FROZEN ELECTRODES. J.B. Merriam. University of Saskatchewan Department of Geological Sciences. Abstract

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1 FROZEN ELECTRODES J.B. Merriam University of Saskatchewan Department of Geological Sciences Abstract Resistivity and induced polarization surveys are a challenge in cold environments because of very high grounding resistance. Frozen formation water is an obvious cause of the elevated resistance but it is shown here that the electrical double layer immediately adjacent to the electrode is also important. The latter is accessible to control and may present some opportunity to reduce the total resistance. It has been found elsewhere that if pore water freezes to an electrode while the electrode is carrying a current, the electrode becomes a diode, with a resistance in the forward direction, (that is, with current in the same sense as when freezing occurred) less than the resistance in the reverse direction. The ratio of reverse to forward resistance can be as large as an order of magnitude, and both forward and reverse resistances are considerably less than the resistance on electrodes frozen without carrying a current. These conditions may persist for as long as a few months, during which time the resistance in both directions increases with time. The diode effect is attributed to the quasi-permanent alignment of water molecules immediately adjacent to the electrodes, such that in the forward direction the transfer of an electron between the electrodes and ice is more easily achieved than in the reverse direction. Introduction In many high latitude locations, such as the Athabaska Basin in northern Saskatchewan, induced polarization and resistivity surveys are restricted to a two week window in the spring and fall. Travel by vehicle is difficult in the summer and grounding resistances are too large in the winter. Temperatures in the ground during the winter may range from 40 o C or lower near the surface to zero at depths of a few m. Recent work on the electrical properties of ice has suggested that contact resistance between a metal electrode and ice depends on electrical conditions at the electrode while formation water is freezing onto it (Evtushenko et al, 1988, Petrenko and Whitworth, 1999). Thus, at least part of the total grounding resistance may be subject to control. It is well known that the resistivity of pure water increases discontinuously by orders of magnitude when it freezes to ice. The behaviour of water saturated rock is quite different. The resistivity of rock increases as the temperature decreases and may not reach the resistivity expected of icein-rock until the temperature is a few tens of degrees below zero. There are several reasons for this. As pore water freezes, dissolved salts are excluded from the ice and the salt concentration of the unfrozen water increases, increasing its conductivity and lowering its freezing point. The expansion of water on freezing may also increase the pore pressure, further depressing the freezing point. Finally, water immediately adjacent to the pore-water boundary may not freeze until the temperature is somewhat below zero degrees centigrade. The reason for this is the large electric field in the electric double layer. Potential differences as small as one hundred mv across a one nanometer Stern layer imply electric fields as high as 10 8 V/m. Electric fields of this magnitude and higher are sufficient to polarize water (Booth, 1951a,b). It is likely that at least the innermost part of the electric double layer in a silicate rock pore has a structure organized by the electric field and inhibited from joining the normal crystal lattice, except through crystal defects. As this layer can make a significant contribution to bulk conductivity, (Revel and Glover, 1998), the issue of the

2 mobility of ions in this layer is important. The work described here suggests that this layer may remain unfrozen for at least a few degrees below zero, so that surface conductivity in the Stern layer may be significant even though conduction through the bulk pore ice has almost ceased. The range of temperatures, solute concentrations and potentials over which this may occur is poorly known and will not be examined in this paper. Electric fields near an electrode surface can be much greater than those near a pore surface and should create a thicker and more structured layer of water than would be observed near the surface of a mineral grain. 60 EVOLUTION OF FROZEN CELL RESISTANCE WITH TIME M Ω POTENTIAL (V) M Ω MΩ 125 MΩ LIMITING CURRENT DAYS FROM START OF FREEZING CURRENT (µ A) Figure 1. The diode effect in frozen electrodes. The red curves are data collected with the current in the same sense as when the cell was freezing. The blue curves are data collected with the current in the opposite sense to when it was freezing. When the cell is initially frozen, and for small currents, the resistance in the forward direction is smaller than it is in the reversed direction by a factor of about four. The diode effect in frozen electrodes The basic phenomenon is shown in Figure 1. A cell with copper electrodes in water is allowed to freeze while carrying a small current. After the cell has frozen, and the temperature stabilized, in this case at 18 o C, the resistance is measured with current in the same direction as when the cell was freezing (this may be called the forward direction) and with the current reversed. The potential across the frozen cell is shown versus the current through it for potential differences of one volt to fifty volt in both polarities.

