Ice Nucleation of Confined Monolayer Water Conforms to the Classical

Subscriber access provided by UNIV OF SOUTHERN INDIANA

Chemical and Dynamical Processes in Solution; Polymers, Glasses, and Soft Matter

Ice Nucleation of Confined Monolayer Water Conforms to the Classical Nucleation Theory Zhuoran Qiao, Yuheng Zhao, and Yiqin Gao J. Phys. Chem. Lett., Just Accepted Manuscript • Publication Date (Web): 22 May 2019 Downloaded from http://pubs.acs.org on May 22, 2019

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry Letters

Ice Nucleation of Confined Monolayer Water Conforms to the Classical Nucleation Theory Zhuoran Qiao1, Yuheng Zhao1 and Yi Qin Gao1* 1Institute

of Theoretical and Computational Chemistry, College of Chemistry and

Molecular Engineering, Peking National Laboratory for Molecular Science, Peking University, Beijing 100871, China Abstract: We confirmed that monolayer water confined by parallel graphene sheets spontaneously crystallizes from a structurally and dynamically heterogeneous liquid phase under moderate supercooling via direct molecular dynamics simulation. Squarelattice like geometric order is observed at the early stage of nucleation and preserves during the entire nuclei growth process. Diffusion coefficient and free energy profile in the cluster space extracted from a Bayesian trajectory analysis agree well with the Classical Nucleation Theory (CNT) prediction and yields thermodynamic quantities exhibiting linear temperature dependence. The effectiveness of maximum cluster size as the descriptor of ice nucleation dynamics in the CNT framework can be attributed to the dynamical timescale decoupling and strong structural pattern dependence of density fluctuation in the liquid phase. TOC Graphic

Ice nucleation from water and aqueous solutions is a complex dynamical process that has been a century-long topic of study1 for its fundamental physical importance2 and promising applications in atmospheric chemistry3, material sciences4 and biology5. Despite considerable efforts, the universal physical picture governing ice nucleation remains elusive. Fabrication condition, interface and solutes have all been discovered to significantly affect the thermodynamics and dynamical mechanism of ice nucleation6. The Classical Nucleation Theory (CNT) is established to quantify nucleation free

ACS Paragon Plus Environment

The Journal of Physical Chemistry Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

energy surfaces and rates considering nucleation as a first-order transition from the parent phase to the final state, in which the nuclei size can be regarded as the optimal reaction coordinate7. The CNT also implicates that microscopic nucleation pathways can be well defined by formation of translational order driven by density fluctuations in the metastable phase, which is justified and extended by the Density Functional Theory8, together constituting a family of one order parameter theories of homogeneous nucleation. Although CNT has been widely employed in countless theoretical and experimental studies of nucleation processes9–11, it is challenged by investigations showing that nucleation passes through multiple intermediate states between which CNT fails to distinguish12–14. This two-step nucleation phenomenology is in accordance of the Ostwald’s step rule and emphasizes structure fluctuation and symmetry development in the metastable liquid15,16, which is validated in various systems including monoatomic liquid models17–19, supercooled bulk water20–22 and aqueous salt solutions23,24. Moreover, a set of theoretical frameworks that embody two-step development of translational and bond-orientational order during crystallization have been proposed. For example, the 2-state model of water developed by Tanaka et al25,26 takes into account the rotational symmetry breaking upon ice crystallization to explain bulk water’s anomalies in homogeneous nucleation. Interestingly, the dimensionality effect may play an important role in nucleation rates and microscopic mechanisms. Seeley et al27 reported that for ice nucleation from single water drops supporting aliphatic alcohol Langmuir films, the critical nucleus is essentially a monolayer; Santra et al28 discovered that for nucleation in 2D and 3D gasliquid systems, CNT prediction on nucleation rate is much less accurate in two dimensions than in three dimensions. However, few systematic nucleation studies have been done on low-dimensional fluidic systems which have attracted great experimental research interests29,30. In the past decade, water16,31 and aqueous solutions32 confined by 2D nanomaterials have been extensively studied. Gao et al33 obtained the phase diagram of water confined by graphene under varied slit width; first-principle calculation34 and electron microscopy imaging experiments35 uncovered that water forms a high-density ice phase with square-like geometry at ambient temperature under strong graphene confinement. More specifically, Kumar et al analyzed structure and thermodynamics during the phase transition in water confined by smooth hydrophobic plates36 and in Janus nanopores37. In addition, recently Gopinadhan et al38 designed graphene nano-capillaries that effectively exclude ions and proton to transport through confined monolayer water. Current understanding of phase behaviors of confined aqueous systems raises the question on their phase transition dynamics, which is addressed in this letter.

