Proton-Enhanced Dielectric Properties of Polyoxometalates in Water under Radio-Frequency Electromagnetic Waves

Electromagnetic waves, such as microwaves, have been used to enhance various chemical reactions over polyoxometalates. The dielectric properties of catalysts are among the relevant parameters facilitating catalytic reactions under electromagnetic radiation. This study describes the dielectric properties of polyoxometalate catalysts in aqueous and organic solutions to understand the mechanism of interactions between polyoxometalates and electromagnetic waves. Specific loss factors of polyoxometalates were observed at lower frequencies (<1 GHz) by the ionic conduction of the polyoxometalate solution. The evolution of ionic conduction depended strongly on cations rather than anions. Proton-type polyoxometalates exhibited significantly higher loss factors than other cations did. The activation energy for ionic conduction in protonated silicotungstic acid (H4SiW12O40) was significantly low in water (7.6–14.1 kJ/mol); therefore, the high loss factor of protonated polyoxometalates in water was attributed to the proton relay mechanism (i.e., Grotthuss mechanism). The results suggested that the proton relay mechanism at the radio-frequency band is critical for generating selective interactions of polyoxometalates with applied electromagnetic fields.


Introduction
Polyoxometalates (POMs) exhibit unique catalysis for many oxidation and reduction reactions, alkene polymerization, and acid and base catalysis reactions [1,2]. POMs comprise oxo-anions of heteroatoms (Si, P, S, Ge, As, Se, B, Al, and Ga) and addenda atoms (W, Mo, V, Nb, and Ta). The general chemical formula for Keggin-type POMs is given by [XM 12 O 40 ] n− (X = heteroatoms; M = addenda atoms). Because of the high stability of POM anions, POMs exhibit very low acid dissociation constants; thus, POMs are used as super acid catalysts [1]. At the same time, the multi-electron-transfer redox property of POMs under relatively mild conditions enables selective oxidative catalysis, such as the high-yield syntheses of epoxides and aldehydes [1,2]. The unique catalytic properties of POMs have been applied for many biorefinery processes, such as hydrolysis of crystalline cellulose [3,4], oxidative where P, E, H, ε 0 , and µ 0 are the absorbed power by volume, electric field intensity, magnetic field intensity, permittivity of free space, and permeability of free space, respectively. The dielectric properties and intensities of the electric and magnetic fields are the key parameters to manipulate to obtain the high-efficiency energy propagation of electromagnetic waves. In addition, dielectric properties are strongly related to the molecular dynamics of dipoles and charges (ions and electrons) under oscillating electromagnetic fields [24][25][26][27]. Therefore, the dielectric properties of a material provide information regarding the molecular dynamics of dipoles and charges under electromagnetic fields, as well as the degree of the electromagnetic wave susceptibility of the material. In this study, the dielectric properties of POMs under applied electromagnetic radiation from the radio-frequency (RF) band to MWs were analyzed to understand the absorption mechanisms of electromagnetic waves by various POMs with different chemical compositions. Dielectric spectroscopy was conducted by the coaxial probe method to characterize the complex dielectric constants of the POMs in different solvents such as water, dimethylsulfoxide (DMSO), and 2-propanol. The dielectric loss mechanism of the POMs was further investigated by applying the Cole-Cole model to reveal the key parameters involved in the dielectric loss mechanisms of POMs in solution.

Materials
Silicotungstic acid (H 4 [28]. The water contents in the POMs were determined by thermogravimetric analysis (TGA, Shimadzu Co., Kyoto, Japan; Table 1). The POMs were used without further purification.

Dielectric Relaxation Spectroscopy
Dielectric relaxation spectra were obtained by the coaxial probe method using a Keysight 5242A Network Analyzer and a Keysight high-temperature probe (100 MHz-20 GHz) or a Rhode & Schwartz ZND network analyzer equipped with a KEYCOM Co. (Tokyo, Japan) probe-type (open mode) dielectric constant measurement kit (200 MHz-8.5 GHz). The POMs were dissolved in pure water, DMSO, or aqueous 2-propanol (0-100 v/v %) solutions of 1-20 mM. Dielectric relaxation spectra were obtained between room temperature (25 • C) and 80 • C by changing the temperature using a bath of aluminum beads with stirring to obtain solutions with homogeneous temperatures. The temperature during the dielectric measurement was monitored by a fiber-optic thermometer (FL-2000, Anritsu Meter Co., Ltd., Tokyo, Japan) under stirring to ensure temperature homogeneity of the POM solutions.

