Letter Cite This: J. Phys. Chem. Lett. 2019, 10, 4285−4290
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First-Order Liquid−Liquid Transition without Density Discontinuity in Molten Sodium Acetate Trihydrate and Its Influence on Crystallization Xun Liu,† Shiyu Liu,† Enyi Chen,† Liang Peng,† and Yao Yu*,†,‡
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†
School of Materials Science and Engineering and State Key Lab for Materials Processing and Die and Mold Technology, Huazhong University of Science and Technology, Wuhan 430074, People’s Republic of China ‡ Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, People’s Republic of China S Supporting Information *
ABSTRACT: Liquid−liquid transition (LLT) refers to the phase transition among thermodynamically distinct liquid states with identical composition in analogy to the polymorphic transition in solid. The growing awareness of its significance to understanding the nature of liquid also provokes curiosity about its potential impact on crystallization. Here, we report a first-order liquid−liquid transition above liquidus temperature in the melt of sodium acetate trihydrate using nuclear magnetic resonance, differential scanning calorimetry, and high-precision density measurements, which show negligible change in density associated with the observed LLT. Further, the kinetics and products of crystallization are significantly influenced by LLT, providing a new way for the controlling crystallization pathway and realizing crystal polymorph selection.
A
La50Al30Ni15,12 the highly density-related NMR variables, such as the Knight shift and quadrupolar spin−lattice relaxation rate, are continuous upon LLT. However, direct density evidence of such type of LLT is still lacking. The significance of LLT can be far reaching. The connection of LLT and polymorphism in crystals is an interesting topic.13−15 As polymorphism is of crucial significance to materials synthesis, vast effort has been devoted to research on polymorphism selection.16−18 The presence of LLT fundamentally increases the number of available states to the liquid, and therefore, the rich diversity of the crystallization process started from different liquid states is theoretically permitted. Unfortunately, direct experimental evidence of this scenario is still lacking. In this work, we report evidence of a first-order LLT without density discontinuity in the melt of sodium acetate trihydrate (CH3COONa·3H2O, abbreviated as SAT), which is a widely used phase-change material for energy storage.19 A first-order LLT is confirmed by nuclear magnetic resonance (NMR) and differential scanning calorimetry (DSC) measurements above its liquidus temperature (Tliq). However, high-precision density measurement (10−6 g/cm3) suggests that no detectable density discontinuity is associated with this transition. The subsequent crystallization behavior of sodium acetate (SA) is further
liquid of certain complexity could assume more than one thermodynamically distinct liquid states with identical chemical composition, and the transition between these polymorphic states is called liquid−liquid transition (LLT).1−3 Similar to the cases in solid−liquid and liquid− gas transitions, most of the previously reported LLTs can be described using density as a single order parameter. Such types of LLTs characterized by a remarkable density discontinuity resulting from dramatic electronic structure change have been reported in several single-element liquids.4−7 However, recent studies suggest that LLT could be a general phenomenon, where at least two order parameters are necessary.8 It is strongly indicated that a first-order LLT taking place without noticeable density change is theoretically permitted. Such LLTs without density discontinuity may offer a unique opportunity for investigating the effect of subtle structural and dynamic changes of liquid, which could be a critical step for understanding liquids. Recently, there have been indications of LLTs with the density changing seemingly continuously. It is shown that the LLT in a molecular liquid, triphenyl phosphite (TPP),9,10 is controlled by a cooperative ordering parameter relevant to the number density of locally favored structures (LFSs). More recently, LLTs without density change were suggested to take place in several metallic glass-forming liquids. For instance, the dramatic volume change (i.e., density anomaly) upon LLT in the case of Vit.1 was excluded according to the area of the liquid drop shadow on the assumption of rotational symmetry. 11 As for the case of glass-forming liquid © XXXX American Chemical Society
Received: April 17, 2019 Accepted: June 17, 2019 Published: June 17, 2019 4285
DOI: 10.1021/acs.jpclett.9b01101 J. Phys. Chem. Lett. 2019, 10, 4285−4290
Letter
The Journal of Physical Chemistry Letters
Figure 1. Transition of structure and dynamics identified via NMR. (a) Typical line shape of 13C spectra acquired at 370.0 (red) and 353.0K (blue). The peaks at around 181 and 25 ppm correspond to 13C atoms in carboxyl and methyl, respectively. The peaks at around 180 ppm are enlarged and shown as insets. (b) Temperature (T) dependence of the 13C chemical shift of the carboxyl group acquired with a temperature interval of 1.0 K. (c) Kinetics of LLT. Chemical shifts at three chosen undercooled temperatures cooled from the same initial temperature of 370.0 K. The open and solid symbols are used to represent the chemical shift before and after LLT. The corresponding incubation times are shown as an inset. (d) Plot of ln(T1) vs 1000/T acquired with a temperature interval of 1.0 K.
