Investigation of the Microwave Effect: A New Approach for the Solvent

Article pubs.acs.org/IECR

Investigation of the Microwave Effect: A New Approach for the Solvent Effect on the Microwave-Assisted Decomposition Reaction of 2,2′-Azobis(isobutyronitrile) Başak Temur Ergan* and Mahmut Bayramoğlu Department of Chemical Engineering, Gebze Institute of Technology (GIT), Gebze, Kocaeli, Turkey S Supporting Information *

ABSTRACT: In this work, the effect of the solvent type on microwave (MW)-assisted decomposition of 2,2′azobis(isobutyronitrile) was investigated by online monitoring of the reaction kinetics in various solvents: n-butanol, dimethyl sulfoxide, dimethylformamide, and n-propanol. The study showed that MW irradiation accelerates the reaction rates, but it does not affect the kinetic law (first order) and mechanism of the reaction. Furthermore, the Arrhenius parameters were found to be higher than their thermal counterparts, depending on the MW power density (P) as well as to the solvent type. On the other hand, two new properties were proposed to investigate the solvent/MW effects: a solvent property (S) defined by means of Hansen solubility parameters and the relaxation time of the solvent (τ). According to experimental results, solvents with high S and with an optimum τ value are favorable for an enhanced MW effect on chemical reaction kinetics, pointing to specific molecular structures for solvent candidates. relatively easy to obtain the dielectric data (ε″ and ε′) at room temperature10−12,15,16 Meanwhile, temperature-dependent measurement of the dielectric properties of liquids (especially ε″ and tan δ) is still cumbersome and requires expensive equipment. So, few studies are available regarding these measurements.11,12 Furthermore, 2,2′-azobis(isobutyronitrile) (AIBN) is a widely used initiator in free-radical polymerizations. The thermal decomposition rate of AIBN in 36 solvents was measured by different authors17,18 and shown to be solventdependent with an overall variation in the rate constant of a factor of up to 4 when the solvents change from nonpolar to strongly polar. However, different values have been reported for the Arrhenius parameters of solvents in previous studies.18−21 In our previous study, MW-assisted decomposition kinetics of AIBN in n-butanol was investigated using an online experimental system allowing accurate control and measurement of the temperature and MW power.21 The main aim of the present study was to investigate the “solvent effect” on the kinetics of MW-assisted radical decomposition of AIBN using various types of solvents. In this way, it is hoped to obatin some clues on the true nature of the “microwave effect” on chemical reactions.

1. INTRODUCTION Microwave (MW) energy provides a versatile tool for efficient and selective heating in various areas of production technology. This technique also has great application potential in synthetic chemistry, especially in the green chemistry area. Since the first reports of MW-assisted synthesis, the technique has been accepted as a method for reducing reaction times often by orders of magnitude and for increasing yields of product compared to thermal (conventional) methods.1−3 Although studies have listed several advantages of using MW heating in synthetic chemistry, the true nature of MW effects has not been completely illuminated; some authors proposed a “specific MW effect” or a “nonthermal effect” based on the changes of the thermodynamic parameters,4−6 the occurrence of an inverted temperature profile during dielectric heating,7 the superheating of solvents or creation of hot spots within the reacting mixture,8 and the selective absorption of MW by some specific compounds such as reactants, intermediate species, or products.9 Materials differ by orders of magnitude in their ability to absorb MW energy, which is eventually converted to heat. The relevant material property is the complex permittivity defined in terms of the dielectric constant (ε′) and dielectric loss factor (ε″), which are both frequency- and temperature-dependent.10−14 Furthermore, the dielectric properties of chemical species depend on various chemical structural characteristics, especially their polarizability and permanent polarity quantified by the dipole moment (μ). In a MW-irradiated chemically active system, reactants, products, and other components such as solvents/inert components absorb MW energy according to their loss tangent (tan δ), which is the ratio of ε″ to ε′, and in this way, they are selectively heated to different temperatures in a time period depending on the local heat dissipation rates. Recent developments in dielectric measuring techniques using wide-band swept frequency instrumentation have made it © 2014 American Chemical Society

2. EXPERIMENTAL SECTION 2.1. Chemicals. Analytical-grade (% 98) AIBN was used as received from Acros Organics. Solvents n-butanol (NBU), dimethyl sulfoxide (DMSO), dimethylformamide (DMF), and n-propanol (NPA) were used as received from Merck. Received: Revised: Accepted: Published: 13016

