High Temperature Pyrolysis of Toluene under Electromagnetic Fields

Research Article pubs.acs.org/journal/ascecg

High Temperature Pyrolysis of Toluene under Electromagnetic Fields at Different Frequencies Yi-Ming Zhang,† Jia-Lin Li,*,† Jian-Peng Wang,‡ and Bing-Zhong Wang† †

School of Physical Electronics, University of Electronic Science and Technology of China, No.4, Section 2, North Jianshe Road, Chengdu 610054, China ‡ School of Optoelectronics, Nanjing University of Science and Technology (NUST), Xiaolingwei 200, Nanjing 210094, China S Supporting Information *

ABSTRACT: To investigate the influence of electromagnetic (EM) fields on toluene decomposition, ReaxFF molecular dynamics simulations have been performed. With Arrhenius analysis, it is observed that Arrhenius parameters can be influenced by EM fields, characterizing a microwave frequency selectivity. On the basis of the collision theory, it is found that the frequency selectivity is due to the perturbation of the orientation factor and collision frequency of a related reaction caused by the polarization effect of electric fields. The rotation performance of toluene dipoles has been studied under microwaves at different frequencies. The normalized amplitude of time evolution of toluene dipoles under microwave conditions is independent of microwave frequency, while the phase lag between the EM field and the time evolution increases along with the rising frequency. Compared with the condition without microwave, introducing EM fields can reduce the total population of C−C bonds and restrain carbon buildup of pyrolysis residue. Finally, a combined EM field with rotation angle of 90° was constructed. It is shown that the combined EM field introduces less influence than a conventional EM field with a rotation angle of 180°. KEYWORDS: Electromagnetic fields, Toluene decomposition, Microwave frequency selectivity, Pyrolysis, Microwave heating, Molecular dynamics

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utilization has been drawing attention in recent years.9−13 As for tar removal, investigation on microwave heating is a hot topic. Santaniello et al. employed a comprehensive mathematic model to simulate the effects of the input power and tar cracking on the pyrolysis of wood blocks for both microwaveinduced and conventional heating.14 Li et al. investigated the ability of char from biomass microwave pyrolysis at 1070 K for tar removal; they found that biomass derived char was utilized as a catalyst for toluene cracking and reforming.3 Eliott et al. reported that the microwave plasma system is capable of destroying and reforming tar efficiently and produces mainly hydrogen gas, carbon monoxide, and oxygen.15 As mentioned above, tar removal has been studied from experiments. However, theoretical investigations of the interaction between microwaves and the tar system on a molecular level have not been performed in depth. It has been demonstrated that molecular dynamics (MD) simulation provides a feasible and potentially valuable way for assessing the influence of electromagnetic (EM) fields on water,16,17 solution,18,19 and some other systems.20−22 In particular, for some reaction systems, ReaxFF MD simulations are capable of

INTRODUCTION As a green and emerging pathway of energy recovery, the utilization of biomass has attracted increasing attention in recent years. In addition to those gas products formed during utilization, for instance, hydrogen gas, carbon dioxide, and carbon monoxide, tar is also a main byproduct.1,2 However, in general, tar is considered as a threat to the process of biomass utilization since tar accumulation may lead to pipeline blockage of chemical reactors.3 Moreover, the quality of synthetic fuels could be reduced due to the mixture of some light tar.4 Thus, to keep pipeline unobstructed and guarantee the quality of fuels, suppression of tar accumulation is of significance. High temperature cracking is often adopted to remove the tar during the process of biomass utilization such as biomass gasification.5,6 The studies for tar removal under conventional heating mainly focused on the selection and development of catalysts. Lu et al. studied the bimetallic Ni−Co/cordierite catalyst for cracking of tar; they found that the performance of bimetallic catalyst is better than monometallic catalyst during biomass decomposition.7 Ammendola et al. researched the effect of sulfur on the performance of Rh−LaCoO3 based catalyst for tar conversion to syngas; they reported that at high sulfur levels reforming is inhibited, while cracking and oxidation are less influenced.8 Compared with conventional heating, using microwave heating as an alternative for biomass © XXXX American Chemical Society

