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Reversible Charging of the Ice–Water Interface
Journal of Colloid and Interface Science 232, 81–85 (2000) doi:10.1006/jcis.2000.7193, available online at http://www.idealibrary.com on
Reversible Charging of the Ice–Water Interface I. Measurement of the Surface Potential ˇ Nikola Kallay1 and Duˇsko Cakara Laboratory of Physical Chemistry, Department of Chemistry, Faculty of Science, University of Zagreb, Maruli´cev trg 19, P.O. Box 163, 10001 Zagreb, Croatia Received April 17, 2000; accepted August 30, 2000
potential,” observed by Workman and Reynolds (1), and it increases with the rate of growth of the solid. The experiments suggested that anions and cations are being selectively incorporated into the growing ice structure, producing charge and potential depending on their ability to be captured in the solid structure. In addition to the freezing potential measurements, the appreciable electrical conductivity of ice (7) enables the application of external electric potential to ice electrode and cyclic voltammetry experiments (8, 9). The latter experiments are related to adsorption of ions and their incorporation into the ice structure. The above experiments reflect nonequilibrium phenomena at the ice–water interface. However, there are some reports on the electrical properties of ice in equilibrium with aqueous electrolyte solutions. Nechaev and Ivanov (10) measured the surface charge of ice (snow) as a function of pH by potentiometric pH analysis. The results were expressed as the amount of counterions adsorbed per mass of solid, which was assumed to be equivalent to surface charge. In the basic region of pH, a negative charge of ice was observed. The magnitude of charge was shown to depend on the nature of counterions compensating the electrostatic repulsion between charged groups at the surface. No positive charge was observed in the acidic region. It was concluded that charging of ice in aqueous electrolyte solutions is similar to that of quartz. In a subsequent report from the same laboratory, Romanov et al. (11) described the results of electrokinetic experiments. Electrophoretic measurements indicated that ice particles were negatively charged in the region of pH > 3. The difficulties with these experiments lie in the stability of the system due to melting or freezing within the ice– water interface. Recently, the original approach of Drzymala et al. (12) solved this problem. Ice was prepared from heavy water (D2 O), with a freezing point of 3.8◦ C. Ice was crushed and dispersed in ordinary water so that at 0.5◦ C the system was assumed to be stable and suitable for electrophoretic measurements. The isoelectric point of ice was found near pH 4, so that the ice surface exhibited negative ζ -potentials in the broad region of pH > 4. An attempt to measure the equilibrium potential between ice and aqueous solution was reported by Heinmets (3) and an approximate linearity of the potential with respect to the logarithm of electrolyte concentrations was found. The
An ice electrode was constructed in order to measure dependency of the surface potential on pH. The electrode had a Plexiglas body with a platinum plate on the bottom, which was cooled by passing the cooling liquid through a tube mounted inside the electrode. The temperature inside the electrode was −7◦ C, while the electrolyte solution was kept at 0.02◦ C, so that an ice layer was formed on the platinum plate. In the acidic region fast equilibration of electrode was observed. The slope dφ0 /dpH was found to be between −40 and −46 mV. The maximum of the slope was observed at pH 4.4, which coincides with the isoelectric point of ice–water interface. In the basic region the equilibration was slow and more pronounced deviation from the Nernstian behavior was observed. The results were explained on the basis of the surface complexation model, assuming an amphotheric nature of surface OH groups. In the basic region the surface bears high negative charge so that binding of sodium ions at the interface influenced the results. °C 2000 Academic Press Key Words: ice electrode; ice–water interface; surface potential; charging of ice.
INTRODUCTION
Although the charging of ice is of great importance, especially for atmospheric processes, very little is known about the detailed mechanism. The aim of this article is to report experimental results on the pH dependence of the reversible surface potential at the ice–water interface and to suggest a corresponding reaction mechanism. Here we show that this reversible electrostatic potential is created by protonation and deprotonation of amphotheric surface OH groups and that equilibrium of the process may be quantitatively described by the surface complexation model developed for the metal oxide aqueous interfaces. The reversible charging of ice surface could also play an important role in atmospheric thunderstorms. It is already known that fast freezing of water results in a substantial potential difference between solid ice and liquid aqueous phase owing to selective incorporation of cations or anions into the growing ice surface (1–6). The effect is known as “freezing
1
To whom the correspondence should be addressed. 81
0021-9797/00 $35.00
C 2000 by Academic Press Copyright ° All rights of reproduction in any form reserved.