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2.2. Solvent Selection. Generally, solvents can have significant effects on the reaction kinetics and mechanism as well. For example, the solvent type often affects the course of free-radical reactions by participating as a reactant. This is evidenced by the incorporation of the solvent into the products of the reaction.22 In this study, solvents were selected based on differences between the molecular structure properties relevant to matter− MW energy interaction and to reaction kinetics such as ε″, ε′, tan δ, dipole moment (μ), relaxation time (τ), and boiling point (bp) as well. These are presented in Table 1 with properties at room temperature.12,23−27

commonly used in MW chemistry because of its higher sensitivity than other sensors such as a thermocouple in a MW field. During the runs, the FO sensor was immersed in the reactor in a glass capillary sheath. The accuracy of the sensor was ±0.2 °C, and the response time of the sensor was 2 s. This sensor was periodically checked using an instrument used for calibration purposes. Furthermore, an IR sensor (accuracy ±1 °C) was used to measure the outer-surface temperature of the (isolated) reactor. On the other hand, continuous MW energy was achieved at a constant rate to the reaction medium by external circulation of the reaction medium between the reactor and spectrometer flow through the cell. 2.4. Online Monitoring of the Reaction Kinetics. In this study, the reaction kinetics was monitored online at 347 nm by a spectrophotometric method. The calibration of UV was performed using an UV−vis spectrophotometer (Lamda-35, PerkinElmer, Shelton, U.S.A.). During the experimental runs, the absorbance (A) was measured at 6 s time intervals, and approximately 100−200 absorbance−time data points were recorded during each experiment. 2.5. Experimental Procedure. In the study, experimental variable temperature (T) and MW power density (P) were investigated at five levels between 75 and 95 °C and 0 and 0.25 kW dm−3, respectively. High levels of the variables were properly selected to avoid solvent boiling during the course of the reaction. In a typical run, 200 cm3 of solvent and 10 mmol of AIBN (50 mM initial concentration) were loaded into the glass reactor and stirred at room temperature for complete dissolution. Then, a AIBN solution was heated quickly in 2 min to the desired temperature under MW irradiation by proper control of the MW power. At the same time, nitrogen gas was bubbled for 2 min in the reactor for purging oxygen. When the temperature of the reaction mixture reached the desired value and the MW power reached a constant value, the nitrogen flow was turned off and solution circulation was started to fill the recirculation line and the flow cell in 2 min, and finally the spectrophotometer was turned on to monitor the reaction. During the run, magnetic stirring was applied at 160 rpm to homogenize the composition and temperature in the reactor. Thermally driven (conventional) experiments were conducted under similar conditions. The temperatures of the reaction mixture and of the inlet stream to the flow cell were measured by Pt-100 sensors with an accuracy of ±0.01 °C tested using Testo-915-1 (Omni Instrument, U.K.) and Julabo F-12 (Labortechnik, Germany) instruments, respectively.

Table 1. Properties of Selected Solvents at Room Temperature solvent NBU DMSO DMF NPA H2Oa a

nature of the solvent

bp (°C)

ε′

tan δ

ε″

μ (D)

τ (ps)

protic/ polar aprotic/ polar aprotic/ polar protic/ polar protic/ polar

117.2

17.1

0.571

9.76

1.66

538

189

46.7

0.825

37.13

3.96

21

153

37.7

0.161

6.07

3.86

13

20.1

0.757

15.22

1.68

332

80.4

0.123

9.89

1.84

9

97.2 100

Water is given for comparative purposes.

tan δ is the primary dielectric property that reflects the fraction of MW energy absorbed (and dissipated as heat) by the irradiated medium; a small tan δ value indicates that MW penetrates deeper into the sample with less heat dissipation. Solvents with high tan δ values are clearly more beneficial for MW heating, but this may not be an obvious condition for MW-assisted chemical synthesis. Besides, solvents with low tan δ values may be more appropriate to investigate the specific MW effect by means of kinetic experiments. On the other hand, solvents are usually labeled as polar/ nonpolar according to their dipole moment (μ) and their affinity toward H+ as protic/aprotic (aprotic solvents have very little affinity for protons and are incapable of dissociating to generate protons, while protic solvents contain proton-donating groups). DMSO is more polar than DMF, NPA, and NBU because of slightly less hydrogen bonding. These solvent characteristics usually have strong influences on the reaction kinetics and mechanism. Table 1 shows that most alcohols and DMSO have suitable dielectric properties to be used effectively as solvents in MW heating (and probably in MW-assisted reactions).11,12 On the other hand, DMF is the poorest MW absorber because it has the lowest loss tangent, which was preferentially selected to investigate the specific MW effect in MW-assisted reactions. 2.3. MW Experimental Setup. The experimental setup and technical details were given in previous studies.21,28 In this study, a multimode MW reactor (Start-S model, Milestone Srl, Sorisole, Italy) was used and has the following specifications: cavity volume 44.73 dm3, dimensions 3.5 × 3.3 × 3.7 dm, MW frequency 2.45 GHz, maximum (nominal) MW power 1000 W. For precise temperature measurements, the MW system is equipped with infrared (IR) and fluoroptic (FO) temperature sensors: The reaction temperature was monitored by the FO sensor (ATC-FO-300008 type, Zhu Electronic, Italy), which is

