Due to high efficiency and environmental friendship, Fenton-like technology is widely used in water treatment and has always received significant attentions, especially in design of novel and efficient Fenton-like catalysts. In this paper, iron/titanium ions doped halloysite nanotubes (HNTs-Fe-Ti) have been developed as Fenton-like catalyst. Here, halloysite nanotubes (HNTs) with high specific surface area and excellent ion exchange capacity were used as carriers, and iron/titanium ions were trace-doped into HNTs via simple ion-exchange reaction. The degradation of the designed catalyst for methylene blue (MB) was greatly accelerated in the presence of titanium ion. It demonstrates that the excellent degradation ability mainly owes to the valence state transformation of titanium and the good adsorption ability of halloysite nanotubes. It shows the mechanism of titanium with multivalent states (Ti3+/Ti4+) on the degradation of MB is similar to the Fenton catalytic mechanism of iron ion trans-formation (Fe2+/Fe3+). In the Fenton-like degradation reaction, titanium and iron play a synergistic catalytic role in MB degradation while titanium has greater impact. When the ratio of titanium to iron is 5:1, the catalyst exhibits superior Fenton-like degradation performance, and the degradation rate could reach 91% at 100 min.
The main purpose of this paper is using the properties of Gauss sums and the estimate for character sums to study the hybrid mean value problem involving the two-term exponential sums and two-term character sums and give an interesting asymptotic formula for it.
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