3.2. Formation of Multicolored Patterns at Constant Voltage in the RDR Setup
Figure 4 shows the spatiotemporal evolution of a multicolored pattern formed in the sample tube using the proposed RDR setup at an applied constant voltage of 2 V for 100 h (plus an additional monitoring period of 50 h without voltage application). The top of this figure illustrates the charges of the electrodes and the directions of reactant ion movement induced by the electric field.
After 15 h of voltage application, a faint, short reddish–brown band formed at ~8 mm from the cathode surface. After 40 h, the color of this band became deeper, suggesting the accumulation of Cu-Fe
II PBA (see
Figure 2). The boundary of the band became clear on the cathode side, and its position did not change over the observation time (100 + 50 = 150 h).
After 40 h, a wide region on the anode side became green. Typically, aqueous Cu
2+ ions give a blue color in gel/solution, but they could appear green when mixed with [Fe(CN)
6]
3− ions, which give a yellow color (
Figure 5). Thus, the green color in the sample tube suggests the accumulation of aqueous Cu
2+ ions without generating Cu-Fe
III PBA, which are typically ocher (
Figure 2b).
After 65 h, the reddish–brown band, which was not periodic but continuous, propagated toward the anode by ~3.5 mm in the movement direction of the [Fe(CN)6]4− ions, and the green color at the anode side deepened. The reason why the precipitate front propagated only toward the anode side is not clear currently. However, one possible cause is that, on voltage application, [Fe(CN)6]3− ions (as well as [Fe(CN)6]4− ions generated from the cathode) become depleted near the cathode over time as a result of their transport to the anode side, thus preventing the precipitation of Cu-Fe PBA near the cathode. Meanwhile, such depletion is less likely at the anode side.
After 90 h, the pattern was well-developed and showed almost no further changes, even after stopping the voltage application at 100 h (compare the images taken at 90 and 135 h). Interestingly, the characteristic yellow color of [Fe(CN)6]3− ions still remained near the cathode after 90 h, suggesting that (1) the applied constant voltage of 2 V only moved [Fe(CN)6]3− ions slowly, and hence (2) diffusion contributed significantly to ion transport, nucleation, and crystallization in the sample tube.
The last image in
Figure 4 was obtained after removing the unreacted ions. The yellow color disappeared, but the reddish–brown band persisted. Interestingly, the characteristic blue color of aqueous Cu
2+ ions also remained over a wide area at the anode side (right side), suggesting that the Cu
2+ ions formed sparingly soluble Cu(OH)
2 precipitates. The formation of Cu(OH)
2 precipitates in the sample tube is possible because OH
− ions could be generated by a side reaction at the cathode (
) and then migrate to the anode side under the influence of the static electric field to react with Cu
2+ ions. Note also that the ocher color characteristic of Cu-Fe
III PBA was not observed, suggesting that [Fe(CN)
6]
3− ions are less reactive with aqueous Cu
2+ ions than [Fe(CN)
6]
4− and OH
− ions in the proposed RDR setup.
It should be noted that Cu-Fe PBA can also be formed on the Cu electrodes.
Figure 6a shows significant amounts of deposits at the cathode and anode after 100 h at 2 V. These deposits were firmly bonded to the electrodes, and hence the electrodes required polishing with sandpaper of different grades (#120, #240, and #400) after the experiments. Moreover,
Figure 6b shows that the boundary between the [Fe(CN)
6]
3− gel and Cu rod is sufficiently reactive to form a small amount of reddish–brown compounds (probably Cu-Fe
II PBA) without voltage application. This reactivity can be explained as follows. At the boundary without an applied voltage, reactant ions of Cu-Fe
II PBA (Cu
2+ and [Fe(CN)
6]
4−) can be generated through the following reactions: Cu → Cu
2+ + 2e
− (at the Cu metal surface) and 2[Fe(CN)
6]
3− + 2e
− →2[Fe(CN)
6]
4− (at the gel surface in contact with Cu). At the Cu cathode/anode, the Cu
2+/[Fe(CN)
6]
4− ions can react with electrochemically generated [Fe(CN)
6]
4−/Cu
2+ ions to produce Cu-Fe
II PBA precipitates. At the anode, direct electrochemical production of Fe-Cu
II PBA is also possible through the following reaction (for simplicity, the Fe(CN)
6 vacancies and the additional H
2O are ignored): Cu + 2K
+ + [Fe
III(CN)
6]
3− → K
2Cu [Fe
II(CN)
6] (Cu-Fe
II PBA) + e
−. Additional discussion concerning the formation of Cu-Fe PBA precipitates near/on the electrodes will be provided later.
