Introduction

The honeycomb-like or the 3D foam structures formed by electrolysis represent a relatively new type of metal electrodes which investigation has been extensively commenced by the beginning of this century [1,2,3]. The advantage of these 3D electrodes relative to 2D ones is its very developed surface area achieved by simultaneous processes of metal electrodeposition and vigorous hydrogen evolution, making them very suitable for application in batteries, sensors, and fuel cells. The method of formation of the honeycomb-like or the 3D foam structures is known as gas bubble dynamic template method or dynamic hydrogen bubble template (DHBT) method where hydrogen bubbles generated by electrodeposition in the hydrogen co-deposition range act as dynamic template around which metal electrodeposition occurs [4,5,6]. Thinking to electrolytically generated hydrogen bubbles, morphology of the honeycomb-like structures is determined by holes formed from detached hydrogen bubbles and dendrites or cauliflower-like particles around them. Almost all metals which can be electrodeposited from aqueous electrolytes can be produced in the honeycomb-like form. Some of technologically important metals obtained in the form of the honeycomb-like or the 3D foam structures are Cu [1, 3, 5, 7,8,9,10,11,12], Ni [13,14,15], Ag [16, 17], Au [18], Pd [19], Pt [20], Ru [21], Pb [22], etc. These structures can be also obtained by molten salt electrolysis [23, 24]. Although both potentiostatic and galvanostatic regimes of electrolysis can be used for their production, galvanostatic regime is more important than potentiostatic from point of view of commercial application.

The surface area of the honeycomb-like structure is determined by the number and size of holes, and distances among them (or so-called wall width) [7]. Regarding the strong effect of evolved hydrogen on morphological and structural characteristics of the honeycomb-like electrodes, the largest challenges in their development for commercial application lie in an increase of number of holes formed from detached hydrogen bubbles and in an improvement of their structural stability. In the case of copper, the increase of number of holes is achieved either by an addition of additives to electrodeposition baths, such as acetic acid [7], chloride ions [7], (NH4)+, polyethylene glycol, and 3-mercapto-1-propane sulfonic acid [25] or by application of periodically changing regimes of electrolysis in the millisecond range, such as pulsating [26,27,28,29] and reversing current [29, 30] regimes. Simultaneously, the significant improvement of the structural stability was achieved by application of the regimes of pulsating (PC) and reversing currents (RC) [28, 30]. This is attained by a decrease of amount of evolved hydrogen spent for formation of the honeycomb-like structures with maximal number of the holes. Also, energy saving in formation of the honeycomb-like structures can be realized by application of the PC regime [28]. The increase of the surface area, improvement of the structural stability, and energy savings just make periodically changing regimes of electrolysis very suitable for the formation of the honeycomb-like structures.

From all periodically changing regimes of electrolysis, the reversing current is the only regime used in the second range [5]. This fact makes this regime suitable for commercial application, owing to lower price and easier construction of pulse rectifiers in the second mode from those working in the millisecond mode. The first investigation of the formation of the honeycomb-like structures by the RC regime in the second range has been performed recently [31]. It was shown that the mechanism of formation of this structure type was completely different from that in the millisecond range. In the millisecond range, electrodeposition process always occurs at the average current density, and morphological and structural characteristics of the honeycomb-like structures are just determined by this current value. On the other hand, an effective time of electrodeposition in the hydrogen co-deposition range during the cathodic pulses determines the same characteristics of the honeycomb-like structures obtained by electrodeposition by the RC regime in the second range.

In this study, regarding the high potential of the RC regime in the second range on the formation of technologically important honeycomb-like or the 3D foam structures, we continue an investigation of formation of these structures with the aim to find conditions enabling formation of the honeycomb-like structures of maximal surface area and the improved structural stability. For that reason, various parameters of this regime, such as the cathodic current density values, the anodic to cathodic time ratios, and the same anodic to cathodic time ratios but attained by various durations of the cathodic and the anodic pulses, will be investigated.

