1226
Anal. Chem. 1984. 56. 1226-1229
Table I. Determination of Ethynylestradiol in Pharmaceutical Preparations by Normal Pulse Stripping Voltammetry brand Estigyn, Glaxo Aust. Pty., Ltd. Mixogen, Organon Aust. Pty., Ltd.
nominal content 10 pg of ethynylestradiol 4.4p of ethynylestradiol 3.3 mg of methyltestosterone Microgynon 30, 30 pg of ethynylSchering AG, Berlin estradiol 150 pg of laevonorgestrel
NPS results 9.7 pg + 2.5% 4.3 pg
5
3.0%
NAa
Not applicable, see Organic Interference, Section G(ii). However, it should be noted that determinations of all formulations of known matrix with and without EDTA gave the same result, within the precision of the experiment. I. Analytical Procedure. On the basis of the above detailed study, a routine analytical method for determination of ethynylestradiol in pharmaceutical preparations was developed. (i) Extraction. A single tablet was taken for ethynylestradiol determination and placed in a 50-mL round-bottom flask. Five milliliters of distilled deionized water was added and the flask shaken until the tablet disintegrated. The residue was extracted twice with 20 mL of hot (50 "C) methanol. The extracts were cooled an pooled and made up to 50 mL. Five milliliters of the methanol extract was then taken for the analytical determination. Recovery experiments were based upon the spiking of a representative portion of 10 finely ground tablets before disintegration that gave yields of 100% within the precision of the experiment. (ii) Determination. To the 5-mL methanol extract, 5 mL of 0.1 M borate buffered pH 11.5 distilled deionized water containing 2 x M EDTA was added in the PAR Model 303 cell. Purified nitrogen was bubbled through the solution for a period of 10 min prior to the analysis. The solution was thermostated to 20 f 1 "C with a water-jacketed cell. NPS voltammetry of the solution was then performed under the following conditions:
(i) Deposition: potential, -0.200 V vs. Ag/AgC1(3 M KCl); time, 30 s (without stirring). (ii) Stripping scan: normal pulse wave form; pulse duration, 20 ms; 1 s rest between pulses at a pulse increment of 5 mV to a final potential of -0.700 V. The precision of the experimental procedure was determined by performing 10 replicate determinations at the 1.6 X M level from a homogeneous sample of 20 tablets and was calculated to be a relative standard deviation of 1.5%. Table I lists the results of the mean and relative standard deviations for 20 individual determinations of two pharmaceutical products. Quantification was based upon the method of standard addition.
ACKNOWLEDGMENT Samples of pure steroids were generously donated by Schering, Wyeth International and Searle Aust. Pty., Ltd. Registry No. Ethynylestradiol, 57-63-6; methyltestosterone, 58-18-4; laevonorgestrel, 797-63-7. LITERATURE CITED (1) Gorog, S.;Szasz, Gy. "Analysls of Steroid Hormone Drugs"; Akademia Klado: Budapest, 1978; pp 372-379. (2) Bagon, K. R.; Hammond, E. R. Ana/yst(London) 1978, 103, 156-161. (3) Johnston, M. J . Chromatog. 1981, 216, 269-274. (4) Glaxo Aust. F-ty., Ltd., Private Communication Aug 1982. (5) Bond, A. M.; Heritage, I. D.; Briggs, M. H. Anal. Chim. Acta 1982, 138, 35-45. (6) Smyth, F. In "Proceedings of Electroanalysis in Hygiene, Environmen-
tal Cllnlcal and Pharmaceutical Chemistry"; Elsevier: Amsterdam, 1979, Analytical Chemlstry Symposia Series 2. (7) Florence, T. M. J . Elechoanal. Chem. 1979, 97, 219-236. (8) Bralnina, Kh. 2. "Stripping Voltammettry In Chemical Analysis"; Wiley: New York, 1975. (9) Palecek, E. Ana. Biochem. 1980, 708, 129-138
(10) Palecek, E.; Frantisek, J. Collect. Czech. Chem. Commun. 1980, 45, 3472-3481. (1 1) Kalvoda, R. J . Nectroanal. Chem. 1980, 111, 325-332. (12) Smyth, F.; Vaneesorn, Y. Anal. Chim. Acta 1980, 777, 183-191. (13) Anderson, J. E.; Bagchl, R. N.; Bond, A. M.; Greenhill, H. B.; Henderson, T. L. E.; Walter, F. L. Am. Lab. (Fairfield, Conn .) 1981, 73 (Feb), 21-32. (14) Anderson, J. E.: Bond, A. M. Anal. Chem. 1981, 53, 504-508. (15) Bond, A. M. "Modern Polarographic Methods in Analytical Chemistry"; Marcel Dekker: New York, 1980. (18) Myers, D. E.; Osteryoung, J. Anal. Chem. 1974, 4 6 , 356-363. (17) Bard, A. J., Ed. "Encyclopedia of the Electrochemistry of the Elements"; Marcel Dekker: New York, 1974, Vol. 2.
