Roles of Surface Energy and Temperature in Heterogeneous Ice

Subscriber access provided by TRENT UNIV

Article

The Roles of Surface Energy and Temperature in Heterogeneous Ice Nucleation Chu Li, Xiang Gao, and Zhigang Li J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 10 May 2017 Downloaded from http://pubs.acs.org on May 12, 2017

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 free 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 accessible to all readers and 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.

The Journal of Physical Chemistry C 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 24

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

The Roles of Surface Energy and Temperature in Heterogeneous Ice Nucleation Chu Li, Xiang Gao, and Zhigang Li∗ Department of Mechanical and Aerospace Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

Abstract Heterogeneous ice nucleation (HIN) is strongly related to the dynamics of hydrogen bonds in water at an interface.

In this work, we investigate the microscopic kinetics of HIN through

molecular dynamics simulations.

The dynamics of hydrogen bond network (HBN) at interfaces

are studied under the coupled effects of thermal fluctuation and water-surface molecular interactions.

It is revealed that the lasting time of the HBN at the interface is critical to HIN.

Under comparable thermal and surface effects, which result in a proper lasting time of the HBN, HIN is promoted.

However, if the thermal effect or the surface effect dominates over the other,

the lasting time of the HBN at the interface would be either too long or too short, leading to the failure of HIN.

By varying the water-surface interaction strength, i.e. binding energy, and

temperature, a diagram of HIN events is presented, which shows that HIN is only favored in certain temperature and surface energy ranges.

May 2017

∗

Email: [email protected]

ACS Paragon Plus Environment

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

Page 2 of 24

Introduction Ice can form either homogeneously in bulk water or heterogeneously at the surface of a foreign material.

Heterogeneous ice nucleation (HIN) is the dominant mode of water

crystallization in nature and is of great importance in a variety of areas, such as atmospheric physics,1,2 cryobiology,3 transportation,4 and the operation of common infrastructures.5

In many

applications, a good control of ice nucleation under the influences of different factors (e.g. surface properties and temperature) is highly desired.6-11

Although HIN at the surface of different

materials has been extensively explored in the literature,12-21 the roles of various parameters in HIN are still unclear.

Previous experimental and numerical studies show that surface defects,

such as cracks and cavities,22-24 may induce HIN through increasing the local density of water molecules.

HIN can also be enhanced through surface functionalization (e.g. hydroxyl

groups).25-28

In addition, the lattice mismatch between ice and the crystalline structure of the

surface29-31 and the surface wettability greatly influence HIN.27,31,32

Unfortunately, how these

factors fundamentally affect HIN is not well understood and some of previous results are even controversial.

For instance, some work suggests that HIN can be boosted by increasing the

surface wettability.33

Other studies, however, show that there is no direct relationship between

surface wettability and ice nucleation ability.27,32

In addition, the findings about the role of

ice-surface lattice mismatch in HIN are also inconsistent.29-31,34,35

Furthermore, the temperature

effect, which is expected to be critical, and how temperature is coupled with other factors have not been systematically examined. Nevertheless, a clear picture about the kinetics of HIN requires not only the knowledge of classical thermodynamics but also a deep, microscopic understanding of ice nucleation processes at water-solid interfaces under the coupled effects of different factors.


2

Page 3 of 24

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


It is known that water molecules interact weakly through hydrogen bonds, which form an unstable hydrogen bond network (HBN)36 in the liquid state.

Under the thermal fluctuations of

water molecules, i.e. the effect of temperature, the HBN breaks and reforms constantly. makes the average lasting time of the HBN quite short in bulk water.

This

With the presence of a

foreign material (e.g. a solid surface), the water-surface intermolecular interactions could greatly affect the dynamics and the stability of the HBN, in addition to the thermal effect.

Under proper

conditions, certain temperature and water-surface interaction strength, water molecules at the interface may reorganize and form hexagonal structure, and the consequent HBN there becomes stable, leading to the formation of ice.

