11750
J. Phys. Chem. B 2008, 112, 11750–11755
Workman-Reynolds Freezing Potential Measurements between Ice and Dilute Salt Solutions for Single Ice Crystal Faces P. W. Wilson* and A. D. J. Haymet Scripps Institution of Oceanography, UniVersity of California San Diego, 9500 Gilman DriVe, San Diego, California 92093 ReceiVed: May 7, 2008
Workman-Reynolds freezing potentials have been measured for the first time across the interface between single crystals of ice 1h and dilute electrolyte solutions. The measured electric potential is a strictly nonequilibrium phenomenon and a function of the concentration of salt, freezing rate, orientation of the ice crystal, and time. When all these factors are controlled, the voltage is reproducible to the extent expected with ice growth experiments. Zero voltage is obtained with no growth or melting. For rapidly grown ice 1h basal plane in contact with a solution of 10-4 M NaCl the maximum voltage exceeds 30 V and decreases to zero at both high and low salt concentrations. These single-crystal experiments explain much of the data captured on this remarkable phenomenon since 1948. Introduction In 1948, E. J. Workman and S. E. Reynolds discovered that an electric charge separation occurs during freezing of slightly ionized water.1 Many workers have seen that when a very dilute solution of particular salts (e.g., NaCl, KCl, NH4Cl) freezes rapidly, a strong potential difference is established between the solid and liquid phases.2-11 This electric charge separation is commonly referred to as the Workman-Reynolds effect or freezing potential, which for almost 50 years has been associated with formation of thunderstorm electricity.12-15 Workman and Reynolds claimed to have measured a potential of -232 V upon freezing a solution of 3 × 10-5 M ammonium hydroxide.1 The potential connection with electrical effects in thunderstorms is obvious and fully elaborated in ref 15. Workman and Reynolds themselves speculate that “100 pounds of ammonia, properly distributed, would be enough to stop electrical discharges in a large storm”. In addition, Finnegan and Pitter16 used cloud chamber measurements to show that for various salts the freezing potential affects the aggregation of single ice crystals, a phenomenon also affecting thunderstorm activity. Cobb and Gross17 examined many salt species and similarly found up to 214 V with (NH4)2CO3 and 43 V with NaCl, a value slightly higher than we report here, for similar growth conditions. In general, the Workman Reynolds (WR) freezing potential (WRFP) remains poorly understood, and despite some careful attempts at experimental studies,4,8 the most recent experiments suffer mainly from lack of reproducibility.7 Rastogi and Tripathi10 measure the WRFP of dilute KCl but note that “[their] results on the FP of aqueous solutions of electrolytes agree with the results of previous workers as regards sign but differ as regards magnitude”. They note further that “no convincing explanation for the observed high potentials is yet available”. Despite two attempts at a theoretical model,18,19 in 1992 Ozeki and co-workers7 claim that WRFP “has been investigated by many researchers, but to date there is no convincing model to describe its occurrence”. This lack of reproducibility and, hence, deficiency in a persuasive explanation of the WRFP seems to us to be simply * To whom correspondence should be addressed.