RECEIVED for review July 21, 1983. Accepted February 21, 1984. Financial assistance was provided by the Australian Research Grants Committee, Schering and Wyeth International.
Nonlinear Least-Squares Analysis of Double Potential Step Electrochemical Data Floyd E. Woodard,* Richard D. Goodin, Patrick J. Kinlen, and John H. Wagenknecht Monsanto Company, 800 North Lindbergh Boulevard, St. Louis, Missouri 63167 A nonlinear least-squares method Is presented for determlnlng the homogeneous rate constant for an Irreversible flrst-order reactlon followlng an electron transfer step by uslng double potential step chronoamperometry. The method was tested by applylng It to simulated data (flnlte difference) and to experlmental data obtalned for the reduction and subsequent decomposition of fert -butyl p-toluate.
Nearly 20 years ago Schwarz and Shain ( 1 ) reported a double potential step chronoamperometric method for determining the rate constant of an irreversible first-order re-
action following an electron transfer step (Le., EC irr). There are several noteworthy aspects of their method: (a) By stepping to sufficiently forcing potentials, the electrode reaction becomes diffusion controlled thus avoiding complications due to heterogeneous charge transfer. (Theory has also been derived for analyzing chronoamperometric data from experiments involving single potential steps to less forcing potentials with either reversible (2,3) or quasi-reversible (4) charge transfer.) (b) By use of the ratio of currents flowing a t corresponding times after the forward and reverse steps, the data become independent of the electrode area and the diffusion coefficient and bulk concentration of starting ma-
0003-2700/84/0358-1226$01.50/00 1984 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 56, NO. 8,JULY 1984
terial. (c) Discrimination against double layer charging or adsorption phenomena (5) can be realized by ignoring current measurements made a t short times after each step. A drawback to the method of Schwarz and S h a h is that multiple working curves are required. Only a single working curve is required if data analysis is restricted to a specific current ratio point. For example, Bard et al. (6) and Dryhurst e t al. (7) used the current ratio point that equaled half the value that would have been measured in the absence of the homogeneous reaction. The experimental data are more fully utilized by considering numerous current ratio points obtained at various times after each step. This gives a more accurate determination of the rate constant and a better indication of the validity of the assumed mechanism. Hanafey et al. (8) did this by simplex fitting of double potential step data. The response to each simplex move was calculated by using multiple working curves (stored on disk) and a surface interpolation routine. In the present work a nonlinear least-squares data reduction technique is presented. This does not require a fide of working curves, yet rapid convergence (typically in less than 5 min) is achieved on a laboratory microcomputer.