Inspired by open questions in ice nucleation in low-dimensional aqueous systems, we studied 2D ice nucleation from monolayer water confined by parallel graphene sheets


Page 2 of 14

Page 3 of 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


based on unbiased Molecular Dynamics (MD) simulations. We first performed MD simulation for a binary solution system that parallel graphene sheets are immersed in a water box (see Supplemental Information for details) in which the spacing between two graphene plates (3.4 Å Van der Waals radius) is maintained at 6.5 Å. Employing different water force fields, we first observed that water in the confinement slit forms a well-defined monolayer and spontaneously crystallizes to a square-lattice like ice phase when it is cooled down to 240 K. We note that the 3.1 Å effective confinement distance is consistent with experimental height of graphene nano-channel to create monolayer water38 and ice phase. To study nucleation dynamics and its temperature dependence, we then performed parallelized MD simulations in NVT ensemble for water confined by periodic bilayer graphene sheets separated at the same distance at different target temperatures, for which 2D density of monolayer water is determined from corresponding equilibrated binary systems (see SI for details). Confined monolayer water is inhomogeneous in structural patterns and dynamics. Within the static hydrogen bonding network of the metastable liquid phase, we observed the coexistence of two types of local structural patterns (Figure 1a). On the one hand, square lattice like patterns similar to the alignment in the crystalline phase (Figure 1b) is enriched in the liquid state, with a typical size of 10-20 water molecules; on the other hand, triangular, pentagonal and hexagonal - ring like and disordered structures can be observed in hydrogen bonding network between square lattice-like patterns, which we call ‘frustrated’ patterns. We emphasize that short-range square-lattice like patterns themselves are of a transient lifetime and are not stable nucleation precursors. In a previous study39, we have confirmed the existence of square-lattice like patterns even in systems above the melting point and characterized that the lifetime of square-lattice like patterns is 13.5 ± 5.0 ps which corresponds to the vibrational relaxation time of local hydrogen bonding network. When the time span for trajectory averaging is beyond 50 ps, however, a more homogenous liquid-like disordered pattern is observed. The short lifetime nature of local structural patterns is also supported by the normal diffusion behavior of the metastable liquid, as no sub-diffusive regime is observed in the mean-square displacement profile of water molecules (Figure 1c). Here we clarify that this timescale dependence of apparent structure can be attributed to rapid hydrogen bond rearrangements between square-lattice like and frustrated patterns; we will further illustrate that these microscopic level dynamic features play an important role in 2D ice nucleation. Apart from transient local structural patterns, in metastable liquid state we also observe clusters in which translational diffusion and hydrogen bond rearrangements significantly slow down and square-lattice like order is retained on a larger length scale. As shown in Figure 1d, such dynamically damped clusters fluctuate on a time scale of nanoseconds and are relatively stable while the surrounding liquid is subjected to rapid rearrangements. The system spontaneously crystallizes when the largest dynamically