a result of inconsistencies in the experimental methods used.1,4,7,9,10 As shown here, any measured value of the WRFP is very sensitive to many variables, including details of ice growth. Numerous studies, including our own, show that the measured WRFP is dependent on the concentration of the ionic solution, forming a parabolic graph when plotting WRFP as a function of concentration;5,10,15 freezing potentials with relatively large magnitudes are achieved only when the aqueous ionic solutions have concentrations between 10-3 and 10-5 M. Pruppacher et al.15 show that FP varies slightly with the type of cation (e.g., Li+, Na+, K+, Cs+) used but varies markedly with the type of anion used (e.g., F-, Cl-, Br-, I-). One can deduce that the dependence relies mostly on the electronegativity7,9 of the solute, which is itself dependent on the ion size and then the solute’s structure. The electronegativity of the ionic atom or molecule needs to be large so that it will be able to replace the largely electronegative oxygen atom of a water molecule in the ice lattice. If the ionic solute in the solution is an atom and is adequately electronegative (e.g., F-), it usually replaces the oxygen atom of a water molecule in the ice lattice. However, if the ionic solute in the solution is a molecule (e.g., NH4+), it must have an electronegativity that is close to that of oxygen and the molecules structure must resemble that of the tetrahedral water molecule so that it will be able to take the place of a water molecule in the ice lattice. Hence, when a solution of NH4Cl or (NH4)2SO4 is frozen, the ammonium ion is preferentially incorporated into the ice and produces a WRFP with a negative sign.9 We have sought to determine the factors which influence the WRFP for two salts and a variety of freezing conditions. Experimental Section All water used was deionized and has a resistivity of 17 MΩ · cm or better, and salts are reagent grade, anhydrous. The water used for growing seed ice crystals is also degassed. Growing seed crystals is done by withdrawing the heat at -2 °C from the top of a well-insulated container of water (100 mL). At approximately 15 mm thick, the ice is then removed and usually three to six individual crystals can be seen through
10.1021/jp804047x CCC: $40.75 2008 American Chemical Society Published on Web 08/23/2008
Workman-Reynolds Freezing Potential Measurements
J. Phys. Chem. B, Vol. 112, No. 37, 2008 11751
Figure 2. Model of the ice-water interface showing, in this case, the positive charges accumulating in the water and a negative space charge within the ice. G is the resulting charge generator, RL is the external load resistance, C is the capacitance of the system, and Ri are the internal resistance components.
Figure 1. Apparatus used for growing ice into the salt solution and measuring the resulting Workman Reynolds Freezing Potential
polarizing filters. These crystals can be separated by illumination for a few minutes with a 500 W halogen lamp where infrared causes melting at the grain boundaries. Further analysis of individual crystals between crossed polarizers then allows determination of the c-axis orientation. In the a-axis experiments the c axis is placed parallel to the ice-water interface, but we do not use Tyndall flowers to determine if the ice-water interface is a primary or secondary prism plane. The experimental arrangement is shown in Figure 1. The cell is cooled by a 65 W Peltier unit from which heat is removed by flowing 1.0 °C cooling fluid through a hollowed aluminum plate. The cold face of the Peltier element also has an aluminum plate in thermal contact, onto which sits a platinum square which makes up the bottom electrode of the cell. It is onto this square that seed ice crystals are frozen prior to the start of each run. The cell is a PVC tube with a platinum electrode protruding halfway in and has a total volume of 15 mL. In single-crystal experiments the seed crystals are grown as described and melted back to be 10 mm square by 5 mm tall and transferred to and frozen onto the bottom Pt plate. The solution is added at +5 °C, which then melts the seed back slightly but since heat is then being withdrawn via the seed crystal the entire solution quickly begins to grow as a single crystal with the same orientation as the seed crystal. In some runs polycrystalline ice is used instead of single crystals. This is produced by adding the salt solution at +10 °C directly into the cell. On cooling the bottom plate this then nucleates in several places at some temperature below 0 °C, and the resulting ice is polycrystalline. The voltage between the bottom platinum plate and the electrode is measured either by a Keithley model 619 electrometer, having approximately 1012 Ω input impedance or a custombuilt instrumentation amplifier with 1013 Ω impedance. The output of these is then digitized by a National Instruments USB6008 multifunction DAQ and logged by a PC. Control to the Peltier is by a purpose-built constant current supply which is able to be set to achieve the required freezing rate of the ice up the cell. Simple Macroscopic Model In this paper we discuss our data below with reference to a simple macroscopic electrostatic model in which the ice/solution
