Graeme Cunningham1, Mustafa Lotya1, Clotilde Cucinotta1, Stefano Sanvito1, Shane D Bergin2, Robert Menzel2, Milo SP Shaffer2 and Jonathan N Coleman1*

We have studied the dispersion and exfoliation of four inorganic layered compounds, WS2, MoS2, MoSe2 and MoTe2 in a range of organic solvents. The aim was to explore the relationship between the chemical structure of the exfoliated nanosheets and their dispersability. Sonication of the layered compounds in solvents generally gave few-layer nanosheets with lateral dimensions of a few hundred nanometers. However the dispersed concentration varied greatly from solvent to solvent. For all four materials the concentration peaked for solvents with surface energy close to 70 mJ/m 2 , implying that all four layered compounds have surface energy close to this value. Inverse gas chromatography measurements showed MoS2 and MoSe2 to have surface energies of ~75 mJ/m 2 , in good agreement with dispersability measurements. However, this method suggested MoTe2 to have a considerably larger value of surface energy (~120 mJ/m 2 ). While surface energy based solubility parameters are perhaps more intuitive for 2-dimensional materials, Hansen solubility parameters are probably more useful. Our analysis shows the dispersed concentration of all four layered materials to show well-defined peaks when plotted as a function of Hansen’s dispersive, polar and H-bonding solubility parameters. This suggests that we can associate Hansen solubility parameters of ~ P  18 MPa 1/2 , ~ D  8.5 MPa 1/2 and ~ H  7 MPa 1/2 with all four types of layered material. Knowledge of these properties allows the estimation of the Flory-Huggins parameter, , for each combination of nanosheets and solvent. We found that the dispersed concentration of each material falls exponentially with  as predicted by solution thermodynamics. This work shows that solution thermodynamics and specifically solubility parameter analysis can be used as a framework to understand the dispersion of 2-dimensional materials. Finally, we note that in good solvents such as