Homogeneous Nucleation of Ice in Transiently-Heated, Supercooled

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Homogeneous Nucleation of Ice in TransientlyHeated, Supercooled Liquid Water Films Yuntao Xu, Nikolay G Petrik, R. Scott Smith, Bruce D. Kay, and Greg A Kimmel J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.7b02685 • Publication Date (Web): 10 Nov 2017 Downloaded from http://pubs.acs.org on November 13, 2017

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The Journal of Physical Chemistry Letters

Homogeneous Nucleation of Ice in Transiently-Heated, Supercooled Liquid Water Films

Yuntao Xu1, Nikolay G. Petrik, R. Scott Smith, Bruce D. Kay* and Greg A. Kimmel* Chemical and Materials Sciences Division, Pacific Northwest National Laboratory, P.O. Box 999, Richland, Washington 99352

1

Current address: University of California Davis, Dept. of Chemistry

*Corresponding authors. Email addresses: [email protected] , and [email protected].

1 ACS Paragon Plus Environment


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Abstract We have investigated the nucleation and growth of crystalline ice in 0.24 µm thick, supercooled water films adsorbed on Pt(111). The films were transiently heated with ~10 ns infrared laser pulses, which produced typical heating and cooling rates of ~109 – 1010 K/s. The crystallization of these water films was monitored with infrared spectroscopy. The experimental conditions were chosen to suppress ice nucleation at both the water/metal and water/vacuum interfaces. Furthermore, internal pressure increases due to curvature effects are precluded in these flat films. Therefore, the experiments were sensitive to the homogeneous ice nucleation rate from ~210 K to 225 K. The experiments show that Jmax, the maximum for the homogeneous ice nucleation rate, J(T), needs to be ≥ 1026 m-3s-1 and is likely to be ~1029±2 m-3s-1. We argue that such large nucleation rates are consistent with experiments on hyperquenched glassy water, which typically have crystalline fractions of ~1% or more.

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Ice nucleation in supercooled liquid water is one of the most common and important processes occurring on Earth.1-3 However, our understanding of fundamental aspects of ice nucleation, such as the maximum rate of nucleation, the temperature at which this maximum occurs, and the size and initial morphology of the ice nuclei, is still incomplete.4-12 Developing a detailed understanding of ice nucleation is impeded by the existence of “no man’s land,” the temperature range from approximately 160 to 230 K in which spontaneous crystallization occurs too fast for most experimental techniques.13,14 It is also challenging for molecular dynamics simulations to study ice nucleation due to the low probabilities for forming ice nuclei and the large number of possible configurations.4,7,9,15 The homogeneous ice nucleation rate exhibits a maximum versus temperature, Jmax, somewhere between ~160 and 230 K.15-17 The maximum arises from the interplay of the thermodynamic and kinetic aspects of crystallization: At temperatures near the melting point, diffusion is fast but the thermodynamic driving force for crystallization is small resulting in a large energetic barrier that makes homogeneous nucleation extremely unlikely. In contrast, near the glass transition temperature (which is ~136 K for water13), the thermodynamic driving force is large but diffusion is too slow to allow the rapid formation of ice nuclei. Jmax occurs where the energy barrier is reduced from its large value near the melting point, but diffusion is still fast enough that the system is not kinetically hindered. Experimentally, there are two directions to enter into supercooled water’s “no man’s land”: One is by cooling water down below the melting point,18-22 and the other is by heating amorphous solid water (ASW) from cryogenic temperatures to above ~ 150 K.23-27 Many experiments have used micron-size water droplets to investigate ice nucleation.17,28-32 For these experiments, the lowest temperatures achieved are typically ~234 K, and determining the temperature of the rapidly-cooled drops is the most important factor.32 To achieve even lower temperatures, crystallization in nanometer-size liquid droplets and confined liquid samples has been investigated.18,33-35

However, interface effects and/or the internal

Laplace pressure associated with nanometer-size droplets and confined liquid samples makes it arguable whether the properties measured in those cases are still pertinent to bulk water.36 Very recently,



