## 3.1. Polarization measurements and formation and characterization of the electrodes

Figures 1a) and b), show polarization curves of pure metals in 3.5 wt.% NaCl, starting from the cathodic potentials of − 0.8 V for silver and − 1.3 V for lead. During the forward scan of the silver electrode, Fig. 1a, hydrogen evolution could proceed, thermodynamic potentials is *E*r(H2O|H2) = − 0.655 V vs. SCE, but taking into account high overpotentials, the cathodic curve is probably controlled with mixed activation-diffusion oxygen reduction reaction. Corrosion potentials are established at − 0.164 V vs. SCE, followed by pseudo-passive like behavior. At ~ 2 mV, sharp increases in the current density can be connected with the formation of AgCl onto the silver surface, characterized by a small peak (A) at the current density of ~ 10 mA cm−2. After point (A) pseudo-passive behavior connected with the growth of AgCl is observed in the forward and backward scans. Below ~ 2 mV solid-state reaction of AgCl reduction to metallic silver occurred, through two peaks, (B) and (C). As pointed out by Pargar et al. [43], those two peaks could be connected with the reduction of the bi-layer structure. The first peak (B), could be connected with an outer layer, while peak (C) with the inner layer. Similar behavior is obtained for the polarization curve of the lead electrode, Fig. 1b). The corrosion potential of − 0.617 V vs. SCE is determined, while PbCl2|Pb corresponding potentials is at − 0.485 V vs. SCE. The reversible electrode potentials for AgCl|Ag and PbCl2|Pb electrodes are given as:

$${E_{\text{r}}}({\text{AgCl|Ag}})=E_{{\text{r}}}^{{\text{\varvec{\theta}}}}({\text{A}}{{\text{g}}^{\text{+}}}{\text{|Ag}})+\frac{{2.3RT}}{F}\log {L_{{\text{sp}}}} - \frac{{2.3RT}}{F}\log a({\text{C}}{{\text{l}}^ - })$$

1

$${E_{\text{r}}}({\text{PbC}}{{\text{l}}_2}{\text{|Pb}})=E_{{\text{r}}}^{{\text{\varvec{\theta}}}}({\text{P}}{{\text{b}}^{{\text{2+}}}}{\text{|Pb}})+\frac{{2.3RT}}{{2F}}\log {L_{{\text{sp}}}} - \frac{{2.3RT}}{F}\log a({\text{C}}{{\text{l}}^ - })$$

2

where *E*rθ(Ag+|Ag) = 0.799 V vs. SHE and *E*rθ(Pb2+|Pb)= − 0.268 V vs. SHE are the standard electrode potential, *L*sp is a solubility product of AgCl and PbCl2 (*L*sp(AgCl) = 1.6⋅10− 10 M2 and *L*sp(PbCl2) = 1.7⋅10− 5 M3). The activity of chloride ions *a*(Cl–) = *c*(Cl–)*γ*(Cl–) = 0.39, where the activity coefficient, *γ*(Cl–) = 0.65, for the concentration of chloride ions of *c*(Cl–) = 0.6 M is estimated using the empirical Davies equation suitable for seawater [27]. Hereafter, the reversible potential of the silver-silver chloride electrode for the given conditions, Eq. (1) is ~ 0.247 V vs. SHE or ~ 2 mV vs. SCE and for the lead-lead chloride electrode, Eq. (2), is − 0.243 V vs. SHE or − 0.484 V vs. SCE that is identical to the observed values, Figs. 1a, and b.

To form the AgCl layer at the silver electrode, twenty successive charge-discharge cycles with a current density of 10 mA cm− 2, from − 0.6 V to 0.6 V are performed, Fig. 2a), and the corresponding capacity is followed, shown in the inset. As can be seen, the capacity is stabilized after ~ 15 cycles to 0.8 mAh cm− 2. For the Pb electrode, performing a similar procedure, but in the potential range from − 0.8 V to − 0.2 V even after one hundred cycles charge was very small less than 0.1 mAh cm− 2, indicating that a compact PbCl2 layer did not form. For that reason, the Pb electrode is five times charged to 2 V where more compact insoluble PbO2 is formed, inset a) in Fig. 2b), and then reduced to Pb during discharge. After that, during fifty charge-discharge cycles in the potential range from − 0.8 V to − 0.2 V, the discharge capacity is stabilized to ~ 0.55 mAh cm− 2, inset b) in Fig. 2b). Even the AgCl and PbCl2 are nonconductive, during charge and discharge, potential plateaus are connected with the solid-state conversion of metallic silver or lead to silver or lead chlorides. Therefore, the conductivity of AgCl and PbCl2 is associated with the presence of metallic silver or lead in the active mass. The potentials of the electrodes are determined by the ratio of *a*(MCln) = *x* and *a*(M) = 1 - *x*. Once the whole Ag or Pb is converted to AgCl or PbCl2, as a nonconductive phase, a sharp increase of the potential is observed, and *vice versa*.

