Investigating the Effects of Solid Surfaces on Ice Nucleation

Jun 28, 2012 - Understanding the role played by solid surfaces in ice nucleation is a significant step toward designing anti-icing surfaces. However, ...
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Investigating the Effects of Solid Surfaces on Ice Nucleation Kaiyong Li,†,‡ Shun Xu,§ Wenxiong Shi,∥ Min He,† Huiling Li,† Shuzhou Li,∥ Xin Zhou,§ Jianjun Wang,*,† and Yanlin Song*,† †

Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, PR China Graduate University of Chinese Academy of Sciences, Beijing 100049, PR China § College of Physical Sciences, Graduate University of Chinese Academy of Sciences, Beijing 100190, PR China ∥ School of Materials Science and Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore, 639798 ‡

S Supporting Information *

ABSTRACT: Understanding the role played by solid surfaces in ice nucleation is a significant step toward designing anti-icing surfaces. However, the uncontrollable impurities in water and surface heterogeneities remain a great challenge for elucidating the effects of surfaces on ice nucleation. Via a designed process of evaporation, condensation, and subsequent ice formation in a closed cell, we investigate the ice nucleation of ensembles of condensed water microdroplets on flat, solid surfaces with completely different wettabilities. The water microdroplets formed on flat, solid surfaces by an evaporation and condensation process exclude the uncontrollable impurities in water, and the effects of surface heterogeneities can be minimized through studying the freezing of ensembles of separate and independent water microdroplets. It is found that the normalized surface ice nucleation rate on a hydrophilic surface is about 1 order of magnitude lower than that on a hydrophobic surface. This is ascribed to the difference in the viscosity of interfacial water and the surface roughness.

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INTRODUCTION Ice formation on exposed surfaces adversely affects the appropriate operation of infrastructures, including aircraft, ships, wind turbines, and power lines.1,2 Because of this, researchers and engineers have been extensively searching for various materials that can effectively retard3−5 or prevent6−10 ice formation or weaken the ice adhesion11,12 to mitigate icing problems associated with many practical applications. The most effective anti-icing surfaces would be ones on which impinging droplets would rebound off of or condensed droplets would be self-removed before ice nucleation occurs. As such, there would be no water frozen on these surfaces. To achieve this, one has to study how soon the impinging droplets will be rebounded off or condensed droplets will be self-removed from the surfaces. At the same time, the effect of surfaces on ice nucleation could not be neglected because this would definitely affect ice formation when droplets are in close contact with surfaces. However, the latter part has been rarely studied.13,14 Ice nucleation is usually dominated by the most active nucleation site in the system. Once ice nucleation is initiated at this site, the metastability of the system is broken and ice formation occurs spontaneously. As such, the effects of other nucleation sites will be smeared off. To elucidate the effects of solid surfaces on ice nucleation unambiguously, there are two major challenges to be overcome. One is uncontrollable impurities in water, and the other is unpredictable heterogeneities of the surface. Both will result in poor reproducibility of the experiment. In this work, we investigate the freezing of © 2012 American Chemical Society

ensembles of condensed water microdroplets on two surfaces with different wettabilities (unmodified hydrophilic silicon wafers and perfluorosilane hydrophobically modified silicon wafers). The sealed sample cell and the designed process of evaporation, condensation, and subsequent freezing ensured that condensed water microdroplets and later formed ice were kept in a saturated environment, and the effects of impurities in water on ice nucleation could be excluded. The effects of surface heterogeneities can be minimized through studying the freezing of ensembles of individual independent water microdroplets. Moreover, these freezing systems can provide the necessary statistics to access information on the nucleation process properly. We find that the normalized surface ice nucleation rate on a hydrophilic surface is about 1 order of magnitude lower than that on a hydrophobic surface at the same temperature. The difference in the surface ice nucleation rates was explained by the viscosity of interfacial water and the surface roughness. The findings shed new light on the freezing mechanism of water droplets on solid surfaces and will be of significance for the construction of anti-icing surfaces.

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EXPERIMENTAL SECTION

Sample Preparation. Silicon wafers and cover glasses were sequentially cleaned by sonication in ethanol, acetone, and ultrapure Received: April 12, 2012 Revised: June 13, 2012 Published: June 28, 2012 10749

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Figure 1. Schematic representation of the experimental apparatus used to study the effect of the surface on ice nucleation. The sample cell on the cryostage is composed of a rubber O-ring sandwiched between two glass coverslips. The right panel illustrates the process of the formation of water microdroplets through the evaporation and condensation process.