Therefore, the dynamics of the HBN at the interface,

under the coupled effects of water-surface interaction and temperature, fundamentally determines water crystallization, which, to our knowledge, has not been fully studied. In this work, we investigate HIN at the molecular level and probe the kinetics of ice nucleation at interfaces through molecular dynamics (MD) simulations.

Our attention is on how the

coupling of surface energy (or wettability), which is described by the water-surface molecular binding energy ε ws , and temperature T affects the stability of the HBN at the interface and consequently influences HIN. important role in ice nucleation.

It is found the lasting time of the HBN at the interface plays an To promote HIN, the lasting time needs to be proper, which can

only be achieved at a certain range of temperatures and water-surface binding energies, out of which, the lasting time of the HBN is either too long or too short and the crystallization of water is hindered.

By varying ε ws and T, a diagram for HIN events in the ε ws -T coordinates is

provided. Methods


3


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

Page 4 of 24

Molecular dynamics simulation. Molecular dynamics simulations are performed using the LAMMPS packages37 with a time step of 2 fs.

The simulation system contains a rigid surface of

hexagonal wurtzite structure and a water film of 1560 molecules sitting on the prism face of the surface, as shown in Figure 1a. 7.357 Å. molecules.

The lattice parameters for the surface are a = 4.519 Å and c =

The TIP4P/Ice water model38 is used to describe molecular interactions among water The ∠ HOH bond angle and O-H bond length in water molecules are maintained by

the SHAKE algorithm.

The Lennard-Jones potential is employed to consider non-electrostatic

forces between surface atoms and the oxygen atoms of water molecules,  σ U ij ( rij ) = 4ε ws     rij 

12 6  σ    −    , rij < rc ,   rij  

(1)

where rij is the separation between oxygen atom i and surface atom j, rc=12 Å is the cut-off distance, σ = 3.1668 Å and ε ws are the water-surface collision diameter and binding energy. The surface atoms are not charged and the surface energy or wettability are tuned by changing the value of ε ws .39,40 Simulations are performed in canonical, i.e. (N, V, T), ensembles.

In all the simulations, the

system is initially heated up to 300 K for 2 ns and then cooled down to a supercooled temperature in the following 1 ns. thermostat.

The temperature of the system is controlled by the Nosé-Hoover

The lengths of the system in the x, y and z directions are 36.2, 36.8 and 70.0 Å,

respectively and periodic boundary conditions (PBCs) are applied in all the directions.

A void

space of ~35 Å in the z direction above water is used to eliminate the unnecessary water-surface interactions caused by PBCs.

The cut-off distance for the short range Coulombic potential in the

TIP4P/Ice water model is set to be 10 Å and the Particle-Particle Particle-Mesh (PPPM) method is applied to consider long range interactions.

The simulation time ranges from 0.3 to 0.6 µs


4

Page 5 of 24

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


depending on whether ice nucleation occurs or not. Totally, more than 40 µs simulations are conducted. Bond-orientational order parameter. To differentiate ice from water, the bond-orientational order parameter41-43 q6 ( i, j ) between a pair of molecules i and j is calculated, which is given as

Y (i ) ⋅Y ( j ) ( i, j ) ≡ ∑ ∑ Y (i ) ∑ Y ( j ) 6

q6

* 6m

m =−6 6 m

m 6m

m

(2)

6m

where Y6m (i) is the spherical harmonics and Y6*m (i ) is its complex conjugate.

For molecule i

having N C nearest neighbors, the average value of q6 ( i, j ) at time t is calculated as,

q6 ( i, t ) = For bulk water molecules, N c = 4 .

1 NC

j = NC

∑ q ( i, j , t ) .

(3)

6

j =1

For water molecules at the interface, the neighboring

molecules are searched in the water layer of 4.3 Å in thickness above the surface and N c = 3 is used.