Received: March 28, 2016 Revised: June 5, 2016

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DOI: 10.1021/acssuschemeng.6b00617 ACS Sustainable Chem. Eng. XXXX, XXX, XXX−XXX

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ACS Sustainable Chemistry & Engineering

the field intensity range21,45 of 0.1−2.5 V Å−1 to observe tangible effects within a limited time scale.

simultaneously modeling large system sizes for a long time while maintaining the accuracy of density functional theory (DFT).23 ReaxFF parameters have been developed for C/H/ O/N systems,24,25 and ReaxFF MD simulations show good results compared with experimental observations, such as oxidation of toluene,26 combustion of JP-10 hydrocarbon jet fuel,27 influence of external microwave on the production of benzyl during the decomposition of toluene,28 etching of diamond surface by hyperthermal atomic oxygen,29 and carbon structure formation during templated multistep carbonization.30 The accuracy of the force field has been compared with results obtained from DFTB and DFT for phenolic pyrolysis.31,32 Here, it was introduced into this work to investigate the decomposition process of tar, under microwave irradiation. The typical composition of the biomass tar consists of toluene, naphthalene, benzene, phenol, and other ring aromatic hydrocarbons.33 However, this composition depends on the type of fuel and the treatment of biomass.33,34 Thus, there are several model compounds of biomass tar for different experimental or theoretical situations, for instance, naphthalene,35−38 benzene,35,38,39 and toluene.33,35−37,39,40 As one of the normally used biomass tar model compounds, toluene, a good representative for biomass tar, was selected in this work. The studies described above have investigated many phenomena of tar removal under microwave heating. However, most of them are related with catalysis, leading to many questions. Without catalysis, do the microwaves at different frequencies have identical heating abilities? Except for thermal effects, do external EM fields promote or reduce reaction rates during toluene pyrolysis? If some reaction rates are definitely influenced by microwaves, does the influence of microwaves on the process of toluene pyrolysis relate to microwave frequency? If this is the case, how is this influence weakened when using microwave as a heating source? In this work, we would like to address these questions.

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RESULTS AND DISCUSSIONS Decomposition of Toluene under Conventional Conditions. Decomposition Simulation. A decomposition simulation of toluene at conventional conditions (i.e., without EM fields, denoted as C-condition) was performed to get an overview of the pyrolysis process by using a heating rate of 30 K ps−1 (Supporting Information section 2 Figure S1). It is found that the degradation of toluene initiates at nearly 2900 K. Several theoretical and experimental data have given evidence for the initial primary product channel being eq 2, leading to benzyl radicals and H atoms.46−48 C6H5CH3 = C6H5CH 2 ·+H·

The main intermediate product at the initial stage of decomposition is benzyl, while hydrogen gas is dominant in main products during the subsequent stage. This is in accordance with those theoretical and experimental results.46−50 As for methane, the high-temperature condition used in this ReaxFF MD simulation restrains the formation of methane, which is consistent with experimental observations.51 Table 1 shows the rate constants for the selected hydrogen atom and toluene molecule related reactions at the initial stage Table 1. Rate Constants for the Selected H Atom and Toluene Molecule Related Reactions at Initial Stage of Toluene Decayeda no. 1 2 3 4

DETAILS OF THE SIMULATION APPROACH

5

Molecular Dynamics Simulations. ReaxFF MD simulations were performed on pure toluene systems under different temperatures and EM fields. These simulations were run in the canonical ensemble using the Berendsen thermostat41 and set at a time step of 0.1 fs. The pure toluene system consisted of 50 toluene molecules with the initial density of 0.7 g cm−3. Before performing high temperature decomposition simulations, the system was minimized using room temperature (298 K) NPT-MD simulations. Then, the system got a density of 0.91 g cm−3 with box dimensions of Lx = Ly = Lz = 20.35 Å. This is in good agreement with the experimental value42 of 0.87 g cm−3. Incorporation of EM Fields. A conventional EM field consists of an electric field (E-field) and a magnetic field (B-field). Based on Maxwell’s equations43 and electromagnetic properties of toluene,44 an EM field introduced into ReaxFF simulation of pyrolysis of toluene can be simplified as E ⃗ ≈ xE ⃗ 0 cos(ωt ),