82
ˇ KALLAY AND CAKARA
slopes were −41, −32, and −21 mV for HCl, NaOH, and KOH, respectively. However, it is surprising that a decrease of potential with increasing of HCl concentration was observed. We believe that this can be attributed to a mistake in presentation or some experimental artifacts. The investigation of the mechanisms involved in the charging of ice–water interface is interesting by itself owing to its great importance in the nature. On other hand, this system is comparable to any other metal oxide–water interface for which the surface complexation model (SCM) combined with a certain model of electrical interfacial layer (EIL) was found to be applicable (13–20). Therefore, the investigation of the ice–water interface, and interpretation based on SCM and EIL, may provide information on the mechanism of its reversible charging, leading to deeper understanding of processes at the ice surface. In addition, the measurements of the surface potential of ice in electrolytes may contribute to the general knowledge on metal oxide surfaces in aqueous environments. A metal oxide interface is commonly examined by potentiometric pH titration of the suspension, yielding the surface charge density of the inner surface plane due to the interactions of amphotheric surface groups with potential determining H+ and OH− ions. Additional electrokinetic experiments provide information on the ζ -potential, which corresponds to a slipping (or shear) plane, i.e., to the hypothetical boundary between the immobile bulk liquid and the liquid moving together with the charged particles in the electric field. In some cases adsorption densities of counterions, ions that are oppositely charged with respect to charges in the inner layer, are reported. For better understanding of the interfacial equilibrium it would be desirable to obtain some additional information. Surface potential, i.e., the electrostatic potential of the plane in which the surface charged groups are located (φ0 ), can be calculated from the respective surface equilibrium constants and other parameters describing the interfacial layer. In the case of metal oxides, it was shown (19, 21, 22, 30) that the slope of the φ0 (pH) function should be lower than (or close to) the slope predicted by the Nernst equation with possible inflection in the zero charge region, depending on the nature of oxide and the ionic strength. Surface potential can be also measured. For that purpose one can use an oxide electrode (metal electrode covered with sufficiently conductive nonporous metal oxide layer) but also the field effect transistors (FET). The origin of the measured potential could be either redox reaction or in some cases the surface complexation, i.e., the interactions of surface groups with potential determining ions from the bulk of the solution. Measurements with oxide electrodes result in so-called “open circuit potential” and were performed with hematite (23), titania (24), and zirconia (25). The slope of φ0 (pH) was found to be negative and close to the Nernstian, which is in accordance with surface complexation model. In the case of redox equilibrium the slope of φ0 (pH) function depends on the number of electrones and H+ ions involved in the reaction. Accordingly, in the case of manganese dioxide (26) the slopes were found to be −90 to −100 mV and also −60 mV, depending on the
pH region. Numerous results obtained with FET were reported (27–30) with the aim to develop ion selective electrodes on the basis of ion sensitive field effect transistors (ISFET). In most of the cases results showed that development of the surface potential is a consequence of the surface complexation, i.e., binding or release of H+ ions at the interface. For example (30), measurements with Al2 O3 ISFET electrode showed that the slope of φ0 (pH) function is lower (in some cases even significantly) than the Nernstian with an inflection around the point of zero charge. Measurements of the surface potential at the ice–water interface by the ice electrode have several advantages; ice is conductive enough and forms a nonporous layer so that one can be sure that the electrode does not behave as a metal oxide electrode of the second kind. Also, it can be assumed that the surface potential of ice is not result of a redox process, but it is rather developed by interactions of surface groups with potential determining H+ and OH− ions. EXPERIMENTAL
The ice electrode constructed for the purpose of this study is presented in Fig. 1. The body was made of Plexiglas. Inside the body there is a tube with the cooling liquid (−7◦ C) supplying it to the reservoir at the bottom which is separated from the platinum electrode by the thin Plexiglas layer so that no contact between the platinum wire and the cooling solution exists. The temperature of the electrolyte solution (0.02 ± 0.01◦ C) was controlled by a second thermostat supplying the cooling liquid to the double-wall cell. The system was stirred by a magnetic stirrer. The heat transfer resulted in the stable ice layer formed
FIG. 1. Ice electrode: (1) ice layer; (2) platinum plate; (3) platinum wire; (4) copper wire; (5) tube for cooling liquid; (6) Plexiglas body; (7) Plexiglas cap.
REVERSIBLE CHARGING OF THE ICE–WATER INTERFACE
on the platinum electrode, the thickness of which was about 10 mm, depending on the temperature conditions. The temperature regime was kept as stable as possible so that all potentials in the circuit remained constant. The glass electrode combined with a Ag,AgCl | KCl(aq) reference electrode (Metrohm 6.0233.100) was used for pH measurements. The same reference electrode was used to detect the potential of the ice electrode. The potentials of glass and ice electrodes were measured with two separate pH meters (Metrohm 713 pH meter) which were connected to a computer for data acquisition. These pH meters were suitable for measuring the potential of the ice electrode since its resistance was found to be approximately 10 times lower than that of the glass electrode. The glass electrode was calibrated with four Metrohm buffers (pH 2.01, 4.003, 7.13, 9.464 at 0◦ C). In order to avoid CO2 contamination the system was always kept under an argon atmosphere. The pH of solution was regulated by automatic additions of acid or base using the Metrohm TITRINO 736 GP. The responses of the electrodes were followed for 1 h after addition of each portion of the reactant solution (1 cm3 of 2 × 10−2 mol dm−3 NaOH) to 200 cm3 of HCl solution (initially 1 × 10−3 mol dm−3 ). The experiments were performed by titrating the acidic solution with the base and vice versa. The first choice was found to result in better repeatability. RESULTS AND DISCUSSION
Figure 2 shows a typical experimental result. It is given for the case of titration of the acid. Each addition of the reactant can be recognized as a step in the diagram. The time dependency of the potential was followed for 1 h. It is clear that, in the acidic region, the potential of the ice electrode follows closely the potential of the glass electrode, while the equilibration time for
FIG. 2. Titration of 200 cm3 of HCl (1 × 10−3 mol dm−3 ) with subsequent additions of 1 cm3 of NaOH (2 × 10−2 mol dm−3 ). Equilibration time for each portion: 1 h. Each portion on the timescale could be recognized as a step. Temperature, 0◦ C.