Whether a molecule is counted as an ice or water molecule depends on the value of I (i , t ) = Θ ( q6 (i , t ) − q 60 ) ⋅ Θ ( q 6 (i , t − ∆ t ) − q 60 ) ,

(4)

where Θ is the step function and q60 is a gate value.

For bulk water molecules, q60 = 0.45 ,26

while q60 = 0.4 for water molecules at the interface.

∆ t = 0.4 ps is the time step used in the

algorithm.

If I (i, t ) = 1 , molecule i is an ice molecule at time t.

If I (i, t ) = 0 , molecule i is a

water molecule. Orientation correlation function. To probe the stability of the HBN at the interface, the orientation correlation function of water molecules, Cvv(t-t0),44 is computed for different times t0. Cvv(t-t0) is defined as

r r Cvv ( t − t0 ) = δ vi (t ) ⋅ δ vi (t0 ) ⋅ψ i (t0 ) ,


(5)

5


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

Page 6 of 24

r where δ vi (t ) is the unit dipole vector of water molecule i at time t, as shown in Fig. 1b, t0 is a

reference time, ⋅

denotes the ensemble average, and ψ i (t0 ) is an indicator, which is equal to 1

or 0 depending on whether water molecule i is at the interface or not at t=t0 (the interface is defined as the layer of 4.3 Å in thickness above the surface).

The stability of HBN is related to

the decay rate of Cvv(t-t0), as will be discussed later. Results and discussion It is known that water can be cooled down to 235 K at 1 bar without freezing,45,46 which roughly offers a reference temperature for water crystallization.

For ε ws = 4.1575 kJ mol-1, at

which the water contact angle is about 25º at 300 K, ice nucleation is observed at T =230 K.

The

evolutions of the number of ice molecules based on the bond-orientational order parameter and the water potential energy are depicted in Fig. 1c.

It is seen that the potential energy remains

almost constant initially, for t < 150 ns, and significant ice crystallization is not observed. Meanwhile, incipient ice-like clusters of hexagonal structure at the interface form and break constantly, and the size of the ice clusters fluctuates, as indicated by the number change of ice molecules (blue curve) in Fig. 1c and the snapshots of the ice clusters at different times in Figs. 1d-1h and Figs. S1a-S1e (top view) in the Supporting Information.

After this “quiescent” period,

for t > 150 ns, the potential energy drops, which corresponds to the continuous growth of ice, as indicated by the number of ice molecules in Fig. 1c and snapshots in Figs. 1i-1k and S1f.

To

confirm that the potential drop is associated with ice nucleation instead of relaxation, a series of independent simulations for ε ws = 4.1575 kJ mol-1 and T = 230 K have been conducted.

As

shown in the inset of Fig. 1c, the starting time of ice formation (the time when water potential starts to drop) roughly follows the Poisson distribution, which agrees with the stochastic process of ice nucleation.


6

Page 7 of 24

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


As discussed in the introduction, the formation of ice is largely determined by the dynamics of the metastable HBN at the interface under the influences of surface and temperature.

The

dynamics of the HBN is affected by the thermal fluctuation of water molecules and the water-surface intermolecular interactions.

The thermal effect is straightforward.

At a high

temperature, the strong thermal fluctuation can break hydrogen bonds easily and the lasting time of the HBN is short, which is associated with a fast decay rate of the orientation correlation function Cvv.

The effects of the surface are two folds.

On one hand, the water-surface

interactions tend to break hydrogen bonds in water and make the HBN unstable.

On the other

hand, they can cause water molecules to reorganize at the interface through position and orientation changes, which may lead to the formation of orderly hydrogen bonds (e.g. hexagonal structure).

Whether ice nucleation occurs or not depends on the competition between the thermal

and surface effects. For the case in Fig. 1c, the thermal effect is comparable to the surface effect.

At the

beginning (constant potential part), the hydrogen bonds at the interface are unstable such that they frequently switch between “formation” and “breakdown”, as shown in Figs. 2a and 2b.