Page 4 of 14

damped region grows and fills the entire confinement slit, hence those clusters can be identified as ice nucleus that drives crystallization. Nucleation pathway with preserved intrinsic order. To discern whether 2D ice nucleation is governed by CNT type or a two-step nucleation mechanism, we analyzed the evolution of the geometric order within a swarm of parallel nucleation trajectories. Clusters are detected using a criterion based on the lifetime of local structural patterns which better recognizes the dynamical process of interest than the static order parameter based criterion40 (see SI for details). To characterize local geometric patterns in 1

𝑁

monolayer water, we introduce an order parameter 𝛹4 defined as 𝛹4 = 𝑁|∑𝑗 = 0𝑒4𝑖𝜃𝑗|, where 𝑗 runs over all hydrogen-bonded water neighbors of the target water molecule, and θj ∈ [0, 2π) denotes the angle between the x-axis and the direction from labelled oxygen to j-th hydrogen-bonded oxygen. The 𝛹4 order parameter quantifies the frustration within the local hydrogen bonding network, and equals to 1 for a perfect square-lattice phase. Figure 2 shows the distribution of 𝛹4 within the simulation system with respect to maximum cluster size, N. We again stress that clusters are detected solely based on local rearrangement dynamics so that no a priori structural order within clusters is imposed. Strikingly, with the growth of the largest cluster, distribution of 𝛹4 reveals a simple first-order phase transition scenario: At the initial state where 𝑁 = 0, 𝛹4 distribution shows a broad band due to the coexistence of square-lattice and frustrated patterns and defects; a minor peak around 0.33 corresponds to vertices shared by polycyclic hydrogen bond rings. For the final ice phase, a single peak around 0.89 marked slightly distorted square-lattice structure in the crystalline. 𝛹4 distribution profile at intermediate N values can be entirely reproduced by superposition of 𝛹4 distributions from the liquid state and the ice phase, and no significant signal from transitional structure is observed, either at the initial stage of nucleation when N is small or during the cluster growth process. These results indicate that the 2D ice nucleation process can be effectively described by the size of a cluster formed from surrounding liquid with preserved internal bond orientational order, which strongly matches the scheme in the Classical Nucleation Theory. Free energy and diffusion profile from Bayesian trajectory analysis. We next computed the free energy and the diffusion constant profile as a function of maximum cluster size N (Figure 3a, 3b) using a Bayesian analysis of non-equilibrium nucleation trajectories based on maximum likelihood estimation of discretized 1D Fokker-Planck Equation41,42 (see SI for method details). The trained nucleation free energy surface and state-dependent diffusion profile is fitted using 2-dimensional CNT with capillary 1

1

approximation43: 𝛥𝐺(𝑁) = 2𝜋𝛾𝑅0𝑁2 ―𝛥𝜇𝑁 + 𝐺0 and 𝐷(𝑁) = 𝐷0𝑁2, where 𝛥𝜇 is the chemical potential difference between the metastable liquid and the ice phase, 𝛾 is the


Page 5 of 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


―

1

surface free energy, 𝑅0 = (𝜋𝜌2𝐷) 2 is the effective radius of water molecules, and 𝐷0 is the pre-factor of diffusion constant in the cluster space. A local minimum near N=15 within the free energy surface that deviates from CNT prediction confirms the dynamic heterogeneity of the metastable liquid state, marking that emergence of pre-critical damped clusters is pervasive and thermodynamically favored. When the cluster size exceeds ~20 water molecules 𝛥𝐺(𝑁) and 𝐷(𝑁) agrees much better with CNT prediction, as the continuum thermodynamic treatments in CNT become an accurate approximation. We also note that the fitted 𝛥𝜇 and 𝛾 show linear temperature dependences (Figure 4a) consistent with CNT. The positive temperature dependence of 𝛾 is resulted from the negative surface entropy compared to the ~0.47 kB𝑇 Å ―1 relatively weak enthalpy contribution. From 𝛥𝐺(𝑁) and 𝐷(𝑁) we then calculated the steady-state nucleation rate as a function of temperature (Figure 4b) based on the Becker-Doering equation 𝐽 =

