Provided that the background does not vary rapidly,
m
5
[d
(A.Pd* =
i--kM
(N7
ci(kd *Y ( x 4
(6)
kM
and (AqAw)Z=
( M = L , R). ( 7 )
di(k.w)2Y(xM) i- -kM
Using the numerical values of reference (4) for kL = kR
=
11,
( A P , ~ )= ~ 0.1 Y ( x M )and (Aqul2 = 0.0036 Y(XM). (8) WL
Considering Equations 5-8 and that T =
+
and B = ~ . ~ [ Y ( x L )Y ( X R ) ] , for IL = the peak area is:
AN
Y(XP 2=
=
U T
+ 1.3B
[R
-u’L
+ i)
= 15, the error of
(9)
For large B, this error is substantially less than the error of Covell’s method ( I ) which gives under the same conditions AN = (T 4.4B)lI2. Using few points ( k < 5 ) or going into the peak region with the fitting, unsatisfactory results were obtained. I n the first case, b(x) depended strongly on the fluctuations of the counts in the individual channels; while in the second, the in. fluence of the peak distorted the base line. Some of the results are summarized in Table I. The measured counts in the peak were compared to the expected counts (NeXp) calculated from the long time measurements. The results 15 measurements, and the errors are the averages of m are the experimentally observed standard deviations :
-
The calculated errors (la) were
1’2
calculated assuming Poisson distribution. The width of the peak, used for the peak area determination, depended upon the NIT ratio and varied for W L = W R 0.8-1.2 FWHM, where F W H M is the full width at half maximum of the peak. The values listed in the table correspond to channel widths, which are expected to give the smallest statistical error (5). It is obvious from Table I that more precise peak area determination can be obtained with nonlinear base line construction, especially when the net peak area is small compared to the total counts in the peak region. I n many cases the distances between the peaks are more than 20 channels, so the base line can be estimated with suitable accuracy. A short computer routine can be written to calculate the coefficients of the polynomials and from that, the net peak area; but it would not be very time consuming to perform the calculations even’with a desk calculator.
+
-
1.
NeXp)*/m
-
ACKNOWLEDGMENT
The author thanks H. P. Yule and W. E. Kuykendall for their help, and R. E. Wainerdi a t Texas A & M University, and W. M. Meinke and P. D. Lafleur at the National Bureau of Standards for the opportunity to perform the calculations and the measurements.
RECEIVED for review April 21, 1969. Accepted May 23, 1969. ( 5 ) J. D. Reber and J. E. Major, Nucl. Instrum. Methods, 23, 162
(1963).
Stopped-Flow Calorimetry for Biochemical Reactions Bohdan Balko and R. L. Berger Laboratory of Technical Development, National Heart Institute, Bethesda, M d . 20014
Walter Friauf Biomedical Engineering and Instrumentation, National Institute of Health Branch, Bethesda, M d . 20014
THEUSE OF CALORIMETRY for the study of fast reactions in solution using a flow apparatus was first introduced by Roughton (1). Although there are many systems (2) presently available for studying fast reactions by measuring other variables such as pH (3), optical density (4-5) and fluorescence (7), a thermal measurement is especially appealing because it allows one to study the reactions directly and along with the kinetics to obtain the heat of the reaction. Most reactions have an associated energy effect and therefore exhibit a temperature change whereas this is not necessarily true for other parameters. The Droblem, however, with thermal measurements is the long (1) H. Hartridge and F. J. W. Roughton, Proc. Cambridge Phil. Soc., 22, 426 (1924).