transition from HTL to LTL was also investigated. The sample was held at 370.0 K for 60 min, and then it was cooled down rapidly (∼20 K min−1) to a chosen temperature T below TLL but above Tliq to avoid the influence of crystallization. At each T, a series of NMR spectrum were taken every 5 min. Figure 1c shows the measured chemical shift with T = 359.5, 357.2, and 353.0 K. The chemical shift initially remains on the straight line extended from the values of the chemical shift versus T above 361.0 K measured during the step cooling process, indicating the existence of undercooling of the HTL. After a certain incubation time τ, the chemical shift jumps to the values expected from the step cooling measurement below 361.0 K. The observation of the undercooling of the HTL reveals the first-order nature of the transition from HTL to LTL. The incubation time measurements were repeated three times, and the average of the three measured τ values for each temperature is plotted versus the undercooled degree (ΔT = 361.0 K − T), as shown in the inset of Figure 1c. The results are very discrete due to the small undercooled degree, which makes it difficult to analyze the incubation time precisely (see the Supporting Information for a more detailed discussion of τ). More quantitative understandings of kinetics of the LLT require further experimental and theoretical studies in the near future. The existence of LLT at 361.0 K is further confirmed by the measurements of the dynamics of the liquid. The sample was cooled from 370.0 K with a temperature step of 1.0 K, and the spin−lattice relaxation time (T1) of 13C in the carboxyl group was measured using the inversion−recovery pulse sequence (180x° − τ − 90x°). T1 refers to the characteristic time for the spin system to reestablish thermodynamic equilibrium with the surrounding fluctuating magnetic field, which is predominantly derived from the rapid reorientation of the molecules.21 T1 is
studied via DSC and X-ray diffraction (XRD). It is shown that the presence of LLT significantly impacts the kinetics and products of crystallization. The LLT in molten SAT was identified via in situ 13C NMR experiments in a magnetic field of 11.7 T. The sample was held isothermally at 370.0 K, 19.0 K above Tliq (Figure S1), for 60 min before experiments started. Then it was cooled down step by step to 343.0 K. NMR spectra were taken at each temperature step after the system was equilibrated for 60 min. The peak position of the NMR spectrum representing chemical shift is sensitive to the local chemical environment. Two representative 13C NMR spectra acquired at 370.0 and 353.0 K are shown in Figure 1a. The peaks at around 181 and 25 ppm correspond to carbon atoms in carboxyl and methyl groups, respectively. The peaks representing the carboxyl group are enlarged and shown as the inset of Figure 1a. Each peak is a single narrow peak of Lorentzian shape with identical integral areas, suggesting that all of the 13C nuclei are in a single macroscopic phase in the whole temperature range. Figure 1b plots the chemical shift of 13C nuclei in the carboxyl group versus temperature (T). It varies linearly with temperature from 370.0 to 361.0 K with a slope of −(4.3 ± 0.1) × 10−3 ppm/K followed by a kink at 361.0 K and continues with another linear temperature dependence down to 353.0 K with a slope of −(3.4 ± 0.1) × 10−3 ppm/K. The increase of the 13C chemical shift is ascribed to an increase of the shielding electron cloud, which results from tighter solvation.20 Also, the change in the slope of the temperature-dependent chemical shift is a signature of structural change of the liquid.12,20 Thus, there exist two different liquid states above Tliq, a hightemperature liquid state (HTL) above 361.0 K and a lowtemperature liquid state (LTL) below 361.0 K. Here, the transition temperature is denoted as TLL. The kinetics of the 4286
DOI: 10.1021/acs.jpclett.9b01101 J. Phys. Chem. Lett. 2019, 10, 4285−4290
Letter
The Journal of Physical Chemistry Letters
Figure 2. Density measurement. (a) Temperature dependence of density. The density of HTL (red) is linearly fitted and extrapolated to the LTL (blue) region. (b) Difference between the measured curve and the fitted curve.
