Observing the formation of ice and organic crystals in active sites

Edited by Pablo G. Debenedetti, Princeton University, Princeton, NJ, and approved November 30, 2016 (received for review October 25, 2016)
December 19, 2016
114 (5) 810-815
Commentary
Crystals creeping out of cracks
Thomas Koop

Significance

Crystal nucleation—the first appearance of a crystalline phase where there was none before—usually occurs at the surface of a foreign material. Ice formation in the atmosphere is dependent upon the number and type of aerosol particles present, but little is known about why some are more effective than others. Here we investigate the role of surface topography in promoting crystallization of ice and different organic crystals and show that acute geometries are highly effective in promoting the growth of a confined crystalline phase, which then gives rise to a bulk phase. This is relevant to crystallization in a large number of real-world systems such as industrial film growth and our climate.

Abstract

Heterogeneous nucleation is vital to a wide range of areas as diverse as ice nucleation on atmospheric aerosols and the fabrication of high-performance thin films. There is excellent evidence that surface topography is a key factor in directing crystallization in real systems; however, the mechanisms by which nanoscale pits and pores promote nucleation remain unclear. Here, we use natural cleavage defects on Muscovite mica to investigate the activity of topographical features in the nucleation from vapor of ice and various organic crystals. Direct observation of crystallization within surface pockets using optical microscopy and also interferometry demonstrates that these sharply acute features provide extremely effective nucleation sites and allows us to determine the mechanism by which this occurs. A confined phase is first seen to form along the apex of the wedge and then grows out of the pocket opening to generate a bulk crystal after a threshold saturation has been achieved. Ice nucleation proceeds in a comparable manner, although our resolution is insufficient to directly observe a condensate before the growth of a bulk crystal. These results provide insight into the mechanism of crystal deposition from vapor on real surfaces, where this will ultimately enable us to use topography to control crystal deposition on surfaces. They are also particularly relevant to our understanding of processes such as cirrus cloud formation, where such topographical features are likely candidates for the “active sites” that make clay particles effective nucleants for ice in the atmosphere.
The growth of a new phase is almost always dependent on a nucleation event. Nucleation is therefore fundamental to a number of processes including crystallization, freezing, condensation, and bubble formation and is typically described in terms of classical nucleation theory. However, because this theory was developed to describe the nucleation of liquid droplets in vapor it cannot give a complete understanding of all nucleation processes, and in particular the formation of crystalline materials. Nucleation in the real world is also usually heterogeneous, occurring on seeds, impurities, or container surfaces. Although simple models consider nucleation to occur on perfectly flat, uniform surfaces, it is clear that real surfaces inevitably vary in chemistry and topography. We focus here on the effects of surface topography. Classical nucleation theory predicts a lower free energy barrier to nucleation in surface cracks or pores on the length scale of a critical nucleus (1). The extent of the reduction is contact-angle-dependent, such that nuclei with a low contact angle experience a more significant reduction from topography.
Topography is known to promote crystallization directly from a vapor (25), because these systems typically exhibit low contact angles. Crystallization from the melt, in contrast, is associated with very high contact angles such that topography is usually ineffective (6). Crystallization from solution provides an intermediate case and has perhaps received the most attention. Roughened surfaces have been shown to enhance the nucleation of a range of crystals (710), whereas the nucleation of proteins and organic crystals is promoted within narrow pores of specific diameters (1113). The geometries of these pores can even determine the orientation and polymorphs of the product crystals (1416). However, although these data provide strong evidence for the importance of surface topography to nucleation, we still have little knowledge of what makes a good nucleation site, or how such sites function on the nanoscale.
One area where these questions have been considered is atmospheric ice nucleation. It has been suggested that surfaces could exhibit a small number of “active sites” that determine the nucleating ability of an entire surface (1719). Each site has its own threshold supersaturation or supercooling above which nucleation becomes probable (20, 21), and the sites with the lowest thresholds dominate. Fukuta (22) suggested that ice nucleation from vapor may proceed by the formation of confined condensates within small pores and cracks, and that bulk crystals emerge from these upon sufficient saturation of water vapor. To understand heterogeneous nucleation, we therefore need to understand how these active sites promote it.
The current study addresses this challenge by investigating the nucleation from vapor of ice and a number of organic compounds within a well-defined topographical feature—the “pockets” that are commonly formed along the steps on cleaved mica substrates. Featuring a highly acute wedge geometry, these structures are possible candidates for the active sites present on clay/dust particles that drive atmospheric ice nucleation. Importantly, we can use optical microscopy to both characterize the geometry of these pockets and to monitor crystallization in situ within them. Our results show that the mica pockets are extremely effective nucleation sites for every compound we have exposed them to. We also provide direct experimental evidence for a condensate-mediated method of nucleation, where growth originates as a confined condensate along the apex of an acute wedge, with a threshold supersaturation required for growth into a bulk crystal.

