Electric Effect during the Fast Dendritic Freezing of Supercooled Water

Article pubs.acs.org/JPCB

Electric Effect during the Fast Dendritic Freezing of Supercooled Water Droplets Sigurd Bauerecker* and Tillmann Buttersack Institut fuer Physikalische und Theoretische Chemie, Technische Universität Braunschweig, Hans-Sommer-Strasse 10, 38106 Braunschweig, Germany ABSTRACT: An electrical phenomenon consisting of two alternating voltage peaks of up to 6 V amplitude was observed during the rapid dendritic freezing phase of supercooled water droplets in the millimeter size range with supercoolings ΔT in the range of 5 to 20 K. For correlation of the dendritic freezing front with the electric potential, a fast recording oscilloscope was combined with a high-speed camera operating at up to 5000 frames per second. The strength of the effect is roughly proportional to the supercooling and dendritic freezing speed. Furthermore, during the subsequent second freezing phase, which is much slower than the dendritic, a qualitatively different electric potential evolution of similar magnitude has been found which resembles the well-investigated Workman−Reynolds freezing potential (WRFP). The experiments show clear evidence that the first rapid dendritic freezing stage significantly influences direction and amount of the electric potential during the second slow freezing stage. Compared to the WRFP, which takes place for much smaller supercoolings of ΔT ≪ 5 K, the evolution of the presented dendritic freezing potential occurs about 104 times faster, is about 10 times smaller in view of the maximum voltage, and shows similar break off concentrations but remarkably does not vanish at low foreign ion concentrations. This phenomenon has direct relevance to atmospheric freezing processes of the Earth, other planets, and satellites.

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INTRODUCTION For supercooling temperatures of lower than −5 °C, the freezing process of supercooled liquid water droplets which are freely suspended in a gaseous vicinity as air splits into a fast adiabatic part (milliseconds), where a spongy network of ice forms by dendritic growth, and a slow part (seconds), where the droplet completely freezes from outside to the interior.1 These two freezing phases have in principle been known for a long time for supercooled water in general.2−4 However, in the real atmospheres of Earth, other planets, and satellites, the freezing of highly supercooled droplets predominates;4−6 the separation into two strongly different processes seems to be scarcely considered in actual atmospheric research and textbooksfor example, in physics and chemistry of clouds5,7 or nucleation theory and applications,6 as well as in simulations of ice growth from supercooled water.8,9 The freezing process strongly depends on droplet size, supercooling temperature, nature and concentration of a solute if present, and nucleation mode (homogeneous or heterogeneous). Thus, structure and density of this dendritic “stage-one ice” in turn depend on these parameters. It is strongly supposableand will be shown by examples in the present workthat this stage-one ice determines or at least influences the texture of the finally forming compact “stage-two ice”. The reason for the freezing split is a thermodynamic one: the bigger droplets (>1−10 μm in diameter) can only release a small portion of the formation heat by cooling via the surface within the short formation time span. So the formation heat must be completely stored in the ice−water system. For example, for a supercooling ΔT = 20 K, the portion of formation heat which © 2014 American Chemical Society

can be taken by the heat capacity of the forming ice and remaining liquid toward 0 °C is about 0.225, resulting in a rapidly formed dendritic ice with this density.4,1 In 1948, Workman and Reynolds observed an electrical phenomenon occurring during the f reezing of dilute aqueous solutions... resulting in remarkably high electric potentials of up to more than 100 V.10 The effect is well investigated11−15 and known as Workman−Reynolds freezing potential (WRFP). Further research concentrated on the role of the WRFP in the formation of thunderstorm electricity16−18 with an exhaustive overview given by Pruppacher.4 Especially, Wilson and Haymet established an experimental setup providing highly reproducible results.19,20 In general, the investigation of the WRFP was associated with low freezing velocities at smaller supercoolings (ΔT ≪ 5 K). The question remains whether there also occurs electric charge separation during the fast stage-one freezing process of higher supercooled aqueous droplets (ΔT > 5 K). There are a few hints in the literature for such an effect for supercooled bulk water21−24 or for contactless electromagnetic investigation of freezing supercooled water droplets24,25 and supercooled films.26 In contrast, in the present work, we concentrate on a combined direct voltage monitoring and high-speed filming of freezing supercooled water droplets which are positioned between thin electrodes during both freezing stages. Primarily, small or atmospherically relevant foreign ion concentrations Received: July 24, 2014 Revised: September 29, 2014 Published: October 29, 2014 13629

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have been investigated. In addition, higher ion concentrations as well as other types of electrodes have been used in order to bridge the gap toward the well investigated WRFP.

