Russian Journal of Electrochemistry, Vol. 39, No. 6, 2003, pp. 650–659. Translated from Elektrokhimiya, Vol. 39, No. 6, 2003, pp. 722–731. Original Russian Text Copyright © 2003 by Gorodetskii.

Chlorine Evolution on Highly Porous Metal Oxide Anodes and the Origin of the Low-Polarizability Portion in Polarization Curves at Large Currents V. V. Gorodetskii Russian Federation Scientific Center “Karpov Research Institute of Physical Chemistry,” ul. Vorontsovo pole 10, Moscow, 105064 Russia Received April 23, 2002; in final form, July 9, 2002

Abstract—Experimental and theoretical data on the chlorine evolution in the region of large anodic currents, where a low-polarizability portion emerges in polarization curves, are exhaustively analyzed. It is shown that this practically horizontal portion must emerge upon reaching an overvoltage at which practically all macropores, rather than only the largest of them, are filled with gas. The dramatic increase in the current, observed in this case, is connected with the chlorine evolution reaction penetrating through the entire depth of the coating and results from the formation of a unified system of gas channels in the porous space of the coating. Chlorine evolved in micropores moves via these channels at a high speed to the front side of the electrode, moving away from it in the form of gas bubbles.

INTRODUCTION Four decades has elapsed since the instant when the first titanium anodes with a metal oxide active coating, known as dimensionally stable anodes (DSA), were created. Among these anodes, the electrodes with coatings based on mixed ruthenium and titanium oxides (ORTA) and the latter with additives of doping oxides of nonnoble metals with partial or complete replacement of ruthenium oxides by oxides of other noble metals in their coatings have enjoyed extensive practical application. By now these anodes practically completely replaced the graphite anodes that had been used in the chlorine industry. This is due to the fact that they substantially exceed the latter by their catalytic activity, selectivity, and corrosion resistance. The presence of such characteristics of anodes explains the tremendous interest that was exhibited in studying the corrosion and electrochemical behavior of anodes of this type. As a result of performed investigations, studied was the kinetics and established was the mechanism of the evolution of chlorine and oxygen and the dissolution of ruthenium from the coating on ORTA in conditions of the chlorine electrolysis. It was shown that the rates of these reactions increase with the solution pH [1–9] and that the reactions are mutually related, which is due to the their occurrence through common stages [2, 5, 9]. It was established that the catalytic activity, selectivity, and corrosion resistance of ORTA depend not only on the rates of these reactions but also on their distribution over the coating depth. In doing so, special attention must be devoted to establishing the distribution of the chlorine evolution reaction over the coating depth, for it is precisely the hydrolysis of evolving chlorine that

defines the distribution of solution pH over the coating depth [9]. By now it has been proved that in concentrated chloride solutions of pH 2–4 at 80–90°ë the chlorine evolution on ORTA in the Tafel range of potential occurs with a diffusion control by the removal of the reaction product molecular chlorine from the electrode, and the reaction itself proceeds predominantly in a thin surface layer of the coating in the presence of a quasi-equilibrium by this reaction inside the porous space of the coating [10–13]. In this case, the concentration of chlorine inside the coating (c∞) is defined by the following equation: c ∞ = c 0 exp ( ηnF/RT ),

(1)

where c0 is the chlorine concentration in the bulk solution (mol cm–3) and η the reaction overvoltage (mV). Due to the fact that, in the conditions stipulated, the chlorine evolution reaction occurs via a basic route of this reaction [9, 14, 15], with the transfer coefficients for the anodic and cathodic processes equal to, respectively, β = 2.0 and α = 0, the depth of the reaction penetration into the depth of the coating does not depend on the anode potential [12, 13]. However, one must bear in mind that the chlorine evolution on ORTA in the chlorine industry occurs not in the Tafel region but in the region of much larger currents, where copious gas evolution occurs now on ORTA. This may lead to fundamental redistribution of the chlorine evolution reaction over the coating depth as a result of a change in the mechanism of chlorine removal from the coating and from the electrode surface. This is precisely the phenomenon that is connected with the emergence, in the polarization curve

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CHLORINE EVOLUTION ON HIGHLY POROUS METAL OXIDE ANODES

(PC) for the chlorine evolution on ORTA, of a portion where the current drastically increases, the portion being known as the low-polarizability portion (LPP). Here, experimental data and theoretical notions on the operation of gas-generating porous electrodes are analyzed in order to more realistically describe chlorine evolution on ORTA in LPP. We were the first to discover this portion in a PC for the chlorine evolution, which was recorded at 87°ë on a vertical stationary electrode ORTA in a 300 g l–1 NaCl solution of pH 2 saturated with chlorine [10] (Fig. 1, curve 1). It was established that in such a PC corrected for the ohmic drop of potential, near equilibrium, there is observed an almost linear portion with a slope of about 20 mV, and at currents in excess of 0.02 A cm–2, the PC slope gradually decreases, after which there occurs a dramatic increase in the current following an insignificant increase in the electrode potential. This is exactly the portion that we labeled as LPP. A decrease in the partial pressure of chlorine and the resultant deceleration of the cathodic process allowed us to obtain an extended Tafel portion with a Nernstian slope of 36 mV in an anodic PC recorded at P = 1.67 kPa (Fig. 3, curve 3). At the same time, we determined more clearly the potential at which there emerged the deviation from a Tafel dependence connected with a gradual reaching of LPP, i.e. with the emergence of a transition portion in PC. The possibility of the existence of LPP in the case of reversible occurrence of electrode processes accompanied by gas evolution was first substantiated theoretically by Losev [16]. He suggested that, in the course of the occurrence of such a process under diffusion control by the removal of the reaction product from the electrode (Fig. 2, portion I), its concentration near the electrode must rise proportionally to the current only until a certain extreme oversaturation, after which, with gas evolution started, a further increase in this concentration and, correspondingly, the shift to the right of a partial cathodic PC must cease. This is precisely the reason for the fact that, in the course of a reversible occurrence of a process, even an insignificant further increase in the overvoltage must lead to a drastic increase in the anodic current, i.e. to the emergence of a practically horizontal LPP in the PC (portion II) [16, 17]. Upon reaching currents that exceed the exchange current of the relevant reaction (i0), the LPP may be followed by the emergence, in the PC, of a Tafel portion (portion III) with the slope ba = 2.3RT/βF, in which the process commences to occur under kinetic control [16, 17]. The notions on the nature of an LPP in a PC, which were developed by Losev, were experimentally confirmed by Losev, with the chlorine evolution on a smooth platinum electrode as an example [17]. He established that in the region of large currents, where intensive gas evolution occurs on the electrode, a practically horizontal LPP appears in a PC (Fig. 2 in [17]). On the basis of the presence of an LPP on platinum, as well as on ORTA, RUSSIAN JOURNAL OF ELECTROCHEMISTRY

