the addition of excess chromous chloride (3 ml. of 0 . i 5 N solution). T h e precipitate is spun down and washed twice with water and once with acetone, and slurried with acetone onto a weighed aluminum planchet. The precipitate is dried under an infrared lamp a t 90-5” C., weighed, and counted, using an end window Geiger counter. Results are calculated by comparison of the weight recovered and the activity with that of a standard sample. The standard is processed and mounted in the same manner as the samples, so that the comparison is exact. Recoveries. This separation scheme gives chemical recoveries of io70 of the antimony originally present. I n addition to t h e 10% loss occurring in the solution of t h e initial antimony precipitate, losses, each of about 5 y G , are encountered in the digestion step, a n d with t h e combined arsenic and ferricyanide precipitate. T h e remainder of the loss occurs in the transference of the final precipitate to the planchet. These were determined by tracer experiments. Similar experiments have been made to show the satisfactorv elimination of interfering elements. Radiochemical Purity of Final Antimonv PreciDitate. T h e radiochemical purity of &the final precipitate is demonstrated by y scintillation spectrometry and half-life considerations. The separation does not remove bismuth, but bismuth activated by neutron capture to give Bizlowill give only 0.3% of the activity of an equal amount of antimony activated to give Sblz2. I n samples with large amounts of bismuth, a circumstance rare in biological samples, counting may be effected by a y scintillation technique, using the 0.57 hl.e.v. y ray of SblZ2. As Bizlo is a pure p emitter, its activity is not detected.
~~
Table 111.
Conditions for Precipitation of Copper with Ferricyanide
Temp. of solution ( ” C.)
HvDoDhosDhite “I soiutiin (satd. at 20” C.) ml.
60 40 20 20 20 20 20 20 20 20 20 20
1 1 1 1 2 5 1 1 1 1 1 1
KaFe(CN)e
HC1, molarity 0.5
(10%
ml.
CONCLUSION
This method eliminates blanks other than the standard sample, which gives the specific activity of the antimony. Microseparations are avoided by the addition of inactive antimony carrier in convenient amounts. The yield recovery technique allows rapid working, and removes the need for time-consuming quantitative transfer operations. ACKNOWLEDGMENT
The authors thank Gilbert Forbes and Edgar Rentoul, of the Forensic Medi-
Percentage Cu retained in solution
0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.1 0.25 0.5
0.5 0.5 0.5 0.5 0.5 0.5 1.1 2.7 0.5 0.5 0.5
Sensitivity. T h e method described above permits the determination of gram of antimony. Trials on solutions containing 10-lo to lo-* gram of antimony under standard irradiation and processing conditions give results which agree with the calculated value within 5%. The difference found in two series of duplicate analysis also gives agreement, within 5%.
W.h.1
2.2 1.3 0.4 0.4 1.2 0.8 0.4 7.2 8.6 30.4 0.4
0.0
cine Department of Glasgow University, and J. M . A. Lenihan, of the Western Regional Hospital Board, Regional Physics Department, for support and laboratory facilities during the investigation. LITERATURE CITED
( 1 ) Kennedy, J. H., Bethard, W. F., Schmidt, R. A,, Olehy, D. A. J . Thoracic and Cardiovascular Surg. 44, 570 (1962). (2) Smales, A. A,, Pate, B. D., ANAL. CHEM.24,717 (1952). ( 3 ) ,Yogel, A. J., “Textbook of Quantita-
tive Inorganic Analysis,” 3rd Ed., p.
227, Longmans, Green, London and New York, 1961.
GRANTS supplied by the Medical Research Council and the International Atomic Energy Agency.
R. A. HOWIE M. M. MOLOKHIA HAMILTON SMITH Department of Forensic Medicine The University of Glasgow Glasgow, W. 2, U. K .
