Substrate-Dependence of the Freezing Dynamics of Supercooled

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Substrate-Dependence of the Freezing Dynamics of Supercooled Water Films: A High-Speed Optical Microscope Study Elzbieta Pach, Laura Rodríguez, and Albert Verdaguer J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b06933 • Publication Date (Web): 18 Sep 2017 Downloaded from http://pubs.acs.org on September 20, 2017

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The Journal of Physical Chemistry

Substrate-Dependence of the Freezing Dynamics of Supercooled Water Films: A High-Speed Optical Microscope Study E. Pach,† L. Rodriguez,† A. Verdaguer§ * †

Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and The Barcelona Institute of Science and Technology, Campus UAB, Bellaterra, 08193 Barcelona, Spain §

Institut de Ciència de Materials de Barcelona ICMAB-CSIC, Campus de la UAB, E-08193 Bellaterra, Spain

*[email protected]

ABSTRACT

The freezing of supercooled water films on different substrates was investigated using a highspeed camera coupled to an optical microscope obtaining details of the freezing process not described in the literature before. We observed the two well-known freezing stages (fast dendritic growth and slow freezing of the water liquid left after the dendritic growth) but we separated the process into different phenomena that were studied separately: two dimensional dendrite growth on the substrate interface, vertical dendrite growth, formation and evolution of ice domains, trapping of air bubbles and freezing of the water film surface. We found all these processes to be dependent on both the supercooling temperature and the substrate used. Ice

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dendrites (or ice front) growth during the first stage was found to be dependent on thermal properties of the substrate but could not be unequivocally related to them. Finally, for low supercooling, a direct relationship was observed between the morphology of the dendrites formed in the first stage, which depends on the substrate, and the roughness and the shape of the surface of the ice, when freezing of the film was completed. This opens the possibility of using surfaces and coatings to control ice morphology beyond anti-icing properties.

INTRODUCTION Despite the presence of ice in our environment in many latitudes, there are still many fundamental aspects related to ice formation dynamics, ice structure and ice interaction with the environment far from being completely understood.1 Studies of ice formation from liquid water, i.e. freezing of water, are of great interest nowadays in different fields such as atmospheric chemistry2, biology3 and materials sciences4 from both fundamental and technological point of view. For example, icing in the troposphere has an important impact on the breaking of outdoor devices, machinery, aircrafts, antennas or transmission lines due to ice accretion. Anti-icing surfaces and coatings have been developed against ice accretion, mainly based on trying to avoid ice attachment to the surface.5 Nevertheless, the accurate prediction of ice accretion requires understanding freezing of supercooled water on surfaces. Pure water droplets are known to stay in a supercooling state at temperatures as low as -40 oC until homogenous nucleation of ice happens.6 When a foreign body is present, by contact of a surface with the water droplet or because the existence of a particle inside the droplet, heterogeneous nucleation of ice can take place at the interface, triggering freezing of the droplet at higher temperatures than homogeneous


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nucleation. Despite of that, water droplets in the atmosphere still predominantly freeze at supercooling temperatures lower than -5 oC. The freezing process of supercooled water droplets has been studied for decades6 and the process has been traditionally described split in two stages if the droplet is large enough (micrometer to millimeter size7): first a fast quasi-adiabatic stage, where a dendritic ice network is formed, keeping the rest of the droplet still in a liquid state, and then a slow quasi-isothermal stage where the droplet completely freezes (from the outside to the interior if the droplet is suspended in cold air8,9 or inside another cold liquid10 and perpendicular to the interface if the droplet is in contact with a cold surface11). The first stage happens in the order of milliseconds and it is kinetically controlled while the droplet is heated to the melting point. The second stage is limited by heat transport. The reason of the presence of two stages is thermodynamic and dominated by the limited amount of the formation heat that can be released by the droplet to the exterior. Most of the formation heat is kept inside the droplet during the first stage, maintaining the water surrounding the ice dendrites in a liquid state at 0 oC. The structure and density of the dendrites formed in the first stage are known to strongly depend on the supercooling temperature12-13 and the size of the droplet14. Other environmental factors, such as gas flow surrounding a droplet15 or the absence of gravity16 have also been studied. The influence of surfaces on the two stages of water freezing has received much less attention and, in many studies of ice crystal growth, the presence of surfaces has been experimentally avoided due to undesirable or uncontrollable effects17. Nevertheless, some studies have investigated the influence of the contact angle on the growth dynamics of dendrites, however some results seem contradictory and a conclusive relationship has not been achieved yet.14, 18,19 Other studies have focused on the influence of the triple line defined by the surface-liquid-air interface14, 20-21 on the initial nucleation point. Very recently, Kong and Liu19 proposed a theory on the icing evolution


