1. Introduction

A perfect storage device with ideal properties would keep the stored item forever, at least for long times, without any loss. With presumably very few exemptions at least ap­proaching this aim, such perfect devices do not exist. This frustrating conclusion applies also to de­vices for energy storage including electrochemical ones. Primary and secondary batter­ies, supercapacitors and redox flow batteries are all affected ^[1]. Rare exemp­tions are reserve batteries wherein the electrolyte solution is stored outside of the cell and re­dox flow battery when the circulated electrolyte solutions are completely drained from the battery. The concept applied in reserve battery, which have only a very narrow and spe­cific market; is not widely useful; the same applies to RFBs which completely drained can hardly be used for e.g. fast response to changing grid demand. Consequently this en­try will fo­cus on the common systems and their self-discharge ^[2].

Although self-discharge of batteries is addressed in passing in standard textbooks ^[3] even a major reference work con­tains just one entry on this fairly significant chal­lenge ^[4] (see below). Recent comprehensive reviews are not available. In supercapaci­tors two fundamentally different modes of charge storage in the electrodes may operate. They are substantially different for electrostatic charge storage in electrochemical double layer electrodes and ca­pacitors and for supercapacitors employing superficial redox proc­esses. In the latter case self-discharge resembles that found also in secondary batter­ies simply because the modes of charge storage in both systems are fundamentally the same. When instead of symmetric devices combining two electrodes of the same type elec­trodes of different types are combined in asymmetric supercapacitors matters may be­come even more complicated. A timely review of self-discharge of supercapacitors is available ^[5]. Given the overlaps between secondary bat­teries and supercapacitors ^[6] the various modes of self-discharge will be addressed together; the separation between the two fundamentally different modes will be taken into ac­count in a second step.

A fresh primary battery and a charged secondary battery are in thermodynamic terms in an energetically higher state than in the discharge or depleted state, i.e. the corre­sponding absolute value of Gibbs en­ergy (free en­thalpy ) is larger. Because dis­charge is a spontaneous process the values carry a negative sign, accordingly describing state­ments and equations must take this into account. This charged state is far away from ther­modynamic equilibrium. The device strives to attain an equilibrium state where the free enthalpy is equal to zero, and the driving force for dis­charge with release of electric en­ergy is exhausted. In addition to the intended way of moving into this state by con­trolled discharge further ways are conceivable and unfortu­nately operative in most cases, they are summarized as self-discharge. The latter is highly un­welcome, but given the thermo­dynamic facts self-discharge can only be decreased by slowing down kinetics of proc­esses causing self-discharge as much as possible. This applies primarily to chemi­cal reactions con­tributing to self-discharge; in addition parasitic currents with non-thermodynamic causes can contrib­ute to self-discharge.

Be­cause self-discharge can be described from an electrical engineering point of view as the flow of an unwanted current the operating chemical and electrical effects and descrip­tions can be summarized into the wish to minimize this unwanted cur­rent(s).Parasitic electric currents not related to chemical processes hardly depend on the type of bat­tery (primary or secondary) and battery chemistry (aqueous or non-aqueous electro­lyte solu­tion), they will be discussed jointly in a section below. Chemical processes caus­ing self-dis­charge strongly depend on battery chemistry, beyond the type of electro­lyte solution also very much on electrode materials. In following two sections exam­ples will be discussed assigned to the two types of electrolyte solutions (Frequently usage of the term electro­lyte ap­pears to include the term electrolyte solution. This saves a word but possibly causes confusion; in addition it oversimplifies the meaning of electro­lyte ^[1][7]). Redox flow batteries based on a very different mode of operation ^[1][8] are treated in a separate section. Some options to remedy self-dis­charge or to keep it as low as possi­ble are similar for both aqueous and non-aqueous electrolyte solutions, they are treated jointly in a final section. In the preceding sections only very specific options to re­duce self-discharge are discussed. First a general overview will be provided.

The particular importance of self-discharge in setups for energy harvesting with superca­pacitors and lithium-ion batteries as storage devices has been discussed else­where ^[9].

2. A General Overview

The energy that can be retrieved from a cell – even when carefully taking into ac­count limited efficiencies caused by overpotentials and other, in part kinetic, effects – will de­crease as a function of the duration of storage (shelf time) of the cell. For some sys­tems this loss will be hardly noticeable (shelf times of ten and more years are claimed for some sys­tems with losses in the range of a few percents per year only ^[1][16]) or will be almost com­plete al­ready after a few months or even less. These losses tend to be more pro­nounced at ele­vated temperatures. Because of the mostly complicated and sometimes only partially known reactions, predictions of temperature dependency of self-discharge are difficult. In­stead empirical data yielding Figure 1 have been collected.

Significant temperature effects, i.e. growing self-discharge with increasing tempera­ture, make it e.g. impossible to fully charge a nickel-cadmium battery at temperatures T > 60 °C because self-discharge becomes faster than the desired charging reactions.