Figure 2. Sequential images of water microdroplets on the (a, b) unmodified hydrophilic silicon wafer surface and (c, d) FAS-17-modified hydrophobic silicon surface (a, c) before and (b, d) after freezing. The insets show magnified images of microdroplets indicated by white circles to make the change in opacity before and after freezing more obvious. The temperatures of water microdroplets are (a) −32.9, (b) −38.7, (c) −37.2, and (d) −39.4 °C. The scale bar is 50 μm. surface were 0.51 ± 0.21 and 1.21 ± 0.07 nm, respectively (the standard deviation was based on five measurements). Formation and Ice Nucleation of Water Microdroplets. A schematic representation of the experimental apparatus used to determine the freezing temperature is shown in Figure 1. It consists of an optical microscope, a homemade sample cell, and a Linkam THMS 600 cryostage. The sample cell consists of a rubber O-ring sandwiched between two glass coverslips. After a 0.5 μL water macrodroplet (MilliQ, 18.2 MΩ cm) was placed at the edges of the solid substrates to be tested, the second coverslip was then placed over the O-ring to form the sample cell sealed with silicone vacuum grease. Then this sample cell was mounted on the cryostage. The whole sample-preparation procedure was carried out in a biosafety cabinet to minimize possible contaminants.

water. Ultrapure water was provided by a Milli-Q reference system. For the preparation of hydrophobic silicon surfaces, the silicon wafer was first treated with a mixture of hydrogen peroxide (30%) and sulfuric acid (98%) (20:80 v/v) for 60 min at 90 °C. (Caution! Piranha solution reacts violently with organic compounds and must be handled with extreme care.) After being blown dry with a flow of highpurity argon, the samples were then placed in a desiccator together with a vial containing liquid 1H,1H,2H,2H-perfluorodecyltrichlorosilane (FAS-17) (Alfa Aesar). The desiccator was evacuated, and the sample was kept in the desiccator for 12 h at room temperature. Finally, the sample was taken out and baked in an oven at 60 °C for 1 h. The contact angles were 55.2 and 113.7° on the unmodified hydrophilic silicon wafer surface and an FAS-17-modified hydrophobic silicon surface, respectively. The root-mean-square roughness values of the unmodified silicon wafer surface and the FAS-17-modified silicon 10750

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Figure 3. Freezing temperature of water microdroplets as a function of the number of freezing events on (a) an unmodified hydrophilic silicon wafer surface and (b) a FAS-17-modified hydrophobic silicon surface.

inclusions in fused silica capillaries (Tm = 0.0 °C). Then the resulting data was synchronized manually to the corresponding sequential images to determine the freezing temperature for each microdroplet in the field of view. We present the freezing temperature histories of 430 and 630 statistical freezing events on the unmodified hydrophilic silicon wafer surface (Figure 3a) and FAS-17-modified hydrophobic silicon surface, respectively (Figure 3b). From Figure 3, the freezing temperatures of water microdroplets on two surfaces exhibit a stochastic distribution ranging from −38 to −40.1 °C on the unmodified hydrophilic silicon wafer surface and from −37.8 to −39.9 °C on the FAS17-modified hydrophobic silicon surface. To characterize the details of the freezing probability on two surfaces quantitatively, we bin the freezing events into 11 temperature bins to produce a freezing probability distribution of ni/Ntotal, where ni denotes the number of nucleation events in the ith temperature bin and Ntotal represents the total number of nucleation events. The resulting freezing probability distribution for two surfaces is presented in Figure 4. From

To realize the compartmentalization of pure water into a large numbers of microdroplets, the water macrodroplet in the sample cell was first evaporated onto the upper coverslip and maintained for a certain time. The sample was then cooled at a rate of 5 °C/min as controlled by the cryostage, and the water on the upper cover glass was transported to the surface of the solid substrate under study with the formation of large numbers of microdroplets. When the solid substrate was cooled further, the water microdroplets on the solid substrate froze. The temperature at the onset of freezing was identified through a video recorded by a high speed CMOS camera (Phantom V7.3) at 200 frames/s. Then the sample was heated to thaw the frozen droplets, and the cycle was repeated to obtain sufficient freezing events.