Experimental

Copper was electrodeposited from 0.15 M CuSO4 in 0.50 M H2SO4 in open cell at a temperature of 21.0 ± 0.50 °C under the following conditions:

  1. (I)

    jc = 240 mA cm−2, ja = 80 mA cm−2, tc = 10 s, ta = 5 s,

  2. (II)

    jc = 320 mA cm−2, ja = 80 mA cm−2, tc = 10 s, ta = 5 s,

  3. (III)

    jc = 400 mA cm−2, ja = 80 mA cm−2, tc = 10 s, ta = 5 s,

  4. (IV)

    jc = 320 mA cm−2, ja = 80 mA cm−2, tc = 2 s, ta = 1 s,

  5. (V)

    jc = 320 mA cm−2, ja = 80 mA cm−2, tc = 20 s, ta = 10 s,

  6. (VI)

    jc = 320 mA cm−2, ja = 80 mA cm−2, tc = 10 s, ta = 2 s, and

  7. (VII)

    jc = 320 mA cm−2, ja = 80 mA cm−2, tc = 10 s, ta = 6.7 s.

The p.a. reagents and ultra pure water were used for a preparation of the electrolyte. The working and counter electrodes were of copper. The working electrode was the cylindrical shape of the surface area of 0.25 cm2 and positioned in the middle of the cell. The counter electrode was in the form of foil situated close to wall of the cell. The honeycomb-like structures were produced with a deposition charge of 10 mA h cm−2.

Morphology of the obtained deposits was examined by a scanning electron microscope (SEM) using Tescan Digital Microscopy - model VEGA3.

Cross-sectional analysis was performed using an optical microscope (Olympus CX41) connected to the computer. Preparation of the samples for cross-sectional analysis is described elsewhere [30].

The average current efficiency of hydrogen evolution, ηI,av(H2), values were determined using an electrolytic cell with the same arrangement of Cu electrodes as that used for the preparation of Cu deposits for morphological and structural analyses. In this case, the electrodes were situated under a burette with the surface facing up so that the total amount of electrolytically generated hydrogen went into the burette.

The current efficiency for hydrogen evolution reaction in a time ti, ηI,i(H2), in %, is presented by Eq. (1):

$$ {\eta}_{\mathrm{I},\mathrm{i}}\left({\mathrm{H}}_2\right)=\frac{V\left({\mathrm{H}}_2\right)}{\mu \left({\mathrm{H}}_2\right){S}_0{j}_c{t}_i}100 $$
(1)

where

$$ \mu \left({\mathrm{H}}_2\right)=\frac{V}{n_eF}=\frac{24120{\mathrm{cm}}^3}{2\times 26.8\mathrm{Ah}}=450\frac{{\mathrm{cm}}^3}{\mathrm{Ah}} $$
(2)

and neF is the number of Faradays per mole of consumed ions, V is the molar volume of a gas at a temperature of 21.0 °C (i.e., 24120 cm3), S0 is the surface of working electrode, and jc is the cathodic current density in the RC regimes.

The average current efficiency of hydrogen evolution, ηI,av(H2), is determined after graphical integration ηI,i(H2) − t as \( {\eta}_{\mathrm{I},\mathrm{av}}\left({\mathrm{H}}_2\right)=\left(1/t\right)\underset{0}{\overset{t}{\int }}{\eta}_{\mathrm{I},\mathrm{i}}\left({\mathrm{H}}_2\right)\mathrm{d}t \).

Results and discussion

Basic facts and the determination of the average current efficiency for hydrogen evolution reaction (ηI,av(H2))

The reversing current (RC) regime consists of periodic repetition of square wave cathodic and anodic pulses and is defined in Eq. (3) [5]:

$$ {j}_{\mathrm{a}\mathrm{v}}=\frac{j_{\mathrm{c}}{t}_{\mathrm{c}}-{j}_{\mathrm{a}}{t}_{\mathrm{a}}}{t_{\mathrm{c}}+{t}_{\mathrm{a}}} $$
(3)

In Eq. (3), jav is the average current density, jc is the cathodic current density, ja is the anodic current density, and tc and ta are durations of the cathodic and the anodic pulses, respectively.

Equation (3) can be given in the form of Eq. (4):

$$ {j}_{\mathrm{a}\mathrm{v}}=\frac{j_{\mathrm{c}}-{j}_{\mathrm{a}}r}{1+r} $$
(4)

where r is the anodic to cathodic time ratio, and is defined by Eq. (5):

$$ r=\frac{t_{\mathrm{a}}}{t_{\mathrm{c}}} $$
(5)

The RC regime in the second range gives optimal results for tc/ta ratios between 1.5 and 5 [5], i.e., for r ratios between 0.67 and 0.20.

