Determination of Trace Metals Using Coordination Chain Reactions with Masking Agents and with Automated Rate Measurement Rudolph H. Stehl, Dale W. Margerum,' and Joseph J. Latterell Department of Chemistry, Purdue University, Lafayette, Ind. 47907 Chemical masking agents are used to achieve selectivity in the determination of trace and ultratrace concentrations of metal ions by a catalytic method of analysis. The masking conditions do not interfere with EDTA catalysis of the exchange reaction between nickel-trien and copper-EDTA. Thiosulfate ion masks Ag(l) and Hg(1I). Cyanide ion fQllOWed by chloral hydrate masks Ni(ll), Co(lI), and Fe(l1l) while Cu(ll) masking i s optional. Automatic measurement of the reaction rate constants permits the determinato lO-*M concentrations of metal ions within tion of 10 minutes to a precision of t 2 x 10-EM.
THEDETERMINATION of ultratrace quantities of metal ions or of strong complexing ligands has been demonstrated ( I ) in a catalytic method of analysis using a coordination chain reaction system (2). The method is based on the measurement of the rate of the exchange reaction given in Equation 1 between triethylenetetraminenickel(I1) and ethylenediaminetetraacetocuprate(I1). The exchange rate is catalyzed by trace levels Nitrien+z
+ CuEDTA-2 + Cutrien+2 + NiEDTA-2
(1)
of EDTA or trien and is inhibited by any metal ions complexing these ligands. The catalysis results from the chain reaction properties of the exchange wherein trien and EDTA are the chain centers present in very low concentrations to 10-BM). Typical chain-propagation steps at pH 9 are given in Equations 2 and 3. Kinetic coupling of the reactions forces the added catalyst into specific ratios of EDTA to trien. Conditions used here make [EDTA]/[trien] large so
+ Nitrienfz + NiEDTA-2 + Htrien+ Htrien+ + CuEDTA-2 + Cutrien+z + H(EDTA)-3 H(EDTA)-s
(2) (3)
the catalyst concentration essentially equals the EDTA concentration. The reactants in Equation 1 are to 10d3M and the reaction is followed spectrophotometrically by the appearance of the blue Cutrien+Z complex. Metal determinations to ultratrace levels are possible because the ions complex EDTA and decrease the exchange rate by removal of the catalyst. The fact that EDTA reacts with so many metal ions has been one drawback to the use of this kinetic method of analysis. In the present work two common masking agents are used to achieve more selective determinations. In addition to the usual requirements, the masking agents in this case must not interfere with the chain-propagation steps. Correspondence to be addressed to this author. (1) D. W. Margerum and R. K. Steinhaus, ANAL. CHEM.,37, 222 (1965). (2) D. C. Olson and D. W. Margerum, J. Am. G e m . SOC.,85,297 (1963).
1346
ANALYTICAL CHEMISTRY
An automated rate instrument is described which uses stopped-flow mixing and automated readout so that ultratrace metal determinations with good precision and accuracy can be achieved within a few minutes. EXPERIMENTAL
Reagents and Procedure. The preparation of copperEDTA and nickel-trien solutions for the chain reaction system has been described (2). Typical conditions for the present kinetic determinations were lO-3M CUEDTA-~, 1 to 2 X lO-4M Nitrien+2, and an ionic strength of 0.025 to 0.050 buffered at pH 8.9 with borate-boric acid at 25.0" C. The studies of thiosulfate masking used a Beckman D U spectrophotometer and a manual work-up of first-order rate plots as before ( I ) . The procedure was to add the metal ion sample to Na2SzO3 (10-3M) followed by the buffer and CuEDTA-* with EDTA catalyst present. The exchange reaction then was initiated by the addition of Nitrien+2. The cyanide masking studies used both conventional and automated kinetic techniques. The metal sample was added to dilute NaCN solution (10-5M) at pH 8.9. After a few minutes, chloral hydrate (initially 5 x lO-3M) was added to destroy the free cyanide ion and the less stable metal cyanide complexes. An equilibrium constant of 10 was measured spectrophotometrically at I.( = 0.025 and 2 5 " , for the formation of the cyanohydrin (Equation 4). CN-
+ C13CCH(OH)2 S CI,CCH(OH)(CN) + OH-
(4)