[∫

―1 1 ∞ . 𝑑𝑁 0 𝜌𝑒𝑞(𝑁)𝐷(𝑁)

]

(𝑇) = 𝐽0 ∗ 𝑒𝑥𝑝 [ ―

Within 273-277 K, 𝐽(𝑇) ―𝑇 exhibits an exponential relationship 𝐽

(𝛥𝐺0 ― 𝛥𝛥𝐺 ∗ 𝑇) 𝑘𝐵𝑇

] which indicates that the nucleation free energy barrier

linearly correlated with temperature while sharing a constant pre-exponential factor. At higher temperature 𝐽(𝑇) drops as transmission coefficients significantly decrease due to lower free energy barrier frequencies, corresponding to more re-crossing trajectories passing through the critical cluster region. A simple gas-liquid like picture for 2D ice nucleation dynamics. Interestingly, as the metastable liquid phase is inhomogeneous in structural patterns, the effectiveness of CNT descriptor may appear counterintuitive. Here, we propose that the consistency between 2D ice nucleation dynamics and CNT can be attributed to the interplay of two nontrivial properties of the system: (a) Dynamical timescale decoupling between microscopic-level rearrangements and fluctuation of clusters, and (b) strong local structure – density dependence. To illustrate this idea, we schematically summarize the nucleation pathway as follows: At the early stage of nucleation, square-lattice like patterns act as building blocks of ice nucleus and merge to a short-range cluster by stochastic collisions; once a cluster is stabilized, its fate is determined on a longer timescale governed by the reactiondiffusion behavior in cluster space along coordinate N. Such a timescale decoupling yields an effective homogeneous description of surrounding liquid state. Although transient square-lattice like and frustrated patterns are mixed together, the spatial distribution of each type of patterns under sufficient time averaging gives a more homogeneous appearance; particularly, a disordered pattern is obtained through hundred-picoseconds averaging, indicating that a mean-field description to the liquid state is robust within the typical lifetime of a cluster.



Additionally, coexistence of structural patterns causes density and structure fluctuation to be correlated at an extremely local scale, as manifested in the normal liquid diffusion behavior. In confined monolayer water, density inhomogeneity and flux is induced by exchanges between high-density square-lattice like patterns and low-density frustrated patterns. In the collision-nucleation stage, a high-density cluster is immediately formed from square-lattice like patterns, and no intermediate geometry is dynamically favorable. In supercooled bulk water and a family of glass formers, however, locally favored structure patterns instead impede the formation of globally stable structures which requires long-range density fluctuation, therefore increase the nucleation barrier44. Intermediate structure emerges from those liquids to avoid simultaneous development of long-range density and crystalline order, manifesting themselves as precursors in two-step nucleation45. The above-mentioned dynamical scheme can be equivalently understood from a coarse-grained perspective, considering square-lattice like patterns as quasi-particles diffusing in the confinement slit with attractive interaction. Therefore, the CNT-type nucleation dynamics can be qualitatively reproduced by the transition from gas-like initial phase to an isotropic condensed phase.

In conclusion, we analyzed the microscopic mechanism and related thermodynamic profiles of 2D ice nucleation from monolayer water confined by parallel graphene plates. From evolution of geometric order parameter 𝛹4, nucleation free energy surface and cluster growth diffusion profile, we confirmed that 2D ice nucleation is dictated by a mechanism that resembles the Classical Nucleation Theory. The CNT-type nucleation dynamics is well explained by unique density and structure fluctuation behaviors resulted from coexistence of transient patterns within the hydrogen bonding network. While lots of previous study on nucleation focused on the evolution of static structural order, our study emphasized the importance of a characteristic timescale in determining a physically relevant nucleation pathway, which can possibly be generalized in further studies on interfacial and confined soft matters. Acknowledgments This work was supported by National Natural Science Foundation of China (21573006, 21821004, 21873007) and National Key R&D Program of China (2017YFA0204702). References (1)

