Today’s low cost (typically 60 to 70 euro in 2023) domestic multimode microwave oven has its origins in P.L. Spencer’s method of treating foodstuffs, US Patent 2,495,429 (1950) [44] . These ovens are primarily designed to defrost and heat foodstuff using a free-running cavity-magnetron operating at a frequency of f₀ = 2.45 ± 0.05 GHz [45] [46] . In many cases, the cavity-magnetron employs a Feinberg voltage-doubler drive circuit [47] that controls the cavity-magnetron voltage and hence the cavity-magnetron rated instantaneous or continuous wave (CW) output power. For this type of applicator, the cavity-magnetron average output power is normally controlled by a pulse-width-modulation (PWM) circuit that sequentially turns on (T_on period) and turns off (T_off) the line-voltage at the step-up side of microwave oven transformer (MOT). The result is a time-modulated power waveform that is expressed as a duty cycle, where T_on plus T_off equals the base-time, and T_on minus base-time equals the duty cycle. This is a key aspect of the oven’s ability to provide macro control of the dielectric volume heating of foodstuff, or in this case microwave-assisted synthesis of Au and Ag nanoparticles and their functionalization. For example, Table 1 shows the relationship between T_on, T_off and base-time and average output power of cavity-magnetron within the Bluesky (model BMG20-8) domestic microwave oven [42] .

With reference to Table 2: in 2007, Nadagouda et al. [22] used an inverter circuit [49] within an unspecified Panasonic microwave oven to reduce HAuCl₄ using α-D-glucose (C₆H₁₂O₆), maltose, and sucrose (C₁₂H₂₂O₁₁). Here the inverter circuit converts the mains supply frequency (50/60 Hz) to a variable rate of some 20 to 45 kHz and by varying this frequency the cavity-magnetron output power is linearly controlled, in this case, 1000 W for 30 and 45 s to achieve the

target Au nanoparticle. Yasim et al. (2014) [23] used an unspecified microwave oven to reduce HAuCl₄ with hibiscus rosa-sinensis leaf extract within an adjusted 8 ml mixture at 420 W and process time of 90 s to achieve their target AuNP product. Bhosale et al. (2015) [25] used an LG intellowave™ sensor microwave oven (model unspecified) to reduce HAuCl₄ with Dimethyl sulfoxide (DMSO) for synthesis of nano-flowers and spherical nanoparticles. They used “360 W, 600 W, and 800 W with on/off mode having time interval of 30 s”. Given this ambiguous text, they found 800 W for 120 s was optimal to produce Au nano-flowers; and 800 W for 180 s was optimal to produce Au spherical nanoparticles. In each case, a 5.5 ml mixture of HAuCl₄ and DMSO was used. Publications [27] [29] and [31] originate from the same institutions with related ambiguous reporting of the microwave parameters used. For example, El-Nagger et al. (2016) [27] used a Galanz microwave oven, (model number unclear) to reduce a 25 ml mixture of HAuCl₄ and bacterial exopolysaccharide (curdlan) with power irradiation time 2 to 10 minutes for an unspecified power level to achieve their Au core shell product. Some four years later, Hussein et al. (2002) [29] used an unspecified microwave oven to reduce a 12 ml mixture of HAuCl₄ and dextran with an unreported microwave power level for an irradiation time of 40 s to achieve the target AuNP product. Finally, Diab et al. (2022) [31] while referencing [27] used an unspecified microwave oven to reduce a 12 ml mixture of HAuCl₄ and carboxymethyl chitosan (CMCT) and for an unspecified microwave power level for an irradiation time of 40 s to achieve the target AuNP product. Given the six-year spacing between these publications and the authors’ unsuccessful attempts to establish the microwave power conditions these three papers are not explored further.

Table 3 provides the Ag nanoparticles and AgHA synthesis information. Within this group of papers, two publications were found to have ambiguous reporting of microwave variables. First, Saha et al (2013) [32] used an IFB-30SC3 (miss-reported as IFM3SC3) microwave oven to reduce a 60 ml of AgNO₃ and Ocimum leaf extract using 900 W for 90 s to achieve the target Ag nanoparticles product. Second, Igbal et al. (2013) [33] used a Samsung MW71B microwave oven (rated 800 W) to reduce 100 ml of AgNO₃ and cetyl-trimethylammonium bromide (CTAB) using a medium high power level (600 W [50] ) with a stated 15 s on and

15 s for a processing time of 420 s. However, the stated ON-OFF time equates to a 50% duty cycle or an average power of 400 W of the cavity-magnetron.

