The preparation method such as Adhesive Tape, Liquid phase, Graphite oxide, Epi. Growth and CVD has an effect on the quality, size, amount and complexity of graphene, however, no effect on graphene solubility has been documented. For more on these methods and the characteristics of the graphene obtained by the different methods, please see the publication contained in the attached file.
LPE Graphene:
Making use of different approaches, unfunctionalized and non-oxidized graphene sheets can be produced; among them an inexpensive and scalable method based on liquid-phase exfoliation of graphite (LPE) holds potential for applications in opto-electronics and nanocomposites. Here n-octylbenzene molecules are used as graphene dispersion-stabilizing agents during the graphite LPE process. It was demonstrated that by tuning the ratio between organic solvents such as N-methyl-2-pyrrolidinone or ortho-dichlorobenzene, and n-octylbenzene molecules, the concentration of exfoliated graphene can be enhanced by 230% as a result of the high affinity of the latter molecules for the basal plane of graphene. The LPE processed graphene dispersions were further deposited onto solid substrates by exploiting a new deposition technique called spin-controlled drop casting, which was shown to produce uniform highly conductive and transparent graphene films.
This text was taken from the publication contained in the following link. The publication does not indicate any effect of the graphene preparation method on its solubility. The major effect is on the quantity (yield) of graphene.
The choise of the solvent for LPE is crucial. The best solvents are those with a surface tension that matches the surface energy of graphene, so solvents with a surface tensions of ~40-45 mN/m. Until now, the best solvent (without any addiction or modification) is N-methyl-2-pyrrolidinone.
It is also possible exfoliate in a water/surfactant solution, but then your graphene flakes will be sorrounded by surfactants molecules. So, the choise of the solvent also depends by the applications that you want to exploit.
See:
Production and processing of graphene and 2d crystals, http://dx.doi.org/10.1016/S1369-7021(13)70014-2
Indeed, graphene is not dispersible in water without impurities as described above (surfactants, partial oxidation). In general, dispersibility in a liquid depends on the interfacial energy between the graphene and the liquid. There are some liquids that manage to minimize sufficiently, as mentioned above. A more thorough discussion can be found in the work of Jonathan Coleman (Trinity College Dublin, Ireland) albeit that we did some work ourselves too.
indeed dispersibility will depend on preparation method and intensity of mechanical input. One step is to get it dispersed were especially at lower energy input chemical interaction will make a big difference. Second is to get it stabilized (solvated).
Titus touches an interesting point: there is the interaction energy between sheets that needs to be broken and subsequently solvent-graphene interfacial tension needs to be minimized. I doubt whether that can be done with the same solvent conditions.