B⃗ ≈ 0

(2)

6 7 8 a

reactions C6H5CH3 + H· = C6H5CH2· + H2 C6H5CH3 + H· = C6H4CH3· + H2 C6H5CH3 + H· = C6H6 + CH3· C6H5CH3 + CH3· = C6H5CH2· + CH4 C6H5CH3 + CH3· = C6H4CH3· + CH4 C6H5CH2· + H· = C7H6· + H2 C6H5CH2· + H· = C6H5· + CH3· C7H6· + H· = C7H5· + H2

A0

n

6.47 × 10

00

3.98

Ea (kcal mol−1)

source

3.39

ref 52

2.51 × 1014

0

1.56 × 1013

0

5.80

ref 53

4.37 × 10−04

5.0

8.3

ref 54

4.37 × 10−04

5.0

12.3

ref 49

5.00 × 1013

0

0

ref 48

4.50 × 1058

−11.9

51.8

ref 55

1.90 × 1008

1.85

16

4.97

ref 49

ref 56

k = A0Tn exp(−Ea/RT).

of toluene decay. The hydrogen atom is observed as an intermediate in the decomposition process. Quickly, it proceeds in the secondary reaction to form hydrogen gas, i.e. the primary product, due to low activation energies and high preexponential factor values. Thus, in addition to toluene, hydrogen gas is also used as a guide in studying the kinetics of toluene decomposition in EM fields. And the formation progress of hydrogen gas can be treated as a zero-order reaction. Arrhenius Analysis. To analyze the kinetics and the details of the decomposition process, a series of NVT-MD simulations were performed at temperatures of 2900, 3100, 3300, 3500, 3700, and 4100 K. To model the decomposition process of toluene, a single rate expression was considered and constructed. The n-order power-law expression of decomposition of toluene can be expressed as

(1)

Details for the derivation of eq 1 are provided in Supporting Information section 1. Equation 1 indicates that the effect of B-field can be ignored, while the instantaneous E-field can be spatially uniform during the simulations of decomposition of toluene. In this work, electric fields of frequency f = 50−200 GHz and of amplitude E0 = 2 V Å−1 were considered. Although the field intensity applied in this study is several orders of experimental and industrial conditions, previous researches of MD simulations with external EM fields on water and other materials have shown it is necessary to use B


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−

dC toluene n = kC toluene dt

The rate constant (k) as a function of inverse temperature using eq 7 is shown in the Arrhenius plot in Supporting Information section 2 Figure S5.

(3)

where Ctoluene is the concentration of toluene, t is time, k is the decay rate constant of toluene, and n refers to the order. The concentration Ctoluene is defined as

C toluene

N = toluene NAV

ln k = ln A 0 −

(4)

⎛ Ea ⎞ 1000 ⎜ ⎟ ⎝ 1000R ⎠ T

(7)

The calculated activation energy of hydrogen formation is 69.17 kcal mol−1, and the pre-exponential factor is 3.02 × 1015 mol L−1 s−1. For eq 2, Szwarc et al.58 gave an activation energy of 77.26 kcal mol−1, while Mizerka et al.54 provided an activation energy of 72.20 kcal mol−1. Observing those data listed in Table 1, it is seen that the Arrhenius parameters obtained from the ReaxFF MD simulations correlate well with the experimental results.54,58 Thermal Cracking of Toluene under the Microwave Environment. Heating Ability of Microwaves. To study the heating ability of microwaves, EM fields with frequencies of 50, 100, 150, and 200 GHz were applied to the toluene simulation system, respectively. Considering that toluene decays at nearly 2900 K in the ReaxFF MD simulation, the temperature was set to 2500 K to study the rotation property of toluene dipole moment in EM field before carrying out decomposition simulation. Figure 1 provides the time evolution of the normalized xcomponent (Dx/Da) of average toluene dipole moment (Da) in