Figure 1. Extrapolated annual capacity losses of selected primary and secondary systems.

Because these disappointing results are similar to the results of intended and proper use (i.e. discharge), this phenomenon is called self-discharge. Strictly speaking the term ap­plies only to complete cells; to self-discharge a single electrode does not make sense. Be­cause many studies of self-discharge focus on processes just at one electrode some­times the term is applied in an expanded meaning nevertheless, below such studies are in­cluded.

Self-discharge’s many causes differ fundamentally. Parasitic electric currents caused by elec­tronically conducting electric pathways between the battery poles inside or out­side of the cell may cause self-discharge (See section 3). Currents due to stand-by func­tions of the device energized by the battery also drain a current from the cell, but they are com­monly not discussed in the present context. But more frequent reasons of self-discharge are chemical reactions between active masses and constituents of the electro­lyte solution. In case of the primary lithium battery (lithium metal batteries LMB) the negative electrode (anode) is stable only be­cause it coats itself with a protective layer of electronically insulating material (solid electro­lyte interphase SEI, see below in section 5) suppressing further chemical reactions be­tween the lithium metal (which is thermodynami­cally unstable versus basically every elec­trolyte solution) and its nonmetal­lic environment. Formation of this SEI consumes some lithium – and the result is a loss of stored energy: self-discharge. During operation the SEI may be partially re­moved, it must be restored when the load is disconnected. Again a loss of lithium hap­pens; correspondingly some energy has become unavailable. The same applies to the graph­ite acting as a host for lithium in lithium-ion batteries. The reac­tions may also sim­ply be called corrosion, but this term would look somewhat out-of-place here. In case of the lead-acid battery it may look more appropriate. Lead be­ing less no­ble than hydrogen re­acts slowly with the battery acid releasing tiny amounts of hydrogen and lead ions. Again stored en­ergy is lost. During charging the dissolved lead ions may be rede­posited, but the released hydrogen cannot be recovered easily (see sec­tion 4 for options to miti­gate or circumvent this problem). A similar problem is encoun­tered with the nickel elec­trode. NiOOH can react with water (of the alkaline electro­lyte solution) yielding oxygen and resulting in lost stored energy.

All reactions associated with self-discharge are chemical or electrochemical reac­tions. Accordingly rate laws of chemical reaction kinetics apply – and this includes in particu­lar the effect of temperature as already illustrated in Figure 1.

Because most electrochemical storage and conversion systems are thermodynami­cally inherently unstable or contain compounds there­in which are un­stable with respect to others, self-discharge is an inherent feature of them, it can only be sup­pressed as well as possible. Proper cell design and careful selection of ma­terials with well- defined proper­ties and composition have helped frequently to reduce self-discharge. Self-discharge tends to be faster with older cells and after extensive cycling. This can at least in part be due to the formation of electrode reaction products acting as catalysts for un­wanted reactions causing self-discharge or degradation of added inhibitors (as present e.g. in the electrolyte solution of alkaline batteries). High-power cells show generally higher self-discharge than high-energy cells (provided a given cell chemistry is available in both forms as reported for lithium-SOCl₂-cells), the former cells show higher self-discharge because they contain electrodes with higher surface area and thus more loca­tions for heterogeneous self-discharge processes. A similar straightforward explana­tion of the obviously higher self-discharge of secondary batteries compared with primary ones is not available because most battery chemistries are either primary or secondary ones (the notable exception is the RAM-system which has already disappeared from the mar­ket and which according to the author’s experience shows wildly varying rates). Possi­bly the structural changes during deposition/dissolution in most electrodes of secon­dary batteries with associated at least temporarily large electrode surface areas may accel­erate self-discharge reactions.

Typical self-discharge data are collected in Table 1.

Table 1: Typical self-discharge rates at room temperature.

Given the omnipresence of self-discharge with devices for electrochemical energy stor­age it surprises slightly that review reports, in particular current ones, on this topic are hard to find. Certainly the term shows up frequently in abstracts and research re­ports. In most cases low self-discharge is claimed for a given device or even a material (al­though the term seems to be hardly applicable in the latter case). But frequently neither the exact way this claim was verified nor the reason for this improvement are provided. In textbooks self-discharge is addressed ^[1], but even in major monographs it is men­tioned only briefly ^{[10][11][12][13][14]} in mostly descriptive ways without too much atten­tion to details in particular of mechanisms and ways of slowing it down. Major reference works provide at least some access to further reading ^[3][15][16], collections of research re­ports and reviews again provide some hints ^[17][18]. Self-discharge of supercapacitors has been extensively reviewed elsewhere ^[5], because of the apparent merger of secon­dary batteries and supercapacitors at all levels from the mode of operation and the used materi­als up to device types ^[6][19] some overlaps with the present entry are likely.