interface is treated as a simple capacitor which forms soon after the ice begins to grow and two resistances, one being the ice/ solution interface itself and the other the bulk ice as it grows. The simple model is shown in Figure 2. Since C ) 0rA/d for a parallel plate capacitor, assuming a typical NaCl result from our data below of 4 µF and choosing the relative permittivity, r, of the interface to be that of water, 88, then we obtain a characteristic thickness d ) 8.85 × 10-11: 3 × 10-4/4 × 10-6 ) 5.8 × 10-7 m. It could be argued that the excess ion concentration at the interface will change the value of r, but the less than millimolar concentrations mean very limited numbers of ions are not expected to change r dramatically. The relative permittivity has also been discussed in various papers.6,13,20,21 This thickness, d, represents the spacing between the layer of ions at the water side of the interface and a plane in the space charge (somewhere in the bulk ice). The position of that plane is continually changing as (1) the ions are being deposited into the ice as the ice gets thicker, (2) the ions are being neutralized by either H+ or OH- (depending on the salt used), and (3) the ions are migrating back to the interface due to the electric field. It is interesting to note that when the “capacitor” is fully charged, values are typically 10 µC of charge (for NaCl), which is ∼6.5 × 1013 charges. The solution volume is 15 mL of say 1 × 10-4 M, and so would have 9 × 1017 charges available. In that case about 1 in 10 000 is playing part in producing the WRFP. In all cases tested between 6 × 1013 and 9 × 1014 charges made up the measured current. Nanis and Klein6 report about 5 × 1014 charges transferred (per square cm). A check can also be made on the simple RC model as follows: For 5 × 10-4 NaCl the unloaded WRFP is about 25 V. With a 100 MΩ load the WRFP is 15 V, and so 10 V is lost across the Ri. The measured current in that case is 1.2 × 10-7 A, and by Ohms Law the voltage lost across 100 MΩ is about 12 V. A detailed macroscopic model of what is happening during the freezing process has been produced by LeFabre.19 However, it relies on a constant capacitance value with time, despite the fact that the bottom “plate” of the capacitor is inside the ice space charge and thus also changing position with time. Some molecular level considerations have been anticipated by Bryk and Haymet22 and others.23,24 Results: Charging the Interface Results are presented here for two salts only, NaCl and NH4Cl. Results with other salts will be described elsewhere. 1. NaCl. A typical data set for NaCl is shown in Figure 3 with the solution positive with respect to the ice and voltage (WRFP) initially increasing as the ice grows. The WRFP has a maximum occurring at approximately 1 mm of ice growth and
11752 J. Phys. Chem. B, Vol. 112, No. 37, 2008
Wilson and Haymet
Figure 3. Typical data from the freezing of 5 × 10-5 M NaCl, grown at the ice c axis, with time. Note that the arrow indicates when the ice was stopped from advancing. Figure 6. Parabolic curve with WRFP as a function of dilution, in this case for NaCl frozen as a-axis crystals at 16 µm s-1.
Figure 4. Typical variability in the WRFP voltage found between runs, for the same stock solution of 1 × 10-4 M NaCl, grown at the ice a axis. Figure 7. Difference in WRFP between a-axis crystals and c-axis crystals for various NaCl concentrations grown at 14 µm s-1.
Figure 5. Some of our data and that of three other workers1,17,26 who also used NaCl and also froze the solutions at 15 µm s-1.
then decreasing with time. This is despite the continual growth of the ice with time. The arrow indicates when the current to the Peltier is turned off. The voltage produced drops to zero rapidly as the growth of the ice stops. This is true for all tested species, concentration, and growth rate measured and has also been reported by previous workers.2,3,25 The variability between measurements where everything else, such as growth rate, crystal orientation, and salt concentration, is held constant is shown in Figure 4. Each point represents the results of a different seed crystal and solution (from the same stock solution). The observed degree of variability is probably due to slight changes in the growth rate of the ice and defects within the ice. It does help to explain the lack of consistency within previously reported work on the WRFP. Comparing now some of our measured WRFP values with those of previous workers who also used NaCl and froze the solutions at the same rate, it can be seen that the results are similar, as indicated in Figure 5. Clearly, although the WRFP is dependent on many things, if these are kept constant it is in fact a relatively reproducible quantity, at least within powers of two. The effect of salt concentration on the WRFP is illustrated in Figure 6, which shows the parabolic curve, in this case for NaCl and a-axis crystals. A common feature for the two salts
tested is that by 10-2 M the WRFP has dropped to negligible values. The dilute end of the curve has the added complication of impurities, especially CO2 absorbed into the solution. In fact, assuming 500 ppm CO2 in the air, then K0 ) 0.034 and K1 ≈ 10-6 at 25 °C, so K1 ) [H][HCO3-]/CO2. In addition, since CO2 + H2O ) H+ + HCO3-, we get 10-6 ≈ X2/(500 × 10-6)(0.034), giving X ≈ 4 × 10-6 M. Therefore, at micromolar concentrations the amount of absorbed CO2 is significant and it is not sensible to draw many conclusions about the WRFP with regard to salt concentration. Early studies used a helium atmosphere above the water in order to probe the dilute end of the curve.11 It is worth noting that Lodge26 also found the WRFP to peak at just above 10-4 M for NaCl frozen at 16 µm s-1. For the first time, the difference in WRFP between a-axis ice crystals and c-axis crystals is reported for various NaCl concentrations grown at the same rate. Figure 7 indicates that c-axis ice produces typically twice as much WRFP than a axis. Polycrystalline ice produces voltages somewhere between cand a-axis ice, which may not seem surprising given that in any particular interface the crystal orientation will be a mix of basal and prism planes. However, it is interesting that the grain boundaries present in the ice and reaching down from the interface seem not to play a significant role in the magnitude of the WRFP. Takahashi27 found that a voltage measured during melting of glacial ice to be about 40% more for c-axis ice than a-axis ice, and this seems to be the only other reported situation where the c and a axes are compared, although it was not directly a WRFP situation. Freeze rate is also very significant to the WRFP, as shown in Figure 8, which shows two different salt concentrations, and since the more dilute salt was not expected to reach the same WRFP it is not surprising that the slopes are different. Our current experimental setup does not allow for faster freeze rates.