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of supercooled water near a solid substrate. They observed water freezing in contact with different substrates, mainly metals, using a high-speed camera and they concluded that the freezing process was dominated mainly by heat transfer between the metallic surface and the ice. On the other hand, it is known that the structure of water at the interface of a solid surface is strongly influenced by the chemical and structural properties of the surface at the nanometer scale.22 For example, the existence of thin ice-like films (formed by a few water molecule monolayers) has been proven on the surface of many substrates at room temperature.23-26 It is thus strongly supposable that ice nucleation and dendrite growth in the vicinity of a surface could also be influenced by the structure of water at the solid/water interface and that this effect would also have an impact on the morphology and the crystallinity of the ice formed at the end of the second stage. In the present work, we used a high-speed camera coupled to an optical microscope to study the freezing process of supercooled water films, with thicknesses lower than 1 mm, on top of well-defined surfaces as a function of supercooled temperature. The surfaces chosen for this study were glass, mica, silicon and quartz. These substrates were chosen as model silicon-based materials that can be found widely in both natural and artificial environments, but showing a wide range of different thermal properties (see Table 1). All of them are hydrophilic and flat in the nanometer range to avoid uncontrolled roughness influence. Only in the case of mica, the presence of crystallographic steps could have an impact on the freezing process, as it has been observed with other water interface phenomena such as wetting or surface reactivity at surface steps of ionic crystals.27-28 EXPERIMENTAL SECTION:


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A LTS120E Linkam chamber (Linkam Scientific Instruments, Surrey, UK) was assembled on the stage of an Olympus BX41M-LED optical microscope to control both the temperature and the environment of the sample. The optical microscope was equipped with a 10×, 20× and 50× long working distance objectives (LMPLFLN10X, SLMPLN20X and SLMPLN50X, Olympus) and a Hamamatsu ORCA-Flash 4.0 Digital CMOS C11440 high-speed camera (Hamamatsu Photonics, Japan). The LTS120E chamber is equipped with a Peltier cooling stage able to cool down to -25 oC with a platinum resistor sensor embedded close to the surface for accurate temperature measurements (0.1 oC). Mica (muscovite mica), glass (glass slices from LINKAM), quartz (0001 face, CRYSTAL 1SIO2401E) and silicon wafer (Silicon Materials INC., USA) with thicknesses from few hundreds of µm to 1 mm were cut to a 1 cm2 area. Backsides of transparent samples (mica, quartz and glass) were coated with a 5 to 10 nm gold layer by evaporation to improve light reflectivity. Mica was cleaved before experiments and the rest of the samples were exposed to UV/O3 (Novascan PSD-UV using 185 nm and 285 nm UV light) for 20 minutes. This treatment eliminates most of the carbon contamination and makes the surface highly hydrophilic24, as corroborated by the low contact angle (less than 10 degrees) when a droplet of water is placed on the sample. The roughness of the surfaces was checked using atomic force microscopy (AFM), obtaining values in the order of few nm. During the freezing experiments 20 µl of MilliQ water was placed on the sample. Water spread over the entire surface due to its high hydrophilicity, covering it completely. Temperature of the Peltier was then lowered to the desired supercooling temperature ∆T (oC) = 0-TPeltier and a sharp tip of ice at 0 oC was manually put in contact with the surface of the sample, inducing contact freezing of the water film, while a high–speed video of the process was recorded (see scheme in Figure 1). Nucleation was triggered always far from the field of view of the optical microscope.