83
FIG. 3. Surface potential at ice–water interface as a function of pH at 0◦ C. Circles, experimental values; solid line, fitted polynom of the third order; dashed line, the Nernst potential.
the ice electrode increases markedly and the data points become significantly scattered in the basic region. The electrode potential of the ice electrode was converted to the surface potential φ0 using the isoelectric point (IEP) of ice at pHIEP 4, as obtained by Drzymala et al. (12). The procedure is based on the assumption that the only pH dependent potential in the circuit is the surface potential of ice, and also that the IEP corresponds to φ0 = 0. According to SCM the second assumption is correct in the absence of specific adsorption of ions other than H+ and OH− and when the association of counterions is symmetric or absent. Figure 3 presents the surface potential of the ice–water system as a function of pH in the acidic region, where a higher repeatability was observed. In the acidic medium an approximate linearity of the function φ0 (pH) was found, with the slope lower in magnitude than the Nernstian (−54.2 mV at 0◦ C). The data in the acidic region were analyzed by fitting them to a third-order polynom so that the pH dependence of the derivative dφ0 /dpH could be obtained. Figure 4 indicates that the magnitude of the derivative has maximum at pH between 4 and 4.5. It corresponds to the isoelectric point, which agrees with predictions based on SCM combined with an EIL model (19, 22, 30). Surface charge (10) and electrokinetic (11, 12) measurements, together with the results of this study, suggest that the ice–water interface behaves in a way similar to that of metal oxide aqueous systems. Accordingly, charging of ice–water interface may be described by the surface complexation model (13–19) and is due to the amphotheric properties of surface hydroxyl groups ≡OH. Protonation of these groups, ≡OH + H+ → ≡OH+ 2; 0(≡OH+ 2) K p = exp(Fφ0 /RT ) · , 0(≡OH) · aH+
[1]
ˇ KALLAY AND CAKARA
84
by ≡ ≡ − ≡ σ0 = F(0(≡OH+ 2 ) + 0( OH2 Cl) − 0( O ) − 0( ONa)) [6] and that of the outer layer (σβ ) by σβ = F(0(≡ONa) − 0(≡OH2 Cl)).
[7]
Association of counterions is significant at higher values of φβ and may be neglected at low ionic strength as well as at low surface potentials (13–19). Ions in the diffuse layer compensate the charge bound to the surface and the equilibrium may be described by the Gouy–Chapman theory. By using the Gouy– Chapman theory one could relate the net surface charge density σs and surface charge density in difuse layer σd , ≡ − σs = −σd = σ0 + σβ = F(0(≡OH+ 2 ) − 0( O )),
FIG. 4. Slope of the surface potential vs pH for the ice–water interface at 0◦ C (solid line). Dashed line represents the Nernst slope of −54.2 mV at 0◦ C.
leads to a positive charge, while deprotonation, ≡OH → ≡O− + H+ ; K d = exp(−Fφ0 /RT ) ·
0(≡O− ) · aH+ , 0(≡OH)
[2]
results in a negative charge. K p and K d are (thermodynamic) equilibrium constants, sometimes called “intrinsic” constants. They account for chemical nonelectrostatic contributions to the change of standard Gibbs energy. Accordingly, the equilibrium concentrations of surface species (0) are determined by two surface equilibrium constants and the electrostatic potential (φ0 ) affecting the state of surface ionic groups. Counterions, such as Na+ and Cl− , could associate with surface charges according to
to the potential at the onset of difuse layer (φd ) which is approximately equal to the φβ -potential. The electokinetic ζ -potential can be calculated from φd , assuming a certain value of the slipping plane separation (31, 32). There are three points describing the zero-charge condition at the surface. The IEP applies to the condition at which ζ = 0, and consequently at σs = 0. The point of zero charge is related to the consumption of H+ ions from the bulk of the so≡ ≡ − lution and is defined by 0(≡OH+ 2 ) + 0( OH2 Cl) − 0( O ) − 0(≡ONa) = 0, which results in σ0 = 0 if there is no specific adsorption. The third quantity applies to condition at which the potential of the inner plane is zero (φ0 = 0). According to SCM these three points will coincide in the absence of any other ions tending to be chemically adsorbed and if the association of counterions is symmetrical or absent. This condition is determined (22) by equilibrium constants of protonation and deprotonation of amphotheric surface sites ≡OH as pHpzc = pHiep = pH(φ0 = 0) = 0.5 · lg(K p /K d ).
