Ionic Conductivity Enhancement

Accepted Manuscript Title: Cause of “Multi-Ionic Conduction” and “Ionic Conductivity Enhancement” in Carbonate-Based Composite Electrolytes Author: H. N¨afe PII: DOI: Reference:

S0013-4686(17)31544-X http://dx.doi.org/doi:10.1016/j.electacta.2017.07.127 EA 29944

To appear in:

Electrochimica Acta

Received date: Revised date: Accepted date:

20-5-2017 6-7-2017 21-7-2017

Please cite this article as: H.N¨afe, Cause of “Multi-Ionic Conduction” and “Ionic Conductivity Enhancement” in Carbonate-Based Composite Electrolytes, Electrochimica Actahttp://dx.doi.org/10.1016/j.electacta.2017.07.127 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Cause of "Multi-Ionic Conduction" and "Ionic Conductivity Enhancement" in Carbonate-Based Composite Electrolytes

H. Näfe* Universität Stuttgart Institut für Materialwissenschaft Heisenbergstraße 3, 70569 Stuttgart, Germany

*

E-mail: [email protected]; Phone: ++49 711 731364

Abstract By re-evaluating the outcome of conductivity measurements recently reported in the literature, it is demonstrated that the disregard of fundamental relationships of electrochemistry makes the interpretation provided in the literature a pure speculation. Therefore, the supposed evidence of multi-ionic conduction and ionic conductivity enhancement must be regarded as completely unfounded.

Keywords:

Multi-ionic conduction; ionic conductivity enhancement; carbonate-based composite electrolyte; electrode polarization

1. Introduction For some time now, mixtures of alkali carbonates dispersed in a porous ceramic oxygen ionic conductor have been regarded as new and promising composite electrolytes for intermediate or low temperature solid oxide fuel cells (IT-SOFC or LT-SOFC). The idea is based on the hypothesis that the dual-phase electrolyte exhibits exceptional conduction properties that are

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provoked by the interfaces between the carbonate and the oxide-ion conductor. According to this hypothesis, the carbonate phase is supposed to become conductive for oxygen ions and/or protons depending on the prevailing conditions [1]. Thus, the term "hybrid ion conductor" has come into play. Since alkali carbonates are conventionally thought to be conductive for carbonate ions, some authors even go so far as to speak of multi-ionic conduction in the dualphase electrolyte. On top of that, the composites are ascribed to evince enhanced conductivity due to an interface effect and a suppressed disposition to the onset of electronic conduction under strongly reducing conditions [1]. None of the above-stated properties has been unambiguously proven. Either they have been pure speculations or unsubstantiated assertions or predictions on the basis of obscure theoretical calculations [2]. The most important argument in favour of the hypothesis of extraordinary conduction properties has been the supposedly higher output power of a composite-based fuel cell in comparison with that of a conventional SOFC. Likewise, this argument has meanwhile been debunked as fallacy [2]. All conductivity data available from the literature indicate that an alkali carbonate as long as it is in the molten state exhibits a significantly higher conductivity than the oxidic constituent of the composite, even if doped ceria as one of the most conductive ceramics is the second phase. In other words, the majority charge carriers in the composites are the same as those of the electrolyte of a molten carbonate fuel cell (MCFC). Therefore, the principle of functioning of a galvanic cell based on such a composite is that of an MCFC. By no means is the cell an SOFC. The terminology to denote the allegedly new fuel cell design is simply misleading, and it is out of the question to compare the output power of the composite-based fuel cell with that of an SOFC. Any argument arising from such a comparison must be invalid as the conditions for the operation of both types of cells are incomparable. Nevertheless, from time to time in the literature there are attempts to prove the correctness of the hypothesis of multi-ionic conduction and conductivity enhancement in the dual-phase electrolyte. A recent example for that is the investigation of Li et al. [1]. In the following, Li's

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experimental findings will be critically assessed. It will be demonstrated that the interpretation of these findings disregards fundamental relationships of electrochemistry, which is why all conclusions drawn by Li et al. about the presence and enhancement of both protonic and oxygen ionic conduction in the carbonate have to be rejected as unproven.