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Depending on the velocity of the freezing process videos were taken with the following conditions: 2048 x 2048 pixels at 100 frames per second (fps), 2048 x 1024 pixels at 200 fps and 2048 x 512 pixels at 400 fps. Because the experiments were performed in an open environment, to allow contact with the ice tip, during the experiments some water condensation from the environment could not be avoided, increasing the initial thickness of the water film. However this thickness was always below 1 mm, as measured using a ruler. Some experiments were also performed with a small droplet of around 2 µl, not covering the entire surface, to visualize better the different stages of the freezing process in the movies. For a better visualization of the freezing contrast, the features of the sample (for example mica cracks, etc..) that can difficult the interpretation of the images were removed by subtracting the last frame recorded before dendrites appear in the field of view from the following frames (Figure S1 in the Supporting Information). Velocity was measured using the software provided by the camera producer, Hamamatsu Photonics, by measuring the distance between the position of a dendrite tip in one frame and its position in the next frame. Time between frames was recorded automatically. Velocity was obtained by dividing distance and time. This process was repeated for each frame while the dendrite tip advanced in the field of view of the microscope. From 20 to a minimum of 5 measurements, depending on the freezing velocity, could be performed in this manner for each recorded experiment. Then, the average velocity was calculated for each experiment. Experiments were repeated 3 to 5 times for each temperature depending on the variations of the dendrite’s morphology observed. Velocity values as a function of supercooling temperature correspond to the average value obtained from all experiments performed at the same temperature. Error bars correspond to the statistical deviation of the measurements.


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In many studies found in the literature supercooling temperatures are always shown with positive values because they are defined as the difference in temperature to the melting point; ∆T (oC) = 0-TSustrate. In this work we decided to show results using the actual temperatures measured on the substrate (TS) keeping their negative values, for simplicity and easiness in understanding of the figures at the first sight, while keeping the supercooling temperature nomenclature in the manuscript and the plots. In addition, when in the manuscript supercooling temperatures are compared, it is considered that a supercooling temperature is “higher” than another temperature when TS is more negative and vice versa for “lower”. The term: “increasing/decreasing supercooling temperatures” means modifying TS to colder/warmer temperatures. RESULTS: As soon as the ice tip entered in contact with the supercooled water film, nucleation was triggered and dendrites started to grow from the nucleation point. After a very short time (from few seconds at the warmest temperature to almost instantly, from eye view, at the coldest temperatures) the first dendrites reached the field of view of the microscope. Evolution of the dendrites was registered as a sequence of images at different frame rates, chosen according to the velocity of the dendrites evolution. In Figure 2 selected frames of a sequence of images taken during the freezing process of water film on a quartz sample at -3 oC is shown. A video, reconstructed using all the frames can be seen in the Supporting Information (Movie S1). Time 0 in Figure 2 has been arbitrary chosen as the time registered for the frame taken just before the first dendrite appeared in the field of view of the microscope. Figure 2a and b correspond to the first stage of freezing, i.e. the fast planar growth of the dendrites, while Figure 2c, d, e and f correspond to the second stage, i.e. the slow vertical growth of ice from the substrate/water


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interface until the surface of the water film is reached. In this case the film was not completely flat and ice reached first the top left corner of the field of view (Figure 2d) then advanced diagonally until all the film was frozen (Figure 2f). Due to the limitation of the depth of the field of view (around a hundred µm at its best), not all the thickness of the water film can be in focus at the same time and therefore in Figure 2f the bottom right corner is out of focus. From the times of the snapshots it can be observed that the first stage was at least one order of magnitude faster than the second stage. Experiments were performed for TS in the range of -0.5 to -10 oC. However, on some substrates (for example quartz) heterogeneous nucleation was triggered by the substrate before TS = -10 oC was reached and hence the range of temperatures in the experiments was limited. In Figure 3 images of the dendritic structures formed during the first freezing stage on mica, glass, quartz and silicon are shown. Images were selected to show the most representative dendrite morphologies found on each substrate when nucleation was triggered at different supercooling temperatures. Videos showing dendrites growth at -3 oC for the four samples can be seen in Movie S2, S3, S4 and S5 in the Supporting Information. Ice structures can generate a large amount of different complex morphologies as it was already stated in the famous snowflake Nakaya diagram29; a diagram that has not been successfully reproduced by models until very recently30. A morphology diagram on non-equilibrium patterns of ice crystals growing in water droplets was also proposed by Shibkov et al.12 They divided the patterns observed in four main morphologies that were found to be dominant in different ranges of supercooling temperatures, some of them coexisting for the same temperature. The main morphologies were: dendrites for supercooling temperatures lower than -4 oC, needle–like crystal from -4 oC to -8 oC, fractal needle branch from -4 oC to -12 oC and compact needle and platelets from -8 oC to -18 oC. Due to limited spatial resolution in their measurement, Kong and Liu19