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E, V (NHE) 1.35

1.30

1 2

1.25 3 1.20

1.15

5

4

3

2 1 –log i [A cm–2]

Fig. 1. Anodic and cathodic PC in a 300 g l–1 NaCl solution of pH 1.9 at 87°C and chlorine pressures of (1) 98, (2) 9.8, and (3) 1.67 kPa.

E III

ba

II

EH E' EP

I ba'

ia log idc

logiH

ic

ic' ic''

logi0

logi

Fig. 2. Scheme of polarization curves; see text for explanations.

and on the basis of identical shapes of the potential decay curves (PDC) obtained on these electrodes after opening up the polarizing circuit, it was assumed that the high catalytic activity of ORTA has nothing to do with the high porosity of ORTA. Authors believe that, as the removal of the gaseous reaction product, which is chlorine, out of the pores of the coating is difficult in these conditions, ORTA, in common with smooth platinum, works in an outer-diffusion mode, i.e. the evolution of chlorine occurs solely from the electrode surface. This assumption is exactly the opposite of the notions about the distribution of the chlorine evolution reaction over the depth of the coating in the vicinity of LPP put forth in [13]. The authors of [13] assumed that, with the potential increasing, the oversaturation by chlorine inside the porous space of the coating may No. 6

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1

1.3

4

2 2'

2

0 –logi [A cm–2]

Fig. 3. PC for chlorine evolution on RDE ORTA (∆ = 5 µm), 5.13 M NaCl, pH 2, 87°C, P = 2.03 kPa, and ω equals (1) 0 and (2) 3500 rpm; curve 2' is PC corrected for diffusion.

reach such a level at which gas evolution will commence in the pores of the coating. This must lead to cessation of the increase in the chlorine concentration inside the pores of the coating and the rate of the cathodic process proportional to it. As a result, with the potential increasing even further, there must occur disruption of the quasi-equilibrium by the reaction of evolution and ionization of chlorine inside the pores of the coating. It is the last that leads to a sharp increase in the current due to the penetration of the chlorine evolution reaction into the coating to an ever increasing depth, which is the reason for the emergence of LPP in a PC. These notions were confirmed experimentally by analyzing PC for the chlorine evolution reaction on a rotating disk electrode (RDE) ORTA with different thicknesses of active coatings [18]. To this end, PC for the chlorine evolution reaction on ORTA with a “thick” coating (5 µm) at the partial pressure of chlorine P Cl2 = 2.03 kPa were recorded at different rotation rates of the disk (Fig. 3; curves 1, 2). By extrapolating a 1/i vs. 1/ ω dependence to infinite agitation, curve 2' was constructed. This curve, which reflects the chlorine evolution rate in the absence of outer-diffusion complications, was compared with curves 1 and 2. The comparison suggested that, in the absence of forced agitation, in the Tafel range of potentials (curve 1), the determining influence on the chlorine evolution rate is exerted by the subsequent stage of chlorine diffusion away from the electrode. On the other hand, in the case of intensive agitation (curve 2), the contribution made by the diffusion stage to the measured chlorine evolution rate becomes insignificant. Nevertheless, an extended LPP was observed in PC 2, as in PC 1, at high currents.1 Furthermore, this particular portion inter1 This

fact is in conspicuous opposition to the Losev conception that an LPP may be observed in a PC only in the case of reversible occurrence of the gas evolution process [16].

sects the continuation of PC 2'. No LPP was observed in a PC (Fig. 2 in [18]), which was recorded in the same conditions (ω = 3500 rpm) on ORTA with a thin coating (0.2 µm), despite the fact that electrodes with thin and thick coatings barely differ in their catalytic activity. These results led to the conclusion that the emergence of LPP in a PC for ORTA with a thick coating at ω = 3500 rpm (after the PC in question crossed curve 2') may be ascribed exclusively to an increase in the working area of the anode surface caused by the penetration of the chlorine evolution reaction into the depth of the porous coating [18]. It was assumed that, in LPP, an intensive gas evolution begins not only on the anode surface but in large pores and cracks in the coating as well ([9], p. 24). With the gas evolution commenced, the mass transfer of chlorine away from the electrode drastically increases, but now the mass transfer process occurs as a result of the formation and removal of gas bubbles from the electrode, rather than at the expense of diffusion of evolved chlorine, as is the case in the Tafel region [3, 9]. It is precisely the increased rate of the chlorine removal from the electrode, which probably leads to the breakdown of equilibrium in regard to the reaction of chlorine evolution and ionization and to a sharp increase in the chlorine evolution rate in LPP ([9], p. 126). However, it had remained unclear how the occurrence of the gas evolution process on a porous electrode might lead to an increase in the chlorine removal rate not only from the ORTA surface but out of the coating depth as well. The most substantiated answer to this question was given in works by Chirkov and coauthors [19–26] on the basis of notions they developed earlier about the occurrence of gas evolution processes on electrodes with a biporous active coating [27–32]. To this end, the authors continued the analysis, begun in [12, 13], of the gas generation process on porous electrodes in the Tafel range of potentials [19]. An equation was derived, which described the distribution of the oversaturation of electrolyte with gas c y = cy/c0 over the depth of a porous coating at a given overvoltage η (in mV). For the chlorine evolution reaction on ORTA (at α = 0 and β = 2.0) the equation has the following form: cy = e