where Ntoluene is the number of toluene molecules, NA is the Avogadro constant, and V is the volume of the simulation box. It is found that the fitting curves (Supporting Information section 2 Figure S2) of the decomposition of toluene as a function of simulation time obtained from NVT ReaxFF MD simulations can be expressed as Ntoluene(t , T ) = 50exp( −k Tt )

(6)

B = kt

(5)

where T is temperature and kT is a temperature-related constant. It is observed that eq 5 would well satisfy eq 3 with n = 1, and kT refers to k. This reveals that the pyrolysis process of toluene can be approximated as a first-order expression. It should be noted here that the first-order expression for toluene decomposition is an empirical fitting work and does not reflect the actual reaction mechanism which is much more complicated. The rate constant of toluene pyrolysis as a function of inverse temperature by using the first-order expression shows a welldefined correlation with the fitting line (Supporting Information section 2 Figure S3). The calculated pre-exponential factor (A0) and activation energy (Ea) of the present work against experimental data are presented in Table 2. From experimental Table 2. Arrhenius Parameters of Toluene Decay Process conditions

Ea (kcal mol−1)

ReaxFF 1011−1122 K 1130−1167 K 1200−1900 K

65.39 73.70 69.20 79.55

A0 (s−1)

source

× × × ×

present work ref 57 ref 57 ref 51

1.25 2.51 3.16 8.67

1015 1012 1011 1014

results, Takahasi57 previously reported an activation energy range of 69.20−104.9 kcal mol−1 by using flow technique under various conditions, while Sivaramakrishnan et al.51 reported a combined activation energy of 79.55 kcal mol−1 by using a single pulse shock tube at high pressures. Given the uncertainties in the experiments, which has been indicated by Takahasi57 that the rate constant at lower temperatures might involve relatively large error, these Arrhenius parameters extract from the ReaxFF MD simulations are in good agreement with experimental results. The formation of hydrogen gas against simulation time obtained from the ReaxFF MD simulations at several temperatures are shown in Supporting Information section 2 Figure S4. These data were used to obtain rate constants of hydrogen gas formation using zero-order kinetics shown in eq 6, where B denotes the concentration of hydrogen gas. For those temperatures that form a low concentration of hydrogen molecules, the data from the entire simulation (0−200 ps) were used. For each of other temperatures, the data used to obtain the rate was obtained from 0 ps until the time when 30 hydrogen molecules were formed. The formation rate as a function of the number of hydrogen molecules was obtained from a linear fit of data adopted above at several temperatures.

Figure 1. Time evolution of the normalized x-component (red dot lines) of average toluene dipole moment in (a) C-condition, and in 2 V Å−1 E-fields of (b) 50, (c) 100, (d) 150, and (e) 200 GHz at 2500 K. Black solid lines are the amplitude of the external E-field.

the C-condition and in 2 V Å−1 E-fields with different frequencies at 2500 K. In the C-condition, the normalized xcomponent (Dx/Da) is almost zero, which means the toluene dipoles have random orientations without EM fields. This is in agreement with actual situation. When introducing external Efields, the toluene dipoles align along the direction of the timeC


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ACS Sustainable Chemistry & Engineering alternating E-fields with tangible phase lag, as shown in Figure 1b−e. Table 3 shows the normalized amplitude of time

