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Nanofluidic systems show great promises for applications in energy conversion, where their performance can be enhanced by nanoscale liquid-solid slip. However, efficiency is also controlled by surface charge, which is known to reduce slip. Combining molecular dynamics simulations and analytical developments, we show the dramatic impact of surface charge distribution on the slip-charge coupling. Homogeneously charged graphene exhibits a very favorable slip-charge relation (rationalized with a new theoretical model correcting some weaknesses of the existing ones), leading to giant electrokinetic energy conversion. In contrast, slip is strongly affected on heterogeneously charged surfaces, due to the viscous drag induced by counter-ions trapped on the surface. In that case slip should depend on the detailed physical chemistry of the interface controlling the fraction of bound ions. Our numerical results and theoretical models provide new fundamental insight on the molecular mechanisms of liquid-solid slip, and practical guidelines for searching new functional interfaces with optimal energy conversion properties, e.g. for blue energy or waste heat harvesting.