Enhancing and Impeding Heterogeneous Ice Nucleation through

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Enhancing and Impeding Heterogeneous Ice Nucleation through Nanogrooves Chu Li, Ran Tao, Shuang Luo, Xiang Gao, Kai Zhang, and Zhigang Li J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b07779 • Publication Date (Web): 19 Oct 2018 Downloaded from http://pubs.acs.org on October 21, 2018

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The Journal of Physical Chemistry

Enhancing and Impeding Heterogeneous Ice Nucleation through Nanogrooves Chu Li,1 Ran Tao,1 Shuang Luo,1 Xiang Gao,1 Kai Zhang,2,* and Zhigang Li1,† 1Department

of Mechanical and Aerospace Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

2Key

Laboratory of Precision Microelectronic Manufacturing Technology & Equipment of Ministry of Education, Guangdong University of Technology, Guangzhou, 510006, China

Abstract In this work, we investigate the effects of nanogrooves on heterogeneous ice nucleation (HIN) through molecular dynamics simulations.

It is found that nanogrooves on a surface significantly

alter the ice nucleation rate by more than two orders of magnitude.

Depending on the width of the

grooves, the nucleation rate can be enhanced or impeded compared with that on flat surfaces.

For

relatively large grooves, ice nucleation enhancement is observed when the effective groove width is a multiple of the ice lattice constant, for which ice crystal nucleus forms in the groove.

For

narrow grooves, strong confinements lead to the formation of solid-like layered structures, which may or may not enhance ice nucleation, depending on their structural match with ice crystal.

The

findings in this work provide critical information for surface designs in controlling HIN.

Oct. 2018

* †

Email: [email protected] Email: [email protected]

ACS Paragon Plus Environment

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Introduction Heterogeneous ice nucleation (HIN), which is induced by foreign materials (e.g., a solid surface) is a popular way of ice formation in nature.

A deep understanding of HIN has significant impacts

on numerous areas, including atmospheric physics,1,2 bioengineering,3 and energy industry.5,6

infrastructures, aviation,4

In many applications, a good control of HIN is desired to either promote

or hinder ice nucleation.7-9

This can be achieved by using surfaces with specific characteristics,

among which surface roughness has been shown critical in affecting ice crystallization.10,11 Usually, an ice crystallization process is triggered by an ice nucleus or nuclei of critical sizes and followed by further ice growth. and promote ice nucleation.

Surface roughness is expected to offer rich nucleation sites

This is supported by the classical nucleation theory (CNT), which

states that a concave surface, compared with a convex or a flat surface, favors a nucleation process through reducing the critical size of the nucleus.12 scenarios of cavitation13 and condensation.14

The CNT has been shown working well in the

However, the validity of CNT for HIN is still under

debate, especially for the role of nano- and sub-nanoscale concave structures in ice nucleation, for which contradictive results have been reported in the literature in both experiments and simulations. For instance, it was shown that ice nucleation could be promoted by certain irregular structures on mineral surfaces, such as hematite15 and kaolinite.16,17 Recent experiments also found that surface defects in feldspars1,18 and the wedges of mica19 could enhance ice nucleation.

However,

roughness on glass, silicon, mica, and some hydrophobic surfaces20,21 was shown having negligible influence in promoting ice nucleation.

Meanwhile, both enhancing and suppressing effects on ice

nucleation on concave surfaces have been reported in numerical simulations.22-25

Specifically, it

was found that ice nucleation could be promoted by surface wedges with certain angles,22 whereas


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carbon surfaces with molecular roughness impeded ice nucleation through disrupting layering structures of ice on the surfaces.23 The inconsistent results about the role of surface roughness in the literature might be related to the effects of the molecular structure of a surface on HIN, which are also under debate.

On one

hand, it was shown that surfaces with a crystalline structure matching that of ice could enhance ice nucleation.24,26

On the other hand, studies found that a structural or lattice match was not a

necessary condition for promoting ice nucleation,23,27,28 which is also true for other crystal nucleation.29,30

Nevertheless, the effects of surface roughness on HIN remains unclear and

intensive investigations are required. In this work, molecular dynamics (MD) simulations are performed to study HIN on surfaces with nanogrooves.