Through

the continuous breaking and formation of the HBN, water molecules adjust their orientations and reorganize at the interface.

Gradually, ice clusters with hexagonal structure form at the interface,

as indicated by the distribution of the polar and azimuthal angles, θ and φ, of the water dipole r vectors δ v in Fig. 3.

r For t < 100 ns, the directions of δ v are rather disordered.

As time

r evolves, δ v tends to assume specific directions as water molecules adjust their orientations, as

shown in Fig. 3 (155-160 ns), which correspond to a hexagonal ice structure.

In this process, the

stability or the lasting time of the HBN is critical, which can be measured by the decay rate of the orientation correlation function Cvv(t-t0) for the molecules at the interface.


As shown in Fig. 4,

7


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 decay rate of Cvv decreases with increasing time.

Page 8 of 24

This indicates that the HBN becomes more

stable as water molecules at the interface reorganize and eventually form hexagonal structures. For t0 ≥ 175 ns, the decay rate remains almost constant, which corresponds to the complete formation of ice at the interface and the further growth of ice. The ice nucleation observed in the case of Fig. 1c is the consequence of comparable thermal and surface effects.

However, if the temperature T and the water-surface binding energy ε ws

are changed, the competition between the two effects may be skewed and ice nucleation may not take place.

By varying T and ε ws , systematic studies are performed and an ice nucleation

diagram is given in the ε ws -T coordinates, as depicted in Fig. 5a, where each case represents at least three independent simulations.

The purple dots in Fig. 5a are the places HIN is observed

and the corresponding shaded area is where ice nucleation is likely to occur.

In the other areas,

HIN is not observed. Nevertheless, the diagram can roughly be divided into five regions, as shown in Fig. 5a.

In region I (purple area), the thermal and temperature effects are comparable

and the mechanism for ice nucleation is similar to the case in Fig. 1c, as explained previously. Another example in this region, εws = 4.1575 KJ mol−1 and T = 240 K, is depicted in Fig. S2. In region II, the temperature is low and the thermal effect is relatively weak compared with the surface effect.

As water molecules at the interface form HBN due to the water-surface

interactions, the thermal fluctuation is insufficient and cannot effectively break the HBN to allow hydrogen bonds to reorganize and form hexagonal structures. decay rate of Cvv as time evolves, as shown in Fig. 6a.

This is confirmed by the slow

As a result, the stable while irregular

structure (Fig. 5b) of the interfacial layer, which produces large free energy barrier for HIN,47,48 is incapable of triggering the growth of hexagonal ice, as indicated by the orientation distribution of interfacial molecules in Fig. 7a.

In region III, however, the thermal effect is strong and can


8

Page 9 of 24

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


easily break the HBN at the interface, reducing the stability of the HBN, as indicated by the fast decay of Cvv in Fig. 6b.

In this case, water molecules at the interface are very dynamic, which

makes it difficult to form ice, as indicated by the random water structure at the interface in Fig. 5c and the water orientation distribution in Fig. 7b. In region IV, the temperature is intermediate while the water-surface interaction is weak compared with the thermal effect.

The surface attraction is not strong enough to capture and

stabilize water molecules at the interface, as shown by the fast decay of Cvv in Fig. 6c. region III, the HBN is unstable and is unable to form ice (Figs. 5d and 7c).

Similar to

In region V, the

surface effect dominates and exerts strong constraints to water molecules at the interface.

Water

molecules cannot move freely and the HBN is stable once it forms, as suggested by Cvv in Fig. 6d, where the decay rate of Cvv slows down with increasing time.

Similar to region II, the stable

HBN leads to the formation of mixed structures, which does not favor the formation of hexagonal ice,47,48 as shown in Fig. 5e and Fig. 7d.

