Introduction

The role of electrochemistry in the education of chemistry in general, especially in physical chemistry, has been in the focus of didactic studies for decades [1,2,3,4]. The statement of De Jong and Treagust [4] meets the experience of the author of the present work in that electrochemistry is the most feared field of physical chemistry in the secondary school education as well as at the undergraduate level. Therefore, the didactic aspects of electrochemistry education arise time to time. As it is well documented [5, 6], even the reproduction of simple-looking historic experiments that are regarded as the major milestones of the development of electrochemistry is often cumbersome and requires a great care. Therefore, education of experimental electrochemistry and its embedding into the entire chemistry curriculum is a very involved task. Due to the difficulties of the conceptual understanding, experience-based and experiment-oriented teaching of electrochemistry gains role in high school [7] and even at the advanced level of electrochemistry education [8].

While the presentation of the galvanic cells is undoubtedly the core of the education of electrochemistry especially at the undergraduate level [9, 10], these experiments are often restricted to the observation of potential difference between the electrodes of the cell without operating it as a current source. In the group of electrolysis experiments, the electrolytic water splitting is the most commonly applied one [11], and experiments related to electrochemical deposition and dissolution of metals appear in the literature less frequently, though in various contexts. The simplest level of such experiments is the electroplating of a single metal and the observation of its colour, for which the description of tested solution compositions is available [12, 13]. The exhaustive electrolysis of a metal salt solution (Ni or Cu) is applicable in an electrogravimetric configuration [14, 15] provided that one single metal is to be plated. Electroplating of cobalt appeared in a radiochemical student lab experiment for the demonstration of the isotope dilution–based analysis [16]. After the scientific description of the fractal formation in electrodeposition [17], the topic became popular in the education literature, too [18]. The simple demonstration of the electrolytic production of diffusion-limited aggregates was followed by papers on the didactic application of the computer simulations of the morphological features of the deposits thus prepared [19] as well as the demonstration of the importance of the transference number of the precursor metal ion in the fractal formation [20]. In recent descriptions of the demonstration experiments, electrochemical writing (electrochemical pen) is often used [21,22,23,24], and the coloration of the substrate is based on different principles (metal plating, metal anodization or formation of a colourful precipitate from the dissolving metal ion).

All of the above-mentioned studies are based on the electrodeposition of a single metallic element. The commonality of these works with many other demonstration experiments is that they rely on one single reaction, hence focusing on one selected phenomenon only, which is well understandable from the didactic point of view. In contrast to the general approach, an electrodeposition experiment and its complete background will be presented below that includes parallel electrochemical reactions. A wide range of knowledge elements will also be highlighted from physical and inorganic chemistry that can be brought up in relation to this experiment, hence illustrating the variety of teaching opportunities in connection with one single problem. A complete guide is offered how to present the experiment and to drive the discussion for an audience with a specific general level of knowledge such as high school and undergraduate level.

Materials and apparatus

Chemicals and electrolyte solutions

The analytical grade chemicals with 99 + % purity used for the bath preparation were as follows: NiSO4·7H2O, CuSO4·5H2O, NiCl2·6H2O, H3BO3, C7H5NO3S /saccharin/, C12H25SO4Na /sodium dodecylsulfate, SDS/ (all purchased from Reanal), Na3C6H5O7·2H2O /trisodium citrate dihydrate/ (Merck) and Ni(SO3HN2)2·xH2O (Alfa Aesar). Solutions were prepared with ultrapure water from an ELGA Purelab Option 7 type water purifier.

The solution for the demonstration experiment was prepared in analogy with those applied in the works of Pellicer et al. [25, 26] with a slight modification of the concentrations, namely 150 g/L nickel sulfate heptahydrate (cNi = 0.575 M), 10 g/L copper sulfate pentahydrate (cCu = 0.04 M), 50 g/L trisodium citrate dihydrate (cCit = 0.17 M), 0.5 g/L saccharin and 0.1 g/L SDS (called hereinafter as the citrate bath). For the bath preparation, it is advised that CuSO4 is added shortly prior to the experiment since the bath is not stable in the long run. Precipitate appears in the Cu2+-containing citrate bath typically 3 days after its preparation. Therefore, a fresh solution is needed for each demonstration. The pH of the freshly prepared solution was 4.0, and it was used without any further pH adjustment.

For a few control experiments, a bath was prepared with the same molar concentrations of nickel sulfamate, copper sulfate, saccharin and SDS (sulfamate bath). A conventional Watts bath was also tested with the addition of the same amount of CuSO4 as in the above baths. The Watts bath contained 240 g/L NiSO4·7H2O, 45 g/L NiCl2·6H2O, 30 g/L H3BO3 and the same amount of saccharin and SDS as the other baths.