(2)

Sosso, G. C.; Chen, J.; Cox, S. J.; Fitzner, M.; Pedevilla, P.; Zen, A.; Michaelides, A. Crystal Nucleation in Liquids: Open Questions and Future Challenges in Molecular Dynamics Simulations. Chem. Rev. 2016, 116 (12), 7078–7116. https://doi.org/10.1021/acs.chemrev.5b00744. Gallo, P.; Amann-Winkel, K.; Angell, C. A.; Anisimov, M. A.; Caupin, F.; Chakravarty, C.; Lascaris, E.; Loerting, T.; Panagiotopoulos, A. Z.; Russo, J.; et al. Water: A Tale of Two Liquids. Chem. Rev. 2016, 116 (13), 7463–7500.


Page 6 of 14

Page 7 of 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(3) (4) (5) (6)

(7) (8) (9)

(10) (11)

(12) (13) (14)

(15) (16)

(17)

https://doi.org/10.1021/acs.chemrev.5b00750. Zhang, R.; Khalizov, A.; Wang, L.; Hu, M.; Xu, W. Nucleation and Growth of Nanoparticles in the Atmosphere. Chem. Rev. 2012, 112 (3), 1957–2011. https://doi.org/10.1021/cr2001756. He, Z.; Xie, W. J.; Liu, Z.; Liu, G.; Wang, Z.; Gao, Y. Q.; Wang, J. Tuning Ice Nucleation with Counterions on Polyelectrolyte Brush Surfaces. Sci. Adv. 2016, 2 (6), e1600345–e1600345. https://doi.org/10.1126/sciadv.1600345. Sear, R. P. Nucleation: Theory and Applications to Protein Solutions and Colloidal Suspensions. J. Phys. Condens. Matter 2007, 19 (3). https://doi.org/10.1088/0953-8984/19/3/033101. Espinosa, J. R.; Soria, G. D.; Ramirez, J.; Valeriani, C.; Vega, C.; Sanz, E. Role of Salt, Pressure, and Water Activity on Homogeneous Ice Nucleation. J. Phys. Chem. Lett. 2017, 8 (18), 4486–4491. https://doi.org/10.1021/acs.jpclett.7b01551. Kalikmanov, V. I. Nucleation Theory; Lecture Notes in Physics; Springer Netherlands: Dordrecht, 2013; Vol. 860. https://doi.org/10.1007/978-90-4813643-8. Ebner, C.; Saam, W. F.; Stroud, D. Density-Functional Theory of Simple Classical Fluids. I. Surfaces. Phys. Rev. A 1976, 14 (6), 2264–2273. https://doi.org/10.1103/PhysRevA.14.2264. Sanz, E.; Vega, C.; Espinosa, J. R.; Caballero-Bernal, R.; Abascal, J. L. F.; Valeriani, C. Homogeneous Ice Nucleation at Moderate Supercooling from Molecular Simulation. J. Am. Chem. Soc. 2013, 135 (40), 15008–15017. https://doi.org/10.1021/ja4028814. El, M.; Azouzi, M.; Ramboz, C.; Lenain, J.-F.; Caupin, F. A Coherent Picture of Water at Extreme Negative Pressure. Nat. Phys. 2012, 9. https://doi.org/10.1038/NPHYS2475. Cheng, B.; Dellago, C.; Ceriotti, M. Theoretical Prediction of the Homogeneous Ice Nucleation Rate: Disentangling Thermodynamics and Kinetics. Phys. Chem. Chem. Phys. 2018, 20 (45), 28732–28740. https://doi.org/10.1039/c8cp04561e. Cacciuto, A.; Auer, S.; Frenkel, D. Breakdown of Classical Nucleation Theory near Isostructural Phase Transitions. Phys. Rev. Lett. 2004, 93 (16). https://doi.org/10.1103/physrevlett.93.166105. Gebauer, D.; Cölfen, H. Prenucleation Clusters and Non-Classical Nucleation. Nano Today 2011, 6 (6), 564–584. https://doi.org/10.1016/j.nantod.2011.10.005. Halonen, R.; Zapadinsky, E.; Vehkamäki, H.; Vehkamäki, V. Deviation from Equilibrium Conditions in Molecular Dynamic Simulations of Homogeneous Nucleation. Cit. J. Chem. Phys. 2018, 148, 164508. https://doi.org/10.1063/1.5023304. Ostwald, W. Studien Über Die Bildung Und Umwandlung Fester Körper. Zeitschrift für Phys. Chemie 1897, 22U (1), 289–330. https://doi.org/10.1515/zpch-1897-2233. Zhao, W.-H. H.; Wang, L.; Bai, J.; Yuan, L.-F. F.; Yang, J.; Zeng, X. C. Highly Confined Water: Two-Dimensional Ice, Amorphous Ice, and Clathrate Hydrates. Acc. Chem. Res. 2014, 47 (8), 2505–2513. https://doi.org/10.1021/ar5001549. Guo, C.; Wang, J.; Li, J.; Wang, Z.; Tang, S. Kinetic Pathways and Mechanisms of Two-Step Nucleation in Crystallization. J. Phys. Chem. Lett.



