.
(REACTIONS OF ARTIFICIAL GRAPHITE) Mechanism of the Oxidation of Graphite at Temperatures of 425" to 575" C. Earl A. Gulbransen WESTINGHOUSE RESEARCH LABORATORIES, EAST PITTSBURGH, PA.
0
NE of the chemical reactions most useful to mankind has been the reaction of carbon-containing materials with oxygen. I n spite of its technical importance and the great number of scientific studies on the nature of the reaction, the mechanism has not been established. The concept of a surface oxide complex as an intermediate stage in the reaction was first proposed by Rhead and Wheeler (39) in 1912 and has been accepted by most workers in the field. However, in terms of modern physical chemical theories of specific rate-limiting processes, the surface oxide concept does not provide a basis for predicting from first principles the actual rate of reaction. In the first article the mechanism of a surface reaction was separated into five distinct processes and discussed briefly. This paper summarizes the kinetic results and correlates these results with the predictions of the absolute reaction rate theory of ' chemisorption, chemical reaction, and desorption-processes which undei the conditions studied probably control the rate of the reaction.
Summary of Kinetic Data I n the first and second parts of this article the primary chemical reaction of pure artificial graphite was studied, using strip specimens over the temperature range of 425" to 575" C. The weight change curves showed no evidence of an initial pickup of oxygen to form a surface oxide as predicted by the theory of Rhead and Wheeler (39). Instead, the weight loss curves could be fitted by the equation W = Kt CtZ,where W is the weight loss in micrograms per square centimeter, K and C are constants, and t is the time. Above 500" C. K and C are positive and the rate of reaction d W / d t increases with time, while below 475 " C., K is positive and Cis negative. The initial rate constant K could be fitted to an exponential function of the temperature-Le., K = Z e - E / R T . An energy of activation, E, of 36,700 calories per mole was found, while the frequency factor, 2, has a value of 7.16 X lo3 for a pressure of 7.6 em. of mercury of oxygen. 2 has the units of grams of carbon reacting per square centimeter of measured area per minute. A study was made of the effect of pressure P on the rate constant K for temperatures of 450" and 500" C. The pressure dependence is given by the equations
+
450' C. K = 2.30 X 500' C. K = 1.35 X
May 1952
W
=
1.7 X
1022
e-
E/RTt
At 500" C., the initial reaction is
Wt
+
0 = 7.2 X 1011 atoms of carbon reacting per sq. em. per second
Any proposed rate-limiting process must account for three essential experimental facts: a n essentially first-order reaction a t pressures of 0.1 atmosphere of oxygen and higher, a linear time dependence during the initial stages of the reaction, and the absolute value of the rate of the reaction as given by the above equation. The proposal of Rhead and Wheeler (39)that a shrface oxide is formed before reaction occurs is not observed, although the sensitivity of the balance could readily show such a phenomenon. It is more reasonable t o assume t h a t the surface oxide complex is the residual monolayer of oxygen atoms associated with the active terminal carbon a t o q s in the graphite lattice, released by heating above 750' C. in vacua or in an inert gas atmosphere. , The one remaining factor in the reaction, which has not been studied effectively, is the composition of the products of the reaction. Mass spectrometer studies on the formation of carbon monoxide and carbon dioxide in large amount of oxygen are difficult and no data of high precision have been obtained. It may be assumed that carbon monoxide is the primary reaction product, although the nature of the primary reaction product is not essential in the development of the theory.
Absolute Reaction Rate Theory This theory when applied to a surface reaction assumes the formation of a complex between the reacting gas and the surface, the chemisorbed gas and the surface, and the chemisorbed reaction product and the surface. The rate of any one of these surface reactions may be considered in terms of reaction complexes passing from one region of configuration space to another (10, IS,8.2'). Along a given reaction path there exists one region of configuration space separating the initial and final states having a maximum free energy. According t o Eyring and coworkers (%?), the number of reaction complexes passing through this region is given by
f 0.83 X 10-10 P
+ 0.505 X 10-9 P
where P is in units of centimeters of mercury and K is in grams of carbon reacting per square centimeter per minute. Above 10 cm. of mercury of oxygen a first-order reaction is found, while at presswes below 1 em. of mercury an essentially zero-order reaction is observed. A plot of K vs. the square root of pressure showed a somewhat poorer correlation. Gas adsorption measurements of the surface roughness showed t h a t a degassed sample has a surface roughness before oxidation of 354 times the measured area. The effect of oxidation of 550' C. is to increase the surface roughness. This may explain the observed time dependence of the oxidation for temperatures above 500" C.