2. Relevant experimental facts Common to all composites that Li et al. [1] investigated was the carbonate mixture comprising Li2CO3 and Na2CO3 (LNC) at the eutectic composition (molar ratio 52/48). LNC was either used as pure phase or was combined with samaria doped ceria (SDC) of the composition Ce0.8Sm0.2O1.9 to form the composite LNC/SDC. Normally, the volume ratio of the constituents was 50/50. Other compositions were additionally materialized, namely those with the volume ratios 70/30, 60/40, 40/60, and 30/70. For the electrical measurements the pure LNC was held in a cylindrical MgO container with two of its opposite inside walls coated with silver; the composites and pure SDC were employed in the form of sintered pellets, likewise with silver coatings as electrodes. The conductivity was either measured by ac impedance spectroscopy with a 5 mV signal amplitude or by potentiostatic dc polarization under a voltage bias of 20 mV. In the latter case, the samples were exposed to either pure oxygen or pure hydrogen. Unfortunately, the authors did not specify the application of an alternative atmosphere different from pure oxygen and hydrogen. Therefore, in the following it is assumed that the samples were kept in ambient air unless a clear statement about the measuring atmosphere was made. The results on the temperature dependence of the conductivity of all pure LNC samples are illustrated in Fig. 1 and those of all LNC/SDC composites are depicted in Fig. 2. As it is theoretically founded for the ionic conductivity, the logarithm of the product between conductivity and temperature is plotted as a function of the inverse temperature. This kind of plotting is maintained here even though in reality the quantity regarded as ionic conductivity cannot al-

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ways be ensured to represent the same. In Fig. 3, the conductivities of the LNC/SDC composites of varying compositions are plotted as a function of the LNC volume fraction at 650 °C. 3. Ionic conduction as electrochemical phenomenon It belongs to the basics of electrochemistry that the process of ionic conduction does not only encompass the transport of ions through the conducting medium but also, respectively, the supply and removal of all necessary species toward and away from the interfaces between the conducting medium and the ambience. The sum of all interface-related processes constitutes the phenomenon of electrode polarization. If electrode polarization considerably affects the total transfer of ions, the quantity regarded as ionic conductivity may drastically differ from the true ionic conductivity. The disregard of this insight is the first aspect of misinterpretation underlying Li's study. The second aspect arises from the unsubstantiated assumption that the chemical species surrounding the ionic conductor determine the character of the ions moving through the same. On the basis of this misconception Li et al. inferred the occurrence of protonic and oxygen ionic conduction in LNC solely from the fact that the carbonate mixture exhibits finite conductivity if it is under the influence of pure oxygen or pure hydrogen. It is well known from the theory of solid-state ion diffusion, which the factors are that govern the nature of the mobile ions in condensed matter with mainly ionic bonding. The type of species surrounding the solid plays the least role, if any at all, in the spectrum of these factors. Similar considerations are transferable from solid-state electrochemistry to the behaviour of liquid ion conductors. Usually, comprehensive studies are necessary in order to gain insight into the character of the conduction process. At any rate, the response of electrically relevant quantities, such as current or voltage, to the change of the concentration of particular species is incapable of providing simple answers. How intricate the matter really may be has recently been exemplified by re-considering the principle of functioning of an MCFC, which led to a paradigm shift in the understanding of the nature of the majority charge carriers in alkali carbonates [2]. Even though the voltage of an MCFC is controlled by the partial pressures of CO2 and O2, all available evidence suggests that the carbonates are conductive for alkali metal

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ions rather than carbonate ions, not to mention oxygen ions. The same applies to the conduction process underlying the function of alkali carbonates as CO2 gas separation membranes [3] or as electrode materials for effective O2 transfer [4]. In the following, it is assumed that the alkali carbonate mixture under consideration is an alkali metal ion conductor and samaria doped ceria is an oxygen ion conductor. Both assumptions are the only ones that are in accord with the majority of experimental facts known up to the present about the electrical behaviour of these two materials. In view of the conditions de+

2-

scribed above, the presence of the two types of ions, i.e. M in LNC and O in SDC, are ensured due to the establishment of the following electrode reactions:

(1)

(2)

(3)

(4)

These reactions illustrate why the presence of particular species in the surroundings of the conducting media is crucial for that the ions are capable of moving unrestrictedly through the media. If only one of the necessary species is completely missing the flux of the ions will come to a standstill and the charge transport will be far away from being related to the ionic +

conductivity. For instance, suppose the surrounding atmosphere is free of CO2, the M -ions arriving at the cathode side cannot be discharged by the backward reaction of (1). As a result, +

M -ions enrich at this interface, due to which a counter voltage is generated and acts against the driving force for the ion movement. In electrochemical terms, the electrode becomes polarized because of the lack of depolarizing species, which electrically corresponds to the effect of an additional resistance in series to the resistance Ri for the ion movement. This is the

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polarization resistance R that commonly grows with the ion flux and may approach infinity at the extreme. The circumstances described above are expected to have prevailed in Li's measurements aiming at the determination of the ionic conductivity of LNC or LNC-containing composites under pure oxygen. The same applies to their measurements on LNC or LNC-containing composites in a pure hydrogen atmosphere. In the latter case, not only was CO2 lacking as depolarizing species of reaction (2), but also H2O. A similar polarization effect may likewise occur if SDC is exposed to a voltage bias under pure hydrogen. According to eqs. (3) or (4), oxygen or an oxygen-bearing species has to be at disposal at the cathode side. However, in pure hydrogen there is no source of oxygen, which is why the cathode side of the SDC body is subject to oxygen ion depletion. The consequence is the same as described before: the charge transport becomes disturbed and, hence, is far away from corresponding to the ionic conductivity.

4. Quantitative impact of electrode polarization Following the approach for rationalizing the behaviour of a carbonate-based composite electrolyte under the influence of a chemical potential gradient [3], the electrical equivalent circuit depicted in Fig. 4 can be used to quantify the relationship between ionic conductivity and electrode polarization resistance. In Fig. 4, Rkp stands for a resistor characterizing the transport of the charge carrier k in phase p. Rkp may be Ohmic or complex but in the following is considered to be purely Ohmic, for the sake of simplification. The indices k = i, e and  refer to ion and electron movement and to the phenomenon of electrode polarization, respectively, whereas the supplemental subscripts p = 1 and p = 2 denote the two constituents of the composite conductor. In the entire circuit of Fig. 4, the directions of all partial currents Ikp plus Ip and of the total current I are equally considered to be positive if positive charges flow in clockwise direction, otherwise they are negative. The same applies to the definition of the

-7-

sign of the voltage source U by considering the direction of the driving force for the generation of U. According to Kirchhoff's circuit laws it follows for the nodes a), b) and c) of the circuit of Fig. 4: (5) (6) (7) and for the loops 1) - 4): (8) (9) (10) (11)

By definition, the resistance Rkp is related to the pertaining conductivity kp and the area Akp through which the charge carrier flows. In the most general case, both of these quantities are functions of the space coordinate x along the distance dkp between the two electrodes of the resistor:

(12)

In eq. (12),

and

represent mean values in the sense of the first mean value theo-

rem for definite integrals. It is well known that the ionic conductivities of LNC and SDC are location-independent constants, which is why

and

. Besides, from the ex-

perimental details of Li's measurements [1] it follows that Akp is independent of the space coordinate, which implies the equality

. Furthermore, since the electrons move

-8-

through the same medium as the ions, it is valid: whereby

and

,

. In view of the aforementioned geometrical conditions, according to

which both phases of the composite electrolyte and the composite itself have the same thickness, the proportions of the areas A1 and A2 to the total area A of the composite can be expressed by the proportions of the respective volumes Vp of each of the two conducting media relative to the total volume V of the composite:

(13)

In general, the total length of microscopic distances that the ions travel when moving through either pure LNC or pure SDC differs from the length of distances that the same ions have to cover in the two conducting media when these media are constituents of a composite. This is due to the meandering nature of the percolation path through the composite. Hence, the ratios between the macroscopic electrolyte thickness d and the distances dkp deviate from unity. Each of them represents a dimensionless factor, fkp, that is called the percolation factor of the charge carrier k in phase p:

(14)

In the most general case, it must be assumed that fkp is even different for the ion and electron transport, which is why fi1, fi2, fe1 and fe2 have to be distinguished. The value of the composite conductivity 1/2 refers to the thickness d and the area A of the composite and results from the measurement of I while U and the composition of the composite, i.e. V1 and V2, are known. Invoking eqs. (5) - (14) leads to the following relationship for 1/2:

(15)

-9-

where the indices 1 and 2 stand for LNC and SDC, respectively.