Results

Substrates were prepared by cleaving Muscovite mica, which generates a pristine surface that is atomically flat over large areas (23). These surfaces often feature a number of step edges, which can themselves support a range of defects. The current study exploits one key type of defect, namely the “pockets” that are created when the top layers of mica are locally detached from those below, leaving a space in between (Fig. 1). A highly acute wedge geometry is formed where the two mica surfaces meet that would be impossible to generate using surface engineering techniques. Importantly, these pockets can be readily studied using optical interference, where the pattern of interference fringes provides information about the separation of the mica sheets at different positions within the pockets (Fig. 1). Interference between reflections from the mica surfaces forming the top and bottom of the wedge produces a reflected light intensity I that is dependent on the mica–mica spacing z as described by the relation
II0+asin22πzλ,
[1]
where λ is the wavelength, I0 is a background intensity from other surfaces, and a is a constant dependent on the reflectance (more details and exact form are given in Supporting Information). As a consequence there is a bright fringe at λ/4 separation and then at intervals of λ/2. This allows a wedge profile to be precisely calculated. The pattern of these fringes also changes on deposition of liquid or solid within the pocket, such that we can monitor the entire growth sequence of crystals within these features. The presence of a condensed phase greatly reduces the reflectance of both surfaces, making I drop almost to I0. With the additional ease of diffusion of material into these features, they are ideal for studying topographically aided nucleation.
Fig. 1.
Experimental overview. (A) Optical micrograph of a pocket and (B) a higher-magnification view of the region outlined in white, showing interference fringes. (C) Schematic illustration of a pocket and (D and E) the growth of a crystalline condensate (in red) that then leads to the growth of twin bulk crystals. (F) A condensate forming in an acute wedge, where the twin reflections of light from closely spaced mica surfaces (green arrows) leads to interference fringes, also showing condensate height h, interface radius of curvature r, and contact angle θ. (G) Light intensity curves across a single fringe highlighted in white in B, corresponding to an empty wedge (black) and a wedge holding a 75-nm condensate of carbon tetrabromide (red). The condensate is visible as a relatively sharp cutoff of fringe intensity. (H) The wedge profile calculated from the black curve in G, with a 0.3° angle shown in green for reference.
Three organic compounds—norbornane, carbon tetrabromide, and camphor—were selected for study because they have high vapor pressures and melting points well above room temperature (23–25 °C); their physical properties are presented in Table S1. Preliminary experiments were also conducted with hexachloroethane, hexamethylcyclotrisiloxane, and tetramethylbutane. These experiments were performed in a sealed cell that contains a reservoir of crystal at the base and the mica substrate at the top, where the mica can be observed throughout the experiment using an optical microscope in reflected light mode (19). Typical pocket sizes are given in Table S2. Saturation is controlled by adjusting the temperature of the reservoir with respect to that of the substrate, which is held at room temperature. The reservoir is initially cooled to 1 °C below the substrate to produce undersaturated conditions. This protocol generated highly reproducible results, as shown by the consistency of the measured saturation at the moment of first emergence of a bulk crystal from the pocket (SI Materials and Methods).
Table S1.
Physical properties of organic compounds at 27 °C and ice at −40 °C
CompoundTm, °C (41)pv, Pa [mmHg] (4246)ΔHsub, kJ/mol (45, 47, 48)γ, mJ/m2 (4951)
Norbornane884,100 [31]4032
Carbon tetrabromide90110 [0.83]5450
Camphor17952 [0.39]5232
Hexachloroethane86 [0.64]4943
Hexamethylcyclotrisiloxane65750 [5.6]6018
Tetramethylbutane1003,100 [23]4520
Ice013 [0.10]51109
Tm is the melting point, pv is the vapor pressure, ΔHsub is the enthalpy of sublimation, and γ is the estimated solid–vapor surface energy. Hexachloroethane has no melting point but sublimes at 187 °C. Liquid–vapor surface energy is assumed to be equal to the solid–vapor surface energy, except for ice where 83 mJ⋅m−2 is used (52). Solid–liquid surface energy of 32 mJ⋅m−2 is used for ice–water (53) and 6.9 mJ⋅m−2 for carbon tetrabromide (54), and 10 mJ⋅m−2 is assumed for all other compounds due to an absence of available data.
Table S2.
Mean and SD of characteristics of mica pockets in two categories
Pocket categorya, mmb/aϕ, °
Large1.4 ± 0.62.9 ± 0.60.72 ± 0.15
Small0.34 ± 0.163.5 ± 1.11.5 ± 0.4
a is the corner–corner distance across the opening, b is the length of the wedge apex, and ϕ is the mean wedge angle between the first two bright interference fringes (note that the wedge angle at the apex will be smaller).
The mica pockets provide extremely effective nucleation sites for every organic compound we studied. A distinctive pattern of growth was observed, in which twin crystals grow from the two “corners” of the pocket where the wedge apex meets the step edge (Fig. 2). Crystal growth is also seen all along the apex of the wedge in each case, although this is sometimes difficult to see in low-magnification images. Fig. 3 AD show high-magnification images of a norbornane condensate near to a corner (camphor and carbon tetrabromide results are qualitatively similar). A condensate begins to form in the wedge apex and then grows steadily, tending to grow thicker close to the corner, consistent with a lower diffusion barrier to growth near the corner (24). For every organic compound a condensate is clearly visible before a bulk crystal emerges from the pocket corner.