The rate constant for the formation reaction is 0.7M-1 sec-' for the same conditions, Twenty minutes were allowed for cyanide removal and the sample was then added to CUEDTA-~ with EDTA catalyst present and treated as before. Automated Measurement of Reaction Rate. A block diagram of the instrument constructed is shown in Figure l . It combines some of the techniques used in rapid mixing (3) with those of automated measurement (4-6). The instrument uses reciprocal time measurement of a selected reaction interval as employed by Pardue and coworkers (4, 7). An innovation is the use of an all-electronic system for the generation of the reciprocal function. Extensive use was made of the McKee-Pedersen modular -analytical instrumentation units to test optimal optical and electronic parameters. MIXING AND SAMPLEHANDLINGwas accomplished by injecting equal volumes of reactants from two 5-ml Multifit syringes into an %jet tangential mixer. The basic design of the mixer was that of Chance (3). The mixer was constructed of Plexiglas and the outlet led directly to the sample cell as shown in Figure 2. The cell also was constructed of (3) B. Chance et ai.,Ed., "Rapid Mixing and Sampling Techniques in Biochemistry," Academic Press, New York, 1964. (4) H. L. Pardue, C. S. Frings, and C . J. Delaney, ANAL.CHEM., 37, 1426 (1965). ( 5 ) H. V. Malmstadt and S. R. Crouch, J . Chem. Educ., 43, 341 (1966). (6) W. J. Blaedel and G. P. Hicks, ANAL.CHEM., 34, 388 (1962). (7) H. L. Pardue and S. P. Perone, Ibid., 37, 175 (1965).
0 Pushing
3-Way Microvalves /5 mt Syringes Pushing
1
Block
Therrnostated Syringes
6- v lomn -
[@-I
Monachromolor
10crn Cell
Block
muit, - Photometer Photo-
,,er
Amplifier
Teflon Mixer c e m e n t e d to
cell
/Out let
Figure 1. Block diagram of automatic rate instrument Specific components used (MP refers to McKee-Pedersen number) : 10-V power supply-MP-1026, monochromator-MP-1018; photomultiplier-RCA 1P28; all operational amplifiers-MP-1006; meter relay-Assembly Products, Inc. Model 503; high voltage power supply-Fluke 409a
Plexiglas with a cell length of 10.0 cm and a volume of 1.5 ml. Borosilicate-glass polarimeter windows were cemented onto the ends of the cell. Several cell volumes passed through the cell from the syringes which were mounted so that a movable block in aluminum guide channels could be used for a manual stopped-flow type push. A bottom outlet permitted the contents of the cell t o be aspirated out and wash solution to be aspirated in without disturbing the syringes. A pinhole leak before the stopcock in the aspirator outlet was used to allow the escape of air trapped in this section when the cell was filled initially. In tests of mixing and filling, equilibrium transmission measurements were obtained within 1 t o 2 seconds for injections of degassed solutions and within 15 seconds for solutions which were not degassed. All kinetic measurements were taken after 15 seconds, which was a satisfactory time interval for the present work, and solutions were not degassed. A smaller pressure drop a t the mixer outlet would probably have given less interference of this type. Reactant solutions were stored in thermostated Teflon bottles and pulled into t h e syringes through 3-way microvalves (Hamilton Co.). Kel-F tubing with Luer fittings were used for the supply lines and the syringes and cell assembly also were thermostated. PRECISION TRANSMITTANCE MEASUREMENTS are important for the automated rate instrument. A McKee-Pedersen MP-1026 power supply gave good regulation (&0.04% output variation for a 10% line voltage change) and a stable visible radiation output when used at 80% rated voltage for a GE1763 (24-W) bulb. A Fluke 409a high voltage power supply was used a t -1000 V with a 1 P28 photomultiplier. The CuEDTA-Nitrien exchange reaction produces C u t r i e d 2 which has an absorption band a t 550 mp. The McKeePedersen monochromator was used with 0.1-mm entrance
yk&+$d Rubber tubing with air l e a k
Figure 2. Mixing system and cell assembly Mixing jets (1-mm dia.) were positioned so that one set of four entered the mixing chamber to give clockwise flow and the other set to give counter-clockwise flow. The mixing outlet was 2-mm dia. The reaction cell was of 4-mm dia. and 10.0 cm long. It had water inlets and outlets for thermostating (not shown)
