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Discharge and Charge Reaction Paths in Sodium-Oxygen Batteries: Does NaO Form by Direct Electrochemical Growth or by Precipitation from Solution? Pascal Hartmann, Markus Heinemann, Conrad Ludwig Bender, Katja Graf, Roelf-Peter Baumann, Philipp Adelhelm, Christian Heiliger, and Jürgen Janek J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b06007 • Publication Date (Web): 15 Sep 2015 Downloaded from http://pubs.acs.org on September 22, 2015

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The Journal of Physical Chemistry

Discharge and Charge Reaction Paths in Sodium-Oxygen Batteries: Does NaO2 form by direct Electrochemical Growth or by Precipitation from Solution? Pascal Hartmann4#, Markus Heinemann2#, Conrad L. Bender1, Katja Graf,4 Roelf-Peter Baumann4, Philipp Adelhelm1, Christian Heiliger2*, Jürgen Janek1,3*

1

Physikalisch-Chemisches Institut, Justus-Liebig-Universität Gießen, Heinrich-Buff-Ring 58, 35392

Gießen, Germany 2

I. Physikalisches Institut, Justus-Liebig-Universität Gießen, Heinrich-Buff-Ring 16, 35392 Gießen,

Germany 3

BELLA, Institut für Nanotechnologie, Karlsruher Institut für Technologie, Hermann-von-Helmholtz-

Platz 1, 76344 Eggenstein-Leopoldshafen 4

BASF SE, 67056 Ludwigshafen, Germany

#

both authors corresponded equally to this work

* Corresponding Author: Jürgen Janek, [email protected]

Abstract Sodium-oxygen cells with sodium superoxide (NaO2) as discharge product show a charge and discharge characteristics with very low overvoltage – different from lithium/oxygen cells. Here it is shown that the discharge of a non-aqueous sodium/oxygen cell proceeds via the electrochemical formation of superoxide (O2−), its dissolution in the liquid electrolyte and subsequent precipitation together with sodium ions as solid sodium superoxide. Charge proceeds in the counter-direction by

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consumption of dissolved superoxide anions and dissolution of NaO2. Indirect evidence for the solution-precipitation route is provided by theoretical results on the electronic structure of NaO2 and the conclusion that the electronic conductivity of NaO2 is too low to allow direct electrochemical growth and dissolution. Direct evidence for the solution-precipitation route is provided by results from charge/discharge studies of a three-electrode cell in which pre-formed NaO2 is being decomposed without direct electronic contact to the charging circuit. An analytical model for the overvoltage as function of electrode coverage with electrically insulating discharge product complements the theoretical and experimental results and supports the mechanistic findings. Keywords: metal-air battery, superoxide, sodium ion battery, rotational disorder, NaO2, oxygen evolution reaction, oxygen reduction reaction

1. Introduction During the last years serious efforts were spent on investigating and developing non-aqueous lithium-oxygen (Li/O2) batteries. The underlying electrochemical net cell reaction can be described by the reversible formation and dissolution of lithium peroxide (Li2O2) during discharge and charge, respectively, but it is now well known that a variety of side reactions take place in addition – limiting efficiency and life time of the cells, in particular a high potentials during charging.1-4 Driven by these observations the reaction steps during charge and discharge of a Li/O2 battery and their details are revisited, and in particular, the formation and growth mechanism of the solid Li2O2 discharge product is recently studied in depth. Different crystal shapes are reported, ranging from donut or toroid shaped Li2O2 particles with a diameter of up to 1 µm to thin film deposits of Li2O2 on the electrode surface.5 Very recently, Aetukuri et al. studied the influence of water impurity in the electrolyte and concluded that it has a major effect on the morphology of the Li2O2 deposits.6 They observed that large toroids are only formed in the presence of water. Interestingly and to the contrary, Zheng et al. were able to grow toroids in the absence of water using an all-solid-state lithium-oxygen battery ACS Paragon Plus Environment

