The energy characteristics and structure of carbon nanoscrolls

Structure and energetics of carbon, hexagonal boron nitride, and carbon/hexagonal boron nitride single-layer and bilayer nanoscrolls

“…We consider the structure and energetics of nanoscrolls made from flat rectangular single-layer and bilayer nanoribbons with the length L and width w. According to the analyt- ical model of single-layer nanoscrolls 44,45 used here, the distance R between the layer and the nanoscroll axis is described in polar coordinates (R, ϕ) by the equation of the Archimedean spiral R = hϕ/2π, where h is the approximate distance between adjacent spiral turns (equal to the interlayer spacing of the nanoscroll). The length L is measured along the spiral line and the width w corresponds to the edge of the nanoribbon parallel to the nanoscroll axis.…”

“…Analogously to Ref. 44, we use here an approximate expression for the layer curvature K = 1/R. Thus the total elastic energy is given by the following expression:…”

“…Third, two types of analytical and semianalytical models have been elaborated. 33,[42][43][44][45] These models allow to calculate dependences of structural and energetic characteristics of a nanoscroll on its dimensions using values of bending elastic constants and interlayer interaction energies obtained in the experiment or by high-level ab initio methods. The first of the models is based on an approximate consideration of the potential energy of a single-layer nanoscroll with a large number of layers and gives an expression for dimensions of such nanoscroll in the stable state.…”

“…The first of the models is based on an approximate consideration of the potential energy of a single-layer nanoscroll with a large number of layers and gives an expression for dimensions of such nanoscroll in the stable state. 33,43 The second one gives the expression of nanoscroll potential energy, 42,44,45 whereas the dimensions of nanoscroll in a stable state can be obtained by numerical calculations. Such a model allows to consider not only large nanoscrolls but also nanoscrolls with a minimal number of layers, which are promising, for example, for enhancement of adsorption properties of nanoscroll-based materials or decreasing the size of nanoscroll-based NEMS.…”

“…Here we use our recent semianalytical model 44 to compare the structure and energetics of single-layer and bilayer carbon nanoscrolls (SCNSs and BCNSs) and single-layer and bilayer boron nitride nanoscrolls (SBNNSs and BBNNSs) as well as CBNNSs made of bilayer graphene/hexagonal boron nitride heterostructure. Not only characteristics of the stable state of nanoscrolls but also the barriers to rolling and unrolling are studied as functions of nanoscroll dimensions.…”