Theory of Derivative Voltammetry with Irreversible Systems SIR: Recently, the applications of derivative techniques to stationary electrode polarography (6) a n d to anodic stripping voltammetry (6) have been reported. In each case significant enhancement of analytical sensitivity was obtained over the respective conventional voltammetric techniques. The theoretical behavior for first-, second-, and third-derivative voltammetry was predicted for reversible depositions at plane and spherical electrodes. Experimental correlations were observed a t the hanging drop mercury electrode (6). The quantitative application of derivative voltammetry to irreversible electrode reactions has not been reported yet. This communication describes the development of a theoretical treatment of the derivative voltammetric behavior
for the irreversible case a t a stationary plane electrode. The rigorous expressions for stationary electrode polarography with irreversible systems have been derived previously (1, 7 ) . The solution given by Nicholson and Shain (4) and derived by Reinmuth ( 7 ) has been used in this work to obtain the derivative expressions, using the mathematical approach described previously (6). The final expressions in both the conventional and derivative case are not in closed form, but rather are in the form of infinite series. The series can be evaluated with the aid of a computer, and tables can be prepared for the construction of theoretical curves. Furthermore, the relationship between derivative current-voltage characteristics and kinetic parameters can be described.
THEORY
The expression for current-voltage behavior for the irreversible case with conventional voltammetry at a plane stationary electrode can be given as (4, 7 )
i
=
nFACo*(~Dob)”2x(bt)
(1)
where b is defined as an,Fv/RT, v is the rate of voltage scan in volts/second, and
(V%’
exp( -jFE’/RT)
(2)
d m ! where
E‘
=
an,(E
- EO) + (RT/F)ln(?rDob)i’z/k,
VOL. 37, N O . 8, JULY 1965
(3)
1061
The other terms have their usual significance (2).
of peak current values for successive derivative curves obtained under identical conditions. For example, a t 25.0’ C.
By differentiation of Equation 1 with respect to time is obtained
di/dt
I’
=
=
~ F A C ~ * ( T D X~ ~ ) ” ~ [dx(W/dEl (dEidt) (4)
where dE/dt = -v, and m
dx(bt)/dE = [ l / ’ ( ~ ) ~ ’ ~ (-l)j+l ]
x
j=1
[(&I7/d(j - 1)!l(-janaF/RT) exp( -jFE’/RT) =
(5)
[ - an,F/(n) 1 ! 2 R T ] ~ l ( b t )(5a)
Thus, three analogous expressions for first, second, and third derivatives, I ’ , I” and I”’ can be obtained.
I’
=
nFACo*Do’/2b3’2~1(bt) (6)
I”
=
nFdCo*Do“2b5/2~2(bt) (7)
E‘, VOLTS
Figure 1 . Plots of theoretical first, second, and third derivative functions A.
Xibf)
xzbt) C. xdbf 6.
1”’ = nFA Co*Do1/zb7’2~3(bt)(8) where m
Xl(bt) =
(-ljj+l
rest of the derivative curves. However, because all the important features of the derivative curves occur before E’ = -0.02, the theoretical data are sufficient for experimental correlations.
(-l)i+I
EXPERIMENTAL CORRELATIONS
j=1
m
Xz(bt) = j=l
(A)i j z exp(-
d
m
jFE’/RT)
(10)
and m
Xp(bt)
(-l)i+l
= j=1
With the IBJI 7090 computer, the ) functions, x l ( b t ) , xz(bt), and ~ 3 ( b t have been evaluated as a function of E‘. Theoretical plots of the functions are shown in Figure 1. Figure 1 also shows that the theoretical characteristics of the derivative current-voltage curves cathodic of an E’ of about -0.020 volt (about 15/an, mv. past the conventional peak) are not available. This is because the series does not conyerge readily when E’ is negative. Thus, it may be questionable as to whether the differentiation is ualid for E’ negative. The only evidence that the differentiation may be valid for negative values of E‘ is that the computed value of Ez’, a t which the derivative signal goes through zero, agrees exactly with the calculated conventional peak potential; and this is a t a negative value of E’ (Ez’ = -0.00534). Xevertheleas, it may not be possible with the present approach to obtain the theoretical points for the 1062
e
ANALYTICAL CHEMISTRY
The first-, second-, and third-derivative currents are directly proportional to concentration (Equations 6, 7 , and 8). Thus, the application of derivative voltammetry to irreversible systems for analytical purposes should be possible. The important characteristics for the enhanced sensitivity expected are analogous to the reversible case and have been discussed previously (6). Correlation of derivative measurements with kinetic parameters can be made readily. For example, the peak potential, E,, of the conventional stationary electrode polarogram is related to k , and an, by the following relationships (4).