(2) F. J. W. Roughton in “Investigation of Rates and Mechanisms of Reactions,” Vol. 111, Part 11, 2nd ed., S. L. Friess, E. S. Lewis, and A. Weissberaer. - . eds... John Wilev and Sons,Inc., New York, N. Y.,1963. (3) L. Rossi-Bernardi and R. L. Berger, J . Biol. Chem., 243, 1297 (1968). (4) R. L. Berger, B. Balko, W. 0. Brocherdt, and W. S. Friauf, Rev. Sci. Instrum., 39, 486 (1968). ( 5 ) R. L. Berger, B. Balko, and H. Chapman, ibid., 39, 493 (1968). (6) R. L. Berger and L. C. Stoddart, ibid., 36,78 (1965). (7) R. Chen, A. Schechter and R. L. Berger, Anal. Biochem., 29, 68 (1969). 1506
ANALYTICAL CHEMISTRY
equilibration time usually required, difficulty of making the very small temperature measurements, and the large amounts of solution required. Nevertheless, no little success has been obtained with continuous flow thermal measurements as shown by Roughton (2) in his latest review of the subject. More recently, Chipperfield (8) has extended the method to obtain thermodynamic and kinetic values for the reaction of carbon dioxide and a number of amino acids. This instrument requires about two hours to come to equilibrium, measures a change in temperature as small as 10-5 “C, and requires about 100 ml of each reagent for a single kinetic curve. Kernohan and Roughton (9) have used the method to study the very fast reaction of carbon dioxide with hemoglobin, Berger and Stoddart (6) introduced a stopped-flow optical-thermal apparatus which was severely limited in response time but had the same sensitivity as Chipperfield and required only 2 ml of each reagent for a complete kinetic curve. The speed limitation was due to the galvanometer used to read the thermocouple and by the thermocouple response time itself. While (8) J. R. Chipperfield, Proc. Roy. Soc., Ser. B, 164, 401 (1966). (9) J. C. Kernohan and F. 3. W. Roughton, J . Physiol. (London), 197, 345 (1968).
A-
stopped flow adds new complexities, these are generally more than offset by its desirable attributes of small amounts of solution needed per run and the ability to obtain the kinetic trace directly. The problems peculiar to stopped-flow have been adequately discussed in the literature (2, 4-6). To these are added, for fast thermal work, obtaining a fast responsing electrically insulated thermal sensor and amplifier. This paper deals with a thermal detection system which has been attached to a standard stopped-flow system. Considerable care has been taken to make all parts of the system from readily available commercial parts or units which can be constructed in any well equipped electronics shop. The problem of rapid equilibration has been at least partially solved and the amounts of solution needed reduced to a few milliliters. Flow System. The flow system ( 4 ) used for these experiments consists of two 40-ml stainless-steel concentric syringes which are discharged pneumatically through a high-speed mixer (5). Figure 1 shows the details of this system. The reactants are stored in B. After mixing at D they enter the observation tube L. Flow velocities from 2 to 30 mjsec through a 3-mm diameter observation tube can be easily attained within 5 milliseconds after the start of flow. After a predetermined flow time, the flow is stopped with the pneumatic stop valve, H, which closes in 40 microseconds. The progress of the reaction in the observation chamber can then be followed. The dead time of the apparatus (4), measured optically was 270 microseconds at a flow velocity of 30 mjsec. The only major changes in the apparatus from that described previously ( 4 ) were those to accommodate the thermocouple, E in Figure 1. C in Figure 1 shows the mixer holder with the thermocouple E, ready to be mounted in place in the lucite block just above the mixer, D. In this configuration the thermocouple sensor junction was 1.5 cm above the output of the mixer. Thermal Sensors. For this set of experiments we used single junction ChromeLConstantan thermocouples 0.00127 cm thick and coated with Parylene C (Union Carbide, Bound
M
Figure 1. Thermal stopped-flow apparatus A , gas accumulator B, concentric syringes C, mixer, observation tube, and detector holder D,ball mixer E , thermocouple in its holder F,threaded retaining cup H , stop valve J, calomel cell used for fast pH work K,fast glass electrode interchangeable with the thermocouple
I
I
I
i
I
I
I
J lNY7il
1'1 ~~~
~~
