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Researchers at the Kazan State Technical University named after A.N. Tupolev  have developed mathematical models that describe structure of various nanotube types. They allow to adjust existing theoretical ideas and design methods for various nanotube characteristics. As model application experience is accumulated, these models can help to forecast nanotube properties as well as to develop their automatic sorting methods. The work was published in the last issue of the Scientific Israel - Technological Advantages journal.

“There is nothing but somehow located atoms in any crystal, including cylindrical ones, – explained one of research authors, Zufar Khalitov, to a reporter of “Informnauka”. – This determines all its properties, including electric ones.”

To use unusual electric properties of nanotubes, it is necessary to get sufficient quantity of tubes with a similar structure. The problem is that there is no synthesis method now that allows to get only one nanotube variety. During any reaction, a mixture of products with different characteristics is formed. It means that effective nanotube application in electronics requires development of methods for sorting reaction products according to certain criteria. Research groups all over the world are solving the task.

Zufar Khalitov and his colleagues believe that the key to this problem solution can be found in diffraction methods of nanotube structure analysis. Utilization of various beams (X-ray beams, electron and neutron streams) and analysis of their interaction with the investigated substance will enable to determine nanotube selection criteria and to develop a method for their isolation. To make diffraction analysis really useful, it is necessary not to determine the crystal structure from scratch but to be guided by a previously developed model.

“The structural model of the crystal is the very “initial point” where everybody begins at: both those who want to calculate some of its properties (for example, conductivity), and those who want to develop methods for its identification and parameter measurement, for example, based on electron diffraction or X-ray beams, – pointed out the researcher. – It is impossible to begin any important developments until structural models are available. One can act as alchemists did, by the hit-and-miss method, which has been done to a large degree during the last 20 years.”

The researchers have got expressions that explicitly determine coordinates of any atom in nanotubes of various geometrical types. The models developed by the researchers applied the notion of unit cell, “building block”, parallel translation of which can provide the whole nanotube. Such method is applied in crystallography to describe crystals that possess natural symmetry.

Three types of multilayer nanotube structure are singled out. In the circular nanotube, the layers are nested like in a nested-doll. The chiral type resembles the circular one, but in this case the layers are curled on-the-mitre to the nanotube axis. Spiral nanotubes are curled like a bolt of wallpaper. This classification is normally used to describe carbonic nanotubes, however, other substances can also form a nanotube: there exist chrisotile, sulfide, and boron-nitride tubes.

The mathematical model based on utilization of unit cells notion enabled to develop equations not only for circular and chiral nanotubes but also for spiral ones. Besides, the suggested model, in contrast to previously developed analogues, allows to describe not only carbonic nanotubes but also tubes of any chemical composition.

The researchers have already compared the developed models to experimental data. “Our models of nanotubes do not contradict to experimental data, and we have managed for the first time to describe some diffraction effects taking place in the experiment, – said Khalitov. – We have also used our models in the course of theoretical analysis of wave processes in the nanotube cavity and obtained very interesting results.”

In the future, the researchers are planning to carry out a larger-scale checkup of obtained models. After improvements are made in accordance with experimental data, the models can be applied for development of new diffraction methods for nanotube identification and measurement of their structural paramenters. Later on, utilization of the model will help in development of methods for automatic sampling of nanotubes of pre-assigned structural type. Moreover, “as experience in such analysis is accumulated, we shall be able to forecast nanotube properties, i.e., to forecast nanotube structure and methods for synthesis of nanotubes with required properties”, – says the researcher.

Khadiev Azat

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