heating ability of microwaves at a very high frequency on a toluene system would reach the ceiling. Arrhenius Analysis. In order to investigate the influence of EM fields at different frequencies on the decomposition process of toluene, ReaxFF MD simulations under different temperatures were performed. It has been studied by Blanco et al.21 that when performing microwave MD simulations using a Nose−Hoover thermostat, the temperature of system may fluctuate at high EM field strength. In present work, it is observed that the temperature is well controlled at each presetting value almost without fluctuation by using the Berendsen thermostat, as expected (Supporting Information section 2 Figure S6). The Arrhenius analysis fits for decomposition of toluene and formation of hydrogen gas in several EM field conditions exhibit well-defined correlations with the data (Supporting Information section 2 Figures S7 and S8). Comparisons of calculated activation energy and pre-exponential factor of toluene decay at different microwave frequencies are shown in Figure 2a and b, respectively. Compared with those parameters from the C-condition simulations, the values of these Arrhenius parameters obtained from EM conditions are apparently higher. This means the introduced EM fields affected the rate constant of toluene decay. Compared with the rate obtained at Ccondition, these impacts promote the rate constant at the high temperatures, while reduce the rate constant at the low temperatures, with a demarcation of nearly 3500 K. Meanwhile, the Arrhenius parameters are closely related to the microwave frequency, exhibiting frequency selectivity and maximized at approximately 100 GHz. Moreover, the activation energy and pre-exponential factor of formation of hydrogen as a function of microwave frequency can draw similar conclusions, as shown in Figure 2c and d. A comparison of the ratio of carbon atoms to hydrogen atoms in the heaviest carbonaceous cluster (more than 2000 amu or at least 50 carbon atoms) at several conditions with different temperatures is recorded in Figure 3. The ratio obtained under C-condition is always higher than that obtained under EM field condition, except a few situations at

Table 3. Normalized Amplitude of Time Evolution of the xComponent (Dx/Da) of Toluene Dipoles and the Phase Lag between the EM Field and the Rotation of Toluene Dipoles frequency

50 GHz

100 GHz

150 GHz

200 GHz

phase lag (angle) normalized amplitude

5° 0.25

18° 0.25

32.4° 0.25

43.2° 0.25

evolution of the x-component (Dx/Da) and the phase lag between the EM fields and the rotation of toluene dipoles. The higher the frequency of EM fields is, the larger the phase lag would be. The normalized amplitudes under four different Efield conditions are identical. It is known that materials can be heated by microwaves due to the friction triggered by the rotations of electric dipoles in the E-field, which was also analyzed in MD simulations by Tanaka et al.18 This implies that toluene system in this work can be theoretically heated in 2 V Å−1 EM fields at a frequency range of 50−200 GHz. On the basis of the Debye-like dipole relaxation,19,59 τd ≅ ζ/2kBT, the microwave energy absorbed by the toluene dipole at the position i per unit time can be expressed as18 dWE ∝ ζ(2πfpE )2 i 0 dt

(8)

where τd is related to the lag time; ζ is the intrinsic friction from adjacent toluene molecules, and pi is the magnitude of the monomer dipole moment at the site i. It is concluded that lower frequency brings smaller intrinsic friction, at least for the frequency range of 50−200 GHz, finally leading to less energy absorbed from EM fields within a same irradiation time. Notice that the higher phase lag between the rotation of dipole moment and external E-fields would lead to less control of microwave to the rotation performance of the dipole.60 Since the phase lag rises along with the increasing of EM field frequency shown in Table 3, it should be reasonable that the

Figure 2. Comparisons of calculated activation energy and pre-exponential factor of toluene decayed and hydrogen formation at various microwave frequencies. D