Since formation of the honeycomb-like structures occurs deep in the hydrogen co-deposition range, the current efficiency for Cu electrodeposition is less than 1, and Eq. (4) can be given in the form of Eq. (6) as [30, 31]:

$$ {j}_{\mathrm{a}\mathrm{v}}\ast =\frac{\eta_{\mathrm{I},\mathrm{c}}\left(\mathrm{Cu}\right){j}_{\mathrm{c}}-{j}_{\mathrm{a}}r}{1+r} $$
(6)

where jav* is the average current density when electrodeposition of Cu occurs parallel with hydrogen evolution, and ηI,c (Cu) is the current efficiency for Cu electrodeposition during the cathodic pulses.

During electrodeposition process, hydrogen evolution occurs during the cathodic pulses, while there is no any gas evolution during anodic pulses [30, 31]. Figure 1 shows the dependencies of volume of hydrogen generated during the cathodic pulses on electrolysis time for the honeycomb-like structures obtained with the cathodic current density, jc, values of 240 and 400 mA cm−2 (Fig. 1a), for the same anodic to cathodic time ratios (r = 0.50) but various durations of both the cathodic and the anodic pulses (Fig. 1b), and for various values of r, i.e., with r of 0.20 and 0.67 (Fig. 1c). The average values of the current efficiency for hydrogen evolution reaction, ηI,av(H2), are determined by graphical integration of the obtained dependencies ηI,i(H2) − t as, \( {\eta}_{\mathrm{I},\mathrm{av}}\left({\mathrm{H}}_2\right)=\left(1/t\right)\underset{0}{\overset{t}{\int }}{\eta}_{\mathrm{I},\mathrm{i}}\left({\mathrm{H}}_2\right)\mathrm{d}t \) and presented in Table 1.

Fig. 1
figure 1

The dependencies of the volume of evolved hydrogen and the current efficiency of hydrogen evolution on the time of electrodeposition obtained by various RC regimes: (a) jc = 240 mA cm−2 and jc = 400 mA cm−2, (b) tc = 2 s; ta = 1 s, and tc = 20 s; ta = 10 s, and (c) tc = 10 s; ta = 2 s, and tc = 10 s; ta = 6.7 s

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Table 1 The values of the average current efficiency of hydrogen evolution (ηI,av(H2)) obtained for various RC regimes
Full size table

Intensification of hydrogen evolution reaction occurred with the increase of the cathodic current density from 240 to 400 mA cm−2, and with the decrease of the anodic to cathodic time ratios from 0.67 to 0.20 (i.e., for the decrease of the length of anodic pulse from 6.7 to 2 s for the same length of the cathodic pulse of 10 s). It is interesting to note by analysis of data from Table 1 that the values of ηI,av(H2) obtained for the same r but with various lengths of the cathodic and the anodic pulses were different, indicating the strong effect of the anodic to the cathodic time ratios on hydrogen evolution reaction. At the first sight, it was very surprising and requires additional analysis, what will be performed later.

Morphological and structural analysis of the honeycomb-like structures obtained by various RC regimes

Figure 2 shows morphologies of Cu deposits obtained with the cathodic current density values of 240 (Fig. 2a), 320 (Fig. 2b), and 400 mA cm−2 (Fig. 2c). Although the honeycomb-like structures, determined by holes formed from the detachment of hydrogen bubbles and cauliflower-like agglomerates of Cu grains around them, were formed with all three the RC regimes, deeper analysis performed at the higher magnifications showed a difference among them. This difference was especially visible in size and shape of holes formed from detached hydrogen bubbles. The numbers of holes formed from detached hydrogen bubbles were 125 ± 5, 215 ± 5, and 200 ± 5 holes/mm2 surface area for the honeycomb-like structures obtained with jc of 240, 320, and 400 mA cm−2, respectively.