2η

+ (1 – e ) 2η

(2)

× cosh [ ( ∆ – y )/L d ]/ cosh ( ∆/L d ). 0

0

In addition, the following equations were obtained, which allowed one to calculate the oversaturation on the front (y = 0) and rear (y = ∆, where ∆ is the thickness of the coating) sides of the coating as a function of the overvoltage [19]: C∆ = e

2η

+ ( C s – e )/ cosh ( ∆/L d ), 2η

0

(3)

C s = [ ϕe tanh ( ∆/L d ) + 1 ]/ [ ϕ tanh ( ∆/L d ) + 1 ], (4) 2η

0

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0

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where η = ηF/RT is the reduced overvoltage, L d = ( nFD* c 0 /si 0 ) 0

1/2

(5)

the characteristic diffusion length (in µm), D* the effective diffusion coefficient (in cm2 s–1), s the specific area of the coating (in cm–1), and ϕ = I d /I g

(6)

a parameter that characterizes the ratio between characteristic diffusion currents in the porous coating (Id) and in the electrolyte chamber (Ig) [19]. The depth of penetration of the gas evolution reaction into the porous space of the coating, δ, depends on the ratio between the inner- and outer-diffusion limitations with respect to the supply of the gaseous reaction product from the coating pores to the front side of the electrode and to its removal from the electrode surface into the bulk solution. This parameter is defined by the equation δ = L d tanh ( ∆/L d )/ [ ϕ tanh ( ∆/L d ) + 1 ]. 0

0

0

(7)

As follows from (7), for the chlorine evolution on industrial ORTA (∆ = 5 µm) in conditions where ϕ Ⰶ 1 and the outer-diffusion limitations are completely eliminated cs = 1 (for example, with the aid of RDE) and the chlorine evolution occurs in a thin surface layer of the 0 coating (in this case tanh ( ∆/ L d ) = 1), the depth of penetration of the gas evolution reaction into the porous 0 space of the coating, δ, is equal to L d . In another special case, where ϕ Ⰷ 1 and the outerdiffusion limitations play a crucial role and the electrolyte oversaturation with chlorine at the front surface of the electrode takes on the maximum possible value 2η C s = e , the depth of penetration of the gas evolution reaction into the porous space of the coating, δ, is equal 0 to L d /ϕ. Once the regularities that govern the chlorine evolution on ORTA in the Tafel region of potential were elucidated, authors considered specific features intrinsic to the occurrence of this process in the region of LPP and in the “transition” region located between them, which they called the initial part of LPP or the d region [21– 24]. The analysis was performed with allowance made for specific features inherent in the structure of the porous space of the active coating. In accordance with [33] it was assumed that two types of pores exist in the coating of ORTA, specifically, micropores with radii from ri1 = 0.001 µm to ri2 = 0.0025 µm and macropores with radii from ri1 = 0.05 µm to ri2 = 0.4 µm, where i = 1 for micropores and i = 2 for macropores. The explanation, which was offered by authors for the mechanism of the LPP emergence in PC for the chlorine evolution, was based on a certain assumption. Specifically, they assumed that the more rapid increase RUSSIAN JOURNAL OF ELECTROCHEMISTRY

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in the chlorine evolution rate following an increase in the potential, with the subsequent emergence of LPP, which is observed after the Tafel region, is due to the emergence, in the porous space of the coating, of a system of “gas” pores connected with one another and the electrode surface. This event creates a powerful channel for collecting gas from micropores filled with electrolyte (where chlorine evolves) and its removal by filtration from the coating into the electrolyte chamber, which is exactly what leads to a drastic intensification of the process [19–24]. Let us consider this mechanism of the emergence of an LPP in more detail. In conditions of the chlorine electrolysis, the evolution of chlorine on ORTA in the Tafel region of potentials occurs in the presence of outer- and inner-diffusion complications as to the removal of evolved chlorine from the bulk coating and from the electrode surface [3]. The oversaturation by chlorine inside the coating is minimum at the front side of the anode and increases with depth, reaching a maximum near its rear side [13, 19]. This allowed the authors of [19, 21] to assume that, with the polarization increasing and the chlorine concentration inside the coating pores rising, it is precisely near its rear side that the gas evolution is likely to begin. In this case, in accordance with the equation [34, 35] C* = 1 + r 0 /R

(8)

the first to be filled with gas are the largest macropores with the radius r2.2 = 0.4 µm. As follows from (8), this event must occur at some critical overvoltage η* . This is the overvoltage at which the oversaturation by chlorine near the rear side of the coating reaches its critical value C* = 3.5. The emergence of the initial part of LPP in PC was attributed in [21–23] precisely to the gas starting to fill the largest macropores. The increase in the rate, at which the current increased with the potential, was attributed by authors to an increase in the magnitude of the effective diffusion coefficient for chlorine, D*, in the porous space of the coating following an increase in the contribution to it made by the gas constituent (the diffusion coefficient for chlorine in a gas is 4–5 orders of magnitude that in a liquid). At η > η* , smaller macropores near the rear side of the coating also start to be gradually filled with gas, and the interface between the gas pores and liquid pores continuously moves toward the front side of the electrode. Authors believe that at η = η** , when C s = C** = 3.5 and the largest macropores with r2,2 = 0.4 µm happen to be filled with gas throughout the entire depth of the coating, there occurs the formation of a unified system of gas channels connected with one another and the front side of the electrode. It is precisely these gas channels through which chlorine is removed from the coating. By authors' opinion, it is precisely the reason that is responsible for the dramatic increase in the current and for the emergence of an almost horizontal LPP in No. 6