Fig. 2.
Optical micrographs showing crystals of various compounds crystallizing from the two corners of one or more mica pockets.
Fig. 3.
Optical micrographs showing crystal nucleation of norbornane (AD, pocket opening at bottom of images) and ice (E and F, pocket opening at right of images) in the corners of mica pockets. Where a condensate exists it is visible as a sharp step in reflected light intensity, in contrast to the gradual transition associated with an empty wedge. Norbornane: (A) empty wedge, (B) small condensate below λ/4 high (indicated by black arrows), (C) larger condensate just before emergence of a bulk crystal, and (D) after emergence of a bulk crystal. Ice (at −39.0 °C): (E) The white arrows indicate the first appearance of an ice crystal at the pocket corner, with no condensate yet visible along the wedge apex; (F) subsequent growth of ice along the wedge apex. (Inset) A refocused view of the bulk ice crystal, demonstrating a hexagonal profile.
Ice nucleation was studied at temperatures down to −45.0 °C in a different cell (SI Materials and Methods), and experiments were performed by reducing the substrate temperature at 0.25 °C min−1 while exposed to gas flow with a steady and adjustable humidity. At nucleation temperatures of −37.0 °C and above the pocket seems to be unimportant, with liquid drops condensing on the mica surface, some of which then freeze and hence cause the others to evaporate. At −38.8 °C and below, the same mode of growth was seen as with the organics, with hexagonal or columnar ice crystals emerging from the pocket corners (Fig. 2). However, unlike the organics, no condensate was ever observed before the appearance of a bulk crystal, down to the observation limit of 15 nm. Fig. 3 E and F show the growth of ice crystals along a wedge apex at −39.0 °C, but this growth was not seen until just after the first bulk crystal growth was observed at the corner. Saturation could not be so precisely quantified as with organics, but ice was seen emerging from the pockets at a saturation of 1.2 ± 0.1 for all experiments.
The “heights” of organic condensates were quantified by taking an intensity profile across an interference fringe and finding the location of a sharp step in intensity from the condensate edge, as illustrated in Fig. 1 FH. This method is accurate to within 1 nm for condensates as small as 15 nm; smaller condensates cannot usually be unambiguously detected. The heights of condensates formed before the emergence of a bulk crystal are plotted in Figs. 4 and 5. Norbornane condensates form in the wedge even in undersaturated conditions (Fig. 5), whereas no evidence for the existence of condensates before saturation was obtained for camphor and carbon tetrabromide (Fig. 4). However, because these compounds have much lower vapor pressures than norbornane their condensates would take longer to grow to an observable size.
Fig. 4.
Graphs of condensate size with increasing saturation (with respect to bulk solid) for camphor and carbon tetrabromide at a ramp rate of 0.1 °C min−1. The first point in each series marks the first unambiguously detectable condensate, and the last marks the first appearance of a bulk crystal emerging from the pocket corner. Error bars represent SE in measurement of condensate heights; horizontal error bars are omitted for clarity. The gray and orange lines predict the condensate size above which there should be no barrier to emergence into a bulk crystal for carbon tetrabromide and camphor, respectively.
Fig. 5.
Graphs of norbornane condensate size with increasing saturation (with respect to bulk solid). The first point in each series marks the first unambiguously detectable condensate; the last marks the first appearance of a bulk crystal emerging from the pocket corner. The circles show growth at various temperature ramp rates in the same mica pocket, and open black squares show growth in a different pocket at 0.1 °C min−1. (Inset) An enlargement of the bottom-left region of the main graph. Error bars (often too small to be visible) represent SE in measurement of condensate heights; horizontal error bars are omitted for clarity. The dashed lines show the predicted equilibrium condensate size for a solid and a liquid (black and gray respectively). The thick gray line predicts the condensate size above which there should be no barrier to emergence into a bulk crystal.
This possibility was investigated further by performing experiments in which the saturations of carbon tetrabromide and camphor were allowed to approach (but never quite reach) unity slowly over several hours. The carbon tetrabromide condensate grew to 84 ± 1 nm after 3 h, whereas that of camphor grew to 60 ± 1 nm after 5 h. The influence of the temperature ramp rate on the condensation of norbornane within a single pocket was also studied (Fig. 5) and showed two clear trends as the ramp rate increases: A higher saturation is required before bulk crystals emerge and the precursor condensates are smaller in size.
Further information about the mechanism of crystallization was obtained by performing multiple crystallization cycles using the same mica pockets, where the cell was flushed after each run to sublime the previous crystals (in the case of ice the substrate was warmed to above 0 °C between runs). For both the organics and ice the two bulk crystals that form at each side of a pocket were seldom in the same crystallographic orientation, as judged by their external geometries. This demonstrates that the two external crystals and connecting condensate are rarely a single crystal. There was also no evidence of a consistent orientation between runs, suggesting that the geometry of the wedge does not determine crystal orientation.