Electrochemical cells

Two cylindrical cells made with beakers of 150 mL nominal volume were used in the demonstration experiments. A Ni foil anode of 70-mm height was wrapped around the internal wall of both beakers, hence providing an anode surface area (~ 120 cm2 at one side of the foil) much exceeding that of the cathode. In one of the additional experiments later, a Cu foil anode with the same shape and surface area was used. The cathode was either a copper or a nickel bar placed into the beaker in coaxial position. If nickel rod is not available, a Ni-plated stainless steel or copper rod can be used. Ni can be plated from essentially any Ni bath (Watts, sulfamate or citrate type), and the thickness of the Ni coating has to be at least 10 µm. The length of the immersed part of the cathode bars was 40 mm, above which the metal was sealed with an insulating tape strip, leaving the top part uncovered for the power source connection. The diameter of the rods was different, 4 mm and 15 mm for the Cu and Ni cathodes, respectively. As it will be shown later, the surface area ratio of the two cathodes is of peculiar importance for the success of the experiments. The initial surface quality of the cathodes is crucial for the eye-catching impression of the experiment, i.e. well-polished shiny cathodes are definitely recommended.

For further experiments (chronopotentiometry and sample preparation for the gravimetric analysis), another cylindrical cell was used in which the cathode was fixed at the bottom of the cell. The cathode surface area was 0.785 cm2 in this cell. The anode was a nickel spiral immersed into the solution from top of the cell. For the observation of the electrode potential, a conventional Hg/Hg2Cl2 reference electrode (SCE; SI Analytics) was connected to the cell through a reference container ending in a glass tube (Luggin capillary) that reached to the close vicinity of the cathode, hence minimizing the ohmic drop between the working and reference electrodes.

Instruments

The demonstration experiments were performed with the help of an inexpensive laboratory power source (EL301R, 30 V / 1 A). The measurement of the potential difference between the cathode and the anode of the demonstration cell was carried out with a handheld multimeter. For comparison, linear potential sweeps were also run by using a potentiostat (IviumStat), which was used to record chronopotentiometric curves as well.

The pH of the solutions was checked with a Consort 860 type pH-meter. For the analysis of the current efficiency, the weight of the samples was measured with a Mettler Toledo XPE26 microbalance with 0.002 mg precision. Optical spectra were recorded with an Agilent Cary 4000 UV–VIS spectrophotometer by using 1-cm-thick cuvettes. Sample composition was determined with an EDAX Element energy-dispersive spectrometer attached to a TESCAN MIRA3 scanning electron microscope.

Demonstration experiment and steps of the explanation search

The primary experiment to show

Let us assemble the cell arrangement with the serial connection of the two cells, the cylindrical Ni foil at the beaker perimeter being the anode for both cells. It is advised that the Cu and Ni bars (i.e. the cathodes) are shown to the audience before fixing them into their holders. Adjust carefully the cathodes at vertical position into the centre of the beakers (see Fig. 1a). Then, show the flask with the plating bath to the audience and ask what ions might make the colour of the solution. In an ideal case, the nickel salt content of the bath will be identified, and the teacher should not reveal that the bath contains Cu2+ ions, too. Even if the lecturer just asks the audience about the possible bath composition, students will likely remember as if the components were identified by the lecturer, not by themselves.

Fig. 1
figure 1

a The cell arrangement with the serial connection of the cells, thin Cu and thick Ni cathode in the left and right beakers, respectively. b The appearance of the cathodes before (left) and after (right) the demonstration experiment

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Then, fill up the cells with the solution from the same flask. Apply 15 mA current (that will pass through both cells) for 4–5 min in order to grow a sufficiently thick deposit. While the experiment is running, read the stabilized voltage on the power source and ask how large potential drop may occur on each cell. By observing the actual polarity and measuring the cell potential differences, it will turn out that the voltage on the cell with the thinner electrode (Cu rod) is approximately twice as large as that on the other cell (typically 1.25 and 2.5 V, resp.). Later these values can be used for the explanation of the phenomena observed.

After turning off the power source, remove the cathode of smaller diameter first (Cu rod), rinse it with distilled water and show it to the audience. The silverish appearance will be obvious, and the audience will likely identify it as nickel. However, when you remove the large diameter cathode and rinse it, the surprising experience is that the originally shiny metal rod with silver colour became red, and it can be easily recognized as copper. The electrodes prior and after the experiment are shown in Fig. 1b.

The confusing nature of the situation is obvious: The same solution was poured into the cells of nearly the same configuration and the same charge was passed through these cells, but different results were achieved. The task is to find an explanation for the astonishing observation. From this point onward, the lecturer’s task is to drive the discussion with well-targeted questions and help the audience find the solution with the minimum possible direct intervention, creating a “chemical escape room” atmosphere.

Equilibrium data and process kinetics

After the first surprise, the initial step to clarify the situation is to conclude that the solution must contain some copper salt, too; otherwise, copper could not be deposited. The lecturer is advised neither to leave the discussion to turn toward an alchemistic direction, tacitly assuming that we could make copper out of nickel, nor to assume that the audience was misled by any magician attraction.