3. RESULTS AND DISCUSSION 3.1. Solvent Effect on the Thermally Driven (Conventional) Decomposition Reaction of AIBN. In thermal experiments, excellent fits with correlation coefficients R2 higher than 0.995 with more than 100 data points were obtained in linear regression for calculation of the rate constants (kth) using the first-order kinetic expression given by eq 1 −ln(1 − XA ) = kt = ln(A 0)/A

(1)

where XA is the conversion of AIBN and A0 and A are the absorbance of the reaction medium initially and at reaction time t, respectively. From replicate experiments, the standard deviation of the rate constant values was found to be approximately 0.2%, 13017

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almost independent of the process conditions and solvent type. The rate constant values of these solvents at various reaction temperatures are given in Table 2, which is in accordance with Table 2. Thermal Rate Constants (kth) at Various Reaction Temperatures T (°C) kth × 10−4 (s−1)

solvent

75

80

85

90

95

NBU DMSO DMF NPA

0.776 1.115 0.804 0.451 2.5

1.199 1.615 2.037 1.382 1.7

2.292 2.903 2.678 2.432 1.3

4.313 4.305 5.332 4.232 1.3

7.068 8.738 8.843 8.713 1.3

kth,max/kth,min

Figure 1. Plot between Ea,th and ln(k0,th)/R at P = 0 (R = ideal gas constant, 8.314 J K−1 mol−1).

17−21

As can be seen, alcohols exhibit the the literature values. lowest and DMSO and DMF have the highest rate constant values in the whole temperature range. In other words, the “solvent effect” is more significant for DMF and DMSO than NPA and NBU. Briefly, the solvent rank is DMSO ≈ DMF > NBU ≈ NPA for a high reaction rate. An inspection of Tables 1 and 2 reveals that the dielectric constant (ε′) and/or the dipole moment (μ) are the candidate properties determining this solvent rank. Furthermore, kth,max/kth,min ratios given in Table 2 indicate that the difference between solvent effects attenuates rapidly with increasing temperature, which points to ε′ (as the temperature-dependent property) as the primary cause for the solvent effect. Furthermore, thermal Arrhenius parameters (the activation energy Ea,th and preexponential factor k0,th) are given in Table 3.

Scheme 1. Mechanism of Decomposition of AIBN under the Solvent Cage Effect

Table 3. Thermal Arrhenius Parameters in Selected Solvents solvent

Ea,th (kJ mol−1)

k0,th × 1014 (s−1)

NBU DMSO DMF NPA

124.4 105.2 133.4 122.3

3.33 0.01 76.65 1.82

cages”, which either diffuse out of the cage or form adducts inside the cage (“cage effect”). The fraction of radicals that can diffuse out of the cage reacts further to produce the main decomposition product, tetramethylsuccinodinitrile (TMSN).31 Furthermore, the kinetic evidence that kth increases with increasing solvent polarity indicates a dipolar interaction between the reactant’s transition state and the solvent medium. 3.2. Solvent Effect on the MW-Assisted Decomposition Reaction of AIBN. The kinetic study showed that the MW-assisted decomposition kinetics of AIBN in all of the selected solvents follows first-order rate law, consistent with previous studies.17−21 Excellent fits with correlation coefficients R2 higher than 0.990 with more than 100 data points were obtained. MW rate constants (kmw) under P = 0.175 kW dm−3 are shown in Table 4; if some fluctuations arising probably from the experimental error are omitted, solvents with high kmw may be ranked as DMSO > DMF ≈ NBU > NPA. This rank is not very different from the thermal one (DMSO ≈ DMF > NBU ≈ NPA). Furthermore, kmw,max/kmw,min ratios (in Table 4) indicate that in MW-assisted experiment solvent effects attenuate with increasing temperature, similar to thermal experiments. On the other hand, the inspection of Figure 2 reveals further important points on the combined MW/solvent effects; a kmw/ kth enhancement ratio indicates a different solvent rank as

