Quantiﬁcation of the Microwave Effect in the Synthesis of 5-Hydroxymethylfurfural over Sulfonated MIL-101(Cr)

: The potential beneﬁts of microwave irradiation for fructose dehydration into 5 hydrox-ymethylfurfural (5-HMF) have been quantiﬁed over a sulfonated metal–organic framework (MOF), MIL 101(Cr)-SO 3 H. The effects of temperature (140–170 ◦ C), batch time (5–300 min), and catalyst-to-substrate ratio (0.1–0.01 g/g) were systematically mapped. After 10 min of microwave (MW) irradiation at 140 ◦ C in a DMSO–acetone reaction medium, practically complete fructose conversion was obtained with a 70% yield of 5-HMF. Without MW, i.e., using conventional heating (CH) at the same conditions, the fructose conversion was limited to 13% without any 5-HMF yield. Rather, 90 min of CH was required to reach a similarly high conversion and yield. The profound impact of moving from CH towards MW conditions on the reaction kinetics, also denoted as the microwave effect, has been quantiﬁed through kinetic modeling via a change in the Gibbs free energy of the transition state. The modeling results revealed an eight-fold rate coefﬁcient enhancement for fructose dehydration owing to MW irradiation, while the temperature dependence of the various reaction steps almost completely disappeared in the investigated range of operating conditions.