Workman-Reynolds Freezing Potential Measurements
Figure 8. WRFP shown for NaCl at 1 × 10-4 and 1 × 10-5 M, frozen at various rates.
J. Phys. Chem. B, Vol. 112, No. 37, 2008 11753
Figure 10. Typical freezing data with a load resistor connected across the platinum probes. In this case, 60 MΩ and 5 × 10-5 M NaCl, grown as a c-axis crystal.
Figure 11. Cartoon of the capacitive charge-up and discharge to model the load resistor data, where τ1 and τ2 are the two time constants.
Figure 9. Typical NH4Cl data: in this case 1 × 10-4 M and c-axis crystal.
Lodge26 found that the freezing rate peaked at 20-30 µm s-1 but that this was somewhat dependent on concentration. Dawson and Hutchinson28 also examined WRFP as a function of freeze rate and reported that the WRFP increased with freeze rate up to 40 µm s-1. They did not freeze at faster rates and so do not report when the WRFP does start to reduce. Unless otherwise stated, our runs are carried out at 15 µm s-1. 2. NH4Cl. In the case of NH4Cl the results are similar results to NaCl, but the ice is positive with respect to the solution, indicating that ammonium ions are more readily soluble in ice than chlorine ions. Figure 9 shows a typical WRFP curve for NH4Cl grown with no load resistor connected, only the 1012 Ω of the electrometer. It should be noted that the peak WRFP values were found at somewhat higher concentrations of salt than NaCl. This lower activity than NaCl has also been reported by Finnegan.16 Results: Discharging the Interface with a Load Resistor 1. NaCl. Load resistances of between 1 and 100 MΩ are now connected across the platinum probes. Typical resulting WRFP data is shown in Figure 10. The voltage reaches a maximum after about 35 s of ice growth and then decays over a period which is proportional to the value of the load resistance. The shape of the curve shown in Figure 10 is cartooned in Figure 11. It is possible to model this curve as a simple charging capacitor which then discharges with a different time constant. The charge-up time constant, τ1, is found to be independent of the value of the load resistor, RL, whereas τ2 is directly proportional to RL. That is, regardless of the load resistance, the WRFP reaches a maximum in the same time. This time constant is also found to be also independent of salt concentration. When a selection of RL values is used for the same salt concentration, the WRFP values lie on a straight line, as shown in Figure 12. The current flowing through the RL is then constant, irrespective of the value of RL; therefore, the WRFP is due to a constant
Figure 12. Data representing the measured WRFP as a function of load resistance for 5 × 10-4 M NaCl, c-axis crystals.
