From the early 1960s, the lasting legacy of the American marine biologist, and author, Rachel Carson (1907-1964) has been to bring to an end the misuse of synthetic herbicides and pesticides by inspiring public opinion, then governments, to consider responsible protection of the environment (Carson (1962) [1] ). The English scientist and environments James E Lovelock is best known for developing the electron capture device that detects poisonous pesticides and the presence of chlorofluorocarbons that destroy the Earth’s ozone layer (Lovelock, Maggs and Wades (1971) [2] ), and the Gaia Hypothesis, which postulates that the Earth functions as a long term self-regulating system (Lovelock (1972) [3] ) have become an important milestone in understanding the deleterious impact of human behavior on the Earth’s biosphere. Perhaps the photograph of the Earth taken some 17,300 kilometer distance from the Earth by crew members of Apollo 17 spacecraft as it travelled to the moon (National Aeronautics and Space Administration (1972) [4] is generally acknowledged as one of the most influential images for the advocacy of Earths protection as it orbits through the Sun’s heliosphere. In light of these examples, and surely many others, a new focus in chemical manufacture from one of pollution control and end-of-pipe waste treatment to one of pollution prevention began to be established. Initially described as “Minimum Impact Chemistry” (Drasar (1991) [5] ), or “Benign by Design Chemistry” (Anastas (1994) [6] ), this approach has many direct and indirect manufacturing cost benefits in various segments of the chemical industry. Now more formally known as “Green Chemistry” (Anastas and Warner (1998) [7] ) it embodies the following twelve principles: 1) waste prevention not remediation, 2) reduce amount of material used (atom efficiency), 3) use benign (less harmful) materials, 4) safer products by design, 5) use less solvents and auxiliaries, 6) use less energy 7) use renewable feedstock (biomass), 8) reduce process time to produce less side-chain products, 9) use catalytic rather than stoichiometric reagents, 10) design products for degradation, 11) develop analytical methods for pollution control and finally, 12) use inherently safer processes.

Since the 1980s, microwave-assisted synthesis of organic compounds within microwave ovens (Gedye, Smith and Westaway (1988) [8] , and Gedye, Rank and Westaway (1991) [9] have been found to encompass five of the twelve principles of Green Chemistry (use of fewer solvents and auxiliaries, use of less energy, reduced process time, and increased product yield). Following this a mass-based Environmental-Factor (E-Factor) metrics, or indicators (Sheldon (2008) [10] , Sheldon (2018) [11] , Abdussalam-Mohammeda, Alia and Errayes (2020) [12] ), have been used to quantify the associated term “environmentally friendly, or benign” conditions that microwave applicators promote in the synthesis of organic compounds (Santra et al. (2014) [13] ), and in transition metal complexes (Gabano and Ravera (2018) [14] ). Recently (2023), it has been demonstrated that the E-Factors metrics can also be used to quantify and mitigate plastic waste and climate change (Sheldon (2023) [15] ). Of further note, if all the material used in a chemical transformation is turned into useful products then there would be no waste, and the mass-based E-Factor would be of zero.

Recently, a historical review of forty-five microwave-assisted synthesis of Zinc oxide (ZnO), palladium (Pd), silver (Ag), platinum (Pt) and gold (Au) nanostructures and five dielectric volume heating of water (H₂O) exhibits a two-variable power-law signature (y = 0.3293x^0.846; R² = 0.7923) over four orders of magnitude (Law and Denis 2023) [16] , Law and Denis (2023) [17] , and Law and Denis (2023) [18] ) In this body the historical data (here termed Database B, n = 50) was mapped using process energy phase-space projection where the applied microwave energy (measured in kJ) is plotted on the horizontal axes and the process energy density (measured in kJml⁻¹) is plotted on the vertical axis. Using this means of projection a systematic energy efficiency index of the microwave-assisted synthesis allows a comparison to be made between different microwave applicator and chemical used, in the projection having a predictive value in designing new microwave synthesis pathways. However, there is a disconnect between established mass-based environmental metrics and the process energy density value that is measured in kg·ml⁻¹ Thus there is a need to reevaluate the projection coordinates for full Green Chemistry integration.

The aim of this work is to remove the current disconnect between the initial process energy phase-space projection (where the energy density is volume-based) and mass-based E-Factor metrics. To achieve this aim, Database B, n = 50 is reexamined for the mass data. However, data mining across fifty different processes encounters many challenges (non-uniform method of reporting and recording of experimental data, or absent data), resulting in a reduction in usable information. To maintain the largest database as possible, a new search for alternative historical publications has been undertaken. This new database is called Database C, n = 49, see Appendix 1, Table A1 . It is shown that using this new database a synergy between mass-based E-Factor metrics and the process energy phase-space projection enables a direct comparison of historical microwave-assisted synthesized transition metal nanostructures can be made. To further address environmental concerns plant-based biomass extract that contains natural bio-reducing agents that contribute to the overall reduction of the metal precursors is considered.