Introduction
Currently, there is a rising need for sustainable production of platform chemicals and renewable fuels, which can be used together with fossil fuels or even replace them entirely.Biorefineries emerge as alternatives to petroleum-based ones, as biomass is an abundant, relatively cheap, renewable feedstock [1].Raw biomass usually has an unfavorable size distribution, low bulk density, and, hence, low volumetric energy density.Therefore, several pre-treatments (e.g., mechanical and chemical) are essential for enhancing the properties of the feedstock [2].For example, degradation of cellulose and hemicellulose results in the formation of sugars, which can be used as versatile starting materials for producing a variety of value-added products, such as 5-hydroxymethylfurfural (5-HMF) which is classified among the top 10 most valuable biomass-based chemicals [3].5-HMF can be obtained from fructose via triple dehydration over Brønsted acid sites [4][5][6].Another possibility is the conversion of glucose, but this is more challenging compared to fructose owing to the additionally required isomerization step.Once formed, HMF can be converted to secondary platform chemicals (SPCs) [7] such as C9-C15 alkanes [8,9], 2,5-furandicarboxylic acid (FDCA) [5, [10][11][12], ethyl levulinate (EL) [13,14], and 5-ethoxymethylfurfural (5-EMF) [15].Through hydrolysis, HMF can be converted into γ-valerolactone (GVL) [13], which has long been known as a potential green fuel-'a liquid with high-energy density', fuel additive and solvent [16][17][18][19][20][21][22][23][24].The intermediate product 5-HMF can be decomposed into levulinic acid or formic acid [25,26], polymerized to humic acids, and converted to dialdehyde in the presence of oxidative species [27].The selectivity towards each type of product that may result from any reaction varies according to various factors including the type of catalyst, the solvent used, and the operating temperature, which can be manipulated to steer the reaction to the desired pathway [28,29].Accordingly, research on developing novel strategies and the optimization of existing strategies to produce this five-membered ring compound using homogenous and heterogeneous catalysis is on the rise [30].The literature offers many examples of 5-HMF production routes comprising thermally induced dehydration of fructose, typically in dimethyl sulfoxide (DMSO) over homogeneous acid catalysts (HCl, H 2 SO 4 , H 3 PO 4 , oxalic or levulinic acid) [31][32][33][34].However, despite the high 5-HMF yields (40 to 60%) obtained via homogenous catalysis, in such processes, the catalysts are difficult to recover and reuse, require energy-intensive separation, and are frequently responsible for equipment corrosion [35,36].Moreover, low product selectivity and stability are contemporary challenges impeding the broad implementation and commercialization of many catalytic biomass conversion processes [37].Hence, the endeavor to develop sustainable processes for the production of added-value chemicals and fuels triggered researchers to overcome these challenges via novel heterogeneous catalysts and non-conventional heating technologies.Non-conventional heating technologies in particular have been explored to improve biomass conversion in relation to conventional heating (CH) [38][39][40][41].Among these techniques, the use of microwave (MW) irradiation to drive chemical reactions seems most widely appreciated and utilized by organic chemists, both in academia and industries such as food processing, textiles, papermaking, and ceramics [42][43][44][45].Since discovery of the beneficial effects of MW irradiation on biomass valorization, its number of applications towards catalysis for organic synthesis has increased dramatically [43,[46][47][48][49]. Early studies reported that MW irradiation could increase reaction rates by a factor of between 5 and 1000 compared to CH [41].Hence, the most significant benefit of MW irradiation in chemical synthesis is the substantial reduction in required reaction time.Moreover, MW irradiation has been claimed to ensure fast and selective heating, lower energy consumption, and controllable processing [42,46].Moreover, under MW irradiation, the production of biomass-based platform chemicals can already occur at distinctly lower temperatures compared to CH.Consequently, fewer functional groups are lost during the reaction, and the obtained molecules thus retain a high degree of functionality compared to the ones obtained after CH [46].
The heat transfer under microwave irradiation depends on several factors, such as the size and the properties of the targeted material.In general, MW dissipation is attributed to (i) dielectric loss heating and (ii) magnetic loss heating [50].The latter refers to the energy dissipated when the alternate magnetic field acts on a ferro-or ferrimagnetic material.Compared to magnetic loss materials, more attention is paid to the investigation of dielectric loss materials [51].Dielectric loss heating is based on the dielectric properties of the material, such as the permittivity or the dielectric constant (ε) and the dielectric loss (ε").While the former represents a measure of the capacity of a dielectric material to store electric energy, that is, to polarize under the varying electrical field [52], the latter quantifies the relaxation time (lag) between the electric field and the polarization movement of molecules, which causes energy dissipation as heat.Dielectric loss (ε") can be parameterized in terms of tangent delta (δ) or loss tangent, which is defined as the ratio of ε" to ε.This ratio represents the dissipation factor of the sample [53], which indicates the ability of a material to absorb electric charges and how efficiently MW energy is converted into thermal energy.
In this context, the application of metal-containing solid catalysts in microwaveassisted organic synthesis (MAOS) was introduced by Varma [54].Due to the excellent microwave-absorbing capacity of metal catalysts, the MW irradiation energy is rapidly and effectively transformed into heat throughout the system.Much attention has also been given in the literature to the actual origin of the rate enhancement under MW heating, such as determining whether it is a purely thermal effect [55][56][57] or, as some researchers suggest, a non-thermal effect [44,[58][59][60] in which the microwave energy itself directly couples to energy modes within the molecule or lattice.Disagreement exists as to whether, in case the microwave effect is not purely thermal, it should be referred to as "non-thermal", "non-purely thermal", or simply a "specific effect".Indeed, the thought of specific microwave effects has been floated by many researchers [42,[60][61][62][63].The occurrence of such a microwave-specific effect has significant implications for reaction chemistry.It proposes that MW effects on solid surfaces might deliver energetic and mechanistic advantages to catalytic reactions [60,64].In this respect, microwave-irradiated catalyst particles have been considered an indirect heat source [65].In addition, upon MW irradiation, electron pairs of the catalyst can be excited directly (electron-hole), generating free radicals at its surface [66].This combined effect can significantly improve catalytic activity.As a result, such a system is often referred to as an MW-enhanced catalytic process.An excellent review by Török and coworkers covers the development of MW instrumentation, theories, and applications, highlighting MW-assisted reactions with transition metal-containing catalysts [67].
Among heterogeneous acid catalysts, metal-organic frameworks (MOFs) recently gained attention for biomass conversion [68][69][70][71][72]. MOFs are a class of nanoporous crystalline materials that consist of regular clusters of positively charged metal ions surrounded by organic linker molecules.The remarkable control, scalability, and modifiable characteristics of the reticular chemistry inherent to MOFs result in materials that are almost unlimited in their functional potential [73][74][75][76][77][78][79][80].Since the discovery of the remarkable catalytic capabilities of MOFs for biomass conversion, a lot of work has been aimed at investigating the dehydration of various hexoses into hydroxymethylfurfural (5-HMF) over a wide range of pristine and modified MOFs.The acidic properties of some MOFs can, indeed, be further enhanced by adding functional groups such as nitro, sulfate, or phosphate to their structure to tune Brønsted and Lewis acid sites [68,69,[81][82][83][84].The high activity and selectivity of sulfonated MOFs make -SO 3 H the 'functional group' of choice for these reactions [65,68,[84][85][86].
Merging microwave-responsive catalysts such as functionalized MOFs (polar absorber hybrid materials) with contemporary MW technology could contribute positively to sustainable biomass conversion towards useful renewable products.One type of MOF exhibiting high thermal and chemical stability, MIL-101(Cr), has been used as a solid catalyst for MW-assisted biomass conversion reactions [82, 87,88].The acronym "MIL" stands for "Material from Institut Lavoisier", while the number "101" refers to the fact that it was the first MOF developed at the Institut Lavoisier.The high catalytic activity of this MOF is attributed to the chromium ions, Cr (III), which are highly active Lewis acid sites.These sites are beneficial for biomass transformation as they can act as binding sites for solvent molecules or fructose to catalyze the formation of 5-HMF [9].However, it should be noted that, when used as a homogenous catalyst (i.e., CrCl 2 ), the chromium ions entail many environmental and health risks [89,90].However, even if the use of the metal (Cr) is not eliminated, embedding them in heterogeneous structures (as is the case in MIL-101(Cr)) significantly reduces these risks [91].Recently, there has also been a drive to investigate the potential replacement of Cr with nontoxic metals such as Sc and Fe to prepare even more environmentally benign catalysts.These MIL-101 analogues have also been assessed for 5-HMF production, but their performance does not meet that of MIL-101(Cr), especially in terms of stability [72].Therefore, several studies selected the latter for further investigations on catalyst performance for biomass conversion [82,87,88].
As previously mentioned, the effects of MW irradiation on organic synthesis remain a subject of intense debate, and experimental research is currently underway to clarify these effects.Therefore, it is imperative to elucidate these effects through kinetic modeling.This work aims to provide novel insights into the MW effect via kinetic modeling, enabling a deeper understanding of the fundamental mechanisms and principles governing reaction kinetics and thermodynamics under microwave conditions.Quantification of the microwave effect in terms of changes in enthalpy and entropy is critical in optimizing reaction conditions and improving reaction performance with the aim of increasing reaction rate and selectivity.Furthermore, an extensive understanding of the thermodynamics of the microwave effect can significantly contribute to the development of innovative microwave-assisted synthetic methodologies and the advancement of novel microwaveassisted reactions.
In this work, we evaluated MIL 101(Cr) SO 3 H as a microwave-responsive catalyst for fructose dehydration to 5-HMF within the temperature range of 140-170 • C. First, we experimentally assessed the improvement in catalyst performance by MW irradiation compared to CH, aiming to elucidate the effects of temperature, solvent, catalyst structure, and MW irradiation.Subsequently, we used the obtained dataset to develop a kinetic model capturing the effects of reaction conditions.Within the model, the MW effect is quantified in terms of a change in Gibbs free energy in the transition state.To the best of our knowledge, this is the first model capable of describing a reaction performed under both CH and MW irradiation.

