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C: Physical Processes in Nanomaterials and Nanostructures

New Nanostructure in a Metastable Ice Phase Yibing Dai, and Xiaofei Xu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b03233 • Publication Date (Web): 20 Jun 2018 Downloaded from http://pubs.acs.org on June 26, 2018

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The Journal of Physical Chemistry

New Nanostructure In a Metastable Ice Phase Yibing Dai1, 2 and Xiaofei Xu 1)

∗1, a)

Center for Soft Condensed Matter Physics and Interdisciplinary Research,

Soochow University, Suzhou, 215006, China 2)

College of Physics, Optoelectronics and Energy, Soochow University, Suzhou,

215006, China ABSTRACT Hydrogen bonds between water molecules can form polygonal structure, which determine the physical properties of different ice phases. Pure pentagonal rings are not stable in crystal ice. In this work, we discover a new nanostructure of ice in heterogeneous nucleation on metal surfaces by molecular dynamic simulation. In this nanostructure, pentagonal rings are connected by dodecahedrons and staggered hydrogen bonds. The presence of dodecahedrons could help the stability of ice structure with pentagons. This nanostructure serves as a skeleton unit in ice. Our results provide a new explanation for the existence of pentagonal rings in ice, which are helpful to understand the complex ice phase behaviors.

a)

Electronic mail: [email protected]; TEL: +86-150-5147-8694

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The Journal of Physical Chemistry 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

I.

INTRODUCTION Understanding the phase behaviors of water is important to our daily life and industrial

application

1–4

. So far, 18 crystalline and 3 amorphous phases for ice have been found 5 .

This large number of phase behaviors are due to the open arrangement of hydrogen bonds in space. In ordinary ice, tetrahedron formed by the four hydrogen bonds around each water molecule is the basic unit in structure. In some ices, however, three-dimensional pentagonal rings play an important role . For example, phase XVI is the least dense of all known crystalline ice owing to its cage structure, which consists of pentagons and hexagons 6 . But pure pentagonal rings are not stable in crystal for the lack of translational symmetry7 . It was believed that pentagonal rings could exist by only two forms: to form a cage6 or as a defect 8 in ice. Here, we report that pentagonal rings can exist in the third form: connected by decahedrons and staggered hydrogen bonds to form a skeleton unit in ice. During ice nucleation, some metastable intermediate phases could exist over a long period of time

9–12

. The structure of those phases and their role in nucleation still need to be

explored. In this work, we explore the structure of one metastable ice by molecular dynamics simulation. It is hard to obtain metastable ice in homogeneous nucleation by molecular simulation, because water usually directly nucleates to the stable phase. In order to reach metastable ice, we use several strategies in our simulation. (1) The nucleation temperature is low enough to give a low nucleation barrier, so that the system has the same probability to pass all possible ice phases. (2) The surface potential is weak to mimic a hydrophobic surface. So the density fluctuation of liquid water is large enough to affect the nucleation process. (3) We simulate heterogenous ice nucleation on a steel surface with doping tens of carbon atom, which increase the heterogeneity of the nucleation. The phase behaviors of ice are determined by the local structure and arrangement of hydrogen bonds. Hydrogen bond may be at staggered/eclipsed state, depending on its torsion angle. It is at staggered state if the torsion angle of the bond (say bond AB) is at a particular value such that A’s neighbor molecules and B’s neighbor molecules is at the maximal distance. The conformational energy is a global minimum. If the distance reaches the minimum value, the hydrogen bond is at the eclipsed state, whose conformational energy is a global maximum. See the supporting information and reference13 for details. Different ice has different number of staggered/eclipsed hydrogen bonds. For example, in cubic ice ACS Paragon 2Plus Environment

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(b)

(a)

(c)

z y x

Carbon FIG. 1. (a) A snapshot of the simulation box. The water molecules, iron atoms and carbon atoms are marked by cyan, pink and red color, respectively. (b) Schematic of coarse grained monatomic water (MW) model. (c) Top view of steel surface. The carbon atoms are randomly placed in the interstitial area between iron atoms.