Self-discharge can also be classified into reversible and irreversible one ^[18]. In the for­mer case lost energy is restored during a subsequent recharging of the battery, this ap­plies to self-discharge by parasitic currents or some cases of chemical self-discharge reac­tions. The second, less clearly defined class contains processes wherein material is ei­ther irreversibly lost or damaged (e.g. lithium lost in formation of SEI). This classifica­tion is not used here.

3. Self-Discharge by Parasitic Currents

A simple cause may be the flow of an electric current even when the device operated with the battery is switched off due to leakage by e.g. electronically slightly conducting traces of dirt on the battery surface or the battery holder between the battery poles as schemati­cally depicted in Figure 2.

Figure 2. Parasitic currents between battery poles by conducting coatings inside and outside a cell.

This flow of current may also proceed inside the cell because of incom­pletely insulat­ing separa­tors or parasitic electric contacts between active masses (see Figure 2). Be­cause the current “leaks” between the electrodes via unintended Ohmic conduction path­ways (thus its name leakage current) it can be represented as an external shunt resis­tor in parallel to the cell, this helps in modeling. Obviously this type of self-dis­charge can be suppressed by careful design and operation of the cell and its environment. A standby function may also draw a small current without explicit knowledge of the user; this may be considered in a broader sense also as self-discharge but is obviously beyond the scope of this research.

4. Self-Discharge in Aqueous Batteries

In a battery energy is stored by using electric energy to drive a chemical transforma­tion, the obtained materials are “richer in energy” (the absolute value of the Gibbs energyis larger) than the starting materials. As an exam­ple, the charging reaction at the negative electrode of a lead-acid battery shall be consid­ered:

PbSO₄ + 2 e^- + 2 H⁺ → Pb + H₂SO₄ (1)

Upon discharge the process is reversed:

Pb + H₂SO₄ → PbSO₄ + 2 e^- + 2 H⁺ (2)

As an alternative the following reaction is conceivable

Pb + H₂SO₄ → PbSO₄ + H₂ (3)

The reaction at the positive electrode can be

PbO₂ + H₂SO₄ → PbSO₄ + H₂O + ½O₂ (4)

Although lead is less noble than hydrogen this reaction (3) is slow because lead is a poor electrocatalyst for hydrogen evolution, a similar argument applies to the positive elec­trode (reaction (4)), which thermodynamically is also not stable versus the electrolyte solu­tion ^[20]. Di­oxygen present in the electrolyte solution of open cells can react at the nega­tive elec­trode according to

Pb + ½ O₂ + H₂SO₄ → PbSO₄ + H₂O (5)

In chemical terms this can be called corrosion, in a battery this is a loss of energy and only welcome as a measure limiting hydrogen evolution during overcharge in valve-regulate lead-acid batteries (VRLA). Otherwise it is self-discharge. The rates of the men­tioned reactions depend on temperature and acid concentration; with higher tempera­ture and acid concentration the rates increase. The rate also depends on the state-of-charge SoC. A fully charged VRLA cell may self-discharge from 100 % to 90 % SoC within one to two weeks, whereas at the same temperature self-discharge from 20 % to 10 % may last ten or more weeks ^[16]. Self-discharge is lower in sealed cells with a small amount of phosphoric acid added into the sulfuric acid electrolyte solution (the cells are of the “starved type”, there is no free solution) ^[21]. The slower self-discharge is attrib­uted to the presence of phosphoric acid, the expander in the negative electrode does not af­fect self-discharge. The antimony-free grids show corrosion, i.e. self-discharge, only at cell voltages > 2 V.

Electrochemically active impurities in the electrodes and/or the electrolyte solution like Fe²⁺/Fe³⁺-ions may establish a redox shuttle mechanism as depicted in Figure 3.

Figure 3. Scheme of an iron ion redox shuttle mechanism

The following reactions result in self-discharge:

At the positive electrode

PbO₂ + 3 H⁺ ++ 2 Fe²⁺ → PbSO₄ + 2 H₂O + 2 Fe³⁺ (6)

and at the negative electrode

Pb ++ 2 Fe³⁺ → PbSO₄+ H⁺+ 2 Fe²⁺ (7)

yielding the cell reaction

PbO₂ + Pb+ 2 H₂SO₄ → 2 PbSO₄ + 2 H₂O (8)

The cell reaction is the already stated process during regular discharge. Both para­sitic electrode reactions proceed as long as the respective electrode potentials enable them. The impurity ions themselves are not consumed; the undesired process may go on. Once discharge goes on the electrode potentials move closer to each other, consequently the electrode potential may not be favorable that much for the parasitic reactions any more. Additives to electrodes and/or electrolyte solutions (like the expanders in lead-acid bat­teries) may decompose during operation, leaving products which either act as cata­lysts for reactions like hydrogen evolution contributing to self-discharge or may establish shut­tle mechanisms. Antimony alloyed into the grid for the positive electrode in a lead-acid battery may corrode and get into the battery electrolyte solution finally depos­ited onto the negative electrode. There it catalyses hydrogen evolution thus decreasing charg­ing efficiency and increasing self-discharge. Instead of antimony calcium has been sug­gested resulting in lower gas evolution and self-discharge ^[14][16]. Substitution comes with new problems because of the loss of other beneficial effects of alloyed antimony ^[16].