E,
=
E”
- (“’> m,F
(0.780
+
d/Dob- In k,)
(12)
(3) 4%
(13)
In
In
Because E , corresponds to the potential where the first derivative current crosses the zero axis, E,, the above correlations can be made easily and accurately with first-derivative voltammetry. This is particularly significant when one considers that irreversible waves may be drawn out with the peak spread over a considerable potential range. Furthermore, the quantity ano may be measured readily by taking the ratio
(14.80 v)an, (15) The simplicity and ease of this method for determining ano is unique. Only two measurements are required, each of which is made under identical experimental conditions, minimizing the introduction of extraneous errors. Furthermore, the only parameter, beside temperature, which must be known is the scan rate. A simpler, but experimentally less accurate, method for determining ann. from the derivative curve is by correlation with the separation of characteristic potentials. This is essentially an abbreviated curve-fitting procedure, but it cannot be done simply with the conventional voltammetric curve because only one characterizing potential can be located. The relationship between an, and the separation of any two characteristic potentials on the derivative curve, El and E2,is given by
ana(Ei
- Ez)
=
El’
- Ez’
(16)
Thus, using the example of a first-derivative curve where EDpl refers to the potential of the first peak, and E , is the potential a t which the derivative signal crosses the zero axis. Another relationship which may be useful can be derived in a fashion analogous to the method of Gokhshtein and Gokhshtein and (3)Xicholson and Shain (4). That is, the surface concentration of reactant 0 a t the derivative peak can be expressed in terms of ~ ( b tand ) E’, and that value can be substituted in the Eyring equation for a totally irreversible electrode reaction (2). A convenient relationship is obtained between the conventional current at a n y potential and an2,,k,, and ( E - E”). The resulting expression can then be differentiated with respect to time to give the derivative current dependence. Thus, using the expression given by Nicholson and Shain CO/CO*= ~ ( € 4exp(E‘F/RT) )
(18)
Substituting in the Eyring equation, differentiating, and evaluating at the derivative peak, one obtains
I,’
=
nFAk,exp( - an,F/RT) X
( E D P- E”) [ C o D P (-an,F/RT) X (dE/dt) (dCo/dt)o~](19)
+
obtaining (dCo/dt)op from Equations 2, 5, and 18 and combining terms, one finds
I,'
=
nPAk,Co*(an,F/RT)K'u
exp(-an,F/RT)
(EDp
- EO)
(20)
where
Equation 20 is consistent with Equation 6, evaluated at E D p . Thus, by experimentally varying the scan rate and plotting ln(I,'/u) against (EDp - E " ) , a linear plot can be obtained with slope a function of an. and intercept a function of k, and an,. This last relationship may have one distinct advantage over a similar one proposed by Gokhshtein and Gokhsh-
tein and (3) and Nicholson and Shain (4) which relates the conventional peak current to ( E , - E"). T h a t is, because the scan rate must be varied over several orders of magnitude to obtain kinetic data, the interference of charging current may be a serious limitation with conventional voltammetry. The derivative measurement minimizes charging current interferences (6) and, therefore, may prove more useful experimentally. Further work is currently in progress in this laboratory to correlate experimentally irreversible behavior with the theoretical relationships described in this communication. I n addition, the application of derivative voltammetry for trace analysis with irreversible systems is being investigated. The results of these studies will be reported in the near future.
LITERATURE CITED
(1) Buck, R. P., ANAL.CHEM.36, 947
(1964). (2) Delahay, P., "New Instrumental Methods in Electrochemistry," Chap. 3., Interscience, Sew York, 1954. (3) Gokhshtein, A. Y., Gokhshtein, Y. P., Doklady Akad. ,Vauk SSSR 131, 601 i 1960). (4) Xicholson, R . S., Shain, I., Au.ir,. CHEM.36, 706 (1964). ( 5 ) Perone, S. P., Birk, J. R., Ibzd., 37, 9 (1965). (6) Perone, 6. P., Mueller, T. R., Ibid., p. 2. (7) Reinmuth, W. H., Ibid., 33, 1793 (1961). S.P. PEROXE C. V. EVIXS Department of Chemistry Purdue University West Lafavette. Ind. I N V E S T I G A T I ~ N supported in part by Public Health Service Research Grant T o . CA-07773-01 from the Sational Cancer Institute. .