Preliminary Screening of the Dehydration Conditions
Preliminary tests for fructose dehydration into 5-HMF allowed reaction performance in response to the MW power mode to be evaluated via the sulfonic acid groups (-SO 3 H) on the catalyst.Additionally, the solvent composition effect on reaction performance was evaluated, as well as that of the catalyst mass.

Sulfonic Acid Group Loading Effect
The effect of sulfonic acid group loading on reaction performance was first investigated.A meager 5-HMF yield was obtained for MIL-101(Cr) without any sulfonic groups, which is not surprising since it does not possess any Brønsted acidity.The 5-HMF yield increased almost linearly with -SO 3 H loading on the other investigated samples (see Table 1).It can also be observed that with higher sulfur content, higher 5-HMF selectivity can be obtained.However, the possibility of 5-HMF reacting with two water molecules in a rehydration reaction will increase, forming levulinic acid and formic acid [82].This finding logically agrees with the increasing number of Brønsted acid sites grafted on the catalyst [101].Apart from that, the excellent microwave absorption ability of the sulfonic groups should not be forgotten.Previous research proved that polar absorber hybrid materials (e.g., materials containing -SO 3 H) significantly impact enhancement of the dielectric and microwave-absorbing properties of the modified material [65,102,103].Those findings can help prepare promising microwave-absorbing materials at 2-18 GHz frequency for absorbing applications [102].
Table 1.Effect of different -SO 3 H loadings on MIL-101(Cr) in terms of 5-HMF yield.Reaction conditions: MW using the standard power mode, 100 mg fructose (0.56 mmol), 3 mL solvent, DMSO/acetone 70/30, performed over 10 mg catalyst for 5 min at 160 • C. The total sulfur content of MIL-101-SO 3 H samples was determined by elemental analysis (C, H, N, S) using a Flash EA1112 instrument.

Catalyst Type
S Content [mmol g −1  The 5-HMF yield with MIL-101(Cr)-SO 3 H(3) was seven-fold higher than that of the parent MOF without sulfonic acid groups (MIL-101(Cr))).The detailed mechanism showing the importance of -SO 3 H acid groups in the elimination reaction can be found in Supplementary Materials S4.In our previous work, the catalyst's stability was proven for at least three cycles [1].
Concerning the performance enhancement under MW conditions, previous research demonstrated that the frequent alignment of polar sulfonic acid groups with the alternating electromagnetic field forces the strong vibration of polar groups and friction with neighboring molecules, thus increasing the probability of molecular collision between reactants and catalysts [104][105][106].In fructose dehydration over MIL-101(Cr)-SO 3 H, the polar sulfonic acid group is envisioned to rotate quickly in the MW field [101,107].This then facilitates the reactant transformation from the ground state to the transition state, which increases reactivity towards 5-HMF formation [41].This can be attributed to the fact that MW irradiation can enhance electron transfer from the MOF's cluster to the attached sulfonic groups, resulting in the enhanced acidity and polarity of sulfonic groups [101].As a result of these rapid motions, heating also occurs faster, which is another factor enhancing catalytic performance [101].Additionally, CH 2 OH groups on the fructose molecules and alcohol functions in 5-HMF respond to MW irradiation and contribute to heating of the reacting system.

