Spatial control of condensation and desublimation using ice nucleating proteins

When the partial pressure of ambient water vapor exceeds a critical supersaturation, heterogeneous nucleation will occur on any adjacent surface.¹ The supersaturation degree represents the ratio of the critical vapor pressure required for embryo formation, P_n, to the saturation pressure corresponding to the surface temperature, P_s,

The magnitude of SSD increases strongly with decreasing wettability and increases weakly for colder surface temperatures.^2–5 On a subfreezing surface, two different modes of heterogeneous nucleation are possible: condensation, where vapor nucleates into a supercooled liquid embryo, and desublimation, where the vapor nucleates directly into an ice embryo.⁶ 

The thermodynamically favorable mode of nucleation corresponds to whichever has a lower value of P_n, which is usually condensation but can be desublimation for sufficiently hydrophilic and/or cold surfaces.⁵ It is also important to consider transient effects: for example, a hydrophilic surface that theoretically favors desublimation beneath a critical temperature will already exhibit condensation as it is being cooled down beneath the dew point. Therefore, supercooled condensation is virtually always the observed mode of nucleation on chilled substrates,^7–13 with the impractical exception of inorganic crystals such as silver iodide,^14,15 kaolinite,¹⁶ or feldspar.¹⁷ Many studies have utilized chemical or physical patterns to spatially control the nucleation and growth of condensate,^15,18–27 but to date, desublimation remains elusive.

Recently, it has become apparent that promoting the desublimation mode of nucleation could be favorable for creating passive anti-frosting surfaces.²⁸ Several reports have observed that surfaces can stay largely dry from condensation or frost by patterning hygroscopic materials on the surface that attract nearby moisture.^29–31 This effect breaks down with conventional hygroscopic chemicals, such as salts and glycols, as they become diluted over time. Ice itself exhibits a depressed vapor pressure compared to supercooled water,³² so there is interest in patterning sacrificial ice features on a surface to keep it otherwise dry from condensation and frost.^33,34 However, it is tedious to have to form these ice patterns by actively depositing or condensing water and waiting for freezing to occur. If desublimation could be enabled to spontaneously create patterns of ice on an otherwise dry substrate, it could open up new possibilities for making practical anti-frosting surfaces.

Ice nucleating proteins (INPs) are renowned for their ability to rapidly freeze water with minimal supercooling.³⁵ This ability stems in part from hydrophilic and hydrophobic patterns on the INPs which lower the energy barrier for ice nucleation.³⁶ Further, the surface of the protein may provide a template that orients water into a lattice structure favorable for nucleating ice crystals.^37,38 While INPs have been used extensively to freeze existing water, to our knowledge there are no reports of using INPs to control the mode of heterogeneous nucleation.

Here, we deposit INPs on a substrate to switch the mode of heterogeneous nucleation from condensation to desublimation. Beneath a critical surface temperature, desublimation occurred exclusively on the portions of the surface laden with INPs, while supercooled condensate nucleated everywhere else. Further, by patterning the surface wettability to create stripes of INPs, we can spatially control the mode of nucleation and spontaneously create ice stripes. These stripes, acting as humidity sinks due to their lower vapor pressure, create overlapping dry zones free of condensation and frost.³⁴ 

Smooth hydrophobic samples were obtained by the vapor-phase deposition of trichloro(1H,1H,2H,2H-perfluorooctyl)silane (Sigma-Aldrich) onto silicon wafers. The commercial product Snomax (Snomax International), produced from the bacterium Pseudomonas syringae, was used as the source of the INP. To control both the surface temperature and the ambient partial pressure of water vapor, the wafer was thermally bonded to a Peltier stage inside a custom-made humidity chamber (ramé-hart) as shown in Fig. 1(a).