The state of charge and consequently self-discharge of a nickel oxide electrode can be moni­tored with electrochemical impedance measurements. According to results expo­sure of the electrolyte solution with the immersed electrode to hydrogen results in faster self-discharge ^[22]. Based on the results the following overall reaction has been pro­posed ^[23]:

NiOOH + 1/2 H₂ → Ni(OH)₂ (9)

NiOOH used as the positive electrode in several aqueous secon­dary batteries is a good mixed-ion conductor readily establishing equilibrium with its aque­ous environment ^[10]. The reaction with water results in incorporation of hydrogen into the electrode and oxy­gen evolution with a decrease of the electrode potential: self-discharge happens:

2 NiOOH + H₂O → 2 Ni(OH)₂ + ½ O₂ (10)

The highly oxidizing capabilities of positive electrode materials like PbO₂ or nickel ox­ide may also result in chemical oxidation of cell components like the separator yielding de­compo­sition products and loss of stored energy (self-discharge). Separators made of polyam­ide (Nylon^®) may also undergo chemical reactions with oxygen and hydrogen in the cell resulting in decomposition and/or degradation ^[16]. Use of more stable other poly­mers, e.g. a composite of polypropylene and polyethylene with some surface treat­ment, help in reducing this form of self-discharge ^[16].

Lower self-discharge of NiMH-batteries has been observed with cobalt-free negative elec­trode materials replacing the conventional AB₅-type alloys ^[23]. Such alloys contain­ing vanadium may support self-discharge because of the solubility of vanadium enabling es­tablishment of a redox shuttle process (see Figure 3) and associated self-discharge ^[16], fur­ther details of reduced self-discharge have been reviewed ^[16].

The iron electrode suggested for various secondary cells (e.g. the Fe-Ni-cell) shows signifi­cant corrosion resulting in self-discharge of the assembled cell because of its elec­trode potential lower than that of the hydrogen electrode ^[24]. In addition to fast self-discharge Coulombic efficiency during charging is low because of the competing hydro­gen evolution ^{[25][26][27][28]}. Because of the basically attractive features of the iron elec­trode attempts to mitigate self-discharge have been reported. Addition of FeS and PbS has resulted in increased storage capacity and inhibition of self-discharge, 1 wt.% of PbS was most effective ^[29]. Formation of metal sulfites which in turn inhibit hydrogen forma­tion and the presence of lead were identified as the causes.

Zinc employed as a negative electrode in several primary batteries with aqueous electro­lyte solutions shows corrosion caused by its electrode potential negative to that of the hydrogen electrode. This basically causes hydrogen evolution, i.e. self-discharge. Figure 4 shows schematically the various options for slowing down corrosion, i.e. self-discharge.

Figure 4. Scheme of reactions during corrosion, i.e. self-discharge, of a zinc electrode in an aqueous elec­trolyte solution with options to decrease it. 1: Slowing down zinc oxidation (the anodic partial reac­tion) and dissolution, 2: Slowing down hydrogen evolution (the cathodic partial reaction).

In pri­mary cells this has been a major challenge with all types of zinc battery chemis­tries as dis­cussed above. Some positive electrode materials like HgO used earlier in some primary batteries with negative zinc electrodes show some solubility in the alka­line electrolyte solution resulting in deposition of mercury at the negative electrode and associated self-discharge ^[30]. This deposit slows down hydrogen evolution (see Figure 4: Option 2, for obvious reasons this process is sometimes called gassing) and thus self-discharge by zinc corrosion. Until the ban of the use of mercury in batteries this was a common additive, now this is history. Instead various other corrosion inhibitors are added to the electrolyte solution, the use of high-purity zinc as well as small amounts of al­loyed elements are further options.

A secondary zinc-air battery with a negative zinc electrode faces the common prob­lems encountered with this metal in aqueous electrolyte solutions in primary batter­ies. In a zinc-air cell remedies suitable for this type of cell are required. Coating the nega­tive zinc electrode with polyaniline for use in a cell with a gelled aqueous KOH-electrolyte solu­tion has been examined successfully ^[31]. Prevention of the direct con­tact between the zinc electrode and the aqueous electrolyte solution afforded by the layer of PANI has been identified as major task of this coating ^[32]. A quaternary ammo­nium-functionalized polyvinyl alcohol membrane as almost neutral electrolyte was em­ployed in a solid state zinc air battery with much reduced self-discharge ^[33]. Dendritic deposi­tion of zinc causes several detrimental effects ^[34]. Dendrites may in the extreme case penetrate the separator, contact the positive electrode and cause a short-circuit. Less dra­matic is the associated increase of surface area by this shape change with enhanced self-discharge

A further application option for the zinc electrode in a self-stratified battery with a nega­tive zinc electrode at the bottom in an aqueous electrolyte solu­tion and an organic electro­lyte solution with an organic redox system insolu­ble in the aqueous solution and a po­rous carbon electrode as current collector on top has been proposed ^[35]. For improved elec­trode kinetics and thus higher current capability the latter electrode is rotating. Self-discharge is basically eliminated because the redox system at the positive electrode is solu­ble only in the top organic electroyte solution. The cell concept goes back to the crow­foot cell popular in the 19^th century with American and British telegraph companies.