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could only differentiate two different structures depending on the substrate used, an homogeneous film for metal substrates and a compact and dendritic needle branch for bad thermal conductors such as glass. Frames shown in Figure 3 reveal important differences on the morphologies of dendrites formed on mica and glass compared to quartz and silicon. Dendrites formed on glass and mica exhibit a continuous evolution as supercooling temperature increases; they start with a needle-like crystal morphology at -1 oC that becomes more fractal when the supercooling temperature increases until around -5 oC when they adopt a morphology similar to what was defined by Shibkov et al. as compact needle-like dendrites structure. No important differences on the morphology are observed for TS between -5 and -10 oC. On the contrary, on quartz a very dense dendrite structure is observed even at TS = -1 oC, similar to the one observed for mica at TS = -9 oC. At higher supercooling temperatures an advancing regular ice front is formed with a very compact dendritic texture that seems to leave very few liquid water inside it. This regular front is observed on silicon already at TS = -1 oC. On this substrate morphology changes with increasing supercooling temperature seem to be limited to an increase of the density of the dendritic texture rather than modifying the morphology of the ice front. One of the commonly measured parameter in the first stage of water freezing is the growth velocity of dendrites or ice fronts. Velocity was measured from the ice advancing front, for the compact structures observed for silicon or quartz, and from the position of a dendrite tip that was following a linear evolution and not directly interfering with other dendrites in the other cases. In Figure 4 measured dendrite velocities are plotted as a function of the supercooled temperature ∆T (oC) = 0-TSustrate for silicon, glass, quartz and mica. Error bars correspond to statistical deviation for different experiments. Our measurements are compared with reported dendrite velocity measured in bulk water12 (no surface present). For all substrates and temperatures,


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dendrite growth was faster than reported values for bulk water. The curves can be fitted by the modified Noyes and Whitney growth mechanism model, where the driving force is represented in terms of the supercooling temperature31: ‫ ܶ∆ܽ = ݒ‬௕

(1)

where v is the front/dendrite velocity (commonly in cm/s) and a and b are fitting parameters. The best fitting parameters found from our measurements were: glass: a=0.07, b=2.29; mica: a=0.095, b=2.06; quartz: a=0.49, b=1.72; silicon: a=0.22, b=1.94. Dendrites created in the first freezing stage grow mainly co-planar with the substrate. Once horizontal growth of the dendrite structure is completed dendrites evolve creating what we call ice domains on the surface (discussed below) that grow vertically. However, as the supercooling temperature was increased, vertical dendrites were also observed to grow starting from the coplanar dendrites. The temperature at which the vertical dendrites were first observed depended on the substrate; while on mica and glass they were first observed at TS between -4 and -5 oC, on silicon and quartz they were not observed until a TS of -7 oC was reached. Our set up does not allow measuring the velocity of vertical dendrites but they can be observed on the images as dark areas growing out of focus (see the dark areas appearing in frames for mica and glass at TS = -7, -9 and -10 oC in Figure 3). In Figure 5 images of the initial growth of vertical dendrites on glass at TS = -6 oC are shown. These images were recorded with the optical focus changed slightly above the substrate’s surface for a better visualization of the dendrites. Figure 5a shows a surface covered by a dendritic structure starting to form ice domains. Some regular circular domains seem to grow faster than the other, forming pillar-like structures growing into the liquid part of the film (Figure 5b). These domains appear mainly at the intersection of dendrite arms or at the


