Decomposition of Methane and Carbon Dioxide in a Radio-Frequency

the unstable electronic state. Mechanisms of dissociation of methane and carbon dioxide by electron impact were proposed and the conversions of each g...
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Ind. Eng. Chem. Res. 1999, 38, 2540-2547

Decomposition of Methane and Carbon Dioxide in a Radio-Frequency Discharge Sergey Y. Savinov,† Hwaung Lee,‡ Hyung Keun Song,§ and Byung-Ki Na* Clean Technology Research Center, Korea Institute of Science and Technology, P.O. Box 131, Cheongryang, Seoul 136-791, Korea

An experimental study of the decomposition of methane and carbon dioxide using capacitive RF discharge was investigated over a moderate range of pressures (5-60 Torr). The decomposition of methane and carbon dioxide molecules is caused by direct electron collision via excitation of the unstable electronic state. Mechanisms of dissociation of methane and carbon dioxide by electron impact were proposed and the conversions of each gas were derived from the proposed mechanisms. As a result, the conversion of each gas only depended on the specific energy of the molecules. The energy costs for the decomposition of methane and carbon dioxide could be determined through the experimental data. The major gaseous products of the decomposition of methane were hydrogen and C2 and/or C3 compounds. In the case of methane, some different reaction mechanisms were observed on the range of input power, and a small amount of film deposition inside the reactor by polymerization was observed at high input power. Carbon monoxide was mainly produced from the decomposition of carbon dioxide. Introduction Many applications using low-temperature plasma are found in natural and laboratory studies as well in technology. An important area of plasma technology in the last few decades is plasma chemistry.1-3 Historically, the plasmachemical technologies started as thermodynamic equilibrium processes using plasma jets for heating. Later, it was recognized that the nonequilibrium plasma has more benefits for a set of technologies. Now, the main attention of researchers is focused on nonequilibrium “cold” molecular plasma. The principal peculiarity of this plasma is its low gas temperature in comparison with the vibration temperature of molecules and the temperature of electrons. Low gas temperature decreases the rates of reverse reactions and conserves the obtained products. At the present time, dc glow, high-frequency, and microwave discharges are widely used for plasmachemical processes. The present study is devoted to the investigation of methane and carbon dioxide decomposition in plasma of a radio-frequency (RF) capacitive discharge. Natural gas, of which about 90% is methane, is a relatively inexpensive and abundant energy resource. It is possible to convert methane to C2 or higher hydrocarbons in plasma of electric discharges. Similar processes have been extensively studied as a possible way to methane conversion for industry in the future.2,4-6 The same situation takes place for CO2 decomposition. The main product of this process is carbon monoxide. * To whom correspondence should be addressed. E-mail: [email protected]. Telephone: +82-2-958-5242. Fax: +82-2-958-5209. † On leave from the Low Temperature Plasma Optics Department, P. N. Lebedev Physical Institute, Russian Academy of Sciences, Leninsky prosp., 53, 117924 Moscow, Russia. Telephone: +7-095-135-8231. Fax: +7-095-938-2251. E-mail: [email protected]. ‡ Telephone: +82-2-958-5246. Fax: +82-2-958-5209. E-mail: [email protected]. § Telephone: +82-2-958-5241. Fax: +82-2-958-5209. E-mail: [email protected].

This gas can be used for metallurgy and chemical industry.1 The purpose of this study is the investigation of gas-phase plasmachemical processes. It is important that for capacitive discharge, it is possible to remove electrodes from the discharge zone. That is, the plasmachemical process can be studied without the influence of metal electrodes in the plasma. It has been experimentally established that capacitive RF discharges are possible in two greatly different forms. The visual difference lies in the glow distribution along the gap, but the essential difference is in the processes at the electrodes.7-10 One of these was called the R form, and the second one was the γ form. It was shown that R and γ discharges differ from the current density by more than an order of magnitude and that the electrode layers of the γ discharge possess high conductivity. For this reason, γ discharge was referred to as the high current mode, and the R discharge was referred to as the weak current mode.10 Under changes in the discharge conditions, one of these forms can transform to the other form, and furthermore, these two forms can coexist together. These situations make the analysis of the plasmachemical processes in the discharge zone very complicated. That is why we used a special type of capacitive discharge. The main peculiarity of this discharge is the small size of electrode sheaths. Practically all the volume of the plasmachemical reactor was filled with the plasma of the positive column. This kind of discharge system was used for designing the RF CO2 laser,10 but for plasmachemical purposes, as far as we know, discharge of this type was used for the first time.