Figure 2. Thermal amplifier Noise with 1 ohm source is 0.04 microvolt peak-to-peak VOL. 41, NO. 11, SEPTEMBER 1969
1507
Figure 3. Exponential input response A , response of the amplifier to an exponential input B C, true endpoint. Time scale is 20 msecicm Brook, N. J.) to a thickness of 0.0006 cm for electrical insulation when in solutions of salts. The response time of these junctions was 1.5 to 2.0 milliseconds. The insulation resistance as measured in brine was greater than 150 Megohms. Details on the manufacture, coating, and testing of these thermocouples are given elsewhere (10). The thermocouples were mounted in a I-cm diameter Lexan rod shaped in the form shown at E in Figure 1 . The thermojunction extended 2.5 mm from the Lexan rod. Special connectors (Type Ceramo Miniature, Thermo-Electric Corp., Saddle Brook, N.J.) were attached to theleads so that the junctions could be readily demounted and interchanged. The thermocouple, E, Figure 1, was then inserted in the block, C, and held in place by a threaded top, F . Shielding of the leads was done with tinned copper mesh wrapped with Connetic foil (Perfection Mica Corp.). Thermal Amplifier. The voltage from the thermocouple was amplified by the circuit shown in Figure 2. (An improved version of this amplifier is available from Instrumentation Laboratory, Lexington, Mass.) A 100 to 1 step-up transformer was used to raise the apparent source impedance by a factor of 10,000, thus providing a better noise figure with available amplifying devices. The transformer also provides a balanced, isolated, and guarded differential input with extremely high common mode rejection. A single ended output is used so that only one active device is required at the point of lowest signal level. From the standpoint of the noise figure of the input FET, an even higher ratio might have been desirable, but the improvement would have been offset by adverse effects on the lower or upper cut-off frequencies, or the introduction into the input circuit of too much extra resistance with its associated thermal noise. Following the transformer, the amplifier input device is a low noise, junction field-effect transistor operated in the common source configuration, direct coupled to two common emitter transistor stages. The input is biased from the output through a level-shifting zener diode and a large feedback resistor, which, in conjunction with the source impedance, also serves to stabilize the voltage gain. The load resistor of the first stage is trimmed so that the FET operates with a very slight positive gate to source voltage, resulting in optimum low (10) B. Balko and R. L. Berger, Rev, Sci.Instrum., 39, 498 (1968). 1508
ANALYTICAL CHEMISTRY
Figure 4. Exponential input response A , response of B, Figure 3, at a sweep speed of 20 msecicm B, response at 100 msecicm C, is the base line noise performance and obviating the need for another supply voltage. The assembly also includes batteries for power, another simple amplifier stage to provide an overall gain of about one million, and a calibrator which injects a square wave voltage into the input loop. The equivalent input noise over the pass band of Hz to 600 Hz with a source impedance of 1 ohm is about 0.05 pV peak to peak, as observed on a Tektronix 535A oscilloscope. The total effective source resistance is the source resistance ahead of the transformer plus the primary and reflected secondary resistances of the input transformer, or about 6 ohms total in this case. The thermal noise of 6 ohms over a 600-Hz bandwidth at room temperature is about 7.6 X 10F9V,r.m.s., or about 0.045 MVp-p. Thus, with a source resistance of only 1 ohm, the transformer winding resistance accounts for most of the amplifier noise. To obtain significant improvement in this parameter, a larger transformer would be required as well as a critical review of the appropriate turns ratio. Amplifier Output Data Correction. The amplifier pass band is 0.5 to 600 Hz. Thus, there is distortion at both the high and low limits and no dc response. However, the possibility of obtaining such good signal to noise ratios with this simple and inexpensive circuit made it rather appealing even with the inconvenience of having to correct the output of the amplifier. The characteristic high frequency response of the amplifier was studied by applying a step function to the input. The response of the amplifier to this input