limited results reported here with a particular stripping reaction scheme must await further study.
ACKNOWLEDGMENT The authors thank Sudershan La1 for assisting in the survey of the medical research literature.
LITERATURE CITED (1) I. Sheka, I. Chaus, and T. Mityureva. "The Chemistry of Gallium," Elsevier Publishing Co. New York. N.Y.. 1966. (2)A. Dymov and A. Savostin, "The Analytical Chemistry of Gallium," Ann Arbor Science Publishers, Ann Arbor, Mich., 1970. (3)R. Zweidinger, L. Barnett, and C. Pitt, Anal. Chem., 45, 1564 (1973). (4)A. Ando and K. Hisada, Radioisotopes, 20, 171 (1971). (5)K. Deckner, P. Schomerus, G. Becker, G. Hornung, and C. G. Schmidt, Life Sci., I O , 1141 (1971). (6)J. Yoe and H. Koch, Jr., "Trace Analysis," John Wiley, New York, N.Y., 1957. (7)H. J. M. Bowen, lnt. J. Appl. Radiat. /sot., 5, 227 (1959). (8)V. W. Meloch and B. L. Beck, Anal. Chem., 28, 1890 (1956). (9)E. King, M. Mason, H. Messinger, and H. Dudley, Radiology, 59, 844 (1952). (10)D. Swartzendrubes, B. Bird, R. Hayes, B. Nelson, and R. Tyndall, J. Natl. Cancer hst., 44,695 (1970). 111) . , Y. Ito. S.Okuvama. K. Sato. K. Takahashi. T. Sato, and I. Kanno, RadiOlOgy, 100, 357 (1971). (12)M. Hart and R. H. Adamson, Proc. Natl. Acad. Sci. U.S.A., 68, 1623 (1971). (13)W. MacNevin and E. Moorhead, J. Am. Chem. Soc., 81,6382 (1959). (14)E. Moorhead and N. H. Furman, Anal. Chem., 32, 1507 (1960). (15)E. Moorhead and G. Frame II, Anal. Chem., 40,280 (1968). (16)E. Moorhead and G. Frame 11, J. Electroanal. Chem., 18, 197 (1968). (17)C. Stoll, G.M. Frame 11, and E. Moorhead, Anal. Lett., 1, 861 (1968). (18)E. Moorhead and P. H. Davis, Anal. Lett., in press. (19)E. Moorhead, J. Am. Chem. Soc., 87,2503 (1965). (20)E. Moorhead and P. H. Davis, Anal. Chem., 45, 2178 (1973),and references therein.
(21)E. Moorhead and P. H. Davis, Anal. Chem., 46, 1879 (1974). (22)K. W. Gardner and L. B. Rodgers, Anal. Chem., 25, 1393 (1953). (23)J. G.Nikelly and W. D. Cooke, Anal. Chem., 29,933 (1957). (24)W. Kemuia and 2. Kublik in "Advances in Analytical Chemistry and Instrumentation," Vol. 2,C. N. Reilley, Ed. Interscience, New York. N.Y., 1963,Chap. 3. (25)I. Shain in "Treatise on Analytical Chemistry," Part 1, Vol. 4, I. M. Kolthoff and P. J. Elving. Ed.. Interscience, New York, N.Y., 1963.
(26)E. Barendrecht in "Electroanalytical Chemistry-A Series of Advances," Vol. 2.,A. J. Bard, Ed., Marcel Dekker, New York, N.Y., 1968. (27)J. R. Delmastro and D. E. Smith, J. Electroanal. Chem., 9, 192 (1965). (28)J. R. Delmastro and D. E. Smith, Anal. Chem., 38, 169 (1966). (29)See also T. Biegler and H. Laitinen, Anal. Chem., 37, 572 (1965). (30)E. Moorhead and G. M. Frame, J. Phys. Chem., 72,3684 (1968). (31)R. de Levie, J. Electrochem. Soc.,118, 185C (1971). (32)Ya. Tur'yan and L. M. Makarova, Electrokhimiya, 9, 1334 (1973). I , Ph.0. dissertation, Rutgers University, New Brunswick, (33)G. M. Frame, N N.J., 1968. (34)W. Demerie, E. Timmerman, and F. Verbeek, Anal. Lett., 4, 247 (1971). (35)D. E. Smith in "Electroanalytical Chemistry-A Series of Advances," Vol. l.,A. J. Bard, Ed., Marcel Dekker, New York. N.Y., 1966. (36)H. L. Hung and D. E. Smith, J. Electroanal. Chem., 11, 237,425 (1966). (37)S.von Bergkampf. 2. Nektrochem., 38,847 (1932). (38)H. Fogg, Trans. Nectrochem. Soc., 86, 107 (1934). (39)0 . Steiling, 2. Elektrochem., 41, 712,779 (1935). (40)G. Challenger, Ph.D. dissertation, Harvard University, Cambridge, Mass.. 1945. (41)W. Saltman and N. Nachtrieb, J. Electrochem. Soc., 100, 126 (1953). (42)W. M. Spicer and H. W. Bartholomay, J. Am. Chem. Soc., 73, 868 (1951). (43)W. Reinmuth, Anal. Chem.. 33 185 (1961). (44)J. E. E. Randles, Trans. Faraday Soc., 44,327 (1948). (45)A. Sevcik, Collect. Czech. Chem. Commun., 13,349 (1948). (46)L. G. Sillen and A. E. Martell, "Stability Complexes of Metal Ion Complexes," The Chemical Society, London, 1964. (47)I. P. Alimarin, A. H. Sherif, and I. V. Puzdrenkova. Zh. Nauk. Khim., I O , 389 (1965). (48)J. Haladjian and G. Carpeni, J. Chem. Phys., 64, 1338 (1967). (49)W. Underkofler and I. Shain, Anal. Chem., 37,218 (1965).
