2.1. Experimental methods
PBNPs were synthesized by mixing potassium hexacyanoferrate (II) (5 mmol, K4[Fe(CN)6]·3H2O, KANTO CHEMICAL) with Fe(III) nitrate (10 mmol, Fe(NO3)·9H2O, WAKO) in aqueous solution. PB precipitates thus formed were rinsed with ultrapure water after centrifugation (3000 rpm), which was performed for five times. Thereafter, PBNPs were dried at 75°C for 12 h and thereafter kept in the vacuum desiccator for 3 h.
Sorption test of PGMs/Mo ion (1 mM) for PBNPs (500 mg) were carried out in 1.5 M nitric acid solution (10 mL) upon shaking for 24 h. Subsequently, the mixtures were centrifuged to separate the PBNPs from the solution, and the concentration (C) of PGMs/Mo ion in the supernatant liquid was measured before (Cinitial) and after (Cfinal) the test, using ICP-AES (ICPE-9000, SHIMADZU), in order to estimate the sorption efficiency, [(Cinitial – Cfinal)/Cinitial × 10 %], of PGMs/Mo ions into PBNPs. We also measured the concentration of Fe ion in the supernatant liquid after the sorption test, and estimated the elution efficiency of Fe ion when compared to the initial amount of PBNPs. Details of sorption test conditions have been described elsewhere.25
Powder XRD patterns and UV-vis-NIR diffuse reflectance spectra of the pristine and PGMs/Mo-sorbed PBNPs were measured using Rigaku RINT2200 (Cu Ka) and Shimazu UV-2600 spectrometer, respectively. The diffuse reflectance spectra thus obtained were converted to the corresponding absorption spectra in terms of the Kubelka-Munk conversion equation.
2.2. Theoretical methods
Theoretical absorption spectra of the pristine and PGMs/Mo-sorbed PBs were obtained using the relativistic configuration interaction (CI) method,26,27 because the present method has been already confirmed to reproduce the experimental absorption spectra of Fe, Co, and Ni ferrocyanides quantitatively, using Fe(II)M(III)(CN–)116– (M = Fe, Co, Ni) cluster model.28 The multiplet energy levels and absorption spectra were calculated using Fe2+Fe3+(CN–)116–, MFe3+(CN–)116–, and Fe2+M(CN–)116– cluster models (M = Mo6+, Ru4+, Rh3+, Pd2+) [see Fig. 1], respectively, for the pristine and PGMs/Mo-sorbed PBNPs. Here, when the PBNPs are applied to the disposal of HLLW in a strong nitric acid solution (2–8 M), the present calculations were performed using an oxidation ionic valence of 6+, 4+, 3+, and 2+ for Mo, Ru, Rh, and Pd, respectively. The choice of the valence values for these ions is reasonable, because the valence of each ion in the nitric acid solution has been already clarified experimentally.29–33 The structural parameters of these cluster models were determined from the optimized structures obtained using density functional theory (DFT) calculations. Details of the CI calculation method were described elsewhere.26,27 As the active space for the CI calculations, all the electronic configurations of the d-d transitions for Fe and PGMs/Mo ions were explicitly treated. On the other hand, the electronic configurations for the charge transfer (CT) transitions from Fe2+/M to M were considered up to two electron excitations. The oscillator strength of the electric dipole transitions averaged over all directions was obtained using the general equation expressing the electric dipole transition. Theoretical absorption spectra were obtained by convolution of the oscillator strength replaced with a 0.30 eV full-width-at-half-maximum (FWHM) Gaussian function.
The surface adsorption, diffusion, and substitution energies of PGMs/Mo ions when incorporated into PBNPs were estimated using the CASTEP34 and QUANTUM-ESPRESSO35,36 based on DFT.37,38 We adopted the Vanderbilt-type ultrasoft pseudopotentials39 throughout all the present calculations. The exchange-correlation potential was considered using the GGA (PBE).40 The cut-off energy of the plane wave was 550 eV, and the Brillouin zone was sampled on the 2×2×2 and 4×4×1 Monkhorst-Pack grid41 for the unit cell and (100) surface models of PB, respectively.
The adsorption energy of PGMs/Mo ions on the (100) surface of PB were calculated using a Fe(III)8Fe(II)8(CN)40 model (see Fig. 3) consisting of two layers of (100) surface (see Fig. 3a side view). In order to reproduce the surface environment, the 10 Å vacuum region was set on the (100) surface of PB model. The surface adsorption energy (Ead) was evaluated using the following equation,
E ad = ET[PGMs/Mo:PB] – (ET [PB] + ET [PGMs/Mo]) (1).
Here, each term denotes the total energy of PGM/Mo-sorbed PBs, pristine PB, and PGMs/Mo themselves, respectively, which were calculated using CASTEP. The maximally-localized Wannier functions (MLWFs) of the C2p and N2p atomic orbitals (AOs) on the (100) surface of PB were obtained using Wannier90.42
The diffusion energy of PGMs/Mo ions through the nanospace of PBNPs was estimated for the unit cell model by using the Nudged elastic band (NEB) method implemented in QUANTUM-ESPRESSO. A diffusion pathway for PGMs/Mo ions in the nanospace of PBNPs was considered to be a route from the center of the square made of the four Fe ions in the (100) plane to the same site of the adjacent (100) plane via the 4c site (see the inset of Fig. 4).
The substitution energy (ES) of PGMs/Mo with Fe of PB was estimated for the unit cell model consisting of 60 atoms, which corresponds to 12.5% Fe ions substituted with PGMs/Mo ions. The ES was evaluated using the following equation,
E S = ET[PGMs/Mo:PB] – ET[PB] + µFe – µPGMs/Mo (2)
Here, the first and second terms denote the total energy of the PGMs/Mo-sorbed and pristine PB models, respectively, whereas the third and fourth terms denote the chemical potentials of Fe and PGMs/Mo, respectively. In the present study, we used the chemical potential of the oxide at the oxidation limit and of the neutral atom at the reduction limit. These calculations were performed by DFT+U method,43 using CASTEP. The U value was set to be 7.0 eV for the high-spin (HS) state of Fe3+ (Ionic radius: 0.645 Å for six coordination number), 3.0 eV for the low-spin (LS) state of Fe2+ (Ionic radius: 0.61 Å for six coordination number), and 2.0 eV for the LS state of PGMs/Mo (Ionic radius: 0.59 Å for Mo6+ with six coordination number, 0.62 Å for Ru4+ with six coordination number, 0.665 Å for Rh3+ with six coordination number, and 0.86 Å for Pa2+ with six coordination number).44–46 All calculations in the present study were performed until the residual forces and stresses below 0.01 eV/Å and 0.02 GPa, respectively. A uniformed background charge, so called the Jellium model, was used to accommodate the non-neutral states.