Molecular simulations of heterogeneous ice nucleation. I. Controlling ice nucleation through surface hydrophilicity

4.6 MB·English

by  Stephen J. Cox

Molecular simulations of heterogeneous ice nucleation I: Controlling ice
nucleation through surface hydrophilicity
Stephen J. Cox,1,2 Shawn M. Kathmann,3 Ben Slater,1 and Angelos Michaelides1,2,a)
1)Thomas Young Centre and Department of Chemistry, University College London, 20 Gordon Street, London,
WC1H 0AJ, U.K.
2)London Centre for Nanotechnology, 17–19 Gordon Street, London WC1H 0AH,
U.K.
3)Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99352,
United States
(Dated: 1 June 2015)
5
1 Ice formation is one of the most common and important processes on Earth and almost always occurs at
0
the surface of a material. A basic understanding of how the physicochemical properties of a material’s
2
surface affects its ability to form ice has remained elusive. Here we use molecular dynamics simulations to

y directlyprobeheterogeneousicenucleationatanhexagonalsurfaceofananoparticleofvaryinghydrophilicity.
a Surprisingly, we find that structurally identical surfaces can both inhibit and promote ice formation and
M
analogous to a chemical catalyst, it is found that an optimal interaction between the surface and the water
exists for promoting ice nucleation. We use our microscopic understanding of the mechanism to design a
9
modified surface in silico with enhanced ice nucleating ability.
2

]
i Upon cooling, liquid water crystallizes into solid ice. transport industries and even as a potential means for
c
Due to the presence of a free energy barrier separating climate control.12,13
s
- the liquid and crystalline states, however, it is possible
l In contrast to fields such as chemical catalysis14 and
r for liquid water to remain in a metastable ‘supercooled’
t materials design,15 there is currently no comprehensive
m state to temperatures far below the equilibrium melting
set of design principles in terms of molecular ‘descrip-
temperature. Heterogeneous ice nucleation, that is, ice
.
t nucleation in the presence of impurity particles such as tors’ for making new substances to control ice forma-
a
tion. Put more simply, we do not know which are the
m mineral dust, soot or certain types of bacteria, gener-
relevant microscopic properties of a material that deter-
ally increases the rate of ice nucleation and is the domi-
d- nant process by which ice forms in nature.1 Recent work mineitsmacroscopicicenucleatingefficiency. Often,the
n hasarguedthatanyiceformationattemperaturesabove so-called ‘requirements’ for a good ice nucleating agent
o −20◦C must necessarily occur heterogeneously.2 Empir- (INA) have been discussed, such as the requirement for
c a good crystallographic match to ice and the ability of
ically, a large variance in the propensity of different ma-
[ water to chemically bond to the surface of the particle
terials to nucleate ice is observed, and due to the impor-
2 tance of ice formation in e.g. the climate sciences, much (i.e. hydrophilicity).16 Although properties such as a
v effort has been expended in identifying and cataloging good crystallographic match are important in heteroge-
9 the effectiveness of different materials to nucleate ice.1 neous nucleation of some systems,17,18 such criteria have
7 neither served as a full set of guidelines to identify good
Thishasmotivatedmanysimulationstudiesofheteroge-
8 INAs,1 nor have they aided the systematic improvement
neous ice nucleation in the presence of different surfaces,
1
0 includinggraphite,3,4kaolinite5,6andsilveriodide.7,8De- oficenucleationinhibitorsorpromoters. Experimentally
thereisdisagreementregardingtheroleofhydrophilicity.
. spite the vast amount of research into heterogeneous ice
1 For example, Alizadeh et al.19 have found ice nucleation
nucleation, majorgapsinourknowledgestillexist, espe-
0
to be slower on superhydrophobic surfaces, which they
5 ciallywithregardtoourunderstandingoftheunderlying
attribute not only to a lower contact area between the
1 chemicalphysics;thisisreflectedinourinabilitytoaccu-
: ratelypredictamaterial’sicenucleatingefficiencyandto water and the surface, but also to a larger free energy
v barrier to nucleation. In contrast, Li et al.20,21 found ice
answer seemingly simple questions such as how does hy-
i
X drophilicity affect the ice nucleation rate? Notonlyisan nucleation to be enhanced at hydrophobic modified sili-
conwafersrelativetotheirunmodifiedhydrophiliccoun-
r understanding of the chemical physics of heterogeneous
a terparts, which was attributed to a faster dynamics of
ice nucleation needed to predict the ice nucleating effi-
ciency of existing materials,9,10 but it is also paramount water at the hydrophobic interface. Recently, Lupi et al.