As can be seen, they differ due to the solvent effect depending on various solvent properties, as mentioned in previous studies.18−21 Ea,th is inversely proportional to the dipole moment (μ) of the solvent. In weakly dipolar solvents such as NBU and NPA, equilibrium-solvent effects are observed in reactions that tend to have sharp barriers. However, in strongly dipolar solvents such as DMSO and DMF, dynamic-solvent effects (such as the dynamic viscosity) play a much more important role in affecting the reaction rate and Arrhenius parameters;21,29 in this respect, the Ea,th values of DMSO and DMF are different despite similar dipole moments, because DMSO is more viscous than DMF (the ratios of dynamic viscosities are 1.83 at 75 °C and 1.64 at 95 °C). On the other hand, k0,th seems to be more strongly (proportionally) dependent on the solvent viscosity to compensate for the negative impact of high Ea,th on kth. On the other hand, the linear plot between Ea,th and ln(k0,th)/ R (corresponding to the entropy of activation) depicted in Figure 1 has usually been explained on the basis of complexing and solvation arguments or the “kinetic compensation effect” as well. The mechanism of thermal decomposition of AIBN is generally accepted to follow a homolytic scission, as shown in Scheme 1.22,30 Primary geminate radicals are formed in “solvent 13018

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Table 4. MW Rate Constants of Experiments under P = 0.175 kW dm−3

the increase of the activation energy by MW exposure points clearly to a higher energy state of the active complex than the thermal counterpart, but this unfavorable effect of MW is compensated for (more or less depending on the solvent type and P) by an increase in k0, pointing to a more favorable structural/conformational arrangement of the active complex. Furthermore, the relationship between Ea,mw and ln(k0,mw)/R at various P values is depicted in Figure 3. A linear dependence

T (°C) kmw × 10−4 (s−1)

solvent

75

80

85

90

95

NBU DMSO DMF NPA

0.783 1.233 0.771 0.659 1.9

1.478 2.897 1.886 1.416 2

2.645 4.186 2.763 2.39 1.8

4.722 6.737 4.945 3.875 1.7

7.362 9.332 9.230 8.663 1.3

kmw,max/kmw,min

Figure 3. Plot between Ea,mw and ln(k0,mw)/R at various P values (R = 8.314 J K−1 mol−1). Figure 2. kmw/kth ratio as a function of the temperature for selected solvents (P = 0.175 kW dm−3).

is obtained, similar to the thermal case but with different parameters; the slope, weakly dependent to P, has a mean value of 0.040, which is greater than that of the thermal counterpart (0.036). A similar situation is also valid for the intercept parameter (0.8, 1.08, 1.03, and 1.13). This finding infers an important result; MW irradiation affects the kinetics but not the mechanism of the AIBN decomposition reaction, as shown in Scheme1. 3.3. New Approach for the Solvent Effect on the MWAssisted Decomposition Reaction of AIBN. In this section, a new approach for the effect of the solvent type on MWassisted reaction kinetics was suggested. We propose two new solvent properties as indicators to evaluate the effect of the solvent type on MW-assisted chemical kinetics. It was planned to use temperature-dependent property data for a more rigorous evaluation (to cancel the interference effect of temperature due to property). Dielectric properties, especially tan δ, are primarily considered in MW applications. Meanwhile, in the open literature, dielectric data are achievable only for a limited number of chemicals. In a study, the dielectric properties of 23 pure solvents having different polarity characteristics were measured between 25 and 85 °C under 5.8, 2.45, and 0.918 GHz MW irradiation.11 In this temperature range, the tan δ and ε″ values of DMF, NPA, and DMSO follow a decreasing trend with increasing temperature, similar to NBU.12,21 However, dielectric measurements become inaccurate at temperatures close to the boiling point of the solvent. By considering this point, Hansen and co-workers proposed a solvent property (S) defined according to eq 2 by means of Hansen solubility parameters (HSPs) as a good-fitting index for the MW-absorbing capacity of solvents.40

