Water permeation through single sub-micron pores in single layer graphene measured by a micro-particle image velocimetry technique

Graphene holds potential as a high permeance membrane material for separation applications owing to its single atom thickness. Transport rates through graphene pores ultimately determine membrane performance and are an area of focus of design efforts. In this regard, single pore flow rate measurements are desirable because they are not influenced by material defects present in large-area samples and are unaffected by modeling assumptions used in simulations. However, measuring liquid flow rates through single graphene pores is challenging. In this paper, we establish a micro-particle image velocimetry technique to measure flow rates through single pores or small permeable areas by comparing the velocity decay rate downstream of the pore to analytical predictions for the flow field. The method is validated on silicon nitride micropores by comparison with microfluidic sensor measurements and then applied to measure water permeation rates through single sub-micron graphene pores, below the detection limit of the sensor. A 200 nm diameter pore is measured to have a pore permeation coefficient of 1.5×10−19 m3 s−1 Pa−1, and 500 nm pores are measured to have pore permeation coefficients of 7.0×10−19 and 14×10−19 m3 s−1 Pa−1. These values are less than half those predicted by continuum theory, but of the same order of magnitude. The results provide measured permeances of experimentally realized flows through single sub-micron graphene pores and a reliable technique for measuring the liquid permeance of micrometer-scale membrane areas.