phase separated and miscible regions of the sample experienced the temperature gradient. The bright (smaller refractiveindex) and dark (larger refractive-index) regions indicate respectively PVME-rich and P2CS-rich domains which arise from the intermediate stage of the spinodal decomposition process. Several features are seen from these optical micrographs. First of all, compared to the low temperature region, the morphology is more coarsened in the
high temperature side of the gradient. This result is simply the consequence of the kinetics of the spinodal decomposition process, i.e. a larger growth rate at a higher temperature [10,11]. Because the morphology already developed into the micrometer scale and also grows with time, the bi-continuous structures shown in Figs. 3a probably correspond to the late stage (nonlinear region) of the spinodal decomposition process. There also exists the anisotropy for the structures shown in Fig. 3a, as revealed by the 2D fast Fourier transform indicated in Fig. 3b. This anisotropy gradually decreases toward the high temperature side of the gradient and finally almost disappears at the distance beyond 0.3 mm from the interface. It is worth noting that the structure in the low temperature region (beyond the position (1)) close to the interface is so small that it cannot be observed within the resolution of optical microscopy. On the other hand, the structures in the high temperature region (beyond the position (4)) are almost isotropic with the characteristic lengths which gradually increase with temperature. Eventually, droplets appear because the mixture in these locations almost reaches the phase equilibrium. In order to confirm the existence of different characteristic length scales induced by the temperature gradient, a similar experiment using a P2CS/ PVME mixture with the same critical composition (30/70) was repeated without a temperature gradient. Namely, the temperatures of the two heating blocks were increased from the same initial temperature (40°C) to 160°C with the same heating rate (0.5 °C/min). The morphology obtained from this experiment is homogeneous and isotropic. An example of such a structure is shown in Fig. 5a. As shown in Fig. 5b, the so-called "spinodal ring" obtained from the 2DFFT power spectra of this optical micrograph assures the isotropic phase morphology of the mixture. These experimental results suggest that the anisotropy seen in Fig. 3a comes from the effects of the temperature gradient on the phase separation process of the mixture. To quantify
J. Okinaka, Q. Tran-Cong / Physica D 84 (1995)2.3-30
27
Temperature Gradient High
~ Low
(a)
(4)
(3)
(2)
(1)
,
(b)
I
I
Fig. 3. (a) Morphology of a P2CS/PVME (30/70) mixture under the temperature gradient described in the text. The scale corresponds to 5 txm. The direction of the gradient is indicated by the arrow. (b) The 2D power spectra corresponding to the optical micrographs shown in (a). The scale corresponds to 5 x 104 cm ~.
these structures, the 1D power spectra in the directions parallel and perpendicular to the temperature gradient are extracted from the 2D FFT data. As an example, the 1D power spectra corresponding to the position (4) indicated in Fig. 4 are shown in Fig. 6. Obviously, the characteristic wavelength along the temperature gradient is smaller than in the perpendicular
p,-
HighTemperature
~
k
I
Low Temperature
0. Phase separated region
Miscible region
Fig. 4. Schematical presentation of the observation area on the sample corresponding to the morphology shown in Fig. 3a.
direction. For convenience, the wavenumbers (q) corresponding to the maxima of the spectra obtained in these two directions are denoted as (qmaxll) and ( q m a x ± ) , respectively. The difference in these two qmax'S, i.e. the inverse characteristic length scales, becomes significant upon approaching the phase boundary as depicted in Fig. 7. These results imply that the morphology observed under the temperature gradient is probably determined by the presence of the two different effects taking place simultaneously in the mixture. One is thermal fluctuations and the other is instabilities propagating along the temperature gradient. At a constant temperature, the thermal fluctuations at an arbitrary position of the sample grow with time and are determined by either the Cahn-Hilliard [12] or the nonlinear phase separation kinetics [13], depending upon the distance from the quench boundary. These
J. Okinaka, Q. Tran-Cong / Physica D 84 (1995) 23-30
28
! }i3 1
il~!i
I
(a)
[
(b)
Fig. 5. Morphology (a) and the corresponding 2D power spectra (b) obtained with a P 2 C S / P V M E (30/70) mixture undergoing phase separation without the temperature gradient. The scales are 5 ~m and 5 x 104 cm 4, respectively.
in the order parameter at the boundary between the already phase-separated and the newly phase-separating portion of the sample. Under this circumstance, the structural anisotropy will be determined by the interactions between the the instability directed by the gradient and the already existing thermal fluctuations. Since the
fluctuations are intrinsically isotropic and their growth rates depend on temperature. On the other hand, in the presence of a temperature gradient continuously changing with time, these fluctuations are also affected by the instabilities propagating from the high temperature region to the lower one. Namely, there exists a mismatch
at p o s i t i o n (4)
•
q ~ = 1 . 4 x 104 (cm i)
©
I
0
r,.)