Dielectric Properties of POMs in Water, 2-Propanol, and DMSO
The complex dielectric constants of the POM solutions were measured by the coaxial method using open probes and a vector network analyzer. The real part and imaginary part of the complex dielectric constant represent the relative permittivity and loss factor, including dielectric loss (ε") and ionic conduction (σ), respectively. Figure 1A,B show the dielectric spectra of H 4 SiW 12 O 40 in water (0-8.8 mM) at frequencies of 100 MHz-20 GHz. The loss factors of H 4 SiW 12 O 40 are strongly affected by the acid concentration. Aqueous H 4 SiW 12 O 40 solutions show particularly elevated losses at frequencies of <2000 MHz, which becomes more prominent in the RF band (<300 MHz) rather than under MWs. The loss mechanism at this frequency range can be attributed to ionic conduction by electrolytes [26]. In contrast, the dielectric dispersion at higher frequencies, peaking at 18-20 GHz, does not significantly change with concentration. The peak is assigned to the cooperative relaxation of long-range hydrogen-bond-mediated dipole-dipole interactions of free water [29]. The dielectric spectra of H 3 PW 12 O 40 show similar behavior to those of H 4 SiW 12 O 40 , exhibiting enhanced loss factors at lower frequencies; however, the magnitudes of the loss factors are smaller than those of H 4 SiW 12 O 40 ( Figure 1C,D). Figure 2 shows the dielectric spectra of binary systems of 2-propanol and water with and without H 4 SiW 12 O 40 . The ratios of 2-propanol to water were varied to investigate the effect of the relative permittivity of the solvent on the dielectric properties of the POM solution. The relative permittivity is decreased from 86.6 to 20.6 with increased 2-propanol concentration ( Figure 2A) [30,31]. Along with the decrease in relative permittivity, the dielectric loss peak is shifted from 18-20 GHz (free water) to 300-400 MHz (2-propanol) with a reduction in peak intensity ( Figure 2B). The loss factor by ionic conduction is gradually weakened by increased 2-propanol concentration, and is buried by the dielectric loss of 2-propanol ( Figure 2D). The decrease in ionic conduction indicates that the dissociation of H 4 SiW 12 O 40 should be prohibited by the addition of 2-propanol. The dissociation of an acid depends on the dielectric constants and proton affinities of the solvents granted by their molecular structures [32]. Smaller dielectric constants provide larger Coulomb potentials, thus prohibiting ionic dissociation. Because 2-propanol has a lower relative permittivity than water, the dissociation constants of acids become higher than those in water.
Materials 2018, 11, x FOR PEER REVIEW 4 of 11 potentials, thus prohibiting ionic dissociation. Because 2-propanol has a lower relative permittivity than water, the dissociation constants of acids become higher than those in water.   potentials, thus prohibiting ionic dissociation. Because 2-propanol has a lower relative permittivity than water, the dissociation constants of acids become higher than those in water.    because DMSO works as an oxygen donor during the reaction [33]. Similar to the case in the aqueous POM solutions, the relative permittivity does not significantly change with increasing POM concentration. The peak for the dielectric loss of DMSO at~8 GHz is not obviously affected by the different concentrations of POMs from 0 to 10 mM. In contrast, the dielectric losses at lower frequencies are increased with increased concentrations of H 4 Figure 3 shows dielectric spectra of H4SiW12O40 and H3PW12O40 in DMSO. DMSO was found to exhibit a specific solvent effect on the oxidation of alcohol via PVxMo(12−x)O40 −(3+x) (x = 0, 2) because DMSO works as an oxygen donor during the reaction [33]. Similar to the case in the aqueous POM solutions, the relative permittivity does not significantly change with increasing POM concentration. The peak for the dielectric loss of DMSO at ~8 GHz is not obviously affected by the different concentrations of POMs from 0 to 10 mM. In contrast, the dielectric losses at lower frequencies are increased with increased concentrations of H4SiW12O40 and H3PW12O40 in DMSO by ionic conduction. H4SiW12O40 has a slightly higher loss factor than H3PW12O40; however, the ionic conduction by POMs in DMSO is much smaller than that in water because of the lower conductivities of the electrolytes in DMSO. The dissociation constant of POMs in DMSO should be between those in water and 2propanol, because the relative permittivity of DMSO (46.9) is between those of water (86.6) and 2propanol (20.6).