Experimental Section 1. Equipment. A flowing plasmachemical reactor was used in this study. Pure gas (or mixture) went through discharge tube, and after cooling down to room temperature, the product gases were analyzed by mass

10.1021/ie980492c CCC: $18.00 © 1999 American Chemical Society Published on Web 03/09/1999

Ind. Eng. Chem. Res., Vol. 38, No. 7, 1999 2541

Figure 1. Schematic drawing of the experimental setup.

Figure 3. Outline of the oil-cooled plasmachemical reactor.

Figure 2. Cross section of a discharge in the plasmachemical reactor.

spectrometer. The input power dependence of CH4 and CO2 conversion was investigated, and the stable product composition was specified. The schematic drawing of the experimental setup is shown in Figure 1. 1.1. Radio-Frequency Plasmachemical Reactor. Yatsenko10 proposed the design of the RF discharge system for producing CO2 lasers. In the same way, capacitive RF discharge was used for plasmachemical purposes. The plasmachemical reactor consists of long Pyrex (or quartz) tube. Four copper wires were located on the outside of the tube and were used as electrodes. The diameter of this wire was d/10, where d is the inner diameter of the tube (Figure 2). Any two of these were connected with a power supply, and the other two were connected to earth. The main peculiarity of this discharge system is the small size of the electrode sheathes; as a result, all the volume of the discharge tube is filled by positive column plasma except for the small ring cylinder near the wall of the tube.10 In a glow discharge, the R and γ forms coexist together in such a discharge system under moderate input power, because the small size of the electrode sheathes makes it possible to neglect the sheath influence on the plasmachemical processes. In other words, this discharge system provides a way for investigating positive column plasma processes. Two kinds of plasmachemical reactors were used in this study. One of them was a Pyrex discharge tube. The total tube length was about 70 cm, the inner diameter was equal to 1 cm, and the wall thickness was 0.1 cm. The lengths of the copper wires were 50 cm (this is the discharge zone length). Air flow from the ventilator was used for tube cooling. The second one was a quartz discharge tube with a total length of 50 cm, an inner diameter of 0.5 cm, and a wall thickness of 0.1 cm. The lengths of copper wires were 25 cm. This tube was positioned inside of the oil-filled glass tube. Cooling water cooled the outside wall of this glass tube. This reactor is represented schematically in Figure 3. The

Figure 4. Four sections of the plasmachemical system.

first reactor was used under gas pressures up to 30 Torr, and the second one was used under gas pressures up to 60 Torr. 1.2. Power Supply. The radio-frequency (ν ) 13.56 MHz) generator, Auto Electric Co. Model ST-350, with a Matching Network, Auto Electric Co. Model LC-1000, delivered on output power from 0 to 300 W. The magnitude of the reflected power did not exceed 5% from the delivered one. The maximum of the unique input power for the first reactor was about 7.2 W/cm3 and for second one was about 58 W/cm3. When measuring the discharge input power, the energy loss through radiation was ignored and furthermore suggested that all input power was absorbed by the positive column of plasma. 1.3. Gas Flow Control. The flow rates of the feed gases (methane and carbon dioxide) were regulated by Bronkhorst High-Tech Type-5534-FA mass flow controllers. The mass flow rate of each gas can be varied between 0 and 100 cm3/min under normal conditions. A silicon oil manometer was used for the gas pressure measurements in the reactor. The pressure scale can be read to an accuracy of (0.05 Torr. An Edwards Model E2.8 vacuum pump was used for gas pumping. CH4 and CO2 with 99.9% purity were used. 1.4. Analysis. A quadrapole mass spectrometer (Balzers Co. QMS 200) with Quadstar 421 software was used for the qualitative and quantitative analysis of the gas mixtures. The mass spectrometer was connected after the postdischarge zone. The temperature of the gas mixture in this section was maintained at room temperature. 2. Measurements in the Flow Systems. Plasmachemical reactions were investigated in a flow system. All systems can be divided into four sections (Figure 4). Section 0 is a flow control part. It is obvious that, for

