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SUPERDENDRITES IN DIRECTIONAL SOLIDIFICATION OF POLYMER-SOLVENT MIXTURES ROLF RAGNARSSON, BRIAN UTTER, and EBERHARD BODENSCHATZ Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, NY 14853-2501

ABSTRACT The directional solidification of the transparent binary alloy succinonitrile-poly(ethylene oxide) was studied in an experiment in which solidification speeds of about 2 mm/sec could be reached without loss of the linear temperature gradient. The low diffusivity of the polymer solute allowed the study of the dynamics of rapid solidification using an optical microscope. For both normal and doublonic dendrites we observed a transition to large triangular “superdendrites” above a certain solidification speed and we report measurements of the primary and secondary spacing as a function of the pulling speed. Our measurements suggest that the observed triangular shape is due to a decoupling of primary and secondary growth at large undercooling.

INTRODUCTION Rapid solidification of metallic alloys at solidification speeds v > 1 m/sec results in a variety of morphological microstructures that have been the subject of extensive studies [1]. The high solidification rates and opacity of metallic alloys make in situ experiments with direct visualization of the growing microstructures difficult [2, 3]. At modest solidification rates, model systems using transparent alloys such as succinonitrile-acetone have given much insight into the spatio temporal dynamics of dendritic growth [4]. However, rapid solidification rates with strongly nonequilibrium growth conditions are difficult to realize experimentally. In addition, time-resolved observation of the rapid spatio-temporal dynamics is impossible with current imaging techniques. We have attempted to overcome these difficulties by using a slowly diffusing polymeric solute, poly(ethylene oxide) (PEO), which has a diffusivity typically three orders of magnitude lower than the diffusivity of its low molecular weight counterparts (e.g. acetone). The time scale for redistribution of solute (“impurity”) is increased which results in a drastic reduction of the solidification speeds for a given undercooling. This makes possible the study of the dynamics of the solidification front using standard video microscopy. The disadvantages of this approach are a low solubility of polymer in the solvent and a relative lack of knowledge of the physical properties of the model system. The solidification of binary polymer-solvent alloys is of interest not only as a model system for metallic solidification, but also in its own right. An understanding of the solidification process may allow the development of methods for the controlled growth of porous polymeric materials with crystalline additives. This was recognized by Smith and Pennings who investigated a number of eutectic polymer-solvent alloys [5, 6], but did not study the dynamics of the evolving liquid-solid interface.

EXPERIMENT Our solidification experiments were carried out using two different temperature stages. In the first design, sample cells of dimensions 50 µm by 15 mm by 75 mm were constructed from polished glass plates that were epoxied together to form a sealed sample container. The cells were then inserted into a temperature stage similar to that of Jackson and Hunt [7]. Due to the thermal response time of the 1.5 mm thick glass plates, the temperature gradient was nonlinear. However, below pulling speeds of 200 µm/sec, it was possible to define the local gradient in the vicinity of the solidification front by measuring the temperature profile with a thermocouple. The pulling speed limitations of the first apparatus were solved by constructing a second setup in which glass capillaries [8] were pulled through the temperature gradient inside an oil-filled outer channel straddling the gap between the hot and cold furnace (Figure 1). The heat-conducting oil and thin capillary walls ensured a rapid thermal response, which made pulling speeds up to 2 mm/sec possible without loss of the linear temperature gradient (as measured with a 25 µm/sec thermocouple embedded in the capillary). In both setups the sample cells were pulled by a linear Burleigh inchworm motor with 4 nm stepsize, which allowed uniform motion up to 2 mm/sec. The temperature of the hot and cold furnaces were controlled to better than ± 10 mK. The interface was observed through an inverted microscope (Nikon Diaphot) using Hoffman modulation contrast optics and imaged with a CCD camera connected to a digital image processing system.

Samples Purified succinonitrile (SCN) and poly(ethylene oxide) of varying molecular weight [9] were used as solvent and solute, respectively. The solvent was purified in a closed system where sublimation of stock SCN, mixing with PEO, degassing, and filling of the sample cell were performed under dry argon atmosphere. The sublimation of stock SCN yields a purified compound with a melting temperature of 58.05± 0.03 ◦ C, corresponding to a purity of 99.98% [10]. Channel walls, 1.5 mm thick Sample capillary, wall thickness 50µm, cell height 50µm Pulling

Oil, between capillary and channel wall, layer thickness 75µm

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Figure 1: The modified experimental setup (not to scale). Note the oil-filled channel for sample capillaries which provides good thermal contact between the moving capillary and the stationary outer walls of the channel.