≡OH+ 2
[8]
[9]
−
+ Cl → ≡OH2 Cl; 0(≡OH2 Cl) K (Cl− ) = exp(−Fφβ /RT ) · − 0(≡OH+ 2 ) · aCl ≡O− + Na+ → ≡ONa; 0(≡ONa) . K (Na+ ) = exp(Fφβ /RT ) · 0(≡O− ) · aNa+
[3]
[4]
These counterions are exposed to the potential φβ , being usually lower in magnitude than φ0 . The relationship between these two potentials is based on the assumption of constant capacity C and is commonly given by σ0 , C= φ0 − φ β
[5]
where the surface charge density in the inner layer (σ0 ) is given
It is well established (17, 20), both theoretically and experimentally, that in the case of the specific adsorption of ions other than the potential determining ions (H+ and OH− in the case of ice) the isoelectric point and point of zero charge would shift in the opposite direction on the pH scale; adsorption of anions would shift the IEP to lower pH values, while p.z.c. would shift to higher pH. Adsorption of positive species would result in opposite effects. However, the direction and magnitude of the shift of the third zero point, i.e., pH(φ0 = 0), would depend on the mechanism of binding of the adsorbable ions, as well as on the structure of the interfacial layer (31, 32). The dependency of surface potential φ0 on pH could be derived from Eqs. [1] and [2] as φ0 = =
Kp RT 0(≡O− ) RT RT + ln ln ln aH+ + 2F Kd 2F F 0(≡OH+ ) 2 0(≡O− ) RT ln 10 RT ln 10 log (pHpzc − pH). [10] + 2F F 0(≡OH+ ) 2
REVERSIBLE CHARGING OF THE ICE–WATER INTERFACE
Accordingly, the magnitude of the slope of φ0 (pH) function should be lower than the Nernstian slope (19, 21). The deviation depends on the characteristics of the interface. For example, high values of the equilibrium constants K d and K p and high density of amphotheric surface groups ≡OH would result in a slope closer to the Nernstian. Also, the slope will be closer to the Nernstian at lower extents of counterion association, i.e., at lower electrolyte concentration. Measurements of inner surface potential under controlled conditions, as described here, may provide additional information for a better understanding of interfacial equilibria in solid–liquid systems. The deviation of the φ0 (pH) function from the Nernst equation provides information on the ratio of charge densities of negative and positive groups and thus more accurate values of equilibrium constants K d and K p , which is important since pH at p.z.c. and IEP yields only the ratio K p /K d . In the basic region the more pronounced deviation from the Nernstian behavior was observed. This finding is comparable to the “sodium error” of glass electrodes and may be explained considering the sodium ion association with negative surface groups as described by Eq. [4]. For example, at pH 7 the surface potential φ0 is approximately −100 mV (Fig. 3) while the ζ -potential is about −30 mV (12). The value of φβ -potential, affecting the state of associated sodium ions, should lie between these two limits. According to Eq. [4], φβ = −80 mV would promote sodium ion association by a factor of 30. This pronounced association would cause significant reduction of the surface potential φ0 with respect to the Nernstian value and the effect would be more pronounced at higher pH values. Slow equilibration of the ice electrode in the basic region indicates the possibility of existence of “gel-like layer” at the ice–water interface through which sodium ions diffuse so that rate of equilibration depends on the rate of diffusion and the thickness of the “soft” layer. The isoelectric point of the ice–water interface, determined by surface protonation and deprotonation equilibrium constants, is at pH ≈ 4 so that under normal atmospheric conditions one can expect a negative charge of the ice and a positive charge of the liquid water. Accordingly, melting of a falling hailstone in the warm part of the atmosphere would cause charge separation at the interface. In the high speed of a falling hailstone the positively charged water would be stripped off the solid in the form of small droplets which will remain dispersed in the atmosphere. The hailstones will charge the ground negatively. Accordingly, the reversible charging of the ice–water interface, as described in this article, could be one of several possible mechanisms of electric field formation in the atmosphere that is responsible for thunderstorms.
85
ACKNOWLEDGMENTS We thank Mr. Z. Dojnovi´c and Mr. D. Grgec for construction of the ice electrode.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.
20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32.
Workman, E. J., and Reynolds, S. E., Phys. Rev. 78, 254 (1950). Gill, E. W. B., and Alfrey, G. F., Nature 169, 203 (1952). Heinmets, F., Trans. Faraday Soc. 58, 788 (1962). Parreira, H. C., and Eydt, A. J., Nature 208, 33 (1965). Caranti, J. M., and Illingworth, A. J., Nature 284, 44 (1980). Sola, M. I., and Corti, H. R., An. Asoc. Quim. Argent. 81, 483 (1993). Fletcher, N. H., “The Chemical Physics of Ice.” Cambridge Univ. Press, Cambridge, UK, 1970. Glenn, D. F., and Ingram, J. C., J. Electrochem. Soc. 141, 113 (1994). Doe, H., Kobayashi, T., and Sawada, H., J. Electroanal. Chem. 383, 53 (1995). Nechaev, E. A., and Ivanov, I. A., Colloid J. USSR 36(3), 583 (1974). Romanov, V. P., Nechaev, E. A., and Zvonareva, G. V., Colloid J. USSR 38(5), 1009 (1975). Drzymala, J., Sadowski, Z., Holysz, L., and Chibowski, E., J. Colloid Interface Sci. 220, 229 (1999). Yates, D. E., Levine, S., and Healy, T. W., J. Chem. Soc. Faraday Trans. 