2542 Ind. Eng. Chem. Res., Vol. 38, No. 7, 1999

this section, the flow of molecules of component i, F ˆ (0) i , is

P0 (0) V ˆ κT0 i

(0) (0) F ˆ (0) ˆi ) i ) ni V

(1)

where n(0) i is the density of molecules of component i in section 0 under pressure P0 ) 760 Torr and temperature T0 ) 300 K, V ˆ (0) is the flow rate of each component i stream through the mass flow controller, and κ is Boltzmann’s constant. Hence, the total flow of molecules is

F ˆ (0) )

∑i

F ˆ (0) i )

P0

∑i

κT0

V ˆ (0) i )

P0

V ˆ (0) κT0

(2)

ˆ (0) where V ˆ (0) ) ∑iV i is the total flow rate of gas mixture, under P0 ) 760 Torr and T0 ) 300 K. Section 1 is the initial part of the plasmachemical reactor, that is, the predischarge zone. P1 is the gas pressure and T1 ) T0 is the temperature in this section. Because the flow passing through each mass flow controller was mixed before entering this section, the flow stream after this section becomes single. Therefore, the flow rate of this section is described as the total flow rate, V ˆ (1). It is obvious that, by virtue of conservation of molecular flow, the next three relations are true for this section:

F ˆ (1) i

)

n(1) ˆ (1) i V

)

P0 (0) n(1) V ˆ i P1

n(1) i ) F ˆ (1) )

P1 V ˆ (0) i κT0 V ˆ (0) P0 (0) V κT0

P0 (0) ) V ˆ κT0 i

(3)

(4)

L vj c

(6)

〈V ˆ (R)〉 S

(7)

(8)

where

V ˆ (R) )

P0 TR (0) TR (0) V ˆ ) 2.53 V ˆ T0 P1 P1

is the gas flow rate in the discharge zone if there are no chemical reactions and δR gives an account of the flow-rate change because of chemical reactions (expression for δR will be obtained below). From eqs 6-8, the residence time is

LS P1 τ ) 0.395 δRV ˆ (0) TR

(9)

Section 3 is the postplasma zone of the reactor. The composition of the gas mixture becomes stable in this section, and the temperature is T3 ) T0. As noted above, the gas pressure in this section is P3 ) PR ) P1. n(3) i is the remainder of the molecular density of component i, and V ˆ (3) is the whole flow rate of the gas mixture in section 3. Then the molecular flow of component i in this reaction zone can be written as (1) (1) ˆ - n(3) ˆ (3) ) F ˆ (R) i ) ni V i V

(

)

(

)

V ˆ (3) ˆ (1) (1) (1) (3) V V ˆ 1 γ ) n V ˆ - γi (10) n(1) i i (1) i V ˆ V ˆ (3) (1) where γi ) n(3) i /ni . The conversion of component i molecules, Zi, is defined as

Zi )

where L is the discharge section length and vj c is the mean convective velocity of gas flow. It is obvious that

vj c )

〈V ˆ (R)〉 ) δRV ˆ (R)

(5)

where n(1) i is the density of the molecules of component i, F ˆ (1) is the molecular flow of component i, and F ˆ (1) is i the total molecular flow for section 1. Section R is the discharge part of the plasmachemical reactor. Chemical reactions take place in this section, and the number of molecules is changed. PR is the pressure and TR is the temperature in this section. The velocities of the gas flows under the conditions in this investigation did not exceed several meters per second; that is, these velocities were much less than the velocity of sound. This means that the pressure in all sections of the plasmachemical reactor is constant; that is, PR ) P1. TR depends on the input power and thermal conductivity of the plasma. The residence time of molecules in the discharge zone is important for the plasmachemical reactor:

τ)

where 〈V ˆ (R)〉 is the mean gas flow rate and S is the crosssectional area of the discharge tube. The mean gas flow rate is

F ˆ (R) i F ˆ (1) i

)

F ˆ (1) ˆ (3) i - F i F ˆ (1) i

V ˆ (3) ) 1 - γi (1) V ˆ

(11)

or by using the degree of dissociation of component i (3) (1) molecules, Ri ) (n(1) i - ni )/ni ) 1 - γi, we obtain

V ˆ (3) Zi ) 1 - (1 - Ri) (1) V ˆ

(12)