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Figure 2: Cells and dendrites in a SCN-2%wt PEO (MW 685000) solution. The temperature gradient was 61 K/cm (temperature decreases to the right) and the pulling speeds were (a) 0.45 µm/sec and (b) 4.5 µm/sec to the right. Scale bar length 100 µm.

RESULTS Slow pulling speeds — Using the first apparatus we initially investigated pulling speeds close to instability of the interface. With increasing pulling speed we observed conventional morphologies, like cells followed by dendrites (Figure 2), as well as arrays of doublons. The overall front behavior at slow pulling speeds was similar to that observed for other model systems [4], but with the instability occurring at lower pulling speeds when a high molecular weight solvent was used (typically the interface went unstable above 10 nm/sec) This suggests that the dominating effect of using a polymer solute is the reduction of solute diffusivity and polymer-specific effects appear to be less important. Superdendrite transition — As the pulling speed was increased the dendrites developed into wedges with a triangular envelope, 90◦ opening angle, and the microstructure of the dendrites became space filling at a micrometer length scale. This scenario was found to be only weakly dependent on solute concentration, and was observed both when the corresponding structures at low speeds were of dendritic (Figure 3) and of doublonic (Figure 4) types. When the solidification speed was increased above a certain velocity (marked by arrows in Figure 5) a morphological transition took place. The amplitude of the (secondary) dendrite sidebranches increased and they in turn became unstable to tertiary and possibly higher order branches. As the diffusion length, D/v, approached the microstructure length scale, the growth became increasingly isotropic and space-filling, leading to superdendrites, i.e. the sidebranches behind dendrite tips grew transversely at speeds comparable to the growth velocity of the primary tips leading to the triangular shape with 90◦ angles. Dendrite spacings — Measured average primary and secondary spacings are plotted in Figure 5. As the solidification speed increased, the average primary spacing of normal dendrites, which for slow pulling speeds decreased with a power-law exponent of −0.41±0.02, showed a cross-over to an almost constant value at the transition to superdendrites. This plateau was accessible only for alloys with a high solute concentration. After the emergence of superdendrites, the average primary spacings again decreased, now with a power-law exponent of −0.53 ± 0.03. This value is close to the expected high-speed value of −0.5 [4]. Secondary spacings, on the other hand, showed no plateau, and decayed with a power-law

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Figure 3: Sequence of micrographs from stage 1 illustrating how the envelope of dendrites growing in a SCN-26%wt PEO (MW 56000) alloy changed to triangular (90◦ angles) with increased pulling speeds: (a) 0.90 µm/sec, (b) 9.0 µm/sec, (c) 26.5 µm/sec, and (d) 141 µm/sec. Local temperature gradient was 90 K/cm and the scale bar lengths 100 µm.

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Figure 4: Sequence of micrographs from stage 2 illustrating doublons growing in a SCN5.5%wt PEO (MW 485000) alloy. The envelope of the dendrites became triangular with increased pulling speeds: (a) 7.8 µm/sec, (b) 65 µm/sec, and (c) 182 µm/sec. In all subfigures, the temperature gradient was 45 K/cm and the scale bar length 100 µm.

Dendrite Spacings

"Doublonic Dendrite" Spacings

26%wt PEO, G = 90 K/cm, MW 56000

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(a) Measured primary and secondary spacings of dendrites in a SCN-26%wt PEO (MW 56000) alloy (corresponding to the micrographs in Figure 3). Power-law fits yield exponents of −0.41 ± 0.02 for low speeds, −0.53 ± 0.03 for high speeds, and −0.55 ± 0.02 for secondary spacings.

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(b) Measured primary spacings of doublonic dendrites in a SCN-5.5%wt PEO (MW 485000) alloy (corresponding to the micrographs in Figure 4). Power-law fit for doublonic dendrite spacings yields an exponent of −0.41 ± 0.02.

