Energy & Fuels 1993, 7, 1141-1145
1141
Correlation between Arrhenius Kinetic Parameters in the Reaction of Different Carbon Materials with Oxygen Ana Cuesta, Amelia Martfnez-Alonso, and Juan M. D. Tasc6n’ Instituto Nacional del Carbbn, CSIC, Apartado 73, 33080 Oviedo, Spain Received April 13, 1993. Revised Manuscript Received August 9, 1 9 9 P
Correlation between Arrhenius kinetic parameters is often found in coal and char reactions, to such an extent that Essenhigh and Misra have recently suggested (Essenhigh, R. H.; Misra, M. K. Energy Fuels 1990,4,171-177) that these parameters are autocorrelated. In order to throw additional light on this point, a self-consistent set of kinetic data for the reaction of carbonaceous solids with oxygen, determined by thermogravimetric analysis, is presented and analyzed in this work. The wide range of carbon materials under study allowed to broaden the scope of correlations with respect to numerous previous studies of this reaction. A generalized correlation between Arrhenius parameters (apparent activation energy and preexponential factor) was found. Unlike previous reports, existence of a systematic curvature in the correlation plot was detected. Thus, optimum fitting to a curve obeying a power equation rather than to a straight line was attempted. An active-centers model adapted to the graphite structure was used to justify the occurrence of compensation effect, differences in behavior among carbon materials being explained as a function of the relative predominance of the various types of factors controlling the reactivity of these solids against oxygen.
Introduction Formal kinetics predicts that the Arrhenius equation parameters, activation energy and frequency factor, are essentially independent from each other. However, this only applies in a strict sense to unimolecular reactions. For more complex reactions, only a phenomenological approach can be adopted, these parameters having a more comparative than conceptual value so that in these cases their names must be changedto apparent activation energy (E) and preexponential factor (A), respectively. It has been found in a number of cases, especially for heterogeneous catalytic reactions, that E and A change in the same direction. Already in 1925, Constable‘ described for the f i i t time the occurrence of such correlationbetween E and A, and later on other researchers213have provided numerous further examples. This fact, which occurs either with change in catalyst for a given reaction or with change in reaction for a given catalyst, is referred to as compensation effect or 0-rule. To date no complete explanation for this interesting experimentallyestablished law has been found. In the case of carbonaceous materials, Essenhigh and Misra have recently4provided a new interpretation of these correlations based on analyzing a number of (E, A) sets of values5 obtained by different authors for various reactions (pyrolysis,combustion, gasification,etc.) of coals and chars. Essenhigh and Misra found a number of correlations between the Arrhenius parameters corresponding to each material, varying from fair to good for the different cases, andattributedit to statistical variations
in the experimental results with respect to the “true”couple of values that should then be independent on coal rank. Even if this assumption was true, it was accepted that in some cases the correlations found were too good to be merely due to random statistical sampling. Moreover,real differences in reactivity among coals or chars of different rank were foreseeable and easily justified. The interest in finding a further source of correlation comes from the fact that it would allow to reduce the number of degrees of freedom from 2 to 1, thus simplifyingthe task of reaction modelling and improving the confidence level of chosen models. The current paper is primarily aimed at providing further data on the correlation between Arrhenius parameters. Test of the log(A)lE relations/correlations can be accomplished either by examining a range of carbons by the same experimental method or by examining a single carbon type in a range of different experiments. This paper addresses the first approach. The second will be attempted as circumstances permit. We have determined a self-consistent set of kinetic data for the C+02 reaction in a group of carbon materials with widely different structures, going from low-rank coals to ultrapure graphite. Interestingly, the set of carbon materials under study covers a very broad scope of changes in structure in comparison with numerous previous studies that have generally dealt with more restricted sets of carbonaceous solids. With this, we hope to contribute to establishing general conclusions on the origin of (auto)correlation between kinetic parameters in the carbon-oxygenreaction.