To define conversion, it is necessary to know the ratio ˆ (1). Mass spectra measurements enable us to define V ˆ (3)/V γi or Ri for each component of the gas mixture. If the overall quantitative analysis of the gas mixture in ˆ (1). section 3 was made, it is possible to calculate V ˆ (3)/V This procedure may be very complex. We determined ˆ (1) from the pressure increment ∆P. ∆P takes place V ˆ (3)/V under ignition of discharge. The pressure in the plasmachemical reactor depends on the flows of pumping up and pumping out. The flow of pumping up was determined by flow controllers. For this flow, eq 2 is true. The value V ˆ (0) is constant under any conditions in the plasmachemical reactor. The flow of pumping out is equal to the flow of particles in section 3; that is,

F ˆ out ) F(3) )

P1 (3) V ˆ κT0

(13)

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This flow was controlled by a special valve between the plasmachemical reactor and the vacuum pump. It ˆ (3) ) V ˆ (3)(P1). is obvious that V ˆ (3) depends on pressure, V The value may be approximated by determining the pressure difference between both ends of a thin capillary. In this case, the flow rate may be written by the Hagen-Poiseuille equation.11

V ˆ )

πr4 δP 8µl

(14)

where r is the capillary radius, l is the capillary length, µ is the viscosity of the gas, and δP is the pressure difference on the ends of the capillary. This pressure difference was measured between both sides of the vacuum control valve. Let us consider two simple cases. 1. Under increasing gas pressure, δP is constant; that is, V ˆ (3) is constant, too. If there is no discharge in the ˆ (0) reactor, there are no chemical reactions; hence, P0V ) P1V ˆ (1) ) P1V ˆ (3), and

P0 ˆ (0) V ˆ (3) ) V P1

(15)

Ignition of discharge increases the gas pressure P1ˆ (3) is not changed, and V ˆ (1) is decreased: (R) ) P1 + ∆P, V

ˆ (0) P0V V ˆ (1) ) R P1 + ∆P

(16)

Subscript R means under discharge conditions. Accordingly,

V ˆ (3) R V ˆ (1) R

)1+

∆P P1

(17)

2. Under increasing gas pressure, δP ) cP, where c is constant; hence, V ˆ (3) ) BP1, where B is constant, also. The value of B may be determined when there is no discharge in the reactor:

ˆ (0) ) P1V ˆ (1) ) P1V ˆ (3) ) B[P1]2 P0V

(18)

Figure 5. Dependence of the ratio of V ˆ (3)/V ˆ (1) on the gas pressure for pure methane. Initial conditions are P1(0) ) 21 Torr and V ˆ (0) ) 25 cm3/min.

was caused by increasing of the gas flow rate V ˆ (0). Figure ˆ (1) on the 5 presents the dependence of the ratio V ˆ (3)/V gas pressure for pure methane. The initial conditions are V ˆ (0)(0) ) 25 cm3/min and P0(0) ) 21 Torr. One can see from Figure 5 that the dependence equation, eq 17, passes below and eq 21 passes above the experimental one. As an approximation, we selected the relation making up the mean of eqs 17 and 21:

V ˆ (3) R V ˆ (1) R

)1+

B)

(19)

2

[P1]

Under discharge conditions, V ˆ (1) R is the same as the case of constant δP, and

V ˆ (3) R )

P0V ˆ0 (P1 + ∆P) [P1]2

(20)

From eqs 16 and 20, we obtain

V ˆ (3) R V ˆ (1) R

)

(P1 + ∆P)2 [P1]2

(

)

∆P ) 1+ P1

(21)

We compared eqs 17 and 21 with experimental results. Two sets of experiments were made. The experiments without discharge were included in the first set. Under this condition, an increase of the gas pressure

(22)

CO2 f CO + 1/2O2

(23)

It can be shown that the next two relations are true for this case. From eqs 10, 12, and 23, where RCO2 ) 1

ZCO2 ) V ˆ (3) R V ˆ (1) R

)

2RCO2

(24)

3 - RCO2 3 3 - RCO2

(25)

- nCO2(3)/nCO2(1) is the degree of dissociation of CO2 (this value can be found from mass spectrometer measurements). From eqs 22 and 25, we obtain

(

RCO2 ) 3 1 2

)

