termined purity of the commercially available dye. However, the actual measurement of the correct barium-to-MTB ratio, by constructing calibration curves using various ratios, is preferred because of possible impact of the presence of absorbing impurities during the spectrophotometric determination. Table I shows typical results obtained with the modified MTB procedure for determination of sulfate. For these, the instrument was calibrated independently with standard solutions, and slope and intercept of the calibration curve were determined by the linear least squares equation. The relative standard deviation for replicate standards was found to be between 0.4-1.4%. The sensitivity for this range (0 to 100 bg/ml) was found to be equal to about 4 pg/ml. Higher or lower sensitivities may be obtained by modifying the flow diagram of the Technicon AutoAnalyzer as described above. In our laboratory, we were able to obtain sensitivities of 0.5 pg/ml in a range up to 10 pg/ml by such modifications. Even with this sensitive range, the calibration curves remain linear when the MTB reagent is prepared using the weight of MTB dye calculated from the results of the linearity study.
Both the high (0-100 bg/ml) and low (0.5-10 fig/ml) ranges are used in our laboratory routinely for determination of sulfate, and the results obtained are always comparable to those described here.
LITERATURE CITED (1) A. L. Lazrus, K. C. Hill, and J. P. Lodge, “Automation in Analytiwl Chemistry, Technicon Symposia, 1965”, Mediad, 1966, pp 291-293. (2) Technicon Industrial Method No. 118-71 W/tentative, Technicon Industrial Systems, Tarrytown, N.Y., 1972. (3)T. Yamane, “Statistics, An introductory Analysis”, Harper and Row, New York, 1967, pp 340, 419-423. (4) T. Yoshino, H. Imada, S. Murakami, and M. Kagewa, Talanta, 21, 211 (1974). (5) V. N. Tikonov. Zh., Anal. Kbim., 22, 658 (1967). (6)0.A. Tataev, S. A. Akhavedov, and B. A. Magomeclova, Zh. Anal. Khim. 25, 1229 (1970). (7) T. Yoshino, H. Imada, M. Kagewa, and K. Iwasa, Talanta, 16, 151 (1969).
RECEIVEDfor review December 3, 1975. Accepted July 8, 1976.
Application of Thermal Analytical Methods in the Characterization of Carbonaceous Materials Ralph T. Yang,” Meyer Steinberg, and Robert Smol Department of Applied Science, Brookhaven National Laboratory, Upton, N. Y. 11973
Thermal analytical methods are applied to a study of the reactivities toward O2 and COPof three kinds of carbonaceous materials which give different rate expressions with respect to the fractional completlon of the reaction. It Is demonstrated that a pseudo-third-order reaction can give a bifurcated peak in the DTA curve and, therefore, the notion of the existence of two kinds of carbonaceous materials based on a bifurcated peak, as has often appeared in the literature, should be asserted with caution.
The thrust of developing more efficient energy systems from coal has renewed a great interest in the application of thermal analytical methods to the study of reactivities of carbonaceous materials toward gases. In the field of catalysis, meanwhile, the employment of differential thermal analysis (DTA) to examine the catalysts poisoned by carbonaceous materials deposited on the surface has attracted wide attention and application. More specifically, in the studies by Rode and Balandin ( I , 2 ) on the nature of the carbonaceous deposits on chromia catalyst, the DTA curve produced by combustion of the deposits showed bifurcation, or two peaks, of the exothermic peak in some instances. The authors interpreted this as an indication of two types of carbonaceous materials on the surface. Thereafter, a bifurcated peak in the DTA curve has been quite commonly related to the notion of the existence of two kinds of carbonaceous materials ( 3 , 4 ) .Furthermore, it has been suggested that, by matching with a synthesized bifurcated DTA peak of a standard reference mixture consisting of two known carbonaceous materials, an unknown carbonaceous material could be analyzed quantitatively (5). In this work, thermal analytical methods are used to study the reactivities of three widely different carbonaceous materials. The quantitative relationship between a single DTA 1696
curve and the kinetic parameters for a “first-order” heterogeneous reaction has been previously developed (6). The qualitative relationship between the general form of the rate expression and the shape of its corresponding DTA curve is examined in this study for two higher-order gas-carbon reactions. More importantly, it will be shown that a pseudothird-order reaction can also produce a bifurcated peak in the DTA curve. Therefore, caution must be taken in relating such a peak to the existence of two kinds of carbonaceous materials.