Figure 3. Crystallization of SA in HTL and LTL. (a) DSC traces of SA crystallization with initial liquid states as HTL (Tinitial = 366 K, red) and LTL (Tinitial = 356 K, blue); DSC traces of SA crystallization with the initial liquid state as HTL (Tinitial = 366 K) but annealed at 356.0 K for an additional 360 min (black). (b) Dependence of SA crystallization temperature TSA on the initial liquid temperature Tinitial. (c) Powder XRD pattern of crystallization products of HTL and LTL from 2θ = 8.2 to 9.4°. The triangle denotes the characteristic peaks of SA-II, and the hexagon denotes the characteristic peaks of SA-I.
emphasized that no density discontinuity at TLL can be discerned within the measurement limit of 10−6 g/cm3, suggesting that density is not the dominant order parameter governing this LLT process. Anhydrous SA crystalline will crystallize in the primary crystallization step as the SAT melt is cooled below Tliq.27 The impact of LLT on this crystallization process is investigated by DSC. The SAT melt was held isothermally at a certain elevated temperature Tinitial for 60 min and then cooled down to 273.0 K at a rate of 3.0 K/min. Two representative DSC cooling curves with Tinitial= 366.0 and 356.0 K (red and blue) are shown in Figure 3a. The corresponding temperature protocols are schematically shown in Figure S2 (red and blue). The exothermic peaks on DSC curves suggest the formation of SA, and the onset of the exothermic peak TSA(indicated by arrows) was systematically measured with Tinitial ranging from 353.0 to 366.0 K, as shown in Figure 3b. TSA shows a notable dependence on the initial liquid states. TSAcovers a range from 294.2 to 339.2 K when the initial liquid state is LTL (Tinitial < 361.0 K). In contrast, TSA covers a relatively narrower range from 294.3 to 315.6 K when the initial liquid state is HTL (Tinitial > 361.0 K). The scattering of TSA reflects the stochastic nature of crystallization. The difference in the range of TSA can be eliminated with a step cooling process with the temperature protocol schematically shown in Figure S2 (black). A typical DSC curve of such a process with Tinitial = 366.0 K and annealed at 356.0 K for an additional 360 min is shown in Figure 3a (black). The above results again suggest a first-order nature of the LLT. Furthermore, it shows that the
plotted on a logarithm scale versus 1000/T in Figure 1d. The curve consists of two linear parts intersecting at about 361.0 K. Such a variation of T1 reveals a dynamic change in molecular motions in liquids22,23 and is considered as typical behavior of the phase transition.24 In the fast motion limit applicable in typical liquids, the spin−lattice relaxation time T1 is inversely proportional to the correlation time τ, reflecting the molecular reorientation motion. The dynamic behavior of liquid molecules can be described by an Arrhenius activation process, τ ∝ e Ea / RT ,25 where Ea is the activation energy and R is the gas
(
constant. Thus, the Ea = −2.303R
∂ log T1 ∂T −1
)
of molecular
motions can be calculated accordingly, which were 0.031 and 0.085 eV for HTL and LTL, respectively. The change of activation energy indicates a change of liquid dynamics. The density change associated with the LLT ws investigated by a high-precision density meter.26 The SAT melt was held isothermally at 365.00 K for 360 min and then cooled down consecutively from 365.00 to 353.00 K. The density (ρ) was measured every 0.02 K after an isothermal time of 1.5 min at each temperature step. It increased from 1.262990 to 1.272435 g/cm3 with decreasing temperature, as shown in Figure 2a. To magnify the subtle difference on the temperature dependence of ρ between HTL and LTL, the ρ(T) of HTL is linearly fitted and extrapolated to the LTL region. The difference between the measured curve and the fitted curve is shown in Figure 2b. Certainly, the difference remains substantially unchanged at zero above 361.35 K. A kink occurs at 361.35 K, and the difference increases gradually below 361.35 K. It should be 4287
DOI: 10.1021/acs.jpclett.9b01101 J. Phys. Chem. Lett. 2019, 10, 4285−4290