The dependence of eq 22 agrees with the experimental one very closely, as shown in Figure 5. The disagreement was not in excess of 2%. The same situations occurred for CO2, N2, and gas mixtures. The second set included experiments under discharge conditions. We analyzed the process of CO2 decomposition. It is known from the literature1,2 and our experiments supported this fact too that the decomposition of pure CO2 in a gas discharge is due to the reaction

From eq 18, we obtain

P0V ˆ (0)

(

1 ∆P ∆P 3+ 2 P1 P1

))

1 1 ∆P ∆P 1+ 3+ 2 P1 P1

(

(26)

As an example, Figure 6 presents a dependence of ˆ (0) ) RCO2 on the input power for P1(0) ) 21 Torr and V 55 cm3/min. One of them was obtained from mass spectrometer measurements (dependence 1). The second one was obtained from eq 26 by measuring ∆P (depen-

2544 Ind. Eng. Chem. Res., Vol. 38, No. 7, 1999

Figure 6. Dependence of the degree of dissociation of CO2 on input power. Initial conditions are P1(0) ) 21 Torr and V ˆ (0) ) 55 cm3/min.

dence 2). We see satisfactory agreement between these curves. The difference does not exceed 10%. We used eq 22 for finding δR (see eqs 8 and 9). Taking into account that eq 22 gives information about the whole increase of flow rate by chemical reactions, for the calculation of the mean flow rate 〈V ˆ (R)〉, it is necessary to employ the relation

δR )

( )

( )

V ˆ (3) R 1 1 ∆P ∆P 1 + (1) ) 1 + 3+ 2 4 P P1 1 V ˆ R

Figure 7. Dependence of the degree of dissociation of methane on input power. (1) P1(0) ) 9.5 Torr, V ˆ (0) ) 100 cm3/min. (b) P1(0) ) 27.5 Torr, V ˆ (0) ) 50 cm3/min. (0) P1(0) ) 9 Torr, V ˆ (0) ) 50 cm3/ min. (2) P1(0) ) 16 Torr, V ˆ (0) ) 25 cm3/min. (() P1(0) ) 9 Torr, V ˆ (0) ) 25 cm3/min. (O) P1(0) ) 28 Torr, V ˆ (0) ) 25 cm3/min.

(27)

We obtained all necessary relations in order to define the conversion of the initial substance and the residence time taking into account the change of the flow rate by the chemical reactions.

Figure 8. Mass spectrum of a gas mixture in a postplasma zone. W ) 120 W, P1(0) ) 23 Torr, and V ˆ (0) ) 55 cm3/min

Results and Discussion Let us consider the methane decomposition process in the plasma of the RF discharge. The methane molecule is quite stable. The strength of chemical bond H-CH3 is equal to 4.51 eV. As an illustration, the dependence of the degree of dissociation of CH4 on input power is presented in Figure 7 for different pressures and flow rates. From this figure, we noticed that the degree of dissociation increased with the increase in input power. As a qualitative illustration of the process, the mass spectra of the gas mixture in the postplasma zone are presented in Figure 8 and Figure 9. The initial pressure was equal ˆ (0) to P1(0) ) 23 Torr, and the flow rate was equal to V 2 ) 3 55 cm /min. Figure 7 corresponds to W ) 120 W, and Figure 8 corresponds to W ) 300 W. From these spectra, we can see that, under low input power (∼100 W), the group of C2 products appears but, under higher input power, the density of C2 increases and the C3 group of products appears. It is important to note that the molecular hydrogen is formed in the plasma. The hydrogen density increases when the input power ˆ CH4(R) ratio on increases. The dependence of the F ˆ H2(3)/F input power is shown in Figure 10 for a discharge in ˆ (0) ) 55 cm3/ pure methane with PCH4 ) 23 Torr and V min. Here, F ˆ H2(3) is the flow of molecular hydrogen in

Figure 9. Mass spectrum of a gas mixture in a postplasma zone. W ) 300 W, P1(0) ) 23 Torr, and V ˆ (0) ) 55 cm3/min.