(Ic ), all four neighbor hydrogen bonds of each water molecule are at staggered state. In hexagonal ice (Ih ), three of them are at staggered state, and one is at eclipsed state. It is not enough to describe more complex phase behaviors only by the idea of staggered/eclipsed state. We need a local order parameter to describe the structure. One popular order parameter is defined by projecting the local structure on a basis of spherical harmonics

14

; see supporting information for details. In this work, we obtain different ices

with performing heterogeneous nucleation from liquid water on a steel surface by molecular dynamic simulation. We then scan the local order parameter in those ices by the CHILL+ algorithm

II.

15

. As a result, we discover the new skeleton structure in a metastable ice phase.

SIMULATION METHODS The simulation model and box are shown in figure 1. The steel surface comprises of 4356

iron atoms, packing by body-centered cubic (bcc) structure as several layers; see figure 1(a). ACS Paragon 3Plus Environment


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The water molecules are coarse-grained by monatomic water (MW) model 16 ; see figure 1(b). The carbon atoms are randomly placed in the interstitial area between iron atoms on the surface; see figure 1(c).There are 5000 water molecules in total. The hydrogen bond between water molecules is described by a tetrahedral short-ranged interaction, which successfully describes the polarizability of water

16

. The interaction between water molecule and iron

atom is described by a truncated Lennard-Jones potential:  h i   4 σ 12 − σ 6 r < rc r r U (r) =  0 r ≥ rc

(1)

where r is the distance between the two spheres. is the interaction strength. The interaction diameter parameter and the cutoff distance are fixed at σ = 2.5 ˚ A and rc = 7.53 ˚ A, respectively. The interaction between water and carbon atom on the surface is described by a force field potential of Stillinger and Weber

17,18

, and the interaction strength is fixed

throughout the simulation. We only change the value between water and iron atom. We run the simulation in NVT ensemble by LAMMPS package

19

. The ensemble temperature

is fixed by a heat bath with a couple of ten Nos´e-Hoover thermostats

20

. The simulation

box is periodic in x or y directions (parallel to the steel surface), and the box height is fixed at 70 ˚ A in z-direction (perpendicular to the steel surface). The time step is 10 fs.

III.

RESULTS AND DISCUSSION

We first calculate the nucleation rate and show the data in figure 2. The data are collected as following. We first equilibrate the system at T = 290 K by running the simulation for about 90 ns, and then select ten snapshots randomly. For each snapshot, the system starts to nucleate by quenching the temperature to T = 205 K. At last, we run the simulation for another long enough time (about 400 ns), which makes the system in dynamic equilibrium after the nucleation. The nucleation rate is calculated by the average results of those ten trajectories of nucleation 21 . In figure 2, value describes the hydrophobicity/hydrophilicity of the steel surface, determined by the atomic structure of the steel in reality (such as manganese-doped steel, sulphur-doped steel, etc.). We consider four cases: one hydrophobic surface ( = 0.500 kcal/mol), two intermediate surfaces ( = 1.555, 2.500 kcal/mol), and one weak hydrophilic surface( = 3.500 kcal/mol)

22–24

.

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×10-7

Nuclation Rate J [ns-1Å-1]

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) = 0.500 kcal/mol

×10-7

3

3

2

2

1

1

0

0 -7

(c) = 2.500 kcal/mol

×10

×10-7

3

3

2

2

1

1

0

(b) = 1.555 kcal/mol

0

4

10 20 30 40 50

0

(d) = 3.500 kcal/mol

0

4

10 20 30 40 50

Number of Carbon Atoms on Iron Surface

FIG. 2. Dependance of nucleation rate on the number of carbon atoms placed on the surface. Each data is the mean value of ten trajectories. The red dashed lines are the homogeneous nucleation rate

24 .

On hydrophobic surface (figure 2(a)) , the density fluctuation of liquid water is large 25–27 enough to retard the formation of an ice cluster

24

. So the nucleation rate is much slower

than that of homogeneous nucleation (dashed lines in figure 2). At hydrophilic surface (figure 2(d)), the liquid water molecules tend to be order, which is helpful for ice cluster formation. In other words, the hydrophilic surface enhances the nucleation and reduce the nucleation barrier. The nucleation rate is faster than that of homogeneous nucleation. At intermediate surface, the nucleation behavior is complex, due to the interplay effect between surface structure and on-forming ice structure. For example, the unforeseeable rapid nucleation rate at 40 C in figure 2(b) is just a result of this interplay effect. The reader may see the radial distribution function in figure S1 in supporting information for details. We observe two types of nucleation process in all the data. Figure 3 shows the two types: The rapid one (red line) and the slow one (blue line). Even if the initial states were selected from the same equilibrated trajectory, nucleation could be either the rapid case or the slow case. Most data are just the rapid case. About 20% of the data are the slow case, and this ACS Paragon 5Plus Environment