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operated in an environmental scanning electron microscope at 200 Pa oxygen gas.7 Obviously, water appears to play a major role in the electrochemical kinetics of non-aqueous Li/O2 cells, but other synergistic factors like e.g. the role of the conducting salt anion on Li2O2 formation cannot be ruled out unequivocally. In fact, nucleation and growth under electrochemical conditions are complex processes, and future mechanistic studies will surely help to obtain a more coherent picture. After an initial report on surprisingly different electrochemical kinetics and the formation of sodium superoxide (NaO2) rather than the peroxide (Na2O2), non-aqueous sodium-oxygen (Na/O2) batteries have recently attracted fast growing interest. It is found that pure sodium superoxide (NaO2) is formed as discharge product and that Na/O2 cells show significantly higher energy efficiency than Li/O2 cells as well as a higher chemical reversibility.8-11 Interestingly, Na2O2 is also reported as discharge product in a number of papers, but the efficiency and reversibility of those cells is even lower than for lithium based cells.12-19 By and large there are two striking differences between lithium-oxygen and sodium superoxide batteries: On the one hand the typical particle size of the discharge products NaO2 and Li2O2 differs by more than one order of magnitude, with NaO2 cubes often having an edge length in the order of 101 µm. On the other hand the decomposition of NaO2 requires a significantly lower overpotential, i.e. offers relatively fast electrode kinetics, during both charging and discharging of the battery. Several theoretical and very recent experimental studies explain the small particle size and sluggish charge kinetics with Li2O2 being a poor electronic conductor.5, 20-22 Thus, charge transport through the oxide particles is considered as rate determining. Hence one might infer that the superior performance of the sodium cells is due to a higher electric conductivity of NaO2 compared to Li2O2. At this point it is worth to consider lithium-sulfur cells and their complex discharge and charge kinetics for a comparison. In fact both the starting material (S8) and the final discharge product (Li2S) at the cathode are electric insulators. Thus, the comparably fast electrode kinetics is only achieved due to the high solubility of reactive intermediates (lithium sulfide and polysulfide Sn2−) within the elec-



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trolyte phase. The idea that soluble oxygen intermediates are key to the cathode kinetics in Li/O2 cells is not new and has already proposed quite early by Read in 2002,23 but until recently not much attention was paid to this idea. In order to shed more light on the mechanism of the cathode reaction, we combine results from four different approaches toward the better understanding of the Na/O2 cell reactions in the present paper: Firstly, we explore the possibility of intrinsic electronic conduction within sodium superoxide (NaO2) by calculating the electronic structure of the room temperature phase – including hindered rotation of the O2− lattice anions. Experimental data on the bulk electric conductivity of sodium superoxide are yet not available, and thus, we secondly attempt to gain direct information on the electric resistivity of NaO2 cubes grown in Na/O2 batteries using electrochemical atomic force microscopy (EC-AFM). Thirdly, we present a dual-working electrode cell which helps to evaluate the role of sodium superoxide dissolved within the electrolyte. The results give unequivocal evidence for the solution-precipitation path. Finally, we present a quantitative kinetic model for the overvoltage at oxygen cathodes in Na/O2 cells, which describes the impact of solution based NaO2 formation and decomposition surprisingly well. On the whole, our findings give unequivocal evidence for solutionprecipitation as the dominating reaction path.

2. Results and Discussion 2.1 Electronic structure of NaO2 (DFT calculations) Sodium superoxide (NaO2) is known to exist in three stable phases in different temperature ranges. For temperatures below −77 °C it crystalizes in the marcasite structure followed by a pyrite phase up to −50 °C.24-25 Here we focus on the high temperature phase which is formed as discharge product in room temperature Na/O2 batteries.8-9 In this case NaO2 crystallizes in a disordered pyrite-type structure that differs from the pyrite phase by additional rotational degrees of freedom of the superoxide


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molecular anions.24, 26 X-ray measurements by Carter and Templeton indicate that the rotational motion of the superoxide dumbbells might be constrained such that they show a preferred orientation along the unit cell diagonals.25 Compared to the ordered pyrite structure, the rotational disorder of the high temperature phase is challenging for computational modeling – which is the reason why previous first principles studies of NaO2 mainly focused on the pyrite or marcasite phase.27-30 As we show in our calculations the rotational disorder in the high-temperature phase affects the total energy of the system and thus can, in principle, influence the transition and diffusion dynamics of charge carriers. Kang et al. recently investigated the phase diagram of Na2O2 and NaO2 using density functional theory (DFT) and addressed the problem of the rotating O2 molecules by additionally taking into account the energetic contributions of the crystal’s phonon system and a rigid rotor model system.31 In this work we address the question how the orbital disorder of the high temperature phase influences the electronic properties of sodium superoxide by simulating multiple possible superoxide orientations beyond the ordered pyrite phase. To assess the impact on the electronic band structure we employ first principles DFT calculations using a hybrid functional approach (HSE) to describe the exchange and correlation interaction (details see section 4). Arcelus et al.29 and Yang et al.30 recently showed that this approach is superior to former first principles descriptions of the pyrite NaO2 phase where the computationally less demanding generalized gradient approximation (GGA) to the exchange correlation functional was used.27-28, 31 Compared to the GGA, which describes the electronic structure of NaO2 as a (semi-)metal, the HSE functional yields a splitting of the occupied from the unoccupied oxygen p-orbitals at the Fermi edge giving an energy band gap of about 2.1 eV for the pyrite NaO2 phase, which is in agreement with Refs. 29 and 30. Yang et al.30 further employed quasi-particle calculations within the framework of the G0W0 approximation on top of their HSE calculations and estimate the band gap in this material to be 5.30 eV. Although the quasi-particle gap is considerably larger than the HSE band gap, the hybrid functional approach also yields the correct insulating description of the electronic band structure. We thus constrain our calculations to the HSE framework to limit the computational demand.