Figure 2 shows the log-log process energy phase-space projection of database C, n = 49. Log-log space is used here as the emphasis is on identifying a function over orders of magnitudes rather than outliers which can give a visually misleading illusion. Where the emphasis is the identification of outlier’s log-linear space is generally used [18] . In this work, the Microsoft linear regression power function is used to calculate the least squares fit through the data points to obtain the trend-line y = 0.007x^1.1303; R² = 0.5392. The function splits the data into twenty above the trend-line, twenty three below the trend-line, and six points on the line. With regard to the applicator spread, the microwave oven (green) and TCMC Blue) applicators are spread across the length of the trend-line, the ERTEC applicators (black) are located high energy region, and finally the Discover^® applicator operating in the continuous-flow mode used to synthesize Au rod-like nanostructures [58] (here denoted as a large yellow filled triangle with black boarder) is located at the extreme lower end (3.2 kJ) energy region. In contrast, the Discover^® batch-process applicator used to synthesize Pd and Pd supported of carbon framework [21] are in the mid (120 kJ) energy region. In the mid energy range are the renewable plant-based biomass data points (large green triangle, square, and circle with black boarder). These data points are made from synthesized of Au nanostructure using white bol guava leaf extract [22] ; synthesized ZnO using Sandoricum koetjape peel extract [32] [33] ; synthesized of Ag from Coleus amboinicus leaf extract [39] ; synthesized Ag using Ocimum leaf extract [47] ; and synthesized Au using Hibiscus rosa-sinensis leaf extract [55] .

Table 3 provides the Microsoft linear regression trend-line parameters (number of data points, slope intercept (c), exponent (n), and regression fit (R²)). A simple

statistical analysis of this data shows the average valve for c and n, and R² are: c = 1.3884 kJ·g⁻¹, n = 1.1406 and R² = 0.5542. Here it is noted that when evaluating a goodness of fit to a power-law using linear regression analysis, a low R² score is not necessary a good measure over two or more magnitudes of range [17] [63] . When removing the Pt data points from this average calculation (due to the low number of data point (4) and relative extreme value of c, a reduced average value of c = 0.064 kJ·g⁻¹ and n = 1.2787 is obtained. Both of which are a close match to the power-law signature values observed in Figure 2 . This outcome shows the need for evaluation tests when determining the contribution of subsets within a power-law signature.

To visualize the each term of Equation (1) a triplet rank plot is generated, where the magnitude and sign of the waste, product and E-F_m value are mapped using a log scale to highlight the dynamic range of the calculated quantities. In general, the main attributes of this representation is twofold: first the extreme ends are candidates for outlier due to possible error in the data analysis and, second if the data is correct then low ranked data points will be associated with a large percentage of reactants transformed into product and high ranked data points with have a low percentage of reactants transformed into product. These two attributes therefore highlight possible uncertainties within the synthesis data, or if correct the “Greenness” of the synthesis within the data is easily identified.

Figure 3 shows this mapping operation using the same applicator-type color representation as in Figure 2 , Table 2 . For numerical ranked data see Appendix 1, Table A1 . Using this representation the E-F_m data forms a slow sign curve that increases in positive magnitude from 2.3 [48] to 4,583.7 [50] . There are four features of interest in the ranking. First, the TCMC microwave applicator-type (blue squares [25] [36] [43] [44] [45] ) are gathered to the right of the ranking indicting that they are likely to generate more waste than products compared to other microwave applicator-types. This is because the applicator-type tends to use more solvents to produce the target product than the other applicator-types. Second, Pt products tend to be aligned in the middle (ranking: 16 to 24) using

either the Discover^® applicator operating in batch-process mode [21] , or microwave oven applicators [34] [35] [54] . Third, the Discover^® 2.0 applicator operating in the continuous-flow mode [58] is ranked 32. It is also noted that the Discover^® 2.0 applicator operating in the continuous-mode to synthesize Au nano-rods has a higher E-F_m value (109) when compared to its batch-process mode (21 to 25) which is used to synthesize Pd nanostructures. Fourth, a direct comparison can be made by comparing the two top ranking positions of 48 and 49, where the same microwave oven applicator is used to reduce hexachloroplatinate(IV) acid (H₂PtCl₆·xH₂O) using ethylene glycol (EG) to form mono Pt nanoparticles, and Pt supported on a graphene framework [50] . Fifth, the six data points associated with plant-based biomass are spread out across the raking (3, 10, 15, 31, 33, and 44).

Of further note, the waste curve (light blue) and product curve (black) do not exhibit the smooth appearance of the E-F_m data, but rather a mirrored irregular appearance is superimposed on their curves. This is because of the construct of the E-F_m equation.

plant-based biomass a meaningful way to assess two of them positioned within the projection is to examine a narrow process energy bandwidth (30 to 48 kJ) and then all six plant-based biomass data points in a broader process energy bandwidth (20 to 98 kJ) Table 4 .

Within the narrow energy band the two highest rank E-F_m values [50] , the up-down arrow involves a one-pot reduction of H₂PtCl₆·xH₂O using EG to form mono Pt nanoparticles and Pt supported on graphene framework. In the case of the mono Pt nanopartcles, all of the reactants (expect the reduced Pt atoms that are transformed into the target product) are form in the numerator waste mass which appears of Equation (1). Conversely the part of graphene oxide (GO) is reduced to graphene that goes into the target metal product supporting framework, that is denominator term of Equation (1). Lastly, the un-reacted GO, released oxygen atoms and EG are formed in the numerator waste mass.