10 4

-5.35

(a)

(b)

-5.4

Potential Energy [kcal/mol]

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-5.45 -5.5 -5.55

(c)

-5.6 67.83 ns -5.65

Ep

-5.7 -5.75

27.14 ns 0

20

40

60

80

100

Time [ns]

FIG. 3. (a) Potential energy evolution during ice nucleation at the surface of = 0.5 kcal/mol and 10 carbon atoms

29 .

The solid lines are the raw data. The dashed lines are the fitting

curves by equation E(t) = a + b/(1 + ec(t−t0 ) ), where a, b, c, τ0 are fitting parameters24 . The final configuration in slow nucleation case (solid blue line in panel (a) ) is shown in panel (b), and the one in rapid nucleation case (solid red line in panel (a)) is shown in panel (c). The potential energy difference between the slow and rapid nucleation case is ∆Ep ≈ 980 kcal/mol. In panel (b) and (c), the hydrogen bonds connected to staggered molecules30 are marked by red color, and the other hydrogen bonds are marked by green color.

usually happens on hydrophobic surface. For the rapid case, the nucleation time is about 30 ns. But for the slow case, the nucleation time could be even slower than 60 ns. There are many interesting differences between these two nucleation processes. The potential energy difference between the two nucleated ice states is about 980 kcal/mol (0.24 kB T per molecule), which is much greater than the entropy contribution during phase transition (about 0.01 kB T per molecule)28 . Following F = U − T S, the free energy difference between these two states is quite large. So the ice nucleated in the slow case must be a metastable state. As the thermal fluctuation is very small in crystal, this metastable state can exist over a long period of time. The physical properties of ice are determined by the local structure and arrangement of hydrogen bonds. It is interesting to observe how hydrogen bonds arrange in details for ACS Paragon 6Plus Environment

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(a)

(b)

(c)

(d)

63.4°

FIG. 4. (a) Nanostructure of hydrogen bond of ice formed in the slow nucleation case. The skeleton unit in the nanostructure is marked by thick green color. There are two skeleton units in the simulation box, and only one is marked for a better view for the whole structure. (b) Schematic of the skeleton unit structure. (c) Structure and connection of hydrogen bonds in the dashed line region in panel (b). (d) The magnified view for the dashed line region in panel (b).

these two states. In supporting information, we show all ices found in our simulations. We focus on two ices shown in figure 3. In panel 3 (b) and (c), we label hydrogen bonds connected to staggered molecule by red color, and the other ones by green color. In panel (c) (the ice nucleated in the rapid case), the staggered and eclipsed hydrogen bonds are packed alternatively layer by layer to form a regular structure (i.e. ice Isd )9 . The packing orientation depends on the growth direction of ice at the surface. In panel (b) (the ice nucleated in the slow case), the two types of hydrogen bonds are packed randomly. There seems no regular unit in the ice structure. The following discovery is the most important result in this work. We discover a new ACS Paragon 7Plus Environment


nanoscale structure in figure 3(b) by searching the local order parameters of hydrogen bonds 14

. The structure in figure 3(b) looks like chaos. However, we can get a skeleton structure

comprised by dodecahedrons, pentagons and staggered hydrogen bonds. The local order parameter of this skeleton structure is much greater than that of the surrounding hydrogen bonds; see Table S1 in supporting information. As is shown in figure 4, the dodecahedron has 12 pentagonal faces formed by 20 water molecules. All these 20 molecules are at eclipsed state. This kind of polyhedral structure is also found in other simulations31 . Every two dodecahedrons are connected by a pipe-like structure, composed by three pentagons and five groups of staggered hydrogen bonds. All hydrogen bonds in the pentagon are at eclipsed state. Adjacent pentagons are connected by one group of staggered hydrogen bonds. The angle between two adjacent pipe-like structure is about 60 degrees.

IV.