Fig. 2
figure 2

The honeycomb-like structures obtained by the RC regime with the cathodic current density (jc) of (a) 240 mA cm−2, (b) 320 mA cm−2, and (c) 400 mA cm−2

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The honeycomb-like structure with an average hole size of 110 μm (Fig. 3a) and small dendrites at its bottom (Fig. 3b) was formed with jc of 240 mA cm−2. The hole size decreases with the increasing jc, reaching a value of 75 μm for the honeycomb-like structures obtained with jc of 320 and 400 mA cm−2 (Fig. 3 c and d, respectively). The numerous small cauliflower-like agglomerates of Cu grains were formed at the bottom of these holes (Fig. 3e). As a result of intensification of hydrogen evolution caused by the increased jc value, an enhanced coalescence of neighboring hydrogen bubbles was observed, as shown in Fig. 3f. The size of the coalesced holes was about 90 μm, and it was for about 20% larger than individual (non-coalesced) holes. The coalescence process is a just reason of smaller number of holes formed with jc of 400 mA cm−2 than with jc of 320 mA cm−2. The values of number and size of holes obtained for these, as well as all other electrodeposition conditions, are summarized in Table 2.

Fig. 3
figure 3

The holes and the bottoms of the holes constructing the honeycomb-like structures obtained with jc of (a) and (b) 240 mA cm−2, (c) 320 mA cm−2, and (d)–(f) 400 mA cm−2

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Table 2 The values of number and size of individual and coalesced holes for the honeycomb-like structures obtained with various RC regimes
Full size table

The honeycomb-like structures obtained with jc of 320 mA cm−2 and the same r (r = 0.5), but with various durations of the cathodic and the anodic pulses, are shown in Fig. 4. The honeycomb-like structure obtained with tc of 2 s and ta of 1 s is shown in Fig. 4a, while the one obtained with tc of 20 s and ta of 10 s is shown in Fig. 4b. The number of formed holes was 225 ± 5 holes/mm2 surface area for the honeycomb-like structure obtained with tc of 2 s and ta of 1 s, and 150 ± 5 holes/mm2 surface area for the one obtained with tc of 20 s and ta of 10 s.

Fig. 4
figure 4

The honeycomb-like structures and holes constructing them obtained with the same r, but with various durations of the cathodic (tc) and the anodic (ta) pulses: (a), (c), and (d) tc = 2 s; ta = 1 s, and (b), (e), and (f) tc = 20 s; ta = 10 s

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The typical hole obtained with tc of 2 s and ta of 1 s is shown in Fig. 4c. The hole size was approximately same as those obtained with tc of 10 s and ta of 5 s (Fig. 3c). The small cauliflower-like agglomerates of Cu grains are formed at the bottom of holes obtained with this RC regime (Fig. 4d). On the other hand, analysis of holes obtained with tc of 20 s and ta of 10 s showed that the formed holes were larger than those obtained with tc of 2 s and ta of 1 s, and tc of 10 s and ta of 5 s. The size of holes obtained with tc of 20 s and ta of 10 s was about 95 μm, as seen from Fig. 4e. The small cauliflower-like agglomerates of Cu grains, similar to those shown in Fig. 4d, were also formed at the bottom of these holes. The noticeable coalescence of neighboring hydrogen bubbles is observed leading to a decrease of the overall number of holes formed with tc of 20 s and ta of 10 s relative to the numbers of holes formed with tc of 10 s and ta of 5 s, and tc of 2 s and ta of 1 s. The typical coalesced hole obtained with tc of 20 s and ta of 10 s is shown in Fig. 4f. On the other hand, the coalesced process was almost suppressed with tc of 2 s and ta of 1 s, causing formation of the honeycomb-like structures with the larger number of holes.

The honeycomb-like structures obtained with r of 0.20 and 0.67 are shown in Fig. 5 a and b, respectively. The number of holes formed from detached hydrogen bubbles was 200 ± 5 holes/mm2 surface area for the honeycomb-like structure obtained with r of 0.20 and 170 ± 5 holes/mm2 surface area for the honeycomb-like structure obtained with r of 0.67. Holes constructing the honeycomb-like structure produced with r of 0.20 were very disperse in size with a dominant presence of coalesced holes (Fig. 5a). The size of holes changed from 65 μm (Fig. 5c) for individual to 90 μm (Fig. 5d) for those obtained by a coalescence of neighboring hydrogen bubbles. The bottom of these holes consisted of small cauliflower-like agglomerates of Cu grains (Fig. 5e). The smaller number of larger holes was formed with r of 0.67 (Fig. 5b). The size of the holes obtained under these RC conditions was up to 100 μm (Fig. 5f). The mixture of small cauliflower-like and dendritic particles was formed at the bottom of these holes (Fig. 5g).