was an exponential with a half-time of 200 microseconds. The amplifier does not have dc response so the output decays approximately exponentially with a half-life of 200 milliseconds. The decay is complicated by a characteristic underdamped ringing due to uncompensated L, C, and R in the transformer. Figure 3 shows the amplifier output A , resulting from a true exponential input, B, with the endpoint dc level of B being shown by C. The horizontal sweep rate was 20 milliseconds/ centimeter. Figure 4 shows the response over an extended time interval to the exponential B, in Figure 3. The horizontal sweep rate for curve A is 20 milliseconds/cm and for curve B, 200 milliseconds/cm. To recreate the original function, three possibilities have been tried. The first was to generate a computer simulation program for the amplifier. This worked well and
Figure 5. HzO flow test A , test pulse which equals 0.0061 “C B, where flow starts C, where flow stops
0.7
-
0.6
-
0.5
-
0.4
-
Chart speed 25 mmisec. Each large division equals 5 mm the program is available on request. The second method was to build an integrator to work with the amplifier and this has worked fairly well. The third method was to try and build an amplifier in which L and R can be compensated for and in which the low frequency response has been extended. A prototype of such a unit has been built commercially (Instrumentation Laboratories, Boston, Mass.) and would appear to be very satisfactory in our preliminary tests. In this paper all of the data has been treated by the computer simulation method (see Hewlett-Packard’s “Handbook for Computers” and 11). The parameters accounting for the amplifier characteristics and the thermocouple resistance were determined experimentally. Test Runs. The dead time (4) of the apparatus for the particular configuration described above is 1.5 msec. The response of the thermocouples is 1-2 msec (IO). These particular characteristics together with the pass band of the amplifier allow one to study easily reactions with half-lives in the range of 5-600 msec with appropriate correction procedures. The thermal leaks are such that after an acid-base neutralization experiment it takes 5-6 min for the solution in the observation chamber to come into equilibrium with the surroundings. During the time a reaction in the range specified above is in progress a negligible amount of heat is lost. The next problem is to determine how well the temperature of the solutions can be controlled and what the flow artifacts are. The high speed flow system is equipped with a thermo“C stat which allows temperature control to within 1 X over the range from - 10 to 40 “C. However, we thought that it would be most interesting if for these fast reactions the thermostating system could be bypassed. This would sim(11) R.
L. Berger and N. Davids, Rec. Sci. Instrum., 36,88 (1965).
Figure 6 . 0.25M NaHC03
+ 0.104M HCI
A thermal response B 0.0061 “C test pulse
2
0.3-
o.2
0.I
t tI
10
20
30 40 TIME (rnsec)
50
60
Figure 7. First order plot of the bicarbonate Reaction A is the initial concentration after mixing, 0.052M HCI, h is the amount reacted at time t plify and shorten the operation procedure and thus would be very convenient. The system was set up as described above and wrapped with a 3-cm thick piece of polyurethane for insulation. Water sitting at room temperature for about 2 hours was loaded into the two syringes and allowed to equilibrate from 2 to 45 minutes. Several runs were then made in succession at a driving pressure of 200 psi and a flow velocity of 10 m/sec. The signal was recorded either on a Hewlett-Packard Model 141A storage oscilloscope or an Offner R.S. dynograph. It was determined that 5-10 min of equilibrating time gave the smallest signal during flow. For shorter times the artifacts increased and longer times made little difference. Figure 5 shows representative runs of water mixed with water lasting about 120 milliseconds each. There is an initial sharp decrease in temperature probably due to a temperature gradient existing between the lucite observation chamber and the stainless steel mixer holder, followed by an increase in temperature which slowly levels off to a constant offset from equilibrium, the level being dependent on flow velocity. Finally, after the flow has stopped, there is a sharp rise in temperature and consequent decay to the equilibrium level. The sharp pulse after stopping can be observed with both water-water runs and actual reaction runs, the magnitude being constant for a particular driving pressure. The source of this pulse could very well be a shock wave developed upon stopping flow. The next step in testing the system was to run a well known chemical reaction. For this test we chose the NaHC03 HC1 reaction. This reaction has been studied optically thermally (12), and by pH measurement (3). The reaction