(18) (19) (20) (21)

(22) (23)

(24)

(25) (26)

(27) (28) (29) (30) (31) (32)

(33)

2016, 7 (24), 5008–5014. https://doi.org/10.1021/acs.jpclett.6b02276. Russo, J.; Tanaka, H. Crystal Nucleation as the Ordering of Multiple Order Parameters. J. Chem. Phys. 2016, 145 (21). https://doi.org/10.1063/1.4962166. Kawasaki, T.; Tanaka, H. Formation of a Crystal Nucleus from Liquid. Proc. Natl. Acad. Sci. 2010, 107 (32), 14036–14041. https://doi.org/10.1073/pnas.1001040107. Moore, E. B.; Molinero, V. Structural Transformation in Supercooled Water Controls the Crystallization Rate of Ice. Nature 2011, 479 (7374), 506–508. https://doi.org/10.1038/nature10586. Nomura, K.; Kaneko, T.; Bai, J.; Francisco, J. S.; Yasuoka, K.; Zeng, X. C. Evidence of Low-Density and High-Density Liquid Phases and Isochore End Point for Water Confined to Carbon Nanotube. Proc. Natl. Acad. Sci. 2017, 114 (16), 4066–4071. https://doi.org/10.1073/pnas.1701609114. Biddle, J. W.; Holten, V.; Anisimov, M. A. Behavior of Supercooled Aqueous Solutions Stemming from Hidden Liquid-Liquid Transition in Water. J. Chem. Phys. 2014. https://doi.org/10.1063/1.4892972. Loh, N. D.; Sen, S.; Bosman, M.; Tan, S. F.; Zhong, J.; Nijhuis, C. A.; Král, P.; Matsudaira, P.; Mirsaidov, U. Multistep Nucleation of Nanocrystals in Aqueous Solution. Nat. Chem. 2017, 9 (1), 77–82. https://doi.org/10.1038/nchem.2618. Jiang, H.; Debenedetti, P. G.; Panagiotopoulos, A. Z. Nucleation in Aqueous NaCl Solutions Shifts from 1-Step to 2-Step Mechanism on Crossing the Spinodal. J. Chem. Phys 2018, 150, 124502. https://doi.org/10.1063/1.5084248. Shi, R.; Tanaka, H. Microscopic Structural Descriptor of Liquid Water. J. Chem. Phys. 2018, 148 (12), 124503. https://doi.org/10.1063/1.5024565. Tanaka, H. Bond Orientational Ordering in a Metastable Supercooled Liquid: A Shadow of Crystallization and Liquid–liquid Transition. J. Stat. Mech. Theory Exp. 2010, 2010 (12), P12001. https://doi.org/10.1088/17425468/2010/12/P12001. Seeley, L. H.; Seidler, G. T. Two-Dimensional Nucleation of Ice from Supercooled Water. Phys. Rev. Lett. 2001, 87 (5), 55702-1-55702–55704. https://doi.org/10.1103/PhysRevLett.87.055702. Santra, M.; Chakrabarty, S.; Bagchi, B. Gas-Liquid Nucleation in a Two Dimensional System. J. Chem. Phys. 2008, 129 (23), 234704. https://doi.org/10.1063/1.3037241. Brovchenko, I.; Oleinikova, A. Interfacial and Confined Water; 2008. https://doi.org/10.1016/B978-0-444-52718-9.X5001-1. Chakraborty, S.; Kumar, H.; Dasgupta, C.; Maiti, P. K. Confined Water: Structure, Dynamics, and Thermodynamics. Acc. Chem. Res. 2017, 50 (9), 2139–2146. https://doi.org/10.1021/acs.accounts.6b00617. Rasaiah, J. C.; Garde, S.; Hummer, G. Water in Nonpolar Confinement: From Nanotubes to Proteins and Beyond. Annu. Rev. Phys. Chem. 2008, 59 (1), 713– 740. https://doi.org/10.1146/annurev.physchem.59.032607.093815. Chen, L.; Shi, G.; Shen, J.; Peng, B.; Zhang, B.; Wang, Y.; Bian, F.; Wang, J.; Li, D.; Qian, Z.; et al. Ion Sieving in Graphene Oxide Membranes via Cationic Control of Interlayer Spacing. Nature 2017, 550 (7676), 1–4. https://doi.org/10.1038/nature24044. Gao, Z.; Giovambattista, N.; Sahin, O. Phase Diagram of Water Confined by Graphene. Sci. Rep. 2018, 8 (1), 6228. https://doi.org/10.1038/s41598-018-