Solvent Effect on Fructose Dehydration Using MW Heating
Fructose dehydration was performed in mixtures of DMSO and acetone with different molar ratios.This system was selected based on previous extensive laboratory screening tests of fructose dehydration over several MOFs [82].The efficiency of various solvents in catalytic fructose dehydration was investigated, including water, ethanol, high-boilingpoint polar aprotic organic solvents such as DMSO, and biphasic systems.DMSO was found to be the most efficient due to its polarity, which promotes reaction steps that lead to a high yield of HMF.However, DMSO's boiling point limits its application.Acetone/DMSO mixtures were discovered to effectively improve selectivity towards 5-HMF formation [82].Moreover, both DMSO and acetone are dipolar aprotic solvents that have a tendency to associate through dipole-dipole interactions.Acetone is employed to stabilize 5-HMF and prevent further reaction to LA and FA [101].At the same time, DMSO is required to ensure good fructose solubility in the solvent [108].DSMO is a high MW irradiation absorber with significant dielectric losses.It thus heats very quickly within the microwave chamber (see Table 2).DMSO alignment to the applied electric field is presented in Supplementary Materials S3.C), which could then take up a catalyzing role [109].Therefore, experiments were performed to ensure the absence of such a homogeneous catalytic effect from the solvent within our selected range of reaction conditions (see Table 3).The result proves that DMSO does not decompose at temperatures below 190 • C within the investigated reaction time.Thus, the homogeneous species were not formed at the targeted reaction temperature range [110,111].Therefore, the assumption that the solvent does not impact reaction rates is justified.Moreover, it is also understood from the full fructose conversion in the absence of a catalyst that the catalyst's role is to steer reaction selectivity towards 5-HMF production, i.e., to not simply activate the fructose but to also enhance the desired reaction compared to others in the reaction scheme.Catalytic reactions showed that 5-HMF selectivity increased with DMSO content in the solvent (see Table 4).A maximum 5-HMF selectivity of 61% was observed after 5 min for the 70:30 DMSO/acetone mixture at MW conditions.Moreover, fructose has been shown to rearrange to the furanoid form, which is more selectively converted into 5-HMF, consequently avoiding undesirable side reactions [108].Thus, the optimal DMSO/acetone ratio of 70:30 was selected for further experimental investigation.It should be noted that the amount of catalyst used can also affect the distribution of products, with higher selectivity to 5-HMF observed when a lower amount of catalyst (10 mg) is employed.This is because catalyst loading determines the number of available acidic sites that facilitate both the formation of the desired 5-HMF and the polymerization of 5-HMF and fructose into undesirable byproducts [112].Therefore, an optimized catalyst loading of 10 mg was used in this study.

Batch Time Evolution
As 'batch time', defined as the product of catalyst mass and reaction time, is one of the major factors determining the extent of a chemical reaction [113], it was screened next.Fructose conversion and product yield as a function of batch time is given in Figure 1.Increasing batch time from 3 to 36 g•s significantly improves 5-HMF yield from 60% to 89%, respectively.However, further increasing batch time resulted in a decrease in 5-HMF yield, while the yield of LA and FA further increased.Furthermore, an unavoidable phenomenon was observed at longer reaction times; the mixture gradually changed from an orange to a dark brown dense liquid due to humin formation [114].This finding was most pronounced at CH conditions and is attributed to an unfavorable caramelization reaction during sugar heating in the presence of the acid catalyst, which is a combination of aldose-ketose isomerization, dehydration, and anomeric-cyclic equilibrium [115].
The most considerable benefit of MW irradiation in chemical synthesis is the significant reduction in total reaction time (see Table 5).The effect of MW irradiation on chemical reactions is generally evaluated by comparing the time needed to obtain the maximum yield of final products with respect to CH.In comparing the two operating modes, as displayed in Table 5, it is clear that the MW-driven reaction is faster than the equivalent CH process.At 160 • C, the batch time in the MW reactor was reduced to 3 g•s, while at CH conditions, a more than 10-fold higher batch time was needed to reach a similar 5-HMF yield.More experimental data for product evolution with batch time are available in Supplementary Materials S5.The microwave effect is hypothesized to arise from selective heating of MW-absorbing molecules, i.e., the sulfonic acid group in the catalyst, DMSO, and fructose.As such, at the molecular scale, temperature inhomogeneities could develop depending on the effectiveness of MW energy absorption and heat dissipation.Nevertheless, only a bulk medium temperature could be measured, and it can be reasonably assumed that no local excessive temperatures developed that would lead to significant humin formation and a decreasing furfural yield.The development of a model capable of simultaneously tracking the evolution of 5-HMF and other substances involved in the dehydration reaction during the reaction time will provide further insight into the MW effect.Accordingly, multiresponse modeling for the dehydration reaction was conducted.

Multiresponse Kinetic Modeling and Reaction Conditions Optimization
Selectivity towards 5-HMF in fructose dehydration was investigated over a wide range of operating conditions.More particularly, a series of representative experiments were performed to elucidate the impact of the heat supply method, i.e., conventional or microwave heating, on fructose dehydration kinetics.In addition to the experimentation, a kinetic modeling approach was also followed to probe the reaction rate enhancement.Such a model may provide an explanation for variations in the maximum 5-HMF yield at different reaction temperatures at specific times.Figure 2 shows a parity diagram of the three responses of all 63 data points of fructose dehydration carried out under CH and MW conditions and reveals that the kinetic model is able to satisfactorily reproduce the experimental trends of each component (fructose, 5-HMF, LA, and FA) within the investigated range of operating conditions.

