We investigated the stability of reduced graphene oxide for oxygen density ranging from 6.25% to 50% with the density functional theory and found the most, the second most, and the third most stable oxygen configurations. The effect of relaxation of lattice on the electronic properties is found to be negligible for low O coverage and crucial for higher O coverage, respectively. The densities of states and the band gaps were calculated. The bandgap is found to be a non-monotonic function of oxygen density, with minima at O/C = 11.1% and 25%.

A quantum-mechanical simulation is carried out to investigate the charge distribution and electrostatic potential along a $1\mu \mathrm{m}$ long (5,5) single-walled carbon nanotube under realistic field-emission experimental conditions. A single layer of carbon atoms is found sufficient to shield most of the electric field except at the tip where strong field penetration occurs. The penetration leads to a nonlinear decrease of potential barrier for emission, which is equally responsible for the low threshold voltage besides the well-known geometrical field enhancement factor.

We simulate the critical relaxation process of the two-dimensional Ising model with the initial state both completely disordered or completely ordered. Results of a method to measure both the dynamic and static critical exponents are reported, based on the finite-size scaling for the dynamics at the early time. From the time-dependent Binder cumulant, the dynamical exponent z is extracted independently, while the static exponents β/ν and ν are obtained from the time evolution of the magnetization and its higher moments. © 1996 The American Physical Society.