Application of independent-channel method for investigation of electrical conductivity of graphene-containing shungite.
Authors:   Syktyvkar State University, Oktyabrskiy prosp. 55, Syktyvkar 167001, Russia, Antonets I.V. , Golubev E.A. ,   Geology Institute Komy SC UrD RAS, Pervomaiskaya 54, Syktyvkar 167982, Russia, Shavrob V.G. ,   Kotelnikov Institute of Radioengineering and Electronics of Russian Academy of Sciences, Mokhovaya 11-7, Moscow 125009, Russia, Shcheglov V.I. ,   Kotelnikov Institute of Radioengineering and Electronics of Russian Academy of Sciences, Mokhovaya 11-7, Moscow 125009, Russia
Published: August 2021

The independent channel method which is intended for the calculation of specific electrical conductivity of graphene-contained shungite is proposed and realized on practice. It is noted that the most important of shungite application is the creation of screen hawing large area which are able to block electromagnetic radiation in wide frequency range. The most important factor which determines the blocking properties of shungite is the specific electrical conductivity of its carbon part which is determined by the spatial distribution of carbon atoms. As a main method of carbon structure investigation is mentioned the high-resolution raster electron microscopy which allows from the surface of specimen to receive the card of distribution of graphene slides and graphene packets. The spatial factor which determines the shungite conductivity is large anisotropy of single graphene slide which reaches three orders and more in the cases along and across the slide. The proposed method independent channels takes into consideration the arbitrary orientation of graphene packets relatively to direction of current flow. As a basis of method is employing the card of carbon spatial distribution which is received by raster electron microscopy method. The card is divided by parallel channels which transverse dimension is near or slightly exceeds the typical dimension of graphene packet. The channels are divided to square blocks which sides are equal to width of channel. The whole resistance of channel is formed by the successive connection of individual resistances of blocks. The resistance of whole card is determined by parallel connection of channels or averaging of resistance of all channels and following filling the whole area of card. The first step of analysis is the determination of advantage orientation of slides inside of every blocks. On the basis of determined orientation the block is filled by periodic structure which period is equal to the width of graphene slide and neighbouring interval. As a parameter which determines the orientation is used the angle between advantage orientation of graphene slides and axis of current flow between contacts. Owing to symmetry of task in comparison of current direction the limited meanings of corner is 0 and 90 degree. It is established two principal different cases of orientation: first – when determining angle is less than 45 degree and second when this angle is more than 45 degree. In the first case the current flows along the stripe with large conductivity. In the second case the current flows across these stripes so as through the stripes with low conductivity. It is found the smooth dependence of block resistivity from the angle of strip orientation. For the characteristic of area which is filled graphene slides it is proposed the coefficient of filling which is determined by binary discretization method. On the basis of analysis of slides orientation and filling coefficients are calculated the resistance of individual blocks. The resistances of all channels of investigated card are proposed. By using two methods – parallel connection and averaging over all channels it is calculated the specific electrical resistance and specific electrical conductivity of material as a whole. It is found that the received values of specific conductivity exceed the determined in experiment value in several (to 10) times. For the coordination of calculated value with experimental value it is made the variation of specific resistances of graphene slides and intervals between its. It id found that the calculation by method of parallel connection of channels ensures several better coordination than method of averaging. It is shown that the resistance is improved in the first turn by the increasing the resistance of interval between slides. In the quality of possible reason of decisive role of interval it is proposed the observed in experiment sharp non-homogeneity of relative arrangement of graphene slides. It is discussed the possible courses of further development of work. As a most important task it is proposed the more circumstantial determination of statistical character of received results.