which is equivalent to Equation 6 if rn were to equal zero. The value of in equals zero when the volume of the pressure measuring device remains essentially constant. CONCLUSIONS
The method described here has been used successfully for the past 6 years. If greater accuracy is required, the following improvements could be made by using: z more accurate pressure measuring device ; a constant temperature bath for
all three containers; a dry pure gas whose compressibility is accurately known; and the temperature of each container, if different, and compressibility factor at each condition as shown in Equation 11. This method can be used to determine the volume of any gastight container. Best results can be obtained when the volumes, VI, V2,and V 3 ,are approximately equal. RECEIVED for review September 8,1961. Accepted November 6, 1967.
A Microcalorimeter Especially Suited for the Study of Small Quantities of Materials William J . Evans, Emile J. McCourtney, and William B. Carney Seed Protein Pioneering Research Laboratory,’ New Orleans, La.
FORSOME TIME we have been using a modified version of the Tian-Calvet heat conduction microcalorimeter. The original version of this calorimeter consists essentially of a thermostated metal block containing twin microcalorimetric elements (1, 2). Each of these elements is covered by an array of closely fitting thermocouples which are connected in opposition. One of the elements serves as a tare with the other containing the process under investigation. The modified version incorporated the main features of the original calorimeter with one important exception-namely, the fabrication of the thermocouple sensing elements. These elements were made by a process of electroplating. In this manner the chief constructional difficulty of the original version of a calorimeter of this type was greatly simplified. Although the modified calorimeter which we have previously described (3), has proved useful (3-6), it has the disadvantage, among other things, of requiring a relatively long time (approximately four hours) for thermal equilibration. In view of the vast potential of calorimetry as an analytical tool in all phases of chemistry, we describe here a calorimeter which possesses features not incorporated in our earlier version. Chief among these features are : relatively short equilibration time (about one hour), Peltier compensation, reduction in the overall physical size of the calorimeter and in the amounts of materials required for its operation, ability to mix equal volumes of reagents, and automatic integration of the EMF-time curves. EXPERIMENTAL
Apparatus and Procedure. The two cell holders were machined from a copper rod with an 0.d. of approximately 0.7 inch and an i.d. of about 0.65 inch. The overall length of the cell holders was 21/4 inches, Two flanges, l/8-inch thick with an 0.d. of 0.95 inch, were machined a t the extreme ends of each holder. Ten l / d n c h holes, 36” apart, (1) E. Calvet, Compt. Rend. Acad. Sci., 226, 1702 (1948). (2) E. Calvet and H. Prat, “Microcalorimetrie.” Masson, Paris, 1956. (3) W. J. Evans and W. B. Carney, Anal. Biochem., 11,440 (1965). (4) H. D. Brown, W. J. Evans, and A. M. Altschul, Life Sciences, 3, 1487 (1964). ( 5 ) H . D. Brown, N. J. Neucere, A. M. Altschul, and W. 3. Evans, Ibid.,p. 1439.