The above results indicate that the loss factors of POMs in a solution are selectively increased at lower frequencies corresponding to the RF band. The dissociation of POMs is required to initiate clear ionic conduction in the dielectric spectra. A relative permittivity of >50 (such as those of 50% aqueous 2-propanol solution and DMSO) is essential for obvious ionic conduction by the dissociation of POM in the solvents. For the molybdenum-based Keggin POM of H3PMo12O40, the dependence of dielectric properties on solvents were in very good accordance with those of H4SiW12O40 and H3PW12O40 ( Figures S1 and S2). Therefore, solvents with relatively high permittivities, such as water, are suitable for improving the specific dielectric losses of POMs.

Mechanism of Interaction of POMs and Electromagnetic Waves in Water
The mechanism of interaction between the POMs and electromagnetic field was further studied by applying the dielectric relaxation model to the dielectric parameters, allowing quantitative evaluation of the POM conductivity in solvents and of the solvent relaxation process. The real and imaginary parts of the complex dielectric constants were further analyzed by a dielectric relaxation model. A general dielectric relaxation model is given by the Debye model (2)

Mechanism of Interaction of POMs and Electromagnetic Waves in Water
The mechanism of interaction between the POMs and electromagnetic field was further studied by applying the dielectric relaxation model to the dielectric parameters, allowing quantitative evaluation of the POM conductivity in solvents and of the solvent relaxation process. The real and imaginary parts of the complex dielectric constants were further analyzed by a dielectric relaxation model. A general dielectric relaxation model is given by the Debye model (2): where ε*, ε s , ε ∞ , j, ω, and τ are the complex permittivity, the permittivity at a static frequency, the permittivity at infinite frequency, the imaginary unit, angular frequency, and relaxation time, respectively. The Debye model can be applied to single components. The Cole-Cole model (3) is more suitable for mixed solutions of more than two components by introducing β (0 < β ≤ 1) as a distribution parameter: For a solution containing an electrolyte, a term for the contribution of ionic conduction can be applied to the Cole-Cole model as follows (4): where ε 0 and σ are the permittivity of free space and conductivity of the electrolyte, respectively. The conductivity and the dielectric relaxation time were calculated by fitting the Cole-Cole model considering the conductivity, as shown in Equation (4) Figure S3).
The temperature dependence of conductivities is shown in Figure 5. The elevated temperature increases the conductivity of H 4 SiW 12 O 40 in both water and DMSO. The temperature-dependent conductivities are further fitted to the Arrhenius Equation (5) to obtain the activation energy (E a ) of the conduction process: where A, R, and T are the frequency factor, ideal gas constant, and absolute temperature, respectively. The activation energy of conductivity in water is estimated at 14.1 kJ/mol, while that in DMSO (1 mM) is~96.6 kJ/mol ( Figure 5). The higher activation energy of H 4 SiW 12 O 40 in DMSO may be due to the constraint of ionic conduction by the strong interaction of DMSO and H 4 SiW 12 O 40 . By increasing the concentration of H 4 SiW 12 O 40 to 5-10 mM, the activation energy is decreased to 8.9 kJ/mol (5 mM)-7.6 kJ/mol (10 mM) in water and to 24.6 kJ/mol (5 mM)-18.9 kJ/mol (10 mM) for DMSO. POMs are well-known highly proton-conductive materials, often used in proton-exchange membrane fuel cells [34]. Horky [35]. The low conductivity of POM anions indicated that their conduction entirely relies on hydrodynamic transport (the vehicle mechanism). However, the large mobility of protons (H 3 O + ) arises from the proton relay mechanism (or Grotthuss mechanism), which involves fast proton transport by the consecutive formation and destruction of H 3 O + . Wang et al. reported that the activation energy for conductivity in H 3 PW 12 O 40 (0.6-6.7 mM) and H 4 SiW 12 O 40 (0.13-3 mM) in dimethyl formamide (DMF) is~7.9-8.3 kJ/mol [33].