Fig. 5
figure 5

The honeycomb-like structures and holes constructing them obtained with ta of (a), (c), (d), and (e) 2 s (r = 0.20), (b), (f), and (g) 6.7 s (r = 0.67)

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Figure 6 shows the cauliflower-like agglomerates of Cu grains formed around holes obtained with jc of 240 (Fig. 6a) and 400 mA cm−2 (Fig. 6b), tc = 2 s and ta = 1 s (Fig. 6c), tc = 20 s and ta = 10 s (Fig. 6d), r of 0.2 (Fig. 6e) and 0.67 (Fig. 6f). Unlike size and shape of holes, it is very clear that the applied RC regimes do not affect morphology of cauliflower-like agglomerates of Cu grains formed around them. Numerous irregular channels originating from evolved hydrogen were also formed around small agglomerates inside the large cauliflower-like agglomerates of Cu grains.

Fig. 6
figure 6

The cauliflower-like agglomerates of Cu grains formed around holes obtained with (a) jc = 240 mA cm−2, (b) jc = 400 mA cm−2, (c) tc = 2 s; ta = 1 s, (d) tc = 20 s; ta = 10 s, (e) r = 0.20, and (f) r = 0.67

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Cross-sectional analysis of the obtained structures showed that the depth of holes did not depend on the applied parameters of the RC regimes (Fig. 7). In all cases, the depth of holes was about 100 μm. This can be ascribed to fact that dissolution effect is primarily determined by the anodic current density value, while an influence of length of anodic pulse was less significant. Namely, the anodic current density was 80 mA cm−2 in all applied RC regimes. The very porous interior structure constructed from numerous intertwined channels, not dependent on the applied RC regime, was also observed.

Fig. 7
figure 7

Cross-sectional analysis of the honeycomb-like structures obtained by various RC regimes: (a) jc = 240 mA cm−2, (b) jc = 400 mA cm−2, (c) tc = 2 s; ta = 1 s, (d) tc = 20 s; ta = 10 s, (e) r = 0.20, and (f) r = 0.67

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Discussion of the presented results

Analyzing the effect of the anodic current density values on the formation of the honeycomb-like structures, it was shown recently [31] that this structure type obtained with jc of 320 mA cm−2, ja of 80 mA cm−2, tc of 10 s, and ta of 5 s showed the maximum surface area determined by the number and size of holes. This honeycomb-like structure was obtained with the average current efficiency of hydrogen evolution (ηI,av(H2)) of 20.5% [31]. As already mentioned, the honeycomb-like structures were formed with both smaller (jc = 240 mA cm−2) and larger (jc = 400 mA cm−2) value than this jc value (jc = 320 mA cm−2). It is understandable because cathodic potential responses of 1060–1150 mV for 240 mA cm−2, 1150–1250 mV for 320 mA cm−2, and 1180–1280 for 400 mA cm–2 were all deep in the hydrogen co-deposition range enabling formation of deposits with the honeycomb-like structure. The final morphological and structural characteristics of the honeycomb-like electrodes were determined by the other parameters defining this regime, such as duration of the anodic pulse (various r) and the same r, but with various durations of the cathodic and the anodic pulses.

The increase of ηI,av(H2), i.e., intensification of hydrogen evolution reaction with increasing the jc values, as well as with decreasing ta values is expected. However, the dependence of volume of evolved hydrogen, and hence ηI,av(H2) values, on the anodic to cathodic time ratios (r) was unexpected, and for that reason, it required additional analysis of the RC regime in the second range on the process of formation of the honeycomb-like structures in the hydrogen co-deposition range, and it can be considered as follows:

The first cathodic pulse with cathodic potential response deep in the hydrogen co-deposition range represents a template for a formation of the honeycomb-like structures. The dissolution process only occurs during anodic pulses, and the value of anodic potential response is exclusively determined by the anodic current density value [31]. For an anodic current density, ja of 80 mA cm−2, anodic potential response was in the 108–122 mV range. Starting from the second cathodic pulse, the initial cathodic potential response corresponds to the final anodic potential response, and it increases with time reaching the value in the hydrogen co-deposition range after some time. The time needed to reach the value in the hydrogen co-deposition range is denoted with tc,est, and during this time there is no hydrogen evolution. Since the value of the anodic potential response is only determined by the anodic current density value, the value of this part of the cathodic pulse does not depend on overall duration of the cathodic pulse, and for ja of 80 mA cm−2, tc,est is 0.82 s [31]. The rest of the cathodic pulse, denoted with tc,eff, corresponds to electrodeposition in the hydrogen co-deposition range, since tc,est + tc,eff = tc. For better understanding, this is schematically presented in Fig. 8 for the same r, but various tc and ta values.