Figure 7 shows the results obtained when changing the applied voltage from 2 to 4 V. The observations are similar to those obtained at 2 V in the following aspects. (1) A single (i.e., non-periodic) reddish–brown band was formed on the cathode side. (2) A wide region on the anode side turned green. (3) The generated pattern showed almost no change after 90 h, and the gel near the cathode remained yellow.
On the other hand, the reddish–brown and green colors generated at 4 V were deeper than those generated at 2 V, suggesting greater amounts of Cu-FeII PBA precipitates and aqueous Cu2+-related compounds, respectively. Moreover, compared to the behavior observed at 2 V, band propagation to the anode side was considerably suppressed at 4 V, and the resultant band was narrower (approximately 2 mm vs. 3.5 mm). This finding suggests that increasing the applied voltage from 2 to 4 V is effective in restricting the broadening of the Cu-FeII PBA precipitation band.
Interestingly, a sharp line structure appeared in the green region after 40 h at 4 V (
Figure 7). This structure remained at the same location and was distinguishable after removing the unreacted ions. As discussed in a previous study concerning Mn-Fe PBA precipitates in water-glass gels [
29], these light-colored band-in-band structures can form in slightly soluble precipitates when there is a local shortage of the constituent compounds. Thus, the line structure in
Figure 7 suggests again the coexistence of slightly soluble precipitates, such as Cu(OH)
2, in the blue region of the gel sample after removing unreacted ions.
In addition, the gel sample occasionally shrunk during the application of 4 V constant voltage, mainly at the cathode side. At higher voltages, such shrinkage occurred more frequently and prevented detailed observations. Additionally, at higher voltages, (1) the yellow color near the cathode rapidly disappeared without forming the reddish–brown band (e.g., within 40 h at 8 V), and (2) the contact between the cathode and gel was frequently lost because of the formation of bubbles (possibly H2) on the cathode. Meanwhile, at applied voltages below 2 V, the reddish–brown color of the band formed in the sample tube was very light, even after 100 h, suggesting that the concentration of generated Cu-FeII PBA was very low. Thus, in the current setup, the applied constant voltages for examining the precipitation patterns in detail were limited to 2 to 4 V.
3.3. Formation of Multicolored Periodic Bands under Cyclic Alternating Voltage in the RDR Setup
Figure 8 shows the spatiotemporal evolution of a typical multicolored pattern formed in the sample tube under an applied cyclic alternating voltage: i.e., 4 V for 1 h and then 1 V for 4 h per cycle for a total of 20 cycles. In this cyclic voltage sequence, fewer reactant ions will be produced at 1 V and diffusion should exert a stronger effect on the residual ions to induce the formation of wide, diffuse precipitation patterns. In contrast, more reactant ions will be produced at 4 V and the stronger electric field should have a greater influence on the ions, thus producing narrow, thick precipitation bands, as suggested by the constant voltage experiments.
After 15 h of cyclic voltage application (3 cycles), the wide region at the anode side became slightly green. However, no marked reddish–brown band was observed, which is unlike the observations at constant voltages of 2 and 4 V (see
Figure 4 and
Figure 7). After 40 h (8 cycles), several short, faint, and reddish–brown bands were formed near the cathode (~10 mm from its surface). After 65 h (13 cycles), the number of thin reddish–brown bands increased. It should be noted that the formation of these periodic bands was stochastic with a probability of ~50% (e.g.,
Figure 9a,b); in the other ~50% of cases, an almost continuous band was formed (e.g.,
Figure 9c,d). Either way, during the formation of the reddish–brown band(s), the green region became gradually deeper in color. Interestingly, even after stopping the voltage application, occasionally the formation of periodic bands continued (compare the patterns obtained after 90 (18 cycles) and 135 h (35 h after 20 cycles) in
Figure 8).
These stochastically formed periodic bands showed the following common features. (1) The periodic bands were formed within a relatively narrow region (<5 mm). (2) The number of residual bands after removing unreacted ions was within 12 ± 5. (3) The spaces between the adjacent bands were within 0.30 ± 0.25 mm after removing unreacted ions (details will be discussed later). (4) The periodic bands maintained their positions during the observation time, similar to the unusual Liesegang bands previously found in a Co-Fe PBA system [
30]. (5) After removing unreacted ions, several periodic bands became blue instead of reddish–brown, strongly suggesting the presence of Cu(OH)
2 precipitates (as already suggested by
Figure 4 and
Figure 7).