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PC [21–23]. The electrochemical reaction of chlorine evolution occurs in these conditions in smaller pores filled with electrolyte, from which chlorine diffuses into gas pores. Then via these pores, without any innerdiffusion complications, chlorine arrives at the front surface of the electrode, leaving the mouths of the gas pores in the form of gas bubbles. As a result, there must occur a complete removal of outer-diffusion limitations and the penetration of the chlorine evolution reaction to the entire depth of the coating [23, 24]. On the basis of a model proposed for the gas evolution on porous electrodes, a set of equations was derived. On the basis of this set of equations, an attempt was undertaken to describe PC for the chlorine evolution on ORTA in different potential regions. The most severe complications arose when describing the initial LPP, for in this potential region it is difficult to quantitatively characterize the distribution of the effective diffusion coefficient over the depth of the coating. This is connected with the probability of the filling of pores with gas being dependent simultaneously on the radii of the pores and the magnitude of the oversaturation of electrolyte with gas. To overcome these complications, authors made use of an approximate “lattice” model for the distribution of gas and electrolyte in the porous space of the coating [21, 23, 24], which was put forth in [36]. To find the characteristics of gas-generating porous electrodes and to calculate theoretical PC, the calculations were based on experimentally found parameters, which are typical for the chlorine evolution on ORTA (∆ = 5 µm) in a 300 g l–1 NaCl solution saturated with chlorine at a temperature of 87°ë, which are equal to, respectively, α = 0, β = 2.0, and i0 = 1.2 × 10–4 A cm–2 [37].2 Other parameters are: c0 = 2.7 × 10–6 mol cm–3 [38] and the roughness factor f = 700 [39]. It was assumed that micropores and macropores in ORTA are uniformly distributed in the above intervals of radii, and the porosity of the coating g, which is equal to the sum of microporosity g1 and macroporosity g2, is equal to 0.5 at g1 = g2 = 0.25. From here calculated were: the effective diffusion coefficient for chlorine in the porous space of the coating D* = D g/ν = 5 × 10–6 cm2 s–1 (at ν = 1), the specific surface area of micropores s1 = 2.69 × 106 cm–1, that of macropores s2 = 1.84 × 104 cm–1, and the overall specific surface area s = s1 + s2 = 2.71 × 106 cm–1. This quantity exceeds the last, calculated on the basis of the roughness factor of ORTA, 2 This

s = f/∆ = 1.4 × 106 cm–1, and it strikes us as less reliable due to the arbitrariness of the selection of the magnitude of the porosity and the character of the pore distribution by radii. On the basis of equations I d = ( nFD*c 0 si 0 ) , 1/2

(9)

I k = si 0 ∆, (10) and equation (5) calculated were: the characteristic dif0 fusion length L d = 1.27 µm, the characteristic diffusion current Id = 21 × 10–3 A cm–2, and the characteristic kinetic current Ik = 84 × 10–3 A cm–2 [26]. On the basis of the ratio between overall current densities of the chlorine evolution on ORTA with different thicknesses of the coatings [12] calculated was the quantity ϕ = 7.5 [19, 21, 23].3 Using the above parameters, a theoretical PC for the chlorine evolution on ORTA was calculated and compared with a relevant experimental PC recorded on a stationary vertical anode [21, 22]. It was established that the theoretical PC nicely coincided with the corresponding experimental curve only in the Tafel region of potentials; the curves substantially deviated from one another in LPP and in the transition region of potentials [21]. This deviation between experimental and theoretically computed PC was attributed by authors to an approximate nature of calculations, which were based on the notions about an “ideal” gas-porous electrode [28]. In order to diminish the deviation between experimental and theoretically computed PC, authors replaced C** in relevant formulas by a certain “free” (i.e. fitting) parameter, which allowed them to obtain the best conformance between experimental and theoretically computed PC [21]. At the same time, it was stated (see [21], p. 554) that this parameter cannot be determined theoretically. Such a fitting allowed them to obtain satisfactory agreement between experimental and theoretically computed PC and between relevant values of η** , under the assumption that C** = 20 [21]. Authors suppose that immediately after reaching an LPP (at an overvoltage that slightly exceeds η** ) all the outer-diffusion limitations are eliminated and the sharp increase in the current in LPP is due to reduced inner-diffusion limitations with respect to the supply of this value of ϕ is of approximate nature. The overall current densities used when computing it [12] were measured on a disk electrode rotated at 3500 rpm, rather than on a stationary ORTA, as was claimed by authors. In these conditions the value of ϕ must be substantially smaller. Besides, the calculation of this

3 Sadly,

value of the exchange current, borrowed from [37] and used in a series of works by Chirkov and coauthors [19–24] is underrated. It refers to 1 M NaCl, rather than to a 300 g l–1 NaCl solution. The correct value of the exchange current, which is found from the overall exchange current density of the limiting stage of the main route of the reaction [37] i0I, 4 = 5.05 × 10–3 A cm–2 and the effective depth of the reaction penetration into the coating [12] δ = 0.3 µm, is i0 = i0I, 4xn∆/fδ = (5.05 × 10–3 × 2 × 5 × 10−4)/(700 × 0.3 × 10–4) = 2.4 × 10–4 A cm–2.

