Letter pubs.acs.org/JPCL
Fast Crystal Growth Induces Mobility and Tension in Supercooled o‑Terphenyl Keewook Paeng,†,§ C. Travis Powell,‡,† Lian Yu,‡,† and M. D. Ediger*,† †
Department of Chemistry, University of Wisconsin-Madison, Madison, Wisconsin 53706, United States School of Pharmacy, University of Wisconsin-Madison, Madison, Wisconsin 53705, United States
‡
ABSTRACT: A photobleaching method was used to measure the reorientation of dilute probes in liquid o-terphenyl near a crystal growth front. Near the glasstransition temperature Tg, mobility in the supercooled liquid was enhanced within ∼10 μm of the crystal growth front, by as much as a factor of 4. This enhanced mobility appears to be caused by tension created in the sample as a result of the density difference between the supercooled liquid and crystal. The maximum observed mobility enhancement corresponds to a tension of about −8 MPa, close to the cavitation limit for liquid o-terphenyl. Whereas the observed mobility near the growing crystal is not large enough to explain the extraordinary fast crystal growth observed near Tg in o-terphenyl and some other low-molecular-weight glassformers, these observations suggest that cavitation or fracture plays a key role in releasing tension and allowing fast crystal growth to occur at a steady rate. SECTION: Glasses, Colloids, Polymers, and Soft Matter
C
ontrolling crystallization of organic molecules is of great importance for the development of organic electronics1,2 and amorphous pharmaceuticals.3,4 For some applications, the higher stability and local order of the crystalline state is required. In other cases, the amorphous state is preferred because of its macroscopic homogeneity1,2 and the ease with which properties can be varied by changing composition. The standard view of crystal growth in a single-component system sees the amorphous state as a fairly passive participant in the process; it supplies the molecules at a rate specified by its bulk diffusion coefficient5 or viscosity.6 There are hints in the literature that this view is incomplete and that crystal growth can alter the state of the liquid nearby.7,8 For example, it has been shown that macroscopic liquid flow can be induced by the growth of spherulites in liquid isotactic polypropylene.9 Most relevant to the experiments reported here are computer simulations by Chan et al. They report that Ni atoms within five monolayers of the crystal/liquid interface diffuse faster than in the bulk liquid and that this rapid motion is an important factor in the fast crystal growth observed far below Tm.10 The interplay between crystal growth rates and molecular mobility has been an important element of attempts to understand the remarkably fast crystal growth that can occur for some glass-forming organic liquids near and below Tg. To provide context for the experiments presented here, Figure 1 summarizes what is known about crystal growth rates in oterphenyl over a broad range of temperature. We first emphasize those features of Figure 1 that are compatible with standard models of crystal growth. The growth rate data between 255 and 330 K demonstrate the competition between the effects of the molecular mobility and the thermodynamic driving force on crystal growth rates. As Tm is approached, © 2012 American Chemical Society
Figure 1. Temperature dependence of o-terphenyl crystal growth rate u (left axis) and translational self-diffusion coefficient D (right axis). The crystal growth rate data are reproduced from the measurements by Hikima et al.,11 Magill et al.,5 and Scherer et al.,12 and the selfdiffusion data are from the measurements by Fujara et al.13 and Mapes et al.14
growth rates decrease as a result of the decreasing thermodynamic driving force. Below 280 K, the rate of crystal growth is controlled by molecular mobility in the supercooled liquid, as illustrated by the excellent correspondence between crystal growth rates (left axis) and self-diffusion coefficients (right axis). At a qualitative level, the behavior shown in Figure Received: August 3, 2012 Accepted: August 29, 2012 Published: August 29, 2012 2562
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Figure 2. (a) Anisotropy decays for dilute DPPC in o-terphenyl at the indicated temperatures, with no crystals present in the sample. The solid lines are fits to the KWW function. The rotational correlation time τc is calculated from the fits. (b) Temperature dependence of τc for DPPC in oterphenyl. The solid line represents dielectric relaxation times of neat OTP (ref 27) and the dotted line is this same data vertically shifted. Inset shows the molecular structures of DPPC and o-terphenyl.