KINETIC ANALYSES OF DTA CURVES Extraction of kinetic information from DTA curves is, in general, limited to reactions with simple rate expressions (6, 7). For reactions with more complicated rate expressions, the approximate methods outlined by Kissinger (8) and by Yang and Steinberg (6) can also be applied; but the results would be lengthy and the mathematics tedious, and therefore such analyses would not be of practical interest. In this section, it is not intended to extract the kinetic parameters from a DTA curve. Rather, the qualitative relationship between the rate expression and the general shape of the DTA curve is to be explored. More specifically, the possible number of peaks in a DTA curve will be predicted from the order of the reaction. The rate of a heterogeneous reaction is expressed in the conventional fashion:
where rn is the instantaneous mass of the reacting solid and t is the time. The rate of a gas-carbon reaction at steady state, or a t constant burnoff ( x ) is normally expressed as a function of the concentrations of the gases involved. However, in the DTA
ANALYTICAL CHEMISTRY, VOL. 48, NO. 12, OCTOBER 1976
measurements the gas concentrations are held constant, the rate is expressed in terms of x, and it can be shown that 1 drn m dt
1 dx 1 - x dt
In this work, the order of a reaction will be expressed in terms of the following form:
where n is the order, ro the frequency factor, E the activation energy, R the gas constant and T the absolute temperature. Now we consider three general types of gas-solid reactions having individually the following characteristics: (1) the rate is independent of x; (2) the rate increases or decreases linearly with x and (3) a rate maximum or minimum exists in the curve of r with x. The corresponding general rate equations are:
dx dt
- = r2e-E/RT(1 - x)(x + I )
Figure 1. Number of solutions for Equations 8-10
(5)
dx - x ) ( x 2 px n) (6) dt where 1, p , and n are constants. According to Equation 3, Type 1 is first order and Types 2 and 3 are referred to as pseudosecond and pseudo-third-order reactions, respectively. In DTA measurements, the temperature differential (AT) is recorded as a function of T . Assuming that the heat of reaction is detected instantaneously and that the thermal effect, either exothermic or endothermic, is dissipated to the flowing gas rapidly, AT is proportional to the mass rate, i.e., the total amount of mass being reacted per unit time, or to dxldt
there possibly exist three solutions for Equation 10. It is also possible that only one solution exists for Equation 10, depending on the constants in the equation. For the reaction with rate increasing monotonically with x, the characteristics of the graphical solution for Equation 9 in Figure 1should also apply, and hence also only one solution would be expected. From this analysis, it can be seen that only one peak is possible in the first-order and pseudo-second-orderreactions while two peaks, or a bifurcated peak, can occur for the pseudo-thirdorder reaction.
(7) The above assumptions are not unrealistic in the gas-carbon reactions in which diffusion is not the rate-controlling step and the reactions proceed uniformly throughout the sample. By substituting the approximate expression for dxldt for the three types of reactions in Equation 7, and setting d(AT)ldt = 0, the following relations are obtained:
A Mettler Differential Thermal Analyzer Model TA-1 was used to obtain the DI'A curves. Reaction rates were measured gravimetrically (TG) and were expressed according to Equation 1. The carbon samples used were: coke from Illinois No. 6 bituminous coal (coked a t 1000 "C for about 20 h in flowing Nz);electrode graphite and a reactor-grade nuclear graphite. The nuclear graphite had less than 100 ppm ash content and more analyses have been given elsewhere (6). The coke gave the following analyses: ash content, 17%; SiOz, 10%;Fe, 1.8%;A1203,2.5%;and the balance of Ca, Mg, and Ti, etc. Analyses of the electrode graphite yielded: ash content, 2.7%; 1% Si; 0.1%B and Cu each; 0.03%Fe, Ni, Ag, and Ca each; 0.01%Mg, Al, Zn, and Mn each; and trace of Cr, Pb, and V. The elemental analyses were performed by emission spectroscopy. Carbon diaxide was supplied by Matheson Gas Products Company and was of Coleman Instrument grade (99.99%).The gas was further purified of moisture and 0 2 in a train of silica gel, Mg(C104)S (both a t room temperature) and copper turnings held a t 500 "C. The DTA measurements, involved dilution of the carbon sample in an inert material (A1203)which was also the reference. The dilution is necessary because of the high heat of reaction. Detailed procedures of the DTA and the rate measurements were given previously (9). It should be noted that a high gas flow rate was employed and that the thermocouples were placed a t the center of the sample which was contained in a platinum sample holder. Under these conditions, the assumptions made for Equation 7 are not unrealistic.