Discussion

Our results provide a striking demonstration that surface topography—and in particular features containing narrow wedges—can provide extremely effective nucleation sites, where the organic compounds studied initially deposit in the apex of the mica wedge, before growing out of the pockets as bulk crystals. The deposition of a condensed phase, be it liquid or solid, within the pockets is driven by the lower interfacial free energy between the mica substrate and the condensate compared with the interfacial free energy between the mica and the vapor. As a consequence the condensate has a contact angle below 90° and may form a concave interface, as shown in Fig. 1F. The Kelvin equation describes a reduction of vapor pressure p over a curved interface:
lnpp0=cosθγVmrRT,
[2]
where p0 is the vapor pressure over a flat surface, θ is the contact angle of the substance in the condensate on mica, γ is the compound–vapor surface free energy, Vm is the molar volume, r is the radius of curvature of the interface condensate, R is the gas constant, and T is the temperature. For a condensate interface that is concave toward the vapor r is negative, and therefore the vapor pressure is reduced below that for a flat surface. Thus, any substance can condense in an acute wedge slightly below saturation, provided that θ is below 90°, which is known as capillary condensation. The largest condensates will occur when θ approaches 0°, which in our case means that 2|r|=h, the condensate height.
We expect the first condensate formed to be a supercooled liquid, which will then freeze to form a solid condensate by normal nucleation. The Gibbs–Thomson effect predicts that a confined phase will suffer a decrease in the melting point inversely proportional to the dimension of the pore; as such, an infinitesimally small condensate is expected to be a liquid (25). This mechanism has been experimentally observed in a highly acute annular wedge (2426).
Theoretically, the size of a supercooled liquid condensate is described by the Clausius–Clapeyron relation, which shows that the vapor pressure pl over a supercooled liquid is higher than ps over a solid at the same temperature:
lnplps=ΔHfusR(1T1Tm),
[3]
where ΔHfus is the enthalpy of fusion and Tm the melting point. This predicts a ratio pl/ps of 1.5 for water/ice at −40 °C, of 1.3 for both norbornane and carbon tetrabromide, and of 2.5 for camphor at 27 °C. We therefore expect a liquid condensate to reach equilibrium at a smaller size than a solid one in the same conditions. The height h of a liquid condensate, assuming θ=0, at solid saturation may be estimated by combining Eqs. 2 and 3:
γVmrT=2γVmhTΔHfus(1T1Tm),
[4]
where γ here refers to liquid–vapor surface tension. At TTm this is only approximate (25). Values of h are predicted in Table 1.
Table 1.
Classical nucleation theory predictions for size of critical nucleus radius (r*) and free energy barrier (Δμ*)
Compoundr*, nmh, nmΔμ*, kT
Norbornane (27 °C)2.89.182
Carbon tetrabromide (27 °C)2.31635
Camphor (27 °C)1.34.318
Ice (−39 °C)1.53.992
h is the predicted size of a liquid condensate at saturation with respect to a solid.
Following this argument, are the condensates that we here observe supercooled liquids or solids? Fig. 5 shows the estimated equilibrium heights of solid and liquid norbornane condensates, assuming θ = 0°. These lines give the maximum sizes these condensates could reach if they were left sufficiently long to equilibrate at any given saturation. The observed condensate heights are well above those possible for a liquid condensate, which provides conclusive evidence that the measured condensates are solid. As Table 1 shows, the expected height of the liquid condensates at saturation with respect to solid are below or close to the lower limit of observation for all compounds. However, this does not rule out the initial presence of a supercooled liquid condensate that then freezes to give rise to a solid condensate before the condensate grows to an observable size. Estimation of the critical nucleus radius for all of our systems (Table 1) shows that the condensate heights are more than twice the critical radii; liquid condensates of this size are large enough to contain a critical nucleus and are therefore metastable with respect to freezing.
So far we have discussed only the formation of a condensate inside a wedge without considering the transition into a bulk phase. As seen in Fig. 3 AD, the confined condensate extends right to the pocket corner where it meets the bulk vapor. There seems to be nothing stopping the crystal from growing out into the bulk, and yet no emergence is observed until a threshold supersaturation is attained. This problem is illustrated in Fig. 6, in which the condensate has a concave interface, provided that θ is below 90°. However, as it begins to bulge out of the narrow opening, it first flattens out and its curvature then becomes convex with respect to the vapor and passes through a minimum in radius of curvature. After this point it can grow unrestricted into the bulk phase. In Eq. 2, r changes sign, necessitating a supersaturated vapor. The minimum in the convex radius of curvature defines a minimum or threshold supersaturation necessary for the condensate to emerge from the pore. Taking this minimum radius to be equal to the pore radius, the threshold saturation S is given by the Kelvin equation:
lnS=γVmrRT.
[5]
It follows that the narrower the mica–mica separation at the pore opening the higher the saturation needed for a bulk phase to emerge. This concept has been verified in simulations by Page and Sear (27), who show that there is a free energy barrier for a crystal to emerge from a narrow pore, which does not exist if the saturation is sufficiently high.
Fig. 6.
(Left) Illustration of how a phase confined in a pore emerges into a bulk phase. (a) The phase initially has a concave interface, allowing it to be stable in confinement even in undersaturated conditions. (b) Before it can emerge into a bulk phase it must briefly form a highly convex interface, requiring supersaturation. (c) As the bulk phase grows its interface curvature reduces, tending toward a planar interface. (Right) Schematic graph of the evolution of vapor pressure over the interface as the new phase emerges, with the labels a, b, and c corresponding to the three stages illustrated on the left.
Although this is clearly a simplified model of our system, it works well to illustrate general trends. The edge of our system can be seen as a slit pore that increases in width with increasing distance from the wedge apex. When a condensate is very small, the mica–mica spacing is too narrow for it to emerge at modest supersaturation (the energy barrier is too large). As the supersaturation increases, the condensate grows further from the apex such that the width of the gap from which the condensate must emerge also increases. At some point the saturation exceeds the threshold for growth through the gap, and a bulk crystal emerges. The threshold lines for camphor and carbon tetrabromide and for norbornane are shown in Figs. 4 and 5, respectively. Although our data are in good agreement with these at low rates of saturation increase, at the higher rates used with norbornane the condensate size and saturation increase significantly beyond the point where emergence would be expected. However, at high rates of crystal growth it is likely that the local supersaturation is no longer accurately given by the temperature difference between substrate and reservoir.
In the case of ice no condensates were seen before the growth of bulk crystals. Rather than implying that there were no condensates, it is extremely likely that the condensates were simply too small to observe (below 15 nm) up to the moment of bulk emergence. The nature of growth, with two crystals at the pocket corners and a continuous line of crystal growth along the wedge apex, is strikingly reminiscent of results with organic compounds where condensates were observed before growth (Fig. 2). Ice at −40 °C has a significantly lower vapor pressure than any of the other compounds studied, and the ramp rate into supersaturated conditions was faster, so observably large ice condensates may not have had sufficient time to form. Eq. 5 predicts that a 15-nm ice condensate could emerge into a bulk phase at a modest saturation of 1.13, so if this saturation was attained before the condensates grew to visible size we would not expect further growth before the appearance of a bulk crystal. It is also possible that the condensate was supercooled water, which on freezing would begin to grow all along the wedge apex at the same time as the bulk crystal emerges, as was observed. As seen in Table 1, the water condensate would be below the 15-nm limit of observation. Calculating the volume of water in a condensate at ice saturation in a 1-mm-long wedge with a constant 0.3° angle and extrapolating published ice nucleation rates (28), we estimate that we would expect to see one nucleation event every 1.2 min at −39 °C. On the time scale of these experiments (a ramp rate of 0.25 °C/min) it is plausible that ice nucleation from water is the limiting step in the process.
The results with ice are immediately relevant to atmospheric ice nucleation on solid aerosol particles. Most studies of atmospheric ice nucleation have focused on the importance of surface chemistry and lattice matching. However, the correlation between lattice match and nucleation is in general not strong (29), and there is a wide scatter in the reported nucleating abilities of atmospheric aerosols (30). The mechanism of ice nucleation in capillary-condensed water that was proposed 50 y ago by Fukuta has only recently been revisited (31, 32), but it has already been suggested that it contributes to the ice nucleation capacity of kaolinite (33, 34) and leads to enhanced ice nucleation by porous aerosol particles (35, 36). It is also noteworthy that alkali feldspars, which have been shown to be particularly efficient ice nucleators (37), usually have a rich microstructure (38) with an abundance of sites where water might condense. We have now directly observed how nucleation via condensed, supercooled water is an important mechanism for nucleation of ice in cleavage defects on mica, thereby highlighting the importance of pore condensation freezing in atmospheric ice nucleation.