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To simulate the orbital disorder of the high temperature phase we performed electronic structure calculations for every possible arrangement of the four superoxide ions along the cell diagonals within the pyrite unit cell. Not taking the crystal symmetry into account yields a total of 256 calculated NaO2 cells. Further, we consider all possible antiferromagnetic alignments of the superoxide ions in our calculations and then choose the lowest energy configuration. Fig. 1 shows the distribution of the total energy per formula unit of the calculated orbital configurations normalized to the lowest total energy configuration. The total energies of the different configurations change only within a small range up to 150 meV/formula unit. Hence, from a thermodynamic point of view it can be possible to find all configurations under room temperature conditions.

Figure 1: Distribution of the total energies of the calculated 256 NaO2 crystal configurations with different superoxide orientations (normalized to the configurations with lowest energy). As the energy differences between the configurations are rather small we assume that all orientations are possible in a room temperature crystal.

The effect of orbital disorder on the electronic band structure of NaO2 is presented in Fig. 2. Here we show the band structures for three selected and exemplary NaO2 crystals with the depicted different superoxide arrangements. Although the three band structures display similar features with respect to the energy gap or band alignment the band dispersion within the Brillouin zone is clearly affected by the orbital disorder of the superoxide ions. Since all possible arrangements within the NaO2 crystal may occur at room temperature a superposition of all the different band structures can be considered as first order approach to the band structure of the disordered pyrite phase. It can be inferred


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from Fig. 2 that the room temperature band structure then features a wide energy gap of about 2 eV as well as a smeared out band dispersion. Especially the conduction band is broadened to a bandwidth of around 1 eV. These considerations are also reflected in Fig. 3 where the electronic density of states of the room temperature NaO2 phase is approximated. In this illustration we average the density of states of around 20 representative structures with different superoxide arrangements to simulate the effect of the superimposing band structures. With respect to the conductivity of NaO2 these results indicate that un-doped and stoichiometric NaO2 is an insulator or wide band gap semiconductor and that the possibility of hindered rotation of dioxygen anions significantly influences the electronic properties of NaO2. Although the band gap is probably lower than of lithium peroxide (approx. 4.832 – 6.65 eV30), our calculations give no evidence for intrinsic electronic conductivity that is high enough for direct electrochemical growth of NaO2.

Figure 2: Electronic bandstructures of three exemplary NaO2 crystals with different superoxide orientations. The orbital disorder of the superoxides affects the band dispersion. In a room temperature crystal many different superoxide arrangements are present which leads to a broadening of the band widths (especially for the conduction band as indicated by the dashed lines).



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Figure 3: Approximated electronic density of states of the room temperature NaO2 phase calculated by averaging over multiple cells with various superoxide orientations.

It is worth to briefly discuss whether nonstoichiometry of NaO2, i.e. oxygen deficiency or excess as expressed by NaO2-x, can lead to significant extrinsic conductivity. Gerbig et al. discussed the defect structure of alkali peroxides and of higher alkali superoxides in detail, but excluded NaO2.33 Recently, Yang et al. published a thorough DFT study of the conduction mechanisms in Na2O2 and pyrite NaO2.30 They find that in NaO2 a combination of electron and hole polarons determines the electronic charge transport, while the several magnitudes higher ionic conductivity is based on positive oxygen dimer vacancies, negative sodium vacancies, and positive sodium interstitials. These findings basically support the following defect model for nonstoichiometric NaO2: If we assume that intrinsic and stoichiometric NaO2 shows cation Frenkel defects as majority defects (assuming Schottky disorder will not significantly change the analysis of extrinsic defects) according to Na V ⇄ V′ Na•

(1)

then we can analyze defect formation by reduction and resulting oxygen deficiency at low p(O2) or by oxidation and corresponding oxygen excess at high p(O2): Reduction/oxygen loss:

Na O ⇄ Na• O e′

(2)

Oxidation/oxygen uptake:

O ⇄ O V′ h•

(3)