Once the audience gets convinced of that the solution composition was not assessed properly by identifying a single component only, we may turn toward some equilibrium data. The obvious comparison is to highlight the standard potential of two redox systems: (i) Cu2+  + 2e = Cu, E0 = 0.342 V; and (ii) Ni2+  + 2e = Ni, E0 =  − 0.257 V. By recalling the rules about which component of a redox systems can oxidize/reduce another, it is easy to draw the conclusion that Cu2+ is capable of oxidizing Ni metal. As we arrive here, several minutes passed after the accomplishment of the experiment while the Ni anodes were left to soak in the electrolyte solution. If we remove one of the anodes and rinse it with water, we can make it obvious that no copper was formed on nickel. This experience will raise doubt again whether the solution had any Cu2+ content due to the above-mentioned assumption on the direction of the possible redox process. By taking a closer look on the table of electrode reaction standard potentials, we can find that the driving force of reducing Cu2+ ions could be much larger if a piece of Al is used since the Al3+  + 3e = Al reaction has a very negative standard potential (− 1.67 V). The test of the solution with an Al rod or foil leads to the same result: No copper is cemented onto the metal immersed.

This is the point of the discussion to realize that, although aluminium is assumed to decompose even water, it is not reactive in near-neutral aqueous solutions. The reason for this behaviour of Al is commonly known, i.e. the native oxide layer on Al is compact and non-reactive. No wonder that for the usual classroom demonstration experiment of cementation, an iron nail and a copper sulfate solution are recommended. By repeating the immersion test with an iron (carbon steel) specimen that is notorious of not bearing a well-adherent protective oxide layer, we can be convinced that the galvanic bath used in the plating experiment indeed contained copper since the reddish discoloration on iron is obvious. This gives rise to the opportunity of mentioning the lesser known fact that nickel is also passive at ambient conditions, which explains why it can be used as a protective metal coating. It is obvious that here one does not have a reversible (nernstian) Ni2+/Ni system. If we measure the electrode potential of the nickel anode as compared to a Cu rod immersed to the test solution without passing any current, the potential obtained will be positive. (The attention of the teachers is to be drawn to the trend that some works mention the Ni2+/Ni pair as a suitable system to construct demonstration cells for potentiometric measurement [9]. However, this is technically not feasible at the demonstration level.)

In order to illustrate why the audience may have misled itself with the solution composition, it is advised to prepare two small portions of the following solution. The first solution is a Cu2+-free version of the citrate bath, and the other one is a CuSO4 solution with the same concentration as the demo bath. As Fig. 2a shows, the colour difference between the Cu2+-containing and Cu2+-free citrate baths is truly small by visual observation, even though it can be observed very well in the absorption spectra as presented in Fig. 2b. It is useful to mention the concentration ratio of the two metal salts (approx. 14.5).

Fig. 2
figure 2

a Photo of the solutions. Left: citrate bath with Ni2+ and Cu2+; middle: citrate bath with Ni2+ only; right: CuSO4 solution with the same Cu2+ concentration as the mixed bath. b Absorption spectra of the solutions in the visible range

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The difference between the absorption spectra of the Cu-containing and Cu-free solution is much larger than expected from the CuSO4 solution of the same Cu2+ concentration as the citrate bath, and the absorption band is also shifted. The explanation is that the cupric ions are complexed with the citrate ions, which causes both the absorption shift and the intensification of the colour.

Serial processes: transport and electrochemical reaction

By arriving at this point, we have already clarified that we have to deal with a solution containing two kinds of reactive metal cation, Ni2+ and Cu2+. The problem to solve can be rephrased as why we see the reaction product of the reduction of Cu2+ only in one of the electrodes while Ni2+ can be reduced on the other electrode under apparently the same condition (the latter term is that should be later confuted).

For starting the discussion on the identical or non-identical nature of the conditions prevailing at the cathodes of the demonstration experiment, it is time to draw the attention to the processes taking place in a non-equilibrium electrode reaction. The didactic aspects of this view were well rationalized by Faulkner [3]. Namely, transport in the electrolyte solution, adsorption of the reactants, desorption of the products and various chemical reactions either preceding or following the charge transfer process may be necessary to include for a complete process description. In the case of metal deposition, surface diffusion of the atoms produced, their incorporation into the existing lattice and nucleation of new crystals can be added to the set of possible processes. Should we be unaware of the subtle details of the entire process kinetics, a key point of the discussion is that only one kind of species is able to take part in the charge transfer process at the electrode surface; namely, the one that is present thereon. Hence, the transport phenomenon must be taken into account, regardless of all other details.