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RESULTS AND DISCUSSION The detection of the freezing events of water microdroplets was identified using an optical microscope. Figure 2 shows the observed sequential images of water microdroplets on the unmodified hydrophilic silicon wafer surface (Figure 2a,b) and the FAS-17-modified hydrophobic silicon surface (Figure 2c,d) before and after freezing. When the silicon wafer was cooled, condensation first occurred and then water microdroplets formed on the surfaces, with the diameter ranging from 14.5 to 66.7 μm on the unmodified silicon wafer surface and from 10 to 31.2 μm on FAS-17-modified silicon surface (Figure 2a,c). When the temperature was further lowered, freezing occurred as signified by the sudden increase in the opacity of water microdroplets. The insets of Figure 2 show the magnified images of water microdroplets outlined by white circles to illustrate the change in opacity before and after freezing. It can be seen from the insets that the freezing of microdroplets is clearly recognizable through the appearance of “ice structure” within microdroplets (Figure 2b,d; see the Supporting Information for a video of the freezing of water microdroplets). Here we want to state that water freezing is divided into ice nucleation and ice growth. Above the homogeneous nucleation temperature, TH ≈ 232 K, ice nucleation is the slower process. Once the ice nucleus is formed, ice grows spontaneously.15 Therefore, it is safe to say that the sudden onset of freezing that we observed is ice nucleation. A phantom V7.3 camera was used to capture all of the freezing events in the field of view at a typical rate of 200 frames/s. The cryostage temperature is recorded about every 300 ms with 0.1 °C accuracy. The temperature lag between silicon surfaces and the cryostage was calibrated through H2O

Figure 4. Freezing probability distribution as a function of temperature on the unmodified hydrophilic silicon wafer surface (△) and FAS-17-modified hydrophobic silicon surface (○).

Figure 4, the peak temperature for the maximum freezing probability density is −39.3 °C for the unmodified hydrophilic silicon wafer surface, which is lower than that for the FAS-17modified hydrophobic silicon surface (−38.9 °C). We employed the method proposed by Walton16 and Inada17 to determine the ice nucleation mode on two surfaces, where they used ψ, the power dependence of the nucleation rate on the diameter of the microdroplets, as the criterion to distinguish 10751

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Figure 5. Freezing temperature of water microdroplets as a function of droplet diameter d on (a) the unmodified silicon wafer surface and (b) the FAS-17-modified silicon surface.

the nucleation mode. When ψ approaches 2, surface-initiated nucleation is dominant, whereas a ψ value approaching 3 indicates volume-initiated nucleation. To apply this method to experimental situations where the water microdroplets exhibited spherical cap shapes on two surfaces, the measured diameter d0 (measured by ImageJ) was converted to an equivalent droplet diameter d, which was defined as the diameter of a droplet possessing the same volume as the observed spherical cap under the optical microscope. Then the d values were calculated to be 0.6d0 and 0.92d0 using contact angles of 55.2° on the unmodified silicon wafer surface and 113.7° on the FAS-17-modified silicon surface, respectively. The plots of freezing temperature as a function of droplet diameter d on two surfaces are shown in Figure 5. First, assuming a freezing ensemble that contains N0 microdroplets in the liquid state where each droplet has the same average diameter d at a constant temperature, if N out of N0 droplets remain unfrozen after a time interval Δt, then the nucleation rate J can be expressed as follows:16,17 J=−

1 N ln Δt N0

Γ=

Because the water microdroplet diameters on two tested surfaces are not constant, J can be obtained by dividing the data in Figure 5 into small domains in which the temperature and microdroplet diameter are assumed to be constant. Thus, eq 1 can be applied for each domain. Then the microdroplet diameters in Figure 5 are divided into 12 bins, and the freezing temperatures are equally divided into 11 bins with a width of 0.2 K. Equation 1 is rearranged to give the following expression16,17

(2)

where ψ is the power dependence of the nucleation rate on the diameter of the microdroplet and g is a geometrical constant. From classical nucleation theory, the nucleation rate can be expressed as18,19 log10 R(T ) = log10 J0 −

Γ 2.303T (Tm − T )2

3q2k

and where J0 is a prefactor, γSL is liquid−nucleus interfacial energy, νi is the specific volume of ice, Tm = 273.15 K is the melting point, q is the latent heat of fusion, k is Boltzmann’s constant, θ is the contact angle of the critical nucleus on the solid substrate, and f(θ) is the contact angle factor. We assume the nucleation rate J in each domain calculated from eq 1 can be described by the classical nucleation theory indicated by eq 3. Thus, the experimental nucleation rate J calculated from eq 1 is fitted to eq 3 as deduced from classical nucleation theory. The nucleation rates Jfitting from the fitted curves were employed to yield ln Jfitting versus ln d curves from which ψ could be obtained for each temperature group. In our case, ψ ranges from 0.94 to 1.38 for the unmodified hydrophilic silicon wafer surface, and it ranges from 0.28 to 2.08 for the FAS-17-modified hydrophobic silicon surface. The values of ψ for both surfaces are much closer to 2 with respect to 3, which clearly indicates that the surface-initiated nucleation mode is dominant on the two tested surfaces. In our experiments, the interface between supercooled liquid water droplets and the sample surface is the only variation; therefore, the freezing of supercooled water microdroplets on two model surfaces is initiated by nucleation at the liquid−solid substrate interface. This coincides with the recent observations by Poulikakos20 et al. where they found that the freezing of supercooled water droplets on a solid substrate without any external gas flow was typically initiated at the liquid−solid interface. Then, the freezing temperature distributions in Figure 3 are divided into 11 temperature bins with a width ΔTi, containing ni nucleation events with a temperature Ti centered on ΔTi. The nucleation rate R(Ti) is calculated as follows21 rni R(Ti ) = n ΔTi( 2i + ∑j > i nj) (4)