The estimated process energy budgets relating to the publications presented in Table 2 and Table 3 are given in Figure 1. Within this limited dataset it is observed that the Green Chemistry has a lower process energy budget compared to the non Green Chemistry: on average 7.531 kJ against 4.775 kJ. In the specific case of HAuCl₄ reduction by α-D-glucose (C₆H₁₂O₆), sucrose, maltose (C₁₂H₂₂O₁₁), hibiscus leaf extract and hydrolyzed 3-Mercaptopropyl trimethoxysilane (MTPMS), the process energy budgets are very similar (30, 48, 48, and 37.8 kJ) indicating that the bio-chemical constituents within the hibiscus extract have a similar reducing efficiency to that of the saccharides. Also not, that the AgNO₃ reduction by Coleus amboinicus leaf extract shows similar process energy budget to that of the saccharides and hibiscus extract. In contrast the organic-bromine compound within CTAB exhibits the highest process energy budget.

Figure 2 shows the energy phase-space projection of data values from Figure 1. In this projection, the process energy budget is plotted on the horizontal-axis over two orders of magnitude (10 to 1000 kJ) and the process energy density is plotted on the vertical-axis over three orders of magnitude (0.1 to 1000 kJ×m⁻¹). The log-log axis enables both large and small scale energy processes to be visualized. This also allows a general power-law function (y = cxⁿ, where y and n are constants, with n being referred to as the exponent) to be fitted to a linearized distribution. However, verification of a power-law behavior is not trivial as the linearized data must extend over at least two orders of magnitude on both the x- and y-axis, and yield at good fit at either end of the linearized dataset (Stumpf and Porter (2012) [51] ). Using Microsoft Excel linear regression analysis software combined with the Stumpf and Porter criteria, it is observed that all of the Au and Ag nanoparticles data

points form a cluster with center of 76.83 kJ and 6.59 kJ×ml⁻¹. When the data points are separated into Green Chemistry and non Green Chemistry a more detailed picture is formed. That is the non Green Chemistry data points tend to be located at the higher process energy budget range and the Green Chemistry data points tend to be located in the lower energy budget range. An attempt to fit a power-law trend line to AuNP cluster yields a regression analysis of R² = 0.1076 indicating a poor correlation. Of further note is that the: cube, flower hexagon, prism Au nanoparticles appear to form a sub-cluster within the middle of the Au nanoparticle cluster. Fitting a power-law function to the Ag nanoparticle dataset yields an exponent n = 1.7874 over approximately one magnitude on the x- and y-axis with a regression analyses of R² = 0.514, these two fitting parameters indicate the number of data points is insufficient to detect a power-law relationships.

Between 2004 and 2005, Hayes [52] , and Hayes and Collins [53] developed the technique of forced air cooling of the outer surface of a vessel containing polar chemicals while administering microwave irradiation, the source of this approach meant it became named as “enhanced microwave synthesis” (EMS). The aim here, is to impart microwave energy directly into the polar molecules, whistle maintaining a relatively low bulk temperature, to induce an increased target product yield by preventing side reactions. In the same time frame the term “non-thermal” and “athermal” microwave-assisted was adopted to highlight a possible difference in the mechanisms involved in microorganism inactivation processes [43] [54] - [59] . The term “temperature controlled microwave chemistry” (TCMC) is also used where the reactants are cooled by refluxing or cooling directly, and where the suspension bulk temperature is monitored and used as an input parameter of a feedback circuit where the output signal controls the cavity-magnetron power. See for example Kormin et al. (2014) [60] . It is noted however that no temperature information was reported in many of the following papers pertaining to TCMC synthesise Ag nanoparticles.