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Laksmono et al.17 reported the homogeneous ice nucleation rate in micron-sized droplets down to 227 K and proposed an upper-limit for Jmax of ~ 1022 m-3s-1. We have developed a technique for rapidly heating and cooling thin water films adsorbed on metal substrates in ultrahigh vacuum using ~10 ns duration laser pulses.37 With this approach, heating (cooling) rates for the water films of ~1010 (109) K/s can be obtained. Starting from cryogenic temperatures where kinetic processes are inhibited, the high heating and cooling rates allow the water films to be heated to higher temperatures where they evolve for ~10 ns before quenching back to cryogenic temperatures. After pulsed heating, the films are interrogated with infrared reflectionabsorption spectroscopy (IRAS) and other surface science techniques. This approach has been used to measure the growth rate of crystalline ice (CI) and the self-diffusion in liquid water from ~180 K to 262 K,38 and the wetting of nanoscale water droplets on Pt(111).39 Here, we investigate the nucleation and growth of crystalline ice in transiently-heated water films that are 0.24 µm thick. By varying the temperature distributions within these films, it is possible to control the location within the films where the ice nucleates and grows. In particular, it is possible to suppress nucleation at the water/metal and water/vacuum interfaces and thus measure the homogeneous nucleation rate in the water films. The experiments show that the minimum time to crystallize the supercooled water is ~200 ns and that a maximum nucleation rate, Jmax , of ~1029±2 m-3s-1 is consistent with the observations. The results also suggest that heterogeneous nucleation at the water/Pt(111) interface does not contribute significantly to ice nucleation at temperatures near where the nucleation rate is maximized.


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Figure 1. a) Schematic of ice nucleation in transiently-heated water films. The metal substrate is heated with a nanosecond laser pulse such that the maximum temperature at the water/metal interface, Tmax(0), is high enough that CI cannot form there, while the low temperatures at the water/vacuum interface prevent significant growth of CI there. Thus, the observed crystallization is due to homogeneous nucleation and growth of ice within the water film. b) Calculated temperature versus height and time, T(z,t), within a 240 nm thick water film. c) Tmax(z) for the calculation in b).

The experimental design is shown in Figure 1. A pulsed laser was used to heat a metal substrate onto which water films were adsorbed at cryogenic temperatures. For water films that were sufficiently thick, the maximum temperature obtained during the heating pulse, Tmax(z), was a strong function of the



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distance, z, from the metal substrate. As a result, experiments could be performed in which ice nucleation at the water/metal interface did not occur because it was too hot (e.g. Tmax(0) > 273 K), while crystallization also did not occur at the water/vacuum interface because it was too cold. In that case, the nucleation and growth of CI must be occurring within the “bulk” regions of the film (Fig. 1a). For example, Figure 1b shows the calculated temperature versus height and time, T(z,t), within a transientlyheated, 240 nm thick water film where Tmax(z) was above the melting point for z < 14 nm, and Tmax(z) was less than 180 K for z > 100 nm (see Figures 1b and 1c). T(z,t) was calculated by solving the one dimensional heat transfer equations for the metal with the adsorbed water film. Details of the calculations have been described previously.37,38 To perform the experiments, water films were deposited on Pt(111) at 90 K and then repeatedly heated with nanosecond infrared (IR) pulses from a Nd:YAG laser. As the number of pulses, Np, increased, CI nucleated and grew within the water films. Because the IR spectra of ASW and CI are distinct,37,38,40 the crystallization kinetics of the water films can be monitored with IRAS. Note that the IR spectra were obtained at 90 K when the laser beam was blocked and thus did not probe the state of the film while it was hot. To investigate the nucleation of ice at different heights within the water films, layered films of pure H2O and H2O labelled with 10% HOD were used. We will refer to the 10% HOD layers as “isolated HOD” layers. The pulsed-heating system has been described previously (see Supporting Information, Text S1).37


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Figure 2. IR spectra of transiently-heated water films with Tmax(0) = 310 K. Crystallization of 240 nm thick water films with a 30 nm thick layer of 10% HOD located from (a) 30 – 60 nm or (b) 150 – 180 nm above the metal substrate, was followed using IRAS in the OD-stretch region. The blue, red and black lines show IR spectra for 1 ≤ Np ≤ 80, 100 ≤ Np ≤ 300, and 400 ≤ Np ≤ 2000, respectively. a) Crystallization was readily observed in an HOD layer (initially) located 30 – 60 nm from the metal substrate, where Tmax(z) varies between ~235 K and 200 K. b) Negligible crystallization was observed in an HOD layer located 150 – 180 nm from the substrate where Tmax(z) was always less than 170 K.