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EXPERIMENTAL SECTION A cylindric vacuum-isolated cooling chamber with a volume of 20 L was constructed for the present experiment to adjust homogeneous temperatures in the range of −70 to 70 °C via a tempered smooth nitrogen gas flow, see Figure 1. The

Figure 1. Schematic of experimental setup. The arrow inside the supercooled water droplet marks the (random) direction of fast dendritic freezing.

temperature accuracy is ±0.5 K. Within the chamber, a droplet of pure water or aqueous solution is placed between a top and a bottom electrode. Two different kinds of electrodes were used to investigate three different freezing modes, see Figure 2: (a) small stainless-steel mantle-thermocouples of 0.25 or 0.5 mm in diameter, performed as a ring-shaped top electrode and a linear bottom electrode, so that the electrodes can serve as temperature sensors; (b) a mantle-thermocouple as top electrode combined with a copper plate as the bottom electrode; (c) two such copper plates with the size of 10 × 10 × 0.5 mm3 showing a considerably bigger heat capacity as the mantle-thermocouple electrodes. The voltage between both electrodes being in contact with the droplet is monitored by a fast recording LeCroy Wavejet 314A oscilloscope with 10−100 MOhm input impedance which delivers up to 109 voltage data points from which we used 5 × 105 per freezing run for the results presented here. The freezing process is monitored synchronously by a highspeed VIS camera MotionPro Y4 of firm IDT/Imaging Solutions with an optical resolution of 1024 × 1024 pixels and frame rates of 400−5000 frames per second (fps) delivering 400−8000 frames per freezing run. The high-speed camera is coupled with a macro-optics system and two xenon electric arc-illumination sources via fiber-optic light-guides leading to an optical resolution of up to 1 μm, which is in the order of the diffraction limit of the used illumination wavelength of about 0.5 μm. The cooling chamber can alternatively be operated with an acoustic levitator if contactless positioning of droplets is needed.27−29,1 The cooling cell temperature and humidity are monitored by a Vaisala HMI41 instrument with a PT1000 resistance sensor and an Ahlborn Almemo 2590−4S instrument with a Pt100 resistance sensor. The used water is HPLC grade with a resistivity of 18 MΩ or better. The NaCl, HCl, and NaOH solvents are diluted from a

Figure 2. Schematic overview of the freezing behavior of a supercooled droplet and the corresponding voltage response for the presented three different experiments with different electrode arrangements. Supercoolings are ΔT = 10 to 20 K in each case. Experiment a: corresponding situation of a freely suspended droplet in the atmosphere, wire mounted, has minimum contact with electrodes, drop diameter is 3 ± 0.5 mm. Experiment b: corresponding situation of a supercooled droplet being in contact with a massive heat capacity (e.g., bigger ice particle), asymmetric electrodes with 3 mm distance. Experiment c: control experiment of a supercooled droplet between symmetric electrodes with 3 mm distance. The dotted line separates freezing and subsequent voltage characteristics of the two freezing stages. The time scale on the right side of this line is compressed by about a factor of 300. More than 400 freezing experiments contributed to this scheme (353 for experiment a, 34 for experiment b, 50 for experiment c).