The use of aluminum as a basically attractive negative electrode material with aque­ous electrolyte solutions has been hampered by its instability in such solutions caused by its negative electrode potential driving hydrogen evolution by corrosion. For diminished self-discharge additives to elec­trolyte solutions, alloying with several further elements ^[16][36] and replacement of the aqueous solution have been suggested.

Modeling of self-discharge has been applied for a better understanding of ongoing proc­esses and for prediction of cell behavior of e.g. nickel/hydrogen cells ^[37].

5. Self-Discharge in Non-Aqueous Batteries

When the reduction potential of the negative electrode material and/or the oxidation po­tential of the positive electrode material (the respective terms anode and cathode may work in case of a primary battery, they become confusing when inspecting a secondary bat­tery and should thus be avoided as suggest by Huggins years ago ^[10][11]) are outside of the window of electrochemical stability of the electrolyte or the electrolyte solution (for a criti­cal examination of this concept see ^[38]) decomposition either of the solvent and/or the electrolyte (salt) may proceed at the positive and/or negative electrode. The effect will be self-discharge. In a few cases materials can be used with aqueous electrolyte solutions nev­ertheless, provided the respective reactions are very slow (see above, lead acid bat­tery nega­tive electrode, zinc battery negative electrode). In most cases this solution, which is actu­ally not a solution but just tinkering, is not applicable. Primary and secon­dary batter­ies with alkali metal negative electrodes, which can decompose the electrolyte (solu­tion) reductively, are the most popular examples. Various metal oxides, which af­ford this decomposition oxidatively, are the popular corresponding positive electrode exam­ples.

Nonaque­ous electrolyte solutions employing suitable organic or inorganic solvents, ionic liquids, gelled electrolyte or solid electrolytes are the frequently applied escape. Even many of these ionically conducting systems are thermodynamically not stable with re­spect to the negative electrode as well as to many highly oxidizing positive elec­trode materi­als. Because of the high reactivity of these electrode materials and the correspond­ingly large driving forces of both the wanted discharge reactions as well as the unwel­come self-discharge reactions slowing down kinetics is no solution. Instead protective lay­ers are formed, which separate the active material from the electrolyte (solution). The solid electrolyte interphase layer (SEI) formed on the surface of a lithium electrode is a classi­cal example. It is the result of reductive decomposition of various components of the electrolyte solution, the actual composition and its properties have been the subject of in­tense research as reviewed elsewhere ^[39][40][41], for some typical insights see ^[42]. Some positive electrode materials are also capable of decomposing electrolyte solution constitu­ents resulting in the formation of a layer (CEI, cathode electrolyte interphase), this phenomenon has been studied less frequently, reviews are available ^[43][44]. In a typi­cal study a CEI on copper nitroprusside (Cu[Fe(CN)₅NO] several electrolyte solution de­composition products were identified ^[45]. CEI’s will have growing importance with high-voltage cells using positive electrode materials with ever higher oxidation capabil­ity.

Formation of these layers, which may also be formed with other ionically conduct­ing phases between the electrodes as mentioned above, consumes active material, it is thus self-discharge. Fortunately it will happen only once when the active masses are brought into contact with the electrolyte solution for the first time. Subsequently these lay­ers act as ion conductors, and ideally they shall remain on the active mass unchanged dur­ing re­peated charge/discharge cycles or, in case of a primary battery, during intermit­tent dis­charge. When left undisturbed growth of the layer will slow down with stor­age time, self-discharge will decrease [16]. Some of these layers have a rather high Oh­mic resis­tance (e.g. those on lithium metal in contact with electrolyte solutions based on SO₂Cl₂ or SOCl₂ or SO₂ dissolved in acetonitrile) causing a voltage collapse when dis­charge is turned on, the “voltage delay”. In particular when high discharge currents are drawn the SEI will crack and will be damaged more or less; in the previously addressed case the cell volt­age will be restored. Thus it will be rebuilt when the load is discon­nected, requiring fur­ther material from the cell inventory – more self-discharge. Self-discharge of different car­bon materials has been compared at various temperatures ^[46], higher self-discharge was found – as expected with respect to the discussion above – to be faster at elevated tem­peratures and with materials having a larger surface area. The rate of SEI formation – part of the self-discharge – was independent on carbon material at lower temperatures but differed significantly with material at elevated temperatures. Self-discharge of cells with SO₂Cl₂ is higher than with SOCl₂ ^[16].