In this region, the density of water at the interface is

about 15% higher than that of hexagonal ice, which impedes ice formation.47,48 As the dynamics of HBN is essential to HIN, comparative simulations for ε ws = 4.1575 kJ mol-1 are also conducted using a coarse-grained water model (mW model18,27), for which ice forms immediately (< 1 ns) after the temperature is reduced to a supercooled temperature (T < 265 K). The nucleation rate for the mW model is several orders of magnitude higher than that obtained using the TIP4P/Ice model.

The latter agrees well with experimental results.

The discrepancy

between the TIP4P/Ice and mW models might be caused by the dynamics of HBN, which cannot be caught by the mW model.

Recently, it was reported that the flexibility of the surface might

affect the process of ice nucleation21,49,50.

We have performed simulations by introducing

flexibility into the surface using a harmonic potential, which is characterized with a spring


9


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

constant of 416 KJ mol-1 Å-2. Fig. 1c is observed.

Page 10 of 24

For ε ws = 4.1575 kJ mol-1, and T = 230 K, HIN similar to that in

The variation of water potential is shown in Fig. S3.

The starting time of

HIN appears to be different from the rigid surface case, but the flexibility of the surface generally does not affect the process of HIN.

Detailed analysis of the effects of surface flexibility requires

extensive investigation, which is beyond the scope of the current work. Conclusions In summary, we have studied HIN through MD simulations.

The dynamics of the HBN of

water under the coupled effects of thermal fluctuation and water-surface molecular interaction determines the crystallization of water at the interface.

Ice nucleation is only observed when the

thermal effect is comparable to the surface effect, which favors the formation of hexagonal structures as the HBN at the interface dynamically reorganizes.

Otherwise, the HBN would be

either too volatile or too stable to trigger ice nucleation. Supporting Information Figure S1, snapshots (top view) of ice clusters at the interface; Figure S2, kinetics of ice nucleation for εws = 4.1575 KJ mol−1 and T = 240 K; Figure S3, an example for flexible surface ( εws = 4.1575 KJ mol−1 and T = 230 K). Acknowledgements This work was supported by the Research Grants Council of the Hong Kong Special Administrative Region under Grant No. 16228216.

C.L. was partly supported by a Postgraduate

Scholarship through the Energy Program at HKUST. Competing financial interests The authors declare no competing financial interests.


10

Page 11 of 24

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


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. Pandey, R. et al. Ice-Nucleating Bacteria Control the Order and Dynamics of Interfacial Water. Sci. Adv. 2016, 2, e1501630. 4. Gent, R. W.; Dart, N. P.; Cansdale, J. T. Aircraft Icing. Phil. Trans. R. Soc. Lond. 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. Kiani, H.; Sun, D. Water Crystallization and Its Importance to Freezing of Foods: A Review. Trends Food Sci. Technol. 2011, 22, 407-426. 8. Kreder, M. J.; Alvarenga, J.; Kim, P.; Aizenberg, J. Design of Anti-Icing Surfaces: Smooth, Textured or Slippery? Nat. Rev. Mater. 2016, 1, 15003. 9. 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. Langmiur 2015, 31, 4807-4821. 10. Ehre, D.; Lavert, E.; Lahav, M.; Lubomirsky, I. Water Freezes Differently on Positively and Negatively Charged Surfaces of Pyroelectric Materials. Science 2010, 327, 672-675. 11. Kim, P.; Wong, T.; Alvarenga, J.; Kreder, M. J.; Adorno-Martinez, W. E.; Aizenberg, J. Liquid-Infused Nanostructured Surfaces with Extreme Anti-Ice and Anti-Frost Performance. ACS Nano 2012, 6, 6569-6577. 12. Freedman, M. A. Potential Sites for Ice Nucleation on Aluminosilicate Clay Minerals and Related Materials. J. Phys. Chem. Letts. 2015, 6, 3850-3858. 13. 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.