investigatedtheroleofhydrophiclityofgraphiticsurfaces
for the rational design of new materials to either pro-
using molecular dynamics simulation:3,4 by varying the
mote or inhibit ice nucleation. Controlling ice formation
hydrophilicity in different ways (by uniformly changing
is desirable in a variety of fields, for example, in the cry-
opreservation of cells, tissues and organs,11 the food and the interaction of water with the surface or by introduc-
ing hydrophilic species at the surface), they found that
the ice nucleating efficacy of the surface could either in-
creaseofdecrease. Also,itisfoundonkaolinite(aknown
a)Electronicmail: [email protected] hydrophilic INA) and platinum22 that the most stable
2
wateroverlayercaninhibitthegrowthofsubsequentwa-
ter layers.23,24 Furthermore, in the case of requiring a (a)
good crystallographic match, evidence for ice-like struc-
turesatsurfacesisingenerallacking25 andtherearealso
instances where materials with a good crystallographic
matchtoicearepoorINAs26,27 (wenotethatrecentsim-
ulation studies7,8 have found the unreconstructed basal
face of silver iodide to act as a template for ice). We are
therefore either faced with the prospect of relying on ex-
perimentstodeterminetheefficacyofINAsonacase-by-
case basis, or we can try and rationalize their behavior
by elucidating the underlying molecular processes that
control heterogeneous ice nucleation.
Here, in the first of a series of two articles, we present
resultsfrommoleculardynamics(MD)simulationswhere
we directly probe heterogeneous ice nucleation in the
presence of a face centered cubic (FCC) nanoparticle homogeneous bare NP modified NP
(NP). The NP exposes its hexagonal (111) surface as its
1.5
principalfacetandcanthereforeactasatemplateforthe (b)
hexagonalbasalfaceofice. WiththisNPcompletelyim-
mersed in water, shown in Fig. 1(a), we perform a series
of studies in which we systematically explore the depen- 1.0
dence of the nucleation rate on the hydrophilicity of the
)
NP. By comparing these results to reference simulations m
o Surfacemodification
h
of homogeneous nucleation we find a very interesting de- R
increasesrate
pendence of the nucleation rate on NP hydrophilicity; R/ 0.5
the NP can both promote and inhibit ice nucleation and (
0
1
exhibits a maximum nucleation rate at intermediate in- g
o
teraction strengths with the water. By examining the l
0.0
molecular level details of the nucleation processes at dif-
ferent hydrophilicities of the NP, we find that the struc-
ture in the immediate vicinity of the interface couples
strongly with the nucleation rate. We then use this un- -0.5
derstanding of the underlying chemical physics to design 0.0 0.5 1.0 1.5 2.0
an improved INA. This first article emphasizes how we E / ∆H
can use our microscopic understanding to control ice nu- ads vap
cleation. Inthesecondarticle,wediscusscertainaspects
FIG.1. (coloronline)(a)Snapshotofatypicalicenucleation
ofthemechanismingreaterdetail,aswellascontextual-
event on the NP. Ice-like molecules are colored blue and the
izingthisworkwithrespecttopreviousstudiesonsurface
NP is colored silver. The NP is totally immersed in water
hydrophilicity and ice nucleation.
(liquid-like molecules are shown by gray dots). (b) Varia-
We have used the single site mW potential to model tion of the nucleation rate with the strength of the water-
the interactions between water molecules,28 which al- NP interaction Eads. As Eads increases, so too does the hy-
drophilicity. The solid blue line indicates homogeneous nu-
lows us to investigate length- and time-scales inacces-
cleation (the dotted lines are an error estimate): data above
sible to ice nucleation simulations that employ more tra-
and below this line indicates promotion and inhibition of ice
ditional empirical potentials.5 The NP was modeled as
nucleation by the NP, respectively. It can be seen that at
an FCC crystal with a lattice constant of 0.392nm, con-
weak and strong water-NP interaction strengths the NP in-
sisting of 380 atoms. Previous work has suggested that
hibits nucleation, while at intermediate interaction strengths
such a lattice may aid in structuring water into ice-like (E /∆H ≈ 0.15–0.6), the NP strongly promotes nucle-
ads vap
arrangements.29 TheFCCNPwashemisphericalandex- ation.