Table 4 lists the microwave parameters of five batch TCMC synthesis of Ag nanoparticles [35] [36] [37] [38] [39] . The first synthesis (Chen et al. (2008) [36] ) reduced and stabilized AgNO using carboxymethyl cellulose sodium (CMS) within an adjusted 200 ml of H₂O. This one-pot Green Chemistry synthesis takes an unusually long time for a microwave-assisted process to complete (1 to 11 hours). Of further note, this extended process time is comparable to the microwave-assisted extraction of CMS from brewer’s spent grain [61] . In 2012, Bahadur et al. [37] used a TCMC-064 oven attached with a refluxing system to synthesize Ag@SiO₂ Tetraethylorsilicate, (TEOS: (Si (OC₂H₅)₄) as a shell agent plus ethanol (C₂H₅OH). This second step was performed at 360 W for 600 s. However they did not report the quantities of TEOS and C₂H₅OH used. By 2015, Karimipour et al. [38] at the University of Rafsanjan, Iran used a similar

TCMC-064 oven attached to a refluxing system to synthesize spherical AgNPs. In this case dimethylformamide (DMF) was used as the reducing agent and oleylamine (OA) as a surfactant and capping agent Using an adjusted 20 ml volume of H₂O. The complete mixture was microwave irradiated as a one-pot synthesis at 540 W for 30 s. In the following year two further papers from the same university and same TCMC attached to a reflux system were published, by Ebrahimi et al. (2016) [39] , and Karimipour et al. (2016) [40] . Ebrahimi et al. synthesized Ag@TiO₂ using a one-pot synthesis of AgNO₃, PVP in 40 ml of C₂H₅OH with a microwave power of 360 W for 60 s. Whereas Karimipour et al. synthesized Ag@SiO₂ core-shells using a two-step process. The first synthesis used water soluble polyvinylpyrrolidone (PVP) and AgNO₃ adjusted to 40 ml volume in C₂H₅OH and microwave irradiated at 360 W for 60 s to produce PVP capped Ag nanoparticles. In the second step 100 μl of aminopropyltriethoxysilane (APTES) was added to the 40 ml of PVP capped Ag nanoparticles followed by 1.2 ml of TEOS as the shell agent to produce the target Ag@SiO₂ core shell; the microwave conditions being 360 W for 600 s.

Using the reported power, process time in Table 4, an estimation of the process energy budgets is given in Figure 3. Here it can be seen the TCMC-102 has a process energy budget (1440 kJ), some 21 times greater than the average energy

budget (67.08 kJ) of five Shikoku Keisoku SMW-064 oven experiments. Undoubtedly the high process energy budget is mathematically derived from the extended process time. Nevertheless, given the absence of temperature data, it is interesting to calculate how far TCMC-102 applied power needs fall to average 67.08 kJ. This equates to 18.7 W, and which needs to be accounted for when comparing the two applicator types (TCMC-102 without reflux systems and the Shikoku Keisoku SMW-064 Sk-064 with reflux system).

An estimation of process energy density of five of the TCMC oven synthesis has been calculated using the data within Figure 3 and their respective mixture quantities (200, 20, 41.2, 41.2 and 40 ml). Bahadur et al. [37] is not included due to lack of quantity information. The estimations are found to range between: 7.2, 0.81, 0.524, 5.24, and 0.54 kJ×ml⁻¹, respectively. This comparison reveals the energy density disparity between the TCMC-102 and the Shikoku Keisoku SMW-064 with a reflux system is a factor of 2.5. The relative reduction in process energy budget may be due to the ability of the reflux system to maintain the solvents in a similar way to that of microwave-assisted extraction that employs reflux systems [62] , in doing so maintaining the rate of Ag reduction. To verify the involvement of these mechanisms further experiments are needed to be undertaken.

This section looks at five publications pertaining to commercial turntable loaded multimode microwave-assisted synthesis of Au-X and Ag-X nanomaterials, where the microwave applicators are primarily designed for digestion (Bizzi et al. (2011) [63] ). These microwave digestion systems have been demonstrated to be very effective in the second step synthesis of Ag nano-rods under Na₃ct conditions (Liu et al. (2005) [15] ), Green Chemistry synthesis of Au-Ag core-shell nanoparticles using C₆H₁₂O₆, H₂O and PVP (Blosi et al. 2008 [16] ), and the non Green Chemistry synthesis of Ag@SnO₂ core-shell (Rai et al. (2015) [17] ). More recently one-pot synthesis of Ag nanoparticles on graphene sheets has been reported by: Alfano et al. (2016) [18] , Miglietta et al. (2018) [19] , and Marinoiu et al. (2020) [20] ). More recently, a one-pot synthesis of Ag and Ag-Cu nanoparticles using ethylene glycol as the solvent and Copper Acetate (Cu(CH₃CO )₂) for the Cu precursor has been reported by Reyes-Blas et al. (2020) [21] . However, little information on the suspension quantities was given. Therefore only the process energy budget is calculated, see Figure 4.