RECEIVEDfor review September 16, 1974. Accepted December 23, 1974. We are grateful to the University of Kentucky Research Foundation for general support of this research and for funds to construct the polarograph/potentiostat. Gratitude is expressed also to the I.B.M., Corp. for grant funds to E.D.M. which enabled purchase of the PAR Model 174 potentiostat. Part of this work was supported by a grant from the National Institutes of Health, No. 1-R01GM-CA-20472-01 for which we are grateful. One of us (P.H.D.) thanks the University of Kentucky for University Fellowship support, and the I.B.M. Corp. for a 1974 summer research assistantship administered by the University of Kentucky.
Measurement of Exothermic Reactions by Differential Scanning Calorimetry M. J. O'Neill The Perkin-Elmer Corporation, Norwalk, CT 06856
An analysis is made of the differential and average heater power contributions during a thermal transition measured by differential scanning calorimetry (DSC). The true differential power measurement is uninfluenced by the average temperature control system, and DSC is applicable equally to exothermic and endothermic sample phenomena. The analysis is confirmed by experimental studies, including a partial-melting technique which allows the examination of freezing behavior without supercooling.
In the decade since DSC was first introduced for quantitative thermal analysis, the method has been widely accepted, and many literature references testify to its accuracy, convenience, and versatility. (1-3). There is, however, some confusion about the measurement principle on which the DSC method is based, particu630
* ANALYTICAL CHEMISTRY, VOL.
47, NO. 4, APRIL 1975
larly in the context of evaluating claims made by manufacturers of competing instruments. There is also some disagreement about the measurement of exothermic sample phenomena; it has even been suggested that exothermic reactions cannot be measured a t all with this technique ( 4 ) . I t is the purpose of this paper to examine the operation of the two temperature control systems characteristic of DSC instruments, to analyze their interaction, and to show that there is no particular distinction between the measurements of exothermic and endothermic reactions. This feature is a result of the symmetry of the differential power control system and its freedom from interference from the average temperature control system. A brief review of differential scanning calorimetry will be presented here. Two sample holders are mounted inside a constant-temperature enclosure. Each sample holder is equipped with a platinum resistance thermometer and a heating element. The sample holder temperatures are con-
tinuously measured and compared with each other and with an indicated temperature, Tp. The temperature differences are amplified and used to control the heaters so that the sample holder temperatures are almost equal to each other and to Tp, while the difference between the power requirements of the two heaters is measured and recorded. A differential power “base line” is recorded while Tp is programmed through the desired temperature interval. A sample material is then placed in one sample holder and the temperature program is repeated. The instantaneous thermal capacity of the sample is given by the indicated sample heat flow rate divided by the temperature program rate. Alternatively, the total heat absorbed or released by the sample during a transition is obtained by integration of the sample heat flow rate. Figure 1 shows a simplified block diagram of the differential temperature control system. W s and W R represent heat flow rates absorbed by the sample and reference materials, respectively. By convention, heat flow into the sample is considered to be positive, and causes an upscale deflection on the chart when viewed in the normal manner, with time increasing to the right. AT is the difference between the temperatures of the sample holders, and AWD represents the differential power generated by the heaters. RT is the incremental thermal resistance between each sample holder and its environment, and K is the amplifier gain in cal sec-’ K-l. Thermal capacities and thermal transport lags have been omitted from the block diagram, and thus the following analysis is valid only for steady-state and lowfrequency phenomena. The responses of AT and AWD to the signals W s and W Rare given by Equations 1 and 2:
The loop gain of the system is KRT, and it is seen that as
K becomes large, the influence of RT on system performance is diminished:
(3)
(4) Thus, the differential temperature approaches zero, and the indicated differential power, A W D ,approaches the true differential power absorbed by the sample and reference materials. In any variable-temperature calorimeter, RT is strongly temperature-dependent and tends to influence the ordinate calibration. Negative feedback of the differential temperature error counteracts this tendency, making the ordinate calibration independent of temperature. Similarly, it can be shown that negative feedback of the error between the indicated temperature, Tp, and the average temperature of the sample holders forces this average temperature to agree closely with the indicated temperature, regardless of the thermal losses to the environment. Thus, the sample holders may be represented by two controlled temperature sources a t the temperature Tp. It is very important to distinguish between the sample holder temperature, Tp, and the true sample and reference material temperatures, Ts and TR. The sample and ref’erence materials are each coupled to the sample holders through a thermal resistance which cannot be ignored in
Figure 1. Differential temperature
system
