Chapter 1: Basics of Microwave Heating and Recent Advances

Even if process intensification (PI) has only been identified as a kind of technological “toolbox” containing some spectacular examples of process improvement for over twenty years, it is one of the most important areas of progress for modern chemical engineering.¹  In 2009, Van Gerven and Stankiewicz²  proposed a fundamental view on PI, with the definition of four basic principles and four domains, which must be considered if the aim is the intensification of a chemical process: spatial, thermodynamic, functional, and temporal. The thermodynamic domain focuses primarily on energy, and the main question for PI is how a source can transfer energy to a recipient in the required form, in the required amount, at the required moment, and at the required position. All the energy that does not meet the requirements (e.g., it cannot be absorbed, it is more than needed, it is in a “wrong” form, it is applied too early or too late, and it is too far away) is not used in an optimal way and it is, consequently, partly dissipated.

A chemical process is conventionally energized by means of conductive heating with a steam boiler as a typical heat source. Nevertheless, a large variety of other forms of energy can be applied for PI, including ultrasound (for reactions or crystal nucleation), light (in photocatalytic processes), electric fields (in extraction or for orientation of molecules), or microwaves. The microwave (dielectric) heating of materials has been known for a long time, and microwave ovens have been developed for more than 60 years. The studies by Gedye et al.^3,4  in 1986 and 1988 opened a period of very intensive investigation of microwave effects on chemical reactions in homogeneous systems. Since then, hundreds of research papers have been published, and research has also expanded toward heterogeneous catalysis and its related chemical processes. This chapter gives an overview of the basics of microwave heating and of some recent advances.

Microwave electromagnetic radiation has frequencies ranging between 300 MHz and 300 GHz, which fall between the radio- and infrared frequencies, which correspond to wavelengths in a vacuum of about 1 m to 1 mm. Current legislation makes the frequencies of 915 MHz, 2.45 GHz, and 5.85 GHz the most commonly available for chemical processes and Industrial Scientific and Medical (ISM) bands, in order to avoid any interference with broadcast and communications bands.¹  The frequency of 2.45 GHz is used as a source of heating commonly found in domestic microwave ovens. In 1946, the melting of a chocolate bar in the pocket of Percy Spencer while he was walking past an open radar waveguide gave him the idea that powerful interactions between microwave radiation and materials (for example, foods) were possible.⁵  Consequently, in 1952, the first commercial microwave oven was developed and patented by the Raytheon Company.⁶  Before the advent of microwaves, high frequency induction heating was commonly used, and as an example, the patent for dielectric heating by means of high frequency induction was issued in 1933.⁷ 

In contrast to communication purposes, in which microwaves typically have a well-defined wave in terms of frequency, phase, and amplitude in order to carry the information, for heating purposes the microwave output power and efficient irradiation apparatus are important factors. In this case, the composition and fabrication of microwave devices are highly different, highlighting the need to combine various technologies and competences.

MWs are electromagnetic waves and travel at the speed of light in a vacuum. If a material has polar, conducting, and magnetic properties, it can be directly heated by microwaves.

In this sense, the possibility of carrying out chemical reactions using the microwave heating technique has been studied in detail by numerous researchers in many scientific fields over the last twenty years. These efforts have made the use of microwaves in different areas of the chemical field rather common, including organic chemistry, analytical chemistry, biochemistry, polymer chemistry, catalysis, photochemistry, and inorganic chemistry of materials. The studies carried out directly in industry on the application of microwave radiation have been particularly important since they have allowed obtaining high-quality microwave-assisted synthesis; however, these processes need further improvements in order to be used for the preparation of significant quantities of high-value chemicals.