Figure 10a is an enlarged image of the multicolored periodic bands after removing unreacted ions (bottom image in
Figure 8) together with 0.5 mm graduations for ease of comparison. These periodic bands are numbered from
n = 1 (the cathode side) to 15 (the anode side). Their positions (
Xn) were measured using the graduations with an accuracy of ±0.05 mm to determine the band spacing
dn =
Xn+1 −
Xn, which is plotted in
Figure 10b.
It is well known that Liesegang bands tend to follow an empirical scaling law, the so-called spacing law, irrespective of the electrolyte pair and the geometry of the system:
Xn+1/
Xn = 1 +
p, where
p > 0 for most systems [
1,
2,
3,
4,
5]. This law can also be described as
because
, indicating that the
dn value increases monotonically with
n (for
p > 0).
Figure 10b indicates that the obtained
dn values did not increase monotonically, thus failing to obey the spacing law. Rather, they were randomly distributed around an average value (0.30 mm) with a broad dispersion (±0.25 mm), as mentioned before. It is not surprising that the
dn values disobey the spacing law, because the mechanism to form periodic bands in the current RDR setup (
Figure 1c) is fundamentally different from that in the conventional RD setup used to examine Liesegang banding (
Figure 1a). Note that the average
dn value (0.30 mm) is comparable to its dispersion (±0.25 mm). This means that the periodic bands can easily overlap to form almost continuous bands (as found in
Figure 9c,d), particularly when relatively broad bands (such as the bands of
n = 1–4 in
Figure 10a) form stochastically. Thus,
Figure 10 implies that expanding the band spacing may improve the probability of periodic band formation. The related experimental issues will be discussed later.
3.4. Fe Kα Intensity Distribution of the Pattern Formed under Cyclic Alternating Voltage
Figure 11 shows the Fe
Kα intensity distribution of the gel sample having multicolored periodic bands (shown in
Figure 8 and
Figure 10) formed under the cyclic alternating voltage. The horizontal axis indicates the distance from the periodic band of
n = 1 (
X), where
X > 0 is on the anode side. The vertical axis is the relative Fe
Kα intensity. As already shown in previous studies [
27,
28], the Fe
Kα distributions of gel samples with formed PBA precipitates provide a good estimate of the Fe elemental distributions. Because the current XRF experiments were conducted after removing the unreacted [Fe(CN)
6]
3− ions, the measured Fe
Kα distribution should approximate the distribution of Cu-Fe PBA formed in the gel sample.
The Fe
Kα intensity was relatively strong in regions close to the electrodes (
X = −9.0 and 26.0 mm). This result is consistent with the fact that considerable amounts of deposits (probably Cu-Fe
II PBA) were present at the electrodes (
Figure 6). Interestingly, a strong Fe
Kα intensity (~125 in
Figure 11) was also observed in the reddish–brown periodic bands on the cathode side (
n = 2–4 in
Figure 10a, named “main bands” hereafter) with a sharp peak at
X = 0.5 ± 0.25 mm (the uncertainty is due to the focus size of incident X-rays), strongly suggesting that Cu-Fe
II PBA specifically accumulated in the main bands. Such highly localized precipitation is expected to cause the depletion of reactant ions (and, thus, also Cu-Fe PBA) nearby. Indeed, the Fe
Kα intensity around the main bands was low, resulting in a broad valley-like structure around
X = 3.0 mm where the blue periodic bands (
n ≥ 12) are located. This finding supports the hypothesis that the blue bands mainly consist of Cu(OH)
2 instead of Cu-Fe PBA, as indicated by the blue color itself. Except for the main bands, other reddish–brown periodic bands (denoted “non-main reddish–brown (RB) bands” hereafter) did not have very strong Fe
Kα intensities, although there was a weak peak at
X = 2.0 mm corresponding to the position of non-main RB bands of
n = 7–9. Therefore, it is likely that the non-main RB bands did not contain significant quantities of Cu-Fe
II PBA.
Note that the Fe Kα intensities of the wide blue region (8.0 < X < 23.0 mm) are comparable to those of the non-main RB bands. Thus, to our surprise, Cu-Fe PBA (reddish–brown or ocher in color) also existed in the blue region. Their amount there is estimated to be ~2/5 of that in the main bands, based on the Fe Kα intensities (approximately 50 vs. 125). Additional explanation of this interesting feature is given in the next section.
3.5. Microscopic Observation of the Pattern Formed under Cyclic Alternating Voltage
Figure 12 shows the optical microscopy images (×1000) of the gel sample having multicolored periodic bands formed under the cyclic alternating voltage (the corresponding Fe
Kα distribution is shown in
Figure 11). The positions where the images were acquired are indicated in the uppermost panel.