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The Journal of Physical Chemistry Letters crystallization kinetics for the formation of SA changes when supercooled from LTL compared to that from HTL. Further, the influence of LLT on the crystalline structure of SA is explored by XRD. Anhydrous SA has three crystal structures,28,29 SA-I, SA-II, and SA-β (Figure S3), among which SA-II is the stable form of the crystal below 512.6 K.30 The detailed crystal parameters are listed in Table S1. Generally, SA-I and SA-II can crystallize from aqueous solution, and SA-β can only be acquired by dehydration of SAT under vacuum.31 The calculated XRD patterns of the three polymorphs are shown in Figure S4, with the characteristic peak corresponding to the (010) plane appearing at 2θ = 8.75, 8.85, and 8.90°, respectively. To clarify the polymorphic composition of the crystallization products, XRD was performed from 2θ = 5.00 to 50.00° (Figure S5), and the sections from 2θ = 8.00 to 9.50° are enlarged and shown in Figure 3c. The crystallization product of LTL shows a single peak located at 2θ = 8.75°, suggesting that only SA-II crystallizes from LTL. In contrast, the crystallization product of HTL shows an additional peak at 2θ = 8.85°, suggesting that both SA-II and SA-I crystallize concomitantly from HTL. The ratio of SA-I to SA-II is roughly estimated to be about 1:1. These results show that the LLT not only affects the crystallization kinetics but also affects the crystallization products. The melt of SAT is a highly concentrated SA aqueous solution (60.3 wt %) containing various ion complexes,32 ranging from free individual ions to ion pairs to multiple ion clusters. Previous molecular simulation on the acetate−water complex has revealed that first-shell waters exist in two states: loosely or tightly bound to oxygen atoms in acetate. The tightly bound locally favored clusters (T-LFCs) accommodate more water molecules than loosely bound locally favored clusters (LLFCs).33 The change in the composition of the hydration structure as the structural original of this LLT can be well comprehended within the two-state model.34 The free energy is given by
Figure 4. Schematic illustration of the mechanism of LLT and crystallization. (a) Structure of HTL (L-LFCs dominate) and LTL (T-LFCs dominate). (b) Illustration of the free energy landscape. When the temperature is higher than TLL, HTL is the stable form of liquid. When the temperature is lower than TLL, LTL is the stable form of liquid. (c) Illustration of the nucleation pathway. The L-LFCs play an important role in the formation of SA-I crystallites.
nucleation theory. 35 The evolution of LFCs can be qualitatively explained by the change of chemical shift. It is worth noting that the chemical shift of the 13C nuclei in the carboxyl group is 181.8 ppm in SAT at room temperature. In this case, the acetate radical is fully surrounded by water molecules. However, the chemical shifts of the 13C nuclei in the carboxyl group are 182.1 and 183.6 ppm in SA-I and SA-II at room temperature, respectively.36 In this case, the acetate radical is fully surrounded by water molecules. Thus, it is reasonable to assume that the 13C chemical shift of the carboxyl group would shift to the upper field when acetate radical is surrounded by more water molecules. Thus, a higher 13 C chemical shift in the carboxyl group in supercooled HTL than that in supercooled LTL reveals that there are more LLFCs in supercooled HTL. The downward shift of the region of TSA with the initial liquid state changed from LTL to HTL suggests that the L-LFCs frustrate the nucleation of the SA-II crystallites. Moreover, the concomitant crystallization of SA-II and SA-I crystals from HTL indicates that the L-LFCs facilitate nucleation of the SA-I crystallites. Thus, a possible scenario for the nucleation of SA from its aqueous solution is shown in Figure 4c. The nucleation process in LTL may be consistent with classical nucleation theory, where only the stable SA-II crystallites are formed. The formation of clusters with genes of SA-I crystallites in HTL consequently facilitates the formation of metastable SA-I and frustrates the formation of stable SA-II. The presence of a metastable form of SA in the crystallization process is in contradiction to the physical pictures described in classical nucleation theory, in which only the initial liquid and final stable crystal are invoked.37,38 This genetic correlation plays an important role in the crystallization process, and such genetic clusters directly link LLT and crystal polymorphism. In summary, a first-order LLT without density discontinuity is identified in the melt of SAT above its Tliq. A notable undercooling phenomenon manifested in the NMR and DSC measurements suggests a first-order nature of the transition.