70, 1807 (1974). Davis, J. A., James, R. O., and Leckie, J. O., J. Colloid Interface Sci. 63, 480 (1978). Westall, J., and Hohl, H., Adv. Colloid Interface Sci. 12, 265 (1980). Hiemstra, T., Van Riemsdijk, W. H., and Bolt, G. H., J. Colloid Interface Sci. 133, 91 (1989). ˇ ˇ Croat. Chem. Kallay, N., Sprycha, R., Tomi´c, M., Zalac, S., and Torbi´c, Z., Acta 63, 467 (1990). Borkovec, M., Langmuir 13, 2608 (1997). Kosmulski, M., Sprycha, R., and Szczypa, J., in “Interfacial Dynamics” (N. Kallay, Ed.), Surfactant Science Series, Chap. 4. Dekker, New York, 1999. Chang, H.-C., Healy, T. W., and Matijevi´c, E., J. Colloid Interface Sci. 92, 469 (1983). Blesa, M., and Kallay, N., Adv. Colloid Interface Sci. 28, 111 (1988). Sprycha, R., J. Colloid Interface Sci. 127, 12 (1989). Penners, N. H. G., Koopal, L. K., and Lyklema, J., Colloids Surf. 21, 457 (1986). Avena, M. J., Camara, O. R., and De Pauli, C. P., Colloids Surf. 69, 217 (1993). Ardizzone, S., and Radaelli, M., J. Electroanal. Chem. 269, 461 (1989). Tari, I., and Hirai, T., Electrochim. Acta 26, 1657 (1981). Ardizzone, S., and Trasatti, S., Adv. Colloid Interface Sci. 64, 173 (1996). Schenck, J. F., J. Colloid Interface Sci. 61, 569 (1977). Cichos, C., and Geidel, Th., Colloid Polym. Sci. 261, 947 (1983). Bousse, L., de Rooij, N. F., and Bergveld, P., Surf. Sci. 135, 479 (1983). ¨ Kovaˇcevi´c, D., Pohlmeier, A., Ozbas, G., Narres, H.-D., and Kallay, N., Progr. Colloid Polym. Sci. 112, 183 (1999). ¨ Kovaˇcevi´c, D., Pohlmeier, A., Ozbas, G., Narres, H.-D., Schwuger, M. J., and Kallay, N., Colloids Surf. 166, 225 (2000).
Reversible Charging of the Ice–Water Interface I. Measurement of the Surface Potential ˇ Nikola Kallay1 and Duˇsko Cakara Laboratory of Physical Chemistry, Department of Chemistry, Faculty of Science, University of Zagreb, Maruli´cev trg 19, P.O. Box 163, 10001 Zagreb, Croatia Received April 17, 2000; accepted August 30, 2000
potential,” observed by Workman and Reynolds (1), and it increases with the rate of growth of the solid. The experiments suggested that anions and cations are being selectively incorporated into the growing ice structure, producing charge and potential depending on their ability to be captured in the solid structure. In addition to the freezing potential measurements, the appreciable electrical conductivity of ice (7) enables the application of external electric potential to ice electrode and cyclic voltammetry experiments (8, 9). The latter experiments are related to adsorption of ions and their incorporation into the ice structure. The above experiments reflect nonequilibrium phenomena at the ice–water interface. However, there are some reports on the electrical properties of ice in equilibrium with aqueous electrolyte solutions. Nechaev and Ivanov (10) measured the surface charge of ice (snow) as a function of pH by potentiometric pH analysis. The results were expressed as the amount of counterions adsorbed per mass of solid, which was assumed to be equivalent to surface charge. In the basic region of pH, a negative charge of ice was observed. The magnitude of charge was shown to depend on the nature of counterions compensating the electrostatic repulsion between charged groups at the surface. No positive charge was observed in the acidic region. It was concluded that charging of ice in aqueous electrolyte solutions is similar to that of quartz. In a subsequent report from the same laboratory, Romanov et al. (11) described the results of electrokinetic experiments. Electrophoretic measurements indicated that ice particles were negatively charged in the region of pH > 3. The difficulties with these experiments lie in the stability of the system due to melting or freezing within the ice– water interface. Recently, the original approach of Drzymala et al. (12) solved this problem. Ice was prepared from heavy water (D2 O), with a freezing point of 3.8◦ C. Ice was crushed and dispersed in ordinary water so that at 0.5◦ C the system was assumed to be stable and suitable for electrophoretic measurements. The isoelectric point of ice was found near pH 4, so that the ice surface exhibited negative ζ -potentials in the broad region of pH > 4. An attempt to measure the equilibrium potential between ice and aqueous solution was reported by Heinmets (3) and an approximate linearity of the potential with respect to the logarithm of electrolyte concentrations was found. The
An ice electrode was constructed in order to measure dependency of the surface potential on pH. The electrode had a Plexiglas body with a platinum plate on the bottom, which was cooled by passing the cooling liquid through a tube mounted inside the electrode. The temperature inside the electrode was −7◦ C, while the electrolyte solution was kept at 0.02◦ C, so that an ice layer was formed on the platinum plate. In the acidic region fast equilibration of electrode was observed. The slope dφ0 /dpH was found to be between −40 and −46 mV. The maximum of the slope was observed at pH 4.4, which coincides with the isoelectric point of ice–water interface. In the basic region the equilibration was slow and more pronounced deviation from the Nernstian behavior was observed. The results were explained on the basis of the surface complexation model, assuming an amphotheric nature of surface OH groups. In the basic region the surface bears high negative charge so that binding of sodium ions at the interface influenced the results. °C 2000 Academic Press Key Words: ice electrode; ice–water interface; surface potential; charging of ice.