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Analyzing eqs. (1) – (3) we find that oxygen deficiency is much more probable from the chemical point of view. Oxygen release of NaO2 will lead to the formation of electrons and positively charged sodium interstitials. The electrons will be formed in the oxygen 2p band. In any case, oxygen release will lead to the formation of n-type electronic defects irrespective of their localization. Considering the band structure in Fig. 2 and the rather narrow bands, it is highly probable that nonstoichiometric oxygen-deficient NaO2-x is a polaron n-type conductor with rather low room temperature conductivity. The excess electrons correspond chemically to doubly charged peroxide anions on superoxide sites. DFT calculations by Yang et al. agree that electron polarons are the dominant charge carriers but show also a surprisingly high contribution to the electronic conductivity arising from hole polarons . This is suggested to be due to a higher mobility that counterbalances the lower hole concentration.30 Another hybrid DFT study by Arcelus et al. focusses on the electronic structure of NaO2 in bulk, surface and small cluster configurations and confirms the insulating character. Considering our experiments, all samples of NaO2 which we studied experimentally were transparent with a very light yellow color, indicating a wide gap semiconductor with low concentration of coloring defects – in line with the results from DFT calculations. In addition, we never found any indication for the presence of peroxide species in the Raman spectra of our samples, thus we assume that the extrinsic electron concentration and the resulting electronic conductivity is very small. By and large, there is clear evidence that NaO2 is a poor semiconductor with negligible extrinsic defect concentrations.

2.2 Electrochemical atomic force microscopy (EC-AFM) In order to add experimental information on the electrical conductivity of the discharge product we carried out EC-AFM experiments on carbon fiber electrodes after discharge in a Na-O2 cell. Using this technique we obtained topographic information of both the carbon electrode and the formed NaO2 crystals as well as information on the local resistivity by applying an electric voltage between the ACS Paragon Plus Environment


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AFM cantilever tip and sample. Figure 4A and 4B show the topographical image of a NaO2 crystal surface at different magnifications, that was removed from a discharge cell and was studied without further treatment. The AFM image shows that the NaO2 surface is covered with small particles with a diameter of approx. 50 nm. Figure 4D (and Figure S1) shows the pristine carbon fiber electrode. As shown in Figure S2, the carbon fibers are covered with a nanoparticle film after discharge as well. Figures 4C and 4E show a NaO2 surface after rinsing the electrode with diglyme. The surface is free of particles, pronounced crystal facets become visible and a funnel-like geometry appears to form. When a DC potential bias was applied to a pristine carbon fiber electrode a resulting electric current of up to 400 nA was measured (Figure 4F), which is not surprising due to the high conductivity of the carbon. In contrast, when the same DC potential was applied to the NaO2 crystal surface, zero electrical current was observed within the resolution of the experimental setup (Figure 4G). We conclude that the NaO2 crystals are highly resistive, i. e. they are electrically insulating within the range of voltage normally applied during operation of the Na-O2 battery. We cannot exclude that only the NaO2 surface is electrically insulating, but as we never observed any current across different NaO2 particles, we exclude the possibility that only an insulating surface film blocks charge transport. Accepting that NaO2 is electrically insulating (an electrically blocking surface film would lead to the same result), we have to assume that O2− species and/or Na+-O2− ion associates can only be generated at the surface of the well conducting carbon fiber. Consequently, we also have to assume that – after nucleation – NaO2 grows by diffusion of superoxide ions through the electrolyte, from the carbon fiber to the NaO2 surface. As NaO2 forms relatively large crystallites, we conclude that sodium superoxide has a reasonably high solubility as also the superoxide anion has a sufficiently high diffusion coefficient.


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Figure 4 EC-AFM results. A) surface of a NaO2 cube within a carbon fiber electrode as taken from the battery (image size 5 µm x 10 µm). b) Same sample position at higher magnification (2 µm x 1 µm). C) and E) surface of an NaO2 cube after rinsing the electrode with diglyme. D) surface of a pristine carbon fiber (diameter approx. 10 µm). F) and G) show the corresponding current-voltage curves measured at a carbon fiber and a NaO2 cube surface as shown in D) and E), respectively.

The funnel morphology of the surfaces indicates that the crystal growth may have started from crystal edges towards the center of the crystal facets. 2.3 Two-working electrode setup Both the theoretical calculations as well as the EC-AFM analysis at this point do not support the idea of a sufficient electronic conductivity being responsible for the growth of large (micrometer sized) NaO2 crystallites during discharge of a Na-O2 battery. In the second part of the manuscript we therefore follow the hypothesis that NaO2 is an insulator and that its formation and decomposition during cell cycling is a solution based process relying on a soluble superoxide (O2−) species. As already mentioned in the introduction, in Li-S8 batteries both sulfur and Li2S are electronic insulators and the key to their electrochemical functionality is the solubility of sulfur and polysulfide compounds in the liqACS Paragon Plus Environment