Experimental Section Abstract published in Adoance ACS Abstracts, October 1, 1993. (1)Constable, F. H. h o c . R. SOC.London 1925,A108, 365-378. (2)Kemball, C. h o c . R. Soc. London 1953, A217,376-389. (3) Schwab, G. M. History of Concepts in Catalysis. In Catalysis. Science and Technology; Anderson, J. R., Boudart, M., Eds.; Springer-Verb Berlin, F. R. Germany, 1981;Vol. 2, pp 1-11. (4) Essenhigh, R. H.; Misra, M. K. Energy Fuels 1990,4,171-177. (6) Misra, M. K.; Essenhigh, R. H. Energy Fuels 1988,2,371-385.
Materials. A total number of 32 carbon materials with different origin and nature, exhibiting a broad variation in their graphitization degree, were used. Studied solids included nine different graphites (five conventional, one amorphous, and three activated ones),three carbon fibers, four carbon blacks, one glassy carbon, eight activated carbons, two pairs of coal chars (two raw
0887-0624/93/2507-1141$04.00/00 1993 American Chemical Society
Cuesta et al.
1142 Energy & Fuels, Vol. 7,No. 6,1993
Table I code
description
GP1 microcrystalline, GC1 GC2 GC3 GC4 GC5 GA1 GA2 GA3 FM1 FT1 FC1 NC1 NC2 NC3 NC4 CTV CA1 CA2 CA3 CA4 CA5 CA6 CA7 CAS CB1 CB2 CDl CD2 CM1 CM2 CM3
natural graphite natural graphite synthetic graphite synthetic graphite synthetic graphite ultrapure, synthetic graphite surface activated, synthetic graphite surface activated, synthetic graphite surface activated, synthetic graphite high modulus, ex-PAN carbon fiber high strength, ex-PAN carbon fiber stapled, pitch-based carbon fiber carbon black furnace carbon black furnace carbon black carbon black glassy carbon activated carbon activated carbon activated carbon activated carbon activated carbon demineralized (CA1) activated carbon activated carbon activated carbon brown coal char brown coal char demineralized (CB1) brown coal char demineralized (CB2) brown coal char anthracite subbituminous coal subbituminous coal
To.6 (K) E (kJ mol-')
.986
173
A* 2.07 x 107
1053 1115 1061 1027 1183
130 159 138 168 177
2.74 x 2.83 X 6.20 X 4.70 X 6.69 X
1004
135
1.10 x 105
952
86
4.18 X lo2
1018
112
5.17 X 103
1127
134
1.44 x 104
1055
117
5.59 x 103
932
160
1.43 x 107
929 949 956 952 1068 837 876 850 935 917 864
131 147 140 191 161 96 110 206 168 125 132
2.90 x 1.72 X 5.27 X 5.56 X 8.28 X 1.07 X 4.44 x 1.15 x 3.71 x 1.64 X 1.45 X
106 106 106 10s lo6 10' 104 1015 107 106 lo6
799 858 771 787 873
131 172 237 184 113
6.83 X 6.13 X 3.31 x 4.68 X 7.50 x
106 10s
874
124
3.81 X lo6
889 697 760
199 61 54
1.09 x 10'0 3.34 x 102 3.72 X 10'
104 106 10'
lo6 los
0
1014
1Olo 104
and the corresponding demineralized ones), and three coals (one anthracite and two subbituminous coals). Their reference codes are given in Table I. Methods. Kinetic data for the gasaolid reaction of carbonaceous solids in air were obtained on a Stanton-Redcroft STA781 simultaneousTG/DTA thermal analyzerprovidedwith CETA data acquisition and processing system. Samples of the different materials (allofthemgroundtopassa63-pmsieve),withastarting mass of 15 mg, were deposited on a Pt crucible 5 mm in diameter and 5 mm in height. Synthetic air 99.9990%pure (by volume) was fed at a constant flow of 50 cm3min-l a t atmospheric pressure. Temperature was measured with Pt/Rh thermocouples located a t the bottom of Pt crucibles, in contact with them. A linear heating rate equal to 10 K min-l was used; measurements were performed over the 298-1473 K range. Calculations. Sample weight changes were corrected to account for moisture and ash contents in the materials under study by taking into account the sample weights at 373 K and at the end of the experiment when, after complete combustion of carbon, only an ash residue remains. Kinetic parameters were determined from pairs of corrected weight loss/actual sample temperature values provided by the instrument, using the integrated form of the kinetic equation
where a is the converted fraction, E the apparent activation energy, and A* a modified preexponential factor that includes the heating rate and the partial pressure of oxygen, which is assumed to be constant. From eq 1, following the procedure
t ( min)
Figure 1. Thermogravimetric curves for various carbonaceous solids heated in air at 10 K min-l. described in the Appendix, one arrives a t the equation
which allowsto determine E and A* by linear regreasion,provided a function f ( x ) (i.e., for a given reaction mechanism). As usual for the carbon-oxygen reaction! we have assumed a pseudofirst-order reaction, taking variable converted fraction (a) intervals for the different materials to avoid problems a t too high or too low conversions (such as loss of volatiles at low temperatures/low conversions, or changes in the mechanism toward a diffusional regime at high temperatures/high conversions) but considering always, as a minimum, the 0.2 < a < 0.5 interval, which was enlarged in many cases to 0.05 < a < 0.8. In these intervals, the correlation coefficient for the linear regression varied between 0.99 and 0,9999, which warrants the applicability of eq 2.
