Polyimide (PI)-matrix composite films containing nitrogen (N) doped graphene sheet have been fabricated by employing in-situ polymerization and their microstructure has been investigated by the small angle X-ray scattering (SAXS) and scanning electron microscopy. The N doped graphene (NG) possess excellent dispersion within the PI matrix, and forming strong links with the polymer to facilitate load transfer. The PI/NG composite films exhibit improved mechanical properties than that of the pure PI film. The tensile strength of the integrated PI/NG composite films with 0.1 wt% loading is 15% greater, and the elongation at break is 230% greater than comparable properties of pure PI film. This approach provides a strategy for developing high performance graphene–polymer composite.

Let (Φ_t)t∈ℝ₊ be a Harris ergodic continuous-time Markov process on a general state space, with invariant probability measure π. We investigate the rates of convergence of the transition function P^t(x, ·) to π; specifically, we find conditions under which r(t)||P^t(x, ·) − π|| → 0 as t → ∞, for suitable subgeometric rate functions r(t), where ||·|| denotes the usual total variation norm for a signed measure. We derive sufficient conditions for the convergence to hold, in terms of the existence of suitable points on which the first hitting time moments are bounded. In particular, for stochastically ordered Markov processes, explicit bounds on subgeometric rates of convergence are obtained. These results are illustrated in several examples.