TECHNOLOGY FOCUS - ENVIRONMENT - Preferred Method: The monitoring includes quantifying the flow-rate of the quantum dots, and calculating a fracture-surface area of the subterranean formation based upon the flow rate of the quantum dots. The flow-rate is quantified using the flow of quantum dots from or within the subterranean formation. In the method, the property is new fracture areas of the subterranean formation, and the injecting step includes injecting a fracture fluid with the solution of quantum dots into the subterranean formation, and the monitoring step includes identifying locations where quantum dots emerge from the formation to identify new or increased fractures. The monitoring is done using size exclusion chromatography with a fluorescent detector. The method further comprises fracturing the subterranean formation prior to the injecting step, where the injecting step occurs simultaneously with the fracturing step. The quantum dots are injected with a carrier fluid.    TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Components: The quantum dots: comprise a semiconductor material, which is cadmium, lead, zinc, mercury, gallium, indium, cobalt, nickel, iron or copper as a cationic component and/or sulfide, selenide, telluride, oxide, phosphide, nitride or arsenide as an anionic component; have a core-shell structure; and include hydrophilic ligands or a scale inhibitor attached to them. The hydrophilic ligands include an alkane, alkene or alkyne functionalized with at least one transit control group including thiol, amine, hydroxy, carboxy, amide, citrate and/or halide groups. The hydrophilic ligand is attached to the quantum dot through a coupling group including amino coupling groups-, mercapto coupling group, hydroxy coupling group and/or carboxy-silane coupling group. The scale inhibitor includes polycarboxylates, polacrylates and/or polymaleic anhydrides. The quantum dots include a semiconductor material substantially encapsulated by a layer comprising oxides of silicon, titanium, zinc, tungsten, molybdenum, copper, iron, nickel, tin, niobium, aluminum, cadmium, and mixed metal oxides of the above compounds. The quantum dots are substantially encapsulated into a single silica nanosphere prior to injection into the subterranean formation. The silica nanosphere: includes many quantum dots that all fluoresce at a common wavelength; has a diameter of 5-150 nm; and includes an organic polymeric compound. The carrier fluid includes water, fracture fluids and/or petroleum-based solvents.