It is found that the ice nucleation rate is sensitive to the groove size.

For

relatively large grooves with widths commensurate with the ice lattice constant, the nucleation rate can be significantly enhanced, up to more than two orders of magnitude, compared with that on flat surfaces due to the formation of ice crystal nuclei in the grooves.

For other groove widths, water

molecules in the grooves remain in liquid state and the ice nucleation is hindered.

For narrow

grooves, nanoconfinement effects dominate and cause the formation of solid-like, non-crystalline, layered structures (LSs).

The LSs, which are topological compatible with ice crystals, can greatly

enhance ice nucleation. Methods Molecular dynamics simulations.

All the MD simulations are carried out using the LAMMPS

package31 with a time step of 5 fs.

The simulation system consists of a slab of water molecules

and a graphene surface, as shown in Fig. 1a.

Nanogrooves with various widths, W, and fixed depth,

H=1.47 nm (unless otherwise specified), are constructed by folding the graphene along armchair


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directions, as illustrated in Fig. 1b. atoms are fixed in simulations.

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The surface is treated as a rigid body such that all the carbon The monatomic water (mW) model, whose melting point for

hexagonal ice is Tm  274.6  1 K32, is employed to simulate water molecules and the water12 6 surface interactions are described by the Lennard-Jones potential, U  4 co  co r    co r   ,  

where  co  0.13 kcal/mol and  co  0.32 nm are the binding energy and collision diameter for carbon-oxygen interactions.23

The mW model treats water molecules as simple particles, which

makes simulations inexpensive as compared with full atomic water models.

This model can

reproduce the primary properties of water, including the liquid state density, the melting temperature of hexagonal ice, as well as the kinetics of ice crystallization.32

It should be noted

that the lack of rotational degrees of freedom in the mW model limits its ability in reproducing the free energy between ice and certain surfaces (e.g., graphite).33

Nevertheless, the mW model has

been widely used for its ability in capturing the ice nucleation dynamics.34-37 The dimensions of the simulation box are 5.903, 4.686, and 8.5 nm in the x, y, z directions, respectively.

Periodic boundary conditions (PBCs) are applied in all the directions.

To eliminate

undesired effects caused by the PBCs, a void space38 of about 3 nm above water in the z direction is incorporated in the simulation system.

The number of water molecules in all cases is more than

4100, which is close to or larger than previous studies.38-41 The temperature of the system is controlled by the Nosé-Hoover thermostat.

Initially, the system is heated up within 0.5 ns and

equilibrated at room temperature for 2 ns and then cooled down suddenly to 220 K, after which the dynamics of the system is monitored and data collection is performed. Estimation of nucleation rate.

Nucleation events are detected by a sudden drop of the potential

energy of water molecules, which is characterized by an induction time tn, i.e., the time needed for a nucleation event to take place.

For each surface, more than 20 independent parallel simulations


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are conducted and the corresponding tn is obtained.

Based on these tn, the survival probability,

PLiq  t  , which is the probability of the system staying in the supercooled liquid state without ice nucleation at time t, is calculated.

Theoretical analysis shows that PLiq  t  can be expressed as

 PLiq  t   exp    t t0   , where t0 is the average nucleation time and  is a parameter accounting  

for non-exponential kinetics.26

t0 and  can be obtained by fitting the curve of ln PLiq  t  as a

function of t, as shown in Fig. 2a.

The linear relationship in Fig. 2a indicates that   1 and t0

can be determined using the slope of the linear fits.

The nucleation rate J is then calculated as

J  1  t0   , where  is the volume of water.

Free energy calculation.

The free energy G  n  for ice nucleation is obtained using the

method developed by Wedekind and Reguera.42

First, the number of ice molecules is obtained

based on the average bond-order parameter 1/2

2  4  m l 1 Ni  , ql (i )   q j      2l  1 m  l N i  1 j 0 l ,m   

where N i is the number of neighbors of molecule i and ql ,m  j  

Yl ,m  r jk  being the spherical harmonics.43-45

(1)

1 Nj



Nj

Y

k 1 l , m

r  jk

with

Here, q6  0.45 is applied to distinguish the

molecular structure of ice (both cubic and hexagonal ice) from that of liquid water with Ni=4 for water molecules in the bulk and Ni=3 for liquid water molecules at the interface or in the groove.43 The number of ice molecules in the largest ice cluster, n, is then used to denotes the state of the system, S = n.

