  Solvents are an essential element in the production and processing of
two-dimensional (2D) materials. For example, the liquid phase exfoliation of
layered materials requires a solvent to prevent the resulting monolayers from
re-aggregating, while solutions of functional atoms and molecules are routinely
used to modify the properties of the layers. It is generally assumed that these
solvents do not interact strongly with the layer and so their effects can be
neglected. Yet experimental evidence has suggested that explicit atomic-scale
interactions between the solvent and layered material may play a crucial role
in exfoliation and cause unintended electronic changes in the layer. Little is
known about the precise nature of the interaction between the solvent molecules
and the 2D layer. Here, we use density functional theory calculations to
determine the adsorption configuration and binding energy of a variety of
common solvent molecules, both polar and non-polar, on two of the most popular
2D materials, namely graphene and MoS$_2$. We show that these molecules are
physisorbed on the surface with negligible charge transferred between them. We
find that the adsorption strength of the different molecules is independent of
the polar nature of the solvent. However, we show the molecules induce a
significant charge rearrangement at the interface after adsorption as a result
of polar bonds in the molecule.