the analysis of sample behavior. This resistance, defined as Ro, is caused principally by the air gap between the sample pan and the sample holder, and typically has a value of 150 K sec cal-I. The true sample temperature may be obtained when necessary by calculating the temperature differential across R o required to produce the measured sample heat flow rate, and adding this temperature differential algebraically to Tp. In the preceding discussion, Tp has been referred to as the “indicated temperature.” In fact, the true average temperature of the sample holders can differ from the indicated temperature unless the temperature scale is calibrated with melting-point standards. It is assumed here that such a calibration procedure has been carried out. Summarizing, each sample holder may be represented by a thermal equivalent circuit consisting of a temperature source, Tp, which can be accurately and reproducibly varied, and a thermal resistance, Ro. In addition, a means is provided for measuring the true differential heat flow rate into or out of the sample and reference materials. Whether or not the sample temperature variation and the instantaneous sample heat flow rate during a transition can be analytically predicted depends entirely upon the thermal properties of the sample. In a few situations, the sample behavior is simple enough to allow experimental confirmation of the thermal equivalent circuit described above. In a previous paper ( 5 ) ,a sharp endothermic transition in a sample was analyzed and the influence of Ro on the temperature resolution of the transition was discussed. Here, a complete analysis of the interaction between the two temperature control systems in DSC will be presented, with the emphasis on measurement of exothermic sample behavior. An analysis of the measurement of a sharp exothermic transition will be presented, and it will be shown that the theory is confirmed by experimental data.
HEATER CONTROL CIRCUITRY Typically, the heat flow rate into a sample is several orders of magnitude less than the heat flow rate from the sample holders to the enclosure; in modern instruments, the minimum detectable heat flow rate is six orders of magnitude smaller than the sample holder losses at the temperature of interest. The precision and common mode rejection necessary in the heater control system are realized by time-sharing the heaters between two temperature control systems a t a switching frequency well beyond the measurement bandwidth of the calorimeter. In one heating mode, the heaters are driven in parallel at a high power level to provide the average power requirements of the sample holders, and every precaution is taken to minimize the generation of differential power. In the second mode, the heaters are driven a t a low power level, and are connected so that differential power can be generated and measured. In the differential power half-cycle, the sample and reference heaters are connected as shown in Figure 2 ( a ) . A constant-current source 210 drives the heaters in parallel, and a differential voltage source AV, proportional to AT, ANALYTICAL CHEMISTRY, VOL. 4 7 , NO. 4 , APRIL 1975
631
I
I
1
I
I
I
( b ) AVERAGE POWER ClRWlT
( a ) MFFERENTIAL P M R CIRCUIT
Flgure 2. Differential and average heater control circuits drives the heaters in series. Then the sample and reference heater powers in the differential mode are given by:
= Io2R, + IoAV
I
T
SAMPLE TEMPERATURE, T, -
i
~
_ _ ___
lime
+AV2
I
Rh
SAMPLE HOLDER TEMPERATURE, Tp
Thus each heater generates a “biasing power” Io‘Rh, a differential power component *IoAV, and an average power component Av2/Rh. The differential power is obtained by subtracting Equation 6 from Equation 5: AW’D = Lf’sD
(7 )
- WTRD = 210A\7
It will be observed that this differential power is independent of Rh, the heater resistance. Thus there is a linear relationship between AV and the true differential power. A voltage proportional t o A V is provided to a chart recorder, after attenuation and filtering. In the average power control half-cycle, the heaters are connected in parallel, as shown in Figure 2 ( b ) ,and driven by a voltage proportional to the difference between the indicated and true average temperatures of the sample holders. Assuming that the heater resistances are equal, the sample and reference heater powers in this mode are given by:
Thus, W Arepresents a steady-state average power, while A W Arepresents an incremental average power component related to sample behavior. I O and V in the above equations are effective values, equal to the true values multiplied by their respective duty cycles in the multiplexing sequence. We now assume that the sample holders are operating a t an elevated temperature, and that the heat flow rate from each sample holder is WT cal sec-l. Thermal transitions are then initiated in both samples, causing additional heat flow rates, W s and W R ,into the sample and reference materials. Four equations may then be written to describe the heat flow distribution: Heat supplied Aver age Sample
(E.,
Reference (ti’*
+
At{’*)
+
AW,)
Figure 3. Analysis of freezing transition sorbed by the sample and reference materials, and is unaffected by the behavior of the average power control system. I t will also be observed that exothermic phenomena on the sample side ( W S negative) cannot be distinguished from endothermic phenomena on the reference side ( WR positive). However, if there is no activity on the reference side, as is generally the case, no uncertainty exists. Equation 1 2 includes the steady-state conditions for the sample holders and the incremental behavior related to sample phenomena. Subtracting steady-state values from each side, and dividing by 2, we have:
or
Examining Equations 9, 10, and 14, it is seen that when the true differential power is small the average power increment AWA is one half of the total heat flow rate demanded by the sample and reference materials, supplied equally to the two sample holders, while the differential power increment ZoAV is one half of the differential heat flow rate, supplied differentially. When the differential power is large, the AV2/Rh term in Equations 9 and 10 represents an additional average power supplied to each sample holder, which must be counteracted by a further decrease in A W A ,as shown in Equation 14. When all heater contributions are added algebraically, the heat flow rate requirements of the sample and reference materials are exactly and independently satisfied. Heat lost
Differential
+ +
lo?Rh + IOAI‘ +
Losses
Sample Behavior
e)
= lvT
+
= WT
+
(9)
Rh
I,AV + *Ir2) (lo2R, -(21,A 1’)
WR
(10)
( W S- IVR)
(11)
+
(12)
Rh
Difference Sum
2(M7,
+
AI+’,)
+
2 Zo2Rh+ -
(
&RhI 7 ? )
Equation 11 shows that the indicated differential power 2ZOAV is equal to the true differential heat flow rate ab632
ANALYTICAL C H E M I S T R Y , VOL. 47, NO. 4, APRIL 1975
-
-
= 2u;.
