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Li et al Dovepress assumed that the reaction occurs in accordance with the Nernst response at the anode and the cathode. We located the anode and the cathode at x = 0 and w, respectively, as illustrated in Figure 5. The detailed derivation is described in the Supplementary materials. The dimensionless current- voltage curves represented by Equation S8 vary with the parameter b. Figure 6 shows variation of the dimensionless current-voltage curves for several values of c+*/cH2*. Large values of (2F/RT)∆E in Equation S8 correspond to the domain of the limiting current, which is equivalent to infini- tesimally small values of (2 – f)(b – f). When f increases from zero, Equation S8 tends to infinity at a smaller value of either 2 or b. Therefore, we have the limiting current, f = 2 for b .2 and f = b for b ,2. Since Equation S9 becomes b = 1.9 c+*/cH2* for D+ = 8.7 × 10−5 cm2 s−1 and DH2 = 4.6 × 10−5 cm2 s−1,41 the condi- tion b .2 corresponds approximately to c+*.cH2*, for which f = 2. Consequently the limiting current is expressed by j =4Fc* D /w forb2 or c* c* lim H2H2 +H2(1) j =2Fc*D /w forb2 or c* c* lim ++ +H2 The “4” involved in Equation 1 arises from both the two- electron oxidation and the accumulation of H2 on the cathode by the reduction of H+ at the cathode so that (cH2)x=0 = 2cH2*, as can be illustrated in Figure 5. Although Equation 1 mentions that the limiting current for c+*,cH2* is proportional to c+*, the experimental results in Figure 3 showed the lower deviation from the proportional 2 1 00 (e) (d) 0.1 ∆E/V (c) (b) (a) 0.2 0.3 cH2 + c+ c+ cH2 2cH2 0wx Figure 6 Current-voltage curves calculated from Equation S8 at c+*/ch2* = (a) 0.2, (b) 0.6, (c) 1.0, (d) 2.0 and (e) 5.0. Notes: The dashed lines are tangents of curves at ∆E=0.25 V. Abbreviations: ∆E, the applied voltage; jw/2Fch2*Dh2, dimensionless current line for c+* .0.3 mM. When c+* is close to cH2* in Figure 6, (a)→(c), a plateau of the limiting current becomes vague. In fact, the slopes (dashed lines (a) and (c) in Figure 6) of the limiting currents increase with an increase in c+*. Experimen- tal values of the limiting currents may be underestimated. The slope of the proportional line in Figure 3 is 90 mA M−1, whereas the theoretical value calculated from Equation S8 is 110 mA M−1. If w is corrected to w + 10 μm for the roundness of the electrode surface, the theoretical slope is 93 mA M−1, which is close to the experimental value. Redox cycling might occur also for O2 + 2H2O + 4e− ↔ 4OH−. We attempted to perform voltammetry for dioxygen and sodium hydroxide instead of H2 and HCl. The voltammograms in the thin layer cell did not show any limiting current, but were similar to those of pure water.12 The disappearance of limiting current may be ascribed to such a large overpotential difference between the cathodic and the anodic reaction of dioxygen that it may overlap with the wave of water decomposition. Redox cycling in the absence of h+ Figure 7 shows voltammograms of water including only hydrogen gas for various values of w, demonstrating appear- ance of the limiting current plateau for ∆E .0.4 V. Since the solution has no ions, the solution resistance should be very large. Nevertheless, the limiting current was observed. This is an advantage of the thin layer cell voltammetry. Equation 1 mentions that limiting current by the redox cycling in solution without deliberate addition of hydrogen ionshouldbe93mAM−1 ×10−7 M=9nAatpH7.However, the observed voltammetric shape and current values are extremely different from the theoretical ones. Specifically, Reports in Electrochemistry 2013:3 Figure 5 Model of thin layer cell and predicted concentration profiles. Abbreviations: x, distance from the anode toward the cathode; ch2, concentration of hydrogen gas; C+, concentration of hydrogen ion. Powered by TCPDF (www.tcpdf.org) 10 submit your manuscript | www.dovepress.com Dovepress jw/2FcH2* DH2PDF Image | Salt-free electrolysis of water facilitated by hydrogen gas
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