11


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

Page 12 of 24

14. 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. 15. Cabriolu, R.; Li, T. Ice Nucleation on Carbon Surface Supports the Classical Theory for Heterogeneous Nucleation. Phys. Rev. E 2015, 91, 052402. 16. Fraux, G.; Doye, J. P. K. Note: Heterogeneous Ice Nucleation on Silver-Iodide-Like Surfaces. J. Chem. Phys. 2014, 141, 216101. 17. Zielke, S. A.; Bertram, A. K.; Patey, G. N. A Molecular Mechanism of Ice Nucleation on Model AgI Surfaces. J. Phys. Chem. B 2015, 119, 9049-9055. 18. Lupi, L.; Hudait, A.; Molinero, V. Heterogeneous Nucleation of Ice on Carbon Surfaces. J. Am. Chem. Soc. 2014, 136, 3156-3164. 19. Glatz, B.; Sarupria, S. The Surface Charge Distribution Affects the Ice Nucleating Efficiency of Silver Iodide. J. Chem. Phys. 2016, 145, 211924. 20. 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. 21. Zielke, S. A.; Bertram, A. K.; Patey, G. N. Simulations of Ice Nucleation by Kaolinite (001) with Rigid and Flexible Surfaces. J. Phys. Chem. B 2016, 120, 1726-1734. 22. Marcolli, C. Deposition Nucleation Viewed as Homogeneous or Immersion Freezing in Pores and Cavities. Atmos. Chem. Phys. 2014, 14, 2071-2104. 23. Christenson, H. K. Two-Step Crystal Nucleation via Capillary Condensation. CrystEngComm 2013, 15, 2030. 24. 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. 25. Croteau, T.; Bertram, A. K.; Patey, G. N. Simulation of Water Adsorption on Kaolinite under Atmospheric Conditions. J. Phy. Chem. A 2009, 113, 7826-7833. 26. Sosso, G. C.; Li, T.; Donadio, D.; Tribello, G. A.; Michaelides, A. Microscopic Mechanism and Kinetics of Ice Formation at Complex Interfaces: Zooming in on Kaolinite. J. Phys. Chem. Lett. 2016, 7, 2350-2355. 27. Lupi. L.; Molinero, V. Does Hydrophilicity of Carbon Particles Improve Their Ice Nucleation Ability? J. Phys. Chems. A 2014, 118, 7330-7337.


12

Page 13 of 24

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


28. Hu, X. L.; Michaelides, A. Ice Formation on Kaolinite: Lattice Match or Amphoterism? Surf. Sci. 2007, 601, 5378-5381. 29. Turnbull, D.; Vonnegut, B. Nucleaton Catalysis. Ind. Eng. Chem. 1952, 44, 1292-1298. 30. Caslavsky, J. L.; Vedam, K. Epitaxial Growth of Ice Crystals on the Muscovite Cleavage Plane and Their Relation to Partial Dislocations. J. App. Phys. 1971, 42, 516. 31. 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. 32. Bi, Y.; Cabriolu, R.; Li, T. Heterogeneous Ice Nucleation Controlled by the Coupling of Surface Crystallinity and Surface Hydrophilicity. J. Phys. Chem. C 2016, 120, 1507-1514. 33. Gorbunov, B.; Baklanov, A; Kakutkina, N.; Windsor, H. L.; Toumi, R. Ice Nucleation on Soot Particles. J. Aerosol Sci. 2001, 32, 199-215. 34. Pedevilla, P.; Cox, S. J.; Slater, B.; Michaelides, A. Can Ice-Like Structures Form on Non-Ice-Like Substrates? The Example of the K-Feldspar Microcline. J. Phys. Chem. C 2016, 120, 6704-6713. 35. 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. 36. Luzar, A.; Chandler, D. Hydrogen-Bond Kinetics in Liquid Water. Nature 1996, 379, 55-57. 37. Plimpton, S. Fast Parallel Algorithms for Short-Range Molecular Dynamics. J. Comp. Phys. 1995, 117, 1-19. 38. Abascal, J. L. F.; Sanz, E.; Fernández, R. G.; Vega, C. A Potential Model for the Study of Ices and Amorphous Water: TIP4P/Ice. J. Chem. Phys. 2005, 122, 234511. 39. Li, C.; Huang, J.; Li, Z. A Relation for Nanodroplet Diffusion on Smooth Surfaces. Sci. Rep. 2016, 6, 26488. 40. Gao, X.; Zhao, T.; Li, Z. Controlling Flow Direction in Nanochannels by Electric Field Strength. Phys. Rev. E 2015, 92, 023017. 41. Steinhardt, P. J.; Nelson, D. R.; Ronchetti, M. Bond-Orientational Order in Liquids and Glasses. Phys. Rev. B 1983, 28, 784-805. 42. Gianetti, M. M.; Haji-Akbari, A.; Longinotti, M. P.; Debenedetti, P. G. Computational Investigation of Structure, Dynamics and Nucleation Kinetics of a Family of Modified