terphenyl is enhanced near an active crystal growth front. The maximum enhancement is roughly a factor of 4, and the mobility is altered over a range of ∼10 μm from the crystal growth front. We attribute this enhanced mobility to tension induced by the higher density of the crystalline state, in qualitative agreement with the analysis of ref 22. However, the observed mobility enhancement is not nearly large enough to account for the faster crystal growth that occurs near Tg in GC mode. As we discuss, the observed 10 μm length scale can be used to deduce submicrometer microscopic features of the fast crystal growth process. A photobleaching method in conjunction with a confocal fluorescence microscope was utilized to measure the reorientation of a dilute probe (∼10−6 M DPPC; N,N′dipentyl-3,4,9,10-perylenedicarboximide) in o-terphenyl, in the presence and absence of growing crystals. Photobleaching uses linearly polarized light to create an anisotropic distribution of unbleached probes, and the reorientation of these probes is described by the anisotropy function r(t).28,29 Figure 2a shows anisotropy decays for dilute DPPC in o-terphenyl at the indicated temperatures. For these measurements, care was taken to ensure that no crystal was present during the anisotropy measurements. As temperature increases, the probes reorient faster and the anisotropy decays more quickly. Anisotropy decays were fitted to the Kohlrausch−Williams− Watts (KWW) function, as shown in solid curves. The rotational correlation time τc was calculated from these fits and is plotted in Figure 2b. Fitting to the KWW function also provides βKWW, which describes the width of the relaxation time distribution. As expected for a probe of this size, βKWW was close to unity (0.97 ± 0.05).28 For smaller probes in oterphenyl, βKWW ranges from 0.39 to 0.89 near Tg. Figure 2b shows that DPPC reorientation is a good reporter of the dynamics of the o-terphenyl host molecules in the range from Tg to Tg + 10 K. The red solid curve in Figure 2b represents dielectric relaxation measurements on neat oterphenyl, reproduced from the literature.27,30 As expected, DPPC reorients more slowly than the smaller o-terphenyl molecules, by roughly two orders of magnitude. Nevertheless, DPPC reorientation has the same temperature dependence as the reorientation of the o-terphenyl molecules. (The dotted line was obtained by vertically shifting the dielectric data.) This result is consistent with previous work on similar size probes in o-terphenyl28 and related systems31−33 and is consistent with
1 above 255 K has been observed for many organic and inorganic liquids. Below 255 K, Figure 1 shows a remarkable decoupling between molecular mobility in the supercooled liquid and the rate of crystal growth. These data are certainly inconsistent with the idea that the translational mobility of the bulk liquid limits the rate of crystal growth at low temperature. For ease of discussion, we refer to the fast crystal growth at low temperature as the GC (glass to crystal) growth mode but note that fast crystal growth also occurs in the supercooled liquid state just above Tg. This remarkable fast crystal growth was first observed by Greet and Turnbull15 in 1967 (in oterphenyl) but was not systematically studied until 1995 by Hikima et al.11 It has now been observed for a number of organic glassformers16−22 and is particularly important to understand in the context of amorphous pharmaceuticals, which must resist crystallization to have increased bioavailability.3,23 To our knowledge, this abrupt increase in crystal growth rate with decreasing temperature has not been observed in metallic, inorganic, or polymeric systems. There have been several attempts to explain the GC crystal growth process, including homogeneous-nucleation-based crystallization,11,17,18,24 solid-state crystal growth by local mobility,21 percolative nanocrystallization,25 and tensioninduced interfacial mobility.22,26 The tension-induced mobility view is most relevant for our experiments and is based on the density mismatch between the amorphous and crystalline states. Because crystalline o-terphenyl is more dense, crystal growth will lead to tension (or negative pressure) in the system if the overall volume cannot reach equilibrium. Unlike crystallization in a free-flowing liquid, a glass or viscous supercooled liquid cannot respond instantaneously to the tension created by the growing crystal because the amorphous state flows very slowly. It has been proposed22 that this tension increases mobility in the amorphous state sufficiently to account for the approximately four order of magnitude enhancement of the crystal growth rate near Tg. Here we report the first molecular mobility measurements near a crystal growth front for a single-component liquid near Tg. An optical photobleaching method was utilized to probe reorientation of dilute fluorescent probes in o-terphenyl. Molecular mobility was measured as a function of distance from the crystal growth front with spatial resolution of a few micrometers. We find that molecular mobility in supercooled o2563
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Figure 3. (a) Normalized anisotropy decays at the indicated distance relative to the GC crystal growth front for actively growing crystals. The anisotropy decays more quickly near the growing crystal front. All measurements were performed at 245 K. The solid lines are fits to the KWW function. (b) Rotational correlation times as a function of distance from the GC growth front for actively growing crystals and crystals that are not growing. The curved line is a guide to eye. The inset is a schematic cross section of the sample.