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center line of dendrite patterns. At some point, from some of this pillars, a new dendritic growth is triggered that advances rapidly into the water at a certain angle from the surface (Figure 5c and d). On most of the vertical dendrites two branches growing from the initial nucleation point are observed, as already observed for initial nucleation on pure water. As soon as the dendrites are formed they start to grow both laterally and vertically with a time rate much lower than the time needed for the formation of the dendritic structure. Crystals from each branch of the dendritic structure grow until they find each other, filling the surface with a complex network of crystals that we will call ice domains (see Movie S1 and S2 in the Supplementary Information). The structure of these domains depends on the original dendrite shape, therefore they depend directly on the substrate and the supercooling temperature. Even if the domains are originated from the same dendrite branch they keep a domain boundary while growing and rarely coalesce to create larger domains. See Figure 6 for an example of domain structures on mica. This domains structure is kept as the ice grows vertically although some dynamics of the domains are observed. The vertical growth of the ice was found to be dependent on TS (not measured due to the experimental set-up configuration displayed on Figure 1). If the freezing process is fast enough, air bubbles get trapped in the crystal and they can be observed decorating the domain boundaries (see Figure S2 in the Supporting Information). This gives the macroscopic ice a whitish appearance while for slow dynamics, i.e. low supercooling, the crystals are transparent. The final stage of the freezing process is the freezing of the water film surface. Ice domains grow vertically until they reach the surface of the film creating a rough ice surface (see for example Figure 2c to f or Movie S1 in the Supporting Information).


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DISCUSSION: Although the freezing dynamics of water have been traditionally separated in two stages, dendritic fast growth and slow solidification of the liquid water left during the dendritic growth, recent works already pointed out the need of taking into account a larger number of differentiate stages that occur during freezing19. From our observations, we differentiate five different processes during the freezing of a water film in contact with a cold surface: planar dendrite growth, vertical dendrite growth, ice domains evolution, trapping of air bubbles and surface freezing. In Figure 7 a scheme of these differentiated processes is shown. All these processes are closely linked and some of them may not be present for some conditions. We think that each one of them should be analyzed separately because each one of them has consequences on parameters considered of importance in water freezing occurring in our daily live: the time needed for the freezing to be complete, the amount of liquid water left inside ice, the macroscopic final structure of ice or the impurities trapped inside it. All these parameters depend strongly on the supercooling temperature but they also depend on the properties of the underlying surface. We are going to discuss our findings for each process in the following paragraphs. Shape, density and growth velocity of the planar dendrites depend on the supercooling temperature, as it has been already widely reported in freezing experiments not involving the presence of a surface.6 As mentioned above, the morphology of dendrites that we found on glass and mica (Figure 3) follow approximately the morphology diagram established by Shibkov et al.12 On the other hand, we found a strong deviation from this classification for dendrites on quartz and silicon. On quartz, dendrites at TS = -1 oC are very similar to dendrites observed on mica at TS = -9 oC (Figure 3) while the ice front structure of silicon is not observed on mica or


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glass for the range of supercooling temperatures studied. Dendrites shape and velocity depend on the heat transfer between the ice being formed, liquid water surrounding the ice and the substrate, also in contact with the ice. Kong and Liu19 found a crucial influence of the substrate’s thermal properties on the morphology and the formation velocity of the dendrites. In Table 1 we are listing the thermal conductivity and diffusivity (calculated from the density and the heat capacity) for each of the four substrates used here. Mica and glass show very similar values, slightly higher than water, while quartz has a thermal diffusivity one order of magnitude and silicon two orders of magnitude higher. Thermal diffusivity of silicon is similar to some of the metal samples used by Kong and Liu19, where they observed an homogeneous ice front growth with no internal structure. However, according to the authors, the front of the ice films was not clearly seen in the magnification used in their experimental set up. At our magnification instead of a homogenous ice crystal we are able to distinguish a complex and dense dendritic-like structure inside the front, especially at low supercooling temperatures (see Figure 3). Dendrite formation happens due to faster growth of the hexagonal ice crystal along the a axes (a1, a2, a3, see scheme in Figure 8a) as compared to the c axis32-34. As ice grows following one of the a axes (a1 in Figure 8a) lateral branches along the other a axes (a2 and -a3 in Figure 8a) can be generated, forming the well-known snowflake dendritic structure. Two different dendrite structures were found to be the most common in our experiments: a) the classical fern-like dendrite, in which branches of both sides form a 60 degrees angle with the primary growth direction (-a2 and -a3 branches in the scheme and picture in Figure 8a) and b) the fishbone-like dendrite with one branch forming 60 degrees and the other 120 degrees with the primary growth direction (a3 and –a3 in the scheme and picture in Figure 8a). Although all a axes and directions are crystallographically equivalent, corresponding to fast growth directions, fishbone structures