Pre-Exponential Factors and Activation Energies under CH Conditions
In the proposed reaction network shown in Scheme 2, an intermediate was included in the reaction network based on the observed trends in the experimental data to account for the 'delay' in 5-HMF formation after fructose conversion.With respect to the source of humin formation, it is clear from the almost instantaneous occurrence of fructose transformation reactions (including its dehydration to 5-HMF) and the slower humin formation that the latter cannot be formed principally from fructose.Rather, side product formation seemed to occur mainly in line with further 5-HMF conversion.Therefore, in order to not overly complicate the reaction network, 5-HMF was the only origin considered for humin formation.The estimated activation entropies ∆S i and energies E i,a for each step are summarized in Table 6.The corresponding rate coefficients at the reference temperature of 150 • C were calculated using the estimated values of ∆S i and E i,a via Equation (9) (see Table 7).Fructose dehydration to the (unspecified) intermediate has a high rate coefficient (k 1 ), making it the fastest step among the consecutive reactions in the scheme.The rate coefficient for the subsequent conversion of the intermediate to 5-HMF (k 2 ) is about half of that for fructose conversion into the intermediate (k 1 ).The apparent activation energy for the former (E 2,a = 103 kJ/mol) is higher than for the latter (E a,1 = 88 kJ/mol), which implies that further intermediate conversion into 5-HMF more significantly depends on temperature.The higher (apparent) activation energy for the further conversion of the intermediate (E 2,a ) may be attributed to the intermediate's ring structure that prevents the preferred planar geometry around the C=O + group [116].The intermediate's structure is illustrated in Supplementary Materials S4, Scheme S1. Figure 3 shows the model simulations for CH at 140, 150, and 160 • C, as well as the experimentally obtained results at these temperatures.It can be observed that fructose dehydration to 5-HMF starts in the early minutes of heating.The maximum concentrations of the intermediate and 5-HMF are consecutively established, followed by degradation due to 5-HMF hydration to LA and FA and humin formation.Other side reactions may also occur with longer reaction times but are not considered specifically, i.e., their potential contribution is embedded in the considered humin formation [84,106,117].At 140 • C and 150 • C (Figure 3a-f), 5-HMF yield reached its maximum values at 85 and 60 min, respectively.Overall, model simulations compared to experimental data for representative kinetic experiments of all experimental data indicate that the model describes experimental trends in CH reactors at various conditions (see Figure 3).