Figure 2a shows IR spectra in the OD-stretch region for a transiently-heated film with a 30 nm thick, isolated HOD layer initially located 30 – 60 nm from the Pt(111) surface (Fig. 2a, schematic). Because the laser power was chosen to match the calculations shown in Figure 1, the maximum nucleation rate is expected to occur within the region where the isolated HOD layer is initially located. For Np ≤ 80, only minor changes are seen (Fig. 2a, blue lines). For 100 ≤ Np ≤ 300, the region with the HOD rapidly crystallizes (Fig. 2a, red lines) with only minor changes evident upon further heating (Fig. 2a, black lines, Np = 400 - 2000). The crystallization of the entire film can also be monitored by following 7 ACS Paragon Plus Environment


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the changes in the OH-stretch region (see Fig. S1). With the same experimental conditions and the isolated HOD layer located in the colder outer regions of the film, e.g. 150 – 180 nm from the Pt(111), negligible crystallization was observed (Figure 2b). The isotopically-layered films demonstrate that ice nucleation at the water/vacuum interface is not important for thick, transiently-heated water films (Fig. 2b). Note however that diffusion in the films progressively spreads the isolated HOD layer during the pulsed heating. For the colder, outer portions of the film, the diffusive mixing is slow and the initial isotopic layering remains largely in place. In contrast, diffusive mixing is quite rapid near the water/metal interface where the temperatures are higher. As a result, isotopically-layered ASW films cannot be used to demonstrate the lack of nucleation at that interface. However, a different experiment demonstrates that crystallization at the water/metal interface is not responsible for the results shown in Figure 2. For this experiment, a 7 nm thick CI layer, labelled with 10% isolated HOD, was grown directly on the Pt(111) by dosing at 140 K and then capped with a 233 nm thick amorphous H2O layer (dosed at 90 K) (see Fig. 3a). The film was then heated such that Tmax(0) = 310 K. The IR spectra show that the first heat pulse melts the CI layer next to the metal substrate (Fig. 3b) and the subsequent crystallization kinetics (Fig. 3c) are essentially indistinguishable from the case where the initial film had no crystalline ice layer (Fig. 2a). If the pre-existing ice crystallites at the water/Pt interface had survived, a thick crystalline ice layer would have rapidly formed without any induction period, in contrast to the observations.


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Figure 3. IR spectra for a transiently-heated water film. A 7 nm thick crystalline ice film with 10% HOD was grown on Pt(111), capped with 233 nm of amorphous H2O and then heated such that Tmax(0) = 310 K. a) Schematic. b) IR spectra in the OD-stretch region of the as-grown CI + ASW film (black line) and the same film after a single laser pulse (blue line). The CI layer, which was in contact with the metal substrate, has completely melted after a single pulse due to the high maximum temperature at the water/metal interface. c) The blue, red and black lines show IR spectra for 2 ≤ Np ≤ 80, 100 ≤ Np ≤ 300 and 400 ≤ Np ≤ 2000, respectively. As the number of heat pulses increases, the HOD diffuses into the cooler regions of the film where crystallization occurs. For Np > 1, the crystallization kinetics are very similar to the results shown in Fig. 2.



