Figure 1a shows a typical image of a monolayer of dodecanethiol-
ligated gold nanocrystals (5.0 ( 0.5 nm in diameter; see
Figure S1 in the Supporting Information for a histogram), selfassembled
on the surface of a water drop and imaged by
transmission electron microscopy (TEM) after dryingone-step drying method results in a well-ordered, close-packed
particle sheet that can drape itself over solid substrates9 as well as
across holes.58 For a given particle type and size, the ligands
establish a characteristic interparticle spacing and provide for
mechanical strength of the assembly.7 In typical nanofiltration
membranes transport occurs through 0.52 nm diameter pores
or channels, while reverse osmosis membranes are based on
diffusion through polymeric networks.10 Well-defined open
pores do not exist in close-packed nanocrystal assemblies because
the ligands extend into the interstices (Figure 1c). In panels
ac of Figure 1 the distances between nanocrystals directly
facing each other are of similar size as the length of the
dodecanethiol (≈1.7 nm), which implies not only a dense but
also a highly interdigitated ligand arrangement in those regions.
However, in the center of triangles formed by three neighboring
particles, the ligands are packed less densely (more chain ends,
less interdigitation) and this makes these regions the most likely
spots for molecular passage (white circle in Figure 1c). Clearly,
transport will be blocked for molecules that cannot fit at all into
the interstices between neighboring particles. The question we
focus on here is what happens for aqueous solution of somewhat
smaller molecules.
In general, transport through a membrane can be described as
arising from two contributions, diffusion due to concentration
gradients and convection due to pressure gradients.11 As a first step
to ascertain the relative magnitude of the two terms, we determine
Figure 1a shows a typical image of a monolayer of dodecanethiol-ligated gold nanocrystals (5.0 ( 0.5 nm in diameter; seeFigure S1 in the Supporting Information for a histogram), selfassembledon the surface of a water drop and imaged bytransmission electron microscopy (TEM) after dryingone-step drying method results in a well-ordered, close-packedparticle sheet that can drape itself over solid substrates9 as well asacross holes.58 For a given particle type and size, the ligandsestablish a characteristic interparticle spacing and provide formechanical strength of the assembly.7 In typical nanofiltrationmembranes transport occurs through 0.52 nm diameter poresor channels, while reverse osmosis membranes are based ondiffusion through polymeric networks.10 Well-defined openpores do not exist in close-packed nanocrystal assemblies becausethe ligands extend into the interstices (Figure 1c). In panelsac of Figure 1 the distances between nanocrystals directlyfacing each other are of similar size as the length of thedodecanethiol (≈1.7 nm), which implies not only a dense butalso a highly interdigitated ligand arrangement in those regions.However, in the center of triangles formed by three neighboringparticles, the ligands are packed less densely (more chain ends,less interdigitation) and this makes these regions the most likelyspots for molecular passage (white circle in Figure 1c). Clearly,transport will be blocked for molecules that cannot fit at all intothe interstices between neighboring particles. The question wefocus on here is what happens for aqueous solution of somewhatsmaller molecules.In general, transport through a membrane can be described asarising from two contributions, diffusion due to concentrationgradients and convection due to pressure gradients.11 As a first stepto ascertain the relative magnitude of the two terms, we determine
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