13


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

Page 14 of 24

Stillinger-Weber Model Fluids in Bulk and Free-Standing Thin Films. Phys. Chem. Chem. Phys. 2016, 18, 4102. 43. 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, 4124-4134. 44. Limmer, D. T.; Willard, A. P.; Madden, P.; Chandler, D. Hydration of Metal Surfaces Can Be Dynamically Heterogeneous and Hydrophobic. Proc. Natl. Acad. Sci. U. S. A. 2013, 110, 4200-4205. 45. Rosenfeld, D.; Woodley, W. L. Deep Convective Clouds with Sustained Supercooled Liquid Water down to -37.5 ºC. Nature 2000, 405,440-442. 46. Mishima, O.; Stanley, H. E. The Relationship between Liquid, Supercooled and Glassy Water. Nature 1998, 396, 329-335. 47. Espinosa, J. R.; Vega, C.; Sanz, E. Ice-Water Interfacial Free Energy for the TIP4P, TIP4P/2005, TIP4P/Ice, and mW Models as Obtained from the Mold Integration Technique. J. Phys. Chem. C 2016, 120, 8068-8075. 48. Espinosa, J. R.; Zaragoza, A.; Rosales-Pelaez, P.; Navarro, C.; Valeriani, C.; Vega, C.; Sanz, E. Interfacial Free Energy as the Key to the Pressure-Induced Deceleration of Ice Nucleation. Phys. Rev. Letts. 2016, 117, 135702. 49. Sosso, G. C.; Tribello, G. A.; Zen, A.; Pedevilla, P.; Michaelides, A. Ice Formation on Kaolinite: Insights from Molecular Dynamics Simulations. J. Chem. Phys. 2016, 145, 211927. 50. Qiu, Y.; Odendahl, N.; Hudait, A.; Mason, R.; Bertram, A. K.; Paesani, F.; DeMott, P. J.; Molinero, V. Ice Nucleation Efficiency of Hydroxylated Organic Surfaces Is Controlled by Their Structural Fluctuations and Mismatch to Ice. J. Am. Chem. Soc. 2017, 139, 3052-3064.


14

Page 15 of 24

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 Captions: Figure 1. Simulation system and a case of ice nucleation. a. A snapshot of a MD simulation system.

Surface, oxygen, and hydrogen atoms are represented by grey, purple, and r green spheres, respectively. b. Illustration of the dipole vector δ v of a water molecule.

c. Time variation of water potential energy and the number of ice

molecules (the inset shows the distribution of the starting time of ice nucleation). d-k. Snapshots showing the evolution of ice clusters at different times (ice molecules are denoted by purple spheres and hydrogen bonds in water are represented by pink dash lines). Figure 2. Snapshots illustrating the dynamics of hydrogen bonds, which break and form continuously (gray and green spheres represent surface and hydrogen atoms, respectively.

Oxygen atoms are purple/pink if they belong to water/ice molecules).

b is 0.08 ps after a.

