Determination of Emissivities with a Differential Sca nning Ca lo rimeter N. ROGERS
R.
and E. D. MORRIS, Jr.'
university of California, Los Alamos Scientific laboratory, P. 0. Box 1663, 10s Alamos, N. M.
Emissivity changes during a determination can cause large errors in heats of decomposition or transition, as determined using a Perkin-Elmer Differential Scanning Calorimeter. Methods for reducing or eliminating such errors are discussed, and a differential method for determining emissivity coefficients with the Differential Scanning Calorimeter is presented.
I
N ORDER TO MAKE MEASUREMENTS
with The Perkin-Elmer Corp. Differential Scanning Calorimeter, Model DSC-1 (4, 6 ) , it is necessary to integrate under heat-effect curves with reference to the assumed position of a base line. The base line represents the null position of the instrument with no thermally active reaction taking place. Because there are nonlinearities in the instrument, the base line is not absolutely straight; but the line should be reproducible in contour and position. Inaccuracies were observed in the use of the instrument that have been traced to the fact that the base line does not remain constant. The base line is a sensitive function of sample handling and of experimental arrangement. Unencapsulated samples require a different zero setting on the instrument than do encapsulated samples, and different unencapsulated samples require different zero settings. Changes in the pan covers (metal covers that fit over the pan support, not to be confused with the lids used on the sample containers for encapsulation) also require different zero settings. These variations can make it difficult or impossible to balance the instrument before starting a measurement. Far more disturbing variations in the base line are observed during a run that involves a decomposition reaction. Extremely large discontinuities in the base line can be seen; the instrument zero setting is different after decomposition than it was before. The contour of the base line during the decomposition reaction cannot be determined; therefore, it is impossible to integrate the curve with any confidence. 1 Present address: University of California, Berkeley, Calif.
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ANALYTICAL CHEMISTRY
The above discrepancies indicate a relatively large effect that can be caused only by differences and/or variations in thermal emission. Calculations according to the Stefan-Boltemann equation show that radiant energy fluxes on the order of several millicalories per second can be expected throughout the temperature range of the DSC-1-e.g., energy can be lost from the 0.3167-~m.~ sample pan a t a rate of calory per second a t 400' K.-more than a full-scale signal on the three lowest ranges of the instrument. The magnitude of the calculated thermal fluxes indicated that it should be possible to determine emissivity coefficients, using known ref-
erence surfaces. Experimental work has indeed proved that excellent measurements of emissivities can be made. Emissivity has been mentioned as a cause for the displacement of the base line in DTA work (6),but no general quantitative study of the phenomenon has been made. Variations in radiative and convective heat transfer have been recognized as potential sources of error in attempting to use conventional DTA apparatus for calorimetric measurements, but the difficulties they cause in differential scanning calorimetry were not mentioned (4). Steps have been taken in the design of DTA equipment to preclude the possibility of radiant heating hot spots as a result of
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6
0.0010
W
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0
0
0.0005
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0.2
0.4
0.6
NET EMISSIVITY Figure 1.
Effect of temperature and net emissivity on the correction
0.8
thermal gradients in the vicinity of furnace windings, indicating that emissivity problems were considered (2). However, DTA equipment has not been used for the determination of thermal emissivities. EXPERIMENTAL
Apparatus. A Perkin-Elmer Corp. Differential Scanning Calorimeter, Model DSC-1, is used for the determinations. The cell compartment cover must be replaced by a cover providing temperature control of the surfaces t h a t face the pan supports. A suitable temperature-controlled cover can be made by modifying the lowtemperature cover furnished by Perkin-Elmer, as follows: remove the formed plastic insulator on the inside of the cover, polish this interior surface, and paint it with optical black paint; inside the Dewar compartment of the cover, fit an aluminum block large enough to slip over the compartment cover for a distance of approximately l/g inch; and drill holes in the block for a cartridge heater and for control and readout thermocouples. Procedure for the Determination of Emissivities. C u t a 1/4-inch disk from t h e sample material, and place it in the standard aluminum sample pan as furnished with the instrument. Place a reference disk of aluminum foil in a sample pan on each pan support, cover t h e assembly, and balance t h e instrument. Replace the reference disk and pan in the sample pan support with the sample in its pan. D o not change the balance setting of the instrument. Cover the assembly with the temperature-controlled compartment cover, and adjust the temperature of the cover t o the temperature of the sample-i.e., the temperature a t which the emissivity is to be determined. Read the energy difference between reference and sample. Remove the temperature control block from the Dewar chamber of the cover, fill the chamber with crushed ice and distilled water, and rebalance the instrument with two reference foils. Reread the difference in energy between reference and sample. Do not change the temperature of the sample between these two sets of readings. The first reading combines all corrections for differences in the characteristics of the two real surfaces being studied. The nature and magnitude of the correction, functions of temperature and net emissivity, are shown in Figure 1. The second reading measures differential emission between the two surfaces. The emissivity coefficient is calculated as follows: En