+ +
- = r,e-E/RT(I
AT = k(dx/dt)
E Cz 7= e-E/RT(ax + b ) RT E c3 -= e-E/RT(cx2 dx + f ) RT2 where C1, Cz, C3 are positive constants and a, b, c, d, and f are constants that can be either positive or negative. Equations 8-10 can be used to predict the peak temperatures of a DTA curve, provided that the functional form x ( T ) is known. The x ( T )function can be approximated in a way similar to that outlined for a first-order reaction (6).However, it is of interest in this study to predict the number of peaks in the DTA curve based on the three general rate expressions as shown. For this purpose, Equations 8-10 are consequently solved graphically. It may be recalled that x increases from 0 to 1with increasing T and assumes a fractional value which changes very slowly with T compared to the other two factors in the equations: 1/T2and exp (-EIRT). The equations are presented in graphical forms in Figure 1. The points of intersection of the curves representing the right-hand-side (RHS) and the left-hand-side (LHS) are the peak temperatures in a DTA curve. From Figure 1,it is clear that there is only one possible solution for Equation 8 or Equation 9, and
+
EXPERIMENTAL
RESULTS AND DISCUSSION The temperature range and the other experimental conditions were chosen such that the overall reaction rates were dominated by the chemical rates. It has been demonstrated that the oxidation of carbons by air in the 500-600 "C range (10)and the oxidation of nuclear graphite by COz a t 1050 "C (6) are all in the chemical-controlled rate regime. In this regime, the rates of the diffusional steps are high compared to the chemical rates and the observed overall rates can be approximated as the chemical rates. The following carbonaceous materials were used in this work, in the order of decreasing reactivities: coke, electrode
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NO. 12, OCTOBER 1976
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I
I
I
10
I
I
I
1
I
,280
20 30 CARBON BURN-OFF,%
I/ k0
Figure 4. BET surface area (N2, 77 K) vs. burn-off
0.0 I
(a) Coke. (b) Electrode graphite. (c) Nuclear graphite I I I I
CARBON BURN-OFF, %
OO
Figure 2. Dependence of oxidation rate of carbon on percentage burn-off
(Top) Coke in air at 525 OC. (Middle) Electrode graphite in air at 600 OC. (Bottom) Nuclear graphite in COPat 1050 OC
ze(deg)
I
I
1
I
I
I
300
400
500
600
700
800
1
.
900
I
1000
1
1100
I
I
1200
1300
Figure 5. X-ray diffractograms of coke at (top) 0% burn-off and (bottom) 31.8% burn-off, copper K a radiation
,
1400
TEMPERATURE.OC
Figure 3. DTA curves
(a) Coke in air. (b) Coke (with 40% burn-off in air at 525 OC) in air. (c) Electrode graphite in air. (d) Nuclear graphite in COn
graphite, and nuclear graphite. Reaction rates were measured on the first two materials with air and on the nuclear graphite with COZ. These three gas-solid reactions demonstrated the general behavior of the three types of reactions which were analyzed above. Some typical results are shown in Figure 2, a t the specified temperatures. The reactions with nuclear graphite and with coke can be represented by rate expressions of the first- and pseudo-third-order types respectively. The rate with the electrode graphite does not increase linearly with burn-off, while i t does increase monotonically. According to the preceding analysis, the reaction with the nuclear and the electrode graphites would give only one peak while the reaction with coke could give two peaks or a bifurcated peak in their corresponding DTA curves. Such predicted behavior was verified by the measured DTA curves; and they are shown in Figure 3. In this figure, three exotherms (C 0 2 ) and one endotherm (C COz) are shown. An interesting feature in this figure is that the reaction with coke with 0% burn-off showed a bifurcated peak while the coke with 40% previous carbon burn-off showed a single peak. This is due to the fact that the
+
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+