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temperatures. Likewise, the numbers of C−C bonds and C−H bonds obtained under the four EM field conditions presents a similar stepwise trend at the time of 100 ps and a smooth trend in the final configuration. Thus, it is reasonable to conclude that the external EM field does not change the main pathways of toluene decomposition and may just influence the reaction rates of the main pathways. However, the numbers of C−C bonds observed under EM field conditions at different frequencies are almost lower than that under C-condition at the corresponding temperatures, while the numbers of C−H bonds exhibit an opposite phenomenon. Combining with the results shown in Figure 3, it is found that the external EM field restrains both the formation of the carbon clusters and the breakage of C−H bonds; this may reduce the rate of hydrogen gas formation. As described in Figure S8 in the Supporting Information, at the temperature below 3500 K, the formation rate of hydrogen obtained under EM field does decline compared with that observed under C-condition, but the rate obtained at high temperature is opposite. A possible reason is that although the external EM field inhibits the cleavage of C−H bonds, it will also restrains the other transformation pathways of hydrogen atom except the way of hydrogen gas formation, at least at the high temperature, for instance, above 3500 K. Analysis Based on Collision Theory. In addition to eq 2, those selected reactions shown in Table 1 make indispensable contributions to the rate of toluene pyrolysis and hydrogen gas formation.48 This indicates that the decay process of toluene can be partially treated as collisions between toluene molecule and hydrogen atom or benzyl radical. The formation of hydrogen gas can be simplified to collisions between hydrogenous fragments, particularly between hydrogen atoms and hydrogenous fragments. Here, the collision theory is introduced to investigate the influence of EM field on the rate of toluene decay and the form of hydrogen gas. According to the classical collision theory, for a bimolecular reaction, the natural logarithmic form of the reaction rate (v) is described as

Figure 3. Comparison of the ratio of carbon atoms to hydrogen atoms in the heaviest cluster at several conditions with various temperatures.

temperature of 4100 K. Moreover, Figure 3 reveals that the influence of the EM field at a frequency of 100 GHz on the ratio is much more obvious than the other three EM field conditions, for the entire temperature range of 2900−4100 K, especially at high temperatures. This is analogous to the frequency selected influence of Arrhenius parameters shown in Figure 2. The result suggests that the external microwave plays a restrained role on carbon buildup of pyrolysis residue. A population analysis of C−C bonds and C−H bonds observed in the middle of decomposition process (100 ps) and the final configuration (200 ps) at several conditions with different temperatures is shown in Figure 4. During the pyrolysis process, C−H bonds are breaking to form hydrogen atoms and C−C bonds are forming to constitute carbon clusters. Under the C-condition at the time of 100 ps, the number of C−C bonds has a stepwise rise, while the number of C−H bonds has a stepwise decline as temperature increases. The abrupt slope of the stepwise rise/decline appears at the temperature ranges of 3100−3300 and 3500−3700 K. With the continued pyrolysis, numbers of C−C bonds and C−H bonds tend to be smooth at the time of 200 ps as shown in Figure 4b. This may be attributed to those reactions occurring at different

Figure 4. Population of C−C bonds and C−H bonds observed in (a) the middle of decomposition process (100 ps) and (b) the final configuration (200 ps) at several conditions with various temperatures. E


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ACS Sustainable Chemistry & Engineering ln v = ln(Z0DA DBP) − Z0 = πdAB 2NA 2

Ec RT

8RT πμ

along with the conventional time-varying E-field. The instantaneous direction of the dipole (Dt) would have a rotation angle of 180° following the orientation of the E-field (Ei), as shown in Figure 5a. On the basis of above

(9)

(10)

where DA and DB are concentrations of reactants A and B, respectively; Z0 is collision frequency which increases with the rise of temperature; P is collision orientation factor which has obvious effects on activation energy Ec that declining of collision orientation factor means rising of activation energy; πdAB2 is collision cross-section, and μ is reduced molar mass. While, based on the Arrhenius function, the natural logarithmic form of reaction rate can be described as ln v = ln(kDA DB) = ln(A 0e−Ea / RT DA DB) E = ln(A 0DA DB) − a RT

Figure 5. Rotation properties of toluene dipole moment with (a) conventional EM field and (b) combined EM field. (11)

investigations, it is expected that the size of the rotation angle should be significant for the influence of EM field on the orientation factor P, on the reaction rates, and a smaller angle should result in a less reactivity of the EM field on the rates. In order to verify this, an E-field with the rotation angle less than 180° needs to be constructed. In present work, the rotation angle of 90° is considered, and a combined expression of the external E-field is given as