To obtain the free energy, two quantities are required in this method.42

steady probability Pst  n  of the system assuming a state characterized by n.


One is the

The other is the

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mean first passage time (MFPT) τ(n), which is the mean time the system takes to reach the state, S = n, for the first time.

Both Pst  n  and τ(n) can be obtained in MD simulations and the free

energy is calculated through42

G  n   ln  B  n    

n

1

dn '  C, B  n '

(2)

where   1/  kBT  with kB being the Boltzmann constant, C is a constant, and B(n) is given by

B n 

 n  n   1 Pst  n ' dn ' ,   n1   Pst  n   1

where n1 is the maximum value of n.42

(3)

To reduce the error caused by τ(n) due to limited data,

practically, for one-step nucleation, τ(n) can be modeled by46

 n 

0  1  erf Z   n  n*   , 2





(4)

where  0 is a characteristic time, Z is the Zeldovich factor, and n* is the critical nucleus size. Results and Discussion Ice nucleation on surfaces with nanogroove widths ranging from 0.492 to 2.952 nm are studied. For convenience, these surfaces are numbered from #1 to #11 and the corresponding groove widths are listed in Table S1 in the Supporting Information (SI).

Figure 2b presents the nucleation rates

for these surfaces, which differ by more than two orders of magnitude.

For comparison, the ice

nucleation rate on a flat surface Jo is also calculated, which is equal to 1.37 1030 m-3s-1 and about 5 orders of magnitude higher than that of homogeneous ice nucleation (ice nucleation in bulk water) obtained using the mW water model.45

Compared with Jo, it is seen that the ice nucleation rate is

enhanced by grooves with W3 =0.984, W4 =1.23, W6 =1.723, and W9 =2.46 nm.

However, for the

other surface, the grooves show hindering effects on ice nucleation.


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Considering the molecular interactions, the effective width of the grooves is estimated as

W   W   co   oo  2 ,47 where  oo  0.23925 nm is the collision diameter for oxygen-oxygen interactions.31

If W  is compared with the lattice constant of hexagonal ice along the c-axis at

220 K, c  0.734472 nm,48 it is found that ice nucleation is significantly enhanced on surfaces with W  being a multiple of c, as shown in Fig. 2b.

This indicates that size match between the

groove width and ice lattice constant plays an important role in promoting ice nucleation. 2c shows snapshots of ice structures formed on different surfaces.

Figure

For surfaces #3, #4, #6, and #9,

where ice nucleation is enhanced, it is seen that ice or solid-like structures form in the grooves. For the hindering cases, e.g. surfaces #2 and #5 in Fig. 2c, molecules in the grooves remain in liquid state and ice nucleation is solely triggered by the flat part of the surface. Figure 2 suggests that whether nanogrooves can promote ice nucleation depends on the formation of ice or solid-like structures in the grooves.

To further understand the effects of

nanogrooves, the kinetics of ice nucleation on different surfaces is investigated.

On the flat surface,

the nucleation follows a typical one-step process, as shown by the free energy in Fig. S1 in the SI. The snapshots of the system at different n values are depicted in the insets of Fig. S1.

It is clear

that an ice nucleus forms at the interface first.

When the

As it grows, the free energy increases.

ice nucleus becomes sufficiently large, characterized by a critical size of n  89 , G reaches the maximum, after which G drops and the continuous growth of ice is triggered.

The free energy

barrier G  , which is the G difference between the local minimum at the initial stage and the maximum at n  89 , as shown in Fig. S1, is 9.27 kBT . For surfaces with grooves, the ice nucleation appears to be different from that on the flat surface. For surface #6 (W6 = 1.723 nm), the effective groove width matches well with the ice lattice constant, the ice nucleation exhibits a two-step process.