+
(a,
(12)
F. J. W. Roughton, J. Amer. Chem. SOC.,63, 2930 (1941). VOL. 41, Nor 11, SEPTEMBER 1969
1509
"i I .4
Figure 8. Colbaltous oxalate and ferrous ammonium sulfate A , where flow starts B, where flow stops Chart speed 120 mm/sec Calibration as per Figure 5 Top curve is 0.02M Fez+and 0.1M Co3Middle curve is 0.04M Fez+and 0.1M Co3Bottom curve is O.lOMFez+and 0.1M Co3-
+
proceeds in two steps. First a simple ionic reaction (H+ HC03- + H2C03)which is too fast for us to observe followed by a mono-molecular step (HzC03 + COS H20)which can be easily observed. The reaction was run at 24 "C with the initial concentration of 0.104M HC1 and 0.205M NaHC03. The same equilibration procedure was followed as with the water-water runs. A typical trace, A , exhibited on the storage scope and photographed with a Polaroid camera is shown in Figure 6. The step function, B, in the figure is a calibration pulse supplied by the amplifier and is equivalent to 6.1 X 10-3 "C. The total is equivalent to 6.1 X lo-' "C. The total step temperature rise is 3.6 X "C and the rate constant obtained from a first order plot shown in Figure 7 is 22.2 sec-1. The results were very reproducible and agree with published values (3, 6, 12). The next reaction of interest was the reduction of cobaltous oxalate ion by ferrous ammonium sulfate ion as shown below
TIME ( m s e c )
Figure 10. Second order plot of Fez+
kr = --1n[-] 1 a(b - x ) b -u b(a - X ) a, initial concentration of Fez+ b, initial concentration of C0(Cz04)3A, a = O.O2M, 0.1M 0 , a = 0.04M. b = 0.1M .,a = O.lOM, b = 0.1M y ' , used when b > n y", used when b = n
+
Fez+
+ c0(c204)33-
+
+
Fe33+ Co2+
+ 3C~04*-
This reaction has been studied optically (13) over regions of low concentration. We wanted to study it at higher concentrations thermally. Three sets of runs were made at 24 "C (13) J. Barrett and J. H. Baxendale, Trans. Faraday Soc., 52, 210 (1956).
+ CO(C~O&~-
following the procedure outlined above. The Fez+ concentration was 0.02, 0.04, and 0.1M. Figure 8 shows three representative traces at the three different concentrations. After initial equilibration the runs were done quickly in succession without allowing the reacted solution to come to equilibrium. One then observes the decrease in temperature when flow starts, at A in Figure 8, and the reacted solution is swept out of the observation chamber. After stopping, at B in Figure 8, one observes the sharp rise in temperature due to the shock wave (constant for all three concentrations) followed by the temperature change due to the reaction. The computer program mentioned above was used to correct the amplifier output and Figure 9 shows a
'T
150r
V
I
1
I
I
I
I
IO0
200
300
4w
500
600
TIME Imrecl
Figure 9. Temperature change vs. time for 0.02M Fez+ 0 . 1 M CO(CZO~)~~1510
ANALYTICAL CHEMISTRY
+
Figure 11. Total temperature rise us. concentration of Fez+ for the Fez+ C O ( C ~ O ~reaction )~~-
+
Table I. Rates and Heats of Reaction Fez+
Set
Concentration Bimolecular of Fez+before rate constant mixing l(sec-mole)-l 0.02
I I1 111
0.04 0.10
51.5 47.9 25.6
+ CO(CZO&~-
AH K cal/mole
37.6 f 1 . 5 40.6 i: 1 . 6 40.1 =t1 . 6
representative output for one of the sets. A second order plot of the reaction is shown in Figure 10. The chamber corrected data was used to make this plot. From these curves the second order rate constants were obtained. Figure 11 shows a plot of the total temperature change as a function of the concentration of Fez+. A summary of the results obtained from the runs is given in Table I. The Debye-Huckel
theory cannot account for the very large reduction in rate at these high ion concentrations. Further experiments should be carried out at high inert salt concentrations, over a range of temperature and at various pH’s. It is hoped that with the commercial availability of the equipment (American Instrument Co., Silver Spring, Md.) such experiments will be forthcoming.