+
(IVS
WR)
It is perhaps not clear how heat can be withdrawn from a sample when the only active element in contact with it is a
heater. The apparent paradox is explained by the fact that there is a steady flow of heat, W T ,from each sample holder to its surroundings, which must be supplied by the heaters. Heat flow out of the sample is accommodated simply by generating less power in the sample heater. The exothermic heat flow rate the instrument can absorb and measure is limited by saturation in the differential power circuit, when one heater is completely de-energized; the differential power is then equal to 4102Rh. Saturation effects are avoided by making 4102Rh very large compared with the differential power rating of the instrument. An analysis too lengthy to be included here shows that if the heater resistances are mismatched by a factor (1 y), the ordinate calibration will depart from perfect linearity by an amount of the order of y/4. In fact, heater resistances are matched within a fraction of 1%,and, thus, the effect may safely be ignored.
+
ANALYSIS OF A SHARP EXOTHERMIC TRANSITION We will now examine the freezing behavior of a very pure metal, a transition which is stable, reversible, and only somewhat complicated by the phenomenon of supercooling. The temperature of a partially-frozen metal is almost constant, and it is therefore possible to develop a simple expression for the heat flow rate out of the sample as a function of time, which can then be experimentally confirmed. This is an example of an “instrument-limited’’ analysis. There is a large category of exothermic reactions in which the sample behavior is irreversible or even regenerative, and in which temperature gradients within the sample must be taken into account. DSC measurements of such “sample-limited’’reactions have been described (6). It will be assumed that the thermal resistance of the sample is very small compared with Ro and, therefore, that temperature gradients within the sample are negligible. I t will be assumed also that the specific heats of the solid and liquid phases of the sample are equal. This assumption is valid for the sample material (indium) used in most of the experimental work to be described, but not for samples in general; however, the analysis may readily be modified to include the effect of specific heat variation. Figure 3 shows the sample and sample holder temperatures and the sample heat flow rate during the transition. Before the transition begins, there is a temperature lag proportional to the program rate Tp and to Cs, the total thermal capacity of the sample and the sample pan: AT, = T ,
-
T , = ROCST,
There is a steady heat flow rate to the transition:
Out
M’, = CsT,
Of
the
(15) prior
(le)
This heat flow rate appears as a base-line offset when a program is initiated, or as the ordinate displacement between base lines obtained with and without the sample and sample pan. The sample holder temperature Tp is decreasing, and therefore Tp, ATl,, and W S are all negative quantities. The sample passes through its true freezing temperature T F and then through a further temperature interval ATsc (defined as a positive quantity), before freezing begins. The subsequent behavior of the sample depends on the sample size and the degree of supercooling. I t is assumed here that the sample is large and that ATsc is relatively small; in this case a small fraction of the available heat of crystallization is sufficient to raise the entire sample and the sample pan to the freezing temperature, where it remains until the
sample is completely solidified. The rise in sample temperature is almost instantaneous. The heat flow rate into the sample from the sample holder is determined by the temperature differential across Ro, and can be separated into three components, as shown in Equation 17:
where t represents time, measured from the beginning of sample solidification. The first term is the original offset from the base line defined in Equation 16, shown as line segment AB on the heat flow diagram. The second term is the apparent initial heat flow rate out of the sample (line segment BC), and the third term is a linearly increasing heat flow rate caused by the increasing temperature differential across Ro. When the sample holder temperature has decreased by an interval ATF (defined as being a positive quantity), the sample is completely frozen, and its temperature decays exponentially to the original program with a time constant In the heat flow rate diagram, area ACDF represents the total heat released by the sample before its temperature starts to fall, which is the heat of crystallization less the heat required to raise the sample through the temperature interval ATsc a t the onset of freezing: AACDF = AH,
-
Cs4Tsc
(18)
Area ABEF represents the heat that the sample would have released while being programmed through the temperature interval ATP: AABEF = C , A T , Finally, area DEG is the heat released by the sample in cooling exponentially through the temperature interval (ATsc + ATF), after freezing completely:
Combining these areas appropriately, it is evident that the heat of crystallization is represented by the indicated peak area BCDG, including the exponential decay to the base line: ABCDG = AACDF - 4 A B E F
f
ADEG = A H ,
(21)