This is manifested by the MFPT   n  in Fig. 3a,


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where the ice nucleation experiences two distinct activation steps. supported by the two free energy barriers shown in Fig. 3b. demonstrated in Fig. 3c.

The two-step nucleation is also

The evolution of ice nucleation is

The first free energy barrier GI*  4.05 kBT is associated with the

development of the ice nucleus inside the groove.

When n increases, the ice formation extends

from inside to outside the groove, as illustrated by the snapshots with n  235 in Fig. 3c. corresponds to the second free energy barrier GII*  2.91 kBT (Fig. 3b).

This

The relatively small

value of GII* is the consequence of the fact that the nucleus structure inside the groove is the same as that of ice (Figs. 2c and 3c). For surface #5 (W5 = 1.476 nm), however, ice nucleation does not occur inside the groove probably due to a large strain energy caused by the structural mismatch between the groove and the ice crystal.29,49

In this case, ice nucleation is induced by the flat part of the surface instead, as

shown in Fig. S2 in the SI.

The free energy change in Fig. S2 shows a similar fashion to that for

the flat surface in Fig. S1.

As the area of the flat part of surface #5 is less than the flat surface, ice

nucleation rate is reduced.

This is consistent with the free energy barrier G *  10.6 kBT in Fig.

S2, which is higher than that for the flat surface. Structural match between the groove and ice crystal can explain the ice nucleation for surfaces with groove widths larger than ~ 1.3 nm.

For smaller grooves, however, ice nucleation becomes

complex due to the strong confinement.

In narrow grooves, water molecules form solid-like but

non-ice crystalline structures under the influence of the groove.

Figure 4a shows the density

profiles and structures of water/ice molecules in the grooves of surfaces #2, #3, and #4. that layered structures (LSs) form in the grooves (front and side views).

It is seen

In the groove of surface

#2 (W2 = 0.738 nm), the solid-like structure is irregular because the small groove width only allows the formation of a monolayer structure, which is less stable compared with the structures formed in


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relatively large grooves.50,51

In the grooves of surfaces #3 and #4, however, relatively stable LSs

form, which are composed of hexagonal rings stacked in an AA fashion, as illustrated by the side views in Fig. 4a.

It is noted that the LSs in grooves #3 and #4 are solid-like but structurally

different from any ice crystal, although the size of grooves #3 matches well with ice crystals. is probably caused by the strong confinement effects. in nanocapillaries.52,53 this work.

This

Similar stable LSs have also been observed

It is noted that cubic ice, hexagonal ice, and LSs are not discriminated in

Instead, they are discriminated from liquid water using the criterion q6  0.45 .

To understand how LSs trigger the formation of structurally-different, hexagonal or cubic ice, the ice nucleation processes are studied for surfaces #3 and #4, as shown in Fig. 4b and Fig. S3, respectively.

For surface #3, the free energy profile in Fig. 4b reveals that at the early stage, water

molecules enter the groove and form LSs without energy barriers.

The local minimum of the free

energy at n~100 corresponds to the accomplishment of the LS in the groove.

To trigger further

crystallization outside the groove, a small free energy barrier, G *  1.67 kBT , needs to be overcome.

Figure 5a demonstrates how the LS in the groove (dark blue) induces ice crystallization

(purple) outside the groove.

First, water molecules attach to the top of the stable LS (Fig. 5(a) i)

and form an array of 5 membered rings, as shown in Fig. 5(a) ii. and form topological cages (Fig. 5(a) iii).

Then, more water molecules join

These topological cages are quite stable and are

structurally compatible with hexagonal/cubic ice, as shown in Fig. 5(a) iv.

Such topological

stability and structural compatibility lead to a relatively small free energy barrier ( G *  1.67 kBT ) and can quickly trigger ice crystallization outside the groove. also applies to surface #4, as shown in Fig. 5b.

Similar ice nucleation mechanism

The only difference is that the free energy barrier,

G*  5.50 kBT (Fig. S3) for surface #4 is higher than that for surface #3 due to the relatively large


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size of the topological cages (two arrays) for surface #4 (Fig. 4a).