Figure 5: Average primary (dendrite tip to dendrite tip) and secondary (sidebranch tip to sidebranch tip) spacings for normal and doublonic dendrites. The error bars extend one standard deviation and the superdendrite transition is indicated by arrows. exponent of −0.55 ± 0.02. The obtained power-law exponent for primary spacings at low speed agrees well with the value −0.37 ± 0.01 obtained by Somboonsuk et al. in SCNacetone [11]. For secondary spacings they obtained −0.56 ± 0.02, close to our measured value. Starting from doublons, we did not observe the constant plateau in the average primary spacings. Instead spacings decrease with a power-law exponent of −0.41±0.02, similar to the value obtained for normal low-speed dendrites. No measurements of the secondary spacings was made due to limitations of the current imaging system.

DISCUSSION AND CONCLUSIONS The term superdendrites was coined by Fainstein-Pedraza and Bolling [12], who saw departures from the parabolic shape of dendrites in an experiment where a Pb-4%Sb alloy was unidirectionally grown from the sides of a graphite boat. When the temperature gradient in the melt was low they observed large wedge-shaped structures, i.e., superdendrites. They conjectured that superdendrites were formed by a transient cooperative growth of 30–50 weakly sidebranched dendrites as the result of deformations of the temperature field. Triangular dendritic structures, of a size up to several millimeters, were also observed by Flemings et al. in undercooled Ni-Sn[3] and a similar growth mechanism suggested. Our experiments do not support the above explanation. We observed superdendrites as a stable phenomenon at a constant temperature gradient and did not find any evidence

for the cooperative growth of dendrites. This is consistent with the theoretical analysis by Brener et al. [13], who showed that for the case of a pure substance, the emergence of a triangular envelope describing the limit of the growth out from a single dendrite stem is a generic phenomenon for solidification at strong undercoolings (short diffusion lengths). We thank Ulf Moslener and Ilarion Melnikov for their contributions. We have also benefitted from the contributions by the technical personnel of the Cornell Materials Science Center and of the Laboratory for Atomic and Solid State Physics. This work was supported primarily by the MRSEC Program of the National Science Foundation under Award Number DMR-9632275 and the Alfred P. Sloan Foundation.

REFERENCES [1] Materials Science and Technology: A Comprehensive Treatment, edited by R. Cahn, P. Haasen, and E. Kramer (VCH, Weinheim, 1991), Vol. 15: Processing of Metalls and Alloys. [2] B. Bassler, R. Brunner, W. Hofmeister, and R. Bayuzick, Review of Scientific Instruments 68, 1846 (1997). [3] Y. Wu, T. J. Piccone, Y. Shiohara, and M. C. Flemings, Metallurgical Transactions A 18A, 915 (1987). [4] For reviews see B. Billia and R. Trivedi in Handbook of Crystal Growth, edited by D.T.J. Hurle (Elsevier, Amsterdam, 1993), Vol. 1, Ch. 14 or H. Mueller-Krumbhaar and W. Kurz in Materials Science and Technology: A Comprehensive Treatment, edited by Cahn, R.W. and Haasen, P. and Kramer, E.J. (VCH, Weinheim 1991), Vol. 5, Chap. 10. [5] P. Smith and J. Pennings, Journal of Polymer Science 15, 521 (1977). [6] P. Smith and A. J. Pennings, Journal of Materials Science 11, 1450 (1976). [7] J. Hunt, K. Jackson, and H. Brown, Rev. Sci. Instrum. 37, 805 (1966). [8] We used rectangular glass capillaries manufactured by VitroCom, Inc. The capillaries had the internal dimensions 50 µm by 1 mm, 50 µm walls, and lengths up to 30 cm. They were flame-sealed after filling. [9] PEO with a polydispersity (normalized molecular weight distribution) of 1.05–1.1 was purchased from Polymer Labs, Inc. [10] M. E. Glicksman, R. J. Schaefer, and J. D. Ayers, Metallurgical Transactions A 7A, 1747 (1976). [11] K. Somboonsuk, J. T. Mason, and R. Trivedi, Metall. Trans. A 15A, 967 (1984). [12] D. Fainstein-Pedraza and G. Bolling, Journal of Crystal Growth 28, 311 (1975). [13] E. Brener, H. Muller-Krumbhaar, and D. Temkin, Physical Review E 54, 2714 (1996).