Efficient microwave hydrothermal preparation of nanocrystalline anatase TiO2 colloids

Titanium dioxide nanocrystals are an important commercial product used primarily in white pigments and abrasives, however, more recently the anatase form of TiO2 has become a major component in electrochemical and photoelectrochemical devices. An important property of titanium dioxide nanocrystals for electrical applications is the degree of crystallinity. Numerous preparation methods exist for the production of highly crystalline TiO2 particles. The majority of these processes require long reaction times, high pressures and temperatures (450–1400 °C). Recently, hydrothermal treatment of colloidal TiO2 suspensions has been shown to produce quality crystalline products at low temperatures (<250 °C). In this paper we extend this idea utilising a direct microwave heating source. A comparison between convection and microwave hydrothermal treatment of colloidal TiO2 is presented. The resulting highly crystalline TiO2 colloids were characterised using Raman spectroscopy, XRD, TEM, and electron diffraction. The results show that the microwave treatment of colloidal TiO2 gives comparable increases in crystallinity with respect to normal hydrothermal treatments while requiring significantly less time and energy than the hydrothermal convection treatment.

An Efficient and Verifiable Solution to the Millionaire Problem

A new solution to the millionaire problem is designed on the base of two new techniques: zero test and batch equation. Zero test is a technique used to test whether one or more ciphertext contains a zero without revealing other information. Batch equation is a technique used to test equality of multiple integers. Combination of these two techniques produces the only known solution to the millionaire problem that is correct, private, publicly verifiable and efficient at the same time.