Density of States Calculations of Small Diameter Single Graphene Sheets

Abstract

The densities of states for the TI-band of single graphene sheets with small diameters were calculated by employing a linear combiriation of atomic orbital approach using as the basis set the carbon p. atomic orbitals together with a modified Huckel approximation wherein the overlap integrals out to the fourth nearest neighbors set were included.These densities of states were used to predict the voltage of lithiated carbon vs. lithium metal, an important characteristic for disordered carbon used as the negative electrode in rechargeable lithium-ion batteries. Calculations were made for isolated single graphene sheets, C0, with n = 24, 54, 96, 150, and 216. The results suggested that the lowest voltage should occur for lithiated carbon electrodes composed of single graphene sheets with the smallest diameter ( 0.7 nm for C24).Disordered carbon has two important electrochemical properties which have attracted considerable interest for its use as the negative electrode in rechargeable lithium-ion batteries3: (i) a relatively high reversible charge capacity (more than one lithium ion can be inserted per six carbon atoms, i.e., x> 1 for Li,C6, thereby exceeding the capacity of classical graphite intercalation compounds (GIC), for which x,4, = 1); and (ii) a low voltage (<0.3 V vs. lithium metal) for much of the range, x> 0.3 (which is similar to the low voltage profile found for GIC.In papers by the Simon Fraser University group,13 the high charge capacity for disordered carbon was accounted for on the basis that single layers of graphitic carbon (graphene sheets) have twice as many low energy lithium sites as would be the case for multilayered "thick" graphitic carbon (graphite molecules for which the c-axis dimension, L0, is >> 0.335 nm, the interlayer distance between layers in graphite).Thus, for graphene sheets one expects Xm = 2.If one takes this reasoning a step further, additional capacity may arise from low energy edge sites for lithium ions, such that x,,,, > 2 may be expected for small diameter graphene sheets, C0, for which there are relatively many edge atoms. For example, at least half (12 out of 24) of the carbon atoms in C24 are edge atoms, (the relative number depends on how one defines an edge atom; in this paper they are defined as atoms with only two nearest neighbor carbons); and if one assumes one low energy lithium site for each edge carbon atom, this allows for a maximum in xof x = 4, i.e., * Electrochemical Society Active Member.Li4C6 may accrue, suggesting the possibility that small diameter graphene sheets may provide a high charge capacity. This leads to the question: would there be a sacrifice in voltage for such a material? To answer the question we carried out a set of density of states (DOS) calculations for planar molecules of homologous symmetry, C0, for n = 24, 54, 96, 150, and 216. Illustrated in Fig. 1 are the first three members of this group. A linear combination of atomic orbitals (LCAO) approach was employed, using as the basis set the carbon p atomic orbitals, together with a m...

Graphene-based multilayers: Critical evaluation of materials assembly techniques

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Enhanced Absorption and Diffusion Properties of Lithium on B,N,VC-decorated Graphene

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High Density Rechargeable Lithium-Ion Batteries Self-Assembled from Graphite Oxide Nanoplatelets and Polyelectrolytes

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