Gruessing standard 0.1 mol/L solvent each. Both the pure water and the used solutions have been degassed and pH controlled to exclude the presence of atmospheric CO2. (Note: The pH in atmospheric droplets is dominated by CO2 followed by SO2.7 The actual atmospheric CO2 concentration of 3.5 × 10−4 ppm leads to a HCO3− equilibrium concentration of 2.2 × 10−6 mol/L, which should influence the freezing potential.19 The equilibrium equations of the concentrations of gaseous and dissolved CO2, H2CO3, HCO3−, and CO32−, lead to the tripels ([CO2]/ppm; pH; [HCO3−]/mol·L−1): (10−5; 6.4; 3.8 × 10−7), (10−6; 6.8; 9.2 × 10−8), (10−7; 6.94; 5.9 × 10−9), (10−8; 7.0; 1.4 × 10−9). Measured pH was between 6.65 and 6.85, which corresponds to a CO2 concentration near 10−6 ppm. This is about more than a factor of 100 below the natural atmospheric CO2 concentration.) The experiments have been carried out in a protective N2 atmosphere to avoid a disturbing influence of atmospheric CO2 forming carbonic acid. On the other hand control experiments with atmospheric CO 2 13630

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outside to inside, no or only a small electric effect occurs, compare voltage behavior from E to F in Figure 3. The stage-one freezing process can be temporally divided in four quarters relating to the electric effect while the dendritic freezing front proceeds through the droplet. The dendritic freezing process is smooth, in accordance to other experiments1 being in the range of 25−250 and 75 mm/s in the example of Figure 3. This is about 103 to more than 105 times faster than the typical freezing velocities in Workman−Reynolds freezing experiments being in the order of 5−15 μm/s.19 After the first quarter the maximum positive voltage is achieved while the dendritic freezing front already reaches one-third of its path through the droplet (B); after the second quarter, the voltage crosses the zero axes and the freezing front takes two-thirds of the droplet (C); and after the third quarter, the minimum voltage is reached at the same time as the freezing front has crossed the whole droplet (D). During the last quarter, relaxation of the voltage takes place. This means that the electric process needs about one-third more time than the dendritic freezing front for crossing the droplet. Compared to the experiments b and c, this experiment is minimally invasive to the droplet and nearest to a freely suspended supercooled droplet in atmospheric nature. Experiment b: Droplet on a Massive Surface. This experiment is similar to the situation of a supercooled droplet which gets in contact with a cold (ice) surface, see Figure 4 and 2. During dendritic freezing, again the typical “alternating spike” occurs (compare A to E). However, compared to experiment a, in the second freezing stage, a Workman−

concentrations have been performed. Droplets with diameters between 2.7 and 3.5 mm have been injected via a sluice through the wall of the cooling chamber.

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RESULTS In the following, three types of experiments have been used for the investigation of the voltage behavior of freezing supercooled water droplets with a volume of about 30 μL (about 3 × 3 × 3.3 mm3) being in contact with different electrode arrangements. Experiment a: Droplet between Two Wires. Primarily, we concentrated on the first freezing stage by using the type a experiment (only thin wires as electrodes), compare Figure 2, and expected to observe a (small) electric effect being similar to and in the same direction as the WRFP. The result was surprising: not only one peak of positive voltage but also an electric double-spike with alternating polarity occurred reproducibly during the fast dendritic freezing stage, see sequence A to E in Figure 3. The freezing direction (top

Figure 3. Electric effect (“alternating spike”) during the fast first freezing stage of a ΔT = 14 K supercooled neat water droplet with about 3 mm in diameter hanging between thin 0.25 mm thermocouple wires (type a experiment, compare Figure 2). The first dendritic freezing stage (A to E) needs typically 20−70 ms. The voltage amplitude is typically around 2 V (here 1.5 V and in rare cases up to 6 V). During the slow second freezing stage, which starts here at around 80 ms (which needs typically 2000−10 000, here 3000 ms), no or only a small electric effect occurs in this type of experiment which is nearest to atmospheric reality. Compare snapshots taken from high-speed monitoring at about 0, 20, 40, and 60 ms (sequence A, B, C, D). The enlarged detail of snapshot B shows the spongy fibrous structure of the dendritic ice. Notice that the big egg-shaped white structure at the droplet in A, B, and C is due to reflection.