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As a result, the ice nucleation

rate for surface #4 is smaller than that for surface #3 (Fig. 2b). The MD studies in this work show that the effects of nanogrooves on ice nucleation are strongly related to the state of water molecules inside the groove, which depends on the groove size.

To

promote ice nucleation, a groove should be able to induce either ice crystal or solid-like LSs that are structurally compatible with ice crystals.

The former is apt to be formed in relatively large

grooves with effective widths matching the ice lattice constant. narrow grooves, where the confinement effects dominate.

The latter is usually formed in

If water molecules inside a groove

remain in liquid state or form structurally incompatible LSs, ice nucleation is impeded. It is noted that the depth, H, of the grooves also plays a role in ice nucleation. the nucleation rate as a function of H for surfaces #3 and #6.

Figure 6a depicts

For narrow grooves (e.g. surface #3),

where LSs form, the nucleation rate is quite sensitive to H and fluctuates as H is varied, as shown in Fig. 6a.

This is because H influences the structure of the LS inside the groove and consequently

the stability and compatibility of the topological cages (top panels of Fig. 6b), which control the ice growth outside the groove. of Fig. 6c.

This is also consistent with the free energy barriers in the top panels

For grooves with a relatively large width (e.g. surface #6), H appears to be important

when it is small.

In this case, the groove-induced ice crystal nucleus inside the groove is not quite

stable and the nucleation appears to be a one-step process with relatively large energy barrier, as shown in Figs. 6b and 6c.

For large H, the nucleation rate is independent of H because the nucleus

inside the groove is sufficiently stable and ice nucleation changes to a two-step process with GI* insensitive to H (Fig. 6c). Conclusions


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In conclusion, we have studied the effects of nanogrooves on HIN.

For large nanogrooves, the

effective width of the grooves, W  , plays a critical role in affecting the ice nucleation rate, which show a commensurate dependence on the groove width, i.e. enhancement is achieved when W  c are roughly integers.

For narrow grooves, instead of ice crystals, LSs are formed and their

structural compatibility with ice crystals determines the ice nucleation rate.

Supporting Information Table S1, dimensions of various nanogrooves; Figure S1, ice nucleation process on the flat surface; Figure S2, free energy of ice nucleation for surface #5; Figure S3, free energy of ice nucleation for surface #4. Acknowledgements This work was supported by the Research Grants Council of the Hong Kong Special Administrative Region under Grant No. 16228216 and Guangdong Science and Technology Program under Grant No. 2017A050506053.


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References: 1. Atkinson, J. D.; Murray, B. J.; Woodhouse, M. T.; Whale, T. F.; Baustian, K. J.; Carslaw, K. S.; Dobbie, S.; O’Sullivan, D.; Malkin, T. L. The Importance of Feldspar for Ice Nucleation by Mineral Dust in Mixed-Phase Clouds. Nature 2013, 498, 355-358. 2. Tabazadeh, A.; Djikaev, Y. S.; Reiss, H. Surface Crystallization of Supercooled Water in Clouds. Proc. Natl. Acad. Sci. U. S. A. 2002, 99, 15873−15878. 3. Kiani, H.; Sun, D. Water Crystallization and Its Importance to Freezing of Foods: A Review. Trends Food Sci. Technol. 2011, 22, 407-426. 4. Gent, R. W.; Dart, N. P.; Cansdale, J. T. Aircraft Icing. Philos.Trans. R. Soc., A 2000, 358, 2873−2911. 5. Stone, H. A. Ice-Phobic Surfaces That are Wet. ACS Nano 2012, 6, 6536−6540. 6. Nagy, Z. K.; Braatz, R. D. Advances and New Directions in Crystallization Control. Annu. Rev. Chem. Biomol. Eng. 2012, 3, 55−75. 7. Kreder, M. J.; Alvarenga, J.; Kim, P.; Aizenberg, J. Design of Anti-Icing Surfaces: Smooth, Textured or Slippery? Nat. Rev. Mater. 2016, 1, 15003. 8. Schutzius, T. M.; Jung, S.; Maitra, T.; Eberle, P.; Antonini, C.; Stamatopoulos, C.; Poulikakos, D. Physics of Icing and Rational Design of Surfaces with Extraordinary Icephobicity. Langmuir 2015, 31, 4807−4821. 9. Kim, P.; Wong, T.-S.; Alvarenga, J.; Kreder, M. J.; AdornoMartinez, W. E.; Aizenberg, J. Liquid-Infused Nanostructured Surfaces with Extreme Anti-Ice and Anti-Frost Performance. ACS Nano 2012, 6, 6569−6577. 10. Murray, B. J.; O’Sullivan, D.; Atkinson, J. D.; Webb, M. E. Ice Nucleation by Particles Immersed in Supercooled Cloud Droplets. Chem. Soc. Rev. 2012, 41, 6519−6554.