Figure 1(b) shows one method of depositing the INPs, where a 1 μl droplet of distilled water containing 10 mg/ml of Snomax was placed onto a hydrophobic sample. The water droplet was evaporated by heating the surface to 40 °C, leaving a circular footprint of INPs on the substrate. The relative humidity of the chamber was set to correspond to a supersaturation of S = P_∞/P_s,w = 1.1, where P_∞ is the partial pressure of water vapor in the chamber corresponding to the air temperature (T_∞) and relative humidity, while P_s = P_s,w is the saturation pressure of liquid water corresponding to the desired surface temperature (T). Once the appropriate humidity was obtained, the Peltier stage was then rapidly plunged down to T = −5 °C, −10 °C, −15 °C, −20 °C, or −25 °C to observe the initial mode of nucleation occurring on the surface. The supersaturation value of S = 1.1 was chosen to ensure that the substrate remained dry from nucleation until it reached the steady-state set-point temperature, as the silanized wafer exhibited a supersaturation degree of SSD ≈ 0.1. The onset of nucleation was observed using a top-down optical microscope (Nikon Eclipse LV150) set at 10× magnification placed above a quartz viewing window embedded in the roof of the humidity chamber [see Fig. 1(a)].

At T = −10 °C, a film of condensation formed on the portion of the substrate containing the INPs [Fig. 2(a)]. The liquid phase of this initial nucleation was evident from rainbow-colored fringe patterns observed within the condensing film (see movie corresponding to Fig. 2). After several seconds, this supercooled liquid froze over into ice, which is known as condensation frosting.²⁸ However, when the surface was brought down to T = −15 °C, discrete ice crystals formed on the particle-laden surface rather than supercooled condensation as evidenced by their irregular shape and sharp contrast [Fig. 2(b)]. This indicates that desublimation occurs rather than condensation frosting.

This desublimation mode of nucleation was observed for all temperatures T = −15 °C and lower. In other words, by the time an embryo grew to ∼1 μm for identification under the microscope, it was already in the ice phase. However, the initial nucleation event cannot be directly observed, as the ∼1–10 nm critical size of an embryo is smaller than the optical resolution of the microscope.¹ Even if a nanoscale embryo did initially exhibit the supercooled liquid phase, the INPs promote freezing at time scales and length scales so small as to be practically indistinguishable from desublimation. Throughout the manuscript, when we refer to nucleation being in the desublimation mode, we are therefore referring to desublimation in this practical (i.e., micro-scale) sense of the word.

In a second set of experiments, hydrophilic stripes were patterned along hydrophobic silicon samples as illustrated in Fig. 1(c). Stripe-shaped holes were cut into aluminum to make a mask, where both the stripes and intermediate areas were 1 mm in width. This mask was placed atop a hydrophobic sample for 5 min in an oxygen plasma cleaner to selectively restore the hydrophilicity of the silicon (Plasma Etch Inc., PE-25). When depositing the aqueous Snomax solution onto the surface, it preferentially spread along the hydrophilic stripes while leaving the hydrophobic background dry. The water was then evaporated and the surface cooled to a subfreezing temperature in the same manner as previously described.

Snomax deposited onto the hydrophilic stripe arrays exhibited the same general behavior as that deposited onto the uniformly hydrophobic surface. In other words, condensation frosting occurred on the stripes for T ≥ −10 °C while desublimation occurred for T ≤ −15 °C. Interestingly, the desublimated stripes of ice were able to keep the hydrophobic regions of the wafer completely dry of condensation and frost even under supersaturated conditions (S = 1.1). This is due to the depressed vapor pressure of ice compared to liquid water at the same temperature,³² such that the ice stripes siphon all nearby moisture from the air.³⁴ Even for the case of condensation frosting at T = −10 °C, the films of supercooled water on the hydrophilic stripes froze quickly (∼10 s) into ice stripes. This allowed for the droplets in the hydrophobic region to be evaporated before they could freeze, drying the surface after about 1 min [Fig. 3(a)]. The design parameters for ensuring overlapping dry zones between ice stripes have already been characterized by a recent report;³⁴ here, we instead focused on the spontaneous nucleation of the ice stripes themselves.

As a control, for hydrophilic stripes not containing INPs, the time required for the filmwise condensate to freeze was longer by about two orders of magnitude (∼10 min). By the time of freezing onset, the droplets growing in the hydrophobic regions were too large to completely evaporate, resulting instead in inter-droplet ice bridging^11,12,39 that spread frost across the surface [Fig. 3(b)]. A second control surface was uniformly hydrophobic without any hydrophilic regions or deposited INPs. This surface promoted dropwise condensation everywhere, which subsequently frosted over due to inter-droplet ice bridging [Fig. 3(c)]. Ironically, these findings therefore show that surfaces with both hydrophilic regions and INPs are able to suppress in-plane frost growth relative to more hydrophobic surfaces.