Fig. 8
figure 8

Schematic presentation of electrodeposition processes by the RC regime in the second range. The same anodic to cathodic time ratio, but various durations of the cathodic and the anodic pulses. In both cases, tc,est is the same: (a) the longer durations of the cathodic and the anodic pulses, and (b) the shorter durations of the cathodic and the anodic pulses

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Regarding this consideration, a correction of Eq. (6) is necessary on the way presented by Eq. (7):

where n is number of the cycles starting from the second cycle. Equation (7) can be re-written in the form:

$$ {j}_{\mathrm{av}}\ast =\frac{\eta_{\mathrm{I},\mathrm{c}}\left(\mathrm{Cu}\right){j}_{\mathrm{c}}{t}_{\mathrm{c}}+{nj}_{\mathrm{c}}{t}_{\mathrm{c},\mathrm{est}}+n{\eta}_{\mathrm{I},\mathrm{c}}\left(\mathrm{Cu}\right){j}_{\mathrm{c}}{t}_{\mathrm{c},\mathrm{eff}}-\left(n+1\right){j}_a{t}_a}{t_c+{t}_a} $$
(7)
$$ {j}_{\mathrm{a}\mathrm{v}}\ast =\frac{\eta_{\mathrm{I},\mathrm{c}}\left(\mathrm{Cu}\right){j}_{\mathrm{c}}{t}_{\mathrm{c}}-{j}_{\mathrm{a}}{t}_{\mathrm{a}}+{nj}_{\mathrm{c}}{t}_{\mathrm{c},\mathrm{est}}+n{\eta}_{\mathrm{I},\mathrm{c}}\left(\mathrm{Cu}\right){j}_{\mathrm{c}}{t}_{\mathrm{c},\mathrm{eff}}-{nj}_a{t}_a}{t_c+{t}_a} $$
(8)

i.e.,

$$ {j}_{\mathrm{av}}\ast ={j}_{\mathrm{av},\mathrm{I}}^{\ast }+{nj}_{\mathrm{av},\mathrm{eff}}^{\ast }+{nj}_{\mathrm{av},\mathrm{est}}^{\ast } $$
(9)

where

$$ {j}_{\mathrm{a}\mathrm{v},\mathrm{I}}^{\ast }=\frac{\eta_{\mathrm{I},\mathrm{c}}\left(\mathrm{Cu}\right){j}_{\mathrm{c}}{t}_{\mathrm{c}}-{j}_{\mathrm{a}}{t}_{\mathrm{a}}}{t_{\mathrm{c}}+{t}_{\mathrm{a}}} $$
(10)

and

$$ {j}_{\mathrm{a}\mathrm{v},\mathrm{eff}}^{\ast }=\frac{\eta_{\mathrm{I},\mathrm{c}}\left(\mathrm{Cu}\right){j}_{\mathrm{c}}{t}_{\mathrm{c},\mathrm{eff}}-{j}_{\mathrm{a}}{t}_{\mathrm{a}}}{t_{\mathrm{c}}+{t}_{\mathrm{a}}} $$
(11)

and

$$ {j}_{\mathrm{a}\mathrm{v},\mathrm{est}}^{\ast }=\frac{j_{\mathrm{c}}{t}_{\mathrm{c},\mathrm{est}}}{t_{\mathrm{c}}+{t}_{\mathrm{a}}} $$
(12)

Hence, \( {j}_{\mathrm{av},\mathrm{I}}^{\ast } \) is the average current density in the hydrogen co-deposition range during the first cycle. \( {j}_{\mathrm{av},\mathrm{eff}}^{\ast } \) is the average current density in the hydrogen co-deposition range during the n cycles starting from the second cycle, and \( {j}_{\mathrm{av},\mathrm{est}}^{\ast } \) is the average current density during the n cycles starting from the second cycle in which there is no hydrogen evolution.