In 2014, Horikoshi and Serpone in a minireview of the role of microwaves in heterogeneous catalytic systems⁸  proposed the classification of microwave chemistry into four main categories, as shown in Figure 1.1. This classification was made by analysing the role of microwave radiation in microwave chemistry as follows: (i) a substance is heated directly by microwaves so that the chemical synthesis can be coupled with some automated robot technology, such as for microwave heating in domestic ovens (operating mode); (ii) microwaves have beneficial effects on green chemistry since they shorten the reaction times even in synthesis requiring no solvents and catalysts (green chemistry applications); (iii) microwaves can enhance the kinetics of many chemical reactions by varying the microwave frequency and other phenomena (chemical reaction applications); and (iv) microwaves are used not only as a heat source, but also in the manufacturing of different new materials (specific heating). Naturally, this classification of the use of microwave radiation in chemistry and catalysis is not exhaustive.⁹  In general, heating up by using microwave radiation in microwave chemistry must be investigated by examining the electric and magnetic radiation fields, and in this sense, it is of extreme importance to understand the difference between the heating phenomenon of microwaves and classical heating methods. In this field, there are thousands of studies reporting the use of microwaves as a heat source in chemical reactions, but only a few report the characteristics of microwave radiation. In the last few years, some researchers have focused their attention on specific microwave effects in the field of heterogeneous catalysis, as described in greater detail in the following sections.⁸ 

Since the wavelengths of microwave radiation (1 m to 1 mm) are sensibly different from the ones of UV, visible and infrared radiation (from 200 nm to 1000s of nm), their effects on molecules exposed are also different. As a starting point, a useful initial classification to understand how microwaves heat a sample is between liquids and solids. In the first case, when a medium with permanent dipole moments (for example, water) is placed in an external electric field E, the dipoles tend to orientate in the E direction (Figure 1.2). If the electric field E has an alternating nature, like microwave radiation, the dipoles can rotate with E, and, in a similar way, the ions are subjected to rapid translational movements. Due to these rotational or translational movements inside a polar medium, an “internal friction” occurs, thus causing the heating of the medium.¹⁰ 

Regarding solid materials, depending on their interaction with microwaves, they are usually divided into four categories: (i) perfect conductors – materials that reflect microwaves from their surface (metals or graphite); (ii) insulators – materials that are transparent to microwaves (polypropylene or quartz glass); (iii) “dielectric lossy materials” – materials that absorb microwaves and are heated by them (for example, silicon carbide); and (iv) “magnetic lossy materials” – materials in which magnetic losses occur in the microwave region (for example, metal oxides such as ferrites and other magnetic materials).

The first aspect to consider in the understanding of the interaction between a material and microwaves is the definition of two important properties of the material: complex permittivity, ε*, and complex permeability, μ*.

In the above equation, the three terms have the following meaning: the first one is the expression of conduction loss heating; the second one is the expression of dielectric loss heating, and the third one is the expression of magnetic loss heating. These phenomena are described in the following sub-sections.

From eqn (1.10), the dependence of the relaxation time on the viscosity of the medium and the dimension of the molecular dipole is evident: a high viscosity of the medium, or a large molecular dipole, implies a slow rotational speed and consequently slow relaxation of a fluctuation. The result is a net dipole moment.

For example, in the case of water, at 25 °C, the penetration depth of microwaves is about 1.8 cm, at 50 °C it increases to 3.1 cm, and at 90 °C, it is 5.4 cm.¹⁴  The penetration depth of microwaves into almost all nonpolar solvents is very deep when compared to polar solvents. On the other hand, if ions are added to water, the penetration depth then decreases since the dielectric loss increases depending on the conductivity σ, as is evident from eqn (1.4). For example, Horikoshi et al. studied the microwave-assisted heating (2.45 GHz) characteristics of aqueous electrolyte solutions (NaCl, KCl, CaCl₂, NaBF₄, and NaBr) of varying concentrations in ultrapure water.¹⁵  In their work, they presented a diagram showing the penetration depth vs. temperature profile for an ultrapure water sample containing NaCl at various concentrations. From this diagram, it is possible to observe that when NaCl (0.25 M) is added to pure water, the penetration depth into this saline solution changes from 1.8 cm (pure water) to 0.5 cm at ambient temperature.¹⁴  A vigorous stirring is mandatory in the case of ion containing solutions to avoid the formation of hotspots on the surface of the reactor due to microwave heating.⁵ 

Metals reflect electromagnetic waves, and in the case of microwaves they reflect most of them when they are irradiated.⁵  An important effect occurring in metals is the skin effect, in which an alternating electric current is distributed in such a way that near the surface (skin) the current density is larger and it decreases with the increase in depth.⁵  The electric current flows starting from the outer surface up to a level identified as skin depth, resulting in an increase in the effective resistance of the conductor at higher frequencies where the skin depth is smaller, with a consequent reduction in the effective cross-section of the conductor.⁵  The alternating current generates a changing magnetic field that induces opposing eddy currents, which are responsible for the skin effect.⁵ 