(6) H. D. Brown, W. J. Evans, and A. M. Altschul, Biochim. Biophys. Acta, 94, 302 (1965). 262
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were drilled in each of these flanges in such a fashion so as to have a spacing of 0.04 inch between the center of the holes and the outer wall of the cell holder (see Figure 1 .). The thermocouple elements were made in the following manner: enameled constantan wire of 0.005-inch diameter was wound on plastic tubing (acetate composition) with a n 0.d. of ‘/l inch and wall thickness of 0.01 inch. The tubing, approximately 2 inches in length, was held on a mandrel in the lathe and exactly 400 turns of the constantan wire were wound on it. While the tube with the wire in place was held on this same mandrel in the lathe, the enamel was removed from the outer periphery of the wire by means of a finegrained emery cloth. Great care is necessary in this operation to avoid abrading or cutting of the wire. Once the enamel had been removed from the wire, the tubing was clamped in a V-bottom jig (brass construction) so as to make good electrical contact with the wire. With the tubing held in this manner, a copper coating, from acid cupric sulfate solution, of about 0.001-inch thickness was formed on one half of the circumference of the wire coils on the tubing. Each line of demarcation between the copper plate and the constantan represents a thermo junction. Thus, each tube with the plated wire constituted a battery of 400 thermocouples. Twenty such batteries of thermocouples were constructed in this manner, 10 for each calorimetric unit. The tubes containing the thermocouples were arranged around the cell holders, taking care that the junctions were in proper line, with one row of junction being in contact with the cell holders. Prior to this operation the tubes as well as the cell holders were coated with an epoxy varnish. AS each tube was placed on the cell holder, as described above, two small pins, approximately inch long, were pushed through the holes in the flanges of the cell holders. As mentioned previously, 10 such thermocouple assemblies were fastened to each cell holder, resulting in a thermopile of 4000 copper-constantan thermocouples for each calorimetric unit. The individual thermocouple assemblies were wired in series through a double-pole, 6-position, 6-deck switch with gold contacts. The two complete thermopiles were also wired in series, but opposed, through this same switch, thereby effecting the differential arrangement, Further, by means of this switch, 4 of the individual thermocouple assemblies, in series (1600 thermocouples), could be isolated from the detecting circuit of each calorimetric unit for Peltier com1 One of the laboratories of the Southern Utilization Research and Development Division, Agricultural Research Service, U. S. Department of Agriculture.
I
2
Figure 2. Schematic wiring diagram of thermocouples. Thermocouple sets 3, 5, 7, and 9 are used for Peltier compensation
A- ALUMINUM CAN B- HOLLOW SHAFTS C- B E A R I N G S
Figure 1.
Thermocouple-cell holder assembly
Figure 3. Thermostat jacket
A . Battery of 400 copper-constantan thermocouples B. Pin used to secure thermocouples to cell holder
pensation. A schematic wiring diagram of the thermocouple elements contained in one calorimetric unit is shown in Figure 2. Once the cell holder-thermocouple assemblies were completed they were enclosed in aluminum jackets which made good thermal contact with the thermocouples (cold junctions). These jackets were machined from aluminum rods with an 0.d. of 2.5 inches. Prior to final machining of the i.d., the jackets were cut into 120" segments. These segments were held together by two retaining rings machined to fit at the ends of the jackets. With the segments held in place by the retaining rings, the i.d. was finished to a size 0.03 inch less than the 0.d. of the cell holder-thermocouple assemblies. As the jackets were placed around the cell holder-thermocouple assemblies, the thermocouples were compressed, thus ensuring good thermal contact. The outsides of the jackets were machined with a 3" taper while matching cavities were machined into a 6-inch 0.d. by 4inch long aluminum block. The block was suspended by means of two truncated 60" cones between the lids of an aluminum can which had an i.d. of 7 inches with OS-inch wall thickness. This can was in turn placed inside three other concentric cans with inch wall thicknesses. The two smaller cans were separated by a '/,-inch air space while an air space of 11/* inches separated the outermost can from the one second from the outside. This space was filled with polyurethane insulation. A heating coil was wound on the outer surface of the can second from the outside while the sensing element of an electronic proportional temperature controller was placed on the inside. These four aluminum cans constituted the thermostat. Access to the
cell holders was provided by means of Bakelite guide tubes fitted through holes in the tops of the cans. Two hollow aluminum shafts, 1'/2-inch 0.d. by 3/4-in~hi d . , were fitted diametrically opposite at the equator of the outermost can of the thermostat. The entire assembly was suspended by means of these hollow shafts which passed through pillar block bearings for rotation (see Figure 3). All lead wires to the outside were passed through these hollow shafts. Among, if not the chief difficulties in microcalorimetry, are the problems of the initiation of the reaction and stirring. This is especially true where it is required to effectively homogenize equal or equivalent amounts of materials while developing a minimum of heat from mechanical effects. Conventional stirring is precluded in a calorimeter of this type because, as quite often is the case, the heat developed by stirring is larger than that of the process under investigation. In particular is this so where small amounts of heat are liberated from a reaction over a period of several hours. The method which was adopted in the present case was rotation of the entire calorimetric assembly, a technique which has been employed in the past (7). For this purpose the special partition type cells were used (Figure 4). These cells were fabricated from tantalum because of its chemical inertness, mechanical strength, and reIativeIy good thermal conductivity. Several variations of the volumes of solutions are possible with these cells. Generally they are used with 1 ml on either side of the partition, or with 1 ml on the one side and from 0.1 ml up to 1 ml on the other. The cells are held in place by tapered stoppers which fit into the tops of the calorimetric units. They are inserted into and removed from the calorimetric (7) J. M. Sturtevant,J . Phys. Chem., 45, 127 (1941). VOL. 40, NO. 1 , JANUARY 1968
0
263
Table I. Electrical Calibration of Calorimeter with Both Fast and Slow Heating Rates (Heat inputs range from 9 to 400 millicalories) Calibration factor x 106 Run No. (cal/integrator count) Deviation X 1 4.4503 0.0035 2 4.4507 0.0039 3 4.4398 0.0070 4 4.4400 0.0068 5 4.4533 0,0065 Mean 4.4468 f O.OOO64"
A
los
Standard deviation.
