e Oxalic Acid
Independent of the anodization mode, if either potentiostatic or galvanostatic, in the steady state both i and V should be constant over the process time t, as for ionic conduction it is i ~ eαV, with α an appropriate constant [5, 14]. However, V(t) is linearly increasing in Fig. 1a after the initial transients, with different rates increasing in turn with J. This behavior shows that we were not in a condition of equilibrium for the different anodization reactions. The reason can be that in our setup immersion of the EL beaker in the cooling bath was not compatible with stirring onto a magnetic plate. Therefore, a local depletion of ions in the EL close to the anode, along with formation of a stable ion concentration gradient, can have occurred over time, which leads to a progressive increase in V in order for the power supply to keep J constant.
The h values obtained at tend = 30 min as a result of the corresponding anodizations have been plotted in Fig. 1b. If the same current efficiency of the process was maintained in all the anodizations and for all the process time period, a linear relationship between J and h was expected [5, 22]. However, after the initial increase in h with increasing J a tendency to saturation is observed in Fig. 1b. Obviously, a progressive reduction of the current efficiency has occurred, probably due to the appearance of side reactions different from the anodization ones .
Actually, side reactions can also occasionally lead to catastrophic events, such as shown in Fig. 1a for the curve at J = 200 mA/cm2. In that case after reaching a critical value Vcrit ~ 95 V in tcrit ~ 12 min, V started to decrease with some fluctuations, and finally increased up to the maximum power supply voltage. The reason for the latter increase was that the Al foil was cut at the air–EL meniscus, and the piece of anode dipped in the EL fell on the bottom of the beaker, opening the circuit. The APA thickness measured for this sample was hcrit = 11 μm, such that the respective critical electric field was Ecrit = Vcrit/hcrit ~ 8.6 MV/m. This is ~36% lower than the dielectric strength of compact alumina, Ebreak = 13.4 MV/m . Whereas this could be partly due to the porous nature of our alumina, we do not think that the origin of this behavior is the dielectric breakdown of the oxide due to the high V reached. Instead, we assign the discontinuity in the curve to a temperature activated fast etching of the Al at the air–EL meniscus, where on fluctuations of the interface the bare Al can locally come into contact with the EL. In fact, when using a 10-fold diluted oxalic acid we could reach a Vcrit ~ 160 V before that any similar catastrophic event occurred, with a respective hcrit ~ 13 μm, which gives Ecrit ~ 12.3 MV/m, much closer to Ebreak. Furthermore, in the latter case, the final steep change of voltage was toward the zero (closed circuit with virtually no resistance), and there was no anode resection of the air–EL meniscus.
The limited improvement inh obtained in the considered time periodtendon increasingJ in bare oxalic acid resulted in a maximum (non-linear) mean growth ratevgmax = hcrit/tcrit ~ 0.83 μm/min (obtained forJ = 200 mA/cm2).
All the quantities in Fig. 2a have been plotted versus the anodization current density J. One can see that dout is approximately constant within the errors, as expected, since it should depend only on the type of EL and on its concentration. The weak increase actually observed can be due to a local rise of the EL temperature and thus of the oxide dissolution rate, probably occurring during anodization. On the contrary, Dout is clearly increasing with J. Indeed, Dout should increase with V [5, 14, 17], and our V(t) curves in Fig. 1a showed a V that increased during each anodization. As a consequence, the roughness is almost constant for the higher J values (i.e., the larger Dout), whereas it is significantly depressed for the lowest J (i.e., the smallest Dout). We attribute this effect to the spatial “low-pass” characteristic of the AFM probe tip, which can hardly penet