In conclusion, optimal microwave heating is achieved by studying the heating efficiency and the penetration depth of microwaves into a substance. It is now clear how microwave heating is fundamentally different from the conventional conduction-based heating, since when microwaves penetrate a material to supply energy, heat is generated in the whole volume and “volumetric heating” occurs (Figure 1.3). Volumetric heating minimizes the processing time, lowers the consumption of power and improves the diffusion rate: microwave heating is attractive from the PI point of view.¹⁷ 

Microwave heating or (pre)heating has several applications in almost every field of chemistry due to the advantages offered by this technology compared to traditional heating methods. The main applications of microwave heating are in the attenuation of environmental pollution, medical uses, food processing, agriculture, ink and paint industries, and wood treatments.¹⁷  Regarding materials processing and microwave chemistry, microwave heating is applied to organic and analytical chemistry, biochemistry, catalysis, photochemistry, inorganic materials, and metal chemistry.¹⁸ 

In the field of organic synthesis, the use of microwaves as a heating medium has increased in recent years due to the reported observation of significant enhancements in reaction rates. In this area, several articles and books have reviewed the studies carried out.^8,10,19–24 

The better performance of microwave-assisted heterogeneous catalytic reaction systems in terms of the reaction rate and selectivity, compared to the conventional heating methods, has attracted increasing attention from the scientific community toward these processes.^8,25–28  Moreover, microwaves can selectively heat a catalyst, thus resulting in a potential heating medium for high-temperature industrial processes, in which it is possible to achieve the temperature required for the reaction to occur.

A synthetic sketch illustrating the heat transfer pathways in a microwave-assisted heterogeneous catalytic system is shown in Figure 1.4.

When a solid catalyst is irradiated with microwaves, its temperature increases, depending on the magnitude of the radiation intensity (I) and the absorption cross-section of the catalyst material (α_cat). In the case of a reaction occurring in a liquid medium, the heating of the solution is dependent on the absorption cross-section (α_med) and the intensity of the radiation (I). In addition, the solution will also be heated indirectly by convective heat transport from the solid catalyst to the medium (h_c). In this last case, if the medium is a good absorber of microwaves, a little temperature difference between the catalyst and the solution (T_med ≈ T_cat) occurs, meaning that a little difference between convective and microwave heating is obtained, since the driving force of the reaction is only the temperature. In contrast, in a gas–solid reaction, T_cat ≫ T_med, since the gas is not heated by microwaves (α_med = 0), and convective heat flow from the catalyst to the surroundings (h_c) will be significantly less than that in a condensed phase reaction. In this case, the heating assisted by microwaves is very selective, and a huge energy saving is possible when compared to convective heating.

In the scheme shown in Figure 1.4, the potential advantage is that further reactions are avoided since the rapid activation of the substrate on the hot surface of the catalysts allows for the ejection of the products from the hot surface to the cooler medium due to the imparted kinetic energy.¹⁴  Moreover, especially in the case of a gas–solid reaction, a proper defined set of operating conditions (including the catalyst and surrounding temperatures) allow for a higher product selectivity.¹⁴ 