Quantification of the Microwave Irradiation Effect
It is essential to assess the origin of the reaction rate enhancements observed in the MW reactor.Thermal and non-thermal effects have been invoked in the literature for such an assessment [44,59,118].The thermal effect of the MW is described to relate to dielectric heating that originates from polar molecules, e.g., the -SO 3 H of the catalyst and CH 2 OH of fructose [119,120].Those groups change their orientation at each alternation of the electric field, which creates friction and locally causes a different c.q. and higher temperature that results in an increased reaction rate.Secondary thermal phenomena such as conduction and convection inevitably occur, once again homogenizing temperature [119].On the other hand, a specific MW effect, non-thermal in nature, is attributed to the rotational excitation of polar molecules and its impact on collision geometry and, hence, on the pre-exponential factor [62,63].
In the kinetic modeling, a homogeneous temperature distribution was considered, i.e., the implicit assumption that the dissipation of the absorbed MW energy via conduction and convection is fast compared to the reaction and eliminates any temperature difference.Additionally, the impact of MW irradiation on the Gibbs free energies of the transition states of the reaction steps was accounted for.Therefore, at MW conditions, two additional parameters occurred in the model, i.e., ∆H MW and ∆S MW (see Equation ( 1)).
Of course, the impact of any potentially remaining residual local temperature difference is then embedded in this shift in Gibbs free energy as well.In summary, for parameter estimation for the MW series dataset, two parameters were added to each of the previously estimated values of ∆S i and E i,a in the CH dataset, namely, ∆S MW and ∆H MW , respectively.Hence, the MW effect was calculated via a unique value applicable to the activation enthalpy and entropy for all considered reaction steps.For the sake of model simplicity, MW impact on all individual reaction steps was considered to be identical in the investigated temperature range compared to CH conditions.Accordingly, these parameters were used to quantify differences in thermochemical properties as they occurred under MW conditions for each rate coefficient (see Table 6).
The two additionally estimated 'activation' parameters for fructose conversion under MW conditions amounted to 16.8 ± 1.3 J/mol/K and −87.5 ± 46.9 kJ/mol for ∆S MW and ∆H MW , respectively.Under MW, the apparent activation energy was significantly decreased.Furthermore, activation entropy became more positive.Hence, under MW conditions overall, the temperature dependence of the reaction rates is much less pronounced, which can be explained by considering that energy is brought into the reaction under a form other than heat.Yet, using a single Gibbs free energy adjustment for all considered reactions ensures that a limited temperature dependence of reaction rates remains.
It could be expected that the magnitude of the −T∆S term would increase in an MW-induced reaction because of quick and random dipolar movement (dipolar polarization).Thus, microwave-molecules interactions increase the value of the second term in the Gibbs free energy equation.This hypothesis is evidenced by the change in ∆S MW, which is attributed to the higher entropy generation in a microwave-assisted reaction and, hence, a higher pre-exponential factor due to a higher probability of collision.Moreover, the thermodynamic advantage provided by the MW is realized at lower temperatures where the free energy (∆G = ∆H − T∆S) of the MW reaction becomes negative.The fact that the MW-driven reaction has a negative ∆G at lower temperatures than CH stems from its significantly lower value of ∆H.Therefore, at a lower temperature, a microwavedriven reaction will become more favorable than a CH reaction as (−T∆S) CH > (−T∆S) MW (see Section 2.2.3).
These findings challenge the controversial MW non-thermal effect and the classical view of MW irradiation as only a heating method.Several demonstrative examples of quantifying the non-thermal effects were enumerated in support of this approach to justify the reduction in activation energy under MW conditions [60,61,118,121].Stiegman and coworkers investigated the dehydrogenation reaction of the steam-carbon process via MW and CH [118].Their work indicated a significant MW-specific effect on the investigated reactions as the MW not only selectively heated the substrate, but also affected the primary thermokinetic steps of the reaction [118].
The rate coefficients under MW conditions at 150 • C are listed in Table 7. Comparatively, it is clear that the reaction is faster under MW irradiation than under CH in the investigated temperature range.Comparison of the rate coefficients shows a 7-to 10-fold enhancement in the reaction rate (e.g., k 1 and k 2 ), as shown in Table 7.
Performance profiles under MW conditions were simulated using the rate coefficients at 140, 150, and 160 • C, respectively (see Figures 4 and 5).As a result, it can be observed that the trends of 5-HMF, LA, and FA are qualitatively similar to those from the conversion of fructose under CH conditions, with the notable quantitative difference that the reaction occurred in a much shorter time under MW conditions, i.e., the rate of 5-HMF formation was faster under MW conditions.Nevertheless, many researchers still doubt whether reactions under MW conditions would occur according to the exact mechanisms that are exhibited under CH conditions [61,122].
Generally, at 140 • C, 150 • C, and 160 • C, MW conditions significantly promoted the consumption rate of fructose to form the intermediate, and higher 5-HMF yields were thus obtained within a shorter time.At 170 • C, more intermediate was formed, and less 5-HMF and other side products were detected (see Figure 6 for a better comparison).Consequently, the decrease in 5-HMF selectivity at 170 • C after 15 min can be attributed to 5-HMF hydration reactions that form LA and FA.This behavior can be explained by the interplay between the rate coefficients of consecutive reactions and the products' concentration.Since it functions as a "trigger" for enhancing one of the successive reactions from another, this in turn determines how the final concentrations of its components change as the reaction proceeds.
Figure 6a displays the formed intermediate's concentration at each temperature and how it is consumed in consecutive reactions, thus leading to 5-HMF formation, hydration, and self-oligomerization (Figure 6b-d, respectively).The interplay between the rate coefficients of the consecutive reactions and product concentrations functions as a "trigger" that enhances one of the consecutive reactions more than the other.In turn, this determines how the concentrations of its components change as the reaction proceeds.For example, under a given set of conditions (such as 160 • C), when the intermediate concentration is low, the reaction follows the direction that produces 5-HMF, leading to a relatively high 5-HMF yield and low side product yield.
To further evaluate the reliability of the developed kinetic model, a comparison of the estimated activation energies for main reactions between this study and previous studies using MIL-101(Cr) and other heterogeneous acid catalysts was conducted and is listed in Section S6 of the Supplementary Materials (see Table S2 in Section S6).Many prior studies have considered direct fructose conversion to 5-HMF without considering the intermediary step; thus, some parameters are expected to deviate from previously reported ones [84,123,124].Still, models investigated previously include the same general reactions as the present work: fructose dehydration, 5-HMF hydration to levulinic acid and formic acid, and humin production from fructose and/or 5-HMF.Thus, some comparison is still possible.For example, Chen et al. [84] reported a kinetic study on fructose dehydration using MIL-101(Cr)-SO 3 H in DMSO in the temperature range of 120-150 • C with a first-order approach (Table S2 Entry 4).The proposed reaction scheme only considered the rate of fructose conversion without other products, thus the intermediate and its concentration were not included in the model.As a result, the apparent activating energy amounted to E = 55 ± 5 kJ/mol (Entry 4).To better compare our results to the prior work, a regression of the CH dataset was also performed without considering the intermediate in the reaction scheme (Table S2, Entry 3).In that case, the apparent activation energy for fructose dehydration was estimated at E = 48 ± 2 kJ/mol (Table S2, Entry 3).Therefore, a model that does not account for the intermediate considered in our work would effectively lead to an (apparent) activation energy within this lower range of values.Hence, the observed deviations in reaction rates and activation energies between the results obtained from this work and those reported in the literature for the same catalyst are primarily ascribed to the different reaction networks proposed (Table S2, Entry 1-4).
Villanueva et al. investigated the kinetics of fructose conversion using ZrPO-700 as a catalyst at 125-145 • C (Table S2, Entry 5) [125].The model was constructed using a similar reaction network to the one proposed in this work involving the conversion of fructose to a common intermediate, which was subsequently converted to 5-HMF before 5-HMF hydration to LA and FA.In parallel, fructose individually reacts to humins.The obtained activation energy for fructose conversion to this intermediate amounted to 186 kJ/mol (Entry 5), while the value obtained in this work was 88 kJ/mol (Table S2, Entry 1), indicating a significant dependence on the catalyst.