3 In this case, the resistance in the forward direction is smaller than that in the reverse direction by a factor of about four. Other trials have yielded factors as high as ten. The numbers along the top and bottom of the figure are the time in days since the cell was first frozen. The forward and reverse resistances both increase with time and the diode effect persists for at least sixty days. In this trial, the final resistance is a factor of ten greater than the initial resistance in the reverse direction and a factor of twenty greater than the initial resistance in the forward direction. It should be noted that at the end of sixty days the cell resistance is still increasing with time and shows no sign of approaching a limit. Thus, the ultimate resistance is actually unknown but may be much larger than the resistance measured at the end of the experiment. Also unknown is the cell resistance that would have resulted if the cell had frozen without an applied potential. The resistance in an unpolarized cell also tends to increase with time. It appears that the initial resistance in an unpolarized cell is similar to or slightly greater than the initial resistance in the reverse direction in a polarized cell, but due to the difficulty in replicating initial conditions exactly, it is impossible to say this is always true. It seems likely that the ultimate resistance for polarized and unpolarized cells would be similar as the polarized state is expected to relax towards an unpolarized state. The cell resistance for the example shown in figure 1 varies from 4.8 Mohm to 125 Mohm. It is likely that most of this variation is due to changing conditions at the electrode rather than in the bulk ice. If all of the variation in resistance during the sixty day experiment is attributed to changes in the electric double layer, then the smallest resistance for the bulk ice is 4.8 Mohm, and the resistance across the electric double layer varies from a minimum of 0 to a maximum of 120 Mohm. These represent the extreme possibilities and reality is undoubtedly somewhere in between. Nevertheless, it appears that the resistance of the electric double layer may in fact be a large fraction of the total grounding resistance. The forward polarity resistance for day one and day two increases with potential at low potentials but approaches infinity at large potentials as a limiting current is reached. A limiting current is characteristic of mass transport control, which suggests that the supply of ions at one or both of the electrodes is quickly exhausted once the measuring potential is applied. This effect relaxes with time, so that the limiting current increases and eventually becomes larger than the largest current used in the measurements. In this particular trial, the limiting current appears to be about 6µA, but in other trials limiting currents as low as 1µA were observed. Current limitation within the experimental range was observed to persist for up to five days. The limiting current is smaller and the effect persists for longer if the potential applied to the electrodes while freezing is allowed to remain on for a longer period of time after the cell has frozen. It is hypothesized that a diffusion front is established at the anode by the initial current if it is allowed to remain on for some time after the cell freezes. No current limitation in the reversed direction was observed over the range of currents used. This is consistent with the above explanation that the limiting current in the forward direction is caused by the polarizing potential itself.

4 120 CELL RESISTANCE vs TIME 100 CELL RESISTANCE (mω) MΩ/day REVERSE CURRENT 4.4 MΩ/day FORWARD CURRENT MΩ/day FORWARD CURRENT TIME (days) Figure 2. The evolution of frozen cell resistance vs time. The frozen cell resistances increase linearly with time and do not approach a limit before the experiment is ended. The rate of increase of the resistance in the forward direction is initially slower than in the reverse direction, but after about two weeks the rate of increase in the forward direction suddenly increased by nearly an order of magnitude. The diode effect is observed to persist for at least sixty days after the cell freezes (Figure 2). Here, the measured cell resistance is plotted as a function of time. The reverse resistance increases linearly at about 1.6 Mohm/day. The forward resistance initially increases linearly with time at a slower rate, 0.6 Mohm/day, but after about two weeks the rate of increase changes abruptly to 4.4 Mohm /day. This is the only trial in which either rate changed abruptly. It is not known what may have been the cause. Other trials have yielded similar results, that is, a forward resistance that increases linearly at a rate two to three times slower than the rate of increase of the reverse resistance. The origin of the diode effect Ice is a poor conductor of electricity because any ions incorporated into the ice become immobilized in the ice lattice and are unavailable to support conduction. The small but finite conductivity of ice is attributed to the passage of protonic point defects along the lattice (Petrenko, 1999). To support a steady state current, hydrolysis would also have to occur, with hydrogen being liberated at the cathode and oxygen at the anode. 2H 3 O + +2e H 2 +2H 2 O at the cathode 2OH 2e 1 2 O 2 + H 2 O at the anode The same reaction occurs in pure liquid water, but in water, physical motion of the hydronium and hydroxl ions carries the current, whereas in ice, current is carried by point defect exchange.

