Carbon-based nanomaterials have successively remained at the forefront of different research fields and applications for years. Understanding of low-dimension carbon material family (CNT, fullerenes, graphene, and graphene quantum dots) has arrived at a certain extension. In this report, graphene quantum dots were synthesized from graphene oxide with a microwave-assisted hydrothermal method. Compared with conventional time-consuming hydrothermal routes, this novel method requires a much shorter time, around ten minutes. Successful formation of quantum dots derived from graphene sheets was verified with microscopic and spectroscopic characterization. Nanoparticles present a diameter of about 2-8 nm, blue emission under ultraviolet excitation, and good dispersion in polar solvents and can be collected in powder form. The synthesized graphene quantum dots were utilized as a hole transport layer in organic solar cells to enhance the cell quantum efficiency. Such quantum dots possess energy levels (Ec and Ev) relevant to HOMO and LUMO levels of conductive polymers. Mixing P3HT:PCBM polymer and graphene quantum dots of sufficient extent notably helps reduce potential difference at interfaces of the two materials. Overall efficiency consequently advances to 1.43%, an increase of more than 44% compared with pristine cells (0.99%).
Error Estimation for Eigenvalues of Unbounded Linear Operators and an Application to Energy Levels in Graphene Quantum Dots