For considered cases, Scheme 1a) and b) shows possible formation mechanism of AgCl and PbCl2 in the potentials range of − 0.6 V to 0.6 V and − 0.8 V to − 0.2 V, respectively. Initially, for silver, dissolved Ag+ reacts with Cl– near the electrode surface and due to low solubility product of *L*sp(AgCl) = 1.6⋅10− 10 M2 precipitate as dense, microporous thin inner layer film. Through micropores, Ag+ diffuses and reacts with Cl– forming the outer AgCl layer. When the outer layer fills all the micro pores of the inner film, the AgCl growth stops, and capacity is stabilized, inset in Fig. 2a). On the contrary, for the lead electrode, Scheme 1b, due to the much higher solubility product of *L*sp(PbCl2) = 1.7⋅10− 5 M3 dissolved Pb2+ have a less tendency to form thin microporous film, and during the initial period only small fraction of metallic lead surface is cowered with macroporous PbCl2. After a prolonged time, most of the dissolved lead, probably diffuse into the solution and produce particles of PbCl2 that precipitates at the bottom of the cell (which is visually observed), and the very low mass of PbCl2 precipitate to the lead surfaces (corresponding to ~ 0.1 mAh cm− 2). For that reason, we charged the electrode in five successive cycles to ~ 2 V, where compact PbO2 is formed, which is further reduced to PbCl2 and metallic lead. After the initial formation of compact PbCl2, the situation becomes similar to the process at Ag, and the formation of PbCl2 practically stops after ~ 50 cycles of charge-discharge, inset b) in Fig. 2b).

Figure 3a shows typical stable cyclic voltammograms of AgCl|Ag, and PbCl2|Pb in 3.5% NaCl. Formation of AgCl starts at ~ 0 V and occurred via solid-state reaction through one broad peak up to the potentials of ~ 0.5 V. Reduction of AgCl to metallic silver starts at ~ − 0.1 V (probably due to the overpotentials necessary to produce metallic Ag, even around 0 V small current could be seen in a magnified CV. Reduction of AgCl, proceeds through one large peak (B) and a smaller one (C), as observed in a polarization curve, and could be associated with the reduction of the outer and inner layer. The cyclic voltammogram of PbCl2|Pb is similar to silver counterpart, but in the potential range from − 1 V to 0 V. Reduction of PbCl2 to metallic lead, also proceeds via two packs, (B) and (C) that probably corresponds to reduction of the outer and inner layer.

Optical micrographs of AgCl and PbCl2 are shown in Figs. 3b) and c). AgCl has a practically nonporous low crystalline structure. PbCl2 is with irregular structure, and some whiskers can be observed, probably developed from the deposition of Pb2+ from the solution produced by the small dissolution of PbCl2.

## 3.2. Charge-discharge characteristics

The charge-discharge curves for AgCl|Ag and PbCl2|Pb in the current density range from 2 to 15 mA cm–2 are shown in Figs. 4a) and b). The charge of the AgCl|Ag electrode occurred under the very flat potential plateau near the reversible potentials. Discharge proceeds initially with a very fast potential drop to the potential of ~ − 0.6 V that could be connected with the formation of metallic silver necessary for the establishing of the reversible AgCl|Ag potential, and discharge continues at the potentials of ~ − 0.1 V. Obtained capacity depends on applied current density, inset in Fig. 4a), and ranges from 1 mAh cm− 2 for 2 mA cm− 2 to 0.7 mAh cm− 2 for 15 mA cm− 2, with practically 100% Coulombic efficiency. The charge-discharge of PbCl2|Pb also occurred over a very flat plateau near reversible potentials. Contrary to AgCl, a huge potential drop for discharge is not observed, suggesting that in the PbCl2 layer, a small amount of metallic Pb necessary for establishing the reversible potentials is present, Fig. 4b). Obtained discharge capacity decreased with increases of applied current density, from 0.55 mAh cm− 2 to 0.4 mAh cm− 2, inset in Fig. 4b), with Coulombic efficiency of the charge-discharge ranging from 75–85%. The increase of Coulombic efficiency with the increase of applied current is controversial and could be suggested that during charge with smaller current density, some of the initially formed Pb2+ has enough time to diffuse into the solution and could not precipitate onto the electrode surface as PbCl2. At higher current density, the saturation concentration of PbCl2 is much more easily formed and precipitates onto the electrode surface.