ˆ CH4(1) - F ˆ CH4(3) is the postplasma zone, and F ˆ CH4(R) ) F the flow of disappeared methane by chemical reactions. This dependence is important for a qualitative description of the plasmachemical processes. The formaˆ CH4(R) ) 0.5, while tion of ethane from methane is F ˆ H2(3)/F an “ideal” polymerization which leads to the formation of saturated and noncross-linked polyethylene of infinite ˆ CH4(R) ) 1. This means from Figure chain length is F ˆ H2(3)/F 10 that, at low input power (∼100 W), the gas-phase chemical reaction of ethane formation predominantly ˆ CH4(R) ) 0.5. When the input power takes place, F ˆ H2(3)/F increases, the unsaturated groups of C2 and C3 begin to form. The acetylene is formed in a detectable amount, and film deposits on the inside of discharge tube wall ˆ CH4(R) ) 1.5). (F ˆ H2(3)/F

Ind. Eng. Chem. Res., Vol. 38, No. 7, 1999 2545

Figure 10. Dependence of the ratio F ˆ H2(3)/F ˆ CH4(R) on input power. Initial conditions are P1(0) ) 23 Torr and V ˆ (0) ) 55 cm3/min and the discharge in pure methane.

Let us suppose that the main process of methane decomposition takes place under electron impact:

CH4 + e- f CH4* + eCH4* f CH3 + H

(28)

Figure 11. Average dependence of δR ln{1/(1 - ZCH4)} on specific energy E for discharge in pure methane.

where Ja is the amplitude of the discharge current density, Ea is the amplitude of the strength of the electric field, e and vj e are the electron charge and mean velocity, respectively, σetr is the effective cross section for momentum transfer, n is the density of molecules in plasma, and w is the specific input power. Taking into account that n ) P1/κTR, we obtain

The frequency of such collisions for the methane molecule with an electron, νe, is

νe ) ne〈veσdiss〉

(29)

where ne is the density of the electron, ve is the speed of the electron, and σdiss ) σdiss(ve) is the effective cross section for collision, which causes methane dissociation. The number of dissociated methane molecules from time t to t + dt, dN, is

ne )

n(t + dt) - n(t) ) -n(t)ne〈veσdiss〉 dt

w

(36)

{ }

n(L) ) n(0) exp

( )

κmevj eσetr Ea C ) 0.395 n e2

E CδR

(37)

(31)

or

dn ) -n(t)ne〈veσdiss〉 dt

(32)

From the solution of eq 32,

n(t) ) n(0) exp{-ne〈veσdiss〉t}

(33)

Here, t ) τ is the mean residence time. From eqs 9 and 33, we obtain

}

LS P1 n(t) ) n(0) exp -ne〈veσdiss〉0.395 TR δRV ˆ (0) 0

(34)

On the other hand, the next relation is true for plasma:9

(35)

-2

〈veσdiss〉 ≈ constant

and E ) wLS/V h (0) is the specific energy for initial gas flow. From eq 37, the relation for conversion is

Z)

e2 Ea w n ) e n e E mevj eσtr a

P1

It can be consider that, in plasma, Ea/n ) constant ) C9 so that from eqs 33 and 36

(30)

where n is the density of the methane molecules at time t. In this case, for a decrease of the number of methane molecules from t to t + dt, we obtain

Ja )

-2κT R

where

dN ) nne〈veσdiss〉 dt

{

( )

mevj eσetr Ea n e2

{

n(0) - n(L) E ) 1 - exp CδR n(0)

}

(38)

We emphasize that eq 38 is the relation for conversion but not for the degree of dissociation, because it takes into account the decrease of particle density through molecule decomposition but not through flow-rate change in the gas mixture. The constant C can result from calculation, but this is very complex. It is possible to find it from experimental results. If the assumption about the process of methane decomposition, eq 28, is true, the dependence of δR ln{1/(1 - Z)} on energy E must be linear and travel through the origin of the coordinates. C must be equal to cot R, where R is the angle between this straight line and the x-axis. Figure 11 shows such an averaged dependence for the data depicted in Figure 7. One can see from Figure 11 that this dependence is linear within the limits of experimental error and travels through the origin of the coordinates. The value of the constant is CCH4 ) 490 ( 100 J/cm3 or, for one molecule, CCH4 ) 120 ( 25 eV/mol (in this case, E is the specific energy per one molecule of CH4).

2546 Ind. Eng. Chem. Res., Vol. 38, No. 7, 1999

Figure 12. Average dependence of δR ln{1/(1 - ZCO2)} on specific energy E for discharge in pure CO2.