The final morphology of the honeycomb-like structure is determined by contribution of these three average current densities. The length of one cycle is defined by the duration of the cathodic and the anodic pulse, and for the same deposition charge, the overall number of cycles is different for the same r. All surface morphologies presented in this investigation are obtained with a deposition charge of 10 mA h cm−2. Hence, for the same r of 0.50, the numbers of cycles to reach this amount of the electricity were 56 for tc/ta = 2 s/1 s, 11 cycles for tc/ta = 10 s/5 s, and 6 cycles for tc/ta = 20 s/10 s.

Formation of the honeycomb-like structure occurs during the first cathodic pulse, since the lengths of the cathodic pulses in all three cases were enough to initiate a formation of this structure type. Since time needed to reach electrodeposition in the hydrogen co-deposition range is only determined by the value of the anodic current density and it does not depend on the length of the cathodic pulse (in these cases, tc,est = 0.82 s [31]), a contribution of \( {j}_{\mathrm{av},\mathrm{est}}^{\ast } \) increases with increasing the number of cycles. Hence, the contribution of \( {j}_{\mathrm{av},\mathrm{est}}^{\ast } \) grows in the following row: 20 s/10 s < 10 s/5 s < 2 s/1 s. On the other hand, it is easy to show that a contribution of electrodeposition in the hydrogen co-deposition range (\( {j}_{\mathrm{av},\mathrm{eff}}^{\ast } \)) increases in the following row: 2 s/1 s < 10 s/5 s < 20 s/10 s. In this way, the effect of the same anodic to cathodic time ratios (the same r), but various durations of the cathodic and the anodic pulses on formation of the honeycomb-like structures are proved.

On the basis of the abovementioned results, the process of formation of the honeycomb-like structures by the RC regime in the second range can be optimized as follows: the increase of the cathodic current density from 240 to 320 and 400 mA cm−2 intensifies hydrogen evolution reaction. Firstly, the increase of number of holes, and hence the increase of the surface area, was observed with a change of jc from 240 to 320 mA cm−2. The further change of jc from 320 to 400 mA cm−2 led to the decrease of number of holes due to coalescence of closely formed hydrogen bubbles. Analyzing the same r, but various durations of the cathodic and the anodic pulses, the decrease of the amount of evolved hydrogen was found with the shortening of durations of tc and ta. This can be ascribed to a decrease of effective time for deposition in the hydrogen co-deposition range during the cathodic pulses. Hence, the use of shorter tc and ta values represents a benefit in formation of the honeycomb-like structures, since the smaller amount of hydrogen is then generated, resulting in an improvement of their structural stability. The decrease of r (the shorter duration ta for the same tc) intensifies hydrogen evolution reaction leading to a coalescence of neighboring hydrogen bubbles and worsening of the structural stability of the honeycomb-like structures. Finally, the honeycomb-like structure with the maximal number of holes (the largest surface area), and minimal amount of hydrogen spent for its formation is obtained with jc of 320 mA cm−2, ja of 80 mA cm−2, tc of 2 s, and ta of 1 s.

Conclusion

The process of formation of the honeycomb-like structures by the RC regime in the second range is optimized by selection of parameters defining this regime. The following conclusions can be derived:

  • Intensification of hydrogen evolution reaction increases number of holes (the surface area) in the honeycomb-like structures up to a certain value of the cathodic current density (up to jc of 320 mA cm−2). After this value, the number of holes decreased due to enhanced coalescence of closely formed hydrogen bubbles caused by the further intensification of hydrogen evolution reaction with increasing jc value.

  • For the same anodic to cathodic time ratios (r), application of the short cathodic and anodic pulses realizes benefits in the formation of the honeycomb-like structures. Application of the shorter tc and ta values leads to a decrease of the overall time of electrodeposition in the hydrogen co-deposition range. As a result of this, the overall amount of produced hydrogen was smaller than with the longer tc and ta values. The final consequences of applied shorter tc and ta pulses are the improved structural stability and the increased number of holes due to additional suppression of coalescence process.

  • The decreasing r values (the shortening of duration of ta pulse) intensify hydrogen evolution reaction enhancing a coalescence of neighboring hydrogen bubbles, and consequently, decreasing the number of holes formed from detached hydrogen bubbles.

  • The upgraded mathematical model defining the RC regime in the second range in the hydrogen co-deposition range is proposed and discussed.

  • The best performance from morphological and structural point of view showed the honeycomb-like structure produced with jc of 320 mA cm−2, ja of 80 mA cm−2, tc of 2 s, and ta of 1 s.