Figure 3: Length metric and edge effects.

(a,b) Representative TEM images of slowly sedimenting MoS₂ nanosheets (small flakes, F1, (a) scale bar, 100 nm, (b) scale bar, 10 nm). (c,d) Representative TEM images of faster sedimenting MoS₂ nanosheets (large flakes, F6, (c) scale bar, 1 μm, (d) scale bar, 100 nm). (e) Extinction (ε), absorption (α) and scattering (σ) coefficients at 345 nm plotted versus nanosheet length. The line represents ‹ε›=69 ml mg⁻¹ cm⁻¹. (f) Ratio of extinction at B-exciton to that at 345 nm, Ext_B/Ext₃₄₅, plotted versus the lateral dimensions of the flake (expressed as mean length, L, obtained by statistical TEM analysis). The line is a fit to equation (4). Also shown is the equivalent data taken from the absorbance spectra (Abs_B/Abs₃₄₅). The inset schematically shows the division of a nanosheet into edge and central regions. (g) Absorption coefficient, α, at both A- and B-excitons plotted versus inverse nanosheet length. The dashed lines are fits to equation (1). (h) Fitted XPS S2p core-level spectra of filtered MoS₂ dispersions with different mean flake lengths. The additional component at higher binding energies is attributed to edge S. (i) Fraction of S2p signal associated with edge S as a function of flake length. This fraction is equal to the ratio of edge S to total S atoms. The line represents a fit to equation (2) and yields the width of the edge region to be x=2.7±0.5 nm. (j) Scanning transmission electron microscopy (STEM) image of MoS₂ nanosheets (scale bar, 20 nm). (k) STEM image of the region marked by the box in j showing the edge region of a typical MoS₂ nanosheet (scale bar, 5 nm). The boxes indicate the regions over which EEL spectra were acquired and analyzed. (l) Summed EEL spectra, normalized to the zero-loss peak, of the regions marked by the boxes in k (same data set as Supplementary Fig. S12c). The EEL spectra exhibited gradual changes when moving from the edge to the centre. (m) Plot of EELS intensity ratio at 2.8 eV to that at 6.4 eV (as indicated in l) as a function of distance from the edge. Data from three different regions are shown. The intensity ratio saturates at ~8 nm from the edge.