In case of secondary batteries numerous cell designs and cell chemistries use host materi­als in the electrodes for metal (ion) insertion/deinsertion which may show volume and shape change during charge. This will negatively affect the deposited SEI/CEI-layers by e.g. cracking or shedding, and again initiate more layer formation with associated mate­rial consumption – self-discharge.

Intrinsically conducting polymers like polyacetylene as active electrode masses may cause decomposition and thus self-discharge of organic solvent-based electrolyte solu­tions ^[47]. In the latter case prod­ucts of solvent decomposition further mediate and acceler­ate self-discharge of the p-doped (charged) polyacetylene. Further options like reac­tion of the p-doped polymer with impurities or intrinsic instabilities of the polymer have been considered ^[48]. Quite differ­ently polypyrrole was not found to “self-discharge” in its oxidized state when brought into contact with an electrolyte solu­tion ^[48]. Obviously its oxidizing capability was insufficient for any reaction with the electro­lyte solution. Only in a complete cell, i.e. with the negative lithium electrode pre­sent, self-discharge was observed. It was conse­quently attributed to some mobile and re­dox-active species generated by reaction of lith­ium with the electrolyte solution. Else­where a composite of polypyrrole and polyethyl­ene oxide showed better performance than polyrrole alone, in terms of storage capability, but much poorer charge retention, i.e. higher self-discharge, for unknown reasons ^[49]. By comparison lowest self-discharge was observed with polyaniline studied as a positive elec­trode, this was tentatively re­lated to lower sensitivity of the polymer towards oxidation ^[50].

Some electrode materials or reaction intermediates present only temporarily during elec­trode reactions show significant solubility and may thus diffuse to the other electrode and react directly with the active mass. This self-discharge is frequently encountered with secondary batteries employing sulfur as the positive electrode mass ^[51]. The mecha­nism is commonly name redox-shuttle mechanism, it causes self-discharge only dur­ing charging of the battery whereas further parasitic reactions of soluble polysulfides may affect the cell negatively at all times ^[52][53]. A simplified reaction scheme is shown in Figure 5.

Figure 5. Scheme of a redox shuttle mechanism

Because sulfur itself shows only low solubility in most employed solvents instead of sufur polysulfide anions with different states of oxidation may diffuse. This shuttle is still a major hurdle in development of lithium-ion batteries which otherwise show very promis­ing performance data. This mechanism will of course also show up with other nega­tive electrode metals like calcium ^[54]. There are numerous studies aiming at reduc­ing this process, for reviews see ^[53][55][56]. Basically this mode of self-discharge can be dimin­ished by keeping the soluble intermediates in the possible electrode or reduce the solubil­ity of the intermediates in the used electrolyte solution. Adding redox mediators for improved performance of lithium-oxygen batteries causes the same redox-shuttle proc­esses and associated self-discharge ^[57], a Nafion^®-based membrane separator with high lithium-ion selectivity is the obvious remedy. Broader perspectives of the associated prob­lems for lithium-oxygen batteries including self-discharge have been reviewed ^[58].

Mixed conduction membranes have been suggested as another option to suppress the polysulfide shuttle ^[59]. Among further possible remedies is physical confinement (trap­ping) of the elements as well as possibly mobile interme­diates, for examples see ^[74]. In a similar approach multilayer encapsulation of sul­fur has been proposed ^[60], this can be traced back to earlier and initial work aimed at bet­ter sulphur utilization and reduc­tion of self-discharge ^[61]. Adsorption (trapping) of polysul­fides, possibly combined with accel­erated conversion of these species into less solu­ble ones has been studied ^[62]. Cata­lytic options to meet the polysulfide shuttle chal­lenge have been reviewed ^[63][64]. Use of an interlayer adsorbing polysulfides and accelerat­ing their transformation into less detri­mental species has been suggested ^[65]. Fur­ther similar approaches have been pro­posed elsewhere ^[66][67]; options to control polysul­fide diffusion and thus reduce self-discharge have been compared ^[68]. The influ­ence of functional binders on self-discharge of Li/S-batteries has been addressed ^[69]. Re­views of the polysul­fide-related challenges in lithium-ion/sulphur batteries are available ^[70][71], self-discharge has been stressed as a still significant bottleneck when comparing lith­ium-ion/sulphur batteries with other lithium-ion systems ^[72].

Basically the same problems of increased self-discharge are found when substituting sele­nium for sulfur or using SeS₂ ^[73].

Measurement of self-discharge as a tool to monitor ageing of lithium-ion batteries has been proposed ^[74]. Among the various options to keep detrimental effects of over­charge of lithium-ion batteries small the addition of redox shuttles has been proposed ^[75], quite obviously these additives may contribute to self-discharge according to the mecha­nism sketched above, in particular when their action becomes effective already at cell voltages and thus electrode potentials within the range of ordinary cell operation.