So far, so good—but how can we rate a transport process? The forthcoming equation might be straightforward for students at the BSc level, but it takes a real effort for high school students to understand. Briefly, we can say that transport is characterized with the amount of material passing through a surface divided by the surface area of the chosen cross-section and by the time we allow for the process. For the sake of simplicity, transport is discussed here as a one-dimensional problem in a Cartesian system where the surface element is chosen to lay perpendicularly to the direction of the material transport. The formulation can be expressed as shown below:

$$J=\frac{1}{A}\frac{\Delta n}{\Delta t}$$
(1)

The meaning of the symbols are conventional (J: transport flux, A: surface area, n: amount of the specific material, t: time). A very important didactic element in the introduction of Eq. (1) is that the amount of the material transported has to be normalized with respect to both the time of the process and the surface area of the cross-section element. This calculation mode makes the flux a fully intensive quantity, i.e. such a one that has the same value when two systems are qualitatively identical. At whichever level of the education, the students will intuitively feel that the transport rate (or, the flux) can be proportional to the concentration difference of the points between which the transport takes place. A more quantitative treatment will be introduced in the next section.

The next point to understand from the demo experiment is that the transport rate at the electrode surface is proportional to the current. Since the amount of a material and the charge needed for its reaction are coupled with Faraday’s law:

$$Q=zFn$$
(2)

with the usual meaning of the parameters (Q: charge, F: Faraday constant, z: electrons taking part in the reaction of the formula unit).

Here, we arrive at the pivotal point of elucidation. If the transport has to be treated as a parameter normalized with respect to the surface area, shouldn’t we treat the current in the same way? Obviously yes! Let’s do it, by introducing current density (j) instead of simply using the current:

$$j=\frac{1}{A}\frac{\Delta Q}{\Delta t}$$
(3)

The analogy between Eqs. (1) and (3) is straightforward. Now, it is obvious that the conditions at the two cathodes in the demo experiment are quite dissimilar from the point of view of the current density (which is the relevant intensive parameter), in spite of the identity of either the current or the overall charge passed through them (that are extensive parameters). However, Eqs. (1) and (3) also mean that the two rates are proportional to each other the same way as Eq. (2) tells. In other words, the transport and the electrodeposition must proceed at identical rates in steady state because they are serial processes.

Is there any transport limitation?

Equation (3) shows how to measure the transport rate but it does not tell us what it depends on. Even at the high school level, we may rely on the intuitive approach of the students that the transport rate of a species is proportional to how abruptly the concentration of the diffusing species varies between the locations that are considered the end points of the transport process. The abruptness of the concentration variation is easy to translate to a gradient:

$$J=-D\frac{\Delta c}{\Delta x}$$
(4)

where the proportionality factor D is the diffusion coefficient.

The surface concentration of a reactive species is decreased as we pass current through the cell, and the level of depletion is a monotonous function of the current density. It is easy to conclude that the depletion level has a limit; namely, when the concentration of the reactive species near the surface decreases to zero. Here, it is likely that we have to resolve the paradox that the relevant chemical species take part in the electrode reaction to the largest extent when “they are not even present” at the surface. The easy solution of the paradox is that the reaction rate is proportional to the transport rate, but the reaction is so favoured that the residence time of the available reactant tends to approach zero. The above train of thoughts illustrates that the concentration difference between the bulk and the surface has an upper limit, which is the bulk concentration of the reactive species itself (c*).

The “abruptness” of the concentration change, however, depends also on the distance over which this difference is observed. The introduction of the nernstian layer helps understand that the concentration decay takes place in a relatively thin layer around the electrode, the thickness of which (dN) is the smaller, the more intensively the bath is agitated (stirred). However, at a particular hydrodynamic condition, this layer thickness is fixed.

With this contemplation, we can combine all the above equations and rewrite them to get the current density for the diffusion-limited conditions (jDL):

$${j}_{\text{DL}}=zFD\frac{c*}{{d}_{\text{N}}},$$
(5)

which means that the larger the concentration, the larger the diffusion-limited current density. The difference in the diffusion coefficients of the two species of interest, Cu2+ and Ni2+, can be neglected here since they are very close to each other in size, weight and composition of the hydration shell.

Figure 3 shows a graphical representation of the problem, illustrating the “concentration profile” of the reactive species in the solution, a concept that is highly important in understanding the diffusion serially coupled with the electrochemical reaction. This figure uses the same bulk concentration ratio as applied in the demonstration experiment, and the concentration decays are proportional to each other. The latter condition means that [c*-c(x)]/[c*-c(0)] = f(x) for both reactants, i.e. the relative depletion of the reactive ions is a function of the distance from the electrode only. This offers also a guideline for how to design such graphs. Even though a well-defined nernstian diffusion layer thickness can be achieved with controlled hydrodynamic conditions only, the approach will prove to be sufficient to discuss the present problem.