Despite the availability of a significant amount of literature, there are still some issues regarding the intrinsic nature of microwave irradiation on chemical reactions and peculiarly on heterogeneous gas-phase catalytic reactions.²⁶  The main question in the scientific community is whether the enhancements observed in the presence of microwave irradiation are due to purely thermal effects, which traditionally include inverted temperature gradients, overheating, hotspots, and selective heating, or whether they are connected to the so-called specific or non-thermal microwave effects (the influence of electromagnetic radiation).²⁷  Regarding thermal effects, many research groups investigated the role of hotspots in microwave-assisted chemical reactions.²⁷  Hotspots, which originate from the inhomogeneity of the field distribution along the sample, may have positive or negative effects on the reactions, and they can be detected through the use of several techniques, such as digital cameras or IR thermography. Different factors may influence hotspots, such as the particle size or the field intensity. The increase in the particle size at a fixed microwave power may result in an increase in electric discharge, as in the case of Mg particles in benzene. On the other hand, a low field intensity may have a positive effect, as in the reaction for the formation of Grignard reagents, since a high field density may result in solvent decomposition, thus preventing Grignard reagent formation.²⁷  Hotspots may also be responsible for a considerable reorganization of the catalyst under microwave irradiation, as reported by Zhang et al.²⁸  The authors reported the existence of hotspots and demonstrated that their temperature was 100–150 K higher than the bulk temperature of the catalytic bed. This hypothesis based on the role of “hotspots” has been considered for many years as the mechanism responsible for microwave-accelerated heterogeneous gas phase catalytic reactions. However, this well-accepted mechanism has been recently questioned because the formation of hotspots on a catalyst surface can be, as stated, sometimes deleterious to microwave catalytic reactions.²⁸  An interesting study by Xu et al.²⁶  reported for the first time that microwaves have an intrinsic catalytic effect since they allow for the lowering of the apparent activation energy: the authors gave a new interpretation, based on experimental evidence, of the microwave-assisted acceleration of heterogeneous gas-phase catalytic reactions, going beyond the mere presence of “hotspots”. In the field of organic synthesis, some studies have shown that in the reactions characterized by electron transfer as the main factor, such as photochemically assisted reactions, the electromagnetic field may have a positive influence (non-thermal effects) since a higher conversion can be obtained using higher microwave power. The case of reactions wherein the main factor is thermal energy is different: in this case, the increase of the microwave power does not result in reaction enhancement since the microwave power delivers an amount of energy smaller than the thermal energy.²⁷  Computational methods may be useful tools since the concepts and properties that influence thermal and non-thermal effects and that cannot be determined experimentally can be calculated separately. For example, the determination of the properties that influence a reaction through thermal effects, such as the polarity of the species, the activation energy, and the enthalpy of the reaction, can allow for the design of reactions that must be improved with the microwaves through the development of a predictive model. Regarding the non-thermal effects, the calculations proved that properties such as the polarizability of transition states and the stabilization of radicals and the triplet state influence the reactivity by means of non-thermal effects. In the case of fixed bed flow reactors, an interesting study was carried out by Haneishi et al.,²⁹  which showed that the generation of local heat at the contact points between the catalyst particles is a key factor for enhancing fixed-bed flow reactions under microwave irradiation. These authors, in the case of the dehydrogenation of 2-propanol over a magnetite catalyst, reported the generation of local high temperature regions between the catalyst particles under microwave heating. The results of their tests highlighted a 17-fold (at 250 °C) to 38-fold (at 200 °C) increase in the reaction rate when heated with microwave irradiation rather than using an electrical furnace. Moreover, the authors demonstrated the presence of microwave-generated specific local heat by means of a coupled simulation of the electromagnetic field and heat transfer as well as in situ emission spectroscopy. They reported that the generation of specific high temperature regions occurs at the vicinal contact points of the catalyst particles due to the concentrated microwave electric field, and they directly observed local high temperature regions at the contact points of the particles during the microwave heating of a model silicon carbide spherical material using in situ emission spectroscopy.

Irrespective of the case, for a complete knowledge of microwave-assisted catalytic heterogeneous reactions, it is important to understand the fundamental physical processes through which microwaves interact with various catalyst materials.

There are several different classes of heterogeneous catalytic materials, each of which displays different microwave absorption processes. As stated in Section 1.2, solid materials can be divided into three categories based on their microwave absorption behaviour (Figure 1.5).

A general classification proposed in the literature⁸  categorized heterogeneous catalysts into three main classes:

1. Solid oxide catalysts: this class includes any bulk oxide used to catalyse a reaction on its surface. Typical examples are simple binary oxides such as SiO₂, Al₂O₃, TiO₂, and ZrO₂ and ternary oxides such as spinels and perovskites. Other materials falling into this class are porous silicate and alumino-silicate materials such as zeolites and templated mesoporous sieves.

2. Metals: this class includes all the metal surfaces that are used in catalytic commercial processes. Typical examples are late transition metals such as Ni, Cu, and Ag.