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The results shown in Figures 2 and 3 provide strong evidence that nucleation of CI at the interfaces is not important in the transiently-heated films when Tmax(0) > 273 K or when Tmax is less than 170 K at the water/vacuum interface. Therefore, the observed nucleation and growth of crystalline ice is occurring in the interior of these films. Because these films are flat, curvature effects, which lead to higher internal pressures in nanoscale water droplets, are not important here. Therefore, these experiments are probing the homogeneous nucleation of ice in supercooled water at low pressures. The amount of CI in the transiently-heated films can be determined from an analysis of the IR spectra (Supporting Information, Text S2).38,41 Figure 4a (black circles) shows the fraction of crystalline ice, fCI, versus Np for the experiments with Tmax(0) = 310 K (see Figs. 2 and S1). For Np ≤ 80, fCI is approximately 0. For 80 < Np < 300, fCI rapidly increases to ~0.4 and then slowly increases thereafter. The rapid increase in fCI occurs as ice nucleates and grows within the water film. The growing crystallites eventually coalesce to form a layer of CI embedded within the water film (see Fig. S2). This CI layer grows towards the Pt(111) until that water/ice interface reaches a kinetic steady state, which occurs when the amount of melting near Tmax(z) just offsets the amount of ice growth occurring during the beginning and end of each heat pulse when T(z,t) is less than 273 K. On the side of the ice layer that is further away from the substrate, T(z,t) is always less than 273 K and the ice front grows with each heat pulse. This leads to the slow, approximately linear increase in fCI observed for Np > 250 in Figure 4a (see also Fig. S3). As the thickness of the embedded ice layer increases, it samples regions where the temperature is lower and hence the CI growth rate also slows.


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Figure 4. Fraction crystallized, fCI, versus the number of heat pulses, Np, for transiently-heated water films determined from the OH-stretch region of the IR spectra. a) Experiment with Tmax(0) = 310 K (black ~ circles) and simulations assuming J = constant for several different values (solid lines). b) & c) Experiments with Tmax(0) = 310 K (black circles), 238 K (blue diamonds), and 220 K (green triangles). Simulations including temperature-dependent nucleation (solid lines) reproduce the observed kinetics for all three experiments to within a multiplicative constant (dotted lines).



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Similar experiments, but with lower laser pulse energies and thus lower temperatures throughout the adsorbed films, produced qualitatively similar results (see Figures 4b and c). At lower overall temperatures, the amount of the film that readily crystallizes is less due to the lower ice growth rates. In addition, the number of heat pulses required for crystallization increases as the temperature decreases. However, the kinetics are qualitatively similar for all three cases. It is important to note that for these experiments, nucleation of ice at the water/platinum interface could potentially be important since the temperature never goes above the melting point anywhere within those films.42 However, if heterogeneous nucleation at the water/metal interface was facile compared to the bulk, one might expect the time to crystallize would decrease. Instead, the time to crystallize increases as the temperature decreases. The longer time to crystallize is primarily due to the lower growth rate for CI at lower temperatures and is probably not strongly affected by heterogeneous nucleation. At even lower temperatures (e.g. Tmax(0) ~205 K), the CI growth rate becomes sufficiently slow that the amount of crystallization remains low even though appreciable nucleation maybe still be occurring. In that case, it is difficult to assess the nucleation rate with this experimental approach. The results shown in Figure 4 can be used to determine the homogeneous nucleation rate of ice in supercooled water. Because of the complicated spatial and temporal variations in the temperature within the transiently-heated water films (see Figs. 1b and 1c), the analysis of the crystallization kinetics must include a number of factors that will be discussed in detail below. However it is important to note that for the results shown in Figure 4a, Tmax(z) spans such a wide range of temperatures (i.e. 170 K ≤ Tmax(z) ≤ 310 K), that the temperature corresponding to Jmax must occur at some height within the film on each heat pulse. As a result, one of the most important pieces of information from these experiments – an estimate for Jmax in supercooled water – can be extracted fairly easily. We will first present this estimate for Jmax, and then describe the factors needed to develop a more quantitative determination of the nucleation rate versus temperature based on a Monte Carlo simulation of the nucleation and growth of CI in the transiently-heated water films.


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Crystallization kinetics such as those shown in Figure 4 typically arise when there is an energetic barrier to the nucleation of a new phase. The kinetics of these transformations were described by Avrami, Kolmogorov, Mehl and Johnson.43-46 For isothermal nucleation and growth of a new phase, the fraction of the

material

transformed

versus

time,

f(t),

at

a

constant

temperature

is

given

by

f (t ) = 1 − exp(−πJG3t 4 / 3) , where J(T) is the volume nucleation rate for the new phase and G(T) is its growth rate. For homogeneous nucleation, J(T) is the number of nuclei formed per unit volume per unit time. If Tmax did not depend on height in a transiently-heated film, then the corresponding equation would be

~~ 4 f ( N p ) = α{1 − exp(−πJ G 3 N p / 3)}

(1)

~ ~ where J is the number of crystalline nuclei formed per unit volume per heat pulse, G is the distance an ice/water interface advances per heat pulse, and α is a factor (≤ 1) included here to account for the fact

~ ~ that the entire film does not crystallize for the current experiments (see Figs. S2 and S3). J and G are both given by the integrals of the rates, J(T) and G(T), over the heat pulse at that height:

~ J (Tmax ( z )) =

∫ J (T ( z, t ))dt .