A Table 11. Chemical Calibration of Calorimeter (0.1 ml0.0283N HCI neutralized in 1 ml0.018N NaOH. Theoretical heat evolved = 0.03772 calories at ionic strength = 0.0163") Temp. = 25" C Run No. Calories Deviation X 10' 1 0.03781 0 2 0,03792 11 3 0,03772 9 4 0.03768 13 5 0,03782 1 6 0.03791 10 Mean 0.03781 + 0.00009* (1 ml0.0071N HCl neutralized in 1 ml0.0327N NaOH. Theoretical heat = 0.09543 calories at ionic strength = 0.0162") Temp. = 25" C 1 0.09541 26 2 0.09584 17 3 0.09609 42 4 0.09557 10 5 0,09543 24 Mean 0,09567f 0 .OOO29* a Ref. 8.
* Standard deviation.
units by means of a threaded metal rod which is accommodated by the threaded boss on the tops of the cells (see Figure 4). The calorimeter is rotated by means of a reversible motor through a speed reducer at 15 rpm. The rotation is automatically controlled by a series of cams and microswitches. One cycle consists of 180" clockwise rotation followed by 360' counterclockwise rotation and then 180" clockwise rotation and stop. Generally four to five cycles are required to effectively homogenize the solutions when equal volumes are employed. As has been pointed out (7) this form of stirring causes a disturbance presumably due to movement of the thermocouples in the Earth's magnetic field. This disturbance has been substantially reduced in the present instance by means of magnetic shielding wrapped around the two innermost aluminum cans of the thermostat. The outputs from the thermopiles are fed to a Leeds & Northrup (Mention of trade names does not imply recommendation by the Department over other, equally suitable products.) dc amplifier and then to a dc recorder and an electronic integrator (Infotronics Digital Readout System) which integrates the EMF-time curve. The dc recorder serves merely to monitor the reaction. 264
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-c Figure 4. Top and crosssectional view of tantalum reaction cell A . Filling hole B. Threaded boss C. Partition for separating solutions
RESULTS
The results of some electrical calibrations of the calorimeter with both fast and slow heating rates are shown in Table I. Here the total amounts of heat liberated ranged from approximately up to 400 millicalories, and the heating times from 1 second to in excess of 4 hours. For chemical calibrations the heat of neutralization of HC1 with NaOH was chosen since two recent studies (8, 9) have been made of this reaction with excellent agreement having been obtained between the two works. These calibration data are shown in Table 11. The reagents were dispensed by 1-ml tuberculin syringes with Chaney adapters. The volumes delivered by these syringes were determined by weighings on a semimicro balance, repeatability being of the order of =kO.l%. Stability of the calorimeter is such that reactions exceeding several hours' duration can be followed. Because of the relative ease of construction of the instrument and the vast importance of thermochemical quantities, it is felt that this calorimeter will prove to be a valuable adjunct in the analytical laboratory.
RECEIVED for review August 11, 1967. Accepted October, 1967. (8) J. D. Hale, R. M. Izatt, and J. J. Christensen, J . Phys. Chem., 67,
2605 (1963). (9) C. E. Vanderzee and J. A. Swanson, Ibid., p. 2608.