Figure 14. Mass spectrum of a gas mixture in a postplasma zone. Discharge in pure CO2. W ) 300 W, P1(0) ) 20.5 Torr, and V ˆ (0) ) 55 cm3/min.

Figure 13 is an ordinary CO2 mass spectrum. Figure 14 shows us the appearance of O2 (peak with m ) 32) and CO. The peak with m ) 28 is a superposition of components from CO and CO2. Because of this, its height is equal to the peak height with m ) 44 (compare with Figure 13). A severe quantitative analysis showed that the density of CO was twice as much as the density of O2. A consequence of the above discussion is the fact that the main process of CO2 decomposition under the conditions investigated is caused by direct electron impact:

CO2 + e- f CO2* + e-

Figure 13. Mass spectrum of CO2 under P1(0) ) 20.5 Torr and V ˆ (0) ) 55 cm3/min.

From our point of view, this fact supports the assumption that the main process of CH4 decomposition under investigation is accounted for by direct electron impact. Let us discuss the physical meaning of C. It is easily understood that, in the framework of the simple model under consideration, the expression of eq 38 for conversion of methane can be considered to be like the dissociation probability of one molecule under E. In this case, the energy cost for one molecule dissociation (under small input power when δR ≈ 1) is

n ) E/Z ≈ C

(39)

Consequently, C is the energy cost for one molecule dissociation in the plasma of the RF discharge in pure methane. The same situation takes place for the carbon dioxide decomposition in the plasma of the RF discharge in pure CO2. Figure 12 shows the average dependence of δR ln{1/(1 - Z)} on E for the discharges in pure CO2. One can see that this dependence is linear within the limits of experimental error and travels through the origin of coordinates. The energy cost for dissociation of one molecule of CO2 under the conditions in this investigation is CCO2 ) 130 ( 15 eV/mol. Moreover, the analysis of the mass spectra of a gas mixture in the postplasma zone shows us that the only products of CO2 decomposition are CO and O2. Figure 13 is the mass spectrum that is obtained without discharge condition, and Figure 14 is the mass spectrum for the gas mixture in the postplasma zone under 300 W of input power. The initial conditions are that the pressure of pure CO2 is P0 ) 20.5 Torr and the flow rate is V ˆ (0) ) 55 cm3/min.

CO2* f CO + 1/2O2

(40)

It should be noted that the energy cost for dissociation of one molecule of CH4 or one molecule of CO2 (C ≈ 100 eV/mol) is much more than the energies of dissociation of these molecules (ED(CH4) ) 4.5 eV and ED(CO2) ) 5.5 eV). This means that the decomposition of these molecules goes via excitation of the unstable excited electronic states. The energy threshold of the effective cross section (σdiss) is determined in this case not by the dissociation energy but by the energy of lowest unstable electronic state (for CO2 and CH4, Ethreshold g 10 eV1). There is no difficulty in understanding that under such conditions, only a small part of the discharge input power is spent on the dissociation, because of only the high-energy plasma electrons are involved in this process. But the number of these electrons is rather small. It is necessary to stress that, in the framework of this simple model under investigation, the conversion is determined practically by one parameter. This parameter is the specific energy per one molecule of initial gas. In order to evaluate the conversion, it is not necessary to know the gas pressure, gas temperature in the discharge, or any other plasma parameters. This has been experimentally established for pressures from 5 to 60 Torr.

Conclusions The decomposition of the methane and carbon dioxide molecules in the plasma of the RF discharge under middle pressure (5-60 Torr) of the pure gases is caused by direct electron impact via excitation of the unstable

Ind. Eng. Chem. Res., Vol. 38, No. 7, 1999 2547

electronic states. The influence of the reverse reaction is very small. The energy costs for decomposition of one molecule of CH4 and one molecule of CO2 were determined. They are CCH4 ) 120 ( 25 eV/mol and CCO2 ) 130 ( 15 eV/ mol. For estimation of methane and carbon dioxide conversions, it is not necessary to measure the plasma parameters such as electron density, mean electron energy, or gas temperature in the discharge zone. We need to have only information about the specific energy per one molecule of initial gas. Under low input power, the main plasmachemical processes for methane discharge are the gas-phase reactions of ethane and hydrogen production. When the input power increases, the density of hydrogen increases and the unsaturated groups of C2 and C3 begin to form. The acetylene is formed in detectable amounts, and surface-phase polymerization reactions occur. As a result of these reactions, the film deposits on the inside of the discharge tube wall.

