The outstanding mechanical properties of graphene have made it a suitable candidate for awide range of sensor and actuator applications in modern technology. However, before the full potential of future applications can be achieved, a proper characterisation of the fundamental properties of graphene is crucial. The aim of this project was to contribute to the understanding of the mechanics of graphene membranes in presence of surface imperfections. To this end two configurations are investigated: ribbons and cantilevers, respectively. Wrinkled graphene nanoribbons are used to investigate the mechanical behaviour during the transition from the wrinkled state to the flat state. A molecular dynamics model has been developed of a single layer graphene ribbon to describe both the formation of wrinkles as well as the transition from the wrinkled state to the flat state. Also, a continuum model was developed to investigate the formation of wrinkles in graphene nanoribbons. Different constitutive laws have been investigated to describe the mechanical response of wrinkled membranes during the transition from the wrinkled state to the flat state. It was concluded that an exponential version of Hooke’s law fails to describe this transition correctly. The transition is however well described by the first order compressible Ogden’s law. Ogden’s law provided further insights into different mechanical properties of the wrinkled layer. Ogden’s law predicted that wrinkledmembranes exhibit a negative Poisson’s ratio at small strains, which is in agreement with previous research. Also, Ogden’s law predicted a decreasing shearmodulus and an increasing Poisson’s ratio after flattening of the membrane. Single layer graphene cantilevers show great potential, however, due to the difficult manufacturing of these fragile structures they remain virtually unstudied. Herein, a molecular dynamics model has been developed to investigate if nanocantilevers could be stabilised by implying a curvature. We found that, depending on the aspect ratio of the membrane and the applied rate of curvature, single layer graphene cantilevers could be (partly) stabilised by implying a curvature. In conclusion, with this research we provided new insights for designing and investigating the next generation of graphene nanoelectromechanical devices.

The Atomic Force Microscope (afm) is a small scale measuring device, with a lot of benefits over other existing measuring techniques. Unfortunately, measurement speed is not one of them. Many have tried and succeeded to improve the measurement speed, but there is still room for improvement.
By passively lowering the Q-factor, a measurement can be sped up, while still be compatible with other speed improvement techniques.
To passively lower the Q-factor, we propose measuring in a medium more dense then air. First in a liquid, de-mineralized water, to prove the effect, and later in a gas, co2, to keep the samples clean.
Our models predict a speed increase of 0.3559 ms per measured point, or 6.941 min per image of 5 μm × 5 μm with 512 lines in liquid. The experiments show an increase of 0.4180 ms per point, or 8.155 min per measurement. In the much less dense gas a 0.031 01 ms per point or 0.6550 min per frame is calculated. The experiments show an increase of 0.027 29 ms per point with a total of 0.5300 min per frame.
Both in liquid and in gas an improvement is observed. When measuring in a liquid, the speed increase of 8.155 min per frame is noticeable when a small area on a single sample is measured. Measurements in gas, with an increase of 0.5300min per frame only become interesting when multiple frames need to be measured, since a gas measurement does take longer to set up. Changing the used measurement gas to a more dense gas could make single frame measurements more interesting.