A similar shuttle mechanism is found with the antipolar mass in nickel-cadmium elec­trodes ^[9]. In case of deep discharge evolution of hydrogen, which might pass to the other electrode oxygen evolving at the positive electrode is reduced at the cadmium of the antipolar mass. Self-discharge is not caused.

Utilization of the redox coupleas the negative half-cell of a battery has been hampered by its chemically aggressive behavior, in particular the lack of a suit­able cur­rent collector ^[76]. Addition of LiCl resulted in the formation of some coordina­tion spe­cies inhibiting intercalation of the tetrachloroaluminate in the negative current collec­tor; in addition this enables the use of established positive electrode materials from lith­ium-ion batteries resulting in a cell with minimal self-discharge.

In high temperature liquid metal batteries with molten salts as electrolyte between the two molten metal­lic electrodes ^[1][77] self-discharge is frequently caused by dissolu­tion of an elec­trode metal in the molten electrolyte ^[78][79]. Changing the composition of the molten electro­lyte or the used metals or metal alloys has been reported as option ^[79][80], using a solid ion conducting electrolyte instead of the molten electrolyte is a further possi­bility which unfortunately may cause new challenges regarding lower ionic conduc­tion, wet­ting, costs and mechanical stability.

A general feature of high-temperature batteries is the need to maintain their operat­ing temperature by heating when the battery stands idle and no Joule heating generated by the flow of current in the operating cell serves this purpose ^[1][80]. The heat needed for this up­keep may be taken from the cell, this amounts to thermal self-discharge.

6. Self-Discharge in Redox Flow Batteries

In a redox flow battery RFB two half cells containing dissolved redox systems with differ­ent redox potentials combining into the cell voltage are connected via a suitable separa­tor ^[1]. Both solutions must be kept separate to avoid chemical reactions between the active ingredients resulting in discharge of the cell. In most device designs this separa­tion is established by inserting a semipermeable ion-conduc­ting membrane ^[8]. Fur­ther options like porous separators for systems with larger redox ions are under considera­tion.

Self-discharge in RFBs can be caused by ion-crossover through the separa­tor/membrane, i.e. unwanted mixing of re­dox components resulting in direct chemical reac­tions and undesired heating of the cell. Fur­ther processes causing self-discharge are chemi­cal reactions between redox constitu­ents and cell components, i.e. oxidation of elec­trode materials by highly oxidizing com­pounds in the positive electrode half-cell. Be­cause the electrolyte solutions in the half-cells will be circulated by external pumps (in case of hybrid systems where a solid electrode is combined with a redox-half-cell there may be one pump only) running the pumps even when the RFB is in idle condition, will cause energy consumption, energy is drained from the amount stored in the device. This will also result finally in “self-discharge”. Further auxiliary devices needed to monitor and control proper opera­tion of the RFB will also cause energy consumption. Similar to de­vices monitoring the state of a battery module or a battery pack, this will also result in con­sumption of electri­cal energy most likely drained in all cases from the energy initially stored in the device.

Self-discharge caused by ion crossover is closely related to imperfections of the used sepa­rator, whether it is a semipermeable membrane or a highly porous material. In case of e.g. an all-vanadium RFB the membrane should completely prohibit transport of vana­dium species and water but permit transport of other charge carrying species in­volved in charge balancing like H⁺, , and . A perfect membrane does not ex­ist; consequently researchers have tried to identify most suitable membranes and have tried to improve their properties (perm selectivity, Ohmic resistance, chemical and mechani­cal stability). Because the currently most frequently used membranes based on per­fluorosulfonated or –carboxylated PTFE tend to be expensive, price considerations, i.e. get­ting cheaper membranes, add a further dimension to the engineering and chemical chal­lenges ^[68]. Improved perm selectivity of a Nafion^®-based membrane (and thus lower self-discharge) can be afforded by incorporating inorganic nanoparticles ^[81][82][83] and by further modifications of the membrane ^[8][84]; this includes application of addi­tional bar­rier layers ^[85] and double layer membranes ^[86]. Use of an anion exchange mem­brane containing silica nanoparticles has been suggested as a further option reduc­ing self-discharge by ion crossover and also reducing costs ^[87].

Modeling of self-discharge of an all-vanadium RFB assuming a diffusion rate of vana­dium ions depending on diffusion coef­ficient, partition coefficient and concentration gra­dient was found to provide a good de­scription of the experimentally observed changes ^[88]. A further modeling approach tak­ing into account further experimental data as well as other processes contributing to self-discharge has been developed aiming at its inclu­sion in the cell control software with par­ticular regard to the need of cell rebalancing ^[89]. In a theoretical study of self-discharge-related reactions in an all-vanadium RFB polymeri­zation reactions of vana­dium ions and participation of multivalent ions have been highlighted ^[90].