Fig. 3
figure 3

Illustration of the concentration profiles near the cathode in steady state. The bulk concentration ratio of the reactant is the same as in the bath used for the demonstration experiment. The concentration gradient ratio of the Cu2+ and Ni2+ species is 1:3. Copper deposition takes place at the diffusion-limited rate

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Figure 3 depicts the situation in which the Cu deposition takes place at a diffusion-limited rate as c(Cu2+) tends to approach zero near the electrode surface. However, Ni deposition is by far not diffusion-limited, although the concentration profile curve has a much larger slope, which is a consequence of the concentration ratio chosen.

How does the system select which reaction is to take place?

If several electrochemical reactions are possible at an electrode, the typical answer of the students is that “the process requiring the smallest energy will take place first”. For a moment, let us disregard the difficulty that the typical manner of speaking of students refers to temporal terms, in spite of the fact that a steady-state process is to be elucidated (the aspects of this contemplation issue will be discussed later). When the reactions of interest are cathode processes, the condition of smallest energy requirement means that one has to choose the process that has the least negative onset potential. In excess of discussing the standard potentials of the Cu2+/Cu and the Ni2+/Ni systems, it is practical to show the polarization curve of the test solution, too. This can be seen in Fig. 4.

Fig. 4
figure 4

Linear sweep voltammograms obtained for the thin Cu and thick Ni cathodes. Sweep rate: 2 mV s−1, sweep direction: from positive to negative potentials. The range between the dashed lines shows the current range that is suitable to run the demonstration experiment

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As the potentiodynamic curves in Fig. 4 show, there is a slight current rise between about 0 and − 0.05 V that refers to the formation of Cu(I) species. This is followed by the nucleation of Cu on the cathode surface which is indicated by the steep current rise. The current shows then a peak that is quite common for sweep methods and indicates the transition from activation to mass transport control. The plateau between − 0.3 and − 0.70 V corresponds solely to diffusion-controlled Cu deposition. In electroplating experiments, the diffusion-limited current density is usually not as stable as for solute reactants because of the increase in the cathode roughness. This can be seen in Fig. 4, too, where the change in the surface quality explains the slightly rising current at potentials where the only reaction is the deposition of copper. The ascending section of the polarization curve till − 0.80 V indicates the occurrence of a side reaction, which is the evolution of hydrogen. The onset potential of the deposition of Ni is about − 0.82 V. For the sake of completeness, both the current efficiency and the deposit composition as a function of the cathode potential are summarized in Table 1.

Table 1 Composition of the deposits obtained at various electrode potentials and the current efficiency as measured with a gravimetric analysis. The expected deposit weight gain was determined as Δm = (Q/zF)M, where M is a weighted average of the molar weight of the alloy components calculated from the actual composition
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The polarization curves can ease the understanding of the cell voltages recorded during the demonstration experiment. The cell voltage higher than + 1 V for the Cu deposition would clearly be impossible if we assume a reversible Ni dissolution at the anode. If it were so, the cell voltage should be negative. However, if the anodic process is either a transpassive dissolution or oxygen evolution, the value of the cell voltage becomes readily understandable. In contrast, we can here refer to the well-known Daniell cell, in which Cu is deposited on the positive electrode if the spontaneous process takes place (unlike in our demonstration experiment which requires an external power source and the Cu deposition proceeds at the negative electrode).

Although it is not very well known even among electrochemists who do not deal with metal plating, the polarization curves shown in Fig. 4 are a prominent example for regular codeposition. The term was introduced by Brenner whose book on alloy codeposition was a milestone in the English literature on metal plating [27]. Shortly, regular codeposition means that the constituents retain their properties in the sense that the order of nobility as elucidated from the standard potentials of the corresponding redox pairs prevails also during the deposition. For regular codeposition, one may regard the process as if the metal–metal atomic interactions were the same, regardless of the environment of the atom of interest, which leads to essentially no additional preference in the deposition but the electrode potential. For metal pairs undergoing regular codeposition, the composition of the alloy formed is directly related to the transport of the metal ions if the electric current is the controlled parameter. As long as the supply of the more noble metal ions is sufficient, this element is deposited alone, while the less noble element is codeposited to the extent of the “excess” current that cannot be used for the deposition of the more noble element due to transport limitations. The above-described situation is visualized in Fig. 5. It is also shown which relation of the actual current density to the diffusion-limited Cu deposition rate can lead to either Cu or alloy deposition. The larger is the filling ratio of the arrow related to the maximum transport rate, the more the electrodeposition process controlled by the mass transport.