CONCLUSIONS

Pentagon is a common structure in soft matter, which has been observed in systems of hard spheres32 , liquids33,34 , colloids35 and glasses36 . In ice nucleation, Li et.al.8 also found a quasi five-fold twin boundary structures. However, they consider pentagonal rings as topological defects. It should be mentioned that, structures composed by pentagons are not stable in space for the lack of translational symmetry. They could exist only by the form of quasicrystal7 . In this work, we find that the existence of dodecahedrons may help the stability of pentagonal structures. Dodecahedron serves as a link point to connect all pentagons. More water molecules nucleate and grow around this skeleton structure to form the ice shown in panel (b). The presence of pentagonal rings was believed to be the structural origin of the slow dynamics in nucleation37 . Our results confirm this prediction, and show that pentagonal rings exist in a complex way. In summary, we show that pentagonal rings could exist in a new form. Our results are helpful to understand the complex ice nucleation and phase behaviors. In this work, we use MW model for the efficiency. Because MW model well predict the thermodynamic and dynamic properties of water16 , we believe that our results could be reproduced by other water model easily, including TIP3P or TIP4P-2005 model. Further theoretical and experimental studies on the skeleton structure are an interesting and important topic in future. ACS Paragon 8Plus Environment

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Supporting Information A brief description of the local order parameter, staggered/eclipsed state of hydrogen bond, and some other phases found in this work are provided in supporting information.

Author Information Corresponding Author: [email protected]

ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China under Grant No. 21674077.

REFERENCES 1

Franks, F. Water: A matrix of life. Royal Society of Chemistry: Cambridge, 2000.

2

Robinson, G. W.; Zhu, S. B.; Singh, S.; Evans, M. W. Water in biology, chemistry, and physics: Experimental overviews and computational methodologies. World Scientific: Singapore, 1996.

3

Baker, M. Cloud microphysics and climate. Science 1997, 276, 1072-1078.

4

Ball, P. Water as an active constituent in cell biology. Chem. Rev. 2008, 108, 74–108.

5

Bartels-Rausch, T.; Bergeron, V.; Cartwright, J. H. E.; Escribano, R.; Finney, J.L.; Grothe, H.; Gutierrez, P.J.; Haapala, J.; Kuhs, W.F.; Pettersson, J. B. C., et al. Ice structures, patterns, and processes: A view across the ice-fields. Rev. Mod. Phys. 2012, 84, 885-944.

6

Falenty, A.; Hansen, T. C.; Kuhs, W. F. Formation and properties of ice XVI obtained by emptying a type sII clathrate hydrate. Nature 2014, 516, 231-233.

7

Hargittai, I. Fivefold symmetry. World Scientific: Singapore. 1992.

8

Li, T.; Donadio, D.; Russo, G.; Galli, G. Homogeneous ice nucleation from supercooled water. Phys. Chem. Chem. Phys. 2011, 13, 19807-19813.

9

Moore, E. B.; Molinero, V. Is it cubic? Ice crystallization from deeply supercooled water. Phys. Chem. Chem. Phys. 2011, 13, 20008-20016. ACS Paragon 9Plus Environment


10

Sanz, E.; Vega, C.; Abascal, J. L. F.; MacDowell, L. G. Phase diagram of water from computer simulation. Phys. Rev. Lett. 2004, 92, 255701.

11

Carr, T. H. G.; Shephard, J. J.; Salzmann, C. G. Spectroscopic signature of stacking disorder in ice I. J. Phys. Chem. Lett. 2014, 5, 2469-2473.

12

Salzmann, C. G.; Kohl, I.; Loerting, T.; Mayer E.; Hallbrucker, A. Raman spectroscopic study on hydrogen bonding in recovered ice IV. J. Phys. Chem. B 2003, 107, 2802-2807.

13

Stereochemistry of organic compounds. Eliel, E.L.; Wilen, S. H.; Mander, L.N. 1994, John Wiley& Sons, Inc. New York. p.1197, p.1207

14

Moore, E. B.; de la Llave, E.; Welke, K.; Scherlis, D. A.; Molinero, V. Freezing, melting and structure of ice in a hydrophilic nanopore. Phys. Chem. Chem. Phys. 2010, 12, 41244134.

15

Nguyen A. H.; Molinero V. Identification of clathrate hydrates, hexagonal ice, cubic ice, and liquid water in simulations: The CHILL+ algorithm. J. Phys. Chem. B 2015, 119, 9369-9376.

16

Molinero, V.; Moore, E. B. Water modeled as an intermediate element between carbon and silicon. J. Phys. Chem. B 2009, 113, 4008-4016.