(2a)

∫ G(T ( z, t ))dt

(2b)

pulse

~ G(Tmax ( z )) =

pulse

~ ~ As indicated in Equation 2, both J and G depend on z through T(z,t). As discussed in more detail below, the height-dependent temperature profile, T(z,t), makes the actual growth kinetics more complicated than the simple form suggested by Equation 1. Because we have previously measured the growth rate, G(T), of CI films during pulsed heating,38

~ Equations 1 and 2 can be used to provide estimates of the values of J for the results shown in Figure 4. If we define N0.5 as the number of pulses needed to reach the midpoint of the crystallization, i.e. f(N0.5) =

~ 0.5α, then Equation 1 can be solved for J using the values of N0.5 determined from the experiments. For ~ example, N0.5 ≅ 500 and G ~ 2 x 10-10 m/pulse for the experiment with Tmax(0) ~ 238 K (Figure 4b), 13 ACS Paragon Plus Environment


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~ ~ which gives J ~ 1018 m-3pulse-1. Similar estimates for the data in Figures 4a and c give J ~1019 and 1021 m-3pulse-1, respectively. Because the time spent near the maximum temperatures, dtp, is ~ 10 ns/pulse, the

~ estimated range for the instantaneous nucleation rates is J ~ J / dt p ~ 1026 – 1029 m-3s-1. These nucleation rates are in the range reported for previous measurements of nanoscale water droplets.18,35

~ To evaluate the temperature dependence of J (Tmax ( z )) (see Equation 2a), it is useful to consider classical nucleation theory (CNT).47,48 In that theory, the free energy of ice particles versus their size has a maximum at intermediate sizes. The maximum arises because there is an energetic cost for creating an ice particle embedded in the liquid, which increases as the area, while the lower free energy of the crystalline phase increases in proportion to the volume of the particle. A “critical nucleus” is defined as a particle whose size corresponds to the maximum in the free energy. On average, ice particles that are larger (smaller) than the critical nucleus grow (melt). Because the free energy barrier decreases at lower temperatures, the size of the critical nucleus should also decrease as the temperature decreases. The nucleation rate corresponds to the rate of formation of ice particles per unit volume that are larger than the critical nucleus. Nucleation is a kinetic process and therefore it is both time- and temperature-dependent. However for most measurements of the nucleation rate in supercooled water, the rate of change of the temperature is slow enough that it is sufficient to consider only the steady-state, temperature-dependent nucleation rate, J(T). In the transiently-heated films, both the time- and temperature-dependencies of the nucleation are important. For example as the film heats up, nuclei that are larger than the critical nucleus at some temperature would continue to grow if the temperature didn’t increase further. However, as the film continues to heat up, the size of the critical cluster increases and the ice growth rate might not keep up. As a result, a small ice particle formed early in a heat pulse might subsequently melt later in the pulse when it is no longer larger than the critical cluster size relevant at those higher temperatures. Similarly, small ice particles formed during the cooldown phase of one heat pulse can also potentially melt during the next pulse. Thus, the local instantaneous nucleation rate can be negative, and the “memory” of prior nucleation 14 ACS Paragon Plus Environment

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events can be (partially or completely) erased. However, ice nuclei that grow larger than the critical nucleus for the maximum temperature at that location in the film should continue to grow on subsequent

~ pulses. The current experiments are sensitive to the rate of formation of these ice nuclei, i.e. J (Tmax ( z )) . Note that the melting of small clusters upon heating is not captured in the typical applications of classical nucleation theory, which assume a steady-state (and positive definite) nucleation rate, J(T). Below, we

~ will discuss how to relate our measurements of J (Tmax ( z )) to previous measurements of J(T).