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uid electrolyte. A first hint on the solubility of NaO2 in the electrolyte can be drawn from SEM analysis of the separator in a discharged battery (see Figure S3). The separator is covered to a large extent by NaO2 cubes and in addition by flake-like particles. In order to form on the surface of the insulating polymer separator NaO2 needs to be transported there by diffusion and precipitation. Interestingly these flake-like particles have also been reported in other Na-O2 studies15-16, 34 and it was claimed that the particles are sodium peroxide (Na2O2). By analyzing the separator with XRD we solely find NaO2 and no significant amounts of peroxide. This does not exclude the presence of amorphous Na2O2, but the formation of Na2O2 in other studies was also only supported by XRD, i.e. Na2O2 appears to form primarily as crystalline phase. In this section we summarize experimental results on the solubility of NaO2 in the battery electrolyte, obtained by employing a dual-working electrode setup. Electrochemical cells with two or more working electrodes are used since decades to analyze soluble redox species. Gerischer et al. introduced a dual working electrode flow cell in 1965,35 and Frumkin et al. introduced the rotating ring disk electrode (RRDE) in 1959.36 In our battery-like cell (Figure 5) two porous carbon electrodes (WE1 and WE2), isolated by a separator, operate versus a sodium counter electrode (CE). Only at one of these electrodes (WE1) sodium superoxide is formed via galvanostatic discharge (I1). At the same time the other electrode (WE2) is set to a constant potential of e.g. 2.4 V vs. Na/Na+ that is high enough to run the oxygen evolution reaction. If soluble reduced oxygen species (O

, HO ) are formed at WE1 they

can be oxidized at WE2, and a current is observed between WE2 and CE (I2). All potentials are given versus a sodium reference electrode placed between the counter and the working electrode 1.


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Figure 5 – Sketch of the dual-working electrode experiment in a Na/O2 cell. At WE1 oxygen reduction reaction (ORR) is carried out via galvanostatic discharge. WE2 is anodically polarized for oxygen evolution reaction. The reference electrode (RE) consists of sodium metal and is used to control the potentials of the two working electrodes. For clarity the connection was not drawn in the sketch.

Figure 6 shows the results of this experiment. For I1 = 0 (no ORR) at WE1 the oxidative current (I2) at WE2 exponentially drops to values below 200 nA at UWE2-RE = 2.4 V. This low current most probably corresponds to side reactions. As soon as WE1 is set to cathodic potentials (I1 = −20 µA), I2 increases by a factor of 30 reaching a value of more than 6 µA. This clearly shows that as soon as reduced oxygen species are produced at WE1 they are able to diffuse to WE2 were they can be oxidized again. A further increase of I1 leads to an increase of I2 as well, meaning that the product formation rate of O

is increased. However, the increases of I1 and I2 are not proportional and it appears that I2 reaches a plateau, i.e. a limiting current. We suppose that this corresponds to solubility and diffusion limited transport of O

within the electrolyte.



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Figure 6 – Results of a dual-working electrode experiment in a Na-O2 cell. The upper panel shows the potential of WE1 vs. CE (light grey line) as well as the discharge current I1 (blue line), which describes oxygen reduction at WE1. The lower panel shows the corresponding charge current I2 (red line) at WE2, which corresponds to the formation of oxygen.

From these data we can get a rough estimate for the concentration of dissolved NaO2 within the liquid electrolyte. We assume that WE1 is the source establishing an equilibrium concentration of c0 = c0( O

; exceeding this value leads to precipitation of NaO2. Then WE2 is considered as sink, where all arriving O

is oxidized to O2 (collecting efficiency equals 1, cWE2 = 0), and the current at WE2 is limited by diffusion through the electrolyte membrane (thickness Δx = 38 µm) driven by a concentration difference ∆c = c0 divided by the distance ∆x of both working electrodes (assuming stationary state and a concentration independent diffusion coefficient):

J=

c j = −D 0 zF ∆x

(1)

The diffusion coefficient for O

in the present diglyme electrolyte is, to the best of our knowledge, not reported in the literature. RRDE experiments on 0.8M TBATFSI in diglyme37 revealed a value of -6 2 −7 D(O

) = 1.4·10 cm /s, with which we estimate the concentration of O to c0 ≈ 10 mol/cm³ or

10−4 mol/L. Very recently Xia et al. have shown that protons may play an important role for the electrochemistry of a sodium superoxide battery.38 Protons acting as phase-transfer catalyst facilitate the


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formation and dissolution of NaO2 by forming HO2 (O2- + H+ HO2) as soluble compound. The dualworking electrode setup is not sensitive to the diffusion superoxide species and it is also possible that instead of O2- ,HO2 is transferred between both electrodes. However, in both cases the experiment clearly proves that a solution-mediated process is responsible for the formation and dissolution of NaO2. The same experiment (Figure 5) was carried out with an analogous Li-O2 cell and the results are presented in the supporting information (Figure S4). The results are qualitatively the same, however, the currents I2 are significantly (almost one order of magnitude) lower indicating that the concentration + of O

is significantly lower in the presence of Li cations. This may be the reason for the significantly

smaller Li2O2 deposits in comparison to the large NaO2 crystals formed during discharge. At this point it is worth mentioning that very recently Aetukuri et al. reported for the case of Li-O2 cells that water leads to an increased solubility of superoxide in the lithium electrolyte.6 The dual-working electrode experiment may be an excellent tool to studies these effects more quantitatively.