1
Parallel to the g r a d i e n t |/ Perpendicular to the g r a d i e n l ]
qm~=2.7 x 10 4 (cm "1}
o o 0 0
•
00000
•
•
Q
0 I 20
000000000 0
0
0
0
0
0~ ~
¢
"
~
40
~ 60
~ 80
~'"
" 3 100x10
q (cm -1) Fig. 6. The 1D power spectra obtained from Fig. 3b for the location (4) of the sample.
J. Okinaka, Q. Tran-Cong / Physica D 84 (1995) 23-30 5.0xtO
29
4
°°°° 4.0 °° °o o°° X °°°" 3.0 °°,
~ °°o° °°°
E 2.0
.°
°°°
°°o o° °°
°-
°° J
1.0 (4)
o°
I (3)
I (2)
(1
Position Fig. 7. The spatial inhomogeneity of a P2CS/PVME (30/70) mixture undergoing phase separation in the presence of the temperature gradient. The interval between two successive positions is 0.1 ram. The notation for the positions on the abcissa is the same as in Fig. 4.
effects of the former are significant in the region close to the quench boundary (low temperature) and are less effective in the high temperature region, the anisotropy of the morphology becomes less significant in the area far from the interface between the phase separated and the miscible regions. The changing rate of the temperature gradient and the intrinsic growth rate of thermal fluctuations probably play an important role in the resulting morphology. It is worth noting that recently Furukawa has performed computer simulation for binary mixtures undergoing phase separation under directional quenching conditions [7]. According to these results, the morphology of the mixtures strongly depends on the velocity of the quench boundary. As the quench boundary velocity increases, the morphology changes from columnar, undulatory lamella to randomly bi-continuous structures. The last one simply results from the time delay of the phase separation at locations with different temperatures in the sample. The situation was obtained when the quench boundary moved too fast toward the side of low temperature. The Fourier power spectra of the undulatory lamella morphology obtained under an intermediate
front velocity in these simulations are quite similar to those shown in Fig. 3b.
3. Summary We have shown the preliminary experimental results of binary polymer mixtures undergoing phase separation far from thermodynamical equilibrium. The control parameter in this work is the velocity of the phase boundary driven by the time dependent temperature gradient. The anisotropic morphology seems to be the result of the interactions between the unstable modes in different parts of the sample. The experiments shown here provide not only a way to observe the mode selection processes of polymer materials under thermodynamically open conditions, but also give an insight into the strategy for morphology control of multiphase polymer materials during processing. Furthermore, polymers with improved physical properties can be obtained, in principle, by controlling these instabilities. Details such as the dependence of the morphology on the velocity of the phase boundary as well as the effects of sample thickness are
30
J. Okinaka, Q. Tran-Cong / Physica D 84 (1995) 23-30
currently u n d e r investigation
and will be re-
p o r t e d later.
Acknowledgement T h e financial support f r o m the Ministry of E d u c a t i o n , Science and Culture t h r o u g h the G r a n t - i n - A i d No. 04805093 is gratefully acknowledged. We thank Professor Hiroshi F u r u k a w a ( Y a m a g u c h i University, Japan) for m a n y helpful discussions and sending preprints prior to publication.
References [1] See, for example, D.R. Paul and L.H. Sperling, eds., Multicomponent Polymer Materials, Advances in Chemistry 211 (American Chemical Society, Washington DC., 1986). [2] See, for example, L.A. Utracki, Polymer Alloys and Blends (Hansen, Munich, Germany, 1989).
[3] See, for example, C. Godre~he, ed., Solids far from Equilibrium (Cambridge University Press, New York, 1992). [4] W.W. Mullins and R.F. Sekerka, J. Appl. Phys. 35 (1964) 444. [5] J.S. Langer, Rev. Mod. Phys. 52 (1980) 1. [6] R. Trivedi, J.A. Sekhar and J. Mazumdar, eds., Principles of Solidification and Materials Processing, Vols. 1, 2 (Trans Tech Publications, Switzerland, 1991). [7] H. Furukawa, Physica A 180 (1992) 128; Morphology Transitions in Ordering Dynamics under Static and Dynamic External Conditions, in: Formation, Dynamics, Statistics of Patterns II, K. Kawasaki, ed. (World Scientific, Singapore, 1993) p. 266. [8] P. Marchand and L. Marmet, Rev. Sci. Instrum. 54 (1983) 1034. [9] Q. Tran-Cong, H. Nakano, J. Okinaka and R. Kawakubo, Polymer 34 (1994) 1242. [10] J.D. Gunton, M. San Miguel and P.S. Sahni, in: Phase Transition and Critical Phenomena, S. Domb and J.L. Lebowitz, eds. Vol. 8, Chapter 3 (Academic Press, New York, 1983). [11] P.G. de Gennes, J. Chem. Phys. 72 (1980) 4756; P. Pincus, J. Chem. Phys. 75 (1981) 1996. [12] J.W. Cahn, J. Chem. Phys. 42 (1965) 93. [13] See, for example, H. Furukawa, Adv. Phys. 34 (1984) 703.