0

quantity used value of L d that had been calculated not accurately enough (we will substantiate this below). Using the equation I = Id e2η/(ϕ +1), which is equation (41) in [19], we obtained a more accurate value of ϕ for a stationary ORTA on the basis of curves 1 and 2' given in Fig. 3. This value is equal to 5.4.

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chlorine, which evolved in the electrolyte-filled pores, to the gas pores. The reason for this is that the halflength L of the electrolyte-filled liquid pores diminishes with increasing number of gas-filled pores because of their convergence [23]. On the basis of notions concerning the mechanism of the emergence of an LPP developed in [19–23] authors performed an analysis of the effect the structure of the porous space of the coating and the kinetic and diffusion characteristics of the system exert on some characteristic features of relevant PC [24]. It was shown that, at a constant macro- and microporosity of the coating, the overvoltage, at which an almost horizontal LPP emerges in PC, increases with decreasing size of macropores. The extension of this portion decreases with decreasing value of ϕ and simultaneously decreases the overall current density in the Tafel region of potentials (Fig. 3 in [24]). It was established that, at a constant macro- and microporosity of the coating, invariant size of macropores, and a constant value of ϕ, an increase in the size of micropores leads to a decrease in the overall current density in the Tafel region of potentials and to a substantial decrease in the extension of LPP, while the overvoltage at which LPP emerges remains invariant (Fig. 4 in [24]). An analysis of these results demonstrated in the long run that, when manufacturing DSA, the overvoltage, at which an LPP emerges in PC, may be reduced by a purposeful increase in the size of macropores, and by a simultaneous decrease in the size of micropores it is possible to achieve a substantial increase in the maximum overall current density in LPP as a result of a simultaneous drastic increase in the overall specific surface area of the coating. It should be remembered, however, that at sufficiently large overall current densities, even before reaching a maximum possible overall current density (in the absence of diffusion limitations), a rapid growth of polarization may begin in PC, the growth being related to an increase in the ohmic drop of potential across the porous space of the coating [25, 26]. The question of elucidation of the LPP origin was also discussed in a series of papers by S.V. Evdokimov [40–44]. The conclusion about the validity of models for the interpretation of the reasons for the emergence of LPP in PC proposed in these works was usually drawn on the basis of a comparison of slopes of experimental and theoretically calculated PC in the region of an LPP under the assumption that the experimentally determined slope of the LPP was close to 20 mV. Such a slope of a PC was indeed observed in [10] on a stationary ORTA (Fig. 1, curve 1) at the current i > 0.01 A cm–2. However, this region is in fact not an LPP but a transition portion of PC, which is distorted by the reverse process, to boot. This was explained in review [9], on p. 98. In later works [42–44], the PC portion with a slope of 20 mV, which was observed on a rotating disk electrode ORTA at ω = 3500 rpm in the interval of currents 0.1 to 2 A cm–2 (Fig. 3, curve 2), was assumed to be an LPP. However, this portion reflects RUSSIAN JOURNAL OF ELECTROCHEMISTRY

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E, V (NHE) 1.40 1.35 1.30 1.25 3

2

1 0 –logi [A cm–2]

Fig. 4. PC for chlorine evolution on ORTA in a 300 g l–1 NaCl solution of pH 2 at 87°C and P Cl = 2.0 kPa, cor2

rected for the ohmic drop of potential with the aid of PDC.

neither the position nor the slope of LPP. The magnitude of the slope was overrated due to the blocking of the central part of the surface by chlorine bubbles accumulated here with increasing current and due to an incomplete automatic compensation of the ohmic drop of potential at currents in excess of 0.4 A cm–2 when performing measurements on a German potentiostat model PS-3 supplemented with a PU-1 device. The last was proved experimentally in [3] with a model system as an example (see the footnote on p. 1427). According to theoretical conceptions developed by Losev in [16, 17], the slope of LPP in PC must be close to zero, which was experimentally confirmed during a study of the chlorine evolution on platinum [17] and on a rotating disk electrode ORTA in 0.12 and 0.46 M HCl chloride solutions of elevated acidity. Only the very beginning of reaching such a close-to-horizontal LPP was observed by us in Fig. 1. Chirkov and coauthors had failed to quantitatively describe in [19–24] the regularities that govern the chlorine evolution reaction on ORTA in the “transition” range of potentials and also in the region of the LPP. Nor had they managed to determine by calculations the overvoltage corresponding to the emergence of an LPP. Nonetheless it seems to us that the assertions, developed in the works cited, which concern the drastic acceleration of the chlorine evolution process on ORTA following the formation in the coating of a system of gas channels connected with one another and the front surface of the electrode, are quite useful. To our mind, however, the observed deviation from the Tafel dependence and the emergence of a transition region in LPP have nothing to do with the beginning of gas evolution in the largest pores near the rear side of the coating, as it was presumed by Chirkov and coauthors in [21–23]. We believe that these phenomena are caused by reaching a critical oversaturation C* = 1 + r0/r21 = 3.5 near the front surface of the electrode at the overvoltage η* , No. 6