Conclusions

These results provide direct experimental evidence that highly acute wedges—the key feature of the mica pockets studied here—are extremely effective nucleation sites for crystallization from vapor. Using direct imaging approaches we demonstrate that bulk crystals form subsequent to generation of a confined condensate in the acute wedge, where this can even occur in undersaturated conditions. Although we used micrometer-scale topographical features for the purpose of easy and unambiguous condensate observation, the principles should equally apply to smaller features that may occur on natural or engineered surfaces. The only compulsory feature is that they must possess a geometry acute enough to allow condensation without an energy barrier. This model also suggests that there will be an optimal feature size for any given supersaturation. Features that are too small may fill quickly but have too narrow an opening to allow emergence into a bulk phase. Conversely, large features may take so long to fill that crystals may have already emerged from smaller features. This phenomenon clearly has many real-world applications. Crystal nucleation from vapor is a vital process in atmospheric science and in technological applications such as chemical vapor deposition film growth. An analogous thermodynamic pathway to nucleation has even been proposed to occur in solution during the formation of biominerals such as calcium carbonate from amorphous precursor phases (39). Understanding topographically directed crystallization, and identification of the most active features, therefore promises a novel strategy for controlling nucleation in a wide range of environments.

SI Materials and Methods

The organic compounds used were norbornane (98%; Aldrich), carbon tetrabromide (99%; Aldrich), camphor [(R)-enantiomer, 98%; Aldrich], hexachloroethane (98%; Alfa Aesar), hexamethylcyclotrisiloxane (98%; Acros), and tetramethylbutane (Aldrich). Table S1 summarizes their properties.