I
,
Gas Liquid Chromatographic Separation of Resin Acid Methyl Esters with a Polyamide Liquid Phase SIR: I n recent years a number of gas liquid chromatographic column systems have been applied to the separation of resin acid methyl esters (1, 4, 6-8). I n spite of these many reports, a liquid phase which cleanly resolves all the seven major resin acids has yet to be found. I n the course of our continuing efforts to find a rapid and simple method of analyzing complex mixtures of the resin acids, we have found that Versamide 900 is a very useful substrate. EXPERIMENTAL
Gas liquid chromatographic separations were made using an F&M Model 500 gas chromatographic instrument equipped with a thermal conductivity detector and utilizing W2 tungsten filaments. Columns were packed by blowing the packing material from a homemade or commercial reservoir inch 0.d. copper into the precoiled refrigeration tubing under a nitrogen pressure of 50 to 55 p.s.i. A mechanical vibrator was employed to aid in fluidizing the packing as it was being loaded into the column. Coating of the Versamid 900 on the solid support was accomplished in the following way. Equal parts of the polyamide and 2-ethylhexanol were heated on a hot plate until homogenous. The resulting solution was then diluted with hot ethanol in a n amount sufficient to give a fairly fluid slurry with the solid support. After slurrying with solid support, the solvent was stripped off i n vacuo with a rotary evaporator. The coated support was reslurried with hot ether and again stripped of solvent. Before use in packing columns the packing material was screened to a 60/80 mesh particle size. Coating on Chromosorb W and Anakrom ABS
supports gave packings with essentially identical performance characteristics. Columns were conditioned for 12 to 16 hours a t 250" C. Peak assignments were verified b y use of samples of purified resin acids. The acids and acid mixtures (rosin) were esterified with freshly prepared diazomethane. Determination of Relative Response of Resin Acid Methyl Esters. Pure resin acid methyl esters were weighed (10 mg.) and dissolved in 2 ml. of a methanol solution containing 5 mg. per ml. of eicosane. Aliquots of each ester solution were passed through t h e gas chromatograph and the areas of t h e ester and eicosane peaks were compared. T h e relative response was calculated by dividing the area of the eicosane peak into the area of the ester peak. T h e relative responses of the methyl esters of the following resin acids were determined : levopimaric acid, 0.56; abietic acid, 0.80; isopimaric acid, 0.79; pimaric acid, 0.80; a n d dehydroabietic acid, 0.78. RESULTS A N D DISCUSSION
Table I lists the retention times for the seven most common resin acids relative t o methyl pimarate ( T ~ ~and ) to the next earlier emerging ester (rI2). Data for a diethylene glycol succinate (DEGS) column of similar efficiency is given for comparison with the Versamide 900 column. DEGS columns have recently been recommended for analysis of oleoresins (6). The r12values obtained with the DEGS column are in good agreement with those reported by Nestler and Zinkel (6). A Golay resolution of 4 (S), corresponding to 98% separation, of the most difficultly separable pair would require about 5500
plates using DEGS as the substrate but only 3500 plates using Versamide 900. As shown in Figure 1, good separation of the resin acids present in slash pine gum was achieved in 35 minutes with a 15-foot Versamide 900 column. Only the methyl levopimarate-methyl palustrate pair failed to separate. The separations of this pair which are reported in the literature (4, 8 ) apparently resulted from the use of old solutions of methyl levopimarate (6). I n all these cases the same relative retention is reported for levopimarate and for dehydroabietate. Hudy (4) observed typical acid catalyzed isomerization of levopimarate during GLC with the appearance of peaks of abietate and neoabietate, while Nestler (6) reported on the basis of
Table I. Relative Retention Data for Resin Acid Methyl Esters on DEGS and Versamide 900 Column
T'ersamide 900a
DEGSb
rlpc
rl,
718
712
Pimarate 1.00 . . . 1.00 , . . Levopimarate/ palustrate 1 . 2 1 1 . 2 1 1.31 1.31 Isopimarate 1.32 1.09 1.41 1 08 Dehydroabietate 1 . 5 1 1.14 2.10 1.07 Abietate 1.74 1 . 1 5 1.96 1.39 Neoabietate 1.96 1.13 2.27 1 . 0 8 " 10 ft. X ' / 4 inch 57, Versamide 900 on Chromosorb W at 250" C., 3000 plates for abietate. b 10 ft. X '/4 inch 20y0 DEGS on Chromosorb W at 220" C., 2700 plates for abietate. Retention relative t o pimarate. Retention relative to preceding peak.
VOL. 37, NO. 8, JULY 1965
1063
