Microwave irradiation is considered an important approach to Green Chemistry, because of its ability to rapidly increase the internal temperature of polar-organic compounds that lead to synthesis times of minutes rather than hours when compared to conventional thermal heating. This works describes a dual allometry test for the discrimination between the solvents and reagents used in the microwave-assisted synthesis of transition metal (zinc oxide, palladium silver, platinum, and gold) nanostructures. The test is performed in log-log process energy phase-space projection, where the synthesis data (kJ against kJ·mol-1) has a power-law signature. The test is shown to discriminate between recommended Green Chemistry, problematic Green Chemistry, and Green Chemistry hazardous solvents. Typically, recommended Green chemistry exhibits a broad y-axes distribution within an upper exponent = 1 and lower exponent = 0.5. Problematic Green Chemistry exhibits a y-axes narrower distribution with an upper exponent = 0.94 and lower exponent = 0.64. Non-Green Chemistry hazardous data exhibits a further narrowing of the y-axes distribution within upper exponent = 0.87 and lower exponent = 0.66. In all three cases, the y-axes is aligned to original database power-law signature. It is also shown that in the x-axes direction (process energy budget) the grouped order of magnitude decreases from four orders for recommended Green Chemistry solvent and reagent data, through two orders for non-Green Chemistry hazardous material and down to one order for problematic Green Chemistry.
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