Preparation of Mica Substrates.

Natural Muscovite mica was cleaved along its (001) basal plane within a laminar flow cabinet. This produces a surface that may be atomically flat and uniform over the length scale of the 4-cm2 samples used, but with occasional defects. The particular geometry of defect we look for was previously shown to be an effective nucleation site for several of the above compounds (19), known as a “cave” geometry in this earlier work but here known as a “pocket” geometry. The characteristics of these features could not be controlled; rather, they are the product of performing enough cleavages until a randomly produced pocket feature was discovered. Substrates were chosen for featuring a single well-defined pocket geometry in their center, with a lack of other features near to it that might provide competing nucleation sites. Pockets were categorised into two broad size ranges, “large” and “small,” as characterized in Table S2. Large pockets were used for the data series presented in Figs. 4 and 5; small pockets were used for all other quantitative results.

Crystallization of Organic Compounds.

Experiments with organic crystals were performed in a cell described in previous work (1). A sealed, polytetrafluoroethylene (PTFE)-walled chamber contains a reservoir of crystal at the base and the mica substrate forms the top surface, which can be observed through a microscope (Vickers M17). Proportional–integral–derivative-controlled electric heaters control the temperature of the reservoir, and the substrate is held at room temperature (23–25 °C). Initially the reservoir is chilled to 1 °C below room temperature to produce undersaturated conditions, at which point the cell is flushed with nitrogen gas for 20 s. The reservoir temperature is then increased linearly (0.1 °C/min unless otherwise stated), always remaining below 30 °C, while twin thermocouples log the temperature of both the reservoir and of the substrate. A sharp increase in the rate of condensate growth as or just after the system passes saturation (visible in Fig. 5) may be due to diffusion being aided by convection currents within the cell as the reservoir at the bottom becomes warmer than the substrate at the top. Observation is in reflected light mode using green LED illumination peaking at 529 nm. Images are captured using a Canon EOS 550D SLR with 14-bit color depth, which has been verified to produce a highly linear signal with respect to green light intensity.
The cell is fitted with Viton O-rings resistant to absorption of all compounds used, excepting only camphor. Experiments with camphor used O-rings exposed to camphor vapor for 3 wk beforehand; however, sufficient absorption was still seen that a temperature difference of 0.3 ± 0.1 °C needed to be applied between reservoir and substrate to achieve saturation (the temperature difference needed for a crystal on the substrate to neither grow nor shrink with time). Hence, when calculating saturations for camphor, 0.3 °C was subtracted from the measured temperature difference before doing so, and the absolute error in saturation is higher at ±0.02. For all other organic compounds, saturation occurred at the expected temperature difference of 0.0 °C.
Saturation S is defined approximately as
S=pp0,
[S1]
where p is the partial pressure of the compound and p0, the vapor pressure over a flat solid surface, is calculated using a form of the Clausius–Clapeyron relation:
lnS=ΔHsubR(1Ts1Tr),
[S2]
where ΔHsub is the enthalpy of sublimation, Ts the substrate temperature, and Tr is the reservoir temperature. Error in saturation is estimated to be ±0.01, from imprecision in the temperature measurement.
The measured saturation at the moment of first emergence of a bulk crystal from the pocket was highly consistent between runs. Six repeated runs in a single pocket (using different pockets for each compound) produced the following saturations (mean ± SD): norbornane, 1.032 ± 0.009; carbon tetrabromide, 1.067 ± 0.004; camphor, 1.115 ± 0.011; and hexachloroethane, 1.098 ± 0.003. In all cases the spread of results is similar to or smaller than the error in measurement of saturation.

Crystallization of Ice.

Experiments with ice crystallization were performed in an alternative manner. A PTFE-walled cell contains a Peltier cooling element, which can be observed through a microscope objective onto which the cell seals directly. Mica samples (1 cm2) are back-painted in black enamel to improve optical properties. A stream of nitrogen of steady humidity is passed through the cell at 15 mL⋅min−1; the temperature of the substrate is reduced at 0.25 °C/min until the frost point of the gas is passed, at which time the water vapor becomes supersaturated. Gas humidity is controlled by mixing a stream of saturated vapor (finely bubbled through a column of water) with dry nitrogen in variable proportion. Control of humidity was not sufficiently precise to justify meaningful estimates of saturation at nucleation. Temperature was controlled by adjusting the power supplied to the Peltier element and the substrate temperature measured using a PT100 resistance thermometer.