THEORY In the following, it is assumed that mass transport is adequately described by Fick's laws for linear diffusion and that adsorption and double layer effects are negligible. Initially the electrode is a t a potential El where charge transfer does not occur, c&, t = 0) = colb and CRed(X, t = 0) = Cprod(X, t = 0) = 0. At time t = 0 the electrode potential is stepped to E2 where the following reactions occur:
Ox
-
+ ne-
Red
(1)
1227
in this work of @(t,r,k)and lFl(cu,y,~)was terminated when a term in the series was encountered with an absolute value less than 1 X lo4 times the absolute value of the sum of preceding terms.) The best measure of the homogeneous rate constant is that value which causes the calculated current ratios ( f i , f,, ...,f,) to most closely match the corresponding measured current ratios (gl, g,, ..., gm), An iterative nonlinear least-squares method for finding that rate constant is outlined below. An initial guess for k (typically chosen to equal 1 / ~ must ) be corrected by an amount Ak, where Ak is the value required to minimize the following error sum: m
error sum =
C (gj- f >)2
(7)
j=l
Here f 5 is the current ratio calculated by using the corrected rate constant (k, = k,, Ak). An approximate expression for f $ can be obtained by using the first two terms in a Taylor expansion of eq 4
+
f '(47,k) E f ( t , ~ , k + ) Ak[af(t,~,k)/dkl
(8)
After substituting eq 8 into eq 7 and then taking the partial derivative of the resulting equation with respect to Ak and setting it equal to zero, we obtain the expression rn
Ak
E
{ C [ g j - @j j=l
rn
+ ( ( t j - 7)/tj)1/2]d@j/dk)/C(d@~/dk)2 j= 1
(9) where is the value of the function @ (eq 5) at time tk From eq 5 and 6 it can be shown that d@/dk = exp(-kt)[-t ,Fl(1/2,l,k7)
+
m
T ,F1(3/2,2,k7)/2] + C(exp(-kt)[(t - 7)kIn/n!) {(-t + (2) n=l n / k ) lFl(n + 1/2, n 1, k7) + E, is chosen so that reaction 1 is diffusion controlled and C ~ ( X [7(n-k 1/2) 1Fl(n + 3/2, n + 2, k T ) ] / ( n + 1)) (10) = 0, 0 < t < 7) = 0. After a time 7,the electrode potential is stepped to E3 where the following reaction occurs under The value obtained for k , after one iteration is not necessarily diffusion control: the best value because eq 9 is an approximation. To obtain a better value for the rate constant, k,,, can be substituted Red Ox + ne(3) for k,, and a new Ak calculated. This loop is continued until and the homogeneous reaction in eq 2 continues. E3 is asAk is much less than laguess (e.g., when Ak < (1 X 10-3)kgues8). sumed to be sufficiently positive that CRed(X = 0, t > 7) = 0. EXPERIMENTAL SECTION If double layer charging times are appreciable, then the applied potentials E , and E3 must be chosen so that soon after each tert-Butyl p-toluate was prepared from the corresponding acid potential step, the voltage across the double layer region is chloride (Aldrich)and tert-butyl alcohol. Tetraethylammonium fluoroborate (Southwestern Analytical) was used as received. sufficiently forcing that the heterogeneous charge transfer Acetonitrile (Burdick and Jackson Distilled in Glass) was dried reaction is diffusion limited. over alumina (ICN Nutritional Biochemicals, W200 Neutral, Schwarz and S h a h (1)have shown that the ratio of currents Activity Grade Super 1). & / i f ) flowing a t corresponding times after the backward and The reference electrode was Ag/O.l M AgN03 in acetonitrile. forward potential steps (to E3 and E,, respectively) is given All potentials given here are referenced to that electrode. by A planar mercury film/platinum substrate electrode (area = 0.079 cm2) was prepared by a method similar to that used by f(t,T,k) = -&/if = @ ( t , ~ , k-)[(t- ~ ) / t ] l / , (4) Bellamy (IO). The three-electrode potentiostat (constructed inwhere f ( t , ~ , kis) the current ratio function, t is the time house) and two-compartment electrochemical cell are described corresponding to the back step current measurement, and the elsewhere ( I I). The potential step experiments were controlled and recorded function 0 is defined as with a microcomputer developed at the University of North @ ( t , ~ , k=) exp(-kt) 1F1(1/2,1,k7) Carolina (12). In those experiments the potential was stepped from -2.4 V to -3.0 V and then back to -2.4 V. (Eljzfor the toluate C{exp(-kt)[(t - 7)kInlFl(n +1/2, n + 1, h ) ) / n !