posed its (111) face as its primary facet (approximately
2.5nmindiameter). FortheinteractionbetweentheNP
atoms and the water molecules, the Lennard-Jones po- ner, but also by introducing hydrophilic species at the
tentialU(r)=4(cid:15)(cid:2)(σ/r)12−(σ/r)6(cid:3)wasused,wherer is surface, and found opposite trends: we discuss the pos-
the distance between an NP atom and a water molecule. sible causes of this apparent discrepancy in more detail
The hydrophilicity of the NP was controlled by varying in our second paper.42 Interactions were truncated after
(cid:15) (a constant value of σ = 0.234nm was used through- 0.753nm. This setup yielded contact layers at a height
out). As mentioned earlier, Lupi et al.3,4 controlled the between 0.2–0.25nm above the (111) surface of the NP,
hydrophilicity of graphitic surfaces not only in this man- which is in reasonable agreement with values obtained
3
(a) optimal (b) too weak (c) too strong
FIG. 2. (color online) Sensitivity of the water structure at the surface of the NP to the water-NP interaction strength. (a) Ice
nucleationattheNPwithE /∆H ≈0.3. ThewatermoleculesincontactwiththeNP(coloredred)formanhexagonallayer
ads vap
commensuratewiththesurfacethatresemblesthebasalfaceofice. Thewatermoleculesdirectlyabovethiscontactlayer(colored
blue)alsoformasimilarhexagonalstructure. (b)ThestructureofwaterattheNPwithE /∆H ≈0.08. Thewater-surface
ads vap
interaction is too weak to stabilize an ice-like structure. (c) The structure of water at the NP with E /∆H ≈ 1.2. The
ads vap
watersurfaceinteractionistoostrongandthewatermoleculescannotrearrangeintoanice-likeconfiguration. Inboth(b)and
(c), nucleation occurs away from the surface in a homogeneous manner.
from density functional theory calculations of water at We are able to determine the ice nucleation rate R by
metal surfaces.30,31 We must emphasize, however, that fitting P (t) = exp[−(Rt)γ], where γ > 0 is also a fit-
liq
we are using simplified model surfaces in order to under- ting parameter. Further details of the fitting procedure
standpossiblegeneraltrendsthatmayunderlieheteroge- and simulation setup are provided in the Supplemental
neous ice nucleation and that one must exercise caution Material.38 In order to gauge the effectiveness of the NP
intryingtomakeone-to-onecorrespondenceswithactual as an INA, we have also studied bulk homogeneous nu-
surfaces. cleation, using identical settings.
All simulations were performed using the LAMMPS sim- Explicit simulations of heterogeneous ice nucleation
ulation package32 with 2944 mW molecules in a peri- have only recently started to emerge in the literature
odic supercell. Previous simulation studies have sug- (see e.g. Refs. 3–5, 7, 8, and 39) and to enable a system-
gestedthatthecriticalicenucleusvariesfrom∼10water atic study, we draw conclusions from over 200 success-
molecules at 180K33 to ∼85–265 at 220K34,35 giving us ful nucleation trajectories in total. Fig. 1(b) shows the
confidence that our simulations should not be subject to dependence of the nucleation rate on the water surface
seriousfinitesizeeffects. Furthermore, simulationsusing interaction, the main finding of this study. Specifically,
a slab geometry (approximate dimensions of 66˚A2) with we have plotted log (R/R ) vs E /∆H , where
10 hom ads vap
4000 mW molecules confirm that the conclusions drawn R isthebulkhomogeneousrateand∆H istheen-
hom vap
from this work are not affected by changes to the box thalpyofvaporizationofbulkmWwater(10.65kcal/mol
size and shape. For each value of the water-NP interac- at 298K).28 A rich variety in the ice nucleating behavior
tion energy, 16 MD simulations were performed at 205K is seen: the NP is seen to both promote and, surpris-
and1bar. Undertheseconditions,bulkliquidmWwater ingly, inhibit ice formation. We expect this inhibition
is still metastable (as opposed to unstable)36 but under- effect to be concentration dependent; as the NP con-
goes homogeneous nucleation on a timescale accessible centration becomes more dilute, we expect the rates to
to computer simulation such that statistically meaning- tend to that of homogeneous nucleation. At low val-
ful rates can be obtained. To detect ‘ice-like’ molecules, ues of E , the heterogeneous nucleation rate is approx-
ads
we have used the CHILL algorithm of Moore et al.37 (As imately two times lower than R . Thus when the par-
hom
the CHILL algorithm was designed for bulk homogeneous ticle is very hydrophobic, it tends to inhibit nucleation.