Results In Figure 1are shown representative thermogravimetric curves for four carbon materials with different degrees of structural order. Taking into accountthe common heating rate of 10 K min-l used in the experiments, this figure clearly illustrates the fact that reaction of the various materials with oxygen took place over different temperature intervals depending on the characteristics of the solids. To illustrate the temperature range in which reaction of the various materials occurs, temperatures necessary to achieve 50 % conversion of the different solids (2'0.5) are given in Table I. Results are in complete agreement with generally accepted views on the trends for reactivity of carbon where structural features (thegraphitization degree) are generally considered to play a major role. Pairs of E and A* values calculated for the different materials are reported in Table I. Figure 2 shows a general
correlation pattern drawn in the usual way of plotting log A* vs E. Alinear correlation coefficientof r = 0.92 between (6) Laine, N. R.;Vastola, F. J.; Walker, P. L. Jr. J. Phys. Chem. 1983,
. . Ed.; Butterworti~~ London, 1989; pp 107-151. (9) Martlnez-Alonso, A.; T d n , J. M. D. The Determining Role of Mineral Matter on Gasification Reactivities of Brown Coal Chars. In Fundamental Issues in Control of Carbon Gasification Reactivity; Lahaye,J., Ehrburger,P., Eds.; Kluwer AcademicPublishers: Dordrecht, The Netherlands, 1991; pp 435-460.
Energy & Fuels, Vol. 7, No. 6,1993 1143
Reaction of Carbon Materials with Oxygen
::j 10
a -
Experimental data log A* = a + bE
a = -265 f 0.74 b = (6 17 f 0 SO) 10-2
=I ,
e
*
e*
50
0
e
,
J
200
250
1
100
150
E (kJ mol-1) Figure 2. Correlation between preexponential factor and apparent activation energy for carbon materials reaction with air, fitted to a straight line. 16
1
12 -
Experimental data - log A* = (1 -(E/a)b)-c a
0
= (8.88t 0 86) 106
50
100
e
150
I
I
200
250
E (kJ mol-1) Figure 3. Data from Figure 2 correlated to a curved line.
Arrhenius parameters is obtained. However, it can be seen that deviations from the thus determined straight line in Figure 2 are not distributed at random, but they arise in opposite directions at the center and the two extremes of the plot, this being indicative of the existence of a curvature. The best fit obtained, shown separately for clarity in Figure 3, corresponds to a curve obeying a with power equation of the type log A* = (1 (E/u)~))-C, parameters a = (8.88 0.86) X lo6, b = (8.40 f 0.57) X 10-1, c = (1.86 f 0.15) X lo4,andareduced X2valueof 0.81.