et al. studied the pressure dependence of the dielectric relaxation time of o-terphenyl up to 80 MPa.34 Using their data and extrapolating to negative pressure, we calculate that a four-fold enhancment in mobility at 245 K is associated with a negative pressure of 7.7 MPa. A similar calculation can be made based on the observed pressure dependence of Tg (dTg/dP = 0.26/MPa);35 by this route, a factor of four enhancement of the structural relaxation time at 245 K is associated with a negative pressure of 7.5 MPa. Tension can also enhance mobility by a mechanism described by Eyring in which the potential energy landscape is tilted; in this process, some barriers are lowered, opening pathways for relaxation under stress.36 Consistent with the above estimates, experiments on polymer glasses near Tg show that an increase in mobility by a factor of four is achieved with stresses between 5 and 10 MPa.37,38 Significantly, on the basis of experiments in which liquid o-terphenyl was cooled under tension, Angell et al. estimated the tensile limit to be −7.6 ± 1 MPa.39 At pressures more negative than this, cavitation must occur. On the basis of these measurements, we present a speculative molecular picture of how fast-growing crystals influence the mobility of the adjacent supercooled liquid. A fast-growing crystal likely creates tension as a result of its higher density relative to the amorphous state. As described in ref 22, flow near Tg is too slow to allow this tension to be dissipated. The tension induces mobility near the growing crystal interface, and it is possible that this contributes to the speed at which crystal growth occurs. When the tension reaches about −8 MPa, fracture occurs locally in supercooled liquid (or in the crystal or at the interface between them). These fracture events do not allow the mobility enhancement in front of the growing crystal to exceed a factor of four. The last part of our interpretation differs from the scenario presented in ref 22. Our measurements indicate that while tension can produce enhanced mobility, it cannot produce sufficient mobility to explain the fast rate of GC growth because the tension is limited by fracture. Our scenario is consistent with the lack of significant time dependence in the GC crystal growth rate11,16,22 because fracture provides a release mechanism to prevent the buildup of tension without limit and allows the system to reach a steady state. We note that cavitation has previously been reported when spherulites impinge during crystallization of isotactic polypropylene; in this case, it is estimated that cavitation occurs at −16 MPa.40
the view that DPPC reorientation is slaved to the dynamics of the surrounding o-terphenyl molecules. We have observed that dilute DPPC probes in supercooled oterphenyl reorient more rapidly near an actively growing crystal of o-terphenyl. Figure 3a shows anisotropy decays for DPPC in o-terphenyl at the indicated distances relative to the crystal growth front. These data were obtained at 245 K, while oterphenyl crystals were growing at the rapid rate associated with the GC mode (Figure 1). The solid lines through the anisotropy decay data are fits to the KWW function. Rotational correlation times are calculated from these fits and plotted in Figure 3b (blue circles). For actively growing crystals, the maximum enhancement of dynamics is roughly 0.6 decade or a factor of 4. Dynamics are enhanced over a distance of ∼10 μm from the crystal growth front. During each anisotropy measurement, the o-terphenyl crystal grows ∼7 μm, and this sets the error range along the x axis for the data in Figure 3b. Errors in log(τc) include temperature variations during the measurements (±0.2 K) and the uncertainty associated with fitting the anisotropy decays, which did not decay to zero. The βKWW parameters observed near the growing crystal front exceeded unity (up to 1.3), consistent with the idea that probe mobility increases as the crystal growth front approaches the position of the anisotropy measurement. The crystal growth rates observed during these anisotropy measurements are consistent with literature values for GC growth of neat oterphenyl.11,16,22 We interpret Figure 3 to indicate that tension is created by the growing crystals of higher density and that this tension enhances mobility. We confirmed that the enhanced mobility depicted in Figure 3 is only observed in the presence of actively growing crystals of o-terphenyl. When GC crystal growth was terminated by a brief excursion to high temperature,20,21 the presence of nearby crystals had no influence on the reorientation of DPPC, as shown by the yellow squares in Figure 3b. We estimate the maximum tension in the supercooled liquid near the growing crystal to be about −8 MPa by the calculations described below. We can think of tension in terms of negative pressure dilating the system and providing more freedom of movement. The pressure dependence of mobility for o-terphenyl has been measured at elevated pressures, and these observations can be used to predict the extent to which negative pressure will enhance mobility. Naoki 2564
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Figure 4. Dependence of the rotational correlation times on the distance relative to the GC growth front for (a) different sample thicknesses and (b) different measurement positions relative to cover glass for a 12 μm film.