Figure 4. Electric effect during the freezing of a ΔT = 14 K supercooled neat water probe with about 3 mm in size between a wire and a plate electrode (type b experiment, compare Figure 2). The first dendritic freezing stage needs about 60 ms (A to E) and the voltage amplitude is 2 V. During the slow second freezing stage (E to H) a Workman−Reynold-like voltage behavior occurs during roughly 25 000 ms with a maximum voltage of about 2 V at F, compare inset taken from ref 19. The snapshots are taken from high-speed monitoring and depict the prominent positions E to H of the second freezing stage at about 0.06, 2, 16, and 23 s. In the enlargement of snapshot F, the bottom-up freezing front is marked by a blue arrow.

down or bottom up) is random. The correlation of the electric polarity with the freezing order is strongly reproducible: the first voltage peak (A to C) is oriented solution-positive and dendritic-ice-negative. The second voltage peak (C to E) is in the opposite order. During the slow second freezing stage where the remaining liquid water in the droplet freezes from 13631

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Reynolds-like voltage behavior can be observed reproducibly (E to H). The inset in Figure 4 shows the voltage behavior of a typical Workman−Reynolds freezing experiment (5 × 10−5 M NaCl solution, 5 μm/s freezing speed).19 Although there are obvious differences in our present experiment because of the different structural situation (i.e., the presence of the dendritic ice during second-stage freezing, a much lower impurity concentration, and about 10 to 20 times larger freezing velocity), the voltage behavior is qualitatively similar. In both cases, the maximum voltage occurs in the beginning (F) and a shoulder (G) can be observed in the end. Although the freezing direction of the first freezing stage is random (wire to plate or plate to wire), the direction of the second freezing stage always starts from the plate electrode due to its bigger heat capacity, which can take more formation heat than the top electrode and therefore has a lower temperature (also compare Figure 2, experiment b). A striking observation is that the strength of the voltage during the second freezing stage obviously depends on the freezing direction of the first dendritic freezing stage: the voltage during stage two is considerably higher if the second stage freezes against the freezing direction of stage one and is about one-third smaller if both freezing processes have the same direction. This was reproducibly checked for 34 freezing runs. Experiment c: Droplet between Two Massive Surfaces. This experiment was performed as a control experiment using a symmetric arrangement with an aqueous droplet between two (massive) metal plate electrodes, compare Figure 2c. Here the fast dendritic freezing direction again is random (top down or bottom up) and shows an electric voltage behavior corresponding to experiment b. However, the longterm freezing of the second stage in this case always takes place from both electrodes (top down and bottom up) at the same time with equal velocity so that both freezing fronts meet at the middle of the electrode distance. Again the electric behavior during the second freezing stage is strikingly dependent on the direction of the dendritic stage-one freezing process: in each case, a resulting voltage with a maximum of 2 to 4 V evolves and, in fact, with a polarity being always against the freezing direction of stage one (top down → positive, bottom up → negative). Together with the results of experiment b described in the preceding paragraph, we have significant hints now that the dendritic ice freezes asymmetrically and that this asymmetric structure influences the stage-two freezing process. Dependence of the Electric Effect on Supercooling. In the following, droplets of aqueous solutions in the size range of 3 ± 0.5 mm have been investigated by use of experiment a. There is a clear dependence of the electric effect (amplitude) on the supercooling temperature difference ΔT for the solutions of HCl, NaOH, and NaCl in the 10−4 − 10−6 mol/ L concentration range, compare Figure 5. The amplitude increases with roughly 0.12 V/K. A dependence on the kind of solute is not clearly evident. Dependence of the Electric Effect on Ion Concentration. In contrast, the dependence of the voltage amplitude during dendritic freezing on the concentration and on the kind of solute is obvious (same type of experiment a), see Figure 6. Similar as in the Workman−Reynolds case, there exists a maximum concentration at which the effect drops to zero. This breakdown concentration is between 10−4 − 10−2 mol/L for HCl, NaOH, and NaCl. It is highest for the alkaline NaOH solution and lowest for the acidic HCl solution. Note that the

Figure 5. Dependence of the voltage amplitude on supercooling during dendritic freezing for NaCl, HCl, and NaOH solutions. The big symbols mark averages, the smaller open symbols minimum and maximum values. The concentration for each solute was between 10−4 and 10−6 mol/L, a range in which the voltage amplitude turned out to be widely independent of the concentration.