(1)

⎧ ln(N /N0) ⎫ ⎬ = ψ ln d + ln(Jg ) ln J = ln⎨− ⎩ ⎭ Δt

16πf (θ )γSL 3νi 2Tm 2

where Σj>inj is the number of water microdroplets remaining in the liquid state in temperature bin Ti and r is the cooling rate. It is noted that eq 3 is deduced from classic nucleation theory and that eq 4 is a mathematically statistical method used to analyze the nucleation process. The obtained values of ψ indicate that the ice nucleation on solid surface is initiated at the liquid−

(3)

where 10752

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in addition to the freezing probability density. The results show that the surface ice nucleation rate on the unmodified hydrophilic silicon wafer surface is about 1 order of magnitude lower than that on the FAS-17-modified hydrophobic silicon surface at the same temperature. The present results provide insight into the fundamental understanding of ice nucleation on solid surfaces and is also beneficial for the effective design of anti-icing surfaces.

solid substrate interface. Thus, the obtained ice nucleation rate R(Ti) according to eq 4 can be normalized by the droplet−solid substrate interfacial area

R s(Ti ) =

R(Ti ) S̅

(5)

where the S̅ is the average droplet−solid substrate interfacial area within each temperature bin. The droplet−solid substrate interfacial areas were calculated under the consideration of spherical droplet caps on the surfaces. The normalized surface ice nucleation rates on two surfaces are shown in Figure 6.

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ASSOCIATED CONTENT

S Supporting Information *

Freezing of water microdroplets on an unmodified silicon wafer surface and a FAS-17-modified silicon surface. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected], [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are very thankful to Yifan Zhang for assistance with AFM characterization. We are grateful for support from the Chinese National Nature Science Foundation (grant nos. 50973117, 21074139, 20904061, 50625312, 50671003, 51173196, 21004068, U0634004, and 20721061), and the 973 Program (2007CB936403 and 2009CB930404, 2011CB932303 and 2011CB808400).

Figure 6. Surface ice nucleation rate as a function of temperature on the unmodified silicon wafer surface (△) and FAS-17-modified silicon surface (○).

(The temperature bins in Figure 6 are the same as those in Figure 4.) The error bars in Figure 6 are based on binomial statistics, and the solid lines in Figure 6 represent the best fits of eq 3 to the experimental data calculated from eq 5. Figure 6 shows that the surface ice nucleation rate on the unmodified hydrophilic silicon wafer surface is about 1 order of magnitude lower than that on the FAS-17-modified hydrophobic silicon surface at the same temperature. And the difference in surface nucleation rates on two surfaces can be understood by considering the viscosity of interfacial water and surface roughness. Houston22 et al. revealed that the viscosity of interfacial water at the hydrophilic surface is much higher than that on the hydrophobic surface. The increased viscosity impedes the diffusion and relaxation of water molecules near the active sites to form the critical nucleus on the unmodified silicon wafer surface and thus leads to a higher activation energy for transferring water molecules across the ice−water interface. This results in the lower surface ice nucleation rate on the hydrophilically unmodified silicon wafer surface. Another possibility is that the roughness of the hydrophobic FAS-17modified silicon surface (1.21 nm) is a little bit higher than that on the hydrophilically unmodified silicon wafer surface, which may facilitate ice nucleation23 and thus leads to a higher nucleation rate.

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REFERENCES

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CONCLUSIONS We have investigated the ice nucleation of condensed water microdroplets on two flat, solid surfaces with different wettabilities through an evaporation and condensation process. In this way, the uncontrollable impurities in water can be excluded and the surface heterogeneity can be minimized. Furthermore, the necessary statistical investigation of ensembles of independent freezing events provides the nucleation rate 10753

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