this with the 10 μm effective sample length, we expect that each fracture or cavitation event will result in two new interfaces about 10 nm apart. While such voids are too small to be measured by optical microscopy, they could plausibly exist between different crystal grains produced by GC growth and account for the ∼4% density mismatch45 between the crystal and glass. For example, a polycrystalline domain of uniform grains 750 nm in size with gaps of 10 nm in between would have the same overall density as the glass. While the size of the crystals produced by GC growth has not been established experimentally, it is known that they are not larger than the ∼1 μm resolution of an optical microscope. We emphasize that our analysis of the microstructure of GC growth is not intended to describe polycrystallite formation generally but applies only for those circumstances in which crystallization-induced tension cannot be released by flow or sustained by deformation. In conclusion, we have shown for the first time that molecular mobility in a supercooled liquid can be enhanced by actively growing crystals. For o-terphenyl near Tg, fast crystal growth in the GC mode exerts tension on the amorphous material as a result of the higher density of the crystalline state, resulting in an increase in molecular mobility by a factor of 4. While this enhanced mobility is not large enough to explain the four orders of magnitude increase in the crystal growth rate near Tg, it does provide access to a hitherto unknown length scale (∼10 μm) that characterizes the tension during GC growth. The data indicate that tension in the amorphous oterphenyl builds until it reaches about −8 MPa. We imagine that fracture (or cavitation) occurs near the crystal/amorphous interface. This fracture defines the (submicrometer) size of a single crystal for GC growth. Fracture produces voids between the single crystals and thus releases the tension that would otherwise grow without bound in the sample. We expect that the features of GC growth revealed in these experiments are generally relevant for liquids that exhibit fast crystal growth near and below Tg. Two questions that remain to be answered are the origins of the 10 μm length scale and the fast crystal growth near Tg.
One could criticize the limited spatial resolution of our experiments and argue that within 1 μm of the growing crystal the enhancement of mobility might be much larger than the measured factor of 4.41 While we do not know what would be observed with higher spatial resolution, on the basis of the calculations above, we note that a mobility enhancement of 104 (needed to account for the observed crystal growth rate at 245 K) would require tension of about −60 MPa. Because this is eight times larger than the measured threshold for cavitation, this seems unlikely. We have performed additional experiments that indicate that the observed ∼10 μm range of enhanced mobility in front of a growing crystal is likely an intrinsic feature of GC crystal growth in o-terphenyl and not an artifact of sample geometry. In Figure 4a, we compare results from experiments on oterphenyl samples with thicknesses of 12 and 24 μm. For these two samples, we observe the same level of enhanced mobility as the crystal growth front approaches the measurement position. In Figure 4b, for a 12 μm thick sample, we compare the mobility in different planes of the sample relative to the substrate. (The resolution of the microscope along the z axis is ∼1 μm.)29,42 The mobility enhancement is observed to be independent of the position of the measurement plane. These two results, showing that the enhanced mobility is independent of sample thickness and measurement position relative to the substrate and coverglass, indicate that the ∼10 μm range of enhanced mobility in front of a growing crystal is likely an intrinsic feature of GC crystal growth in o-terphenyl. (Note that the heat liberated by crystal growth does not raise the temperature enough to explain the observed mobility.) While the explanation for the 10 μm length scale shown in Figure 4 and its generality at other temperatures and in other systems requires further investigation, its existence allows us to understand some important aspects of GC growth. The origin of enhanced mobility in the o-terphenyl glass adjacent to a growing GC crystal is presumed to be tension or negative pressure. Tension implies the existence of an anchoring point that resists movement. Without anchoring, either the glass or the crystal would drift to compensate for the density mismatch, and thus no tension would result. The data in Figures 3 and 4 indicate that the effective anchoring point for the glass is ∼10 μm away from the interface with the growing crystal. Lowmolecular-weight glasses are extremely brittle in tension,43 and we can estimate the strain at break for glassy o-terphenyl to be ∼0.1% by calculating σJg/3, where σ is the tension at break and Jg is the glassy shear compliance (= 10−3.35/MPa).44 Combining