5. Interpretation of Li's findings 5.1. Pure LNC As Fig. 1 concerns only one conducting medium, viz. pure LNC, eq. (15) can accordingly be simplified by cancelling all quantities referring to SDC. Besides, by definition one has V1 = V and fi1 = fe1 = 1. Another simplification ensues from the fact that the extent of electronic conduction in carbonates can be neglected under the conditions at issue. As a consequence, eq. (15) changes into:

(16)

The curve representing

in Fig. 1 is the result of an ac measurement at quite high

frequencies, whereby the current polarizing the carbonate is extremely small. Therefore, it is justified to assume that in this particular case the polarization resistance RLNC is negligible compared to the resistance RiLNC for the ion movement through LNC: (17)

Another argument in favour of the validity of inequality (17) is the alleged use of air during the measurement. Unlike pure gases, ambient air in addition to O2 always contains 350 ... 400 ppm CO2, which commonly has been proven to be sufficient in order to guarantee the establishment of equilibrium (1) at both electrodes. Thus, it follows from entering eq. (17) into eq. (16) that the curve for

really represents the ionic conductivity of LNC:

(18)

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This is additionally verified by a good agreement of the erature data on

-curve in Fig. 1 with lit-

[5], at least as far as the temperature region above about 500 °C is con-

cerned. With regard to the experimental determination of the curves for

and

in

Fig. 1, the circumstances for upholding equilibrium conditions at the electrodes are unfavourable. As discussed above, species necessary for equilibrating electrode reactions (1) and (2) are absent in pure O2 and H2. Furthermore, both curves result from dc polarization measurements during which, unlike the situation under ac load, a polarizing current is permanently forced to flow in one and the same direction. As a consequence, the polarization resistance rises and may become comparable to RiLNC or even larger so that inequality (17) is no longer valid. At the extreme, the condition:

(19)

may be fulfilled. Then, instead of eq. (16), the relationship reads:

(20)

According to eq. (20), the outcome of the measurement has nothing to do with the ionic conductivity of LNC, but represents a quantity that is significantly lower than the ionic conductivity and is related to the inverse of the polarization resistance of the electrodes attached to LNC. This resistance is a complex function of several factors. Among others it depends on time since the depletion or enrichment of the mobile ions including respective neutral species is subject to a certain time lag. After starting the polarization process, it simply lasts a while until steady-state conditions throughout the electrolyte and within the electrodes are reached and the electrode polarization resistance takes an apparently time-invariant value. Such a time-dependence was indeed observed by Li et al. [1] in respect of the polarization current, which strongly underlines the reasonableness of the present supposition concerning the role of

- 11 -

electrode polarization. Contrary to Li's interpretation, the present supposition is also fully consistent with the conventions underlying the widespread technique of impedance spectroscopy. This technique allows the separation of electrolyte from electrode polarization not least because the latter phenomenon is related to a much larger relaxation time that expresses itself in the characteristic frequency dispersion. The question may arise as to why Li's measurements lead to finite conductivity values and, thus, to values that do not completely vanish. Indeed, it could be expected that creases up to infinity and causes

in-

to approach zero according to eq. (20), especially since

theoretically the establishment of equilibria (1) and (2) should be totally obstructed. The answer to this question is that even in a nominally CO2-free electrode gas there will always be traces of CO2 because in the vicinity of a carbonate kept at elevated temperatures CO2 will permanently be released due to thermal dissociation. It follows from thermodynamic stability data that a CO2 partial pressure of up to 2.5 10-5 bar may build up over pure Li2CO3 at 650 °C, at least under equilibrium conditions. This value will be accordingly smaller in a carbonate mixture. At 450 °C it reduces to 1.2 10-8 bar. The noticeable reduction may be one among several other factors to explain why the curve for the true ionic conductivity, i.e.