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are not found in natural snow because in a fishbone structure one of the side branches is growing backwards with respect to the growth direction of the main branch and these side branches would then have to grow between two of the six main branches which would be excluded because of diffusion problems. In our case, the fast growth of dendrites along the primary branch allows the growth of fishbone-like dendrites because they don’t interfere with any other dendrite branch. Fishbone was the most common morphology found for mica and glass at low supercooling. Kong and Liu19 also found that the growth velocity of the dendrites/ ice front was also strongly influenced by the substrate’s thermal properties for supercooling temperatures up to -7 oC. For higher supercooling temperatures, other authors18 found that substrate’s influence on the growth velocity is negligible. In our measurements, we found a clear dependence on the velocity with increasing thermal diffusivity of the substrate, but not a monotonous increase. Mica and glass displayed a similar trend, with silicon showing higher velocities. Dendrite growth velocity on silicon is remarkably higher than on glass, despite having a surface chemically similar to glass (on a Si wafer exposed to ambient conditions the surface is covered by a thin hydrophilic amorphous silicon oxide layer24) and with similar roughness. It is thus clear that velocity of dendrites in this case is dominated by the difference in thermal diffusivity between silicon and glass (see Table 1). However, quartz, which has a lower thermal diffusivity than silicon (see Table 1) exhibited higher velocities than silicon for TS lower than -3 oC. In Figure 9, the fittings of eq (1) to our data are compared with fittings reported by Kong and Liu for copper, brass and glass19. Thermal conductivities of brass and silicon are very close and when the fitted curves of brass and silicon are compared they show a very similar trend. In the same line, reported curves for glass follow a more deviated trend compared to our measurements but still close to it. However, reported tendency for copper is very similar to our fitted curve for quartz, despite


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having thermal diffusion coefficient (1.15 × 10-4 m2s-1) two orders of magnitude higher1. Our results thus indicate that differences in thermal diffusivity are not enough to explain variations on the velocity of the ice front and the morphology of dendrites. Since the surface of the silicon wafer (amorphous SiO2) and the surface of quartz have the same stoichiometry and chemical elements, this suggests that the crystallographic structure of quartz could have a strong influence on dendrite growth. As an additional example of the influence of the surfaces’ structure or morphology to the velocity of dendrites, in Figure S3 in the Supplementary Information faster growth of dendrites induced by a mica step can be observed. However, more experiments are needed to study this hypothesis in detail. During the slow freezing stage, dendrites grow laterally until they completely cover the surface and vertically, following the thermal gradient; from the coldest point (the surface of the sample) to the warmest (the surface of the water film that is furthest from the surface)11. During this evolution, ice domains are formed with shapes and densities directly related to the morphology of the original dendrites: the denser the branches of the dendrites; the smaller the ice domains formed. Once formed, these domains are stable, although the boundaries between them show some dynamics as the ice front grows vertically. As mentioned above, during the vertical growth, if the planar ice-water interface becomes unstable it can generate new dendritic growth, in that case the new dendrite grows into the bulk and it is not coplanar with the surface (see Figure 5b). According to molecular dynamics simulations of ice growth, growth on the basal plane (along c axis) is compatible with a layer-by-layer growth mechanism and thus generating a very flat surface.32-34 On the other hand, growing of prism faces or secondary prism faces (a axes) is compatible with a collective three-dimensional growth mechanism that generates a rough and thus unstable surface (see scheme in Figure 8b). A dendritic growth theory was proposed by