5 A further distinction is that in liquid water, the liberated O 2 and H 2 can diffuse away from the electrodes. In ice, their mobility is restricted so that, at least in the short term, they remain at the electrode surface and contribute to an increase in resistance with time. The immobility of water molecules also restricts the total charge either electrode can pass. This effect undoubtedly contributes to the limiting currents observed in experiments where the initial current was on for some time after the cell first froze. If the diameter of a water molecule is m, then the molecular density in the first rank on the electrode surface is /m 2. This implies that only 2.7C/m 2,orequivalently,2.7As/m 2, is available for hydrolysis, at least on time scales shorter than the time for products to diffuse away from the surface and be replaced with water molecules. The ice-electrode interface clearly cannot pass even modest currents for any length of time unless the electrode area is very large. The application of a polarizing potential during freezing increases the surface density of water molecules favourably oriented for hydrolysis so that larger currents of greater duration are possible than would otherwise be the case. However, it must be concluded that while the diode effect can be used to lower the contact resistance and increase the availability of water molecules near the electrode, the total charge that can pass through the interface is limited. 300 THRESHOLD POTENTIAL FORWARD RESISTANCE REVERSE RESISTANCE RESISTANCE (Mohm) THRESHOLD POTENTIAL APPLIED POTENTIAL WHILE FREEZING (V) Schematic showing the origin of the diode effect in frozen elec- Figure 3. trodes. Figure 3 is a schematic illustrating the conditions at both electrodes of a cell that has frozen while carrying a current. On the left hand side, the condition of the cell is shown when the applied potential is in the same direction as when the cell was freezing. The water in the Stern layer is polarized in the direction of the initial electric field and immobilized by attachment to the bulk crystal lattice through point defects. On the right hand side, the applied potential is reversed, but the water molecules in the Stern layer remain in their original orientation. It is hypothesized that the orientation of water molecules in the cell on the left hand side is favourable for hydrolysis and

6 the orientation in the cell on the right hand side is not. Thus, the cell resistance in the forward direction (the cell on the left hand side) is lower than it is in the reverse direction (right hand side). If no potential difference is applied across the cell, except for infrequent pulses of short duration to measure resistance, then as time progresses the structure of the Stern layer at both electrodes relaxes as point defects are eliminated. This process gradually reorients water molecules in the Stern layer to the bulk crystal lattice, with the result that fewer molecules are favourably oriented to the electrode for electrolysis to occur. As a result, the cell resistance should increase with time, as is observed. The favourable orientation of water molecules for hydrolysis has some implications for the limiting current discussed earlier. It is observed that the forward resistance is very nearly independent of potential or measurement duration over a fairly wide range. Resistance in the reverse direction, as well as resistance in an unpolarized cell, are extremely dependent on pulse duration. This suggests that activation energy is smaller for current in the forward direction and that diffusion fronts are more easily developed in the reverse direction and in the unpolarized state. The question arises as to what magnitude of potential is required to produce the diode effect. Preliminary experiments have shown that the diode effect disappears if the applied potential during freezing is below some threshold. Furthermore, the magnitude of the diode effect, as measured by the ratio of forward to reverse resistances, is only weakly influenced by higher applied potentials. Thus, rather small applied potentials are sufficient to induce the diode effect but larger potentials have little further effect. If the model described above is correct, that is, that the phenomenon is ultimately due to the attachment of an electrically polarized layer to the bulk ice lattice by a plane of point defects, then the existence of the polarized layer is important and its thickness less so. This is consistent with the above observation that a threshold potential exists above which the dipole effect is observed and below which it is not. The proposed model requires that the magnitude of the electric field in the electric double layer exceed the field needed to cause strict orientation of water molecules. This requires field strengths greater than 10 8 V/m in at least the first rank of water molecules. The Debye screening length, itself determined largely by the solute concentration, and the potential difference between the electrode and bulk water are the important factors in determining both the strength of the electric field and the thickness of the layer of structured water (Albery, 1975). The Poisson-Boltzman equation can be used to calculate the electric field E in the diffuse layer; E = 0.051V z o 2tanh(V/2)e ( z zo ) 1 tanh(v 2 2z ( /4)e zo ) where z o is the Debye length and V = ev o /2kT is the dimensionless potential difference between the electrode and the bulk water. Assuming a Debye length of 10 8 m, which would be appropriate for a solute of unit molar concentration, the first rank of water molecules experiences an electric field greater than 10 8 V/m if the electrode potential is greater than about one volt. That is, under these conditions, at least the first rank of water molecules near the electrode surface will be in an electric field strong enough to orient them. For potentials less than a volt the electric field in the first rank is less than that necessary to orient the water and no diode effect should be seen. Higher concentrations allow a dipole effect to occur at smaller threshold potentials. Thus, the theory of the electric double layer supports the idea of a threshold potential below which water molecules closest to the electrode are not oriented by the electric field. Note that the fact that water molecules may be oriented does not prove that they will preserve that orientation when they become attached to the bulk lattice. Summary It has been shown elsewhere that when a metal electrode is passing a current into water which is freezing onto the electrode, the contact becomes a diode with a resistance that depends on the