The mid range rank E-F_m values microwave-assisted synthesis involves Ocimum leaf extract [39] and Coleus amboinicus leaf [47] extract to reduce silver nitrate (AgNO₃) to form mono Ag nanoparticles. In each case the synthesis is claimed to be “eco friendly” as renewable biomass is used in the synthesis.

The two lowest rank microwave-assisted synthesis E-F_m values involve Sodium citrate (Na₃Ct) to reduce Chloroauric acid (HAuCl₄·3H₂O) [59] , and dimethyl sulfoxide (DMSO) to reduce Gold (III) chloride (AuCl₃) [56] to form mono Au nanoparticles. In these two cases the synthesis is claimed to be a “green” or “greener” approach to nanofabrication based on the use of microwave energy alone.

The six data points associated with renewable plant-based biomass have a Microsoft fitted power function trend-line y = 1 × 10¹¹x⁻²; R² = 0.3032 that crosses the 49 data points trend-line at 30 kJ and 107.7. These data points are made from synthesized of Au nanostructure using white bol guava leaf extract [22] ; synthesized ZnO using Sandoricum koetjape peel extract [32] [33] ; synthesized of Ag

GO = graphene oxide, EG = ethylene glycol, Na₃Ct = Sodium citrate, and DMSO = dimethyl sulfoxide.

using Coleus amboinicus leaf extract [39] ; synthesized Ag using Ocimum leaf extract [47] ; and synthesized Au using Hibiscus rosa-sinensis leaf extract [56] .

Today’s environmental concerns encourages the use of renewable plant-based biomass in chemical reactions by attaching an environmental quotient to the environmental factor, the quotient represents the benign or non-benign nature of the waste [11] . Consequently, the E-F_m values presented here need to be adjusted in some quantified way. The data presented in Figure 4 and Table 4 exhibits a dynamitic energy component when considering the process energy budget. For example, using a simple multiplying factor of 0.01 for [39] [47] would bring them in line with [56] [59] in the narrow energy band, but not outside this energy region. One way of achieving a quotient for all the plant-based biomass data points is to use the power-law function. For example, at 10 kJ a multiplying factor of 0.005 is used, and at 100 kJ a multiplying factor of 0.018 is used. It is important to note the quotient would be suitable for [22] [32] [33] and for [39] [47] as they deal with the reduction of AgNO₃ to form Ag nanostructure, the later when leached into the aquatic environment are toxic to crustaceans and protozoa [19] .

This paper has constructed a mass-based process energy phase-space projection of microwave-assisted synthesis (widely considered as a useful Green Chemistry energy source) of transition metal (ZnO, Pd, Ag, Pt, and Au) nanostructures. The synthesis data has been obtained from forty-one publications published between 2004 and 2023. Using the reported chemical mass data (rather than volume data) and microwave power multiplied by process time (J·s⁻¹ × s = J) of the synthesis, a simple environmental-factor (E-F_m = waste measured in grams divided by product measured in grams) has been incorporated into the process energy phase-space projection. Collecting and collating the synthesis data is in line with the: second, sixth and eleventh principles of the twelve principles of Green Chemistry. Moreover, this analytical approach enables future microwave-assisted synthesis to be developed with the aim of reducing the amount of materials and energy consumed.

Highlights of this work are as follows:

Firstly, the using mass-based approach a power-law signature of y = 0.0073x^01.1303; R² = 0.5932 over three orders of magnitude is obtained. With an R² value of 0.5832 it can be postulated that the microwave energy transfer is directly proportional to the energy density (kJ·g⁻¹). This differs from volume-based two variable sub-linear power-law signature y = 0.3293x^0.846; R² = 0.7923 over four orders of magnitude. Given that the transition metal precursors investigated here have a density ranging 2 to 13.9 g·ml⁻¹ compared solvent investigated here (H₂O, EG, and ethanol) that are in the range of 1 to 1.2 g·ml⁻¹, this may a have an important role in the 1/4 difference. However further investigation is required.

Secondly, rank plots have a useful role in revealing and exploring E-F_m progression in regard to applicator-type the chemistry used.

Thirdly, as E-F_m metrics does not include an environmental impact of the generated waste (all waste is assigned the same environmental quotient), but for today’s environmental concerns environmental quotient needs to be considered. In this work, it is shown that E-F_m falls with increasing process energy budget with an exponent −2. Using this dynamic reference it is proposed a plant-based biomass equivalent E-F_m to the best performing non-biomass syntheses of ZnO, Pd, Pt, and Au may be achieved by using a multiplying factor of 0.005 at 10 kJ, or 0.018 at 100 kJ. The use of this dynamic reference, should be used with caution when the synthesis process generates Ag nanostructures as they are known to have a toxic effect on crustaceans and protozoa.

Fourthly, by extension, the quotient process may be used for environmentally benign solvents. Where transition metals, such as Ag are present in the waste further work is required to identify a more robust environmental quotient factor.