12

Page 13 of 25 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


11. 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, 7078−7116. 12. Turnbull, D. Kinetics of Heterogeneous Nucleation. J. Chem. Phys. 1950, 18, 198. 13. Borkent, B. M.; Gekle, S.; Prosperetti, A.; Lohse, D. Nucleation Threshold and Deactivation Mechanisms of Nanoscopic Cavitation Nuclei. Phys. Fluids 2009, 21, 102003. 14. Page, A. J.; Sear, R. P. Heterogeneous Nucleation in and out of Pores. Phys. Rev. Lett. 2006, 97, 065701. 15. Hiranuma, H.; Hoffmann, N.; Kiselev, A.; Dreyer, A.; Zhang, K.; Kulkarni, G.; Koop, T.; Möhler, O. Influence of Surface Morphology on the Immersion Mode Ice Nucleation Efficiency of Hematite Particles. Atmos. Chem. Phys. 2014, 14, 2315-2324. 16. Salam, A.; Lohmann, U.; Crenna, B.; Lesins, G.; Klages, P.; Rogers, D.; Irani, R.; MacGillivray, A.; Coffin, M. Ice Nucleation Studies of Mineral Dust Particles with a New Continuous Flow Diffusion Chamber. Aerosol Sci. Technol. 2006, 40, 134-143. 17. Wang, B.; Knopf, D. A.; China, S.; Arey, B. W.; Harder, T. H.; Gilles, M. K.; Laskin, A. Direct Observation of Ice Nucleation Events on Individual Atmospheric Particles. Phys. Chem. Chem. Phys. 2016, 18, 29721-29731. 18. Kiselev, A.; Bachmann, F.; Pedevilla, P.; Cox, S. J.; Michaelides, A.; Gerthsen, D.; Leisner, T. Active Sites in Heterogeneous Ice Nucleation-the Example of K-Rich Feldspars. Science 2017, 355, 367−371. 19. Campbell, J. M.; Meldrum, F. C.; Christenson, H. K. Observing the Formation of Ice and Organic Crystals in Active Sites. Proc. Natl. Acad. Sci. U. S. A. 2017, 114, 810-815.


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20. Campbell, J. M.; Meldrum, F. C.; Christenson, H. K. Is Ice Nucleation from Supercooled Water Insensitive to Surface Roughness? J. Phys. Chem. C 2015, 119, 1164-1169. 21. Heydari, G.; Thormann, E.; Järn, M.; Tyrode, E.; Claesson, P. M. Hydrophobic Surfaces: Topography Effects on Wetting by Supercooled Water and Freezing Delay. J. Phys. Chem. C 2013,117, 21752-21762. 22. Bi, Y.; Cao, B.; Li, T. Enhanced Heterogeneous Ice Nucleation by Special Surface Geometry. Nat. Commun. 2017, 8, 15372. 23. Lupi, L.; Hudait, A.; Molinero, V. Heterogeneous Nucleation of Ice on Carbon Surfaces. J. Am. Chem. Soc. 2014, 136, 3156−3164. 24. Zhang, X. X.; Chen, M.; Fu, M. Impact of Surface Nanostructure on Ice Nucleation. J. Chem. Phys. 2014, 141, 124709. 25. Metya, A. K.; Singh, J. K.; Plathe, F. M. Ice Nucleation on Nanotextured Surfaces: The Influence of Surface Fraction, Pillar Height and Wetting States. Phys. Chem. Chem. Phys. 2016, 18, 26796-26806. 26. 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. 27. Cox, S. J.; Kathmann, S. M.; Purton, J. A.; Gillan, M. J.; Michaelides, A. Non-Hexagonal Ice at Hexagonal Surfaces: The Role of Lattice Mismatch. Phys. Chem. Chem. Phys. 2012, 14, 7944−7949. 28. Pedevilla, P.; Cox, S. J.; Slater, B.; Michaelides, A. Can Ice-Like Structures Form on Non-IceLike Substrates? The Example of the KFeldspar Microcline. J. Phys. Chem. C 2016, 120, 6704−6713.