increasingly deviates from

, as the temperature falls. The difference amounts to 2

orders of magnitude at 650 °C but 4.5 orders at 450 °C. Likewise, it becomes understandable why the curve for which were measured under pure H2, lies further below the

of Fig. 1, the data of -curve, actually by half

an order of magnitude, on average. One has to keep in mind that in this case the obstacles for depolarization of the cathode are still higher, because a second species, viz. H2O, is additionally missing in the surrounding gas atmosphere. This will further increase

. Again, wa-

ter will not totally be absent, since traces of it are always present in H2, even if the gas is deliberately dried. Apart from that, water may also stem from smallest leaks in the experimental set-up. Therefore, the reproducibility of the data for little controllable factors.

is certain to depend on several

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As outlined above, the electrode resistances governing the conductivity measurements in pure O2 and H2 will neither be negligible nor infinite. They have finite values. Proceeding from eq. (16), these values can be calculated as follows:

(21)

Results for

and

are plotted in Fig. 5 as a function of the in-

verse temperature. The curves were calculated on the basis of the conductivity data of Fig. 1 and by taking account of eq. (18). As to the geometrical factor d/A, allowance was made for the electrolyte dimensions as specified by Li et al. In terms of the quantitative relation of the electrode resistances relative to each other, the curves of Fig. 5 confirm what has been discussed before qualitatively.

5.2. LNC/SDC composites 5.2.1. Percolation factor fiLNC In order to quantify the effect of electrode polarization on the composite conductivity data, the magnitude of the percolation factors has to be known. It follows from eq. (15) that for the boundary conditions

, fiLNC can be attained ac-

cording to:

(22)

In this case, an assumption has to be made concerning the magnitude of fiSDC. Approximately, in a 50/50 composite it is obvious to presume that from:

. Then fiLNC follows

- 13 -

(23)

In Fig. 6, Li's results on . According to eq. (18), sponds to

and

are depicted in comparison with defines

. Moreover

corre-

as the data on the composite were obtained

under conditions that exclude any influence of electrode polarization and electronic conductivity. The same conditions apply to valid. This is verified by the fact that

, which is why the identity agrees well with literature data on

is [6]

(cf. dashed line in Fig. 6). It becomes apparent from Fig. 6 that the conductivity parison with

is negligibly small in com-

. Therefore, the calculation of the percolation factor fiLNC leads to re-

sults largely independent of whether eq. (22) or (23) is invoked. This is illustrated in Fig. 7, in which fiLNC is plotted in percentage terms, once calculated on the basis of the assumption (solid line) and once assuming that fiSDC takes an arbitrarily chosen fixed value, viz. fiSDC = 0.7 (dotted line). In both cases fiLNC is a temperature-independent constant between 500 and 650 °C and amounts to 17.3±0.4 %. Contrary to Li's interpretation, the peaklike increase of fiLNC up to nearly 84 % below 500 °C has nothing to do with a conductivity enhancement. The peak is simply the result of the capillarity effect, due to which the melting temperature of LNC dispersed in the porous network of SDC is by about 30 K lower than the melting point of pure LNC. Therefore, there is a narrow temperature region in which pure LNC is still solid upon heating up while LNC as constituent of the composite is already molten. By taking this effect into due consideration, the true percolation factor is expected to follow the dashed line in Fig. 7.

5.2.2. Polarization resistance of the 50/50 composite By comparing the conductivity curves for the 50/50 composite (Fig. 2) with those for pure LNC (Fig. 1), two features are apparently different: (i) in the case of the composite the diver-

- 14 -

gence between the ac-air and the dc-O2/H2 curves is much smaller; (ii) with regard to the ratio between the conductivities in H2 and in O2, the situation in the composite is the exact opposite to that in pure LNC. At first glance, these differences seem to suggest that the influence of electrode polarization varies from pure LNC to the composite. Quantitative information about that is available from exact calculation. It can be assumed that in an O2 atmosphere the oxygen ion conductivity through SDC and, thus, through LNC/SDC is largely free of electrode polarization, even though the measurement is undertaken under dc load. That means:

. As a first approximation,

it is likewise opportune to presume that the electronic conductivity of SDC is negligible under this condition:

. The same applies to the electronic conductivity of LNC:

. Therefore, it follows from eq. (15) for the electrode resistance of the ion current flowing under oxygen through LNC as constituent of the 50/50 composite:

(24)

For the purpose of calculating the electrode resistance, data for

,

,

and fiLNC were adopted from Fig. 1 (cf. eq. (18)), Fig. 2, Fig. 6 and from the dashed line of Fig. 7, respectively. As to the factor fiSDC, the computation alternatively made use of the presumption fiSDC = fiLNC or fiSDC = 0.7, and with regard to the geometrical factor d/A, the data as given by Li et al. were taken into account. The temperature dependence of

calculated according to eq. (24) is

plotted in Fig. 8. For the sake of comparison, the same figure shows data on

,

that is the electrode resistance for the case that LNC is the sole conductor held under the same conditions. It is adopted from Fig. 5. Fig. 8 reveals that orders of magnitude smaller than

is by at least 2

, which on the whole is independent of the

assumption about the percolation factor fiSDC. Quantitatively, the latter only plays a marginal role at the lower edge of the temperature interval.

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According to general relationships of electrochemical kinetics, it is to be expected that the disparity in the electrode resistances is caused by a disparity in the polarization currents flowing through the respective resistances. Usually, Rp is a function of the polarization current Ip insofar as it falls with decreasing Ip and rises if Ip increases. This is at any rate true provided that the character of the processes accounting for the electrode resistance does practically not change. In terms of the current, the functional dependence of Rp means that the portion of the ion current that flows through the LNC section of the composite under pure O2, i.e. , is much smaller than the current

through pure LNC under

the same conditions. The reality, however, is the exact opposite, as Fig. 9 demonstrates. In this figure the currents Ohm's law by making allowance of

and

are plotted as they result from ,

and

from Fig.

1 (cf. eq. (18)) and Fig. 8, respectively. In both cases, these currents are alkali metal ion currents. That means, their flow direction is opposite the oxygen ion current through SDC. The fact that Fig. 9 is in conflict with the expectation seems to indicate that the preconditions for the validity of the expected relationship are not given. In view of the prevailing circumstances the only feature governing the disparity in the magnitudes of

and

is the occurrence and absence of the occurrence of the oxygen ion current that passes the composite along its SDC paths. This current transports oxygen that stems from the electrolyte/gas interface into the interior of the composite (cf. Fig. 10b). By comparison, in the case that the electrolyte is comprised of pure LNC, the only possible source of oxygen is exclusively restricted to the electrolyte/gas interface, which is represented by the electrode embracing LNC, the surrounding gas atmosphere and silver as the electronically conducting phase (cf. Fig. 10a). That means, there is a noticeable change in the circumstances causing electrode polarization. The role of oxygen as participant in the cathode process becomes obvious from electrode reaction (1). The reaction can be split into two steps:

- 16 -

(25)

The first step depolarizes the current of cations arriving at the electrolyte/gas interface by the formation of alkali metal oxide M2O, which is dissolved in the LNC phase. The depolarization may proceed until the enrichment of M2O causes the counter process to come into effect or the concentration of M2O is reduced by reaction with CO2, in compliance with the second step of eq. (25). On the contrary, in the composite the first step of the cathode process is not restricted to proceed in the electrode only but may additionally take place along all interfaces between LNC and SDC according to:

(26) Unlike the discharging process as per eq. (25), in which three phases are involved, the process described by eq. (26) requires two phases only, viz. LNC and SDC. The contact area between these two phases as depicted in Fig. 10b is by orders of magnitude larger than the threephase boundary in Fig. 10a. The same concerns the size of the LNC volume available for the dissolution of M2O. On the one hand, this volume is practically identical with the overall volume of LNC present in the composite and, on the other hand, it is confined to solely a finite layer close to the electrode interface. All these factors make sure that the depolarization is incomparably more effective in the case of the composite, which implies a lower electrode resistance and, at the same time, a higher cation current flowing upon polarization. The second step of process (25) will be massively hindered unless CO2 is present in sufficient amounts. That means, in a gas atmosphere totally free of CO2 this step will eventually rule the overall electrode regime and will cause the flow of cations to fade away after a certain period of time. As a consequence, the differences in the cation-related electrical properties between composite and pure LNC will disappear completely. As discussed above, the cation current through the composite grows as a consequence of the depolarization due to the oppositely directed flow of anions. The anion current itself is at