~ To improve upon the simple estimates of J and J given above, we performed Monte Carlo simulations of the nucleation and growth of crystalline ice in these experiments (Supporting Information, Text S3). The basic idea was to stochastically nucleate ice particles within the film and follow their growth versus the number of heat pulses. On any given heat pulse, a temperature-dependent nucleation

~ rate, J (Tmax ( z )) , was used to create new ice particles at random locations within the films using the appropriate maximum temperature for that height in the film. The growth of these ice particles was then

~ followed on subsequent pulses using the known, temperature-dependent growth rate, G(Tmax ( z )) . As the ice particles grew, the surface closer to the metal substrate reached higher maximum temperatures than the surface further from the metal leading to different growth rates at those surfaces.49

~ Because J (Tmax ( z )) is an integral of the instantaneous nucleation rate over the heat pulses (see Equation 2a) and the maximum for J(T) is expected to occur below ~225 K,5,17,50 we might expect that

~ J (Tmax ( z )) will not be strongly temperature-dependent for Tmax(z) > 225 K. To test this idea, we

~ performed several Monte Carlo simulations in which J was assumed to be independent of temperature (Fig. 4a). This assumption corresponds to little or no melting of smaller ice particles as the films heat up.

~ Simulations with Tmax(0) = 310 K, Tmax(240 nm) = 170 K and J ~ 1018-19 m-3pulse-1, which corresponds to J ~1026-27 m-3s-1 (Fig. 4a, blue and red lines, respectively), are consistent with the experimental results and with the simple estimate given above. In contrast, nucleation rates of ~1025 m-3s-1 or less are inconsistent with the experiment. The simulation with J ~ 1022 m-3s-1 is of interest since it has been 15 ACS Paragon Plus Environment


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suggested that this should be the maximum value for J(T).17 However with such low nucleation rates, essentially no crystallization would be observed in the pulsed heating experiments. Simulations with a temperature-independent ice nucleation rate can also match the observations for the experiments with Tmax(0) = 238 K and 220 K (see Fig. S4). However, those simulations require significantly different values

~ ~ for J , which indicates that the temperature dependence of J (Tmax ( z )) needs to be included. To quantify the physical phenomena described above, we use the following relationship for

~ J (Tmax ( z )) based on the steady-state nucleation rate, J(T):

~ J (Tmax ( z )) =

∫ J (T ′( z, t ))(dt / dT ′)dT ′ ~

pulse

δt (T ) ∆

T

∫ J (T ′)dT ′ ,

(3)

T −∆

where δ(T) is time it takes for the temperature to change from T - ∆ to T in the heat pulse (e.g. see Fig. 1b). In Equation 3, the width of the integration region, ∆, reflects the extent to which earlier nucleation events persist to higher temperatures – larger values of ∆ indicate that more small nuclei survive and grow at higher temperatures. Figures 4b and c show simulations of the crystallization kinetics using Equation 3

~ to determine J (Tmax ( z )) with ∆ = 8 K and a form of J(T) suggested by Ickes, et al.50 The agreement between the simulations and all three experiments is reasonable. (The red dashed line in Figure 5 shows J(T) suggested by Ickes, et al. along with some experimental results.17,28-32,34,35) Figure S5 shows the results of simulations for several different values of ∆ for Tmax(0) = 310 K and 238 K. Note that while the simulations with ∆ = 8 Κ match the observed crystallization kinetics for Tmax(0) = 238 K and 220 K (Fig. 4b and c, dotted lines), they underestimate the total amount of the film that crystallizes. However, the total amount that crystallized in the simulations was sensitive to some factors, such as the temperature difference between the top and bottom of a growing ice particle, that did not appreciably affect the kinetics or impact the determination of J(T).