and 0.5-mm exit slits and gave a spectral band width of about 1 mp, and gave good light intensities through the cell. This combination of source, monochromator, and detector gave photocurrents of 7 pA with a signal-to-noise (peak-to-peak) ratio of I O 3 to IO4 over a 10-msecond to 30-minute time period. The total drift was less than 0.1 % per hour after warm-up. THEELECTRONIC SCHEMATIC of the automatic rate instrument is given in Figure 3. Operational amplifiers (McKeePedersen 1006) were used t o convert the photocurrent t o voltage and for the subsequent analog operations. Photocurrent offset is achieved by applying a reference voltage equal t o the 100% transmittance voltage t o the second input of the MP-1006 differential amplifier. The voltage output, which corresponds to the difference between the signal and reference, is dropped across a variable resistor (ZR) in series with the meter relay. Thus, the sensitivity of the meter can be varied by changing the Z R where R = 50K. The A%T between the settings of the meter relay can be calculated from the meter resistance. A 100-pA double set point meter relay (Assembly Products, Inc.) was used. The relay determines the %T levels at which the integrator shorting switch S is opened and closed, Thus, the absorbance is sampled at pre-set values of the fraction of the reaction elapsed as shown in Figure 4a where the relay is opened after 21.5% reaction ( A 1 ) and is c1osed:after 29.0% reaction (Ad.
- 1000 v. all 0,l.
b Figure 3. Electronic schematic of the automatic rate instrument Capacitors and resistors =kt10 % except RIi O . l % , CI i O . l % Mylar. Operational amplifiers 1, 2, and 3 are MP-1006. El is MP-1008.
- - A -
Lop f .B meg
-
A
TO
e3 RECORDER
VOL. 3 9 , NO. 12, OCTOBER 1967
1347
a
perform an integration, a logarithm, and a differentiation, For a constant voltage, El, applied to amplifier 1 the output is a voltage ramp. el
=
E1 ~
RiCi
(t
-
tl) = Kl(t
-
tl)
The output of amplifier 2 is e2 =
50
'
b
(7)
dt
m a!
Combination of Equations 5 , 6, and 7 gives
m 0)
0;
Figure 4. Absorbance L'S. time curve for the chain reaction with the fraction of reaction sampled between A I and A2 (6) Output of reciprocal generator (c) Linearity of reciprocal generator (a)
ELECTRONIC MEASUREMENT OF THE RATEOF CHANGE was obtained as a voltage proportional to the reciprocal of the time required (t2 - tl in Figure 4) for the reaction t o proceed over a given interval ( A l to A2). To provide an all electronic system for the generation of the reciprocal function, use was made of operational amplifiers as shown in Figure 3. The operational amplifiers 1, 2 , and 3 successively Table I. Thiosulfate Ion Masking of Silver(1) and Mercury(I1) in the Coordination Chain Reaction EDTA, M x 107 Per cent metal Metal ( M X lo7) Added Found Masked Found 14.1 14.3 101 Ag(50.0) .,. Ag(50.0) 14.1 14.2 101 ... ... 9.44 9.25 98 Ag(500) ... 9.44 8.42 89 Ag(5000)a 14.1 13.9 98 Hg(50.0) *.. ... 14.1 14.0 99 Hg(50.0) ... 9.44 9.58 102 Hs(500) Hg(5000) 9.44 10.30 109 ... Ag(5001, Hg(5OO) 14.2 13.3 94 ... ... Ag(50.0) 17.9 12.2 ( 100) Pb(5.64) ... 101 ... Hg(50.0) 17.9 12.0 (100) 104 Pb(5.64) ... ( 100) Hg(50.0) 17.9 12.2 Pb(5 64) ... 101 ... ~g(500),~ g ( 5 0 0 ) 14.2 8.6 (100) ... 85 Cd(6.64) ... Ag(500), Hg(500) 18.9 8.5 (100) Pb(5.65), Cd(6.64) 85 ... and 1.18 X 10-3M [CUEDTA-~]= 2.63 X [Nitriencz] = 1.9 X 10-4M [S203-2] = 1.0 X 10-aM except as noted Ionic strength = 0.05M pH = 8.9 25.0" 4 [s,o,-2] = 1.0 x 10-2M. I
a
(6)
where Eo is 59.6 mV per decade at 27" and Io is a constant which is a function of construction and of temperature, The output from amplifier 3 is the time derivative of its input:
e3 = -R3C3 de2 -
E
1348
el R2
- Ea log - + Ea log Io
ANALYTICAL CHEMISTRY
e3
=
-0.434EO R3C3
(&) (A) = K3
Thus, the final output shown in Figure 46 is a voltage whose magnitude is inversely proportional to the time elapsed after tl when the meter relay opens S. In Figure 4c values of e3 are plotted against the reciprocal of the elapsed time. This demonstrates the excellent linearity of the reciprocal generator. When t = t2, e = eo and
(--)-
eo = KB
tl
1
tl
=
~3
(k)
(9)
The value of eo is indicated in Figure 4b as the voltage immediately before S closes at t 2 causing e3 to drop momentarily to the negative limit of the amplifier before returning to zero. RESULTS AND DISCUSSION