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Page 15 of 25 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


29. van Meel, J. A.; Sear, R. P.; Frenkel, D. Design Principles for Broad-Spectrum Protein-Crystal Nucleants with Nanoscale Pits. Phys. Rev. Lett. 2010, 105, 205501. 30. Tóth, G. I.; Tegze, G.; Pusztai, T.; Gránásy, L. Heterogeneous Crystal Nucleation: The Effect of Lattice Mismatch. Phys. Rev. Lett. 2012, 108, 025502. 31. Plimpton, S. Fast Parallel Algorithms for Short-Range Molecular Dynamics. J. Comput. Phys. 1995, 117, 1−19. 32. Molinero, V.; Moore, E. B. Water Modeled as an Intermediate Element Between Carbon and Silicon. J. Phys. Chem. B 2009, 113, 4008-4016. 33. Qiu, Y.; Lupi, L.; Molinero, V. Is Water at the Graphite Interface Vapor-Like or Ice-Like? J. Phys. Chem. B 2018, 122, 3626−3634. 34. Lupi, L.; Molinero, V. Does Hydrophilicity of Carbon Particles Improve Their Ice Nucleation Ability? J. Phys. Chem. A 2014, 118, 7330−7337. 35. Cox, S. J.; Kathmann, S. M.; Slater, B.; Michaelides, A. Molecular Simulations of Heterogeneous Ice Nucleation. I. Controlling Ice Nucleation Through Surface Hydrophilicity. J. Chem. Phys. 2015, 142, 184704. 36. Cox, S. J.; Kathmann, S. M.; Slater, B.; Michaelides, A. Molecular Simulations of Heterogeneous Ice nucleation. II. Peeling Back the Layers. J. Chem. Phys. 2015, 142, 184705. 37. Lupi, L.; Hudait, A.; Peters, B.; Grünwald, M.; Mullen, R. G.; Nguyen, A. H.; Molinero, V. Role of Stacking Disorder in Ice Nucleation. Nature 2017, 551, 218−222. 38. Li, C.; Gao, X.; Li, Z. Roles of Surface Energy and Temperature in Heterogeneous Ice Nucleation. J. Phys. Chem. C 2017, 121, 11552−11559. 39. Fitzner, M.; Sosso, G. C.; Pietrucci, F.; Pipolo, S.; Michaelides, A. Pre-Critical Fluctuations and What They Disclose about Heterogeneous Crystal Nucleation. Nat. Commun. 2017, 8, 2257.