It is now possible t o give the absolute initial rate of oxidation of a pure sample of graphite in terms of atoms of carbon reacting per square centimeter of actual area per second for a pressure of 7.6 em. of mercury of oxygen. The equation is:
where
C = total number of complexes in initial state at time t
H
= probability t h a t the reaction complex crosses the
Y
= frequency with which the complexes cross t h e
barrier in any one attempt *
energy barrier n, i = uantum numbers associated, respectively, with &e degree of freedom along the reaction coordinate and with the remaining degrees of freedom of the reaction complex
INDUSTRIAL AND ENGINEERING CHEMISTRY
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Fuel Gasification To carry the theory along further, two approaches have been used. The first utilizes a quantum-mechanical method for calculating the energy of activation. This is difficult, even if approximation methods are used and good agreement is not achieved. The second approach utilizes the experimental activation energies together with an evaluation of the partition functions of the initial and activated states. From this method it has been possible t o calculate absolute rates for surface reactions which are in agreement with the experimental ones. The transmission coefficient, H , has been considercd in some detail by Hirschfelder (18, 19) and Wigner (169, who state that only in exceptional rases does H differ from unit,y.
\
3. DESORPTION C ‘ -)/‘
1
/
>C4\
\
/
+
- -- G O -c -c\ /--c)C-c\
I. ADSORPTION
an angle of 120” to each other. The fourth carbon electron is locat,ed in a p orbital and forms a figure eight perpendicular to the layer. This electron participates in forming a r bond with the three adjacent carbon atoms. As the terminal carbon atoms participate in only two bonds Trith adjacent carbon atoms, the reartivity of these atoms is greatly increased. Let us now describe the rate equations as given by the ahsolute reaction rate theory. Rate of Adsorption. Adsorption processes ( I S , 28) may lie considered as bimolecular reactions involving an atom or a molecule from the gas phase and an active point in a fixed position on the adsorbing surface. -4n activated complex is assumed to form between the molecule or atom and the fixed.point on the surface. The rate of adsorption is given by the rate of passage of this coniplex over the potential energy barrier. According to postulates of the theory (13, 22), equilibrium exists between molecules of the gas, adsorption centers, and activated complexes. For ideally behaving compounds
co
C-SURFACE
where thef terms are complete partition functions of the indicated species. Let F , = f g / V or partition function for unit volume of gas; then
I
I
2.CHEMICAL REACTION
02
ENERGY CHEMI-
’
3. DESORPTION
CHEMI1 SORBED
!
co
GO
I
DISTANCE
f; differs from $;’ by the ”removal of one degree of translational freedom in the reaction coordinate. Extracting the zero-point energy contribution
-
i I
According to the theory, the rate of adsorption of gas on the sites of the (i)th kind per square centimeter is given by
i
DISTANCE R E A C T I O N COORDINATE
To apply the above relationship, several types of adsorption processes may occur, depending upon whether the atom or inolecule forms a mobile or immobile layer and whether the adsorption process or the dissociation process is rate-determining. The partition functions for the various degrees freedom are substituted directly in the equation. Eyring and coworkers (13, 22) have given the following expressions&forthe several types of adsorption processes.
Figure 1. Energy os. Reaction Coordinate Curves for Processes Involved in Oxidation of Graphite I n correlating the predictions of the absolute reaction rate theory with experiment, the method of experimental activation energies is used plus partition functions for evaluating the equilibrium between initial and activated states. This method is applied to the various surface processes of adsorption, chemical reaction, and desorption. An analysis of the predicted rate of reaction with experiment is used to suggest a possible mechanism for the oxidation reaction.
1. Immobile Adsorption, Adsorption of Molecule, RateDetermining
Rate Expressions Figure 1 shows a coordinate diagram of energy us. reaction for three processes of chemisorption, chemical reaction, and desorption. The values of el, e2, and e j represent the energies of activation of forming the activated complex Fhich exists a t the maximum of the energy curves. The dashed line in the center represents the carbon atom about which adsorption and desorption take place. Because this carbon atom is involved in the carbon monoxide that is formed, the reaction coordinate is not shown here for the chemical reaction process. The three schematic equations are given, assuming carbon monoxide is the primary reaction product t o help describe the process. The chemisorbed bonds are denoted by the dashed line or and indicate distances much greater than the normal >C-C< -C=O bonds, The activity of the terminal carbon atoms is seen from the fact that each carbon atom forms three u bonds, by means of three sp2 hybrid orbitals which are in one plane and a t 1046
2. Immobile Adsorption, Dissociation Is Rate-Controlling Process
3.
