Role of solubility parameters in understanding the steric stabilization of exfoliated two-dimensional nanosheets by adsorbed polymers

In this paper we show that graphene, hexagonal boron nitride, and molybdenum disulfide can all be exfoliated and stabilized against aggregation in solvents that cannot alone exfoliate these materials, provided that dissolved polymers are present. In each case we demonstrate this steric stabilization for a range of polymers. To understand this, we have derived an expression for the free energy of adsorption of polymer chains onto the surface of nanosheets in a solvent environment. Critically, we express all energetic interactions in terms of the Hildebrand solubility parameters of solvent, polymer, and nanosheet. This allows us to predict the dispersed nanosheet concentration to display a Gaussian peak when plotted against polymer Hildebrand parameter. This is borne out by experimental data. The model correctly (within ∼2 MPa ^1/2) predicts the peak to occur when polymer and solvent solubility parameters match. In addition, the model describes both the peak width and the dependence of nanosheet concentration on polymer molecular weight. Because of the wide availability of solubility parameters for solvents, polymers, and many nanomaterials, this work is of practical importance for the production of polymer-nanosheet composite dispersions. However, more importantly it extends our understanding of the conditions required for steric stabilization and provides simple rules which define the required combination of solvent and polymer to best stabilize a given type of nanomaterial or colloid.