If there is no supercooling, the sample will begin to freeze a t the temperature T F (point H on the heat flow rate diagram), and a triangular crystallization peak will be observed, of exactly the same shape as the fusion peak for the same sample a t the same program rate. If the supercooling - interval i T s c is large, or the sample is small, the heat of crystallization will not raise the sample to the true freezing temperature, and a sharp heat flow rate pulse will be observed. Experimental work has been performed to confirm the theory developed above. Very large samples were used to obtain the trapezoidal exothermic peak shapes predicted, and to show that exothermic peak areas are equal to endothermic peak areas for a given sample transition. In a second set of experiments, a wide range of sample sizes was used to demonstrate the linearity and dynamic range of the DSC method in the measurement of exothermic sample behavior, and it was shown that the ordinate calibration was independent of the temperature program rate. An experiment was also performed to show that the ordinate calibration is insensitive to variations in the value of Ro, the thermal coupling resistance. Finally, a partialANALYTICAL CHEMISTRY, VOL. 47, NO. 4, APRIL 1975 * 633
429
5 -
.I0
431
433
MILLICALORES
$AMPLE W D E R TEMPEPATIX€. K
AH
i
fREElpwi
\
2 MINUTES -15
-
011
Flgure 4. Fusion and freezing of large indium sample
GI
'
'
"""'
'
31
'
""" ' '"'.',' ' '',,,,'' I0 10 IOC SAMPLE WEIGHT - MILLIGRAMS
'
"
"
1000
Figure 5. Variation of calorimetric response with sample size
melting procedure was used to demonstrate the symmetry and linearity of heat transfer between the sample holder and the sample.
EXPERIMENTAL Most of the experimental work to be described was done with a Perkin-Elmer Model DSC-2 Differential Scanning Calorimeter. This instrument operates over a wider temperature range, and provides more sensitivity and stability than the Model DSC-1B. However, the ordinate linearity investigation was performed on both instruments. The samples used were high-purity (99.999%) indium and lead. Sample weights were determined with a Perkin-Elmer Model AD2 Autobalance. All peak areas were measured with an Ott planimeter, using the average value of five successive readings for each peak. This technique was found to have a precision approaching 0.1% for the largest areas measured, and falling off to about 2% for the smallest areas. Absolute ordinate calibration was established using one of the largest samples of indium and a literature value (6.79 cal g-l) for its heat of fusion. The attenuator linearity is within 0.1% on the DSC-2, and within 0.25% on the DSC-1B; no attempt was made to correct the data for attenuator errors.
RESULTS AND DISCUSSION Freezing with Supercooling. A 206.7-mg indium sample was melted on the Model DSC-2 a t a program rate of 1.25 K min-I, then cooled a t the same rate to observe its freezing behavior. The two analyses are shown together in Figure 4. For clarity, the melting and freezing base lines have been aligned in the figure, but the peaks were, in fact, so large that it was necessary to use the recorder zero control to displace the base line between analyses. The maximum endothermic heat flow rate was 16.1 mcal sec-', or about 80% of full scale (Range 20), and the maximum exothermic heat flow rate was 17.8 mcal sec-I, or 89% of full scale. The total heat of fusion was 1.403 calories, and Cs, the thermal capacity of the sample and sample pan, was determined to be 0.018 cal K-l. The abscissa scale was calibrated by extrapolating the leading edge of the fusion peak down to the base line and taking a literature value (429.76 K) for the melting temperature of indium. A correction of 0.07 K was made for the calculated dynamic sample temperature lag RoCsTp. The error between the indicated and true temperatures was measured, and a true temperature scale was then constructed for the exothermic analysis. The exothermic peak shape is trapezoidal as predicted. By extrapolation of the sloping portion of the peak back to the base line, it was determined that the supercooling interval was approximately 1.3 K. 634
ANALYTICAL CHEMISTRY, VOL. 47, NO. 4, APRIL 1975
The exponential decay of the trailing edge exhibits a larger time constant than predicted by the theory; this effect is due to the low-pass filtering in the ordinate readout circuit of the instrument. Filtering effects are also apparent a t the leading edge of the peak. Low-pass filtering causes some distortion of rapidly changing ordinate data, but has no effect on integrated area measurements. The area of the fusion peak, measured as described earlier, is 1046.2 planimeter units, with a standard deviation of 0.8 unit, while the crystallization peak has an area of 1046.6 units, with a standard deviation of 0.5 unit. For each measurement, the standard deviation is less than 0.1% of the peak area. The ratio of these two areas is given by: Exothermic area 1046*6 - 1.00038 Endothermic a r e a 1046.2 The limiting error in this calculation is the uncertainty in drawing the base line for the shorter of the two peaks. The fusion peak has a height of 18.7 cm, and it is estimated that the base line uncertainty is 0.05 cm, or 0.3% of the peak height. Clearly, therefore, the two peak areas are equal to within the experimental error. Sample Size Variation. T o determine the linearity of the instrumental response to exothermic phenomena, thirteen samples of indium, varying in weight from 0.0605 to 206.7 mg, were analyzed on the Model DSC-2. All samples were programmed a t 1.25 K min-I except the largest one, which was programmed at 0.625 K min-l. Table I shows the relationship between the sample weight and the measured exothermic peak area. The first three columns show the sample weight, the attenuator setting used, and the chart speed. The fourth column shows the numerical factor used to correct all peak areas to a standard set of operating conditions (Range 1, chart speed 160 mm min-l). The fifth and sixth columns show the measured and corrected peak areas, in planimeter units. The seventh column shows the area/weight ratio, and the last column shows this ratio normalized with respect to the largest sample. Figure 5 shows these data in graphical form, demonstrating the linearity of the exothermic measurement over a range of almost four orders of magnitude. The experiment was repeated on the Model DSC-lB, using a group of lead samples, freezing a t 600.58 K. The samples varied in weight from 0.9956 to 309.6 mg, and a