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at which these macropores happen to be filled by gas almost to the entire depth of the coating and gas bubbles commence leaving them for the electrolyte chamber. With the current increased even further, the emergence of an almost horizontal LPP in PC occurs at a certain critical value of overvoltage η** and a certain critical value of the oversaturation C** = 1 + r0/r22 = 21 near the electrode surface, which corresponds to it. This is the overvoltage value, at which all the macropores, rather than only the largest of them (as was erroneously assumed in [21–23]) happen to be filled with gas practically over the entire depth of the coating. The accompanying drastic increase in the overall current density is caused by a substantial intensification of the process of chlorine removal from the coating via gas channels and also by decreased inner-diffusion limitations on the supply of chlorine that evolved in electrolyte-filled micropores to these gas channels. The last is explained by assuming that the half-length of liquid micropores, which connect the gas-filled macropores, decreases with increasing the number of gas-filled macropores [23]. The gas filling the macropores at a large excess pressure leaves the mouths of these macropores in the form of bubbles rapidly increasing in volume. Such an evolution of gas bubbles and the emergence, during this process, of pulsations of the gas and the electrolyte is likely to substantially intensify the solution agitation both near the electrode surface and in macropores of the coating adjacent to it [45]. All this is exactly what leads to a complete elimination of the outer-diffusion limitations. Unfortunately, these factors had been ignored by Chirkov and coauthors in their work. They describe the chlorine evolution process in the electrolyte chamber both in the Tafel region and in the region of LPP by the same equation, specifically, equation (23) given in [22]. To reconcile the sharp increase in the current of the chlorine evolution in the porous space of the coating in the region of LPP with the rate of the chlorine evolution process in the electrolyte chamber, Chirkov and coauthors evoked a far-fetched assumption that the oversaturation by chlorine at the front surface of the electrode dramatically increases in the region of potentials corresponding to an LPP (Fig. 6 in [22]). In order to corroborate the notions on the origin of LPP we developed on the basis of a comparison between theory and experiment, it is necessary to refine the diffusion and kinetic characteristics pertaining to the chlorine evolution process on ORTA and obtain additional information on the structure of the porous space of the coating. Chirkov and coauthors usually calculated the char0 acteristic diffusion length L d with equation (5). The exchange current required for the calculations was computed with the formula i 0 = i 0ov ∆/ fδ,

(11)

where i0ov is the overall exchange current measured experimentally. This procedure of determining the characteristic diffusion length strikes us as not rigorous 0 enough, as in this case the correctness of finding L d is severely dependent on the accuracy of experimental determination of δ and s. The characteristic diffusion length may be calculated much more accurately on the basis of (5), provided the experimentally found value of δ in equation (11), which is used for calculating i0, is replaced by the corresponding quantity defined by equation (7). 0 Ld

nFD*c =  --------------------0  i0 s 

1/2

0

nFD*c 0 f L d tanh ( ∆/L d ) - --- -----------------------------------------= ------------------si 0ov ∆ ϕ + tanh ∆/L 0d + 1

hence L d =

0

0

1/2

, (12)

0 nFD*c 0 tanh ( ∆/L d ) -. -------------------- ---------------------------------------i 0ov ϕ tanh ( ∆/L 0d ) + 1

At ϕ Ⰷ 1, when the chlorine evolution occurs at a high rate, in the presence of outer-diffusion complications, nFD*c 1 0 L d = --------------------0 ------------. (13) i 0ov ϕ + 1 At ϕ Ⰶ 1, when outer-diffusion complications are absolutely absent, nFD*c ∆ 0 L d = --------------------0 tanh -----. (14) 0 i 0ov Ld Here, if tanh ( ∆/ L d ) = 1 and consequently δ = L d , then nFD*c 0 L d = --------------------0 . (15) i 0ov 0

0

From (9), (11), and (15) we obtain the following expression for the characteristic diffusion current in the absence of outer-diffusion limitations: i 0ov  1/2 ∆ I d =  nFD*c 0 s ---i 0ov ------------------= i 0ov . (16)  f nFD*c 0 The last means that, at a sufficiently high catalytic 0 activity of the electrode, when ∆ > 1.6 L d , the overall exchange current measured in the absence of outer-diffusion limitations is nothing more nor less than the characteristic diffusion current of the system. Its magnitude is defined by the catalytic activity of the coating i0 and the depth of penetration of the chlorine evolution reaction into the coating δ in the absence of outer-diffusion limitations. The latter in turn is defined by the magnitude of i0 and the structure of the porous space of the coating, which influences the magnitude of the effective diffusion coefficient for chlorine in the coating, D*. If the characteristic diffusion current is calculated in a correct fashion, its magnitude will not depend of the accuracy of the determined effective diffusion

RUSSIAN JOURNAL OF ELECTROCHEMISTRY

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Calculation Experiment model of Chirkov and coauthors

2 × 10–4

21

47

19.4

(21.3)

(21.3)

49.6

2 × 10–4

42.0

69.0

19.4

40.2 (43.6)

40.2 (43.6)

62.4

0.53 × 10–5

66.4

87.3

25

65.4

65.4

97.8

0.96 × 10–6

85.0

40.5

82.3

82.3

116.2

Vol. 39

η*, mV; beginning of deviation from Tafel dependence

η**, mV LPP C y = 0.1 = 21

1.01 × 10–2 L d = (nFD*c0)/[i0ov(ϕ + 1)] = 0.1 (002)

η*, mV at C y = 0.1 = 3.5; at ( C y = C s = 3.5)

5.4

i0 , A cm–2 η**, mV LPP at C y = 0.1 = 3.5; at ( C y = C s = 3.5)

5.13 M NaCl, pH 2, 87°C ω = 0 (Fig. 3)

0

L d (δ, µm)

η*, mV at C ∆ = 3.5

ϕ

η**, mV LPP

Solution

i0ov, A cm–2, at ω ∞

No. 6

0

model proposed here

2003

5.13 M NaCl, pH 2, 87°C ω = 3500 rpm (Fig. 3)

0

0.36 1.01 × 10–2 L d = (nFD*c0)/[i0ov(ϕ + 1)] = 0.49 (036)