2.4 Model for the overpotential during galvanostatic charging As proven in the previous section, the solubility of reduced oxygen species plays an in important role for the functionality of sodium-oxygen cells forming NaO2. In the following we discuss the voltage profile of the cells during re-charge in depth. The profile shows some characteristic features – namely a voltage peak at the beginning followed by a flat plateau and a steep increase in potential at the end of the charge process. Figure 7 visualizes a simple kinetic model for the dissolution of a NaO2 cube during galvanostatic charging: the positive electrode overpotential is here described as result of a certain interface resistance Ri ([Ri] = Ω·cm2) for chemical and/or charge transfer processes at reactive interfaces Ai ([Ai] = cm²). The considered active interfaces are i) the NaO2/electrolyte interface (AO, RO), ii) the free carbon electrode/electrolyte interface (AE, RE) and iii) the NaO2/electrode interface



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(AEO, REO). For simplicity all resistances are considered as ohmic and constant, and hence for serial processes the electrode overpotential can be described by:

η = I ⋅∑ i

Ri Ai

(2)

Figure 7 - Sketch of a kinetic model describing the overpotential during galvanostatic recharge in terms of ohmic resistances Ri of reactive interfaces Ai.

In the following Q denotes the amount of transferred charge during NaO2 oxidation. Further we assume that the volume V0 = a03 of a NaO2 particle is about 203 µm3 and directly proportional to the discharge capacity Qdis, hence for Qdis = 2 mAh one would assume the presence of approx. 2.33·105 cubes on an electrode surface (Vm = 25 cm3/mol, z·F = 96485 C/mol). The values for Qdis and a0 are well in line with experimental findings.8 Further we assume that the volume of each cube V(Q) = a3 during re-charge changes according to the following expression:

V (Q) = V0 −

Vm ⋅Q FN

and the edge length a(Q) of each cube therefore results as

1/ 3

V   a(Q) = V0 − m ⋅ Q  FN  

As the cubes shrink during re-charge the areas AO and AEO of the NaO2 interfaces decrease and AE increases as function of Q, meaning that the overpotentials for reactions at the NaO2 interfaces increase with Q. ACS Paragon Plus Environment

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V   AO = 5 N V0 − m ⋅ Q  FN  

AEO

V   = N V0 − m ⋅ Q  FN  

2/3

2/3

For Qdis = 2 mAh the total covered electrode area is approx. AEO = 0.93 cm2. The free electrode/electrolyte interface AE on the other hand increases and therefore the overpotential for reactions at this interface decreases with increasing Q.

AE = A0,E

V   − N V0 − m ⋅ Q  FN  

2/3

The free interface for Q = 0 (after discharge) here is denoted by A0,E. In the following two hypothetical limiting cases for the cathodic overpotential of electrochemical decomposition of NaO2 on the basis of this simple kinetic model are distinguished. As a total cell current we assume I = 200 µA.8 1) If we assume that NaO2 is electrically conducting and the OER takes place only at the oxide surface (AO), the overpotential ηel is given by

 RO REO   +  AO AEO 

η el,1) = I ⋅ 

Here REO describes the charge transfer between NaO2 and the electrode at AEO, and RO represents the kinetics of the electrochemical reaction at the oxide/electrolyte interface AO: NaO2 ⟶ Na+ + O2 + e−. In this case, the overpotential increases monotonous as function of Q. Neither an initial potential peak nor a plateau region is expected according to this model (see Figure 8)). The course of the overvoltage resembles directly the shrinking area of the electroactive surface of NaO2.



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2) If we now assume that NaO2 is soluble in the electrolyte we have to consider two reactions. First reaction is the dissolution of NaO2 at AO with a kinetics described by RO for the reaction: NaO2 ⇋ (Na+)solv + (O2-)solv. Secondly the oxygen evolution reaction at the electrode/electrolyte interface AE has to be considered: (O2−)solv ⟶ O2 + e− (OER), with a kinetics described by RE

 RO RE   +  AO AE 

η el,1) = I ⋅ 

In this case the overpotential for the dissolution of NaO2 increases with Q, but the overpotential for the OER at the carbon electrode surface decreases with Q. In the same way one may describe the reactions involving a phase-transfer catalysis of protons as proposed by Xia et al.38. In this case RO represents the kinetics of the reaction: NaO2 + (H+)solv ⟶ (Na+)solv + (HO2)solv and for RE: (HO2)solv ⟶ O2 + (H+)solv + e-.