3. Supported catalysts: this class includes the so-called supported catalysts, defined primarily as oxide supports with active sites deposited on the surface that perform all or part of the catalytic function. The active sites can be isolated transition metal ions or complexes or metal particles.

All the materials falling into the three classes defined above display different microwave absorption processes, originating from different loss processes. Based on the classification shown in Figure 1.5, the choice of an appropriate material as the catalyst or support is fundamental for realizing a successful microwave-assisted heterogeneous catalytic reaction/process. An understanding of what kind of loss process, due to the interaction of the electric field component and the magnetic field component with the material, and how it affects chemical reactions on the surface of the catalyst is also important.

The electric field component (E) of microwaves is responsible for the dielectric heating of a material (heating through dielectric loss). This heating mechanism, in the frequency range of microwaves, is caused by two primary mechanisms: (i) dipolar polarization and (ii) ionic conduction.³⁰  In the polarization mechanism, the dipoles will try to align themselves with the field by rotation due to their sensitivity to external electric fields. Under a high frequency electric field, the dipoles are not able to respond to the oscillating field, and as a consequence of this phase lag, the dipoles mutually collide as they attempt to follow the field and the power is dissipated to generate heat in the material.¹⁶ 

In the conduction mechanism, the movement of any mobile charge carriers back and forth through the material under the influence of the microwave E field induces an electric current: heating is caused by these induced currents which causes collisions of charged species with neighbouring molecules or atoms. In some systems, such as the ones in which a conducting material is included in a non-conducting medium, these two mechanisms cannot be separated from each other and work together in microwave heating.

The dielectric heating of a solid sample has different features when compared to that of a liquid sample. In the case of liquid samples, since they have molecules with a high mobility, their heating efficiency is affected by their dielectric parameters. In solid samples, characterized by crystalline units, heating is possible only by the motion of these crystalline units, and the heating efficiency may be different even if the same type of solid substance is heated using the same microwave equipment, since solid samples may have a different crystallinity.⁵  In solids, the conduction losses are in some cases temperature-dependent since they tend to be minimal at ambient temperature but can change when increasing the temperature. A typical example is alumina (Al₂O₃) whose dielectric losses are negligibly small (∼10⁻³) at ambient temperature but can reach fusion levels (high dielectric loss) in a microwave cavity in a few minutes. This is due to a strong increase in conduction losses associated with the thermally activated migration of electrons from the 2p valence band of oxygen to the 3s3p conduction band of aluminium.⁵  Moreover, conduction losses in solids are usually enhanced by defects in materials, which help in reducing the energy needed to generate electrons and holes in the conduction and valence bands, respectively.

As stated in Section 1.2, magnetic loss processes can occur through the interactions of the magnetic moment of the materials with the magnetic field component of the radiation. Such loss processes generate heat with the magnitude of the loss being measured using the real (μ′) and imaginary (μ″) components of the permeability and the associated loss tangent. Differently from electric field heating, there are not many papers ascribing the microwave heating effect to the magnetic field (H) component. In a paper by El Khaled et al., some interesting results were reported from studies carried out to verify the effect of the magnetic field in microwave heating.¹⁷  In particular, (i) the studies of Cheng et al., published in the first years of the twentieth century, proved that some magnetic dielectric materials are more efficiently heated by a microwave magnetic field rather than an electric field; (ii) the studies by Zhiwei et al., published in 2012, gave a relevant importance to the magnetic component of an electromagnetic field and presented its main advantages over electric field heating described earlier in a larger number of publications. Moreover, in 2016, Rosa et al. reported on how the microwave heating of ferromagnetic powders presents a strong contribution by the H field interaction with matter, which, in regions of predominant magnetic field, can be significantly higher than the electric field related contribution.³³  In terms of catalysis, the effect of the E and H fields on the Pd-catalyzed Suzuki–Miyaura coupling reaction for the synthesis of 4-methyl bipyridine was investigated by Horikoshi and Serpone.³⁴  The authors used microwave apparatus with a single mode cavity TE103 that could separate the E and H fields. It was found that the yield dramatically increased in the H-field. This was attributed to the generation of a microwave E field which, in this reaction, led to the degradation of the product.³⁴ 

Based on recent findings, mechanisms of multiple losses can contribute to microwave magnetic heating, among which are eddy current losses, hysteresis, magnetic resonance, and residual losses.