5 M NaCl, 0.12 M HCl, 87°C ω = 3500 rpm

Ⰶ1

4.67 M NaCl, 0.46 M HCl, 87°C ω = 3500 rpm

Ⰶ1

2.0 × 10–3

0

L d = (nFD*c0)/[i0ov] = 2.7 (27)

CHLORINE EVOLUTION ON HIGHLY POROUS METAL OXIDE ANODES

RUSSIAN JOURNAL OF ELECTROCHEMISTRY

Kinetic and diffusion characteristics of the chlorine evolution process on ORTA for various electrolysis conditions; experimental and theoretically calculated values of overvoltages η* and η**

0

5.62 ×

10–4

L d = [(nFD*c0)/i0ov] × 0

112

tanh(∆/ L d ) = 6.2 (414) 657

658

GORODETSKII

coefficient and specific surface area of the coating, which is in glaring contradiction with the corresponding quantities obtained by Chirkov and coauthors in [19–23].4 To determine the value of the effective diffusion coefficient more accurately, we experimentally obtained the value of porosity of ORTA, g, using a gravimetric analysis. This correct value proved to equal 0.1, which is five times as small as the quantity used in calculations in [23–25]. It follows that the effective diffusion coefficient for chlorine in the porous space of the coating is D* = Dg/ν = 1 × 10–6 cm2 s–1. In view of what we stated in the foregoing, on the basis of notions as to the mechanism of the emergence of LPP developed by Chirkov and coauthors and the modification of these notions we proposed above, using equations (2)–(4), values of η* and η** were computed for a variety of the chlorine evolution conditions and compared with experimental data (table). It was established that the experimentally determined values of η* and η** substantially differ from corresponding values calculated on the basis of assertions maintained by Chirkov and coauthors [28–30] in practically all the cases. At the same time, quite a satisfactory agreement between experimental and theoretically calculated values of η* and η** was observed under the assumption that these corresponded to reaching critical oversaturations C* and C ** near the front surface of the anodes. In the absence of outer-diffusion limitations, the oversaturation of solution by chlorine near the front surface of the electrode is equal to unity and drastically increases with moving into the depth of the coating. Therefore, for the values of η* and η** in these conditions we adopted values of overvoltages at which values of critical oversaturations by chlorine equal to C* and C** , respectively, were reached at the distance y = 0.1 µm from the front surface of the electrode.5 This allowed us to sufficiently accurately estimate, later on, the overvoltage at which an LPP must appear in PC for systems with known kinetic parameters and known structure of the porous space of the coating.6 As assumed in the foregoing, the deviation from a Tafel dependence and the emergence of LPP in PC are connected with reaching corresponding critical concen4 Values

of Id that were found in these works, specifically, 21 mA cm–2 [26, 28] and 29.6 mA cm–2 [29, 30] (depending on the technique used for finding the value of the specific surface area of the coating) were 2–3 times its correct value Id = i0ov = 10.1 mA cm–2. 5 In the presence of outer-diffusion limitations, η* and η** were computed at y = 0, and these values appear in the table in parentheses. 6 The performed analysis does not rule out the possibility of the emergence of LPP connected with the commencement of gas evolution near the electrode surface in PC for a highly reversible process.

trations C* and C** in the porous space of the coating near the front surface of the electrode (not near its rear side). An unambiguous proof for this assumption is the increase in overvoltages η* and η** observed with increasing rotation rate of RDE (Figs. 2a, 3 in [3]). The change in the chlorine distribution inside the coating near the front surface of the electrode, which occurs in these conditions, is caused by the fact that, with increasing intensity of solution agitation, the oversaturation of the electrode surface by chlorine decreases; in the limit, as the outer-diffusion limitations disappear, this oversaturation tends to unity. As follows from the data we listed in the table, the conclusion made by Evdokimov that an LPP may be observed in PC for the chlorine evolution only at i0 > 10–4 A cm–2 [42] is groundless. The one and only condition for the emergence of a low-polarizability portion (connected with the formation of gas channels in the porous space of the coating) in PC is the reaching of relevant oversaturation C** near the front surface of the anode. The magnitude of the overvoltage, at which this event can occur, increases with decreasing exchange current i0 and transfer coefficient β for the anodic process. However, for an LPP to emerge, there is absolutely no need for β to unfailingly be equal to 2.0, as was declared by Evdokimov [42]. The purposeful correction of the ORTA technology and the removal of inaccuracies in the correction of PC for the ohmic drop of potential in the region of high currents (when recording potential decay curves) allowed us for the first time to obtain in PC for the chlorine evolution on ORTA (Fig. 4) in conditions that are close to industrial conditions not only an extended (in the interval of currents 0.1 to 1 A cm–2), almost-horizontal LPP, but also to discover a subsequent sharp increase in the potential according to an almost-Tafel dependence. REFERENCES 1. Gorodetskii, V.V., Pecherskii, M.M., Yanke, V.B., et al., Elektrokhimiya, 1981, vol. 17, p. 513. 2. Gorodetskii, V.V., Doctoral (Chem.) Dissertation, Moscow: Russian Federation Scientific Center “Karpov Research Institute of Physical Chemistry,” 1991. 3. Evdokimov, S.V., Gorodetskii, V.V., and Losev, V.V., Elektrokhimiya, 1985, vol. 21, p. 1427. 4. Erenburg, R.G., IV Simpozium “Dvoinoi sloi i adsorbtsiya na tverdykh elektrodakh” (VI Symp. on Double Layer and Adsorption at Solid Electrodes), Tartu: Tartus. Gos. Univ., 1981, p. 382. 5. Krishtalik, L.I., Kokoulina, D.V., and Erenburg, R.G., Itogi Nauki Tekh., Ser.: Elektrokhimiya, 1982, vol. 20, p. 44. 6. Uzbekov, A.A. and Klement’eva, V.S., Elektrokhimiya, 1985, vol. 21, p. 758. 7. Zhinkin, N.V., Novikov, E.A., and Fedotova, N.S., Elektrokhimiya, 1989, vol. 26, p. 1094.