rate of the reaction decreases monotonically after 40% burnoff, as shown in Figure 2. The reaction with the coke that has 40% burn-off can be categorized as a pseudo-second-order reaction and, hence, can produce only one peak in the DTA curve. Although it is not intended in this work to study the factors involved in determining the reactivities of the various carbonaceous materials, it is illustrative to study the specific rates, or the rates per unit reacting surface area. The total surface area of the materials was measured a t various carbon burn-offs and the results are shown in Figure 4.From the data in Figures 2 and 4,the specific rates of the reactions with the two graphites were nearly constant with increasing burn-off. The specific rate of the coke was also nearly constant below about 309/0carbon burn-off but decreased monotonically upon further increasing burn-off. The decrease may be due to two factors: (1)the increasing surface area of the mineral matters and (2) a possible decrease of the concentration of the active sites on the carbon surface which predominantly contribute to the rates ( I I , 1 2 ) . T o further examine the possibility of the existence of two kinds of carbons, x-ray diffraction patterns were obtained of the coke samples a t various burn-offs. In Figure 5 , the diffraction patterns of the coke a t 0%and a t 31.8%burn-off are shown. The peak at 20 = 26.5’ is due to the (002) planes of the graphitic structure in the crystallites. No difference can be detected between the patterns and therefore it is unlikely that “two kinds of carbons” exist. Based on the preceding kinetic analyses and the experimental results, one may conclude that a bifurcated peak, or two peaks, in the DTA curve does not provide a sufficient
ANALYTICAL CHEMISTRY, VOL. 48, NO. 12, OCTOBER 1976
condition for the existence of two kinds of carbonaceous materials. Furthermore, the same assertion should be valid in the application of DTA to the analyses of solid materials in general.
ACKNOWLEDGMENT The authors acknowledge helpful discussions with G. Adler, C. R. Krishna, and D. J. Metz and a critical review by D. J. Metz. We also thank W. M. Reams for performing the x-ray diffraction analyses. LITERATURE CITED (1)T. V. Rode and A. A. Balandin, J. Gen. Chem. USSR. (Engl. Trans/.),28, 2937 (1958). (2)A. A. Balandin, froc. Second lnt. Gong. Cafal., Paris, 1135-1157, (1960). (3)T. Honda, T. Saito, and Y. Horiguchi, J. Carbon (Jpn), 72, 14 (1973).
(4)J. W. Hall and H. F. Rase, lnd. Eng. Chem., frocep Des. Dev., 2, 25 (1963). (5) D. J. Swaine, “Thermal Analysis”, R. F. Schwenker, Jr., and P. D. Garn, Ed., Academic Press, New York and London, 1969,Vol. 2,p 1377. (6)R. T. Yang and M. Steinberg, J. Phys. Chem., 80,965 (1976). (7)C.B. Murphy, Anal. Chem., 46,451 R (1974). (8)H. E. Kissinger, Anal. Chem., 29, 1702 (1957). (9)R. T. Yang and M. Steinberg, Carbon, 13,41 1 (1975). (IO) P. L. Walker, Jr., F. Rusinko, Jr., and L. G. Austin, Adv. Catab, 11, 133 (1959). (11) N. R . Laine, F. J. Vastola,and P. L. Walker, Jr., J. Phys. Chem., 67,2030 (1963). (12)P. L. Walker, Jr., and€. J. Hippo, Am. Chem. Soc., Div. FuelChem., frepr., 45-51 (1975).
RECEIVEDfor review March 15,1976. Accepted June 25,1976. This work was performed under the auspices of the Office of Molecular Sciences, Division of Physical Research, US.Energy Research and Development Administration,Washington, D.C.
Determination of Aluminum in Bulk iron Ore Samples by Neutron Activation Analysis Mihai Borsaru* and Ralph J. Holmes CSIRO Division of Mineral Physics, P.O. Box 124, Port Melbourne, Victoria 3207,Australia
Neutron activation analysis has been applied to the determination of aluminum in 25-kg iron ore samples at -6-mm particle slze. By measuring the thermal and epithermal neutron fluxes reflected by the samples durlng irradiatlon, an accuracy of better than 4~0.3% (95% confidence Intervals) was achieved for alumina concentrations between 1 and 6%. Ore samples should be dried to