Eddy current losses occur when induction currents are established in a conducting material by an oscillating magnetic field, which causes resistive heating of the solid. The eddy current density can be expressed as J = σE, where σ is the electrical conductivity and E is the electric field induced by the alternating H field.

When magnetic materials are subjected to an alternating magnetic field, the magnetic dipoles will oscillate as the magnetic poles change their polar orientation in every cycle. This rapid flipping of the magnetic domains causes considerable friction and heating inside the material: heating due to this oscillation mechanism is known as hysteresis loss. Hysteresis losses occur only in magnetic materials such as ferrous materials, steel, nickel, and a few other metals.

Magnetic resonance losses are primarily induced by domain wall resonance and electron spin resonance (ESR). For example, magnetite (Fe₃O₄) is rapidly heated by microwaves, but this is not the case with hematite (Fe₂O₃) since the latter is not a magnetic material.³⁵  Moreover, since transition metal oxides (e.g., iron, nickel, and cobalt oxides) have high magnetic losses, they are usually added to induce losses within these solids for which the dielectric loss is too small.

In summary, (i) microwave heating of a broad range of conductor and semiconductor materials is mainly due to the eddy current loss, (ii) the hysteresis loss occurs inside ferrous magnetic materials, and (iii) when ferrite and other magnetic materials are exposed to an alternating magnetic field, the magnetic resonance loss/residual loss contributes to their induction heating. In some cases, when some conductive magnetic materials (e.g., ferrite materials) are exposed to an alternating magnetic field, the three mechanisms of eddy current loss, hysteresis loss and residual loss can together contribute to their heating.¹⁶ 

Microwaves, which can be produced from the electricity obtained from renewable energy sources, can be effectively used for heating chemical reactors, which are currently operated by burning fossil fuels, thus helping in electrification of the chemical industry.^36,37  Apart from its peculiar characteristics (rapid, volumetric and selective), microwave heating can result in a huge process intensification since it may allow an improvement in at least one of the main process parameters, such as yield, selectivity, or capital or operating cost, and may reduce the environmental impact of a process. In recent years, microwave heating has been successfully applied in commercial fields, including food processing, physical and chemical treatments of wood, plastic, rubber and ceramics.³⁸  Regarding the application of microwave heating in chemical engineering processes, some main issues must be further investigated.³⁹  In the last decade, several research efforts have been focused on this direction, with several groups investigating the possibility to intensify some chemical processes, such as ammonia production at low pressure⁴⁰  and methane and biomass valorisation,^41,42  through the use of MW heating. These recent studies obtained interesting results and provided the basis for further research. One of the main features of most industrial chemical reactors is that they have (i) a fixed bed, (ii) a fluidized bed, (iii) slurry or (iv) a monolithic configuration, thus being multiphase. MW heating, being selective (microwaves may preferentially heat a phase or a material with respect to others), may have a fundamental importance in multiphase reactors. For example, in a silicon carbide (SiC) monolith, the selective heating realized, since only the solid absorbs microwaves (thus heating itself), may cause a temperature difference between the hot solid and the cold gas present in its channels, therefore influencing the homogeneous and heterogeneous reactions inside the reactor. This behaviour is peculiar for the microwave heating of multiphase reactors and cannot be achieved in conventional heating.⁴³  Selective heating can also result in highly localized heating or hotspot formation,⁴⁴  sometimes related to arcing or plasma,⁴⁵  which can occur in the case of the concentration of the electric field in a small gap between microwave absorbers, such as activated carbon and silicon carbide.^46,47  Thus, arcing or plasma occurs when the electric field strength becomes higher than the dielectric strength of the continuum phase (∼3 MV m⁻¹ for air).³⁴  Sharp edges and other surface irregularities, allowing the accumulation of free charges with a consequent increase in the charge density and the resulting electric field, may help arc formation.^34,47  The occurrence of hotspots in multiphase reactors can be productive^48,49  or deleterious.⁵⁰  In fact, either hotspots can reduce the catalyst activity by promoting, for example, the crystallization of the metal nanoparticles dispersed on it,^51,52  or the localized higher temperature may result in enhanced reaction performance by means of (i) higher temperatures for the heterogeneous reactions to occur^53,54  or (ii) the desorption of the products from the catalyst surface at a higher rate.⁵⁵  In the past decade, several research groups have focused their attention on microwave multiphase reactors, such as monoliths,^42,55–59  fixed beds^60–63  and slurry reactors.^51–53  Applications of these studies include polymerization,⁶⁴  biomass valorisation,^65,66  epoxidation,^67,68  methane nonoxidative coupling,⁴²  methane steam reforming,⁵⁷  MW-assisted CO₂ desorption from zeolites 13X⁶³  and propane dehydrogenation.⁵⁹  These studies evidenced effective process intensification obtained through MW heating, since higher yields and selectivity, as well as a lower processing time, have been achieved. One of the main issues that still remains unaddressed is the accurate measurement of temperature in MW-assisted processes; in this sense, only in a few cases^42,56,58  have the temperatures of different phases been reported with sufficient spatial resolution. Some reviews have been published in the recent past, which either deal with specific areas of chemical engineering⁹  or provide a broad overview of the applications of microwave heating in chemical engineering processes.^69,70 