-
Discussion The set of carbon materials studied is sufficiently wide and the materials are different enough to allow considering that differences in reactivity are really significant. Moreover, we have separately foundlo that apparent activation energy values for the C+02 reaction correlate well with structural parameters such as the widths of peaks in Raman spectra that are indicative of the degree of structural order at the surface of the material. This suggests that the dispersion in results follows a definite and rational sequence, it being not merely due to errors in experiments or calculations. A particularly significant fact was the difference in reactivity, discussed elsewhere? between raw and demineralized coal chars, whose reactivities strongly decreased after demineralization as it could be expected (10) Cuesta, A. Researchwork, Departmentof Physical and Analytical Chemistry, University of Oviedo, Oviedo, Spain, 1992.
from the removal of catalytic impurities. It would thus seem that some specific source for correlation is added to the statistical one proposed by Essenhigh and Misra.4 Nevertheless, as stated by Essenhigh,” “The statistical correlation is not expected to account for all the variations in A and E values for different carbons. Some mechanistically-based variations can reasonably be expected to occur. What the statistical approach can do is to reduce the data base to a definitive minimum number of values for a small set of carbons where the sources of the A and E differences can then be sought in mechanistic differences. At the same time, this should also establish whether the residual variations are of the same order as the statistical variations, or whether they are essentially only second order”. Unlike previous reports, our results suggest a correlation between Arrhenius parameters which does not follow a linear law. This adds new features to existing knowledge and, on the other hand, deviates from the Essenhigh and Misra statistical model? according to which a straight line should be obtained. A plausible reason for this disagreement can be the big differences in reactivity among the studied materials; consequently, our measurements were carried out over different temperature intervals. In this respect, studies with more restricted sets of materials could lead to “local” linear fittings of data. Nevertheless, in spite of the very wide reactivity interval covered in the current work, the range of E values (Table I) is not wider than that covered in previous work, so that from this point of view the possibly “local” character of fittings found in other studies could be disregarded. In order to get more specific insights from results of Table I, we have separately plotted in Figure 4a-e the results corresponding to each of the types of materials studied. One can observe that different straight lines corresponding to the various groups of materials can be drawn, and only when all of these straight lines are superimposed the continuous curvature in the overall line (Figure 3) becomes evident. In this context, we can mention that a systematic curvature has been found12in revisiting previously assigned linear correlations between activation parameters for the fluidity of aqueous electrolytes (AH*and AS*)on the basis of Exner’s suspicionl3 that there exist straight lines (especially in cases where the slope is close to unity) that cannot have a physical sense, although they might have a mathematical one. On the other hand, if the slope and ordinate at origin parameters of the separate straight lines corresponding to the various groups of materials are plotted against each other (Figure 4f), a straight line (with a certain dispersion of results, r = 0.9) is again obtained. This “supercompensation” effect has also been found by Galwey and after reviewing numerous data from heterogeneous catalytic reactions exhibiting correlation between Arrhenius parameters. In comparing the results obtained with the different groups of carbon materials, one can observe that the studied graphites, which vary from highly crystalline to practically amorphous including some surface-activated samples (likely containing a high number of defects) cover a rather broad scope of intermediate E values. The highest (11)Eseenhigh, R.H.Private communication. (12) Good, W.; Stone, J. Electrochim. Acta 1972, 17, 1813-1819.
(13) Exner, 0.Collect. Czech. Chem. Commun. 1964,29,1094-1113. (14) Galwey, A. K.;Brown, M. E. J. Catal. 1979,60, 335-338.
Cuesta et al.
1144 Energy &Fuels, Vol. 7, No. 6, 1993 16
l4
keQ
0
16 . -
12
-
10
-
@
-8 Graphites
+ Carbon Fibers
l4
12
* 6 eQ
8 -
0
-eGraphites 4 Coal Chars
10 8 -
M
6 -
6 -
4 -
4 -
2 -
2
0 -
0
I
E (kJ mol-1)
* 6
lo
I
I
I
E (kJ mol-1) I
16 I
12 l4
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-eGraphites +-Carbon Blacks
4
12
Coals
* 6
t
bD 0
m
,
0 0
16
l4 12
k
10
r
50
100
I
I
I
150
200
250
0
I
,
I
I
I
50
100
150
200
250
E (kJ mol-1)
E (kJ mol-1)
r
I
@
-e Graphites 4
Activated Carbons
-
8 -
6 4 2 01 0
I
50
,
100
I
1
150
200
I
250
E (kJ mol-1)
'
-7 0.04
, 0.05
, 0.06
0.07
0.08
I 0.09
slope
Figure 4. (a-e) Separate correlations for different types of carbon materials; (0 supercompensation plot.