current source. In the case of Figure 12, the current produced for 5 × 10-4 M NaCl, c-axis crystals is 1.2 × 10-7 A (for each value of RL). Note that for 5 × 10-5 M NaCl the measured current was 0.06 µA. Of course, the curve shown in Figure 12 cannot be linear for all values of RL since for the open-circuit case RL is 1012 or 1013 Ω but the WRFP only peaks at approximately 30 V. The graph also implies a WRFP of 3 V even if the Pt electrodes are shorted out, which in turn suggests an internal resistance in the ice which would allow that to happen. Gill23 also varied RL and found similar currents. Typical data for the discharge time constant, τ2, as a function of RL, are shown in Figure 13 (for 1 × 10-5 M NaCl and c-axis crystals). In the case of simple capacitive discharge implied by Figure 9, τ ) RC, the ice interface is producing a capacitance of 6.3 µF with an internal resistance, Ri, of 40 MΩ (if RL ) 0). Note that for 5 × 10-4 M NaCl C ) 8 µF and Ri ) 27 MΩ, and for 5 × 10-5 M NaCl C ) 2 µF and Ri ) 73 MΩ. 2. NH4Cl. As shown for NaCl, by varying the value of the load resistor the capacitance and internal resistance can be determined for that solution, grown at that rate, with that ice face as the interface. As an example, Figure 14 shows that for 1 × 10-4 NH4Cl grown as a-axis ice, C ) 0.6 µF and Ri ) 12 MΩ, both of which are lower values than their NaCl counterparts. The lower three data points are the τ1 values, and as with NaCl they were independent of the load resistance values.
11754 J. Phys. Chem. B, Vol. 112, No. 37, 2008
Wilson and Haymet
Figure 15. Data for calculated internal resistance Ri of NaCl grown as c-axis crystals, plotted as a function of salt concentration.
Figure 13. Data for τ2 as a function of load resistance for 1 × 10-4 M NaCl and c-axis crystal. The trend suggests a capacitance of 6.3 µF discharging through an internal resistance, Ri, of 40 MΩ.
Figure 16. Data for NaCl showing calculated capacitance (from plots of load resistance vs WRFP) as a function of salt concentration.
numbers of NH4+ ions are affecting both the capacitance and the internal resistance. Figure 14. Data for 1 × 10-4 NH4Cl grown as a-axis ice with various value load resistors. The plot gives C ) 0.6 µF and Ri ) 12 MΩ.
Discussion As the ice grows, layers of cations and anions freeze in with unequal numbers. This inequality results in a volume distribution in the ice of one species and an equal amount of opposite charge appearing in the solution, presumably concentrated at the liquidice boundary. This causes an electric field in the ice at all places where there is charge, and this field tends to move the charges in the ice back to the boundary. How rapidly they move back depends on the ice resistance. So long as fresh charge is freezing in (i.e., the ice is growing), this field is increasing. A limit is reached when the field at the boundary prevents any more charge freezing in. Thereafter the space charge is either gradually neutralized by conduction of H+ ions through the ice lattice or neutralized by moving to and through the boundary. A discussion of the actual thickness of the density transition which makes up the ice-water interface is beyond the scope of this report. As shown, there is an inherent internal resistance in the ice, measured to be between 10 and 100 MΩ (for NaCl), and this is dependent on salt concentration. Figure 15 shows a plot of Ri as a function of salt concentration. Clearly the fewer ions frozen into the ice, the greater the resistance. Levi and Milman29 also found Ri to be about 100 MΩ and capacitor plate thickness to be about 10-7 m. The calculated capacitance as a function of salt concentration also shows dependence, as shown in Figure 16. It can then be argued that having more capacitance at higher salt concentrations is due to the space charge being more dense, and so d is smaller. It is worth noting also that for NH4Cl, the negative WRFP and lower values of capacitance and internal resistance directly suggest that (a) the NH4+ ions have more affinity for the ice than Cl- ions, (b) the difference in ice solubility between NH4+ and Cl- is less than that between Cl- and Na+, and (c) the
Conclusions We have shown that ice grown with the basal plane as the interface with dilute solutions causes a significantly larger Workman-Reynolds freezing potential to be produced than planes perpendicular to the basal plane. This ice plane dependence on the WRFP will be of interest to future molecular dynamics simulations of the ice-water interface where ions are added.22 The ice/solution interface can be modeled as a simple charge generator connected across an RC network where the capacitance forms during the differential exclusion of ions but then after some time the charged up capacitor discharges through internal resistance in the growing ice. Both the capacitance and resistance values are functions of the salt concentration. It is likely that the dependence of the WRFP on the rate of freezing of the ice can help elucidate further work on the diffusion of ions within the ice. Previously reported issues with reproducibility of WRFP values have meant some difficulty in comparing studies. We have clearly shown that this is due to the details of the experimental arrangements and the critical nature of the ice growth procedure. Measured values of WRFP are sensitive to (a) salt species, both anions and cations, (b) salt concentration, showing maximum around 10-4 M, (c) ice growth rate, with faster rates producing more voltage (up to a point), (d) ice face, with basal plane producing more voltage than prism planes, and (e) external load resistance. Acknowledgment. We are grateful to Prof. Andrew Dickson for helpful suggestions and advice. A.D.J.H. is grateful to Dr. Charlie Knight for introducing him to the WR Effect. References and Notes (1) Workman, E. J.; Reynolds, S. E. Phys. ReV. 1950, 78 (3), 254– 260. (2) Gill, E. W. B. Br. J. Appl. Phys. 1953, Suppl. 2, 16–19.