INTRODUCTION
Although the charging of ice is of great importance, especially for atmospheric processes, very little is known about the detailed mechanism. The aim of this article is to report experimental results on the pH dependence of the reversible surface potential at the ice–water interface and to suggest a corresponding reaction mechanism. Here we show that this reversible electrostatic potential is created by protonation and deprotonation of amphotheric surface OH groups and that equilibrium of the process may be quantitatively described by the surface complexation model developed for the metal oxide aqueous interfaces. The reversible charging of ice surface could also play an important role in atmospheric thunderstorms. It is already known that fast freezing of water results in a substantial potential difference between solid ice and liquid aqueous phase owing to selective incorporation of cations or anions into the growing ice surface (1–6). The effect is known as “freezing
1
To whom the correspondence should be addressed. 81
0021-9797/00 $35.00
C 2000 by Academic Press Copyright ° All rights of reproduction in any form reserved.
82
ˇ KALLAY AND CAKARA
slopes were −41, −32, and −21 mV for HCl, NaOH, and KOH, respectively. However, it is surprising that a decrease of potential with increasing of HCl concentration was observed. We believe that this can be attributed to a mistake in presentation or some experimental artifacts. The investigation of the mechanisms involved in the charging of ice–water interface is interesting by itself owing to its great importance in the nature. On other hand, this system is comparable to any other metal oxide–water interface for which the surface complexation model (SCM) combined with a certain model of electrical interfacial layer (EIL) was found to be applicable (13–20). Therefore, the investigation of the ice–water interface, and interpretation based on SCM and EIL, may provide information on the mechanism of its reversible charging, leading to deeper understanding of processes at the ice surface. In addition, the measurements of the surface potential of ice in electrolytes may contribute to the general knowledge on metal oxide surfaces in aqueous environments. A metal oxide interface is commonly examined by potentiometric pH titration of the suspension, yielding the surface charge density of the inner surface plane due to the interactions of amphotheric surface groups with potential determining H+ and OH− ions. Additional electrokinetic experiments provide information on the ζ -potential, which corresponds to a slipping (or shear) plane, i.e., to the hypothetical boundary between the immobile bulk liquid and the liquid moving together with the charged particles in the electric field. In some cases adsorption densities of counterions, ions that are oppositely charged with respect to charges in the inner layer, are reported. For better understanding of the interfacial equilibrium it would be desirable to obtain some additional information. Surface potential, i.e., the electrostatic potential of the plane in which the surface charged groups are located (φ0 ), can be calculated from the respective surface equilibrium constants and other parameters describing the interfacial layer. In the case of metal oxides, it was shown (19, 21, 22, 30) that the slope of the φ0 (pH) function should be lower than (or close to) the slope predicted by the Nernst equation with possible inflection in the zero charge region, depending on the nature of oxide and the ionic strength. Surface potential can be also measured. For that purpose one can use an oxide electrode (metal electrode covered with sufficiently conductive nonporous metal oxide layer) but also the field effect transistors (FET). The origin of the measured potential could be either redox reaction or in some cases the surface complexation, i.e., the interactions of surface groups with potential determining ions from the bulk of the solution. Measurements with oxide electrodes result in so-called “open circuit potential” and were performed with hematite (23), titania (24), and zirconia (25). The slope of φ0 (pH) was found to be negative and close to the Nernstian, which is in accordance with surface complexation model. In the case of redox equilibrium the slope of φ0 (pH) function depends on the number of electrones and H+ ions involved in the reaction. Accordingly, in the case of manganese dioxide (26) the slopes were found to be −90 to −100 mV and also −60 mV, depending on the
pH region. Numerous results obtained with FET were reported (27–30) with the aim to develop ion selective electrodes on the basis of ion sensitive field effect transistors (ISFET). In most of the cases results showed that development of the surface potential is a consequence of the surface complexation, i.e., binding or release of H+ ions at the interface. For example (30), measurements with Al2 O3 ISFET electrode showed that the slope of φ0 (pH) function is lower (in some cases even significantly) than the Nernstian with an inflection around the point of zero charge. Measurements of the surface potential at the ice–water interface by the ice electrode have several advantages; ice is conductive enough and forms a nonporous layer so that one can be sure that the electrode does not behave as a metal oxide electrode of the second kind. Also, it can be assumed that the surface potential of ice is not result of a redox process, but it is rather developed by interactions of surface groups with potential determining H+ and OH− ions. EXPERIMENTAL
The ice electrode constructed for the purpose of this study is presented in Fig. 1. The body was made of Plexiglas. Inside the body there is a tube with the cooling liquid (−7◦ C) supplying it to the reservoir at the bottom which is separated from the platinum electrode by the thin Plexiglas layer so that no contact between the platinum wire and the cooling solution exists. The temperature of the electrolyte solution (0.02 ± 0.01◦ C) was controlled by a second thermostat supplying the cooling liquid to the double-wall cell. The system was stirred by a magnetic stirrer. The heat transfer resulted in the stable ice layer formed
FIG. 1. Ice electrode: (1) ice layer; (2) platinum plate; (3) platinum wire; (4) copper wire; (5) tube for cooling liquid; (6) Plexiglas body; (7) Plexiglas cap.