nucleation,itdoesnotnecessarilycapturethefullbehav- Asthewater-surfaceinteractionstrengthincreasessotoo
ior in regions of broken symmetry i.e. interfaces. Never- does the nucleation rate until it reaches a maximum at
theless, it is useful as a qualitative visual aid.) By mon- E /∆H ≈ 0.4 that is nearly 25 times faster than
ads vap
itoring the potential energy, we are able to determine bulk homogeneous nucleation. Beyond the maximum,
the induction time to nucleation for each simulation and the rate steadily decreases until E /∆H ≈1.0. Fur-
ads vap
thus the probability P (t) that a given system remains ther beyond this, the rate remains roughly constant and
liq
liquid after a time t from the start of the simulation. slightly below R .
hom
4
We now try to understand this intriguing dependence
of the nucleation rate on the hydrophilicity of the NP.
To this end, we have examined in detail the mechanisms
by which nucleation occurred on the NP for the vari-
ous interaction strengths. As the (111) surface of an
FCC crystal exhibits hexagonal symmetry, one possible
mechanism for heterogeneous ice nucleation is a tem-
plate effect whereby the molecules in the contact layer
formanhexagonalstructurecommensuratewiththesur-
face. Fig. 2(a) confirms this, where we show a typi-
cal ice nucleation event in the presence of the NP with
E /∆H ≈0.3(closetothemaximumrate). Herewe
ads vap
can clearly see that the water molecules in contact with
the(111)surfaceoftheNPdoindeedformanhexagonal
structure commensurate with the surface that resembles
the basal face of ice. We can also see that the water
molecules directly above this contact layer also form a
similarhexagonalstructure. Thesurfaceisthereforeact-
ing to promote ice nucleation by providing an arrange-
ment of adsorption sites that resemble the structure of
ice, thereby stabilizing structural fluctuations towards FIG. 3. (color online) Surface modification to promote
ice-like arrangements in the liquid. ice nucleation for strong water-NP interaction strengths
NowthatwehaveestablishedthattheNPactstopro- (Eads/∆Hvap > 1.0). By introducing small adsorbates (col-
ored yellow) at the (111) surface, the template effect can be
mote ice nucleation by acting as a template for ice, the
recovered (c.f. Fig. 2(c)). The nucleation rate is increased
dependence of the rate on E can easily be understood
ads by approximately a factor 50 compared to the bare NP for
as a competition between water-water and water-surface
E /∆H ≈1.2, as indicated in Fig. 1(b).
ads vap
interactions. In Fig. 2(b) we show the structure of wa-
ter in contact with the NP for E /∆H ≈ 0.08 (the
ads vap
weakestE investigated,whichinhibitsicenucleation).
ads
Clearly, such a weak water-surface interaction is unable
with sub-monolayer coverage i.e. not all of the available
to stabilize ice-like configurations and in fact, ice nucle-
adsorption sites are occupied by water molecules. We
ationisseentooccurawayfromthesurfaceinahomoge-
refer to these unoccupied adsorption sites on the (111)
neousmanner. WillardandChandlerhavefoundthatthe terrace as “excess” sites. For Eads/∆Hvap >∼ 0.6, these
structureoftheinterfacebetweenwaterandahydropho-
excesssitesareoccupiedforlongtimesandfornucleation
bic substrate is akin to the liquid-vapor interface;40 a re-
to occur, an area of decreased coverage at the surface
centsimulationstudyfromHaji-Akbarietal.41hasfound
must occur such that an hexagonal motif can form. This
thaticenucleationisdisfavoredattheliquid-vaporinter-
motif can then act as a template for the hexagonal basal
face. Thisappearstobeconsistentwithourobservations
face of ice (a movie showing this for E /∆H ≈ 0.9
ads vap
and with those of Lupi et al. in Ref. 3. Fig. 2(c), on the is provided38). When E > ∆H it becomes favor-
ads vap
other hand, shows the structure of water in contact with
ableforawatermoleculetooccupyasiteonthesurface,
the NP for E /∆H ≈ 1.2. While this NP also in-
ads vap including the excess sites, rather than a position in the
hibits ice nucleation, it does so for the opposite reason:
bulk liquid. This prevents the water molecules in the
the water-surface interaction is too strong, meaning that
contact layer from forming the hexagonal arrangements
the water molecules cannot rearrange to form an ice-like
requiredforicenucleationatthisNP.Bythisrationale,if