Fig. 5
figure 5

Graphical representation of the serial and parallel processes during the two cases shown in the demonstration experiment. Arrows at the transport steps indicate the maximum transport rate of the corresponding ion. The surface area of the arrows here is proportional to the solution concentrations in the demonstration experiment and inversely proportional to the relative hindrance of the ion transport. The filling ratio of the arrows indicates how the actual current is related to the diffusion-limited current. Fully filled arrows at the charge transfer step are proportional in surface area to the actual partial current density of the reduction of each metal

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In order to evidence that the current density is the decisive factor in the composition of the deposit as opposed to the current itself, it is worthwhile of repeating the original experiment with a slight modification. For the cathode of 15-mm diameter, a current of about 90 mA will lead to a uniform silverish deposit (Ni-rich alloy). Also, if we decrease the current down to 3 mA, the smaller electrode will be covered by pure Cu. For these control experiments, we can apply the metal rods previously used, and the test are recommended to perform separately (i.e. not with cells connected in serial, unlike in the original experiment).

Many textbook examples take regular codeposition as the only means of electrolytic alloy formation. It must be stressed that this is not true. For instance, the element of the iron group metals with zinc undergo anomalous codeposition, and the less noble element is usually much overplated as compared to the expectation as derived from the concentration ratio of the precursor ions.

What is the desired deposit thickness? How fast is the steady state achieved?

The desired deposit thickness in the demonstration experiment is determined by several factors. First, the coating with a colour dissimilar to the substrate should be thick enough so that the original surface is covered with a non-transparent layer. For this goal, a coating of 1–2 µm in thickness is sufficient. For very thick deposits (> 10 µm), the roughening of the deposit may become significant [28], which destroys the visual impression.

However, the optimal visual appearance is not the sole factor that impacts the desired deposit thickness. The steady-state concentration profile of the precursor ions as shown in Fig. 3 does not set in instantaneously. Hence, one has to count with an initial transient that is required for the depletion of the cathode vicinity with respect to the Cu2+ ions and for the onset of Ni codeposition. During this transient period, solely the deposition of pure Cu takes place, and all other processes set in thereafter only. There is ample evidence for the accumulation of the preferentially deposited alloy component in the near-cathode region for various metal pairs and triplets [29,30,31,32]. This is the consequence of the change in the partial current densities with time as the near-cathode solution layer gets depleted first with respect of the preferentially deposited alloy component.

Therefore, the typical manner of speaking heard from students proves to be right in that the process taking place first is the one that requires less energy. However, we have to remember that this is merely the consequence of the current control applied (where the overall process rate is fixed). If we use potentiostatic deposition, we set the “energy” of the electrons (or, rather, their electrochemical potential). By choosing a cathode potential where Ni deposition is also possible, the ratio of the rates of the metal deposition processes may vary in time, but the metal deposition processes themselves are not separated in time.

The forthcoming experiments can be shown even at the high school level, but the corresponding quantitative analysis is recommended at the undergraduate level only. If the experiment is carried out in galvanostatic mode, the transient from Cu to Cu–Ni alloy deposition can be followed with chronopotentiometric measurements, which is presented in Fig. 6. The curves shown were measured with the following protocol: A cell with a cathode fixed with an O-ring at the bottom side was used. A potentiodynamic curve was recorded in the same cell in order to observe the diffusion-limited current density around − 0.4 V vs. SCE (jDL ≈ − 0.75 mA), and then the current values to be applied were chosen as a bit lower and significantly larger than this value.

Fig. 6
figure 6

Chronopotentiometric measurements for the electrodeposition experiments by using the citrate bath. Numbers shown in the graph indicates the ratio of the actual current applied to the minimum of the potentiodynamic curve observed around − 0.4 V vs. SCE in the same cell. The inset shows the inverse square root of the transition time (inflexion point of the chronopotentiometric curves) as a function of the current applied

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As the chronopotentiometric curves show, the cathode potential is around − 0.2 V if the actual current is lower than the diffusion-limited one. Once the latter value is exceeded, the potential becomes significantly more negative as the cathode vicinity becomes depleted with respect to the Cu2+ ions but does not reach the onset of the Ni deposition for quite a while. This is the clear indication for that the hydrogen evolution precedes the Ni deposition, as it is also seen in the potentiodyanamic curves between − 0.4 and − 0.8 V (see also the quantitative data in Table 1). The large fluctuation at the j/jDL = 1.13 ratio is due to the spontaneous convection caused by the hydrogen evolution accompanying the Cu deposition. By increasing the j/jDL ratio further, a short secondary step can still be observed in the chronopotentiometric curves due to the hydrogen evolution, but the electrode potential finally exceeds the onset potential of the Ni deposition.

The chronopotentiometric curves are suitable to calculate the diffusion coefficient of the Cu2+ ions. By applying the Sand equation:

$$\frac{I{t}^{1/2}}{c*}=\frac{zFA}{2}{(D\pi )}^{1/2}$$
(6)

D is obtained as 6.5 × 10−11 m2/s. This value is nearly an order of magnitude lower than the diffusivity of Cu2+ ions without any complexing agent [33, 34]. The deviation is due to the presence of citrate ions that change the speciation and hence hinder the transport of the metal ions.

How important is the cell geometry?