To determine the specific capacity of the investigated materials, the following procedure is performed. Using connections of Faraday law with obtained charge capacities, insets in Figs. 4a) and b):

$$m({\text{MC}}{\operatorname{l} _n})={Q_{\text{c}}}\frac{{M({\text{MC}}{\operatorname{l} _n})}}{{nF}}$$

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the mass for every corresponding charge is calculated, and shown in the inset in Fig. 5 as the dependence of the mass on applied current, and extrapolated to zero current density. In that way, the maximum available AgCl mass of 5.2 mg cm− 2 and for PbCl2 4.4 mg cm− 2 is estimated. With the obtained mass the specific currents are calculated by dividing current densities by mass. As can be seen in Fig. 5 for AgCl specific current ranges from 0.4 to 2.9 A g− 1, while for PbCl2 ranges from 0.45 to 3.44 A g− 1. The theoretical specific capacity per gram of corresponding metal chlorides is determined using the following equation:

$${q_{{\text{s,T}}}}=\frac{{M({\text{MC}}{\operatorname{l} _n})}}{{nF}}$$

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where *M*, g mol− 1, is the molar mass of metal chlorides, *n* is the number of exchanged electrons, and *F*, 26.8 Ah mol− 1, Faraday constant. The theoretical specific capacity for AgCl is 188 mAh g− 1, and for PbCl2 is 193 mAh g− 1. From Fig. 5 can be seen that obtained specific capacity for AgCl tends to the theoretical values for low current densities, while for PbCl2 obtained discharge capacity of ~ 125 mAh g− 1 for smaller current density is significantly reduced compared to the theoretical values. Considering theoretical specific capacity and specific currents it can be calculated that electrodes are discharged with a very high *Q*-rate, from 2*Q* to 15.4*Q* for AgCl, and from 2.3*Q* to 17.8*Q* for PbCl2, so it could be suggested that solid-state conversion of PbCl2 to Pb is not so fast and utilization of the active mass is limited.

The cyclic stability of the materials is investigated over 200 cycles, at the current density of 15 mA cm− 2. Some unusual behavior is observed, as can be seen in Fig. 6. For AgCl, after initial practically constant capacity, some small decay is observed followed by ~ 20% increase of the initial capacity, inset in Fig. 6. PbCl2 electrodes show a practically constant increase of charge-discharge capacity and after 200 cycles are higher for ~ 50% than the initial value. The increase of the capacity could be explained that under the very high charge-discharge rate, 15.4*Q* for AgCl|Ag and 17.5*Q* for PbCl2|Pb, due to the extensive mechanical straining some cracks in the relatively compact chloride deposits are formed, allowing further dissolution of underlying metals and formation of more metal chlorides onto the electrode surface.

## 3.3. Potential characteristics of magnesium quasi-rechargeable cells

To investigate the potential characteristic of quasi-rechargeable Mg-based cells, during the charge-discharge experiments, potentials are also recorded versus the quasi-reversible Mg alloy AZ63 reference electrode. Due to the very small polarization of Mg alloy [27], the potential could be considered, in the first approximation, as cell voltage. As mentioned in the experimental, this is done to avoid the formation of the Mg(OH)2 and pH change in limited cell volume, which is not the case for the real systems potentially applied in seawater. For AZ63|AgCl system very flat potentials around 1.5 V are obtained, while for AZ63|PbCl2 around 1 V, Figs. 7a) and b). Reactions that occurred during the charge are, at the positive electrode:

Ag + Cl– → AgCl + e– (5)

or

Pb + 2Cl– → PbCl2 + 2e– (5a)

and at a negative AZ63 electrode, because Mg2+ cannot be deposited from an aqueous solution, will be hydrogen evolution:

2H2O + 2e– → H2 + 2OH– (6)

Discharge can be associated with the following reactions, at the positive electrode:

AgCl + e– → Ag + Cl– (7)

or

PbCl2 + 2e– → Pb + 2Cl– (7a)

and at the negative electrode:

Mg → Mg2+ + 2e– (8)

To roughly calculate the specific capacity, energy, and power of the potential cell, first, the specific current, *I*s is calculated based on the following equation:

$${I_{\text{s}}}=\frac{I}{{m[{\text{MC}}{\operatorname{l} _n}]+m({\text{Mg}})]}}$$