Table I. Freezing of Indium on the Model DSC-2 Sample weight, mg
rihttenuator settinri
1 1
0.0605 0.0925 0.3128 0.5714 0.9493 2.901 7.944 10.48 30.19 63.60 100.85 168.3 206.7 __ ~
~
-
1 2 5 10 20 20 20 20 20 20 20 ~
Chart speed, mm/min
160 160 160 160 160 160 160 160 80 80 80 40 40
Factor
1 1 1 2 5 10 20 20 40 40 40 80 80
Areal weight,
Measured
Corrected
area
area
Areaiweiqht
normalized
25 37 124 116 76 118 160 213 306 642 1,023 854 1,043
25 37 124 232 380 1,180 3,200 4,260 12,240 25,680 40,920 68,320 83,440
413.22 400 .OO 396.42 406.02 400 -29 406.76 402.82 406.49 405.43 403.77 405.75 405.94 403.68
1.024 0.991 0.982 1.006 0.992 1.008 0.998 1.007 1.004 1.ooo 1.005 1.006 1.ooo
__~ ___ _
-
Table 11. Freezing of Lead on the Model DSC-1B Sample wriqlit, mij
Attenuator setting
Chart speed, nim ' m i n
Factor
0.9956 3.444 9.778 29.06 103.28 210.2 309.6
4 8 8 16 32 32 32
80 80 80 80 40 40 40
2 2 4 16 16 16
1
program rate of 0.625 K min-' was used. The largest sample had a heat of fusion of 1.703 calories. Table I1 shows the results of this experiment, arranged as in Table I, and demonstrates the linearity of the Model DSC- 1B for exothermic measurements in the somewhat smaller dynamic range for which this instrument was designed. P r o g r a m R a t e Variation. T o determine the influence of the program rate on the exothermic response of the Model DSC-2, an indium sample weighing 10.48 mg was frozen a t all program rates up to 40 K min-'. (For this particular sample, the maximum exothermic heat flow rate at faster program rates exceeded the 20 mcal sec-l measurement capability of the instrument.) Table I11 shows the results of this experiment; the first and second columns show the program rate and the exothermic peak area in planimeter units, and the third column shows the peak area normalized with respect to the area measured a t the slowest program rate. There is clearly no systematic dependence of the peak area upon the program rate. Influence of T h e r m a l Source Resistance. In a previous paper ( 5 ) , it was stated that calorimetric accuracy in DSC is not affected by the value of Ro, the thermal resistance through which all heat transfer to a sample takes place, provided that the sample is properly enclosed in the sample holder. Clearly, DSC would never have been accepted as it has been for quantitative thermal analysis if this claim were invalid, since small changes in Ro inevitably occur whenever samples are removed and replaced, or when different kinds of sample pans are used. To demonstrate that ordinate accuracy is indeed insensitive to Ro, a very large exothermic transition was measured on the Model DSC-2, with and without a disc of aluminum oxide cloth placed between the sample and the sample holder. The alumina cloth (Union Carbide Corp., type AL15),had an uncompressed thickness of 0.015 inch, and had
Measured area
Corrected area
Arealweight
44 75 2 14 3 12 279
44 150 428 1,248 4,464 9,152 13,584
44.19 43.55 43.77 42.95 43.22 43.54 43.88
572 849
Area .\eiqht, nom allied
1.007 0.992 0.997 0.979 0.985 0.992
1.ooo
-
Table 111. Effect of Program Rate on Ordinate Calibration Program r a t e , K/min
Area
A r a a , normalized
0.3125 0.625 1.25 2.5 5 10 20 40
225 .O 222.8 222.0 224.6 225.8 225.2 228.2 223.2
1.ooo 0.990 0.987 0.998 1.004 1.001 1.014 0.992
a density of 0.35 g cmP3, which is about 9% of the density of pure alumina. Figure 6 shows the freezing of a 206.7-mg indium sample a t a program rate of 0.625 K min-l, with and without the alumina disc. The Ro values are 480 and 130 K sec cal-', respectively, and thus the alumina increases Ro by a factor of 3.7. Measured as described previously, the two peak areas are 1043.2 and 1041.4 planimeter units, respectively, and the area ratio is given by: A r e a with large R , - ~0.998 - 1041'4 A r e a with n o r m a l R , 1043.2 Clearly, the effect of even this large change in Ro is smaller than the experimental error. Freezing without Supercooling. If a sample is partially melted and then cooled through its freezing point, there can be no supercooling (7). Such an experiment is illustrated in Figure 7. The Model DSC-'2 was programmed a t 1.25 K min-' to a temperature about 0.7 K above the melting point of a 168.3-mg indium sample, and then the temperature program was reversed. The sample holder temperature profile is shown in the lower portion of the figure; the upper part of the figure shows the sample heat flow rate ANALYTICAL CHEMISTRY, VOL. 47. NO. 4, APRIL 1975
635
430
429
428
427
SAMPLE HOLDER TEMPERATURE, K 430 429
I
428
427
,
426
425 r
0
-5 \
WS
\
SAMPLE HEAT F L W RATE
ma. sec.-l
\
\
-10
\'
-15
- 20 Flgure 6. Variation of calorimetric response with
lo
F
a!