Thus, the pre-exponential factor A0 can be denoted as Z0P, and Ec denotes Ea. As studied in ref 60, during the pyrolysis of epoxy resin, introducing the microwave would affect the orientation performance of hydrogenous polar fragments, leading to decline the collision orientation factor on the process of forming hydrogen gas based on collision models. Consequently, based on the collision models in ref 60, it can be concluded that external EM field reduces the collision orientation factor of toluene decayed and hydrogen gas formed, resulting in a decline of the pre-exponential factor, and also leading to the promotion of relevant activation energy as shown in Figure 2a and c. As for the pre-exponential factor, it is mainly constrained by the collision frequency and collision orientation. Research61 on the influence of microwave heating on the hydrothermal treatment indicated that external microwave could increase the collision cross-section between polar fragments, due to the interactive collision caused by the rotation of dipoles under microwave irradiation. Thus, it is rational to conclude that the collision frequency related with toluene decay and hydrogen gas formation under EM field condition could increase along with the increase in the collision cross-section, compared with C-condition. The influence of the external EM field on the preexponential factor has two aspects: (a) the promotion of collision cross-section leads to the rising of the pre-exponential factor and (b) the decline of the collision orientation factor results in the reducing of the pre-exponential factor. The power of the former should be larger than that of the later, since the pre-exponential factor obtained under EM field condition is always higher than that obtained under C-condition shown in Figure 2b and d. As mentioned above, the higher phase lag between the rotation of dipole moment and external E-field would result in less control of microwave to the rotation performance of the dipole.60 It is logical to deduce that the influence of EM field on pyrolysis of toluene would have an upper limit at a certain frequency, at this case of 100 GHz. When the frequency exceeds the threshold, the strength of the effect of EM field on the reaction rates by controlling the rotation of those reactant dipoles would wane, resulting in the effect of EM field on Arrhenius parameters to be a frequency selected reaction, as shown in Figure 2. Thermal Cracking of Toluene in a Combined EM Field Condition. Dipoles, such as toluene molecules, would rotate

E ⃗ ≈ e1⃗ E1 cos(ωt ) + e 2⃗ |E1 cos(ωt )|

(12)

where directions e1⃗ and e2⃗ are orthogonal, E1 is set as E0/√2 (E0 = 2 V Å−1) to ensure the uniformity of the amplitudes of the combined EM field and conventional EM field. The rotation character of dipoles, taking toluene molecule as example, along with the E-field is shown in Figure 5b. Theoretically, the implementation of the waveform expressed in eq 12 is not difficult. The first item of eq 12 is the traditional trigonometric function waveform. For the second item, it can be factorized into Fourier series as ∞ ⎡2 2( − 1)n cos(2nωt ) ⎤ ⎥ e 2⃗ |E1 cos(ωt )| = e 2⃗ E1⎢ + 2 ∑ ⎢⎣ π (1 − 4n2)π ⎥⎦ n=1

(13)

where cos(2nωt) is the nth harmonic component. A limited order of the series n can lead to a satisfactory performance of the waveform given in eq 12, setting to 3 or more is suitable for this case. Meanwhile, the waveform described by eq 12 can be realized by the superposition of several EM fields. A ReaxFF MD simulation of toluene system under the external orthogonal EM field expressed as eq 12 at a frequency of 100 GHz was performed at 2500 K. Here, the directions e1⃗ and e2⃗ were x⃗ and y,⃗ respectively. Figure 6 shows the rotation performance of toluene dipoles. The direction of toluene dipole moments rotate between the directions of (y⃗ − x⃗) and (y⃗ + x⃗) as expected. The curve of the combined component of toluene dipole moments has a normalized amplitude of 0.25 and shows a phase lag of 18° compared with the E-field. This is identical with those obtained under the conventional EM field at 100 GHz, as presented in Table 3. The rotation character of toluene dipoles indicates that the toluene system can be heated by the combined EM field, although the heating efficiency may be a bit poorer than that obtained under the conventional EM field at the same frequency, due to the less friction because of the smaller rotation angle. F