G(T , nL) = nLE L + (1 − nL)E T + [nLvL + (1 − nL)vT]P ÄÅ ÉÑ ÑÑ ÅÅÅ n 1 n − ÑÑ L L ÑÑ + JnL(1 − nL) + kBT ÅÅÅnL ln + (1 − nL) ln ÅÅ ÑÑ g g ÅÇ L T Ñ Ö
where nL and 1 − nL are the ratios of L-LFC and T-LFC, respectively; EL, vL, and gL are the energy, specific volume, and degeneracy of L-LFC; ET, vT, and gT are the energy, specific volume, and degeneracy of T-LFC accordingly; J represents the cooperativity. An additional valley can be formed in the free energy landscape, where the number of L-LFC in HTL is higher than that in LTL. LLT arises as a result of a jump from one valley to another, associated with differentnL (Figure 4a,b). Obviously, the discontinuous change of nL does not necessarily lead to the change of density. In our experiments, the change of the density at the transition temperature is very subtle compared to various LLTs corresponding to large density changes with significant changes in bonding characters.4,5 The present work provides direct support for the existence of firstorder LLT without density discontinuity, and such direct observation has not been reported before. Qualitative changes of liquid structures have significant influence on the kinetics and products of the subsequent crystallization processes. The LFCs may play an essential role, and their effect could be an important complement to classical 4288
DOI: 10.1021/acs.jpclett.9b01101 J. Phys. Chem. Lett. 2019, 10, 4285−4290
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(9) Tanaka, H.; Kurita, R.; Mataki, H. Liquid-liquid transition in the molecular liquid triphenyl phosphite. Phys. Rev. Lett. 2004, 92, 025701. (10) Mosses, J.; Syme, C. D.; Wynne, K. Order Parameter of the Liquid-Liquid Transition in a Molecular Liquid. J. Phys. Chem. Lett. 2015, 6, 38−43. (11) Wei, S.; Yang, F.; Bednarcik, J.; et al. Liquid−liquid transition in a strong bulk metallic glass-forming liquid. Nat. Commun. 2013, 4, 2083. (12) Xu, W.; Sandor, M. T.; Yu, Y.; et al. Evidence of liquid−liquid transition in glass-forming La50Al35Ni15 melt above liquidus temperature. Nat. Commun. 2015, 6, 7696. (13) Desgranges, C.; Delhommelle, J. Role of liquid polymorphism during the crystallization of silicon. J. Am. Chem. Soc. 2011, 133, 2872−2874. (14) Russo, J.; Tanaka, H. The microscopic pathway to crystallization in supercooled liquids. Sci. Rep. 2012, 2, 505. (15) Russo, J.; Tanaka, H. Selection mechanism of polymorphs in the crystal nucleation of the Gaussian core model. Soft Matter 2012, 8, 4206−4215. (16) Weissbuch, I.; Torbeev, V. Y.; Leiserowitz, L.; et al. Solvent effect on crystal polymorphism: Why addition of methanol or ethanol to aqueous solutions induces the precipitation of the least stable β form of glycine. Angew. Chem., Int. Ed. 2005, 44, 3226−3229. (17) Hilfiker, R.; Markus, V. Polymorphism in the pharmaceutical industry; Wiley Online Library: Hoboken, NJ, 2006. (18) Desgranges, C.; Delhommelle, J. Controlling Polymorphism during the Crystallization of an Atomic Fluid. Phys. Rev. Lett. 2007, 98, 235502. (19) Sharma, S. D.; Sagara, K. Latent heat storage materials and systems: a review. Int. J. Green Energy 2005, 2, 1−56. (20) Cainelli, G.; Galletti, P.; Giacomini, D. Solvent effects on stereoselectivity: more than just an environment. Chem. Soc. Rev. 2009, 38, 990−1001. (21) Slichter, C. P.; Griffin, R. G. Principles of magnetic resonance. Phys. Today 1991, 44, 95−96. (22) Jalabert, D.; Robert, J. B.; Canet, D.; et al. Changes in the anisotropy of quinoline molecular reorientation in the liquid state as probed by 13C and 14N nuclear magnetic resonance relaxation times. Mol. Phys. 1993, 79, 673−683. (23) Robert, J. B.; Boubel, J. C.; Canet, D. Indications for change of dynamical regime in pure liquids. Mol. Phys. 1997, 90, 399−406. (24) Webb, G. A. Annual Reports on NMR spectroscopy; Academic Press: Cambridge, 1995. (25) Simpson, J.; Carr, H. Diffusion and nuclear spin relaxation in water. Phys. Rev. 1958, 111, 1201. (26) Bouchot, C.; Richon, D. An enhanced method to calibrate vibrating tube densimeters. Fluid Phase Equilib. 2001, 191, 189−208. (27) Cabeza, L. F.; Svensson, G.; Hiebler, S.; et al. Thermal performance of sodium acetate trihydrate thickened with different materials as phase change energy storage material. Appl. Therm. Eng. 2003, 23, 1697−1704. (28) Hsu, L.-Y.; Nordman, C. Structures of two forms of sodium acetate, Na+. C2H3O2−. Acta Crystallogr., Sect. C: Cryst. Struct. Commun. 1983, 39, 690−694. (29) Helmholdt, R. Ab initio crystal structure determination of βsodium acetate from powder data. Z. Kristallogr. - Cryst. Mater. 1998, 213, 596−598. (30) Kemper, K. A.; Jouse, J. E., Jr. A DSC and IR study of the phase transition in anhydrous sodium acetate. Thermochim. Acta 1990, 170, 253−261. (31) Xu, M.; Harris, K. D. Altering the polymorphic product distribution in a solid-state dehydration process by rapid sample rotation in a solid-state NMR probe. J. Am. Chem. Soc. 2005, 127, 10832−10833. (32) Marcus, Y.; Hefter, G. Ion pairing. Chem. Rev. 2006, 106, 4585−4621.
