Oxygen evolution (EO) from water in heterogeneous photocatalyses is one of the most significant chemical reactions. It has been believed that number of electrons in this multielectron-transfer (MET) process is four with standard electrode potential (SEP) 1.23 V (vs SHE), but there seems to be no effective method to determine the number for any OE reactions, not limited to photocatalysis, except for electrolytic OE in which its electrode potential might suggest n_et. Here we present the light intensity-dependent kinetics of titanium(IV) oxide (titania)-photocatalyzed OE and show, for the first time for non-electrochemical METs, n_et depending on the titania photocatalysts and reaction conditions. This also suggests that MET kinetics depends digitally on its thermodynamics, i.e. possible SEPs, as a novel concept, to result in the appearance of "singularity" in chemical kinetics. Digitally controlled kinetics is important to clarify the true mechanism and to design, for example, highly efficient photocatalytic artificial photosynthetic systems.

Highly intense 365-nm UV-LEDs (NS Lighting ULEDN-101 (NSL) and Hamamatsu Photonics L11921-400 (HMP)) were used in this study. The maximum power of focused NSL light beams and that of unfocused HMP light beams from those LEDs measured by a Hioki 3664 power meter with a 9742 optical sensor through a 1 cm-square aperture in front of a rectangular quartz cell were ca. 340 mW and 500 mW, respectively. Light intensities were adjusted by changing the LED-cell distance or source power. Those maximum intensities were more than one-order of magnitude higher than those of UV light from ordinary mercury or xenon arc lamps (ca. several tens of mW cm^-2). Commercial titania powder (30 mg) was suspended in aqueous 0.05 mol-L^–1 sodium iodate (pH 10) or iron(III) chloride (pH ca. 2) solution (3.0 mL) in a quartz cell. Air was purged off from the head space by argon, and the cell was tightly sealed with a rubber septum. UV irradiation on such titania suspensions containing strong electron acceptors (EAs), as photoexcited-electron scavengers, induced OE, and the observed OE rate (R_a/µmol h^–1) was measured by gas chromatography.

Figure 1 shows the I_L-dependent OE rate (r) for suspensions of two sets of anatase and rutile titania samples, including small anatase ("SA"; 4 nm), small rutile ("SR"; 13 nm), large anatase ("LA"; 170 nm) and large rutile ("LR"; 360 nm), using iodate (IO₃^–) as an EA. Although all of the samples except for LR showed an almost linear correlation, i.e., r was almost proportional to I_L, at the middle I_L region (0.5 < I_L < 2), plots for small particles (SA and SR) at the lower I_L region seemed to be deviated downward from the straight lines. From the simulation curves of double logarithmic LID, the order of LID for SA and SR can be presumed to be 2 at the lower limit of I_L and the order was gradually decreased to 1. In addition to this bimodal "spoon-like" behavior, r for SA showed a sudden increase, i.e., singularity, at ca. 2.3 W cm^-2, and the order seemed to be suddenly changed from 1 to 4, i.e., "singularity" was observed . To the best of the authors’ knowledge, this is the first report of such higher-order LIDs for photoreaction induced by ordinary (non laser) continuous-light irradiation. The former second-order LIDs were also observed when iron(III) (Fe³⁺) was used as an EA with threshold I_L (I_thr), at which the LID order is changed from 2 to 1, higher than that for IO₃^–, though fourth-order LID could not be observed even for SR (One of the possible reasons for SR not showing a fourth-order LID even at higher I_L is shorter lifetime of one positive-hole bearing particle (t₁) which is presumed from the I_thr of SR being higher than that of SA for IO₃^– EA as discussed later. Therefore, at further higher I_L, fourth-order LID may be observed.). The reactions of those EAs are assumed to be one-electron and six-electron processes as: Fe³⁺ + e^– = Fe²⁺ and IO₃^– + 3H₂O + 6e^– = 6OH^– + I^–, but bimodal (second-to-first order) LIDs were commonly observed, suggesting that the hole-transfer (oxidation) step, i.e, OE from water (See SI.), is attributable to the bimodal LIDs.

The observed multimodal (unimodal) LIDs can be interpreted using a model in which the number of accumulated positive holes in each photocatalyst particle is counted, taking the individual action of each particle into account. The detailed mechanism and effect of particle size in this OE reactions are discussed.