REVERSIBLE CHARGING OF THE ICE–WATER INTERFACE
on the platinum electrode, the thickness of which was about 10 mm, depending on the temperature conditions. The temperature regime was kept as stable as possible so that all potentials in the circuit remained constant. The glass electrode combined with a Ag,AgCl | KCl(aq) reference electrode (Metrohm 6.0233.100) was used for pH measurements. The same reference electrode was used to detect the potential of the ice electrode. The potentials of glass and ice electrodes were measured with two separate pH meters (Metrohm 713 pH meter) which were connected to a computer for data acquisition. These pH meters were suitable for measuring the potential of the ice electrode since its resistance was found to be approximately 10 times lower than that of the glass electrode. The glass electrode was calibrated with four Metrohm buffers (pH 2.01, 4.003, 7.13, 9.464 at 0◦ C). In order to avoid CO2 contamination the system was always kept under an argon atmosphere. The pH of solution was regulated by automatic additions of acid or base using the Metrohm TITRINO 736 GP. The responses of the electrodes were followed for 1 h after addition of each portion of the reactant solution (1 cm3 of 2 × 10−2 mol dm−3 NaOH) to 200 cm3 of HCl solution (initially 1 × 10−3 mol dm−3 ). The experiments were performed by titrating the acidic solution with the base and vice versa. The first choice was found to result in better repeatability. RESULTS AND DISCUSSION
Figure 2 shows a typical experimental result. It is given for the case of titration of the acid. Each addition of the reactant can be recognized as a step in the diagram. The time dependency of the potential was followed for 1 h. It is clear that, in the acidic region, the potential of the ice electrode follows closely the potential of the glass electrode, while the equilibration time for
FIG. 2. Titration of 200 cm3 of HCl (1 × 10−3 mol dm−3 ) with subsequent additions of 1 cm3 of NaOH (2 × 10−2 mol dm−3 ). Equilibration time for each portion: 1 h. Each portion on the timescale could be recognized as a step. Temperature, 0◦ C.
83
FIG. 3. Surface potential at ice–water interface as a function of pH at 0◦ C. Circles, experimental values; solid line, fitted polynom of the third order; dashed line, the Nernst potential.
the ice electrode increases markedly and the data points become significantly scattered in the basic region. The electrode potential of the ice electrode was converted to the surface potential φ0 using the isoelectric point (IEP) of ice at pHIEP 4, as obtained by Drzymala et al. (12). The procedure is based on the assumption that the only pH dependent potential in the circuit is the surface potential of ice, and also that the IEP corresponds to φ0 = 0. According to SCM the second assumption is correct in the absence of specific adsorption of ions other than H+ and OH− and when the association of counterions is symmetric or absent. Figure 3 presents the surface potential of the ice–water system as a function of pH in the acidic region, where a higher repeatability was observed. In the acidic medium an approximate linearity of the function φ0 (pH) was found, with the slope lower in magnitude than the Nernstian (−54.2 mV at 0◦ C). The data in the acidic region were analyzed by fitting them to a third-order polynom so that the pH dependence of the derivative dφ0 /dpH could be obtained. Figure 4 indicates that the magnitude of the derivative has maximum at pH between 4 and 4.5. It corresponds to the isoelectric point, which agrees with predictions based on SCM combined with an EIL model (19, 22, 30). Surface charge (10) and electrokinetic (11, 12) measurements, together with the results of this study, suggest that the ice–water interface behaves in a way similar to that of metal oxide aqueous systems. Accordingly, charging of ice–water interface may be described by the surface complexation model (13–19) and is due to the amphotheric properties of surface hydroxyl groups ≡OH. Protonation of these groups, ≡OH + H+ → ≡OH+ 2; 0(≡OH+ 2) K p = exp(Fφ0 /RT ) · , 0(≡OH) · aH+
[1]
ˇ KALLAY AND CAKARA
84
by ≡ ≡ − ≡ σ0 = F(0(≡OH+ 2 ) + 0( OH2 Cl) − 0( O ) − 0( ONa)) [6] and that of the outer layer (σβ ) by σβ = F(0(≡ONa) − 0(≡OH2 Cl)).
[7]
Association of counterions is significant at higher values of φβ and may be neglected at low ionic strength as well as at low surface potentials (13–19). Ions in the diffuse layer compensate the charge bound to the surface and the equilibrium may be described by the Gouy–Chapman theory. By using the Gouy– Chapman theory one could relate the net surface charge density σs and surface charge density in difuse layer σd , ≡ − σs = −σd = σ0 + σβ = F(0(≡OH+ 2 ) − 0( O )),
FIG. 4. Slope of the surface potential vs pH for the ice–water interface at 0◦ C (solid line). Dashed line represents the Nernst slope of −54.2 mV at 0◦ C.