Furthermore, the associated density change is directly measured using a high-precession vibrating-tube density meter. The subtle density change at the transition temperature reveals that density is not the dominant order parameter governing this LLT. Such a LLT may offer a unique opportunity for investigating the subtle structural and dynamic changes of liquid, which could be a critical step for understanding liquids. In addition, LLT shows a significant impact on the crystallization process. The kinetics of SA crystallization and the crystal form of SA are closely related to the initial liquid state. The realization of selection of polymorphic phases not only contributes to the fundamental understanding of the nature and process of the first-order phase transition but also is of great importance to industrial application.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.9b01101.
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Experimental details, determination of the melting temperature and liquidus temperature, temperature protocols in DSC experiments, crystal structures of SA-I, SA-II, and SA-β, calculated XRD patterns, powder XRD pattern of crystallization products of HTL and LTL, kinetics of LLT, and lattice parameters of SA-I, SA II, SA-β, and SAT (PDF)
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Yao Yu: 0000-0002-3566-1904 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We acknowledge financial support from the National Basic Research Program of China under Grant No. 2015CB856801 and the National Natural Science Foundation of China under Grant No. 51872105.
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REFERENCES
(1) Poole, P. H.; Grande, T.; Angell, C. A.; et al. Polymorphic phase transitions in liquids and glasses. Science 1997, 275, 322−323. (2) Yarger, J. L.; Wolf, G. H. Polymorphism in liquids. Science 2004, 306, 820−821. (3) McMillan, P. F.; Wilson, M.; Wilding, M. C.; et al. Polyamorphism and liquid−liquid phase transitions: challenges for experiment and theory. J. Phys.: Condens. Matter 2007, 19, 415101. (4) Cadien, A.; Hu, Q.; Meng, Y.; et al. First-order liquid-liquid phase transition in cerium. Phys. Rev. Lett. 2013, 110, 125503. (5) Katayama, Y.; Mizutani, T.; Utsumi, W.; et al. A first-order liquid−liquid phase transition in phosphorus. Nature 2000, 403, 170− 173. (6) Sastry, S.; Angell, C. A. Liquid−liquid phase transition in supercooled silicon. Nat. Mater. 2003, 2, 739−743. (7) Glosli, J. N.; Ree, F. H. Liquid-liquid phase transformation in carbon. Phys. Rev. Lett. 1999, 82, 4659. (8) Tanaka, H. Importance of many-body orientational correlations in the physical description of liquids. Faraday Discuss. 2014, 167, 9. 4289
DOI: 10.1021/acs.jpclett.9b01101 J. Phys. Chem. Lett. 2019, 10, 4285−4290
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The Journal of Physical Chemistry Letters (33) Payaka, A.; Tongraar, A.; Rode, B. M. QM/MM dynamics of CH3COO(−)-water hydrogen bonds in aqueous solution. J. Phys. Chem. A 2010, 114, 10443. (34) Tanaka, H. General view of a liquid-liquid phase transition. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 2000, 62, 6968. (35) Zeldovich, Y. B. On the theory of new phase formation: cavitation. Acta Physicochem., USSR 1943, 18, 1. (36) Xu, M.; Harris, K. D. Triple-quantum 23Na MAS NMR spectroscopy as a technique for probing polymorphism in sodium salts. Cryst. Growth Des. 2008, 8, 6−10. (37) Oxtoby, D. W. Homogeneous nucleation: theory and experiment. J. Phys.: Condens. Matter 1992, 4, 7627. (38) Ten Wolde, P. R.; Ruiz-Montero, M. J.; Frenkel, D. Numerical evidence for bcc ordering at the surface of a critical fcc nucleus. Phys. Rev. Lett. 1995, 75, 2714.
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