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Figure 5. Homogeneous nucleation rate in water versus temperature. The shaded region shows the range of values for J that is consistent with the current results and previous results on water droplets (symbols). The red dashed line is the fit to previous experiments proposed by Ickes, et al.50 Using this fit for ~210 K ≤ T ≤ ~225 K (solid black line) in simulations of the crystallization kinetics for the transiently-heated water films reproduces the observations (see text for details). The blue dotted line shows a potential form of J(T) that connects the results of Laksmono, et al.17 with the current results and previous measurements.28-32,34,35

Because the pulsed-heating experiments are sensitive to nucleation occurring over a range of temperatures, it is difficult to determine a unique function for J(T). We performed additional simulations with various choices for J(T) (see Fig. S6) to assess the range of nucleation rates that are consistent with the experimental observations (Figure 5, shaded region). An important conclusion from the simulations is that existing forms for J(T) with large values for Jmax derived from nucleation experiments on nanoscale 17 ACS Paragon Plus Environment


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droplets are consistent with, and probably required to explain, the experimental results for transientlyheated water films presented here. The lower limit of Jmax that is consistent with the current experiments (~1026 m-3s-1, see Fig. 4a) is about 4 orders of magnitude higher than largest value of Jmax suggested by Laksmono et al.17 Their estimate for Jmax was based on the experimental observation that micron-sized drops of water vitrify when quenched at cooling rates of ~107 K/s. However, that estimate of Jmax was made before measurements of the growth rate of crystalline ice over the relevant temperature range were available.38 The growth rate measurements allow us to revise the estimates of the nucleation rates that are consistent with the experiments on hyperquenched glassy water. That analysis indicates that values of Jmax in the range of 1029 – 1030 m-3s-1 are consistent with the previous observations (Supporting Information, Text S4 and Fig. S7). The results presented here, which are most sensitive to ice nucleation occurring at T < 225 K, do not necessarily contradict the low nucleation rates reported by Laksmono, et al. for 227 K ≤ T ≤ 232 K.17 For example, simulations using the form of J(T) suggested by Ickes, et al.50 for T ≤ 225 K, while setting J(T) = 0 for T > 225 K, are indistinguishable from the simulations shown in Figure 4b (red line). In addition, the experimental approach and analysis presented by Laksmono, et al. appear to be sound. However, to connect the prior nucleation rate measurements, which show that J(T) is a stronglydecreasing function of temperature for T ≥ 234 K,5,17,50 with the nearly temperature-independent nucleation rates measured for 227 K ≤ T ≤ 232 and the current results would require J(T) to exhibit a “plateau” between ~ 227 K and 232 K that connects two strongly temperature-dependent regions (see Figure 5, blue dotted line). Further research is needed to address this issue. In conclusion, we have measured the crystallization kinetics in flat, transiently-heated, 0.24 µm thick water films. For experiments with the highest laser pulse energies and the highest overall temperatures, the maximum temperature at the water/metal interface during the heat pulse was well above 273 K and thus nucleation and growth of ice at that interface was completely suppressed. In the same experiments, the water/vacuum interface was too cold to allow appreciable crystallization. Therefore, the 18 ACS Paragon Plus Environment

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observed crystallization was due to homogeneous nucleation of ice within the bulk of the film. Analysis of the results shows that homogeneous nucleation rates of at least 1026 m-3s-1 in the temperature range from ~210 – 225 K are needed to account for the observations. Experiments at lower overall temperatures, where heterogeneous nucleation at the water/metal interface was possible, suggest that the nucleation rate at that interface was lower than the homogeneous nucleation rate in the same temperature range. Homogeneous ice nucleation rates of ~1029±2 m-3s-1 are needed to explain those experiments. The results presented here are consistent with a previously suggested form for J(T) that smoothly connects nucleation rate measurements on micron-sized drops at T ≥ 234 K with measurements on nanometer-size drops at T ≤ 215 K.50

Acknowledgements: This work was supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences. Pacific Northwest National Laboratory (PNNL) is a multiprogram national laboratory operated for Department of Energy by Battelle. The research was performed using Environmental Molecular Sciences Laboratory, a national scientific user facility sponsored by the Department of Energy’s Office of Biological and Environmental Research and located at PNNL.

Supporting Information Text S1 – Experimental method; Text S2 – Analysis of IR spectra; Text S3 – Kinetic Monte Carlo crystallization simulations; Text S4 – Analysis of Jmax for hyperquenched glassy water experiments. Figures S1 – S7.

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Height, z z = 240 nm (not to scale)

(a) Tmax (z)

Homogeneous Nucleation of Ice in Transiently-Heated, Supercooled

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