A further option to reduce ion crossover is the use of redox-active electrolyte compo­nents large enough in the solvated state to slow down or even inhibit their un­wanted passage through the membrane. Numerous materials have been proposed, poly­oxometalates ^[91] are among them. Self-discharge by ion crossover has also been ob­served when using a ce­rium-based half-cell ^[92].

Oxidation of cations in the negative half-cell of e.g. an all-vanadium RFB by dioxy­gen from ambient air in an essentially open system may also result in self-discharge ^[93]. The suggested remedies are obvious: Smaller surface area of the electrolyte solution reser­voir exposed to air is obvious, higher electrolyte concentrations apparently also slow down oxidation of V(II) by dioxygen.

In practical setups frequently several RFBs are connected in series. Distribution of the electrolyte solution with manifolds etc. results in shunt currents, this in turn causes self-discharge. It has been modeled ^[94]. Growing self-discharge with increasing number of connected cells does not come as a surprise, because the larger overall voltage drop pro­vides a higher driving force. An extensive study of a practical 200 kW/400 kWh all-vanadium RFB has been reported ^[95]. Up to 24 % of the delivered energy was con­sumed by peripherals necessary to operate the RFB, separate numbers directly indicative of self-discharge were not provided. When the RFB was kept in an operational state needed for fast response (spinning reserve, primary operating reserve) up to 80 % of the charge were lost in 48 h.

In addition to the prototypical RFB with two circulated liquid electrolyte solutions with a membrane or another separating item other electrode combinations have been pro­posed, for an overview see [1,8]. Among them is the combination of a solid metal nega­tive electrode with a second half cell with a circulated dissolved electrolyte, another one is the use of two solid electrodes with an electrolyte solution as suggested in ^[96] with a negative cadmium and a positive lead dioxide electrode. The cell reaction is

PbSO₄ + 2 H₂O + Cd²⁺ Æ⇄ Cd + PbO₂ + 4 H⁺ + (11)

with an aqueous electrolyte solution of 1 M CdSO₄ and 2 M H₂SO₄. Self-discharge is caused by reduction of water by the cadmium electrode thermodynamically unstable in this electrolyte solution with associated hydrogen evolution. The rather high overpoten­tial of the hydrogen evolution reaction at the cadmium electrode already limits self-discharge, electrolyte solution additives (DPE-3) have been suggested for further inhibi­tion ^[97]. A similar design with a negative zinc electrode faced even more serious self-discharge by hydrogen evolution at the negative electrode ^[97].

Half-way between the two cell principles addressed above are RFBs with a solid elec­trode combined with another half-cell containing a redox system. The zinc/bromine or zinc/iodine systems are typical examples. Self-discharge in these cells proceeds by forma­tion of local elements on the negative zinc electrode involving dissolved impurities and chemical reactions between the halogen and zinc possible when the separator does not work perfectly ^[98].

7. Remedies: Ways to Limit Self-Discharge

Numerous approaches to limit or slow-down self-discharge have already been ad­dressed above when presenting examples. Because electrode reactions are by definition hetero­geneous processes at the electrode/electrolyte interface researchers have tried to make this interface as large as possible. Because most self-discharge reactions are also heteroge­neous processes any increase of surface area will help both the wanted and the un­wanted electrode reactions. When having achieved an optimized electrode morphol­ogy in terms of surface area and porosity this should not change too much during charge/discharge (e.g. by disintegration of active mass particles caused by volume expan­sion or pulverization initiated otherwise) because this will also enhance self-discharge; in addi­tion it might consume active material during formation of surface lay­ers.

Additives in the electrolyte solution have been applied with both aqueous and non-aqueous electrolyte solutions. Their task varies from inhibition of parasitic electrode reac­tions (“corrosion”) to binding unwanted and detrimental impurities introduced via the electrodes and/or the electrolyte solution to catalyzing processes participating in the re­moval of unwanted species. The case of lithium batteries has been reviewed in ^[99].

Taking a broader perspective of self-discharge including energy consumed by periph­eral devices (keeping in mind that there appears to be no well-defined boundary be­tween essential components of a battery and a peripheral device) the obvious contribu­tion to reduced self-discharge from these components can be obtained by select­ing energy-efficient pumps in an RFB, and using electronic circuitry for control and monitor­ing with lowest possible energy consumption, and switching off devices when­ever possi­ble. Avoiding overcharge of a battery seems to be an option both simple and effec­tive to main­tain battery health and reduce self-discharge.

8. Conclusions and Prospects

Because of the fundamentally thermodynamic driving force attempts at mitigating self-discharge will fo­cus on slowing down kinetics of the involved chemical reactions as well as transport proc­esses. Unwanted side-reactions like corrosion of active masses may be suppressed by higher purity of components, excessive electrode potentials causing decom­position of electro­lyte solution and active masses may be suppressed by better elec­trode potential and cell voltage control. Overall a better understanding of the mecha­nism(s) of self-discharge will result in improvements.