Maximum 5-HMF Yield as a Function of Temperature
The temperature dependence of the dehydration of fructose over MIL-101(Cr)-SO 3 H was explored using the developed model.Generally, the production of 5-HMF requires elevated temperatures (>100 • C), which can be supplied by MW irradiation or CH.However, undesirable side reactions to humins are more favored at higher temperatures.Therefore, the dehydration of fructose to 5-HMF as a function of reaction time was simulated in a temperature range of 140 • C to 170 • C. The maximum simulated 5-HMF yields were plotted vs. reaction temperature for MW and CH conditions (see Figure 7).For CH, an increase in temperature leads to a rise in the maximum 5-HMF yield from fructose though this was obtained over a longer reaction time than under MW conditions (Figure 7), indicating the higher activation energy for fructose dehydration under CH conditions.For example, 5-HMF yield increased from 54.3 to 70.1% under CH conditions by increasing the reaction temperature from 140 • C to 160 • C. The results showed that, at 170 • C, the highest yield of 5-HMF was achieved using CH (74.2%).
At 140 • C, more 5-HMF is generated under MW than under CH conditions.Based on the results, it is clear that the MW enhances selective conversion into 5-HMF at a significantly lower temperature, making it more energy efficient.It was hinted before (Section 2.2.2) that as the temperature decreases, MW conditions would become more favorable than CH as −(T∆S) CH > −(T∆S) MW .Moreover, under MW conditions, a more negative ∆G will already be obtained at lower temperatures compared to CH conditions.This arises from the significantly lower value of ∆H [60].This conclusion supports the findings that at a higher temperature, such as 170 • C, the obtained 5-HMF yield by CH is higher than under MW conditions.Therefore, it can be concluded that under MW conditions, temperatures exceeding 160 • C may accelerate side reactions of 5-HMF, leading to species such as humins [115,126].It can be concluded that milder reaction conditions associated with reduced reaction time are the key advantages brought about by the use of MW conditions for MW-susceptible reactions.
To evaluate the potential for industrial-scale applications, it is important to consider the amount of fructose that can be processed.Therefore, simulations were conducted for different substrate quantities ranging from 100 to 800 mg of fructose in a DMSO/acetone (70/30) solvent mixture, which corresponded to catalyst-to-substrate ratios of 0.1, 0.03, and 0.01.It was observed that fructose conversion occurred rapidly under microwave conditions regardless of the fructose-to-catalyst ratio, which is consistent with previous findings [48].Figure 8 illustrates the highest achievable dehydration yield under MW and CH conditions.As hinted before, a similar maximum 5-HMF yield in both reactors was obtained at different reaction times.Additionally, the results of experiments included in the Supplementary data (Section S7) indicate that selectivity towards 5-HMF remained stable as fructose concentration increased from 100 mg to 800 mg.This finding is consistent with the existing literature [127,128].It is important to note that the impact of fructose concentration on 5-HMF selectivity can vary depending on the specific reaction conditions, including the catalyst type, reaction temperature, and reaction time.

Catalyst Testing
Two different heating methods, i.e., conventional heating (CH) and microwave (MW) heating, were used to produce 5-HMF from D-fructose.Both methods were performed and compared under similar conditions.Note that this comparison includes the difference in time required to reach the desired reaction temperature, which is much shorter when using MW heating.5-HMF yield and selectivity were investigated in a fructose concentration and reaction temperature range of 0.1-0.8g within 3 mL of solvent and from 140 to 170 • C, respectively.The reaction time for CH varied between 60 and 300 min, while the examined time range for MW heating was from 5 to 50 min.Before the reaction, the catalyst was pre-treated at 180 • C under vacuum for 4 h.This thermal activation under vacuum was employed to release solvent molecules, specifically water, and was coordinated to the chromium centers in MIL-101(Cr)-SO 3 H.This process facilitated the liberation of the metal node and the creation of open chromium sites, which can be more readily accessed by potential reactants [129].The absence of mass and heat transfer limitations for dehydration reaction over MIL-101(Cr)-SO 3 H was confirmed by verifying the necessary criteria [82].

General Procedure for the Reaction of Fructose Using Microwave Irradiation
The catalytic tests involving microwave heating were performed with a Discover microwave reactor (CEM Corporation, Charlotte, NC, USA).The CEM Focused Microwave™ Synthesis System Discover ® SP is designed to enhance the ability to perform chemical reactions under controlled conditions on the laboratory scale [130].In a typical experiment for the transformation of fructose, a 10 mL reaction tube was charged with fructose, MIL-101(Cr)-SO 3 H (10 mg), and solvent (3 mL); the reaction mixture was then heated to the desired temperature for the specified time.The 10 mL batch reaction vessel was placed in the center of the equipment for heating at 2450 MHz.In addition, a solenoid valve automatically released air jets over the surface of the flask to assist with temperature control.In all cases, the contents of reactors were magnetically stirred.
The standard power mode was examined as suggested by the manufacturer for the control of routine organic syntheses [130].The reactor employs a feedback loop that automatically varies MW power to establish and maintain the desired temperature.In this mode, temperature and reaction time can be controlled; the temperature gradually increases to reach the set value (see Figure 9).Moreover, a short pre-heating or ramp time over the first 0-1 s was selected for all runs.The cooling option consists of the necessary valves and ports to direct a cooling gas (air) onto the vessel in the system cavity.Cooling will decrease the temperature of a 3 mL solution in a 10 mL reaction vessel from ~150 • C to ~50 • C in less than 120 s.Standard power mode pressure and power profiles are displayed in Supplementary Materials S1.