9

The mass of magnesium in grams is calculated using the Faraday law and obtained discharge capacities, *Q*d in Ah, of the AgCl and PbCl2, shown in the insets of Figs. 4a) and b):

$$m({\text{Mg}})={Q_{\text{d}}}\frac{{M({\text{Mg}})}}{{2F}}$$

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where *M*(Mg) = 24.3 g mol− 1, and *F* = 26.8 Ah mol− 1. The estimated mass of the Mg for AgCl system (1 mAh cm− 2 for 2 mA cm− 2 to 0.7 mAh cm− 2 for 15 mA cm− 2), is in the range of 0.45 mg to 0.32 mg. The corresponding dissolved Mg mass for the PbCl2, for discharge capacities from 0.55 mAh cm− 2 to 0.4 mAh cm− 2 are in the range of 0.25 mg to 0.18 mg. It is obvious that dissolved Mg mass is much below 10% of the mass of the positive electrodes, so using the few centimeters thick Mg alloy and taking into account Mg corrosion, ~ 50 µA cm− 2 [27], the cell that will be charged-discharged many times could be easily produced. For example, for the corrosion current density of 50 µA cm− 2 the loss of AZ63 due to corrosion will be 0.2 g cm− 2 or ~ 0.1 mm per year. Therefore, depending on the applied current and time the thickness of the negative electrode could be calculated for the desired number of charge-discharge cycles. Using calculated specific currents, that for the AZ63|AgCl ranges from 0.35 A g–1 to 2.7 A g–1, and for AZ63|PbCl2 from 0.45 A g–1 to 3.3 A g–1, the specific capacity of the possible cells is calculated and shown in the inset of Fig. 7c. For AZ63|AgCl is in the range of 180 mAh g− 1 to 130 mAh g− 1, while for AZ63|PbCl2 are in the range of 118 mAh g− 1 to 80 mAh g− 1.

The theoretical capacity of the cell can be estimated as:

$${Q_{{\text{cell}}}}=\frac{{{m_+}{q_{{\text{s,}}+}}+{m_ - }{q_{{\text{s,}} - }}}}{2}$$

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and specific capacity as:

$${q_{{\text{s,cell}}}}=\frac{{{Q_{{\text{cell}}}}}}{{{m_+}+{m_ - }}}$$

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The mass of the positive electrode *m*+ could be taken as 1 g, and the corresponding mass of, the negative, magnesium, the electrode can be calculated from:

$${m_ - }=\frac{{{m_+}{q_{{\text{s,+}}}}}}{{{q_{{\text{s,-}}}}}}$$

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The theoretical specific capacity for AgCl is 188 mAh g− 1, for PbCl2 is 193 mAh g− 1, and for Mg is 2.2 Ah g− 1. Hence, the Mg dissolved mass for the cell with AgCl will be 0.085 g, and for the cell with PbCl2 0.088 g. The theoretical capacity of the AZ63|AgCl cell will be 187.5 mAh, or the theoretical specific capacity 172.8 mAh g− 1, while for the AZ63|PbCl2 will be 190 mAh and 174.6 mAh g− 1. For AgCl based system theoretical value is in good agreement with obtained value, but for PbCl2 is smaller, probably due to low active mass utilization that can be connected with slow solid-state transformation.

Specific discharge energy, *w*s,d, of the cell is estimated by the integration of discharge curves and using the following equation:

$${w_{{\text{s,d}}}}=\frac{{{I_{\text{s}}}\int\limits_{0}^{{{t_{\text{d}}}}} {{U_{\text{d}}}} {\text{d}}t}}{{3600}}$$

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while specific discharge power, *P*s,d, of the cell is calculated by:

$${P_{{\text{s,d}}}}=\frac{{{w_{{\text{s,d}}}}}}{{{t_{\text{d}}}}}$$

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The calculated values are shown in Fig. 7c). Specific energy for AZ63|AgCl is in the range of 260 to 190 Wh kg− 1, and for the AZ63|PbCl2 in the range from 125 to 80 Wh kg− 1. The estimated specific power, for AZ63|AgCl, ranges from 260 to 4000 W kg− 1, and for AZ63|PbCl2 from 450 to 3300 W kg− 1.

Even though the obtained specific capacity, energy, and power are promising for the real applications of such systems, obtained areal capacities are relatively small, ~ 0.5 to 1 mAh cm−2. So for some hypothetical real cells, the positive electrode surface will be very high. For that reason, it could be suggested that some other method for preparing metal chlorides should be considered. Pargar et al. [43] using the galvanostatic anodization of the silver in 0.1 M HCl, obtained much ticker AgCl, and for example with 4 mA cm− 2 during one hour 40 µm of AgCl is obtained, corresponds to AgCl mass of 0.022 g cm− 2 (4 mAh cm− 2). Similar results are obtained by Lin et al. [44]. It should be also mentioned that all silver and lead could be regenerated by dissolving in HNO3 which is not the case with classical casted or pressed electrodes.