3.1. Crystal phase and morphology analyses
The XRD patterns of products prepared with different metal cation were characterized and shown in Fig. 1. The peaks of products with Bi3+、Sr2+、Pb2+ ions have no difference with the products without metal cation as additive. Indexed in accordance with JCPDS 65-2448, all the diffraction peaks are consistent with orthorhombic brookite phase. No diffraction peaks of anatase or rutile phase can be observed in Fig. 1. It shows that the addition of three kinds of metal cation did not change the crystalline phases, which remain the pure brookite phase TiO2.
It's worth noting that the diffraction peaks mentioned above obviously broaden relative to the synthesis without metal cation. Scherrer equation deduced theoretically the relation between grain size and degree of diffraction line width, D = Kλ/βcosθ. It shows the smaller size of the product, the wider diffraction peaks. The broadened diffraction peaks in Fig. 1 show the addition of Bi3+, Sr2+ and Pb2+ ions result in smaller size brookite nanoparticles successfully. It is generally known that the reduction of particle size can increase the surface area of brookite nanoparticles, thereby show better performance in DSSC. The ionic radius of Ti4+ ions is 0.605 Å while the ionic radius of Bi3+, Sr2+ and Pb2+ ions is 1.03 Å、1.18 Å and 1.19 Å, respectively. The ionic radius of metal cation is much larger than Ti4+ ions. During the process of crystal nucleation and growth, termination of crystal growth will take place when the heterogeneous atoms bring in inerratic arrange crystal. Hence, the metal cation as additive can inhibiting crystal growth and then obtain smaller size brookite nanoparticles. Moreover, according to the previous research on synthesis metastable phase brookite, Na+ or Ca2+ ions usually used as a stabilizer when hydrothermal reaction. It's worth noting that the ionic radius of Na+ (0.97 Å) or Ca2+ (0.99 Å) ions are similar to the ionic radius of Bi3+, Sr2+ and Pb2+ ions, which larger than that of Ti4+ (0.605 Å). Thus the Bi3+, Sr2+ and Pb2+ ions with similar ionic radii relate to Ca2+ and Na+ ions can also act as stabilizers. In conclusion, smaller nanoparticles and high purity brookite TiO2 can be obtained by introduction of Bi3+, Sr2+ and Pb2+ ions.
Moreover, there is no shift of the diffraction peak indicate metal cation did not doped in crystal. Generally speaking, the difference of the ionic radius should be less than 20% so that the heterogeneous ionic can be doped in crystal. The ionic radius of metal cation above are almost two times larger than Ti4+ ions, so it is hard to be doped. The diffraction peaks of at 2θ = 30.8° become slightly weaker, this is due to crystallinity of present product be not a patch on brookite without metal cation. From the above, the addition of metal cation can result in smaller size brookite nanoparticles, which is benefited to be used in DSSC.
The crystallite dimension and morphologies of the brookite TiO2 synthesized with different metal cation can be observed in Fig. 2 FESEM micrographs. As can be seen in Fig. 2a, brookite without metal cation (denoted as BTN) have a uniform pseudo-cube morphology, which size is about 50 nm. All the brookite products with metal cation exhibit much smaller sizes than BTN particles, which is consistent with the result of XRD patterns. The brookite adding Bi3+ ions (denoted as BTB) displayed regular aggregated nanoparticles, the average particle size was found to be 10 nm. At the same time, the brookite adding Sr2+ (Fig. 2c, denoted as BTS) or Pb2+ ions (Fig. 2d, denoted as BTP) are a mixture of nanoparticles and a small quantity of nanorods. The size of spherical particles is about 10 nm and the rods have a length of 100 nm.
3.2. Photovoltaic performance analyses of the solar cell
All the brookite nanoparticles with different metal cation used as photoanode to fabricate DSSCs, the current density-voltage (J-V) graphs are presented in Fig. 3a. The corresponding photovoltaic parameters of the DSSCs can be obtained according to the J-V graphs and given in Table 1.
As compared to anatase solar cells, the VOC of all brookite solar cells tends to increase. This can be explained with the help of higher Fermi level of brookite TiO2 than anatase TiO2. Not only that, but charge recombination can also be decreased effectively on account of the lower reactivity of the brookite surface. It should be noted that BTB, BTS and BTP based solar cells show slightly lower VOC values than the BTN one. On one hand, there is typical function relation between band gap and grain diameter according to the transformed Kubelka-Munk equation. The band gap presented a positive correlation to the grain diameter from 29 to 17 nm, which because of quantum size effect and delocalization of molecular orbitals. On the other hand, comparing with the BTN particles, smaller particle size of BTB, BTS and BTP result in more boundaries. The boundaries cause more surface trapping and electron recombination phenomenon. To sum up, it can be concluded that lower band gap value and more surface boundaries influence on the lower VOC of the BTB, BTS and BTP based solar cells.
Nevertheless, as shown in Table 1, the BTB, BTS and BTP film-based solar cells give superior efficiency than BTN film-based one even though the lower VOC. The photovoltaic conversion efficiency (η) of BTB, BTS, BTP and BTN film-based solar cells is 6.12%,6.48%, 6.46% and 3.22%, respectively. All the small size brookite solar cells show excellent photovoltaic performance comparable to anatase solar cells. The key reason is the much higher JSC. The JSC of BTB, BTS and BTP film-based solar cells is almost twice as large as BTN. The much smaller particle sizes of BTB, BTS and BTP particles result in larger specific surface areas as compared to the BTN. Larger specific surface areas can provide more adsorption sites to increase dye loading, increasing the absorption of visible light. In addition, a small quantity of nanorod brookite with ~ 100 nm long diameter in BTS and BTP can have a synergistic effect. The nanorod brookite with larger size can be used as a scattering material to enhance light harvesting, improving the JSC value of the solar cell.
3.3. Photoelectrochemical behavior analyses of the solar cells
The electrochemical impedance spectra (EIS) can further study of the electronic and ionic processes during the DSSCs operations. Figure 3b shows their Nyquist plots of DSSCs fabricated from different brookite photoanode. The impedances of Rs of BTB, BTS and BTP were 19.09, 18.07 and 18.20Ω, respectively. All the Rs with smaller size brookite are lower than that of BTNs (31.83 Ω). The smaller particle sizes of brookite make for reduced contact resistance. As shown in Table 1, the electron transfer resistance (R2) of BTB, BTS and BTP is almost half of BTN. This can be ascribed to the increased charge transfer capacity. The smaller particles size brookite can adsorb more dye molecule and show better electron injection efficiency, resulting an in overall photovoltaic performance boost.