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, where Prad, Pchem, and Pout are radiation power density of source (139.238 μW/cm2), chemical power density in water, and, output power density of device (75.02 μW/cm2), respectively. One possible reason for the high output power density under irradiation is that a certain level of the EHP ionisation energy of beta particles can easily excite electrons because the EHP ionisation energy is much higher than the band gap of each material while a large portion of the spectrum of solar light is below the TiO2 band gap, indicating that the TiO2 layer does not absorb sunlight well. Therefore, beta particles are a reliable energy source for electricity generation via water splitting..jpg)
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, ·OH, H·, HO2·, H3O+, OH−, H2O2, H2. High levels of these products are formed by the absorption of 100 eV in the medium. The generated radicals are powerful redox reagents, i.e., eaq− is a strong reducing agent, H· is an equally strong reducing and oxidising agent, and ·OH is a powerful oxidising agent. In water at high pH, eaq− and ·OH are produced in the largest quantities by the beta radiation. The standard potentials of eaq− and ·OH are E0 (H2O/eaq−) = −2.9 VNHE and E0 (·OH/H2O) = +2.7 VNHE, respectively. These two species (eaq− and ·OH) react with water molecules during water radiolysis and then remain in the aqueous solution. They can then no longer react with each other or with surrounding water molecules. Once these two species (eaq−and ·OH) are solvated in an aqueous solution, they can be surrounded by water molecules in a meta-stable state for a few μs. It is well known that water has a very large dielectric constant and consists of polar molecules, which prevent the electrostatic attraction between positive and negative charges and maintain the separated state of charges surrounded by oppositely charged ends of water dipoles. During the long lifetime of solvated electrons, beta radiation will continuously increase the number of solvated electrons in the water until they finally move to the surface of the water, where they are emitted as thermal energy. The floated electrons form the negatively charged surface of water. Theoretically, water has lower standard potential (E0 (H2O/O2) = +0.82 VNHEand E0 (H2O/H2) = −0.41 VNHE) than free radicals, indicating that electrochemical energy of water is lower than that of free radicals. It was also reported that high electrochemical energy of solvated electrons (eaq−) can enable difficult chemical reactions to happen. Moreover, the presence of an external electric field or electromagnetic field can release the solvated electrons from their confined environment of surrounding molecules. This is because eaq− in water has very small diffusion efficiency (4.8 × 10−5 cm2/s) and electron mobility (1.84 × 10−3 cm2/V·s). Solvated electrons in water also need to get over the potential barrier of 0.2 ~ 0.5 eV set by the surrounding rigid water molecule network. Moreover, because water is located between both Pt electrodes (plasmonic layer and counter electrode), if same electrochemical reactions occur on both Pt surfaces, simply no current flow is expected.
, where e is the electronic charge, vis the electron velocity, (x0, y0) represents the position of the focused electron beam, z is the direction of the electron velocity, and ûz is the unit vector along the z direction. In the simulation, the current density was modelled as a series of dipoles with a temporal phase delay (z/v) related to the electron velocity, v (in this simulation, v = 0.875c, corresponding to the beta particle's kinetic energy of 546 keV used in the experiment, and c is the velocity of light in free space). We conducted our simulations for three different points denoted 1–3 in the middle of a pore, at the side wall of a pore, and between two pores, as depicted in the figure..jpg)
, where k ( = k′ + ik″), ω and c are the wave number and the frequency of the wave, the speed of light, respectively. For k′ not to be purely imaginary, ε′1 = (n12 − κ12) < 0 and |ε′1| > ε′2 = (n22 − κ22). Based on this relationship, we have plotted a graph shown in Fig. S7. Since the surface plasmon energy occurs around |ε′1| ≈ ε′2, the surface plasmon wavelengths can be found from crossing points on the Pt line (black line). Compared to the water/Pt (green/black) interface, the air/Pt (blue/black) interface shows the surface plasmon phenomena at a slightly shorter wavelength. These wavelengths at the crossing points (red and green dots) of water/Pt and air/Pt in Fig. S7 are very close to the wavelengths at the strongest reflection peaks (red and green dots) as marked 1 and 4 in Figure 5b. Furthermore, the surface plasmon energy at the Pt/TiO2 interface is consistent with a dip (blue dot) near 450 nm. Therefore, matched data from the emission peak shown at mark 4 in Fig. 5b and the green dot shown in Fig. S7 indicate evidence of plasmon resonant coupling in air/Pt nanoholes under e-beam irradiation. There are only very small amounts of variation among the two layer calculation data (Fig. S7), the multi layer simulation results (Fig. 5b-1 ~ 3) and the experimental data (Fig. 5b-4). In addition, as shown in the electron profiles in Figs. 5c–h, the highest electric field intensities can trace electron irradiation paths (electric dipoles), and simultaneously, the electric field intensities in the Pt/nanoporous TiO2 structures are also strengthened near the electron irradiation paths by surface plasmons generated at the Pt nanoholes..jpg)
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