Figure 8 – Calculated overpotential profiles for the charge process of a Na/O2 battery according to the kinetic model for NaO2 dissolution introduced above. For mechanism 1, electronic conductivity of NaO2 is assumed as well as that the OER takes place exclusively at the NaO2/electrolyte interface (AEO, REO). For mechanism 2 it is assumed that NaO2 is soluble in + − the electrolyte (NaO2 → (Na )solv + (O2 )solv at AO) and that oxygen evolution takes place exclusively at AE. AE0 denotes the 2 2 remaining free electrode surface after full discharge. Further RO = 150 Ωcm and RE = 1500 Ωcm was assumed.

Figure 8 shows calculated overpotential profiles according to the two mechanisms for different values of Ri. For mechanism 2 the potential peak at the beginning of the charge process is very sensitive to A0E, the remaining free active electrode/electrolyte interface after discharge; the lower the value ACS Paragon Plus Environment

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the higher the potential peak. The overpotential in the plateau region is mainly determined by the reaction kinetics, RE and RO. And finally the steep potential increase at the end of the charge process is dominated by RO as the NaO2 cubes are vanishing: AO ⟶ 0 for Qdis - Q ⟶ 0. From this analysis we conclude that the presence of the initial potential peak corresponds to the activation of the electrode surface for the OER by removal of electrically insulating discharge product. This is well in line with experimental cycling studies. The peak is observed only during full discharge of the cells (until voltage break down) while it is not observed when cells are cycled with capacity limitation (“shallow cycling”).39 Post-mortem analysis of fully discharged cathodes, however, shows that NaO2 cubes do not cover the entire surface area. This is, at first glance contradictory to the model above. However, a closer look of the allegedly free electrode areas shows that these are covered to a large extent by a nanoparticle film (Figure SX A). The chemical identity of this film is unknown at this point, but EC-AFM analysis shows that these regions are in fact highly insulating in comparison to the pristine carbon electrode (See Figure SX B). This insulating nanoparticle film is probably the reason for cell death even when only a small fraction of the cathode is filled with large NaO2 cubes. Finally, one has to keep in mind that this simple kinetic model – amongst other phenomena – does not account for mass and/or charge transport within the volume phases, which in reality will also influence the overpotential of the positive electrode. For mechanism 1) the electric transport within NaO2, and hence the electric conductivity of the material is neglected. For mechanism 2) the transport of (O2−)solv from the NaO2 surface to the active electrode surface is not taken into account: Due to the low concentration of (O2−)solv it is not only necessary that free electrode sites for the OER are accessible but in addition that they are located in the vicinity of the NaO2 cubes; otherwise O2− diffusion will limit the OER rates and hence determine the overpotential. It is this solubility and diffusion limitation which causes parts of the kinetic problems of Li-O2 batteries. Using soluble redox mediators reduces these kinetic problems, as recently demonstrated.40-42



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3. Conclusion The results of our theoretical calculations and experiments give clear evidence that the growth of large NaO2 particles, in comparison to the smaller Li2O2 deposits in Li/O2 cells, is a result of the solubility of NaO2 in the liquid electrolyte. Hence charge transport is not restricted to the solid oxide phase, providing superior cycling performance of the battery. Ab initio calculations of the electronic structure of NaO2 were carried out, in which the possible rotational disorder of the O2− anions within the crystal lattice at room temperature is fully taken into account. A bandgap of about 2.0 eV is obtained, indicating that pure and stoichiometric NaO2 is insulating at room temperature. It is assumed that NaO2 might be oxygen-deficient, but that oxygen deficiency leads to electron polarons with low mobility and results not in significant electronic conductivity. By means of electrochemical AFM we were able to show that the surfaces of NaO2 crystals as well as the carbon fiber electrode are insulating after discharge of the battery. The solubility of sodium superoxide in diglyme was proven by employing a dual-working electrode setup in which oxygen reduction and evolution was run at the same time at different positions within the electrolyte – corresponding to a simplified RDE experiment in different electrode geometry. From a quantitative analysis of the results we estimate the solubility of NaO2 in diglyme based electrolyte at room temperature as about 10−4 mol/L. Finally we introduced a kinetic model for the overpotential during galvanostatic recharge of a Na-O2 battery (which can also be used for other Me-O2 batteries with a solid discharge product). The characteristic features of the voltage profile, namely a potential spike at the beginning of the charge process, followed by a flat potential plateau can be well explained by a solution mediated oxygen evolution process. While the model is simple, it clearly shows that a solution based electrode process is well able to explain the observed kinetics. The experimental results clearly indicate that the conductivity of the solid discharge products is of minor importance for practical cells, if the solution based route is operative. Once the solubility of the discharge product is too small, the use of redox mediators may improve the kinetics of the solution route. ACS Paragon Plus Environment