Many reddish–brown crystallites approximately 1–10 μm in size are visible in
Figure 12, not only in regions close to the electrodes (
Figure 12a,e, where the crystallite sizes were relatively large) and the main bands (
Figure 12b) but also in the blue region (
Figure 12c,d). This finding strongly suggests that micrometer-sized Cu-Fe
II PBA crystallites (which are too small to be seen by the naked eye) were generated over a wide region in the gel sample under the applied cyclic alternating voltage. The existence of these crystallites in the blue region can explain the non-negligible Fe
Kα intensities observed at 5.0 < X < 23.0 mm in
Figure 11. On the other hand, the approximately flat Fe
Kα distribution in the blue region suggests an even probability of Cu-Fe
II PBA crystallite formation there. The mechanism that generated these widely dispersed crystallites remains unclear at present and requires future research.
At position b in
Figure 12 (the main band,
n = 2), the crystallites are visible against the reddish–brown background, suggesting that finer Cu-Fe
II PBA crystallites (<1 μm) also contribute to the main bands. The ratio between the quantities of larger crystallites (particles in
Figure 12b, 1–10 μm) and smaller crystallites (reddish–brown background in
Figure 12b, <1 μm) in the main bands was estimated as follows. A comparison between
Figure 12b and 12d shows that the main bands and the blue region have comparable numbers of large crystallites. As mentioned above concerning the Fe
Kα distribution, the amount of Cu-Fe
II PBA in the blue region (where most of the crystallites are larger ones) is ~2/5 of that in the main bands. Thus, approximately 1 − 2/5 = 3/5 of the Cu-Fe
II PBA are expected to exist as smaller crystallites in the main bands. In other words, the quantities of larger and smaller crystallites have a ratio of ~2/3, suggesting a dominance of smaller crystallites in the main bands.
3.6. SEM Observation of the Pattern Formed under Cyclic Alternating Voltage
Figure 13 shows SEM images of the gel sample having multicolored periodic bands formed under the cyclic alternating voltage (other results related to the same sample are shown in
Figure 8 and
Figure 10,
Figure 11 and
Figure 12).
Figure 13a–c was obtained for the periodic bands of
n = 1 (the non-main RB band), 2 (the main band), and 12 (the blue band), respectively. For comparison, a region close to the anode is also shown in
Figure 13d.
As shown in
Figure 13d, precipitates close to the anode consisted of crystallites that were definitely cubic, which is characteristic of PBA [
23]. In accordance with the relatively high Fe
Kα intensity in
Figure 11 (i.e., a large amount of Cu-Fe PBA), there were numerous crystallites. The crystallite sizes (1–3 μm on each side) are somewhat smaller than those of Mn-Fe PBA crystallites formed in agarose gels in the conventional RD setup for Liesegang banding (3–10 μm on each side) [
23]. Despite the different (but comparable) sizes,
Figure 13d is very similar to the SEM images acquired previously for precipitation bands of Mn-Fe PBA in agarose gels [
23,
31].
Figure 13b is an SEM image of precipitates formed in the main band of
n = 2. These precipitates also consisted of cube-like crystallites, even though their sizes were considerably smaller (0.1–0.8 μm on each side) and the shapes were not perfectly cubic, suggesting the existence of many defects. These small crystallites can be considered to form the reddish–brown background observed in
Figure 12b.
The somewhat irregular shapes of the crystallites in
Figure 13b may be a disappointment if one expects well-defined PBA crystallites with few defects for use as electrodes [
15,
16,
20] or magnets [
19]. However, when used as adsorbents or catalysts, smaller PBA crystallites with many defects would be advantageous because of their inherently large surface area. Indeed, the importance of defects (i.e., porosity) has been reported in several studies on the adsorption/catalytic properties of PBA [
17,
18,
20,
21,
22,
32].
Figure 13a is an SEM image of the precipitates formed in the non-main RB band of
n = 1. Interestingly, in addition to the cube-like crystallites, there were also plate-like crystallites (indicated by white circles). This finding strongly suggests that the non-main RB bands consisted of two types of crystallites, namely plate-like Cu(OH)
2 and cube-like Cu-Fe PBA.
Figure 13c is an SEM image of the precipitates formed in the blue band of
n = 12. Unlike the other images, this image shows only a few cube-like crystallites as expected. Instead, plate-like crystallites were dominant and even formed laminates with the size of ~25 μm. This finding also suggests the large contribution of Cu(OH)
2 to the blue periodic bands.