=
S(C
+ RJ + R , Tlr
where en = total normal emissivity a t the specified temperature; S = sensitivity factor for the instrument and recorder for the range setting used in the measurement, cal./cm. second;
C = result from correction run, in cm. of recorder deflection; R, = result from second run, in cm. of recorder deflection; R, = emission of reference surface in cal./second at the speci0.00036 cal./ fied temperature-e.g., second for a 0.3167 sq. cm. aluminum foil reference at 400’ K.; and W = emission of a black body at the specified temperature. Note that all emissions must be adjusted to the same surface area, and all apply to the specified temperature only. RESULTS A N D DISCUSSION
There are extremely large differences between different sets of emissivity data in the literature. This is due to the fact that surface characteristics, particularly those that determine emissivity, are extremely difficult to specify, Disagreements may usually be attributed to the use of adjectives such as “polished,” “thick,” “fresh,” “oxidized,” etc. To demonstrate the feasibility of the present method, materials were selected for which the greatest number of data were available, or for which literature agreement seemed to be best, and for which surface conditions were specified in greatest detail. Results are shown in Table I. The literature values for emissivities of aluminum oxide coatings quoted in the table are those that the authors of the compilations designated “best values,” but the emissivity of aluminum oxide coatings varied considerably with methods of preparation (see Figure 26, p. 2i7, of Reference 3 ) . We believe that the data demonstrate the feasibility of measuring emissivities with the DSC-1. The DSC method for determining emissivities has several unique advantages: i t requires an extremely small sample, it can be used as a ‘hullJJ method to compare the emissivities of two surfaces, it is very rapid, and i t requires little skill. Calculations of the net emission of the sample/reference system were quite successful when both surfaces were metals or nonmetals with similar emis-
Table 1.
PI w
1, I
2c
I10
I15
120
125
135
I30
OC.
Figure 2. Effect of operating conditions on deviations caused by thermal emission. a.
b. c.
Benzoic acid in open sample pan Benzoic acid in open sample pan, cover maintained a t 1 2 0 ’ C. during run Benzoic acid in open romple pan, reference and sample pan supports covered by polished gold pan covers
sivities; however, widely different surfaces could not be handled satisfactorily. Calculations are difficult because absorbance is dependent on the spectral distribution of radiant energy in the system (hence, the black paint inside the cover) and because emissivity is directionally dependent on the nature of the surface (a thick film emitting most of its energy in a direction normal to the surface, but a thin film or metal emitting best a t a low angle). The empirical cor-
Total Thermal Emissivities as Measured by Perkin-Elmer DSC-1
Surface Found Lead, rolled surface as received 0.069 Brass, rolled surface as received 0,095 Copper, polished on 600 grit 0.038 Molybdenum 0.07 Monel, smooth, not polished 0.13 Aluminum, 0.25-micron electrolytic oxide 0.11 Aluminum, 0.35-micron electrolytic oxide 0.12 Aluminum, 0.5-micron electrolytic oxide 0.20 Aluminum, 0.65-micron electrolytic oxide 0.27 Aluminum, 1. 0-micron electrolytic oxide 0.41 Aluminum, 3.0-micron electrolytic oxide 0.63 Aluminiim, 5.0-micron electrolytic oxide 0.60 Aluminum, 7.0-micron electrolytic oxide 0.62 Black optical paint 0.98 Literature (1,3 ) values are for a “polished” surface.
Literature ( 1 , 3 ) 0.057 0.07” 0.03-0.04 0.07 0.16 0.06 0.09
0.11 ... 0.30
0.70 0.70
0.75 0.98
VOL. 38, NO. 3, MARCH 1 9 6 6
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rection specified in the procedure (sample, reference, and cover at the same temperature) provides a direct measurement of the deviations from ideality in the system. It should be emphasized that emissivity data should not be judged too harshly; complete agreement with published values is impossible. Impurities, surface roughness, and extremely thin coatings have a profound effect on the radiation properties of surfaces. Measurements apply only to a specific surface at a specific temperature. Emissivity changes in the sample or sample container during a run can easily cause the DSC-1 signal to run off scale. A solid nonmetal] melting in an open sample container, changes emissivity to such an extent that measurement is impossible. Figure 2a shows an example of the deviation in the recorded curve that is observed in such a transition. Even worse deviations are observed when a sample melts, exudes onto the top of the covered sample container, and then chars. The metal capsule has a very low emissivity; the melt-oozing out over the top-has a high emissivity,
and its effective area is changing as a function of time; the charred material has a very high emissivity. Fortunately, simple procedural changes eliminate the errors. Two methods can be used effectively: covering the pan supports with highly polished inert metal covers, or programming the temperature of the compartment cover at the same temperature and rate as the sample/reference system, A variant on the second method is to control the temperature of the cover a t the same temperature as that of an expected transition. The first method is simple and completely effective. Aluminum pan covers with a small central hole mere originally supplied by Perkin-Elmer for the DSC-1, but production was discontinued. Polished gold pan covers without a central hole seem to be best. Figure 2b shows the effect of maintaining the temperature of the compartment cover a t the temperature of the transition. Figure 2c shows an example of the effect of using gold pan covers; this curve could be integrated with complete confidence.