DMSO > NBU > NPA > DMF; more specifically, in the case of DMSO, this ratio reaches 1.8 (at T = 80 °C), while in the case of DMF, it is less than 1; consequently, MW irradiation has a slightly negative effect on the reaction kinetics. As seen in Table 5, the ratios k0,mw/k0,th and Ea,mw/Ea,th reflect more strongly the effect of MW on the Arrhenius parameters; Table 5. Arrhenius Parameters of Selected Solvents at Various MW Power Values P Arrhenius parameters solvent NBU

DMSO

DMF

NPA

a

ratios

P(kW dm−3)

Ea,mw (kJ mol−1)

k0,mw × 1014 (s−1)

Ea,mw/ Ea,th

k0,mw/k0,th

0 0.15 0.175 0.2 0.25 0 0.15 0.175 0.2 0.25 0 0.15 0.175 0.2 0.25 0 0.15 0.175 0.2 0.25

124.4 127.8 127.2 135.4 130.9 105.2 143 109.9 153.6 131.2 133.4 140.8 136.2 143.1 137.9 122.3 123.1 123.6 126.8 122.9

3.33 10.96 9.06 132.13 32.26 0.01 1927.17 0.04 67091 37.86 76.65 1018.73 207.6 2046 379.29 1.82 2.24 2.96 8.02 2.17

1.00 1.03 1.02 1.09 1.05 1 1.36 1.04 1.46 1.25 1 1.06 1.02 1.07 1.03 1.00 1.01 1.01 1.04 1.01

1.00 3.29 2.72 39.68 9.69 1 135716 2.85 4.72 × 106 2665.97 1.01 13.38 2.73 26.87 4.98 1.00 1.23 1.63 4.41 1.19

S = (2δ p + δ h)Vδ d

(2)

where δd is the energy from dispersion bonds between molecules, δp is the energy from a dipolar intermolecular force between molecules, and δh is the energy from hydrogen

The rows in bold indicate the “highest” values for each solvent. 13019

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bonds between molecules. V is the molar volume of the solvents (dm3 mol−1). HSPs were developed for predicting the mutual solubility of materials and were related to various intermolecular energy terms as defined above.32−34 The solvents can be classified rationally by using these solvent parameters; for example, polar molecules have higher δp, while protic solvents have higher δh.35 HSP data are usually given at a standard temperature (e.g., 25 °C).33,36,37 In this study, Beerbower relationships were used to calculate HSPs as a function of the temperature.33,34 Calculation details are given in the Supporting Information. As can be seen in Figure 4, S exhibits quasi-linear functional dependence on T for Figure 6. kmw−S plots of solvents at reaction temperatures (P = 0.175 kW dm−3).

electric field by virtue of molecular polarization processes; τ is the time required for molecular polarization to decay to 1/e of its initial value upon removal of the external electric field.38 For a pure polar liquid, the relationship between the complex permittivity (ε) and τ can be expressed by the Debye equation: ε − ε∞ ε = ε∞ + s = ε′ − jε″ 1 + jωτ (3) where ε is the complex permittivity, εs is the static permittivity in a static field, ε∞ is the permittivity at frequencies much greater than the inverse τ, and ω is the angular frequency of the electromagnetic radiation. τ depends critically on the nature of the functional groups and the volume of the molecule. For example, τ of alcohols is a function of the chain length and isomer type. As the chain length increases, τ becomes longer. However, a significant decrease in τ is noted for alcohols when the hydrocarbon chain contains a double bond or a phenyl ring. This means that a more rigid molecule and a more limited rotational process are being observed under MW irradiation; consequently, the relaxation process in the MW region corresponds to cooperative rotational movements of the molecules. Generally, τ of the polar solvents decreases monotonically with increasing temperature according to Eyring equation (4):39

Figure 4. Profiles of the S parameter and temperature (T) in selected solvents.

all solvents. Furthermore, Figure 5 depicts the linear relationship between S and tan δ for NBU as an example, which supports the idea that S may replace tan δ for investigating the solvent effect on kmw.