ws
2
-6
431
.
It should be clear from the heat flow rate curve that while the sample is partially melted, between points A and D, the heat flow rate into the sample is directly proportional to the temperature differential ( T p - T F ) .In particular, it should be observed that there is no discontinuity in the heat flow rate or its first derivative with respect to time at point C, where the heat flow rate is zero, clearly demonstrating the linearity of the heat transfer mechanism.
E
t
CONCLUSIONS
1
TP
TEMPERATURE. K
429
420
0
2
4
6 B TIME. MINUTES
10
12
Figure 7. Partial fusion and freezing of indium
behavior. As usual, heat flow into the sample is indicated by an upscale deflection from the base line. A quantity of inert material was placed in the reference holder to balance the thermal capacity of the sample; this ensures that the two base lines are collinear. The sample begins to melt at point A, where the sample holder temperature is equal to T F ,the melting temperature. The sample heat flow rate then increases linearly with time, as in a conventional melting procedure with a large sample. At point B,the program is reversed, and the heat flow rate into the sample decreases linearly toward zero. At point C, the sample and the sample holder are in thermal equilibrium at the melting temperature T F .The area ABC represents the total heat transferred to the sample, or 0.703 calorie; since the heat of fusion is 1.143 calories, 62% of the sample is in the liquid state at point C. As T p continues to decrease, heat is withdrawn from the sample at a linearly increasing rate until the sample is completely frozen, at point D. The heat flow rate returns to the original base line a t point E. the area CDE is of course exactly equal to the area ABC.The maximum heat flow rate into the sample, at point B, is 8.14 mcal sec-I, while the maximum heat flow rate out of the sample, at point D, is 10.68 mcal sec-l. 636
ANALYTICAL CHEMISTRY, VOL. 4 7 , NO. 4, APRIL 1975
It has been shown by analysis of the heater control circuits in DSC that no distinction can be made between the responses to endothermic and exothermic sample phenomena. The symmetry of the measurement technique makes it impossible, on the basis of recorded ordinate data alone, to distinguish exothermic behavior in the sample material from endothermic behavior in the reference material. Measurements can be made with any combination of sample and reference heat flow, rates, whether individually exothermic or endothermic, provided that the maximum differential power rating of the instrument is not exceeded. It has been shown experimentally that for a large sample transition, analyzed under conditions where the sample heat flow rate approaches the limitations of the instrument, the exothermic peak has the trapezoidal shape predicted, and that the exothermic and endothermic peak areas are equal. It has also been demonstrated that the integrated ordinate response to exothermic behavior is linear over the entire dynamic range of the instrument, and is unaffected by variations in the temperature program rate, or in the coupling resistance Ro. Finally, it has been experimentally demonstrated that there is no instrumental discontinuity associated with the transition from endothermic to exothermic sample behavior. This was shown by programming the sample holder from 0.7 K above the temperature of a partially-melted sample to 1.3 K below this temperature, and recording the smooth and linear variation of the heat flow rate from a large positive value to an even larger negative value. Intuitively, it might appear that exothermic phenomena cannot be measured by an instrument equipped only with heating elements in contact with the sample. In fact, the sample holders are in a state of dynamic equilibrium, in which the power generated by the heaters exactly matches the thermal losses. Thus, heat flow out of the sample is absorbed and measured by reducing the heater power, just as endothermic phenomena are measured by increasing it. It should be explicitly pointed out that the use of the
may simply reflect a more complicated sample behavior than that anticipated by the analyst.