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CONCLUSION

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ASSOCIATED CONTENT

ReaxFF MD simulations have been performed for the decomposition of toluene, a model compound of tar, under microwave conditions. The simulation results obtained from conventional condition without introducing microwave are well consistent with experimental and theoretical results. This suggests that ReaxFF offers useful and reasonable insights into the high-temperature pyrolysis of toluene. Then, the heating ability of microwave on toluene system has been investigated. The toluene system can be heated by microwave range of 50 to 200 GHz, where lower frequency brings smaller intrinsic friction, finally leading to less energy absorbed from EM fields. It is also found that the external EM field plays a restrained position on carbon buildup of pyrolysis residue and does not change the main pathways of toluene pyrolysis. But, some reaction rates are influenced by the EM field. By using Arrhenius analysis, it is seen that both the activation energy and pre-exponential factor of toluene decay obtained at EM field conditions with the selected frequency range are always higher than those obtained at the conventional condition. Moreover, the influence strength of EM field on the Arrhenius parameters is microwave frequency selective. The effect on the formation rate of hydrogen is similar. And based on the collision theory, it is clear that the EM field reduces the orientation factor of the toluene decay and hydrogen formation, leading to the promotion of activation energy. Compared with the conventional condition, the pre-exponential factor under EM field condition is influenced mainly through the two pathways: (a) increasing with the rising of the collision frequency due to the rising in the collision cross-section; (b) reducing with the decreasing of the orientation factor caused by the external EM field. Meanwhile, it is found the power of the former is larger than that of the later. For the frequency selectivity, it may be caused by the phenomenon that higher phase lag between the rotation of dipole moment and external E-field would result in less control of external EM field to the rotation performance of dipoles. Finally, in order to investigate the effect of the rotation angle of dipole moments under EM field on simulation system, a combined EM field with rotation angle of 90° has been constructed and several MD simulations have been performed. The results show that the combined EM field introduces less influence than conventional EM field with rotation angle of 180°. This provides a potential way to avoid nonthermal effects during the application of microwave heating.

Figure 6. Time evolution of the normalized (y + x) and (y − x) components of average toluene dipole moments in the combined 100 GHz E-field at 2500 K. The black solid line is the amplitude of the external E-field.

To investigate the effect of the combined EM field on the decomposition of toluene, several ReaxFF MD simulations were carried out. The calculated activation energy for decomposition of toluene is 66.19 kcal mol−1, and the preexponential factor is 1.42 × 1015 s−1 (Supporting Information section 2 Figure S9). For the formation of hydrogen gas, they are 76.10 kcal mol−1 and 8.23 × 1015 mol L−1 s−1 (Supporting Information section 2 Figure S10). The values of Arrhenius parameters obtained under the combined EM field are in between those of C-condition and the conventional EM field (where the frequency is 100 GHz). That is, the influence of the combined EM field on the Arrhenius parameters is similarly with the one under the conventional EM field. Likewise, the influences of the combined EM field on population of C−C bonds and C−H bonds observed in both the middle of toluene decomposition (100 ps) and the final configuration (200 ps) are lower than those of the conventional EM field, as shown in Figure 7. Therefore, referring to the C-condition, the influence strength of the combined EM field on toluene decayed is weaker than that of the conventional EM field, as supposed above.

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acssuschemeng.6b00617. Details of incorporation of EM field into molecular dynamics simulation; time evolution of compounds obtained during decomposition of toluene; Arrhenius analysis of toluene pyrolysis and hydrogen formation at C-condition and EM-condition; temperature profiles resulting from the ReaxFF MD simulations with Berendsen thermostat at EM-condition (PDF)

Figure 7. Population of C−C bonds and C−H bonds observed in (a) the middle of decomposition process (100 ps) and (b) the final configuration (200 ps) at several conditions with various temperatures. G


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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported in part by the Natural Science Foundation of China (NSFC) (No. 61271025) and the Program for New Century Excellent Talents in University (NCET-12-0094).

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High Temperature Pyrolysis of Toluene under Electromagnetic Fields

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