layer at the surface. It is also clear that the coverage
the density of available adsorption sites was lower, then
is higher than when ice forms at the (111) surface, as
the template effect (and the enhanced nucleation rate)
shown in Fig. 2(a) (we also show this quantitatively in
may be preserved at higher values of E . To this end,
ads
thesecondpaperinthisseries42). Forthisstronglyinter-
we have modified the (111) surface of the NP by ad-
acting scenario, we also see that ice forms away from the
sorbing small molecules, at the excess sites, which only
surfaceinahomogeneousmanner. Thisisalsoconsistent have a weak interaction with water,43 and recomputed
withtheobservationsofReinhardtandDoye39onice-like
the nucleation rate with E /∆H ≈ 1.2. As seen in
ads vap
surfaces. The observed coupling between the molecular
Fig. 3, the template effect is indeed recovered. It is also
mechanism and the ice nucleation rate as we change the
seen in Fig. 1(b) that this modified surface enhances ice
surface hydrophilicity is actually rather simple; we now
nucleation by a factor of 50 compared to the unmodified
demonstratehowwecanexploitsuchsimplicitytodesign
surface. Thisisacleardemonstrationofhowthemolecu-
a surface with improved ice nucleating efficiency.
lar insight into heterogeneous ice nucleation can be used
When an ice-like hexagonal overlayer forms at the to rationally design surfaces of different ice nucleating
(111) surface of the NP, such as in Fig. 2(a), it does so ability. Experimentally, this could be realized through
5
adsorptionofsmallmolecules tothesurface(e.g. carbon tobeconsideredwhentryingtounderstandwhatmakesa
monoxide) or through surface alloying. In fact, alloying good INA. Other properties such as the crystallographic
a platinum (111) surface with tin is observed to promote matchtoiceandtheroleofsurfacedefectsarealsolikely
theformationofanhexagonalice-likebilayerunderultra- to be important, as will more complex interactions such
high vacuum conditions,44,45 in a fashion analogous to as electrostatics and explicit hydrogen bonding. The re-
our modified surface (the tin atoms at the surface act in sults presented in this letter serve as a platform upon
part to reduce the density of adsorption sites). We also which future studies can be conducted.
notethatinoursimulations,thenucleationratecanalso Dr. Gabriele C. Sosso is thanked for sharing his data
be decreased by adsorbing small molecules such that the fromlargersimulationsinaslabgeometry. Wearegrate-
NP can no longer act as a template. ful to the London Centre for Nanotechnology and UCL
More generally, the sensitivity of the nucleation rate Research Computing for computation resources, and the
on surface hydrophilicity could be tested by e.g. using UK’snationalhighperformancecomputingservice(from
nanoparticlesofgoldorsilicafunctionalizedwithorganic which access was obtained via the UK’s Material Chem-
molecules of varying hydrophobicity. In addition to us- istry Consortium, EP/F067496). S.M.K. was supported
ingwellestablishedmethodssuchasthedropletfreezing fully by the U.S. Department of Energy, Office of Ba-
techniques,46 itmayalsobepossibletoexploitrecentad- sic Energy Sciences, Division of Chemical Sciences, Geo-
vances in femtosecond X-ray scattering techniques that sciences & Biosciences. Pacific Northwest National Lab-
haveallowedreal-timemonitoringofhomogeneousicenu- oratory (PNNL) is a multiprogram national laboratory
cleationinmicronsizedwaterdroplets.47 Notonlycould operatedforDOEbyBattelle. S.J.C.wassupportedbya
such an experimental protocol be used to compare rates studentfellowshipfundedjointlybyUCLandBES.A.M.
of ice nucleation in the presence of immersed NPs, but issupportedEuropeanResearchCouncilundertheEuro-
informationregardingtheimpactofsuchNPsonthemi- peanUnion’sSeventhFrameworkProgramme(FP/2007-
croscopic structure of the liquid should also be available. 2013) / ERC Grant Agreement number 616121 (Het-
eroIce project) and the Royal Society through a Royal
Insummary,wehaveusedcomputersimulationstosys-
Society Wolfson Research Merit Award.
tematically compare heterogeneous ice nucleation rates
in the presence of a simple model nanoparticle of vary-
inghydrophilicity. Thiscomplementsanumberofrecent
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