w ) specific input power, W ˆ (1) Z ) conversion, F ˆ (R) i /F i Greek Letters R ) degree of dissociation, 1 - γi δR ) factor for calibrating the flow-rate change by chemical reaction, 〈V h (R)〉/V(R) (1) γ ) ratio of densities of molecule, n(3) i /ni -23 κ ) Boltzmann’s constant, 1.381 × 10 J/K µ ) viscosity of gas, kg cm-1 s-1 ve ) collision frequency, s-1 σetr ) effective cross section for momentum transfer, cm2 σdiss ) effective cross section of collision, cm2 τ ) mean resident time, s Subscripts i ) component 0 ) initial section of plasmachemical reactor 1 ) predischarge section 3 ) postdischarge section R ) discharge section Superscripts

Support from the Ministry of Science and Technology and Daelim Daeduk R&D Center is greatly appreciated.

(0) ) initial section of plasmachemical reactor (1) ) predischarge section (3) ) postdischarge section (R) ) discharge section

Nomenclature

Literature Cited

B ) proportional constant, P0V ˆ (0)/[P1]2 c ) proportional constant, δP/P C ) proportional constant,

(1) Rusanov, V. D.; Fridman, A. A Physics of chemically active plasma (in Russian); Nauka: Moscow, 1984. (2) Slovetskii, D. I. Mechanisms of chemical reactions in nonequilibrium plasma (in Russian); Nauka: Moscow, 1980. (3) Lieberman, M. A.; Lichtenberg, A. J. Principles of plasma discharges and materials processing; John Wiley & Sons: New York, 1994. (4) Molinary, E. Homogeneous and Heterogeneous Reactions in Plasmas of Moderate Pressure. Pure Appl. Chem. 1974, 39, 343. (5) Canepa, P.; Castello, A.; Munari, S.; Nicchia, M. Low Pressure RF Plasma reactions in Light Hydrocarbons: methane. Radiat. Phys. Chem. 1980, 15, 485. (6) Marafee, A.; Liu, C.; Xu, A.; Mallinson, R.; Lobban, L. An Experimental Study on the Oxidative Coupling of Methane in a Direct Current Corona Discharge Reactor over Sr/La2O3 Catalyst. Ind. Eng. Chem. Res. 1997, 36, 632. (7) Levitsky, S. M. Investigation of High-Frequency Discharge Sparking Potential. ZH. Tekh. Fiz. (in Russian) 1957, 27, 970. (8) Levitsky, S. M. Space Potential and Electrode Pulverization in High-Frequency Discharge. ZH. Tekh. Fiz. 1957, 27, 1001. (9) Raizer, Y. P. Gas Discharge Physics; Springer-Verlag: Berlin, 1991. (10) Raizer, Y. P.; Shneider, M. N.; Yatsenko, N. A. RadioFrequency Capacitive Discharges; CRC: New York, 1995. (11) Bird, R. B.; Stewart, W. E.; Lightfoot, E. N. Transport Phenomena; John Wiley & Sons: New York, 1960.

Acknowledgment

0.395(κmevj eσetr)

( ) Ea n

-2

〈veσdiss〉

d ) inner diameter of the plasmachemical reactor, cm e ) electron charge, 1.602 × 10-19 C Ea ) strength of the electric field, V/cm E ) specific energy, wLS/V ˆ (0), J F ˆ ) flow of molecules, min-1 Ja ) discharge current density, A/cm2 L ) length of the plasmachemical reactor, cm me ) electron mass, 9.11 × 10-31 kg n ) particle density, cm-3 ne ) electron density, cm-3 P ) pressure, Torr δP ) pressure difference on the ends of the capillary, Torr S ) area of cross section of the plasmachemical reactor, cm2 T ) temperature, K vj c ) mean convective velocity, cm/s ve ) velocity of electron, cm/s vj e ) mean electron velocity, cm/s V ˆ ) flow rate of gases, cm3/min 〈V ˆ (R)〉 ) mean gas flow rate in the reactor, cm3/min

Received for review July 30, 1998 Revised manuscript received November 24, 1998 Accepted December 19, 1998 IE980492C