Figure 6. Dependence of the electric effect (amplitude) on the solute concentration during dendritic freezing for NaCl, HCl, and NaOH solutions. About 30 freezing runs at supercoolings of 15 ± 1 K contributed to each colored point.

effect does not diminish at low concentrations 50 μm/s, the WRFP even tends to decrease toward zero, while in the dendritic freezing case, the freezing potential increases with freezing rate. The dendritic matrix which remains after the fast dendritic freezing stage is responsible for the fact that the second freezing stage does not have the initial conditions of usual WRFP freezing. In the Earth’s atmosphere, conditions of supercooled droplets are prevailing.4−6 Therefore, the freezing in the real atmosphere occurs predominately by the described splitting into the fast dendritic and the slow subsequent process, which is the object of research in the present work, and rather not at the conditions for WRFP freezing. However, there are similarities if one compares the second freezing stage of our experiments (only experiment b and c) with the WRFP behavior: the same electric polarity occurs for the same solutes and the shape of the second freezing-stage potential run is similar to the WRFP even to the point of breakoff shoulder, compare inset in Figure 4. The sharper maximum voltage peak in our experiment may be mostly due to the more than 10 times higher freezing speed. First Freezing Stage Affects the Second. Further control of experiments b and c has been achieved with electrodes of bigger masses in order to break the symmetry of the stage-two freezing which, in the normal case for freely suspended highly supercooled spherical droplets, occurs symmetrically from outside to inside, transforming the liquid between the dendritic ice network into compact ice. Experiment b resembles the situation of a supercooled droplet which gets in contact with a bigger cold mass. For both experiments, it turned out that the amount (experiment b) and the direction (experiment c) of the second-stage voltage run strongly depend on the direction of the preceding dendritic freezing stage. This means for experiment b that the second-stage voltage is considerably higher in case the direction of the preceding first-stage freezing is against the direction of the second-stage freezing, compare Figure 2. For experiment c, this means that the first-stage freezing direction also determines the direction of the secondstage voltage run. So there is clear evidence that the secondstage voltage depends on the direction of the first-stage freezing. Our preliminary interpretation for this behavior is that the structure of the dendritic ice which is formed during the fast freezing stage is asymmetric. This means that, for example, ramifications of the dendrites cause a symmetry break which in turn should be responsible for an asymmetric distribution of the present (salt) ions during stage-two freezing which even could get solidified in the final compact ice. Here X-ray photoelectron spectroscopy (XPS), near-edge X-ray absorption fine structure spectroscopy (NEXAFS), and synchrotron-based microtomography should be appropriate tools to verify this hypothesis.33,34 To our knowledge, such a symmetry breaking effect of the first

co-workers,22 who investigated similar effects in 0.3 m long polyethylene tubes using pure water and water solutions with supercoolings between 2 and 11 K, our experimental setup aims predominantly at the freezing of supercooled droplets hanging between two thin electrodes where wall effects can be minimized. In spite of these experimental differencesin particular our objects are about 100 times smallerthere are a few similar results, but other results differ. Supercoolings of up to ΔT = 11 K and voltage effects of up to 15 V have been observed in the Pruppacher experiment while we reached up to 20 K and 6 V. The ice growth rate was with 2 to 89 mm/s lower in the polyethylene tube, probably due to the lesser supercoolings, compared to ours, which was between 25 and 250 mm/s, mostly about 120 mm/s in accordance with refs 1, 4, 30. The voltage behavior during the dendritic freezing stage was in several aspects similar in both experiments concerning polarity, namely, the first peak is solution-positive and dendritic-ice -negative, the second peak is solution-negative and dendritic-ice-positive. However, in the Pruppacher experiment, there is a pause between both peaks over roughly 10 s, whereas in our case, the second peak follows directly after the first, which is probably due to the hundredfold smaller size of our freezing object. Here each voltage peak covers a time span of about 20 ms that correlates with the linear dimension of roughly one millimeter in the droplet which the freezing front passes while the peak evolves. In some cases, we observed differences of the temporal distances of the alternating voltage peaks, that is, little overlapping or little pauses of up to 10 ms correlating with the droplet size. With regard to the ion concentration range, there is accordance in both experiments: the voltage reaches the highest values between 10−5 to 10−3 mol/L with a breakup concentration in the range of 10−4 to 10−2 mol/L, see Figure 6. However, a clear disagreement is the finding in which we see no vanishing electric effect for concentrations smaller than 10−5 mol/L in our experiment compared to Pruppacher, see Figure 6. This is of importance for atmospheric research as ion concentrations in water droplets in the range of 10−5 to 10−7 mol/L are prevalent in the atmosphere of the Earth.31,32 The reason for this discrepancy is not clear at the moment and remains topic of a future work. It may lie in the differences of the experimental conditions as described above. Down to a supercooling of ΔT = 20 K, both the speed of the dendritic freezing front (not shown here, compare ref 1) and the electric effect seem to be roughly proportional to the supercooling, see Figure 5. The occurrence of a maximum at about ΔT = 13 K cannot clearly be identified in our experiments so far, as claimed by Weiss et al. based on computational calculations.8 Studies which investigate the electric behavior of both freezing stages of water in one single voltage run, as we present here, are scarce in the literature. Dawson and Hutchinson23 also use a cylindrical tube as Pruppacher (but with a bigger inner diameter of 74 mm and a smaller height of 13 mm compared to ref 22) and smaller supercoolings up to ΔT = 6.5 K. They observed a voltage peak in the start phase but no alternating spike as in our experiment. Both Freezing Stages: Comparison with WRFP. The comparison of our results with the well-investigated WRFP is also interesting. In the latter, the fast dendritic freezing stage lacks completely as the supercoolings are smaller than 5 K. Thus, the electric alternating spike feature is completely missing there. 13633