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CHLORINE EVOLUTION ON HIGHLY POROUS METAL OXIDE ANODES 8. Bune, N.Ya., Serebrikova, E.V., and Losev, V.V., Elektrokhimiya, 1973, vol. 9, p. 894. 9. Gorodetskii, V.V., Evdokimov, S.V., and Kolotyrkin, Ya.M., Itogi Nauki Tekh., Ser.: Elektrokhimiya, 1991, vol. 34, p. 84. 10. Pecherskii, M.M., Gorodetskii, V.V., Evdokimov, S.V., and Losev, V.V., Elektrokhimiya, 1981, vol. 17, p. 1087. 11. Evdokimov, S.V., Yanovskaya, M.I., Roginskaya, Yu.E., et al., Elektrokhimiya, 1987, vol. 23, p. 1509. 12. Evdokimov, S.V., Gorodetskii, V.V., Yanovskaya, M.I., and Roginskaya, Yu.E., Elektrokhimiya, 1987, vol. 23, p. 1516. 13. Erenburg, R.G. and Krishtalik, L.I., Elektrokhimiya, 1987, vol. 23, p. 8. 14. Erenburg, R.G., Krishtalik, L.I., and Rogozhin, N.P., Elektrokhimiya, 1984, vol. 20, p. 1183. 15. Evdokimov, S.V. and Gorodetskii, V.V., Elektrokhimiya, 1987, vol. 23, p. 1587. 16. Losev, V.V., Elektrokhimiya, 1981, vol. 17, p. 733. 17. Losev, V.V. and Selina, L.E., Elektrokhimiya, 1989, vol. 25, p. 1155. 18. Evdokimov, S.V. and Gorodetskii, V.V., Elektrokhimiya, 1989, vol. 25, p. 1139. 19. Chirkov, Yu.G., Elektrokhimiya, 2000, vol. 36, p. 526. 20. Rostokin, V.I. and Chirkov, Yu.G., Elektrokhimiya, 2000, vol. 36, p. 735. 21. Chirkov, Yu.G. and Chernenko, A.A., Elektrokhimiya, 2001, vol. 37, p. 546. 22. Chirkov, Yu.G. and Rostokin, V.I., Elektrokhimiya, 2001, vol. 37, p. 557. 23. Chirkov, Yu.G. and Rostokin, V.I., Elektrokhimiya, 2001, vol. 37, p. 336. 24. Chirkov, Yu.G. and Rostokin, V.I., Elektrokhimiya, 2001, vol. 37, p. 409. 25. Chirkov, Yu.G. and Rostokin, V.I., Elektrokhimiya, 2001, vol. 37, p. 987. 26. Chirkov, Yu.G. and Rostokin, V.I., Elektrokhimiya, 2001, vol. 37, p. 1107.

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27. Markin, V.S., Chizmadzhev, Yu.A., and Chirkov, Yu.G., Dokl. Akad. Nauk SSSR, 1963, vol. 150, p. 596. 28. Pshenichnikov, A.G., Dokl. Akad. Nauk SSSR, 1963, vol. 148, p. 1121. 29. Chirkov, Yu.G. and Pshenichnikov, A.G., Elektrokhimiya, 1990, vol. 26, p. 1545. 30. Chirkov, Yu.G., Rostokin, V.I., and Pshenichnikov, A.G., Elektrokhimiya, 1991, vol. 27, p. 235. 31. Chirkov, Yu.G., Rostokin, V.I., and Pshenichnikov, A.G., Elektrokhimiya, 1993, vol. 29, p. 892. 32. Chirkov, Yu.G., Rostokin, V.I., and Pshenichnikov, A.G., Elektrokhimiya, 1996, vol. 32, p. 1090. 33. Roginskaya, Yu.E. and Morozova, O.V., Electrochim. Acta, 1995, vol. 40, p. 817. 34. Chirkov, Yu.G. and Pshenichnikov, A.G., Elektrokhimiya, 1984, vol. 20, p. 1542. 35. Chirkov, Yu.G. and Pshenichnikov, A.G., Itogi Nauki Tekh., Ser.: Elektrokhimiya, 1988, vol. 27, p. 199. 36. Burshtein, R.Kh., Vakhonin, V.A., Tarasevich, M.R., et al., in Toplivnye elementy (The Fuel Cells), Moscow: Nauka, 1968, p. 306. 37. Evdokimov, S.V., Mishenina, K.A., and Gorodetskii, V.V., Elektrokhimiya, 1988, vol. 24, p. 1475. 38. Pasmanik, M.I., Sass-Tisovskii, B.A., and Yakimenko, L.M., Spravochnik (A Reference Book), Moscow: Khimiya, 1966, p. 101. 39. Kokoulina, D.V., Ivanova, T.V., Krasovitskaya, Yu.I., et al., Elektrokhimiya, 1977, vol. 13, p. 1511. 40. Evdokimov, S.V., Elektrokhimiya, 1998, vol. 34, p. 979. 41. Evdokimov, S.V., Elektrokhimiya, 2000, vol. 36, p. 265. 42. Evdokimov, S.V., Elektrokhimiya, 2000, vol. 36, p. 552. 43. Evdokimov, S.V., Elektrokhimiya, 2000, vol. 36, p. 677. 44. Evdokimov, S.V., Elektrokhimiya, 2000, vol. 36, p. 687. 45. Korovin, N.V. and Feoktistov, A.F., Elektrokhimiya, 1970, vol. 6, p. 335.

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