Workman-Reynolds Freezing Potential Measurements (3) Gill, E. W. B.; Alfey, G. F. Nature 1952, 169, 203–204. (4) Gross, G. W. Ann. N.Y. Acad. Sci. 1965, 125, 380–389. (5) Murphy, E. J. J. Colloid Interface Sci. 1970, 32, 1–11. (6) Nanis, L.; Klein, I. J. Colloid Interface Sci. 1970, 32, 3–10. (7) Ozeki, S.; Sashida, N.; Samata, T.; Kaneko, K. J. Chem. Soc., Faraday Trans. 1992, 88 (17), 2511–2516. (8) Parreira, H. C.; Eydt, A. J. Nature 1965, 208, 33–35. (9) Pruppacher, H. R.; Steinberger, E. H.; Wang, T. L. Proceedings of the 4th International Conference on UniVersal Aspects of Atmospheric Electricity; S. C. Coronili, J. Hughes, Eds.; Gordon and Breach: New York, 1969. (10) Rastogi, R. P.; Tripathi, A. K. J. Chem. Phys. 1985, 83, 1404– 1409. (11) Drzymala, J.; Sadowski, Z.; Holysz, L.; Chibowski, E. J. Colloid Interface Sci. 1999, 220, 229–234. (12) Caranti, J. M.; Illingworth, A. J. Nature 1980, 284, 44–46. (13) Kalley, N.; Caraka, D. J. Colloid Interface Sci. 2000, 232, 81–85. (14) Nelson, J.; Baker, M. Atmos. Chem. Phys. Discuss. 2003, 3, 41– 73. (15) Pruppacher, H. R.; Klett, J. D. Microphysics of Clouds and Precipitation; 2nd ed., Vol. 18, Chapter 12; Kluwer Academic Publishers: Dordrecht, 2000. (16) Finnegan, W. G.; Pitter, R. L. J. Colloid Interface Sci. 1997, 189, 322–327.
J. Phys. Chem. B, Vol. 112, No. 37, 2008 11755 (17) Cobb, A. W.; Gross, G. W. J. Electrochem. Soc.: Electrochem. Sci. 1969, 116, 796–804. (18) Bronshteyn, V. L.; Chernov, A. A. J. Cryst. Growth 1991, 112, 129–145. (19) LeFebre, V. J. Colloid Interface Sci. 1967, 25, 263–269. (20) Kalley, N.; Cop, A.; Chibowski, E.; Holysz, L. J. Colloid Interface Sci. 2003, 259, 89–96. (21) Kallay, N.; Drzymala, J.; Cop, A. Encyclopedia Surface Colloid Sci. 2006, DO1, 1899–1907. (22) Bryk, T.; Haymet, A. D. J. J. Chem. Phys. 2004, 117 (22), 10258– 10268. (23) Vrbka, L.; Jungworth, P. Phys. ReV. Lett. 1995, 95, 148501–148505. (24) Jungworth, P.; Rosenfeld, D.; Buch, V. Atmos. Res 2005, 76 (1), 190–205. (25) Drost-Hansen, W.; Curry, R. W. J. Colloid Interface Sci. 1970, 32 (3), 464–468. (26) Lodge, J. P.; Baker, M. L.; Pierrard, J. M. J. Chem. Phys. 1956, 24 (4), 716–719. (27) Takahashi, T. J. Atmos. Sci. 1969, 26, 1253–1258. (28) Dawson, R.; Hutchinson, W. C. A. Q. J. R. Met. Soc. 1971, 97, 118–123. (29) Levi, L.; Milman, O. J. Atmos. Sci. 1965, 23, 182–186.
JP804047X