17

Lupi, L.; Hudait, A.; Molinero, V. Heterogeneous nucleation of ice on carbon surfaces. J. Am. Chem. Soc. 2014, 136, 3156-3164.

18

Stillinger, F. H.; Weber, T. A. Computer simulation of local order in condensed phases of silicon. Phys. Rev. B 1985, 31, 5262-5271.

19

Plimpton, S. J. Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 1995, 117, 1-19.

20

Martyna, G. J.; Klein, M. L.; Tuckerman, M. Nos´e-Hoover chains: The canonical ensemble via continuous dynamics. J. Chem. Phys 1992, 97, 2635-2645

21

Walsh, M. R.; Beckham, G.T.; Koh, C.A.; Sloan, E. D.; Wu, D.T.; Sum, A.K. Methane hydrate nucleation rates from molecular dynamics simulations: Effects of aqueous methane concentration, interfacial curvature, and system size. J. Phys. Chem. C 2011, 115, 2124121248.

22

Previous theoretical and simulation results show that the adsorption energy between water and metal ranges from 0 to 13 kcal/mol. See reference 23 and 24 for details. The thermal fluctuation of bulk liquid water is of the order 1 kB T , which equals to about 0.4 kcal/mol at T = 205 K. So, these values range from 1.25 kB T to 8.75 kB T .

23

Carrasco, J.; Klimes, J.; Michaelides, A. The role of van der Waals forces in water adsorpACS Paragon10 Plus Environment

Page 10 of 12

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tion on metals. J. Chem. Phys. 2013, 138, 024708 24

Fitzner, M.; Sosso, G. C.; Cox, S. J.; Michaelides, A. The many faces of heterogeneous ice nucleation: Interplay between surface morphology and hydrophobicity. J. Am. Chem. Soc. 2015, 137, 13658-13669.

25

Evans, R.; Wilding, N. B. Quantifying density fluctuations in water at a hydrophobic surface: Evidence for critical drying. Phys. Rev. Lett. 2015, 115, 016103.

26

Evans, R.; Stewart, M. C. The local compressibility of liquids near non-adsorbing substrates: A useful measure of solvophobicity and hydrophobicity. J. Phys.: Condens. Matter 2015, 27, 194111.

27

Dai, Y.; Xu, X.; Liu, Y. Density fluctuations of carbon dioxide in cylindrical nanopore. J. Phys. Chem. C 2016, 120, 9520-9526.

28

Handbook of chemistry and physics, 81st ed. CRC: Boca Raton, 2000 pp.6–119

29

After nucleation, there are few liquid water molecules nearby the box boundary. We do not show those molecules in the snapshot in figure 3(b) and (c). However, the potential energy in figure 3(a) is of all water molecules, including liquid water molecules.

30

We say one molecule at staggered state if all four neighbor hydrogen bonds are at staggered state.

31

Jacobson, L. C.; Hujo, W.; Molinero, V. Thermodynamic stability and growth of guest-free clathrate hydrates: A low-density crystal phase of water. J. Phys. Chem. B 2009, 113, 10298-10307.

32

O’Malley, B.; Snook, I. Crystal nucleation in the hard sphere system. Phys. Rev. Lett 2003, 90, 085702.

33

Frank, F. C. Supercooling of liquids. Pro. R. Soc. Lond. 1952, A215, 43-46.

34

Reichert, H.; Klein, O.; Dosch, H.; Denk, M.; Honkimaki, V.; Lippmann, T.; Reiter, G. Observation of five-fold local symmetry in liquid lead. Nature 2000, 408, 839-841.

35

Royall, C. P.; Williams, S. R.; Ohtsuka, T.; Tanaka, H. Direct observation of a local structural mechanism for dynamic arrest. Nat. Mater. 2008, 7, 556-561.

36

Hirata, A.; Guan, P. F.; Fujita, T.; Hirotsu, Y.; Inoue, A.; Yavari, A. R.; Sakurai, T.; Chen, M. W. Direct observation of local atomic order in a metallic glass. Nat. Mater. 2011, 10, 28-33.

37

Hu, Y. C.; Li, F. X.; Li, M.Z.; Bai, H. Y.; Wang, W.H. Five-fold symmetry as indicator of dynamic arrest in metallic glass-forming liquids. Nature. Commun. 2015, 6, 8310. ACS Paragon11 Plus Environment


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