In the scale-up of a microwave-assisted process, it is important to assure a good microwave flow inside the cavity.⁷¹  In the last few years, different research groups compared, also by means of dedicated software simulations, different types of microwave applicators, including multi-mode, single-mode (or mono-mode), and traveling-wave microwave reactors (TWR).⁷²  In multi-mode applicators, the microwaves are reflected by the internal walls and by the sample, resulting in a non-homogeneous microwave field and, consequently, in a non-uniform heating profile and hotspot formation.³⁶  The low field density compared to the high generated microwave power (1000–1400 W) is another problem of these applicators, which results is a weak performance in the case of small-volume samples. Even if their use is limited by these problems, multi-mode applicators are often used in industry, due to their low cost, simplicity of construction, and versatility. Mono-mode applicators have only one mode, and they generate a standing wave inside the cavity. The sample to be irradiated by microwaves is placed at the location where the electromagnetic field has the maximum intensity. The main limitations of mono-mode applicators are (i) the limited volume of the sample (maximum 200 mL) that can be irradiated and (ii) the dependence of the microwave field pattern inside the cavity on frequency changes, as well as on the position and dielectric properties of the heated sample. One advantage of these cavities is that they can provide a higher field strength with less energy consumption.³⁵  The abovementioned problems of these two types of applicators make their use critical if controlled chemical reactions must be carried out. Differently from multi- or mono-mode cavities, TWR, if properly designed such that the microwave field inside the reactor travels in only one direction, can assure a more uniform microwave heating, since it avoids reflections and resonant conditions.⁷⁰  In this way, non-uniform electromagnetic interference patterns and non-uniform heating along the reactor are avoided. Microwave chemistry applications have been investigated for more than three decades, and the TWR can be used for a process scale-up.³⁷  One of the newest proposals in this sense is the coaxial structure traveling-wave microwave reactor proposed by Sarabi et al.⁷¹  Their studies, based also on simulations performed using dedicated software, demonstrated that, working at a frequency of 2.45 GHz, the overall structure displays a reflection coefficient of −20 dB (≈ %1), proving the absence of any standing wave generated along the structure. Furthermore, their simulations demonstrated that the catalyst loading inside the reactor is also important in order to minimize microwave reflections, and a uniform temperature distribution is assured when the reactor is partially filled with the catalyst. Irrespective of the case, in order to obtain a successful scale-up of a microwave-assisted catalytic process, a multidisciplinary approach and collaboration among different skills and competencies, such as catalysis, materials science, and electrical and chemical engineering, are necessary.