- 17 -

maximum when pure oxygen is prevailing. Consequently, if the total conductivity of the 50/50 composite exceeds that under pure oxygen, as it is the case for the conductivity under pure hydrogen (cf.

in Fig. 2), the depolarizing effect of the oxygen ions alone

cannot be invoked to explain the experimental behaviour. Therefore, the only adequate interpretation is the additional occurrence of electronic conduction, which is induced in SDC by the oxygen depletion and/or the reducing effect of H2. Electrons move through SDC instead of or in addition to oxygen ions and depolarize the counterflow of cations, which may cause to be still higher than

(cf. Fig. 2). This suggestion is totally in ac-

cord with the generally accepted knowledge about the impact of the oxygen chemical potential on the electrical properties of doped ceria (cf. [3]). However, it fundamentally contradicts the interpretation of Li et al. [1] who simply declared

to be the consequence of a

new phenomenon, protonic conductivity in LNC, and at the same time introduced another new phenomenon, viz. suppressed disposition of SDC to the onset of electronic conduction under strongly reducing conditions.

5.2.3. Composition dependence of the conductivity In view of the highly polarizing conditions associated with the presence of pure oxygen and hydrogen as electrode gases, it is obvious that the composition dependence of the conductivity as illustrated in Fig. 3 is dominated by the interplay between polarizing and depolarizing effects whose extent varies with the composition of the composite. On the one hand, since the ionic conductivity of LNC is by far larger than that of SDC, the amount of charge transported through the composite tends to increase with increasing LNC-content. On the other hand, the increasing current loads the electrodes, at least one of them, and causes the pertaining electrode resistance to rise, which counteracts the growing current flow. In addition, as long as the proportion of SDC relative to the total volume of the composite is high enough, the depolarizing effect of oxygen ions and electrons flowing through SDC reduces the increase of the elec-

- 18 -

trode resistance. In conclusion, the superposition of these counteracting effects causes the total conductivity to rise in the region of low LNC content and to fall if the composition approaches 100 % LNC, with a maximum in-between. For the reasons mentioned above, all details of the graphs of Fig. 3, apart from the outermost left point of the

-curve,

will be little reproducible as they depend on the presence of impurity traces in the electrode gases. Therefore, a more detailed quantitative attempt of interpretation is out of the question. It follows from eq. (15) that under ideal conditions with regard to electrode polarization and unless electronic conductivity becomes noticeable, implying that

and

, the composition dependence of the conductivity reads:

(27)

where the percolation factors fiLNC and fiSDC are unknown functions of VLNC/V. Despite these unknowns, the terminal points of and between

. Hence, the curve for and

are well defined. They correspond to is a line, at first approximation a straight line,

. It is indicated in Fig. 3 as dashed line.

The dashed line of Fig. 3 describes the maximum possible ionic conductivity of the composite. Since all experimental data are significantly below this line, except the point at VLNC/V = 0, there is not the slightest indication of ionic conductivity enhancement, as it was brought into play by the interpretation of Li et al. [1]. Without any evidence and against electrochemical common sense these authors claimed that the character of ionic conduction of LNC changes from cationic to protonic or oxygen ionic depending on the composition of the composite and on the surrounding atmosphere. Consequently, the authors' discussion of the conductivity peaks in Fig. 3 as expression of an enhancing effect due to sophisticated microstructure of the composite is totally unsubstantiated. It is as unsubstantiated as other claims of ionic conductivity enhancement known from the literature (cf. [7-11]).