simple exothermic phenomenon of pure metal crystallization in this study does not limit the applicability of the conclusions. The instrument simply measures the heat flow rate into or out of a sample, whether the flow of heat is a consequence of reaction or crystallization or any other sample behavior. Thus a demonstration of the instrument's correct response to one exothermic phenomenon is sufficient to establish its correctness for all others. Provided that the instrument is operated within its specified dynamic range and in accordance with recommended sampling techniques, the user can be sure that it will record exothermic and endothermic phenomena with equal fidelity. Apparent errors of substantial magnitude in the measurement of exothermic events must be due either to improper experimental techniques or errors in base-line interpolation, or
LITERATURE CITED (1) E. S. Watson, M. J. O'Neill, J. Justin, and N. Brenner, Anal. Chem., 36, 1233 (1964) (2) E. M. Barrall II and J. F. Johnson, Mol. Cryst. Liq. Cryst., 8, 27 (1969). (3) E. E. Marti, Thermochim. Acta, 5 , 173 (1972). (4) E. M. Barrall 11, M. A. Flandera, and J. A. Logan, Thermochim. Acta, 5, 415 (1973). (5) M. J. O'Neill, Anal. Chem., 36, 1236 (1964). (6)A. A. Duswalr, Thermochim. Acta, 8 , 57 (1974). (7) J. H. Flynn. "Thermal Analysis," Vol. I, H. G. Wiedemann, Ed., Birkhauser, Switzerland, 1972, p 127.
RECEIVEDfor review September 6,1974. Accepted January 2, 1975.
Simultaneous Determination of 35 Elements in Rhodium Samples by Non-Destructive Activation Analysis with 10 MeV Protons J. L. Debrun, J.
N. Barrandon, P. Benaben, and Ch.Rouxel
Groupe d'Application des Reactions Nucleaires a I'Analyse Chimiuue, Centre National de la Recherche Scientifique, Service du Cyclotron, 45045 Orleans-Cedex, France
The performances of activation analysis with 10-MeV protons from a cyclotron were tested in the case of Industrial rhodium samples. ?-Ray spectrometry with a Ge-Li detector was performed directly on the activated samples, after irradiation. Ti, Zn, Cd, Sn, and Sb were present at the partper-million level: the concentration of Ca, Cr, Fe, Cu, Br, and Ru ranged from -10 ppm to -80 ppm, while Ir and,Pt were present at concentrations of several hundreds of parts per million. Upper limits of concentration were calculated for 22 other undetected elements; most of these limits range from several tenths of ppm to several ppm.
Rhodium is very important for modern industry where it is used pure or alloyed. The purity needed varies with the type of industrial application, and must therefore be known. For instance, in the making of thermocouples or wire gauzes for catalysis, the purity must be as high as possible because the alloy Rh/Pt is fragile when impure rhodium is used. As explained in an article by Gijbels and Hoste (1 ), the control of the purity of rhodium is a difficult problem because of the lack of sensitivity or the lack of precision of the methods generally used. It might be added also that many analytical procedures necessitate a liquid sample, and it is well known that rhodium is very difficult to dissolve. It is partially dissolved by a lengthy treatment with hot sulfuric acid or dissolved in a basic medium, and in both cases there are many possibilities of contamination. Several researchers (1, 2 ) have used thermal neutron activation analysis to determine iridium in rhodium. This method, usually very sensitive, is here nondestructive because short-lived radioisotopes only are produced by (n,?) reactions on lo3Rh, the stable isotope of rhodium. But the analysis of rhodium by activation with thermal neutrons is rather limited, for the two following reasons.
First, the cross-section of rhodium for thermal neutrons is high, and this leads to difficult corrections or to tedious standardizations. An alternative is to irradiate small samples, but this decreases the experimental sensitivities. Second, iridium is a major impurity of rhodium and it is well known that this element becomes very radioactive. The presence of lg41r and of lg21r,the last one being longlived, leads to poor detection limits for many elements. In this work, we intend to show that nondestructive analysis by activation with 10-MeV protons, can be used to determine many elements simultaneously, under good conditions of sensitivity and precision. A comparison will be made on the same sample between neutron activation and proton activation.
EXPERIMENTAL Irradiations with Protons. The variable energy cyclotron of the "Service Hospitalier F. Joliot" at Orsay, was used for these experiments. As shown in Figure 1, the irradiations take place in the air. The energy of the protons delivered by the cyclotron is 11 MeV, energy that is reduced to 10 MeV a t the surface of the sample because the particles have to pass through 3 metallic foils. The titanium window separates the vacuum of the cyclotron from the atmosphere. The Havar (alloy containing mainly Fe, Co, Ni, Cr, W) foil is used as a flux monitor by means of the reaction 56Fe(p,n)56Co.The aluminum foil prevents a direct contact between the sample and the monitor. Three different qualities of sintered industrial rhodium were irradiated; the irradiations lasted for 1hour with an intensity of 0.6 to 2 MAaccording to each sample. The dimensions of these samples were 12.5 X 12.5 mm, the thickness was equal to 1 mm. A surface of 0.5 cm2 only was irradiated, and this corresponds to an actual sample of -130 mg, since the range of 10-MeV protons is equal to 261.5 mg/cm2. This range corresponds to 210 microns and, consequently, the samples could have been thinner, e.g. 300 microns. Irradiations with T h e r m a l Neutrons. Rhodium number 2 was irradiated with thermal neutrons in order to make a comparison between neutron activation and proton activation on the same sample. The errors due to the absorption of neutrons were made ANALYTICAL CHEMISTRY, VOL. 47, NO. 4, APRIL 1975
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