ACKNOWLEDGMENT It is a pleasure to acknowledge the assistance of Robert Erkman, Keithley Instrument Company, with his suggestion of the use of the James Electric Company transformer, Mr. John Macatician, Science Products Corp., for fabrication of the thermocouples, and Dr. William Loeb, Union Carbide, Bound Brook, N.J., for taking special efforts in the parylene C coatings. RECEIVED for review March 27, 1969. Accepted June 12, 1969.
Multiple Isothermal Degradation Method for Determination of Combined Vinyl Acetate in Vinyl Acetate-Ethylene Copolymers Jaroslaw Kaczaj and Richard Trickey Borden Chemical, Division of Borden, Inc., Central Research Laboratory, Philadelphia, Pa. I9124 INOUR INVESTIGATION, in order to determine the composition of the vinyl acetate-ethylene copolymers, various methods of analysis as reported in the literature were compared such as NMR ( I ) , glass transition temperature (Tg) measurements (2), carbon-hydrogen analysis, and saponification (3). Although these methods, with the exception of saponification, correlate reasonably well, they are time-consuming and rather expensive. It was felt that a thermodegradative approach would be appreciably faster and less expensive and tedious. A unique device especially developed for the rapid and reproducible analysis of these types of copolymers and described later can handle twenty or more samples at the same time, which makes it possible to run multiple determinations. The reproducibility of this method depends upon the very small sample size and the even heating of the sample in an enclosed container. This multiple device can also be ideally applied to the kinetics study of the polymerization reaction of vinyl acetate and ethylene copolymers. The thermodegradative quantitative approach applied to the copolymers of vinyl acetate-ethylene originates from the fact that a polyvinyl acetate yields quantitative amounts of acetic acid, when thermally treated ( 4 , 5), whereas the ethylene moiety, containing the carbon hydrogen structure only, remains unaltered at this temperature. The formation of the acetic acid occurs when the C-0 bond, weaker than other bonds in the structure, dissociates and extracts hydrogen from the adjacent carbon. The mechanism can be represented in the following way ( 4 ) : H H H H C-C--C--CH H O 0
1 I
H H H H
+ A + -C--C--C=C-
O=C-CHg
H H
cis
+ CH3COOH
rearranging to H H H -C-C-C==CH H H
+ crosslinking structure
trans A configurational study to prove the above mechanism was made using a Perkin-Elmer Model 21 double-beam infrared spectrophotometer. Based on the infrared spectra of the ethylene-vinyl acetate copolymer (sample 6 from Table I) run before and after the heat treatment, 5.75,7.30, 8.10, 8.90, 9.80, 10.6, and 12.6 microns bands belonging to the vinyl acetate moiety completely disappear, Figure 1. The band which appears instead at 10.35 I.( is assigned to the double bond C-H out of plane bend of a trans configuration. At lower temperatures initial formation of the cis configuration, as judged by the formation of a couple of weak bands, believed to be due to out-of-plane =CH deformation vibrations at longer wave lengths (10-13 p ) was observed. These bands disappear with longer heating periods and higher temperatures. However, there is no infrared evidence for the presence of a cis configuration at the end of 20 hours at 270’ C, which shows that the double bonds in the residual material are entirely in the trans configuration. Insolubility of this residual material in proper solvents indicates that crosslinking mechanism took place. (1) H. Y.Chen and M. G. Levis, ANAL.CHEM., 36, 1394 (1964). (2) . , P. Reding. J. A. Faucher. and R. D. Whitman. J. Polvm. Sci.. 57,483 (1962). (3) R. F. B. Davis and G . E. J. Reynolds, J . Appl. Polym. Sci., 12, 47 (1968). (4) Samuel L. Madorsky, “Thermal Degradation of Organic Polymers,” Interscience Publishers, New York, N. Y.,1964. ( 5 ) Jen Chiu, Applied Polymer Symposia No. 2, Atlantic City, N. J., Sept. 17, 1965. VOL. 41, NO. 11, SEPTEMBER 1969
0
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