- 19 -

6. Conclusions In the recent investigation of Li et al. on the conductivity of carbonate-based composites the experimental findings are misinterpreted due to the disregard of electrode polarization and due to the purely speculative assumption that the nature of ions mobile in the materials is determined by the surrounding species. Therefore, the supposed evidence of multi-ionic conduction, of ionic conductivity enhancement and of a suppressed electronic conductivity in the electrolytes under consideration is completely unfounded.

- 20 -

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[9]

H. Näfe, Enhancement of Ionic Conductivity: Fiction and Facts, Manuscript submitted to Ionics (2017).

[10] H. Näfe, Nanoscale Effect on the Oxygen Ionic Conductivity of Zirconia/Ceria Heterostructures, Manuscript submitted to Ionics (2017). [11] H. Näfe, "Ionic Conductivity Enhancement" and the Handling of Literature Data, Manuscript submitted to Int. J. Hydrogen Energy (2017).

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Figure captions: Figure 1:

Temperature dependence of the conductivity of pure LNC exposed to various gas atmospheres (data adopted from Li et al. [1]).

Figure 2:

Temperature dependence of the conductivity of the composite LNC/SDC (50/50) exposed to various gas atmospheres (data adopted from Li et al. [1]).

Figure 3:

Conductivity of LNC/SDC composites with variable composition, exposed to pure oxygen and hydrogen, as a function of the percentage of the LNC volume fraction in the composite (data adopted from Li et al. [1]; dashed line calculated according to eq. (27)).

Figure 4:

Electrical equivalent circuit for the dc polarization of a composite electrolyte comprising the mixed ionic-electronic conductors 1 and 2 with taking finite electrode resistances into account (Ri1, Ri2: Ohmic resistances for the ionic currents Ii1 and Ii2 through the conductors 1 and 2, respectively; Re1, Re2: Ohmic resistances for the electronic currents Ie1 and Ie2 through the conductors 1 and 2, respectively; R1, R2: electrode resistances for the ionic currents Ii1 and Ii2 through the conductors 1 and 2, respectively; I1, I2: partial currents; I: total polarization current; U: polarization voltage).

Figure 5:

Temperature dependence of the electrode resistance for the ionic current through LNC, exposed to either pure oxygen or pure hydrogen (calculation according to eq. (21)).

Figure 6:

Comparison of the temperature dependence of the conductivity of pure LNC, pure SDC and the composite LNC/SDC (50/50) in air (data adopted from Li et al. [1] [solid lines] and Dirstine et al. [6] [dashed line]).

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Figure 7:

Percolation factor fiLNC for the cation conduction through LNC as constituent of the composite LNC/SDC (50/50) (calculation according to eqs. (22) and (23) depending on the assumption about the magnitude of fiSDC; solid line: fiSDC = fiLNC; dotted line: fiSDC = 0.7; dashed line: extrapolation by taking the influence of the capillarity effect into consideration).

Figure 8:

Electrode resistance for the cation current through LNC with the electrolyte being represented by either pure LNC or the composite LNC/SDC (50/50), in each case exposed to pure oxygen (calculation according to eqs. (21) [upper curve] and (24) [lower curve]; solid line of the lower curve: fiSDC = fiLNC; dashed line: fiSDC = 0.7).

Figure 9:

Cation current through LNC with the electrolyte being either pure LNC or the composite LNC/SDC (50/50), in each case exposed to pure oxygen (calculation according to Ohm's law; solid line of the upper curve: fiSDC = fiLNC; dashed line: fiSDC = 0.7).

Figure 10:

a) Electrode reaction at the three-phase boundary electrolyte/gas/Ag with the electrolyte being pure LNC and the surrounding gas exclusively containing +

oxygen (M : alkali metal ion flow through LNC; M2O: alkali metal oxide, +

that is formed due to the reaction between M , e' and O2 and that is afterwards dissolved in LNC). b) Electrode reaction at the two-phase boundary LNC/SDC inside the electro+

lyte with the electrolyte being the composite LNC/SDC (50/50) (M : alkali 2-

metal ion flow through LNC; O : oxygen ion flow through SDC; M2O: al-

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+

2-

kali metal oxide, that is formed due to the reaction between M and O and that is afterwards dissolved in LNC).

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