Page 8 of 14

Page 9 of 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(34) (35) (36) (37) (38)

(39) (40)

(41)

(42) (43)

(44) (45)

24358-3. Corsetti, F.; Matthews, P.; Artacho, E. Structural and Configurational Properties of Nanoconfined Monolayer Ice from First Principles. Sci. Rep. 2016, 6 (May 2015), 1–12. https://doi.org/10.1038/srep18651. Algara-Siller, G.; Lehtinen, O.; Wang, F. C.; Nair, R. R.; Kaiser, U.; Wu, H. A.; Geim, A. K.; Grigorieva, I. V. Square Ice in Graphene Nanocapillaries. Nature 2015, 519 (7544), 443–445. https://doi.org/10.1038/nature14295. Han, S.; Choi, M. Y.; Kumar, P.; Stanley, H. E. Phase Transitions in Confined Water Nanofilms. Nat. Phys. 2010, 6 (9), 685–689. https://doi.org/10.1038/nphys1708. Kumar, H.; Dasgupta, C.; Maiti, P. K. Phase Transition in Monolayer Water Confined in Janus Nanopore. Langmuir 2018, 34, 17. https://doi.org/10.1021/acs.langmuir.8b02147. Gopinadhan, K.; Hu, S.; Esfandiar, A.; Lozada-Hidalgo, M.; Wang, F. C.; Yang, Q.; Tyurnina, A. V; Keerthi, A.; Radha, B.; Geim, A. K. Complete Steric Exclusion of Ions and Proton Transport through Confined Monolayer Water. Science 2019, 363 (6423), 145–148. https://doi.org/10.1126/science.aau6771. Cai, X.; Xie, W. J.; Yang, Y.; Long, Z.; Zhang, J.; Qiao, Z. Structure of Water Confined between Two Parallel Graphene Plates. J. Chem. Phys 2018, 150, 124703. https://doi.org/10.1063/1.5080788. Falk, M. L.; Langer, J. S. Dynamics of Viscoplastic Deformation in Amorphous Solids. Phys. Rev. E - Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 1998, 57 (6), 7192–7205. https://doi.org/10.1103/PhysRevE.57.7192. Innerbichler, M.; Menzl, G.; Dellago, C. State-Dependent Diffusion Coefficients and Free Energies for Nucleation Processes from Bayesian Trajectory Analysis. Mol. Phys. 2018, 116, 2987–2997. https://doi.org/10.1080/00268976.2018.1471534. McGibbon, R. T.; Pande, V. S. Efficient Maximum Likelihood Parameterization of Continuous-Time Markov Processes. J. Chem. Phys. 2015, 143 (3), 34109. https://doi.org/10.1063/1.4926516. Loeffler, T. D.; Henderson, D. E.; Chen, B. Vapor-Liquid Nucleation in Two Dimensions: On the Intriguing Sign Switch of the Errors of the Classical Nucleation Theory. J. Chem. Phys. 2012, 137 (19), 194304. https://doi.org/10.1063/1.4766328. Tanaka, H. General View of a Liquid-Liquid Phase Transition. Phys. Rev. E. Stat. Phys. Plasmas. Fluids. Relat. Interdiscip. Topics 2000, 62 (5 Pt B), 6968– 6976. https://doi.org/10.1103/PhysRevE.62.6968. Santra, M.; Singh, R. S.; Bagchi, B. Nucleation of a Stable Solid from Melt in the Presence of Multiple Metastable Intermediate Phases: Wetting, Ostwald’s Step Rule, and Vanishing Polymorphs. J. Phys. Chem. B 2013, 117 (42), 13154–13163. https://doi.org/10.1021/jp4031199.