ACKNOWLEDGMENT
The authors thank A. G. Fox of this laboratory for preparing the anodized aluminum surfaces. LITERATURE CITED
(1) American Institute of Physics Hand-
book, D. E. Gray, ed., 2nd ed., Section 6, McGraw-Hill, New York, 1963. (2) Barrall, E. M.,11, Porter, R. S., Johnson, J. I?., ANAL. CHEM.36, 2172 (1964). > - -
- - I
( 3 ) Gubareff, G. G., Janssen, J. E., Torborg, R. H., “Thermal Radiation Properties Survey, Honeywell Research Center, Minneapolis-Honeywell Regulator Co., Minneapolis, Minn., 1960.
( 4 ) O’Neill, M. J., ANAL. CHEM. 36,
1238 (1964). (5) Smothers, W. J., Chiang, Y., “Differential Thermal Analysis: Theory and Practice,” Chemical Publ. Co., New York, 1958. (6) Watson, E . S., O’Neill, M. J., Justin, J., Brenner, N., ANAL. CHEM. 36, 1233 (1964). RECEIVED for review September 20, 1965. Accepted December 29, 1965. This work was performed under the auspices of the U. S. Atomic Energy Commission.
On Estimating Activation Energies with a Differential Scanning Calorimeter R. N. ROGERS and
E.
D. MORRIS, Jr.’
University of California, los Alamos Scienfific laboratory,
A Differential Scanning Calorimeter indicates the heat effect of a reaction as a function of the absolute temperature. These data can be used for calculations of rate constants and activation energies. A method is presented for estimating the activation energy of a decomposition reaction using an extremely small, unweighed sample.
T
or evolution of heat during a transition or a reaction is measured directly in terms of calories per second as a function of the absolute temperature with a PerkinElmer Corp. Differential Scanning Calorimeter, Model DSC-1 (9, 16). This form of data presentation is ideal for studies of reaction kinetics. Three completely different methods have been proposed for using conventional DTA equipment for the determination of kinetics parameters (2, 6 , 10, 15). A critical review of the two dynamic methods has recently appeared in the literature (11). I n the dynamic methods it is tacitly assumed HE RATE OF ABSORPTION
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ANALYTICAL CHEMISTRY
P.
0. Box 7 663, 10s Alamos, New Mexico
that all thermal parameters pertaining to the cell system remain constant with temperature. Barrall has shown that nonlinear DTA sensitivity can be quite important (1). The isothermal method (10) is not as convenient, because it requires multiple determinations for the calculation of an activation energy, a disadvantage it shares with the Kissinger D T A method ( 5 ) . It has also been shown that the Kissinger method is based upon somewhat erroneous assumptions and theoretical development (11).
Krein has published an excellent review on the application of thermal methods to the study of explosives (6). H e gives several data for activation energies of explosives determined by D T l l and more conventional methods, and he discusses possible sources of the error observed in the DTA method. Krein also concludes that the DTA method is not applicable to calorimetric measurements. If accurate calorimetric measurements cannot be made by use of DTA apparatus, reliable results for kinetics parameters should not be expected.
The design of an energy proportioning differential scanning calorimeter (9, 16) largely obviates difficulties inherent in conventional DTA apparatus. If sample size, heat of reaction, and heat evolution rate are known, the rate constant a t any temperature can be calculated. .4n Arrhenius plot of the data can be made, and the activation energy of the reaction can be determined from the slope of the line. Such an approach is extremely simple and, with the DSC-1, permits studies of decomposition kinetics with samples as small as a few tenths of a milligram. Data from the DSC-1 are in the form of distances between the reaction curve and a baseline a t the associated absolute temperature. The distance measured is proportional to the rate of heat evolution or absorption and is, therefore, proportional to the rate constant. Provided that the Arrhenius plot is a straight line, the activation energy can be calculated from the expression 1 Present address, Department of Chemistry] University of California, Berkeley, Calif.