Generally, these digestion systems (MARS-5, Mars-6, Milestone MicroSYNTH plus (μSYNTH), and the Anton Paar Multiwave (APM)) have a cuboidal multimode cavity that contains a removable turntable that holds a multiple of vessels for single, or, multiple batch processing. Under microwave illumination conditions the rotating turntable smoothes out electromagnetic standing waves and acts as a microwave absorbing dumpy load, in the case of the μSYNTH, a mode stirrer is used to disperse the electromagnetic standing wave [64] .

Table 5 lists the reported microwave operating conditions for the five publi

cations. Briefly the experimental conditions are as follows. Liu et al. used 11 ml of reactants within a MARS-5 system with a microwave irradiated 1200 W at 100% duty cycle for a series of process times: 60, 120, 240, and 480 s. After characterization of their rod and spherical Ag nanoparticle products, a process time of 240 s was considered acceptable. Blosi et al. used the μSYNTH system that employs two cavity-magnetrons. The power was ramped-up and held, as determined by software that controls the cavity-magnetron pulse width modulated power level for 300 s. The mixture quantity was not given, but the manufactures recommend a value between 10 and 50 ml [64] . Rai et al. also used the MARS-5 digestion system with a mixture volume of 21 ml. The applied power is not reported, but it is known that the process involved a ramp time of 5 minutes to reach a bulk temperature of 70˚C and held there for 1 hour, again using PWM of the cavity-magnetron to produce the Ag@SnO₂ core-shell nanoparticles. Alfano et al. and Miglietta et al. used the APM system, with two aliquots of 3 ml reactant volumes. The applied power was set to 700 W with a 91.67% duty cycle (T_on = 120, T_off = 10 s) for a process time of 45,000 s to produce AgNP decorated graphene sheets [65] . Finally, Marinoiu et al. used the MARS-6 at cavity-magnetron power of 800 W for a process time of 300 s to produce their target product of Ag nanoparticle supported on a graphene sheet.

Using the reported information within the six publications [15] - [21] and private commutation [65] an estimation of the five synthesis process energy budget has been made with the following duty cycles. For the processes that use a 100%, duty cycle, the applied power is multiplied by the process time [15] [20] and [21] . For the processes that use a 91.67%, duty cycle, the applied multiplied by 91.67% and then multiplied by the process time is used [18] [19] and [65] . For the two processes that use a ramp-time and hold time a best estimation is obtained by multiplying the applied power by 75% then multiplying by the hold process time. The computed values for each synthesis are presented in Figure 4. Figure 5 depicts the computer energy density calculations for references 15 to 20, where the process energy density for [21] is not shown due to insufficient data.

The use of axial field helical antenna applicator entails placing the reactants to be processed within the internal electromagnetic field (reaction zone) of a helical antenna. This type of applicator comprises a solid-state microwave oscillator (λ_o = 2.45 ± 0.05 GHz) and amplifier connected to a 1/4 (or multiple of) wavelength air filled helical antenna without any structural modes (Öhrngren et al. (2012) [66] ). Under these load conditions the dielectric properties of the reactants will

reduce the electrical length of helical antenna, thereby frequency-pulling the coupled oscillator. As long as the degree of pulling is within the oscillator −3 dB bandwidth, which depends on the coupling factor between the oscillator and antenna (Law (2008) [67] , Amry, Law and Boyd (2012) [68] ) power is maintained to the antenna. In effect the applicator has an auto impedance matching circuit, similar to the cavity-magnetron waveguide bandwidth of a domestic microwave oven (Law and Dowling (2021) [46] ).