Hydrogen bonds are denoted by pink dash lines. Red arrows

show the places where hydrogen bonds form after 0.08 ps, while blue arrows indicate the locations of broken hydrogen bonds. Figure 3. Orientation distribution of water molecules at the interface during different periods of time for ε ws = 4.1575 kJ mol-1 and T=230 K. r angles of δ v ).

(θ and φ are the polar and azimuthal

Figure 4. Orientation correlation function of interfacial water molecules for ε ws = 4.1575 kJ mol-1 and T=230 K at different t0. Figure 5. Surface and temperature effects on HIN. a. Diagram of ice nucleation in the ε ws -T coordinates. b-e. Interfacial water structures in different regions of the diagram at t=250 ns (b: ε ws = 4.1575 kJ mol-1 and T=225 K in region II; c: ε ws = 4.1575 kJ mol-1 and T=250 K in region III; d: ε ws = 2.4945 kJ mol-1 and T=230 K in region IV; and e: ε ws = 5.8205 kJ mol-1 and T=230 K region V).


15


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

Page 16 of 24

Figure 6. Orientation correlation function of interfacial water molecules at different water-surface binding energies and temperatures, where ice nucleation is not observed. a. ε ws = 4.1575 kJ mol-1 and T=225 K.

b. ε ws = 4.1575 kJ mol-1 and T=250 K.

c.

ε ws = 2.4945 kJ mol-1 and T=230 K. d. ε ws = 5.8205 kJ mol-1 and T=230 K. Figure 7. Orientation distribution of interfacial water molecules for the cases in Fig. 6. a.

ε ws = 4.1575 kJ mol-1 and T=225 K. b. ε ws = 4.1575 kJ mol-1 and T=250 K. c. ε ws = 2.4945 kJ mol-1 and T=230 K. d. ε ws = 5.8205 kJ mol-1 and T=230 K.


16

Page 17 of 24


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


17


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

Page 18 of 24

Figure 2


18

Page 19 of 24


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

Figure3


19


1.0

0.8

0.6

Cv v(t-t0)

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

Page 20 of 24

0.4

t0 = 15 ns t0 = 55 ns t0 = 95 ns t0 =115 ns t0 =135 ns

0.2

0.0

0

2

t0 t0 =155 ns t0 =175 ns t0 =215 ns 4

6

8

10

t-t0 (ns)

Figure 4


20

Page 21 of 24

aaaa

7.4835

6.6520

V

III

5.8205

εws (kJ mol-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


II 4.9890

I 4.1575

3.3260

2.4945

IV 1.6630 215

220

225

230

235

240

245

250

255

260

265

T (K)

Figure 5


21


1.0

1.0

b

a

t0= 45 ns t0= 85 ns

0.8

t0= 145 ns

0.8

Cvv(t-t0)

t0= 185 ns 0.6

t0= 225 ns

0.4

t0= 25 ns

t0= 305 ns

t0= 65 ns

t0= 385 ns

t0= 125 ns

0.6

0.4

t0

t0= 165 ns 0.2

0.2

t0= 225 ns t0= 265 ns t0= 305 ns

0.0

1.0

c

0.0 1.0

d

t0= 25 ns t0= 85 ns

0.8

0.8

t0= 145 ns t0= 205 ns

Cvv(t-t0)

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

Page 22 of 24

t0= 265 ns

0.6

0.6

0.4

0.4 t0= 25 ns

0.2

0.0

0

2

4

6

8

10 0

t0= 65 ns

t0= 265 ns

t0= 105 ns

t0= 305 ns

t0= 225 ns

t0= 325 ns

2

t-t0(ns)

4

6

t0 0.2

8

0.0 10

t-t0(ns)

Figure 6


22

Page 23 of 24


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 7


23


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

Page 24 of 24

TOC Graphic


24

Roles of Surface Energy and Temperature in Heterogeneous Ice

Recommend Documents