Xobile Adsorption
4. Mobile Adsorption, No -4ctivation Energy
’
Here the symbols have the following definitions:
C, = concentration of molecules per cubic centimeter in the gas phase, C, 7 concentration of adsorption sites per square centimeter, .T = symmetry number of the gas molecule, ut = symmetry number of the activated complex, h = Planck’s con-
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 44, No. 5
Fuel GasificatioTable I. Correlation of Predictions of Absolute Reaction Rate Theory with Experimental Rate of Oxidation of Graphite at 500' C. Rate Mechanism Immobile adsorption, adsorption of molecule, rate-controlling Immobile trolling
adsorption,
dissociation rate-con-
"I VI
Mobile adsorption, no activation energy (HertzKnudsen equation)
Equation h' e-eI/kT = CuCe:$8a21(2amkT)a/2 kT h3 I ¶ = Cg"2Cs h (2amkT)3 y l .5)'/2(8azIkT)'/2
Theory 4.8 x 105
P 0 1 / 2
=
cg
kT
Mobile adsorption
VI
Desorption
v1 = Co k? e - Q / k T
h (2srnkT)'/g
7 . 2 X 10''
1.7 X 1 0 2 2
7 . 2 X 10"
x
10"
7 . 2 X 10"
1.4 X 10'8
7 . 2 X 1Q"
x
105
7 . 2 X 10"
1.4 X 10's
7 . 2 X 10"
7.3
e-el/kT
h
Chemical reaction, first-order kinetics Chemical reaction, zero-order kinetics
V2
=
' / z ah4
coca u t 81r21(2amkT)3// 0
Ca kT h
4.8
-ez,kT
e-e2/hT
stant, I = moment of inertia, IC = Bolteman's constant, m = mass of molecule, T = absolute temperature, and e = energy of activation. Rate of Desorption. Desorption from an immobile layer may be regarded as involving an activated state in which a molecule attached to an adsorbing center acquires the necessary configuration and activation energy t o permit it to escape from the surFace. In the following rate expressions given by Eyring and coworkers ( I S , $2) both activated complexes and adsorbed molecules are considered immobile.
Here uz represents the rate of desorption in molecules per square centimeter per second, C, represents the concentration of adsorbed molecules per square centimeter, and eZ is the energy of activation. Chemical Reaction. Let us assume the reaction involves one molecule of oxygen and the active surface site, S. This active site may consist of an oxygen-free site or one on which oxygen has been previously adsorbed. The activated complex consists of an adsorbed molecule which has acquired the appropriate amount of energy and the proper configuration. FIRST-ORDER KINETICS.If the surface is sparsely covered by adsorbed molecules or atoms, the concentration of sites C , is nearly constant and identical with the number of sites for a bare surface. Under these conditions the rate of the reaction is proportional to the concentration of the molecules in the gas phase C, and the reaction is of first order. The rate expression is
where s is the total number of possible sites adjacent t o any reaction center, u and a: are the symmetry numbers of the molecules of reactant and activated complex, respectively, and ea is the energy of activation for this type of reaction. The above equation may also apply when the active sites already have an oxygen atom attached t.0 the carbon atoms. ZERO-ORDERKINETICS.Let us assume the surface is covered by adsorbed molecules t o an appreciable extent. The value of C, varies with the pressure of the gas. If the surface is nearly
x
No. of C Atoms Sq. Cm./Sec. Experiment 7 . 2 X 10"
10'2
2.1
-
=
dW
dt Lo
completely covered by adsorbed molecules, C, is nearly constant and the rate of reaction is nearly independent of the pressure. The following equation treats the reaction from the viewpoint of the adsorbed molecules, with the surface activation energy being the difference in energy between the activated state and the adsorbed reactants, or eo e:
+
v2
=
C, -e
- E/RT
h
where E is the observed activation energy, e is the heat of adsorption, and eo is the difference in energy between the activated state and the initial gaseous reactant.
Comparison of Theory with Experiment Table I shows a comparison of the rates of the various processes a t 500" C . as predicted from the absolute reaction rate theory with the experimentally determined rate of reaction. The calculations are based on an experimental activation energy of 36,700 calories per mole. The fact that several processes occur with a theoretical rate slower than the experimental value means that the energy of activation used is too high for this particular process. The comparison is significant only for those processes that give good agreement. Two mechanisms are found in Table I to give a reasonable degree of agreement: immobile adsorption with dissociation as the rate-controlling step, and mobile adsorption. Theextremely close agreement of the latter process with the experimental value may be fortuitous, since the assumptions involved in the calculations do not warrant such agreement. The effect of pressure on the rate of reaction would tend to rule out the immqbile adsorption with dissociation as the ratecontrolling step. However, a plot of the rate constant us. pressure shows a rough correlation and this mechanism cannot be eliminated. The evidence points rather strongly to the mobile type of adsorption or immobile adsorption with dissociation as the rate-limiting process in the oxidation of graphite over the temperature range of 425" to 575" C. and over a pressure range of 0.15 to 10 cm. of mercury of oxygen. RECEIVEDfor review November 16, 1951. Scientific paper 1623.
ACCEPTED March 15, 1952.
e + +
May 1952
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