Two-dimensional nanomaterials such as MoS 2 are of great interest both because of their novel physical properties and their applications potential. Liquid exfoliation, an important production method, is limited by our inability to quickly and easily measure nanosheet size, thickness or concentration. Here we demonstrate a method to simultaneously determine mean values of these properties from an optical extinction spectrum measured on a liquid dispersion of MoS 2 nanosheets. The concentration measurement is based on the size-independence of the low-wavelength extinction coefficient, while the size and thickness measurements rely on the effect of edges and quantum confinement on the optical spectra. The resultant controllability of concentration, size and thickness facilitates the preparation of dispersions with pre-determined properties such as high monolayer-content, leading to first measurement of A-exciton MoS 2 luminescence in liquid suspensions. These techniques are general and can be applied to a range of two-dimensional materials including WS 2 , MoSe 2 and WSe 2 .

We investigate the tight-binding approximation for the dispersion of the and * electronic bands in graphene and carbon nanotubes. The nearest-neighbor tight-binding approximation with a fixed ␥ 0 applies only to a very limited range of wave vectors. We derive an analytic expression for the tight-binding dispersion including up to third-nearest neighbors. Interaction with more distant neighbors qualitatively improves the tight-binding picture, as we show for graphene and three selected carbon nanotubes.The band structure of carbon nanotubes is widely modeled by a zone-folding approximation of the graphene and à electronic states as obtained from a tight-binding Hamiltonian. [1][2][3][4][5] The large benefit of this method is the very simple formula for the nanotube electronic bands. While the tight-binding picture provides qualitative insight into the one-dimensional nanotube band structure, it is more and more being used for quantitative comparisons as well. For instance, attempts to assign diameters and chiralities of carbon nanotubes based on optical absorption and Raman data rely heavily on the assumed transition energies. 2,6 Differences between the zone-folding, tight-binding -orbital description and experiment, as observed, e.g., in scanning tunneling measurements, are usually ascribed to ''curvature effects.'' 1 However, the common -orbital tight-binding approach for the nanotube band structure involves two approximations: ͑i͒ zone folding, which neglects the curvature of the wall; and ͑ii͒ the tight-binding approximation to the graphene bands including only first-neighbor interaction. Whereas the first point received some attention in the literature, 7-9 the second approximation is usually assumed to be sufficient.In this paper we compare the tight-binding approximation of the graphene orbitals to first-principles calculations. We show that the nearest-neighbor tight-binding Hamiltonian does not accurately reproduce the and * graphene bands over a sufficiently large range of the Brillouin zone. We derive an improved tight-binding electronic dispersion by including up to third-nearest-neighbor interaction and overlap. The formula for the electronic states we present may readily be used, e.g., in combination with zone folding to obtain the band structure of nanotubes.The first tight-binding description of graphene was given by Wallace in 1947. 10 He considered nearest-and nextnearest-neighbor interaction for the graphene p z orbitals, but neglected the overlap between wave functions centered at different atoms. The other-nowadays better known-tightbinding approximation was nicely described by Saito et al. 4 It considers the nonfinite overlap between the basis functions, but includes only interactions between nearest neighbors within the graphene sheet. To study the different levels of approximation we start from the most general form of the secular equation, the tight-binding Hamiltonian H, and the overlap matrix S, 4where E(k) are the electronic eigenvalues. We used the equivalence of the A and B carbon ...

We report the chemical reaction of single-layer graphene with hydrogen atoms, generated in situ by electron-induced dissociation of hydrogen silsesquioxane (HSQ). Hydrogenation, forming sp3 C--H functionality on the basal plane of graphene, proceeds at a higher rate for single than for double layers, demonstrating the enhanced chemical reactivity of single sheet graphene. The net H atom sticking probability on single layers at 300 K is at least 0.03, which exceeds that of double layers by at least a factor of 15. Chemisorbed hydrogen atoms, which give rise to a prominent Raman D band, can be detached by thermal annealing at 100-200 degrees C. The resulting dehydrogenated graphene is "activated" when photothermally heated it reversibly binds ambient oxygen, leading to hole doping of the graphene. This functionalization of graphene can be exploited to manipulate electronic and charge transport properties of graphene devices.

We present a comprehensive study of the chiral-index assignment of carbon nanotubes in aqueous suspensions by resonant Raman scattering of the radial breathing mode. We determine the energies of the first optical transition in metallic tubes and of the second optical transition in semiconducting tubes for more than 50 chiral indices. The assignment is unique and does not depend on empirical parameters. The systematics of the socalled branches in the Kataura plot are discussed; many properties of the tubes are similar for members of the same branch. We show how the radial breathing modes observed in a single Raman spectrum can be easily assigned based on these systematics. In addition, empirical fits provide the energies and radial breathing modes for all metallic and semiconducting nanotubes with diameters between 0.6 and 1.5 nm. We discuss the relation between the frequency of the radial breathing mode and tube diameter. Finally, from the Raman intensities we obtain information on the electron-phonon coupling.