The activation energy of <15 kJ/mol indicates the proton relay mechanism, whereas that of >20 kJ/mol is due to the vehicle mechanism. Therefore, dielectric loss of H 4 SiW 12 O 40 in water under RF-band electromagnetic waves can be attributed to fast proton conduction. In DMSO, the conduction process is much lower than that in water, indicating the importance of water in enabling high dielectric loss by the proton relay mechanism.
where ε0 and σ are the permittivity of free space and conductivity of the electrolyte, respectively.
The conductivity and the dielectric relaxation time were calculated by fitting the Cole-Cole model considering the conductivity, as shown in Equation (4). The conductivities of H4SiW12O40 in water and DMSO are indicated in Figure 4A,C. The increased concentration of H4SiW12O40 in water linearly increases the conductivity. In contrast, a concentration of >5 mM is required for H4SiW12O40 to exhibit conductivity in DMSO. The conductivity of H4SiW12O40 in water is much higher than that in DMSO. The relaxation times for water and DMSO are shown in Figure 4B,D. In aqueous solutions, the relaxation time of water remains almost constant between 8 and 8.5 ps. However, the relaxation time of DMSO is linearly increased from 16 to 18 ps with increased H4SiW12O40 concentration. Therefore, the restriction of the molecular motion of DMSO is gradually strengthened by the addition of H4SiW12O40. This indicates strong interactions between DMSO and H4SiW12O40. H3PW12O40 and H3PMo12O40 also showed very similar tendencies in DMSO and water ( Figure S3).  The temperature dependence of conductivities is shown in Figure 5. The elevated temperature increases the conductivity of H4SiW12O40 in both water and DMSO. The temperature-dependent conductivities are further fitted to the Arrhenius Equation (5) to obtain the activation energy (Ea) of the conduction process: where A, R, and T are the frequency factor, ideal gas constant, and absolute temperature, respectively. The activation energy of conductivity in water is estimated at 14.1 kJ/mol, while that in DMSO (1 mM) is ~96.6 kJ/mol ( Figure 5). The higher activation energy of H4SiW12O40 in DMSO may be due to the constraint of ionic conduction by the strong interaction of DMSO and H4SiW12O40. By increasing the concentration of H4SiW12O40 to 5-10 mM, the activation energy is decreased to 8.9 kJ/mol (5 mM)-7.6 kJ/mol (10 mM) in water and to 24.6 kJ/mol (5 mM)-18.9 kJ/mol (10 mM) for DMSO. POMs are well-known highly proton-conductive materials, often used in proton-exchange membrane fuel cells [34]. Horky et al. previously reported the infinite dilution conductivity of cations (Λ° H3O + ) and POM anions (Λ° anion) for H4SiW12O40 and H3PW12O40 in water [35]. The low conductivity of POM anions indicated that their conduction entirely relies on hydrodynamic transport (the vehicle mechanism). However, the large mobility of protons (H3O + ) arises from the proton relay mechanism (or Grotthuss mechanism), which involves fast proton transport by the consecutive formation and destruction of H3O + . Wang et al. reported that the activation energy for conductivity in H3PW12O40 (0.6-6.7 mM) and H4SiW12O40 (0.13-3 mM) in dimethyl formamide (DMF) is ~7.9-8.3 kJ/mol [33]. The activation energy of <15 kJ/mol indicates the proton relay mechanism, whereas that of >20 kJ/mol is due to the vehicle mechanism. Therefore, dielectric loss of H4SiW12O40 in water under RF-band electromagnetic waves can be attributed to fast proton conduction. In DMSO, the conduction process is much lower than that in water, indicating the importance of water in enabling high dielectric loss by the proton relay mechanism. The dielectric properties of several types of POM with different compositions and structures are analyzed in water (1 mM) ( Figure 6A). The degree of ionic conduction varies depending on the type of POM. H4S2W18O62, a Wells-Dawson-type POM, shows the highest ionic conduction (0.223 S/m), followed by H4SiW12O40 (0.133 S/m) and H3AsW12O40 (0.129 S/m). The conductivities of the POMs are further plotted over their acidities, as described by the Hammett indicator ( Figure 6B) [28]. The acidities of the POMs show good accordance with their conductivities because of the higher   Figure 6B) [28]. The acidities of the POMs show good accordance with their conductivities because of the higher concentrations of protons in the systems. Therefore, the degree of acid dissociation is another important factor to obtain better ionic conductivity by POMs. Therefore, the large conductivity of protons significantly affects the loss factors of POM solutions. In DMSO at 1 mM, however, no proton-dependent enhancement was observed. These results coincide with the large activation energy required for ionic conduction at low POM concentrations in DMSO, compared to the very small activation energies required in water ( Figure 5). As a summary, protonated POMs exhibit specific loss factors at lower frequencies in aqueous media than in nonaqueous ones because of the proton relay mechanism. Interestingly, we have previously observed similar proton-enhanced ionic conductivity in an aqueous system of natural polysaccharides obtained from seaweeds [36,37]. The dielectric properties In DMSO at 1 mM, however, no proton-dependent enhancement was observed. These results coincide with the large activation energy required for ionic conduction at low POM concentrations in DMSO, compared to the very small activation energies required in water ( Figure 5). As a summary, protonated POMs exhibit specific loss factors at lower frequencies in aqueous media than in non-aqueous ones because of the proton relay mechanism.