General Procedure for the Dehydration Reaction of Fructose Using Conventional Heating
A round-bottom glass flask equipped with a magnetic bar was charged with fructose, catalyst, and solvent and was then placed in a pre-heated oil bath at the desired temperature.The temperature was kept at the desired value, which ranged from 140 to 170 • C. A time of 10 to 12 min was needed for the oil bath to reach the set temperature.

Analysis
The reaction mixture was analyzed using a Shimadzu high-performance liquid chromatography (HPLC) (Shimadzu LC-20AB, Kyoto, Japan).The instrument used for HPLC was equipped with a refractive index (RID) detector (in the range of 1.00-1.75),a photodiode array detector, and a Biorad Aminex HPX-87H column (Bio-Rad Laboratories N.V., Hercules, CA, USA).The RID detector was used to detect fructose, while 5-HMF, FA, and LA were individually detected on the UV detector at wavelengths of 355 nm, 211 nm, and 254 nm, respectively.A 0.005 M H 2 SO 4 solution was used as the mobile phase at a flow rate of 0.6 mL/min, and the column temperature was maintained at 65 • C. The content of fructose, 5-HMF, levulinic acid (LA), and formic acid (FA) in samples was quantified from calibration curves established from the standard compounds.Fructose, FA, LA, and 5-HMF were eluted at 10, 13.1, 14.7, and 37.1 min, respectively.The typical relative standard error was 1% for multiple injections from the same sample and 5-8% for replicate samples during HPLC analysis.Reactant conversion, product yield, and selectivity were obtained by Equations ( 2 Fructose conversion [%] = converted moles of fructose Initial moles of fructose ×100 The yields of FA and LA are calculated in an analogous manner to 5-HMF.For detailed information regarding the quantification of the reaction products, see Supplementary Materials S2.Due to HPLC lacking the ability to detect humins, their quantification was performed by employing the carbon mass balance method, which accounts for the total quantities of 5-HMF, LA, and FA.

Procedure for Multiresponse Kinetic Modeling
Apart from the experimental assessment, the effect of microwaves in fructose transformation into 5-HMF was also quantified by multiresponse kinetic modeling.The kinetic parameters, including those employed to capture the 'microwave effect', were determined by regression against a total of 63 experimental data points, i.e., 27 using CH and 36 using MW irradiation.Simultaneous regressions were run for CH and MW heating.
The kinetics of the reaction presented in Scheme 1 has been assessed by making use of the reaction network in Scheme 2. One of its key features is that fructose conversion occurs via an intermediate (Int.)(see Section 2.2), which subsequently gets converted into 5-HMF.Upon further transformation, the latter can decompose into FA and LA and can lead to the possible formation of side products such as humins.The following simplifying assumptions were made when developing the kinetic model: (i) all reactions are irreversible and firstorder and (ii) humins are predominantly formed from 5-HMF.The latter assumption was made as distinguishing the source of humin formation was impossible and to avoid over-parameterization of the model.
Each reaction step was assigned a rate coefficient (k).Finally, the reaction network was translated into a mathematical model by setting up differential equations for each reaction step as they occurred within the batch reactor.As presented in Scheme 2, this reaction network yielded four ordinary differential equations and included multiple concentration responses (Equations ( 5)-( 8)).This set of differential equations was simultaneously integrated over the experimental reaction time (time interval 'c' in Figure 9) using the Athena Visual Studio engineering software.
In the expressions, the rate coefficients are calculated in a reparameterized manner (Equation ( 9)) [131]: The model accounts for MW irradiation via a change in Gibbs free energy between the reactants and the activated complex, i.e., ∆G CH and ∆G MW (∆G = ∆H − T∆S).Refer to Section 2.2.2 for the relevant assumptions.The Bayesian estimation method was used, which considers the error covariance matrix between responses and aligns the objective function accordingly [132].The kinetic model was evaluated with the estimated parameters' highest posterior density (HPD) intervals.

Conclusions
In this work, a microwave-responsive catalyst was used in the assessment of fructose dehydration kinetics to 5-HMF over a MIL101(Cr)-SO 3 H(3) catalyst comprising polar sulfonic acid groups in addition to the inherently available Cr +3 with coordinatively unsaturated sites.Due to intense rotations of the active site and the response of the polar

Figure 2 .
Figure 2. Parity diagram for all experimental and simulated points of fructose dehydration carried out under CH and MW conditions.(∆) stands for fructose conversion, (o) denotes LA + FA, and ( ) denotes 5-HMF.

Figure 9 .
Figure 9. Temperature profile of a microwave irradiation experiment using the standard power mode: (a) ramp time or heating time (heating from an ambient temperature to the final reaction temperature over the first 0-1 min), (b) total time, (c) reaction time, (d) end of hold reaction time at the desired reaction temperature, and (e) heat dissipation time without power supply.
DMSO has been demonstrated to dissociate into [CH 2 O] and [CH 3 SH] at high temperatures (i.e., >180

Table 6 .
Entropy change ∆S i and apparent activation energy E i,a, including 95% highest posterior density (HPD) intervals.obtained by Bayesian estimation against the CH dataset for fructose dehydration over MIL-101(Cr)-SO 3 H(3).