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Semi-permeable membranes are important elements in water purification andenergy generation applications, for which the atomic thickness and strength ofgraphene can enhance efficiency and permeation rate while maintaining goodselectivity. Here, we show that an osmotic pressure difference forms across asuspended graphene membrane as a response to a sucrose concentrationdifference, providing evidence for its semi-permeability. This osmotic pressuredifference is detected via the deflection of the graphene membrane that ismeasured by atomic force microscopy. Using this technique, the time dependenceof this deflection allows us to measure the water permeation rate of a single3.4 $\mu$m diameter graphene membrane. Its value is close to the expected valueof a single nanopore in graphene. The method thus allows one to experimentallystudy the semi-permeability of graphene membranes at the microscale when theleakage rate is miniscule. It can therefore find use in the development ofgraphene membranes for filtration, and can enable sensors that measure theconcentration and composition of solutions.

Semi-permeability of graphene nanodrums in sucrose solution