The edges of the circles or stripes feature a more dense assemblage of INPs compared to the middle region, as evident in Figs. 2 or 3(a). This is due to the well-known coffee-stain effect, which is ubiquitous to evaporation-induced colloidal deposition.⁴⁰ However, scanning electron microscopy revealed that the degree of inhomogeneity is less extreme than appears with optical microscopy (Fig. 4). Regardless of the extent of inhomogeneity of the deposited INPs, they promoted the same behavior for both the circles and stripes with regard to the mode of nucleation.

The critical nucleation pressure for embryo formation, p_n, can be calculated using the equation^1,5

where v is the molar volume of water (v ≈ 18.016 ml) or ice (v ≈ 19.65 ml), R = 8.314 J/mol K is the universal gas constant, σ is the surface tension of water (for condensation) or ice (for desublimation), k = 1.38 × 10⁻²³ J/K is the Boltzmann constant, I* = I₀/I_c ∼ 10²⁴ is the ratio of the kinetic constant to the critical embryo formation rate, and $f=(2+cos θ)(1−cos θ)2$ captures the effects of surface wettability. Note that the saturation vapor pressures of water (p_s = p_s,w) and ice (p_s = p_s,i) have already been estimated over a wide range of subfreezing temperatures.³² 

Figure 5(a) shows the critical nucleation pressure for condensation (p_n = p_n,w, blue curve) and desublimation (p_n = p_n,i, red curve) as a function of surface temperature and wettability. It can be seen that p_n,w and p_n,i intersect each other along a critical curve, with p_n,w being favorable (i.e., lower) on one side and p_n,i being favorable on the other. By zooming in to focus on the intersection in Fig. 5(b), it can be seen that desublimation is only favored for colder temperatures and lower contact angles.

These three-dimensional plots can be simplified into 2D plots by exclusively graphing the intersecting curve. In Fig. 5(c), the critical nucleation pressure where p_n,w = p_n,i is plotted as a function of surface temperature (red dashed line). Above this dashed line, condensation is predicted to be favorable, whereas desublimation is favorable beneath. This graph also contains experimental measurements, where each data point represents the vapor pressure required for phase-change to first occur on the INP-laden surface for a given temperature. As expected, the observed mode of nucleation was condensation (blue squares) when the experimental p_n fell above the critical curve, whereas desublimation (red circles) was observed for p_n values beneath the curve. Using Eq. (2), the effective value of θ for embryos was extracted for each experimental value of p_n and T. This revealed that the surface areas laden with INPs exhibited an effective wettability of θ ≈ 30°, such that desublimation becomes favorable for T < −10 °C Fig. 5(d). It is also possible that the INPs modify the value of I^* in Eq. (2), rather than just θ, but we presume that a change in the effective wettability is more likely due to the much weaker dependence of p_n on I^*.⁵ 

In summary, substrates laden with INPs exhibited the desublimation mode of nucleation for temperatures of T ≤ −15 °C, in contrast to surface regions free of INPs which always exhibited supercooled condensation even at T = −25 °C. Even for moderate subfreezing temperatures, such as T = –10 °C, the INPs served to quickly freeze supercooled condensate two orders of magnitude faster than a conventional hydrophilic surface. By using wettability patterns to selectively deposit INPs onto a substrate, we gained spatial control over which regions of a surface promoted condensation versus desublimation. The ability of a surface to passively attain micro-patterned ice features in humid and subfreezing environments is useful for suppressing condensation frosting, as the templated ice features are hygroscopic which keeps the intermediate surface dry. Future works should examine the durability of surfaces laden with various types of ice nucleating particles or alternately explore whether patterns of superhydrophilic features could serve the same role of promoting desublimation.

This work was supported by the National Science Foundation (CBET-1604272) and the 3M Company (Non-Tenured Faculty Award).