In 2016, Bayazit et al. [41] ) reported on a one-pot constant flow microwave-assisted anisotropic growth of Au nanowires and rods. In this synthesis, HAuCl₄×4H₂O is reduced using Na₃ct, The synthesis apparatus comprise the commercial Discover 2 (CEM Microwave Technology Ltd), applicator within which is placed a coiled flow reactor constructed from approximately 6 ml volume of 3.4 mm outer diameter Teflon tubing. Using this diameter tubing, the microwave penetration depth is > the tubing diameter (Ye et al. (2020) [69] ) thereby assuring uniform dielectric heating whilst providing minimal disturbance of the antenna electric field. Finally, the reactants are forced through the reactor using a syringe pump at a rate of 4, 7, and 10 ml×min⁻¹ that equated to a residence time (τ) between 1.5, 0.85, and 0.6 minutes. The residence time (τ) is calculated using Equation (3).

τ = volume flowrate , where time is measured in minutes (3)

The residence time measured in seconds multiple by the applied microwave power equates to the process energy budget. For reproducible anisotropic growth of Au nano-rods with an aspect ratio (length × width) of approximately ~10 × 7 nm, the power, flow rate and residence time are presented in Table 6.

Using the same energy calculation methodology as in 3.1, and converting minutes to seconds a process energy budget of 3.2 kJ and energy density of 0.81 kJ×ml⁻¹ is obtained. This equates to an energy transfer efficiency of 0.253 kJ×ml⁻¹ per applied kJ at 36 W applied power.

This section describes energy phase-space projection mapping and comparison of the microwave energy parameters obtained for the four microwave applicators types and their NP synthesis. The results of the computation are given over four orders of magnitude on both the horizontal x-axis (1 to 10,000 kJ) and the vertical y-axis (0.1 to 100 kJ×ml⁻¹) Figure 6. The figure reveals a number of identifiable features within the datasets.

Firstly, the mapping process reveals that the axial field helical field antenna applicator (star) exhibits the least energy density (3.2 kJ, 0.81 kJ×m⁻¹; at an

applied power of 36 W). Followed by microwave oven (76.83 ± 39 kJ and 4.47 ± 3.9 kJ×ml⁻¹), TCMC (343 ± 321.5 kJ, and 2.86 ± 2.3 kJ×m⁻¹), digester systems (1010 ± 620 kJ, and 36.2 ± 50.7 kJ×m⁻¹). In the case of the axial field helical antenna applicator data point, this is clearly separated from the nearest TCMC data points indicating the log-log scale is still enabling small and large values to be visualized.

Secondly, a power-law fitted through the digester (circles) and TCMC (squares) datasets provide a local ( n = 0.8412 and 0.6199, and regression analyses of R ² = 0.7642 and 0.8974, respectively. In addition the digester dataset power-law trend-line (by eye) projects back from the Au nano-rod data point, through the microwave oven crystal morphology cluster and on to the axial field helical antenna Au nano-rod data point (3.2 kJ and 0.8 kJ×m ⁻¹). This projection is quantified by a power-law fit over two orders of magnitude (dash-dash trend-line) with an exponent n = 0.7719, and regression analyses R ² = 1. When the digester, microwave oven and axial field helical antenna exponent n values are averaged, an exponent n = 0.806 is obtained. In comparison the exponent n = 0.699 TCMC dataset is offset by some −10 kJ×ml ⁻¹ to the digester-to-axial field helical antenna power-law trend-line, indicating there is an additional mechanism involved. Finally, Au and Ag microwave-assisted synthesis exponent may be derived by averaging all exponents which equate to n = 0.730 ± 0.07.

Thirdly, the Au and AgNP morphology outcomes within their respective applicator type reveal a degree of correlation. For example, the constant flow axial field helical antenna applicator (star) that uses the non Green Chemistry Na₃ct reducing agent yields the lowest process energy budget and process energy density for all the datasets reported in this study. The five TCMC data points representing spherical and core shell Ag nanoparticles have the second least energy efficiency for both Green Chemistry and Non Green Chemistry. The digester dataset has the lest energy efficiency performance, but this may be due to the estimated 75% duty cycle used to characterize the ramp and hold-time power levels.

Fourthly, assuming a microwave-assisted nanoparticle synthesis power-law exponent n = 0.730 ± 0.07 reflects the historical nanoparticle datasets. It is reasonable to assume that the relative phase-space location of a given target Au, or, Ag nanoparticles and their yield (counts per ml) along this exponent will be altered by an informed change the in synthesis variables: bulk temperature, concentration, pH, solvent medium, and process time, or purification of plant extract suspension (thereby removing potential side reactions) prior to the nanoparticle synthesis step.