Measurement of Heights of Condensates.

To quantify condensate heights, an intensity profile across a set of fringes (averaging over a 15-µm-wide line) is taken; the location of a sharp step in intensity corresponding to the condensate edge is located. Because the intensity profile of an empty wedge (immediately after flushing) can be used to find a wedge profile (from interference principles) like that in Fig. 1H, it is therefore possible to infer the height to which the condensate extends (gray line in Fig. 1 G and H). At separations below about 15 nm, the reflected light intensity is too low to be able to distinguish the condensate edge, or to precisely characterize the profile of the wedge. Hence, no condensates below 15 nm could be detected, and the exact position of the wedge apex is uncertain. Profiles were taken between 100 and 150 µm from the pocket opening, because the fringes closer to the edge are usually curved and overlaid with step edges, which makes obtaining a high-quality profile difficult (Fig. 1B).

Reflectance of Filled Pores.

The ratio of reflected to incident light intensity R from an interface at normal incidence is dependent upon the refractive indices n1 and n2 such that, from a simple case of the Fresnel equations,
R=(n1n2n1+n2)2,
[S3]
and we can define the coefficient of finesse F of the surface as
F=4R(1R)2.
[S4]
For a mica–air interface a refractive index of 1.62 (40) predicts F=0.24. A mica–liquid or mica–solid interface has a much lower F; for example, a water–mica interface with n=1.33 would lead to F=0.039.
If we make the approximation that the two reflecting surfaces are parallel, then we may refer to the equation describing the transmittance T through a Fabry–Pérot etalon at normal incidence:
T=11+Fsin22πzλ.
[S5]
The total light reflected from the mica also depends on other surfaces, but assuming these are too widely separated for coherent interference their contribution can be reduced to a constant intensity I0. The total intensity can thus be expressed as a combination of I0 and 1T:
I=I0+b(111+Fsin22πzλ),
[S6]
where b is a constant describing the relative contribution of the two components. This is the form used for calculations of wedge profiles; however, in the limit F1 Eq. S6 can be expressed in a more intuitive form, as given in Eq. 1 in the main text:
II0+bFsin22πzλ.
[S7]

Acknowledgments

This work was supported by Leverhulme Trust Grant RPG-2014-306 (to H.K.C.) and Engineering and Physical Sciences Research Council Grants EP/M003027/1 and EP/N002423/1 (to H.K.C. and F.C.M.).

Supporting Information

Supporting Information (PDF)
Supporting Information

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Information & Authors

Information

Published in

Go to Proceedings of the National Academy of Sciences
Go to Proceedings of the National Academy of Sciences
Proceedings of the National Academy of Sciences
Vol. 114 | No. 5
January 31, 2017
PubMed: 27994140

Classifications

Submission history

Published online: December 19, 2016
Published in issue: January 31, 2017

Keywords

  1. nucleation
  2. confinement
  3. topography
  4. pores
  5. active sites

Acknowledgments

This work was supported by Leverhulme Trust Grant RPG-2014-306 (to H.K.C.) and Engineering and Physical Sciences Research Council Grants EP/M003027/1 and EP/N002423/1 (to H.K.C. and F.C.M.).

Notes

This article is a PNAS Direct Submission.
See Commentary on page 797.

Authors

Affiliations

James M. Campbell
School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom;
Fiona C. Meldrum
School of Chemistry, University of Leeds, Leeds LS2 9JT, United Kingdom
Hugo K. Christenson1 [email protected]
School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom;

Notes

1
To whom correspondence should be addressed. Email: [email protected].
Author contributions: J.M.C. and H.K.C. designed research; J.M.C. performed research; J.M.C. analyzed data; and J.M.C., F.C.M., and H.K.C. wrote the paper.

Competing Interests

The authors declare no conflict of interest.

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    Observing the formation of ice and organic crystals in active sites
    Proceedings of the National Academy of Sciences
    • Vol. 114
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    • pp. 783-E905

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