Thiosulfate Masking. Metal ions which form strong thiosulfate complexes include Hg(I1) > Ag(1) * Cu(1) > Cd(I1) = Pb(I1) > Zn(I1). Only in the case of the first three is thiosulfate able to compete effectively with EDTA for the metal ion. Thus, the stability constants (8) show that greater than 99% Hg(I1) or Ag(1) should be masked with less than 10-3M S203-2 when EDTA is 10PM. Complete masking of copper could mean the destruction of the C U E D T A - ~ reactant to liberate EDTA. In fact, a t 0.05M S203-2 the chain reaction system contained more free ligand than had been added, indicating that Cu(11) had been complexed and reduced by the thiosulfate so EDTA had been liberated. It would be possible to mask copper if the CuS203- and Cu(s203)2-3 complexes were slow to react with EDTA and if the excess S203-2 were slow to react with CUEDTA-~. However, this is not the case. A series of 18 kinetic runs showed no statistical difference in the rate of the Nitrien-CuEDTA exchange in the presence and absence of 1.0 x 10-3M thiosulfate. The standard deviation for the observed first-order rate constant ( k o = k$F$: [EDTA]) was 2z and corresponded to an error of k l . 3 X 10-*M in determining the EDTA concentration. These data and those in Table I were obtained before the automated rate instrument was put into operation and permit comparison of the point-by-point graphical work-up with the later automatic ones. Table I shows the results of masking up to 5 X lO-'M Ag(1) and Hg(I1) with thiosulfate. The catalyst concentration (EDTA) was 0.9-1.4 x 10-6M and the metals are fully (8) L. G. Sillen and A. E. Martell, "Stability Constants of MetalIon Complexes," The Chemical Society, London, 1964.
masked. The determination of lead and cadmium in the presence of silver and mercury also is shown. The average deviation for all the cases from the EDTA expected and that found are about 5 % . Thus the accuracy is poorer than the precision. The main source of error is known to be the dayt o d a y reproducibility of a trace EDTA reactant in the nickeltrien solution. Cyanide Masking. Cyanide ion has been used as a masking agent in EDTA titrations in conjunction with formaldehyde (9) or chloral hydrate (10, 11). The aldehyde removes the excess cyanide ion (Equation 4) and also destroys the weaker metal-cyanide complexes. At pH 9 and a total cyanide ion concentration of 10-5M only 10-3M chloral hydrate is required to reduce the free CN- concentration to 10-aM. Under these conditions, with 10+M EDTA, zinc, cadmium, and lead are not masked by cyanide while iron, copper, nickel, and cobalt can be masked. The order of addition of reagents is important because the successful application of cyanide masking is based on kinetic rather than equilibrium conditions. The steps are: (1) NaCN (to give l O + M ) and buffer are added to the sample; (2) chloral hydrate (to give 5 X l O - 3 M ) is added; (3) after 20 minutes the sample is added to the copper-EDTA with EDTA catalyst; (4) the exchange reaction with nickel-trien is initiated within 1-2 minutes. Using this procedure, iron, copper, nickel, and cobalt do not react with the EDTA catalyst and the cyanide ion cannot react with copper-EDTA or nickel-trien. Results are given in Table 11. In the case of Cu(I1) reduction occurs with complexation to give CU(CN)-~and in this form the copper does not interfere in the chain reaction. However, after chloral hydrate and EDTA are present, oxygen can reoxidize the copper to give CUEDTA-~. Therefore, if the above procedure is altered after step 3 and the mixture is shaken with air for 45 minutes before initiating the chain, the copper ion is not masked. Table I1 includes results from the manual-graphical method and from the automatic rate instrument. The accuracy was about the same but much lower concentrations (= 5 X 10-sM) were determined in the automated method and it would therefore be preferred in this case for sensitivity and speed. Performance of the Automatic Rate Instrument. The rate constant for a first-order reaction is given in Equation 10 in terms of the fraction of the reaction completed, &, at time t i . This is expressed in Equation 11 in terms of the absorbance measured to follow the reaction.
