NOVELTY - Solution or dispersion of graphene using a solvent having a chi value of less than 0.08, a surface tension value of 36-43 mJ/m2 and a dispersion limit of the graphene within the solvent of greater than 0.05 mg/ml, is claimed.    USE - The solution or dispersion of graphene is useful for preparing a polymer composite and exfoliating graphite to obtain graphene (claimed), where the graphene is used as graphene sheets in fuel cell, electrodes for a battery structure, lubricant, fuel additive, as a matrix for the construction of catalysts, production of tires, constructing a flow sensor for measuring liquid flow velocities along a direction of liquid flow, as carriers for drugs, as a taggant to identify materials or as a tracker, as sunscreen agent, as a synthesis scaffold for building biological materials, for the construction of solar cells as an electrode, light pipe, or as a basis for deposition of other materials including zinc and tin oxide, for separation of mixed solutes mixtures of carbon nanotubes of different sizes or different numbers of walls, as surface coatings that is used as an electrode, e.g. on the touchscreen or as a cathode for an LCD display or plasma television panel, for fabricating conductive ink or paint, for constructing an electrochemical capacitor or super capacitor, and constructing a fire or flame retardant material.    ADVANTAGE - The solution or dispersion of graphene: has a chi value of less than 0.08, preferably 0 to -0.13, and a surface tension value of 36-43 mJ/m2, preferably 39.4 mJ/m2 (claimed); permits improved chemical processing of the macromolecules including functionalization, absorption, adsorption and entrainment of other chemicals, coatings with other chemicals, etching, and oxidation; provides conductive composite materials having a relatively high resistance for protection against static electricity and electrical shielding, or relatively low resistance for printed wiring; and utilizes low cost raw materials.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are also included for:    (1) exfoliating graphite to obtain graphene, comprising dispersing the graphite in a solvent to form a dispersion or solution, and separating the exfoliated graphene from the dispersion or solution;    (2) preparing (M1) a polymer composite, comprising (a) dispersing graphene in a solvent, where the graphene-solvent solution has a chi value of less than 0.01, and (b) capturing the dispersed graphene in a solid phase polymer matrix; and    (3) a polymer composite comprising sufficient amounts of single layer graphene dispersed in a polymer matrix to provide for improved strength, electrical conductivity, thermal conductivity, flame retardancy or UV absorptivity.