As already mentioned, one of the main challenges in the development of microwave heating-based technologies is the proper design of the microwave cavity, in particular with the aim to scale up a MW-assisted reactor. In fact, the sensitive nature of the standing wave pattern of electric and magnetic fields and the inefficient heating of the reactor due to the penetration depth becoming smaller than the reactor size make this step very difficult. Therefore, these drawbacks must be overcome for a widespread application of MW heating in chemical processes. In this sense, the fast progress in computational resources and the availability of the user-friendly Multiphysics commercial software could be helpful, for example, in providing the exact distribution of the 3D temperature and electromagnetic field in a microwave cavity and reactor.⁷³  However, the progress in CFD is slow with respect to the advances in experimental tests. In fact, the presence of different aspects that must be considered makes the modelling of microwave multiphase reactors very challenging, including aspects that are related to the peculiar nature of the reactors, simultaneously being multiphase (characterized by the presence of more than one phase, such as gas and solid or gas and liquid), multiphysics (characterized by the presence of different physics, such as electromagnetism, transport processes and chemical reactions) and multiscale (characterized by a variable length scale, from a single catalyst particle to a microwave cavity). Due to these difficulties, only a few comparative studies are available in which the simulation results are validated with experimental tests.^74–78  In any case, the majority of these studies have been performed considering only single-phase systems, such as the microwave heating of liquids in a glass vial.^74,75,78  In the case of multiphase systems, several simplifications are needed to effectively manage the complexity of the system and obtain results at a reduced computational cost. For example, some studies are available in which a multiphase fixed bed reactor, constituted by large uniformly arranged particles,²⁹  biphasic solid hydrides⁷⁹  and zeolites,^63,80  was considered a continuum, and in the simulations the experimentally measured effective permittivity of the sample was employed. However, these simplifications should be carefully chosen since they can introduce large uncertainties in model predictions, which can lead to uncertainties in the reactor design.

A lot of examples of microwave-assisted fundamental reactions have been reported over the last few decades, and in recent years some industrial applications of microwave assisted catalytic processes have also been reviewed. Some researchers have focused on understanding what happens when a material is exposed to microwaves and what are the mechanisms responsible for its heating. A phenomenon known as “hotspot formation” arising due to microwave heating has been explored and accepted for a long time as the main mechanism responsible for microwave heating, but in the last few years different studies have demonstrated the catalytic mechanism of microwaves in decreasing the activation energy of reactions, especially in the gas phase. It is clear that, in heterogeneous catalysis, choosing an appropriate material as the active species and/or support is mandatory in order to achieve its heating as well as a successful microwave assisted catalytic reaction.

The literature survey and the consequent discussions reported in the above sections revealed that the better performance of MW-assisted catalytic reactions compared to the conventional ones is attributed to both thermal and non-thermal effects. More detailed fundamental investigations are, however, required to better explain and unravel the role of the latter. A future direction for improving the knowledge, and a wider use of MW-assisted processes, is to gain a better understanding of how to tune the solid–fluid temperature difference as a function of the operating conditions and materials. In this sense, the very recent introduction of fixed bed micromonoliths provides some advantages, such as the improvement of catalyst loading, thereby allowing flexibility in material selection and the prevention of hotspot formation. Moreover, additive manufacturing, enabling the production of complex structures, could be effectively employed in the future for the development of microwave reactors.

D_p

Penetration depth

|E|

Strength of the microwave electric field

f

Frequency of the microwaves

|H|

Strength of the microwave magnetic field

h_c

Convective heat transport from the solid catalyst to the medium

I

Radiation intensity

J

Eddy current density

k_B

Boltzmann constant

P

Thermal power produced per unit volume originating from microwave radiation

P_d

Dipolar polarization

T

Temperature

T_cat

Temperature of the catalyst

T_med

Temperature of the medium

U_a

Potential barrier separating dipole positions

α_cat

Absorption cross-section of the catalyst material

α_med

Absorption cross-section of the medium

ε

Frequency dependent dielectric constant

$ε*$

Complex permittivity

ε₀

Free space permittivity

$ε′$

Real permittivity

$ε″$

Imaginary permittivity

$ε eff ″$

Effective loss factor

$ε r ″$

Relative dielectric loss factor

ε_s

Static dielectric constant

ε_∞

High frequency dielectric constant

η

Viscosity of the medium

λ

Wavelength of the radiation

$μ*$

Complex permeability

μ₀

Magnetic permeability in vacuum

$μ′$

Real permeability

$μ″$

Imaginary permeability

$μ r ″$

Relative magnetic loss

σ

Electrical conductivity

tan δ

Loss tangent

τ

Relaxation time

ω

Frequency of the radiation