,001
.-.-
80
0 v)
.-u>
60
c L 0
r
.. 40
0
aP 20
z 1
0
2
3
4
5
Figure 5. Comparison of rate constants measured automatically (eo) and graphically (ko) Standard deviations of eo values are shown. = 1.78
CUEDTA-2
x
10-3~
Nitrien+* = 1.89 X 10-4M KCI
=
0.025M
pH 8.9, 25.0" Z E = 70.0, %R = 5.0 Set points = 70 (21.5 reaction) and 30 (29.0 ~~
reaction)
_ _ _ _ _ ~
~
Table 11. Cyanide Ion Masking of Nickel(II), Iron(III), Cobalt(II), and Copper(I1) in the Coordination Chain Reaction EDTA, M x 107 Per cent metal Metal ( M X IO)' Added Found Masked Found Ni( 8 .50) 11.3 10.9 ... Ni(8.50) 11.3 11.3 .,. Cu(7.80)b 11.3 10.9 ... Cu(7.80)b 11.3 11.1 ... Cu(0,52)a3C 7.61 7.09 100 Fe(O.48)a 3.88 ... 3.92 Co(0.52)a 4.55 4.78 ... cO(5.20) 11.3 11 .o ... Zn(O.54)~ 3.88 3.24 118 Zn(21.6) 34.6 10.7 111 34.6 11.5 ... Zn(21.6) 107 34.6 10.9 ... Zn(21.6) 110 Ni(0.85) 3.88 3.23 ... Pb(0.57) 114 3.88 3.29 ... 92 Fe(0.48) ... 3.88 2.96 86 Zn(0.54) Ni(O.85) ... 3.28 2.82 ... Fe(0.48) Cu(0.53) 96 Pb(0.57) a Measured with automatic rate instrument. Measured immediately after EDTA addition. e Measured 45 minutes after EDTA addition (with shaking).
1
(i
I t is apparent from Equation 9 that ko = (K/K3)eoand that the automatic rate instrument can be used to determine the rate constant of a first-order reaction. Figure 5 shows the expected linearity between eo and k o for a set of reactions in which the EDTA concentration was varied to give different ko values. At each EDTA concentration 5 to 10 values of
(9) K. L. Cheng, ANAL.CHEM., 35,783 (1961). (10) J. Kinnumen and B. Merikanto, Chemist-Analyst, 41, 71 (1952). (11) R. Pribil, CoNection Czech. Chem. Commun., 18, 783 (1953).
t
Other conditions: [CUEDTA-~]= 1.0 X lO-3M [Nitrien+2]= 1.0 X lO-4M [CN-lhbi = 1.0 X 10-6M [CIKCH(OH)p]totai = 1.0 X lW3M Ionic strength = 0.025 pH = 8.9, 25.0" ~~
VOL 39, NO. 12, OCTOBER 1967
0
1349
eo were obtained and then the entire ZT VS. time curve was recorded. A plot of In@, - A gave the k o value. The standard deviations of the eo measurements, which are shown in Figure 5, range from 2 to 5 Z. The precision of the graphical k o values was approximately the same. In terms of EDTA concentration, the average of the standard deviations corresponds to + 7 X 10-9M EDTA. Figure 6 gives a typical calibration curve obtained for eo in terms of the EDTA added. About 10 minutes were required to oLtain 5 to 10 determinations of eo a t each EDTA concentration. The curve does not pass through zero because the reagents have trace metals present which will react with EDTA. Most of the “EDTA-consuming-impurity” comes from the nickel-trien and is a result of an equilibration reaction of this complex. Although the “impurity” is only 0.2% of the nickel-trien, it is present at 10 times the level of EDTA sensitivity and is troublesome because its presence necessitates frequent calibration curves. The standard deviation of eo for 63 measurements used to obtain the calibration curve was h 2 . 4 chart divisions which corresponds to +2.4 X 10-8M EDTA. The fact that the precision was not as good as in Figure 5 seems to be caused by the lower concentration of nickel-trien which gave only half as large a total absorbance change. The fraction of the reaction which is sampled for automated measurement affects both the sensitivity and the precision of the eo value obtained. For a given ko value, eo will be larger as At becomes smaller. Hence, for high sensitivity the reaction should be sampled when the rate is fastest and a small fraction dfl - 5 ) is desired. Therefore the f i and f 2 values generally corresponded to l G 2 0 Z or 15-25z of the reaction. However, the smaller the fraction sampled the greater the relative error which was observed as shown in Table 111. The conditions used represented a compromise between sensitivity and precision. The major source of random error arises from photometric noise. This accounts for the better results when larger absorbance changes were used for a smaller fraction of reaction (Figure 5 data cs. Figure 6 data). The
I 50
I/
t
‘Ot 0;
J’
z/=
I
$
4 ; 6
; A
iEDTA] a d d e d , x IO:&
Figure 6 . Calibration curve for eo with EDTA (catalyst) added Standard deviations are shown.