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4. Experimental and Numerical section Numerical Methods The presented electronic band structure calculations are all based on a projector augmented wave (PAW) approach43-44 to DFT as implemented in the VASP software package.45-48 To describe the exchange correlation interaction the choice of the density functional is critical. Here, we employ the HSE06 hybrid functional where,49-51 basically, a portion of 25 % of exact Hartree Fock exchange is mixed to the generalized gradient approximation (GGA) and long range contributions to the Coulomb potential are screened with a screening length of μ=0.2 Å-1. For the description of the electronic structure of many oxide based compounds, including Li2O2,52 and recently Na2O227, 30 as well as NaO2,27, 29-30 the hybrid functional has proved to be superior to traditional DFT functionals like the local density approximation (LDA) or the GGA and often gives results close to the highly demanding GW approximation.30, 53 In our study of the disordered NaO2 phase it exactly reproduces the experimental superoxide ion O2- bond length of 1.33 Å where GGA tends to give higher values.24-25 As discussed in Sec. 2 the hybrid functional calculations also yield an opening of a band gap in NaO2 whereas traditional DFT functionals like the LDA or GGA predict a metallic electronic structure.

Solovyev et al. recently studied the magnetic structure of NaO2 and found a weak isotropic antiferromagnetic (AFM) interaction that is based on the orbital disorder in the high temperature phase of NaO2.28 In our computations of the disordered structures we see that the AFM ordering has an essential influence on the band structure and band gap. Hence, we take all three AFM configurations of the superoxide molecules into account that are realizable within the unit cell. The band structure is then calculated for the AFM configuration that shows the lowest total energy.

For the numerical computations we use a Γ-centered k-point mesh with a sampling of 4 x 4 x 4 points to cover the Brillouin zone. The PAW cut-off energy is set to 800 eV for the band structure and total



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energy computations. With these parameters total energy differences between the NaO2 structures are converged within 2 meV/formula unit. For the construction of the disordered high temperature NaO2 unit cells we use the experimental lattice constant of a=5.49 Å and calculated O2- bond-length of 1.33 Å.24, 26 Materials and electrochemical cells All chemicals were purchased from Sigma-Aldrich: diethylene glycol dimethyl ether (diglyme, 99.5%), was dried over molecular sieve (0.3 nm) prior use. Sodium triflate (NaCF3SO3, NaOTf, 98%) was used as conducting salt and was pre-dried under vacuum at 175 °C for 24 hours. The used cell housing consists of a modified ½ inch Swagelok Union Tee. Sodium metal (provided by BASF SE) was used as anode, polymer separator (2340, provided by Celgard), and a binder-free gas diffusion layer (Freudenberg H2315, Quintech) as cathode. See Ref.39 for details on the cell construction. The average cathode area, thickness and mass were 0.78 cm², 210 µm and 7.4 mg, respectively. The electrolyte solution of 0.5 M NaOTf in diglyme was prepared in a glove box, and the amount of electrolyte in the cell was 26 µL. Cell assembling was done in argon filled glove boxes (GST4, Glovebox Systemtechnik) at water and oxygen contents below 3 ppm. A dual working electrode setup (see also schematic graph in Fig. 5) included the following stack of battery components (given values correspond to the diameter): Sodium electrode (10 mm), Whatman GF separator (12 mm), H2315 electrode (10 mm), Celgard 2340 (12 mm), H2315 electrode (10 mm). 75 µL of electrolyte was added to the system. Further details on the carbon electrodes can be taken from ref 39.

EC-AFM investigations For AFM investigation of carbon electrodes Na-O2 cells as described above were discharged at constant current (j = 200 µA/cm²) and a total capacity of 2 mAh – 3 mAh. After discharge the cells were


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disassembled in a glovebox and were transferred into the AFM glovebox. The AFM with a conducting tip (Bruker EC-AFM setup) was operated in an argon filled glovebox (MBraun) with water and oxygen content below 5 ppm.

Acknowledgement M. H. and C. H. acknowledge financial support within the LOEWE program of excellence of the Federal State of Hessen (project initiative STORE-E). P.H. and C.L.B. thank Fonds der Chemischen Industrie (FCI) for a Ph.D. scholarship. The project was supported by the BASF International Scientific Network for Electrochemistry and Batteries.

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