Graphics and Tables (a)

(b)

(c)

(d)


Page 10 of 14

Page 11 of 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 1. Snapshots of metastable liquid state, crystalline and dynamically damped clusters. (a) Top-down view of the metastable liquid state of monolayer water under 273 K; coexistence of short range square-lattice like and frustrated structural patterns can be observed. (b) The crystalline phase possesses long range uniform square lattice order with a minor proportion of defects and distortions. (c) Meansquare displacement of water oxygen 〈(𝑟 ― 𝑟0)2〉 exhibits strict linear time dependence. (d) Snapshot of a cluster and surrounding liquid-like water, in which the configuration at time t is shown as opaque material, and configurations at t – 20 ps and t + 20 ps are plotted in transparent material. Water molecules in surrounding liquid undergoes rapid rearrangement while the cluster region remains relatively stable.



Figure 2. 𝛹4 distribution with respect to the size of the largest cluster in monolayer water, N. Data is collected at every frame for water in both clusters and surrounding liquid, and each line shows 𝑃(𝛹4|𝑁), the conditional distribution of 𝛹4 over frames of equal N.


Page 12 of 14

Page 13 of 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(a)

(b)

Figure 3. (a) Free energy and (b) diffusion coefficient profile in the cluster space from a series of MD simulation under 273, 274, 275, 276, 277, 279 and 281K. CNT fitting results are plotted in solid lines; error bars are visualized in transparent shades.



Figure 4. (a) Chemical potential difference 𝛥𝜇 and surface free energy 𝛾 as a function of temperature from CNT fit. Linear regression results 𝛥𝜇 = 0.571 ― 1.96 ∗ 10 ―3𝑇 and 𝛾 = ―0.763 + 3.18 ∗ 10 ―3𝑇 are shown in dashed lines. (b) Nucleation rate – temperature profile. Dashed line shows an exponential fit result: 𝐽(𝑇) = 0.615 ∗ 𝑒𝑥𝑝 [ ―0.319(𝑇 ― 278)]𝜇𝑠 ―1𝑛𝑚 ―2.


Page 14 of 14

Ice Nucleation of Confined Monolayer Water Conforms to the Classical

Recommend Documents