New method for calculations of nanostructure kinetic stability at high temperature

Abstract

A new universal method is developed for determination of nanostructure kinetic stability (KS) at high temperatures, when nanostructures can be destroyed by chemical bonds breaking due to atom thermal vibrations. The method is based on calculation of probability for any bond in the structure to stretch more than a limit value Lmax, when the bond breaks. Assuming the number of vibrations is very large and all of them are independent, using the central limit theorem, an expression for the probability of a given bond elongation up to Lmax is derived in order to determine the KS. It is shown that this expression leads to the effective Arrhenius formula, but unlike the standard transition state theory it allows one to find the contributions of different vibrations to a chemical bond cleavage. To determine the KS, only calculation of frequencies and eigenvectors of vibrational modes in the groundstate of the nanostructure is needed, while the transition states need not be found. The suggested method was tested on calculating KS of bonds in some alkanes, octene isomers and narrow graphene nanoribbons of different types and widths at the temperature T=1200 K. The probability of breaking of the C–C bond in the center of these hydrocarbons is found to be significantly higher than at the ends of the molecules. It is also shown that the KS of the octene isomers decreases when the double C˭C bond is moved to the end of the molecule, which agrees well with the experimental data. The KS of the narrowest graphene nanoribbons of different types varies by 1–2 orders of magnitude depending on the width and structure, while all of them are by several orders of magnitude less stable at high temperature than the hydrocarbons and benzene.