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Mullins and Sekerka35 and revised by Warren and Langer36. This theory has been proven to be accurate for organic crystals37 solidification. In this theory the temperature field is considered steady and the stability of the ice-water interface is determined by the direction of the temperature gradient. According to the theory, when a substrate with high thermal diffusivity is present, the stability should be improved and it should be independent of the supercooling temperature. The dependence of the stability with thermal diffusivity is in line with the fact that we observed more instability and vertical dendrites on samples with lower thermal diffusivities, i.e. mica and glass. On the other hand, the independence on temperature is not observed in our experiments; vertical dendritic growth was never observed in our measurements for supercooling temperatures lower than -4 oC. In addition, our findings show that the supercooling temperature at which the vertical dendrites appeared depended on the substrate. If that dependence is due to the morphology (or structure) of ice domains or just to the thermal diffusivity properties of the substrate is a subject to be studied in more detail in future work. The ice domains structure show very well-defined boundaries, with large regions of aligned domains because of the alignment of the original dendrite branch structure (see Figure 7 and the end of Movie S2 and Movie S3 in the Supplementary Information). The boundaries probably contain liquid water between ice crystals. When the freezing was fast enough, a decoration of air bubbles concentrated at these boundaries (see Figure S2 in the Supplementary Information) because they were expulsed from the ice crystal structure being created. It is very surprising to see how the ice domains structure is kept as the freezing advances vertically. Although there are some dynamics in the domain boundaries as the vertical ice front grows, the shape and density of boundaries (that depend directly on the morphology of the dendrite originated at the surface) are approximately constant as the ice front advances vertically. Therefore, once the freezing process


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is finished, the roughness of the ice surface is determined by the morphology of the dendrites created during the first stage of the freezing, despite having a water film of hundreds of microns thick between the substrate and the surface of the ice. This can be observed in the freezing event shown in Figure 2, where three different dendrites created in the first stage (Figure 2a and b) generate three different ice domain areas (Figure 2c) that are translated to the final roughness of the surface of the ice (Figure 2c, e, f). See also Movie S1 in the Supplementary Information. This matching between the surface dendrites morphology and ice surfaces is altered if vertical dendrites are created during the vertical growth of the ice front because they generate new ice domains. CONCLUSIONS: In summary, we have investigated the freezing process of water films on flat silicon–based surfaces characterized by different thermal properties such as mica, silicon wafer, glass and quartz. The freezing process was investigated using a high-speed camera coupled to an optical microscope able to obtain details of the process not described in the literature until now. We observed the two well-known freezing stages (fast dendritic growth and slow freezing of the water liquid left after the dendritic growth) but we separated the process into different phenomena that can be observed and studied separately, schematized in Figure 7. We found that all this phenomena depend on the supercooling temperature of the water film and on the substrate used. Morphology of dendrites and dendrite growth velocity in stage one was found to be dependent on the substrate. Although the observed differences can be related to thermal properties of the substrate (such as thermal diffusivity) not all the results found can be fitted with the models found in the literature to explain dendrite growth. At low supercooling temperatures, where no vertical dendrite growth was observed, the morphology of the dendrites formed at the


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substrate surface during the first stage determines the polycrystalline morphology and surface roughness of the frozen water film once the freezing process ends. All the results showed here could open new methodologies to study the effect of surface properties on the formation of ice and strategies to control it.

TABLES

Table 1. Thermal conductivity and thermal diffusivity of the samples used in this work.

Thermal conductivity (W m-1 K-1) Thermal diffusivity (m2 s-1)

Mica

Glass

Quartz

Silicon

0,6

0,7

11

168

5.2×10-7

3.54 ×10-7

1.4×10-6

8.8×10-5


18

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FIGURES

Figure 1. Scheme of the experimental set up for the observation of water films freezing.


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Figure 2. Sequence of optical microscopy images of the complete freezing process of a water film on a quartz substrate. Stage 1 corresponds to the fast dendritic growth, co-planar with the surface, a) and b). Stage 2 corresponds to the slow freezing of the rest of the film: c) ice domains created from the dendrites structure grow vertically, d) the ice reaches the surface of the water film, e) advancing diagonally from the top-left border of the image until f) all the films in frozen. Time = 0 s corresponds to the time of the first frame when the first dendrite appears in the field of view of the microscope. Images reveal how the domain structure in c) determines the final roughness of the ice surface in f).


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Figure 3: Optical microscopy images of the most common morphologies of dendrites found as a function of supercooling temperature and substrate used. Glass and mica, with low thermal diffusivity show similar morphologies and very different from quartz and silicon, with a much higher thermal diffusivity (see Table 1).


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Rate [cm/s]


21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0

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Glass MICA Si wafer Quartz "No surface (Ref 11)"

0

1

2

3

4

5

6

7

8

9

10

ΔT (oC)= 0-TSubstrate

Figure 4: Velocity of dendrites/ice front as a function of supercooling temperature for the four samples used in this work. Results are compared with reported values for supercooled water droplets with no interaction with a surface12. Data fitting using Eq. (1) is shown as dotted lines.