The cell arrangement in the original demonstration experiment is quite symmetric and the coatings on both the thick and thin rods appear to be homogeneous even at the bottom of the rods, which part of the cathode does not face the anode. Let us modify the experiment a bit along with the following guideline. Put the 15-mm diameter Ni cathode to an off-axial position so that the closest edge to the anode is about 5 mm apart, while the largest anode–cathode distance at the edge across is some 6 times more (Fig. 7a). Definitely mark the cathode so that the near-anode side can be easily identified when the experiment is accomplished. Obviously, the current distribution will now be uneven. Set the current to 26 mA and run the experiment again for 5 min, and meanwhile, ask the audience about the expectation. The standard answer for the problem is that the closer the surface, the smaller the solution resistance, and hence, the majority of the current will pass through this pathway. In other words, the local current density will be the larger, the smaller the interelectrode distance. The latter answer can be expected at the undergraduate level, while high school student are typically not able to phrase the conclusion with the same precision by using the intensive quantities. Here, it is appropriate to introduce a quite simplified equivalent circuit applicable for the steady state that includes three resistors, two for the charge transfer at the anode and the cathode and one for the solution resistance. The knowledge of even the undergraduate students usually accounts for the solution resistance only, even though the full current distribution is determined by all contributions together (the limiting case of the current distribution when the charge transfer resistances tend to approach zero is often termed as the primary current distribution).

Fig. 7
figure 7

a Top view of the off-axial electrode arrangement with the thick Ni cathode. b Side view of the cathode after the plating experiment. The boundary of the Cu-rich zone is diagonal. The blue strip indicates the insulator and the pink arrow is the side indicator that corresponds to the same mark in Fig. 7a. c Cell arrangement with a truncated anode

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Concerning the consequence of the uneven current density on the local composition, students are usually uncertain at the beginning. By following the message of the first demonstration experiment, a few of them may answer that the increase of the local current density leads to the increase of the contribution of Ni deposition to the total current, which may lead to an uneven deposit composition. If they answer at all, the hint exclusively is that the side of the cathode in the close vicinity of the anode will hence be more Ni-rich than the other.

The next surprise comes when we stop the experiment with the asymmetric electrode configuration and show the result to the audience. As Fig. 7b shows, strangely, the near-anode side and the bottom of the Ni rod are reddish, indicating a Cu-rich deposit, but the other side is not. The first impression is that the impact of the uneven current distribution is exactly the opposite what we deduced from the earlier experiment (i.e. that a Ni enrichment is anticipated as the current density increases). Again, we encounter a paradox to resolve.

The solution of the asymmetry-related paradox lies in the behaviour of the Ni anode. As it was explained at the discussion of the lack of the cementation process, the Ni anode is passive. This also means that the anode reaction is by far not only the Ni dissolution. In other words, Ni does not behave as a purely sacrificial anode, as one might expect from the nernstian potential of the Ni2+/Ni system. In contrast, the Ni anode is partly inert, and one of the parallel anode reactions is the decomposition of the solvent (oxygen evolution). As a weight loss measurement related to long-term electrolysis showed, the current efficiency of Ni dissolution at the anode is about 50% only. This means that the density of the solution in the small gap between the anode and the cathode decreases during the electrolysis, first because of the reduction of the metal ion at the cathode and secondly (also dominantly) because of the gas evolution at the anode. This gives rise to a buoyancy effect, and the gravitation instability induces an upward solution stream in the gap. Therefore, the convection in the small interelectrode gap is fundamentally different from the one at the other size of the cathode. Even though the current density effect would rationalize the deposition of a nickel-rich layer, the fresh solution supply counterbalances it, and the two competing impacts result in the unexpected outcome, i.e. the deposition of a reddish Cu-rich layer. The explanation of this effect has a high didactic value, shedding light to the role of all parts of the cell and their operation altogether, not only a selected part of the cell (like one of the electrodes).

Additional aspects of the cell geometry can be explained with two more experiments. Change in the configuration presented in Fig. 7a by replacing the Ni anode with a Cu foil and pass 26 mA current. Copper dissolves actively in the test solution (Cu is a sacrificial anode), yielding an anodic current efficiency of about 105%. The latter data was calculated with the assumption that only Cu2+ ions can form, but the abnormally large current efficiency indicates that Cu+ ions are also produced. In spite of the fact that the dissolution of the Cu anode leads to a Cu2+ supply near the cathode, the side of the Ni rod will be plated with a deposit of similar colour than the other side, simply because the electrolysis time is too short for the diffusion/migration of the cupric ions to the cathode. Only the bottom of the thick cathode rod will be copper-rich due to the uneven current distribution. Another interesting aspect of the experiment with the Cu anode is that the cell voltage is much lower than with the Ni anode, even though the Nernst potentials of the reversible systems suggest just the opposite. This is the consequence that the passive Ni anode is replaced with a reversibly working Cu anode.