7 direction of current. If current is in the same direction as it was when the water was freezing, the resistance will be low and when current is flowing in the opposite direction the resistance will be higher, but still marginally lower than if the cell had frozen without an applied potential. A model is proposed which suggests that the diode effect requires electric fields greater than about 10 8 V/m in at least the first rank of water molecules. Such fields will orient water molecules, and it is assumed that they maintain this orientation while becoming attached to the bulk ice matrix through crystal defects. This model explains the observations that characterize the dipole effect. The orientation of water molecules near the electrodes is favourable for the hydrolysis that must occur to pass a current (Figure 3) and less favourable to current in the opposite direction. This orientation is also more favourable to hydrolysis than the random orientation that might result if the cell froze while no current was passing between the electrodes. Thus, an electrode frozen while passing a current has a lower contact resistance to current of either polarity than does an electrode frozen while passing no current. The resistance in either polarity is observed to increase with time. At least initially, the reverse polarity resistance increases faster than the forward polarity resistance. It is hypothesized that the crystal defects attaching the electrically oriented water to the bulk ice are unstable, so that the electrically structured ice slowly cures to become part of the regular ice lattice. As this happens, the number of near electrode sites with a favourable orientation of water molecules for hydrolysis decreases and so the resistance increases. This suggests that conditions at the electrodes progress towards the state that would have occured had no current been flowing when the ice formed. Thus, the application of a small potential during freezing lowers the resistance in both polarities not just in the forward polarity. Experimentally the forward resistance is much smaller than the unpolarized resistance and the reveres resistance is only slightly smaller than the unpolarized resistance. The phenomenon persists for at least sixty days, during which time the resistance in both direction increases. Extrapolating the straight lines in figure 2, the diode effect in this experiment would have disappeared at about day seventy. Subsequent to that time, the resistance would probably have continued to increase towards some ultimate value. It is hypothesized, but as yet unconfirmed, that the rate of change of resistance is dependent on temperature. There is some experimental evidence that a threshold potential exists below which the diode effect is not seen. This is predicted by the model, which requires that the near surface electric field be greater than 10 8 V/m. Fields this high can be expected within a water molecule diameter of the surface for potentials as small as one volt. A calculation of the electric field strength to be expected in different solute concentrations suggests that the threshold potential will decrease as the solute concentration increases. There is evidence that the diode effect does not occur until the temperature at the electrode has fallen a few degrees below zero. This suggests that water molecules in the polarized region are initially not attached to the bulk ice lattice and may retain angular and lateral mobility until that temperature is reached. At very high concentrations, even the electric field established near the pore water - silicate rock interface, which might involve a potential difference of only a few hundred mv, may be large enough to polarize water and prevent it from joining the bulk lattice at zero degrees C. Thus, in shales and clays especially, the Stern layer may remain mobile below 0 o C and contribute to the bulk conductivity even though the bulk pore water has frozen. The purpose of this work was to examine the possibility of lowering contact resistance in frozen formations by taking advantage of the diode effect. While it appears that quite large reductions in resistance can be achieved, and that the contact can be conditioned to pass a larger current for a longer time, it also seems that the contact is not able to handle the large currents and long pulse durations required in induced polarization and resistivity.

8 Acknowledgments This work was supported by a Natural Sciences and Engineering Research Council of Canada Discovery Grant. References Albery, J., Electrode kinetics, Clarendon Press, Oxford. 183 pp. Booth, J., The dielectric constant of water and the saturation effect. Jour. Chem. Phys., 19, Booth, J., Errata, The dielectric constant of water and the saturation effect. Jour. Chem. Phys., 19, Evtushenko,A.A., M.B. Martirosyan, V.F.Petrenko, 1988, Experimental investigations of electrical properties of ice grown in a static electric field. Soviet Physics - Solid State, 30, Petrenko, V.F. and Robert Whitworth, Physics of Ice, Oxford U.P. Oxford, 373 pp. Revel, A., and P.W.J. Glover, Nature of surface electrical conductivity in natural sands, sandstones and clays. Geophys. Res. Let. 25, No. 5,