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Figure 5: Sequence of optical miscopy images of vertical dendrites growth. a) Ice domains formed by the dendrites grown parallel to the surface; b) rounded domains emerge from the surface, growing faster than the rest; c) and d) some of the rounded domains become unstable, generating new dendrites that grow vertically.

Figure 6: a) Optical microscopy image of the complex ice domain structure formed during the second stage of freezing on mica; b) and c) insets of the image for a better appreciation of the regular domain structure.


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Figure 7: Schemes of the differentiated processes observed during the freezing of the water film. Vertical dendrites growth and trapping of bubbles are not observed for slow freezing dynamics at supercooling temperatures only a few degrees below the melting point.


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Figure 8: a) Scheme and image examples of the dendrites formation. Fast growing happens in one of the a crystallographic axes while side branches grow following other a axes. Depending on the growth directions of side branches fern-like and fishbone-like dendrites are observed. b) Scheme and example images of the vertical dendrites growing from an unstable vertical ice domain.


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Rate [cm/s]


20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0

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Glass Mica Si wafer Quartz Glass (Ref. 18) Brass (Ref. 18) Copper (Ref. 18)

0

1

2

3

4

ΔT

(oC)=

5

6

7

8

9

10

0-TSubstrate

Figure 9: Fitted curves of dendrite/front ice velocity as a function of supercooling temperature obtained using Eq. (1) from data in Figure 4. Curves from our data are compared with data from ref 18. Brass and silicon wafer have a similar thermal diffusivity and show similar trends. Glass curve from our data show a faster velocity than reported data for glass. Quartz, despite having much lower thermal diffusivity than brass, copper or silicon wafer, show the highest velocities at supercooling temperatures above 3 oC.

ASSOCIATED CONTENT Supporting Information.


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A PDF file containing: Image processing example (Figures S1). Growth of dendrites along a mica step (Figure S2). Air bubbles trapped between ice domains (Figure S3). Movie of a complete freezing process (Movie S1, AVI) Movies of dendrites formation: mica (Movie S2), glass (Movie S3), quartz (Movie S4) and silicon (Movie S5). (AVI) ACKNOWLEDGMENT We acknowledge the MINEICO project MAT2016-77852-C2-1-R (AEI/FEDER, UE) and the “Severo Ochoa” Program for Centers of Excellence in R&Db(SEV-2015-0496) REFERENCES

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29. Nakaya, U., The formation of ice crystals. In Compendium of Meteorology: Prepared under the Direction of the Committee on the Compendium of Meteorology, Malone, T. F., Ed. American Meteorological Society: Boston, MA, 1951; pp 207-220. 30. Demange, G.; Zapolsky, H.; Patte, R.; Brunel, M. A phase field model for snow crystal growth in three dimensions. npj Computational Materials 2017, 3 (1), 15. 31. Mullin, J. W., Crystallization. 4th ed.; Butterworth-Heinemann: Oxford ; Boston, 2001; p xv, 594 p. 32. Nada, H.; Furukawa, Y. Anisotropic growth kinetics of ice crystals from water studied by molecular dynamics simulation. J Cryst Growth 1996, 169 (3), 587-597. 33. Nada, H.; Furukawa, Y.,Anisotropy in molecular-scaled growth kinetics at ice-water interfaces. J Phys Chem B 1997, 101 (32), 6163-6166. 34. Rozmanov, D.; Kusalik, P. G. Anisotropy in the crystal growth of hexagonal ice, I-h. J Chem Phys 2012, 137 (9). 35. Mullins, W. W.; Sekerka, R. F. Stability of planar interface during solidification of dilute binary alloy. J Appl Phys 1964, 35 (2), 444-&. 36. Warren, J. A.; Langer, J. S. Prediction of dendritic spacings in a directional-solidification experiment. Phys Rev E 1993, 47 (4), 2702-2712. 37. Losert, W.; Shi, B. Q.; Cummins, H. Z. Evolution of dendritic patterns during alloy solidification: From the initial instability to the steady state. P Natl Acad Sci USA 1998, 95 (2), 439-442.


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TOC 81x44mm (300 x 300 DPI)


Substrate-Dependence of the Freezing Dynamics of Supercooled

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