τ (T ) =

⎛ ΔH ⧧ ⎞ ⎛ −ΔS ⧧ ⎞ h ⎟ exp⎜ ⎟ exp⎜ kBT ⎝ RT ⎠ ⎝ R ⎠

(4)

where h and kB are the Planck and Boltzmann constants, respectively, R is the gas constant, and ΔH⧧ (kJ mol−1) and ΔS⧧ (kJ mol−1 K−1) are the molar enthalpy and molar entropy of activation of the molecular motion, respectively. ΔH⧧ and ΔS⧧ are calculated using temperature-dependent specific heat capacity values. Thus, as can be seen in Figure 7, τ of the solvents decreases with increasing temperature, with a slope depending on the solvent type. Figure 8 depicts the dependence of kmw on τ at various temperatures for P = 0.175 kW dm−3 (similar plots were obtained for other P values). As can be seen, maximum points on the plots tend to lower the τ values and become sharper with increasing temperatures. Furthermore, Figure 8 presents a very interesting and important clue; at a given reaction temperature, solvents with an optimum τ value or in a narrow (optimal) τ range and perhaps with specific molecular structure must be selected among other candidates for faster MWassisted reaction kinetics.

Figure 5. S parameter−tan δ linear profile of NBU at reaction temperatures.

Figure 6 displays the dependence of kmw on S at various temperatures (where the solvent type is quantified by the S value) under P = 0.175 kW dm−3; kmw increases monotonically with S after exhibiting a very weak minimum (which may arise from the experimental error). A similar situation is valid for other P levels. The obvious result from this evaluation is that solvents with higher S values at the reaction temperature are recommended for faster reaction kinetics. The second property proposed to investigate the solvent effect is the characteristic relaxation time (τ) or resonant frequency; solvent molecules react to an externally applied 13020

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structures that may be selected among various solvent candidates.

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ASSOCIATED CONTENT

S Supporting Information *

Conventional and MW experimental data tables of selected solvents and procedure for calculation of HSPs as a function of the temperature according to previous studies.24,33,36,37,40 This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Phone: (+) 90 262 605 21 13. Fax: (+) 90 262 605 21 00. Email: [email protected].

Figure 7. Relaxation times (τ) of polar solvents as a function of the temperature.

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the GIT research fund for partial support.

Figure 8. kmw−τ plots of solvents at given temperatures (P = 0.175 kW dm−3).

4. CONCLUSION An online experimental system was set up to investigate the kinetics of chemical reactions under MW irradiation, with precise control of constant-temperature and constant-MW energy supplies during the experiment. The decomposition of AIBN under MW irradiation in various solvents was investigated to assess the solvent effect on the reaction kinetics. In this way, it was also aimed at obtaining some clues to elucidate the nature of specific MW effects on chemical reactions. The study showed that the decomposition kinetics of AIBN followed first-order rate law under MW exposure similar to thermal heating. Furthermore, the Arrhenius parameters were found to be dependent on the MW power density as well as the solvent type; the increase of these parameters points clearly to a higher energy state but also to a more favorable structural/conformational arrangement of the active complex. Furthermore, a linear dependence is obtained between Ea,mw and ln(k0,mw)/R similar to the thermal case, indicating that MW irradiation does not affect the reaction mechanism. Dielectric properties such as tan δ are primarily considered to explain the (specific) MW effect on chemical reactions. Meanwhile, by considering the scarcity and limited achievability of the dielectric data, two new properties were proposed in this study to investigate the solvent/MW effects: a solvent property (S) defined by means of HSPs and the relaxation time (τ). Experimental results showed that solvents with high S and with an optimum τ value are beneficial for an enhanced MW effect on the chemical reaction kinetics, pointing to specific molecular

SYMBOLS Ea activation energy (kJ mol−1) k0 preexponential factor (s−1) T temperature (°C) k first-order rate constant (s−1) P MW power density (kW dm−3) XA conversion of AIBN A absorbance ε″ dielectric loss factor ε′ dielectric constant tan δ loss tangent (ε″/ε′) τ relaxation time (ps) ΔH⧧ molar enthalpy of activation of the molecular motion (kJ mol−1) ΔS⧧ molar entropy of activation of the molecular motion (kJ mol−1 K−1) μ dipole moment (D) δd energy from dispersion bonds between molecules δp energy from dipolar intermolecular force between molecules δh energy from hydrogen bonds between molecules V molar volume of solvents (dm3 mol−1)

Abbreviations

AIBN 2,2′-azobis(isobutyronitrile) TMSN tetramethylsuccinonitrile MW microwave NBU n-butanol DMSO dimethyl sulfoxide DMF dimethylformamide NPA n-propanol HSPs Hansen solubility parameters FO fluoroptic sensor IR infrared sensor Subscripts

mw MW-assisted method th thermal (conventional) method 13021

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dx.doi.org/10.1021/ie5021359 | Ind. Eng. Chem. Res. 2014, 53, 13016−13022