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EXPERIMENTAL SECTION Materials and Sample Preparation. o-Terphenyl was obtained from Aldrich and recrystallized in methanol three times before use. DPPC (N,N′-dipentyl-3,4,9,10-perylenedicarboximide) was also obtained from Aldrich. A ∼10−6 M solution of DPPC in o-terphenyl was heated to ∼340 K and sandwiched between a silicon wafer and a cover glass, using either 2565
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The Journal of Physical Chemistry Letters aluminum foil (24 μm) or tantalum foil (12 μm) as a spacer. Before sample preparation, the silicon wafer was cut to 5 × 5 mm2 to fit into the sample holder. Both the silicon wafer and the cover glass (5 mm in diameter and 0.15 mm in thickness) were cleaned using 3:1 mixture of H2SO4 and H2O2, followed by several distilled water and ethanol rinses. Samples were placed in a cryostat dewar (Oxford Microstat N) using a home-built sample holder described previously.42 The dewar was evacuated during optical measurements to provide good thermal insulation and also to increase the photostability of DPPC. Crystal nucleation was controlled in the dewar by seeding either with a small piece of sodium chloride crystal at the edge of the sample or with an o-terphenyl crystal. Mobility measurements in front of the growing crystals were independent of seeding method. No other crystals were present in the sample besides the spherulite whose growth was initiated by seeding. GC crystal growth appears below 249 K (Tg + 6 K) for oterphenyl, as shown in Figure 1, and crystals grow at a steady rate once activated. However, if a sample growing in the GC mode is temperature cycled above the onset temperature, then GC growth is interrupted.20,21 Here we heated the sample to 252 K for 20 min to stop GC growth for periods up to 12 h, thus allowing mobility measurements immediately adjacent to GC crystals that were not growing (Figure 3b). Optical Measurement of Dye Reorientation. A photobleaching method in conjunction with a confocal microscope was utilized to measure DPPC reorientation in o-terphenyl.29,42 Intense linearly polarized light selectively photobleaches fluorescent probes with transition dipole moments aligned with the polarization direction, creating anisotropy in the orientation distribution of unbleached probes. The subsequent reorientation of unbleached probes creates an isotropic distribution. This process is probed using less intense circularly polarized light and two detectors simultaneously monitoring fluorescence polarized parallel and perpendicular to the bleach polarization. Typically, an area of 4 × 4 μm2 was photobleached, and the signal was obtained by averaging a 2 × 2 μm2 area inside this photobleached area. The anisotropy r(t) is a measure of the orientation distribution of transition dipole moments, and its decay describes probe reorientation.28,29 It is proportional to the orientation autocorrelation function for the transition dipole. The anisotropy data were fitted with the KWW function: r(t)/ r(0) = exp{−(t/τ)βKWW}. The integration of this autocorrelation function provides the orientation correlation time τc. During crystal growth, wide-field images were taken before and after every anisotropy measurement. The distance from the middle of the anisotropy measurement area to the crystal growth front was calculated before and after each anisotropy measurement. These measurements determine the error range for the x axis shown in Figures 3 and 4.
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ACKNOWLEDGMENTS
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REFERENCES
Letter
We gratefully acknowledge support from the National Science Foundation (0907031 and 1012124). C.T.P. thanks the National Science Foundation for a Graduate Research Fellowship.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Present Address §
Department of Chemistry, Columbia University, New York, NY 10027. Notes
The authors declare no competing financial interest. 2566
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