and lowestE values for the whole set of materials correspond to peculiar solids that for their particularly high impurity content are suspicious of either catalytic or inhibitory effects. For instance, CM2 and CM3 subbituminous coals contain mineral matter which typically acts as a catalyst for coal combustion and gasification.9 Conversely, CA3 carbon black contains a nonnegligible amount of phos-
phorus (0.16 w t % ) , this element being well-known for its inhibiting effect in the reaction of carbon with oxygen.'5J6 In some cases, parallel lines are observed; for instance, A* values for activated carbons are systematically larger than for graphites at equal E values. Thus, although our results differ in some respects from the predictions from Essenhigh and Misra: their model
(15) Ehrburger,P. Protective Layers for Special Types of Composites. In CarbonFibers, Filaments and Composites;Figueiredo,J . L., Bernardo, C. A., Baker, R. T. K., Hdttinger, K. J., Eds.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1990; pp 327-336.
(16) McKee, D. W.Inhibition of Carbon Gasification.In Fundamental Issues in Controlof Carbon GcrsificationReactiuity;Lahaye, J.,Ehrburger, P.,Eds.;KluwerAcademicPublishers:Dordrecht,TheNetherlands, 1991; pp 483-514.
Energy & Fuels, Vol. 7, No. 6,1993 1145
Reaction of Carbon Materials with Oxygen
can be considered as valuable within each subset of carbonaceous solids. In other words, the ensemble of carbon materials could be regarded as a common basic type of material on which different types of structural, textural, catalytic, and inhibiting effects act in specific ways for the different groups of carbonaceous solids. This would lead to the above-mentioned Ylocal”fittings, which would be restricted to specific cases. All the above considerations can be summed up into a generalized view if, from a mechanistic point of view, the explanation given by Schwab3to the compensation effect in catalysts (based, in turn, on the active centers model of Taylor) is adapted to carbons using the graphite structure as a model. In a perfect basal plane of graphite, there is a large number of surface centers all of them with a high apparent activation energy. In a real graphite crystal there exist defects and impurities which will lower the activation energy for the C+Oz reaction. For statistical and thermodynamic reasons, as in the case of a typical catalyst surface, there should be more numerous centers with a decreasing energy. An increase in the number of active centers corresponds to a higher value of A*. At the same time, the lower the energy of the active centers, the higher the activation energy. It thus becomes clear why A* and E can vary in the same sense. On the other hand, the defects thus introduced in the structure will alter the normal vibration of graphitic planes, giving rise to phonons which are directly detectable by Raman spectroscopy. This agrees with our above-mentioned finding of correlation between values of E and Raman peak widths in the set of materials under study.1° One can thus conclude that occurrence of the compensation effect in carbon materials can be described by the same models previously developed for heterogeneous catalysts, provision being made to consider that in the former case carbon is the reaction substrate and acts, too, as a catalyst in the sense that structural defects constitute the active centers at the carbon surface. For the solids exhibiting E values higher than those for graphites, one must accept the prevalence of concurrent inhibiting effects (remember the above-cited effect of phosphorus in CA3 sample). Alternatively, if by a purposeful activation treatment the number of active centers at a carbon surface is increased with respect to that statistically or thermodynamically corresponding to the material, features such as the higher A* values for a given E observed when activated carbons are compared with graphites can be justified. The relative prevalence of all of these different reactivity-controlling factors in the various groups of carbon materials justifies why different slopes were found for the separate fittings in Figure 4a-e. Conversely, the overall mechanistic model justifies the finding of a single unique fit and also, probably, the supercompensation effect. The question as to whether the nonlinear nature of the fit can provide any further specific mechanistic insights remains to be elucidated.
limited sets of carbonaceous solids. An active-centers model based on graphite structure allows to explain the occurrence of compensation effect in carbon materials. Differences in behavior among carbons of different types can be justified by the relative prevalence of the various types of factors controlling the reactivity of these materials in oxygen.
Conclusion
Using this approach, and assuming that %TIE