x
= 1.19
C~EDTA-2
10-3~
Nitrien+2 = 0.95 X 1 0 - 4 M KCI = 0.025M pH 8.9, 25.0” Z E = 75.0, Z R = 5.0
Set points
=
70 (7.1
reaction) and 45 (17.1 2 reaction)
photometric noise was traced to the light source, so despite the fact that it had relatively good stability this was still a limiting factor. The second most probable source of error is the reproducibility of the meter relay. Direct experimental measurements of the meter relay response gave the error in making or breaking the switch relay as zt0.05Z of the full scale meter deflection. The calculated error for fl = 0.1 and& = 0.2 under the conditions used in Table I11 is a maximum of + 2 z . Table IV gives data for the determination of copper (down t o 3 ppb in water) with an accuracy range of +3.5 X 10-8M. There is a small but regular trend in the accuracy of the data which suggests a slight contamination from some source, but the accuracy was close to the limiting precision (==t2 X 10-8 for these conditions) so this was not investigated. CONCLUSIONS
Table 111. Observed Error in the eo Values for Different Fractions of Reaction Sampled AZT 0.7
h -fi
2.
0.03 0.10 0.13
11
2.1 4.5 10 measurements for each eo [Nitrie~~+~] S 1 .O X [CUEDTA-~]E 1.O X
8 4 fi =
0.025
p H 8 . 9 25.0”
Table IV. Determination of Copper Using Automated Measurement Cu+2 added A (EDTA) found x 107M X 107M Error X 10iM 10.50 10.14 -0.36 5.25 5.06 -0.19 2.63 2.72 -0.09 1.05 1.15 $0.10 0.53 0.88 +0.35 Conditions: Background “metal impurity” = 9.25 X 10-’M Range [EDTA] added = 15.2 to 22.8 X lO-’M [CUEDTA-~]= 7.25 X lo-‘ [Nitrienfz] = 1.35 X 10-4 p = 0.025, pH 8.9, 25.0” Set points 30 and 60; Z E = 75.0; X R = 10.0
1350
ANALYTICAL CHEMISTRY
Use of the automatic rate instrument offers a relatively inexpensive and a rapid method for kinetic analysis. The precision of the determinations was limited primarily by the photometric noise, the magnitude of the absorbance change, and the time required for the reaction. The total absorbance change in the coordination chain reaction system was not large, corresponding to only 0.12 to 0.25 absorbance unit, Therefore, the results, which ranged from 2 to 10% precision for ultratrace levels of metal ions, are quite satisfactory. The coordination chain reaction system offers extreme sensitivity for metal ion determinations. Selective analysis is possible for a number of metal ions. In addition to the thiosulfate and cyanide masking reported here, p H control can also be used for selectivity. Rapid analysis at the 0.01- t o 0.001-ppm level can be achieved by this catalytic method. ACKNOWLEDGMENT
The authors are indebted to Harry Pardue for helpful discussions concerning the electronics.
RECEIVED for review May 25, 1967. Accepted July 24, 1967. This work was supported in part by the Air Force Office of Scientific Research, Grant AFOSR 136-65 and the National Institutes of Health, Grant G M 12152.