leads to a positive charge, while deprotonation, ≡OH → ≡O− + H+ ; K d = exp(−Fφ0 /RT ) ·
0(≡O− ) · aH+ , 0(≡OH)
[2]
results in a negative charge. K p and K d are (thermodynamic) equilibrium constants, sometimes called “intrinsic” constants. They account for chemical nonelectrostatic contributions to the change of standard Gibbs energy. Accordingly, the equilibrium concentrations of surface species (0) are determined by two surface equilibrium constants and the electrostatic potential (φ0 ) affecting the state of surface ionic groups. Counterions, such as Na+ and Cl− , could associate with surface charges according to
to the potential at the onset of difuse layer (φd ) which is approximately equal to the φβ -potential. The electokinetic ζ -potential can be calculated from φd , assuming a certain value of the slipping plane separation (31, 32). There are three points describing the zero-charge condition at the surface. The IEP applies to the condition at which ζ = 0, and consequently at σs = 0. The point of zero charge is related to the consumption of H+ ions from the bulk of the so≡ ≡ − lution and is defined by 0(≡OH+ 2 ) + 0( OH2 Cl) − 0( O ) − 0(≡ONa) = 0, which results in σ0 = 0 if there is no specific adsorption. The third quantity applies to condition at which the potential of the inner plane is zero (φ0 = 0). According to SCM these three points will coincide in the absence of any other ions tending to be chemically adsorbed and if the association of counterions is symmetrical or absent. This condition is determined (22) by equilibrium constants of protonation and deprotonation of amphotheric surface sites ≡OH as pHpzc = pHiep = pH(φ0 = 0) = 0.5 · lg(K p /K d ).
≡OH+ 2
[8]
[9]
−
+ Cl → ≡OH2 Cl; 0(≡OH2 Cl) K (Cl− ) = exp(−Fφβ /RT ) · − 0(≡OH+ 2 ) · aCl ≡O− + Na+ → ≡ONa; 0(≡ONa) . K (Na+ ) = exp(Fφβ /RT ) · 0(≡O− ) · aNa+
[3]
[4]
These counterions are exposed to the potential φβ , being usually lower in magnitude than φ0 . The relationship between these two potentials is based on the assumption of constant capacity C and is commonly given by σ0 , C= φ0 − φ β
[5]
where the surface charge density in the inner layer (σ0 ) is given
It is well established (17, 20), both theoretically and experimentally, that in the case of the specific adsorption of ions other than the potential determining ions (H+ and OH− in the case of ice) the isoelectric point and point of zero charge would shift in the opposite direction on the pH scale; adsorption of anions would shift the IEP to lower pH values, while p.z.c. would shift to higher pH. Adsorption of positive species would result in opposite effects. However, the direction and magnitude of the shift of the third zero point, i.e., pH(φ0 = 0), would depend on the mechanism of binding of the adsorbable ions, as well as on the structure of the interfacial layer (31, 32). The dependency of surface potential φ0 on pH could be derived from Eqs. [1] and [2] as φ0 = =
Kp RT 0(≡O− ) RT RT + ln ln ln aH+ + 2F Kd 2F F 0(≡OH+ ) 2 0(≡O− ) RT ln 10 RT ln 10 log (pHpzc − pH). [10] + 2F F 0(≡OH+ ) 2
REVERSIBLE CHARGING OF THE ICE–WATER INTERFACE
Accordingly, the magnitude of the slope of φ0 (pH) function should be lower than the Nernstian slope (19, 21). The deviation depends on the characteristics of the interface. For example, high values of the equilibrium constants K d and K p and high density of amphotheric surface groups ≡OH would result in a slope closer to the Nernstian. Also, the slope will be closer to the Nernstian at lower extents of counterion association, i.e., at lower electrolyte concentration. Measurements of inner surface potential under controlled conditions, as described here, may provide additional information for a better understanding of interfacial equilibria in solid–liquid systems. The deviation of the φ0 (pH) function from the Nernst equation provides information on the ratio of charge densities of negative and positive groups and thus more accurate values of equilibrium constants K d and K p , which is important since pH at p.z.c. and IEP yields only the ratio K p /K d . In the basic region the more pronounced deviation from the Nernstian behavior was observed. This finding is comparable to the “sodium error” of glass electrodes and may be explained considering the sodium ion association with negative surface groups as described by Eq. [4]. For example, at pH 7 the surface potential φ0 is approximately −100 mV (Fig. 3) while the ζ -potential is about −30 mV (12). The value of φβ -potential, affecting the state of associated sodium ions, should lie between these two limits. According to Eq. [4], φβ = −80 mV would promote sodium ion association by a factor of 30. This pronounced association would cause significant reduction of the surface potential φ0 with respect to the Nernstian value and the effect would be more pronounced at higher pH values. Slow equilibration of the ice electrode in the basic region indicates the possibility of existence of “gel-like layer” at the ice–water interface through which sodium ions diffuse so that rate of equilibration depends on the rate of diffusion and the thickness of the “soft” layer. The isoelectric point of the ice–water interface, determined by surface protonation and deprotonation equilibrium constants, is at pH ≈ 4 so that under normal atmospheric conditions one can expect a negative charge of the ice and a positive charge of the liquid water. Accordingly, melting of a falling hailstone in the warm part of the atmosphere would cause charge separation at the interface. In the high speed of a falling hailstone the positively charged water would be stripped off the solid in the form of small droplets which will remain dispersed in the atmosphere. The hailstones will charge the ground negatively. Accordingly, the reversible charging of the ice–water interface, as described in this article, could be one of several possible mechanisms of electric field formation in the atmosphere that is responsible for thunderstorms.
85
ACKNOWLEDGMENTS We thank Mr. Z. Dojnovi´c and Mr. D. Grgec for construction of the ice electrode.
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20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32.
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