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Page 16 of 25

40. Cabriolu, R.; Li, T. Ice Nucleation on Carbon Surface Supports the Classical Theory for Heterogeneous Nucleation. Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 2015, 91, 052402. 41. Zielke, S. A.; Bertram, A. K.; Patey, G. N. Simulations of Ice Nucleation by Model AgI Disks and Plates. J. Phys. Chem. B 2016, 120, 2291−2299. 42. Wedekind, J.; Reguera, D. Kinetic Reconstruction of the Free-energy Landscape. J. Phys. Chem. B 2008, 112, 11060-11063. 43. Li, C.; Gao, X; Li, Z. Surface Energy-Mediated Multistep Pathways for Heterogeneous Ice Nucleation. J. Phys. Chem. C 2018, 122, 9474-9479. 44. Steinhardt, P. J.; Nelson, D. R.; Ronchetti, M. Bond Orientational Order in Liquids and Glasses. Phys. Rev. B: Condens. Matter Mater. Phys. 1983, 28, 784−805. 45. Li, T.; Donadio, D.; Russo, G.; Galli, G. Homogeneous Ice Nucleation from Supercooled Water. Phys. Chem. Chem. Phys. 2011, 13, 19807−19813. 46. Song, H.; Sun, Y.; Zhang, F.; Wang, C. Z.; Ho, K. M.; Mendelev, M. I. Nucleation of Stoichiometric Compounds from Liquid: Role of The Kinetic Factor. Phys. Rev. Mater. 2018, 2, 023401. 47. Kumar, P.; Buldyrev, S. V.; Starr, F. W.; Giovambattista, N.; Stanley, H. E. Thermodynamics, Structure, and Dynamics of Water Confined Between Hydrophobic Plates. Phys. Rev. E 2005, 72, 051503. 48. Röttger, K.; Endriss, A.; Ihringer, Lattice Constants and Thermal Expansion of H2O and D2O Ice Ih between 10 and 265 K. J. Acta Cryst. 1994, B50, 644-648. 49. Shen, C.; Simmons, J. P.; Wang Y. Effect of Elastic Interaction on Nucleation: I. Calculation of The Strain Energy of Nucleus Formation in an Elastically Anisotropic Crystal of Arbitrary Microstructure. Acta Mater. 2006, 54, 5617-5630.


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50. Zangi, R.; Mark, A. E. Monolayer Ice. Phys. Rev. Lett. 2003, 91, 025502. 51. Corsetti, F.; Matthews, P.; Artacho, E. Structural and Configurational Properties of Nanoconfined Monolayer Ice from First Principles. Sci. Rep. 2016, 6, 18651. 52. Zhu, Y.; Wang, F.; Bai, J.; Zeng, X.; Wu, H. Compression Limit of Two-dimensional Water Constrained in Graphene Nanocapillaries. ACS Nano 2015, 9, 12197-12204. 53. Zhu, W.; Zhu, Y.; Wang, L.; Zhu, Q.; Zhao, W.; Zhu, C.; Bai, J.; Yang, J.; Yuan, L.; Wu, H.; Zeng, X. Water Confined in Nanocapillaries: Two-Dimensional Bilayer Square Like Ice and Associated Solid–Liquid–Solid Transition J. Phys. Chem. C 2018, 122, 6704-6712.


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Figure Captions: Figure 1. Molecular dynamics simulation system.

(a) A typical system consisting of a grooved

graphene surface (gray) and a slab of water (blue). (b) Illustration of groove generation. Figure 2. Ice nucleation for various surfaces. (a) Survival probability as a function of time.

The

slope of the linear fits is used to calculate the ice nucleation rate. (b) Ice nucleation rate for groove widths. (c) Snapshots showing ice crystallization.

Ice crystals are pink and

water molecules in the liquid state are cyan. Figure 3. Ice nucleation for surfaces #6 (W6=1.723 nm). (a) MFPT. (b) Free energy. (c) Snapshots at different n values. Figure 4. Ice nucleation for narrow grooves (surfaces #2, #3, and #4). the grooves. views).

Top panels: Density distribution.

Bottom panels: Snapshots (side views).

surface #3.

(a) Layered-structures in

Middle panels: Snapshots (front (b) Free energy of ice nucleation for

The error bars represent the standard deviation of three free energy profiles

obtained from three groups of independent simulations.

The insets show the evolution

of the largest ice nucleus. Figure 5. Snapshots showing how LSs trigger ice formation for surfaces #3 (a) and #4 (b). Water inside and outside the grooves are represented by dark blue and purple spheres, respectively.

Left and right panels in (a) and (b) are side and front views.

i: Stable

solid-like LSs inside the grooves. ii: Formation of 5 membered rings. iii: Formation of topological cages. iv: Hexagonal ice crystal compatible with the topological cages. Figure 6. Effects of groove depth H.

(a) Nucleation rate for surfaces #3 and #6.

showing the states indicated in (a).

(b). Snapshots

(c). Free energy profiles at different H for the cases

in (a).


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Figure 1


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Figure 2


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Figure 3


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Figure 4


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Figure 5


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Figure 6


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TOC Graphic


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Enhancing and Impeding Heterogeneous Ice Nucleation through

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