Interestingly, we have previously observed similar proton-enhanced ionic conductivity in an aqueous system of natural polysaccharides obtained from seaweeds [36,37]. The dielectric properties of acidic polysaccharides, such as κ-and λ-carrageenan (sulfated galactan), are significantly affected by the conductivities of their cations. When the cation of carrageenan was exchanged from the K + -form (as-prepared) to the proton-form by a strong cation-exchange resin, a significant enhancement of ionic conductivity was observed in the RF band (<300 MHz). Therefore, the proton-enhanced ionic conductivity may be a general phenomenon in many materials. Ionic conductivity is among the key parameters needed to obtain efficient dielectric heating, as described in Equation (1). Because the power of dielectric heating strongly depends on the conductivity, ionic conductivity has been used to improve the MW susceptibility of reaction systems [38][39][40]. The presented results indicate that stronger and more selective interactions can be obtained between protonated POMs and electromagnetic waves by applying RF fields rather than MWs. Therefore, the large conductivity of protons significantly affects the loss factors of POM solutions. In DMSO at 1 mM, however, no proton-dependent enhancement was observed. These results coincide with the large activation energy required for ionic conduction at low POM concentrations in DMSO, compared to the very small activation energies required in water ( Figure 5). As a summary, protonated POMs exhibit specific loss factors at lower frequencies in aqueous media than in nonaqueous ones because of the proton relay mechanism. Interestingly, we have previously observed similar proton-enhanced ionic conductivity in an aqueous system of natural polysaccharides obtained from seaweeds [36,37]. The dielectric properties of acidic polysaccharides, such as κ-and λ-carrageenan (sulfated galactan), are significantly affected by the conductivities of their cations. When the cation of carrageenan was exchanged from the K +form (as-prepared) to the proton-form by a strong cation-exchange resin, a significant enhancement of ionic conductivity was observed in the RF band (<300 MHz). Therefore, the proton-enhanced ionic conductivity may be a general phenomenon in many materials. Ionic conductivity is among the key parameters needed to obtain efficient dielectric heating, as described in Equation (1). Because the

Conclusions
Electromagnetic waves have been used to activate various chemical reactions catalyzed by POMs. The dielectric properties of irradiated materials are important factors in obtaining good energy propagation during reactions under electromagnetic fields. The dielectric properties of POMs were, therefore, characterized by dielectric spectroscopy under fields at frequencies between the RF band and MWs in this study. Selective loss factor increases of POMs in water were observed at frequencies below <1 GHz; these became more prominent in the RF band (<300 MHz). This process was due to the ionic conductivity of the POMs and strongly depended on their concentration. Dielectric constants of >50 were required to initiate POM dissociation and thus ionic conductivity. The very low activation energy for ionic conductivity by POMs indicated that the proton relay mechanism is involved in the dielectric loss of POMs. The contribution of the proton relay mechanism was further confirmed by varying the acid strength and cations of POMs. Namely, POMs with greater acidity exhibited more intense ionic conduction. In addition, the protonated POM exhibited larger ionic conductivity than the K + -form and NH 4 + -form. Because a similar proton relay mechanism was previously observed for protonated natural polysaccharides, this phenomenon may be a general mechanism during the dielectric heating of many electrolyte materials.