If we start from the original cell arrangement and replace the annular Ni anode with a much narrower anode strip as shown in Fig. 7c, we arrive at the situation that the impact of the higher current density at the near-anode side manifests itself by the change in the deposit colour from red to silver, in accord with its higher Ni content. Should it look surprising, the appearance of the cathode bar in this experiment will be nearly the same as shown in Fig. 7b.

Why do we use an unstable bath for the demonstration experiment?

As reusability and long-term stability are key issues in the recent environmentalist contemplation, the question arises naturally why an instable bath is recommended for the demonstration experiment. The answer is simple: This is what works. Should you try the same experiments with a Watts-type bath doped with a Cu salt, the deposit will never be silverish but turns black, even though the Ni deposit from the Watts bath is shiny. A bath based on nickel sulfamate is a wrong choice again since the Ni–Cu alloys plated from such baths exhibit a matte finish with visibly alternating Ni-rich and Cu-rich parts. In other words, there is a hindrance in the atomic-scale miscibility, despite the phase diagram suggests just the opposite! The same tendency of segregation was mentioned in several works dealing with codeposition of Cu and Ni from sulfate baths [35,36,37,38,39]. It is not because of negligence that citrate baths [25, 26] or glycine baths [40] were used in several recent works where the goal was the production of homogeneous electroplated Ni–Cu alloys. The formation of homogeneous alloys was clearly evidenced for the glycine bath, demonstrating also the prevalence of the Vegard law.

The discussion of the solution composition yields an opportunity to teach the role of complexing agents and additives in the electrodeposition process. The general trend is that alloying can be facilitated if the ions of the metal with more positive deposition potential are complexed so that the deposition potentials of the alloying elements are brought closer to each other. As the spectrophotometric analysis showed (see Fig. 2b), complexation of the Cu2+ does take place, but the deposition potentials of the two metals, Cu and Ni, are much apart (see Fig. 4). Nevertheless, the citrate bath tends to yield homogeneous deposits. The key factor is the additive effect of the citrate ions that promotes alloying. The classification of additives can be found in the work of Oniciu and Muresan [41]. The simultaneous effect of the additives and the current density can be discussed on the basis of two-dimensional representation of the inhibition and that of the current density on the basis suggested by Winand [42, 43] and later re-elaborated in various forms in several works [44, 45].

An additional materials science aspect: how reliable is the colour for the composition estimation?

It is well known that only two of the metallic elements are coloured: copper and gold. The occurrence of the colour comes from the reflectance properties of these two metals: They both absorb some portion of the blue light, which gives rise to their appearance with the complementary colour. The discussion of such properties drives us to the fields of atomic physics. The origin of the colour is the [X](n-1)d9ns2 electron configuration of the coloured metals (where [X] is the electron configuration of the preceding noble gas atom). The absorption capability of Cu and Au stems from the interesting interplay of the atomic size, ionization energy and the electron configuration, allowing the excitation of the electrons between the (n-1)d9ns2 ↔ (n-1)d10ns1 energy levels [46, 47]. The corresponding excitation energy is 2.7 eV for Cu and 1.9 eV for Au, while the larger atomic size shifts the same difference to 4.8 eV for Ag, making it colourless. The visual appearance of gold alloys exhibits topmost importance in the jewellery industry; hence, binary or even ternary composition–colour diagrams for Au-based alloys are available [48].

For the Cu–Ni system, no detailed assessment of the colour as a function of the composition is known to the author. However, it is commonly known from the colour of commercial alloys containing Cu and Ni that below 40 at.% Cu content (1/2.5 part), the colour of the alloy cannot be distinguished from pure nickel with naked eye. In order to make our demonstration experiment fully safe, the surface area ratio of the thin and thick cathode rods makes it possible to produce an even more dilute Cu alloy on the thinner electrode (< 30 at.% Cu, ~ 1/3.5 part). This threshold is recommended for the unambiguous result that is easy to observe and elucidate for the audience.

Summary

The present work explains the use of an electrodeposition experiment in an experience- and problem-based education process. Electrodeposition seldom occurs in the tool kit of the demonstration experiments. Additionally, the arrangement presented above is rather unique in the sense that two parallel processes can take place in the experiment, which allows to elucidate a relatively complicated phenomenon. The experiments arranged around a single problem helps to teach the following aspects of physical chemistry: electrode properties, electrode classification based on the direction of the current, electrodeposition, polarization curve, cell voltage, passivity, current distribution on electrodes, serial and parallel processes in electrochemistry, role of the transport, nernstian diffusion layer, transient and steady state, and Sand equation. In excess of the related physico-chemical phenomena, the experiment yields an opportunity to mention various materials science aspects such as the application of additives in electrodeposition and the colour of the alloys. The experiment is suitable at both the high school and undergraduate levels with a little difference in the depth of explanation.