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freezing stage has not yet been described in the literature up to now. We are of the opinion that this finding is of general importance for basic research as well as for atmospheric applications and plan to investigate it in detail in a separate study. Considerations for an Explanation. There exist several sources for temporary surface charges of water ice:35 salt ions,10,22,19 ionic or orientational lattice defects18,36,37 which may be separated by solid−solid phase transitions of metastable ice phases,38−40 hydronium and hydroxide ions,41 ordering of dipole moments at the surface,42−44 asymmetries in the environments of water molecules which cause charge transfer.45,46,35 The temporarily present charge in the freshly formed ice network can be (partially) neutralized by the liquid phase by orientation or diffusion of water molecules and ions. Further, the strong temperature gradients during dendritic freezing in the order of up to 20 K/mm1 have to be considered. All these charge separation sources may play a role in the whole process of the two presented very different freezing processes. As mentioned above, our findings resulting from experiment a resemble in some aspects the results of the Pruppacher experiment with longish polyethylene tubes (ref 22, p 576). Most noticeable is that there exists in both cases a “starting” and an “ending” phase with comparable positive and negative voltage peaks which are separated by a long intermediate phase in the Pruppacher case. Pruppacher gives the following explanation for his results: the spontaneous growth of a thin ice layer along the electrode plane with selective incorporation of ions into the lattice could be the starting point for the first potential peak. It is followed by a further charge separation mechanism during the dendritic phase in which hydronium, hydroxide, or salt ions are selectively incorporated into the ice lattice at the surface of the spontaneously growing ice dendrites, thus building up a space charge which is combined with a recombination mechanism taking place some distance behind the growing ice dendrite tips. When the first dendrites reach the counter surface including the counter electrode area, it will be quickly covered by a thin layer of compact ice which in turn causes a charge separation effect which is similar but with the opposite electrical sign compared to the starting peak. If this mechanism is applicable to our case, it should be smeared to a certain extend because there are no plain surfaces at the beginning and ending of the dendritic freezing as in the Pruppacher case due to the curvature of the droplets. The main interface in the Pruppacher experiment is polyethylene−water, whereas in our experiment, an air−water interface (as in the natural atmosphere) prevails. This means that the second freezing phase spreading from the outer surface into the interior begins much slower in the droplet case because of the much lower heat capacity and conductivity of air compared to polyethylene, which should have an impact on the electric potential evolution. One can summarize that although there are a few analogies to our results, we cannot adopt the Pruppacher conclusions as a satisfactory explanation for our observed electric phenomena during the complex freezing process of supercooled aqueous droplets with respect to the differences of both experiments and results as discussed above. Nevertheless, they can serve as valuable hints for a comprehensive explanation which is reserved for a future work.

Article

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by the Deutsche Forschungsgemeinschaft (Grant BA 2176/3-2 and Grant BA 2176/4-1).

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REFERENCES

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