(5) ester was determined to be -2.88 V for quasi-reversible cyclic n=l voltammetric data (100 V s-') using a semiintegral technique where lFl(a,y,x) is the confluent hypergeometric series given described by Saveant and Tessier ( I 3 ) . ) Relaxation currents by obtained in the absence of the redox couple were subtracted from m the currents measured with toluate present before data reduction techniques were applied. lFl(WY,X) = 1 + C ( [ a ( a+ l)...(a + n - 1 ) ] / n=l The nonlinear least-squares fitting routine was written in interactively compiled BASIC (Digital Specialities, Chapel Hill, NC) [Y(Y -t 1)...(~ + n - l ) l ) x n / n !(6) and executed on the U.N.C. microcomputer. (This computer is Equations 4 and 5 are obtained after simple algebraic mabased on a Z80 microprocessor working in conjunction with an nipulations of eq 4.251 and 4.252 in ref 9. (The evaluation AM9511 math processor.) For 250 current ratio points each
Red
k
prod
-
+
LI)
+
1228
ANALYTICAL CHEMISTRY, VOL. 56, NO. 8, JULY 1984 101
i
O.8-/
-10
0.0
1
I
0
0.2
1
I
1
0.8
0.8
1
I
0.4
J
-
1
0.00
0.05
relative time Figure 1. Current ratio data as a function of a dimensionless time
variable (relative time = (t - T ) / T where tis time after the back step) from double potential step data for 1.05 mM ferf-butyl p-toluate and 0.1 M tetraethylammonium fluoroborate in acetonitrile: experimental nonlinear least-squares fits assuming an EC irr mechanism data (-). Step reversal times were (A) 0.03 s, (B) 0.06 s, and (C) 0.12 s. Homogeneous rate constants determined from fitting procedure were (A) 10.8 s-', (B) 10.5 s-', and (C) 9.9 s-l.
5 0.15
0.10
0.20
5 0.25
t/s Flgure 2. Relaxation current vs. time plot for experiment C in Figure 1: experimental data (-); finite difference simulation assuming an EC irr mechanism with k = 9.9 s-' and fast heterogeneous charge transfer (-).
(..e);
0.6 7
iteration required approximately 1min. As each iteration was completed the corresponding current ratio vs. time profile was displayed on the CRT. Typically, adequate fits were obtained after fewer than five iterations. Finite difference calculations were written in FORTRAN and executed on an IBM 370 computer.
RESULTS AND DISCUSSION To verify the accuracy of the theory presented here, it was applied to six simulated (finite difference (14))data files with k~ values ranging from 0.0316 to 10.0. In every case the homogeneous rate constant determined by the nonlinear least-squares method agreed with that used in the simulation to within less than 0.1% . Varying the initial guess for k from zero to more than ten times the correct value had no effect on the final value obtained for the rate constant. T o test the sensitivity of the technique to the quality of the relaxation data, noise with a Gaussian distribution (15)was added to the simulated data. The standard deviation of the noise was made equal to 0.1% or 1%of the magnitude of the first simulated data point (Le., that point corresponding to a measurement made at 7/250). (The 0.1% noise level was similar to that in the experimentally obtained data shown in Figure 1.) The values found for data with 0.1% noise were within several percent of the original values. As expected, analysis of the more noisy data resulted in rate constants with larger errors (as large as 13%). The rate constant obtained for data with k7 values near one were least affected by the addition of noise. Even with noise present, the initial guess for k had no effect on the final value obtained for the rate constant. In a recent report from this laboratory (16),the reduction and subsequent decomposition of a series of benzoate esters were investigated. Since the rate of decomposition of the radical anion increased as the stability of the cleaved alkyl radical increased, the following EC irr mechanism was proposed: PhCOzR + e-
k
tj
PhC02R-.
PhC02- + R- (11)
From the series of esters, tert-butyl p-toluate was chosen to demonstrate the use of the nonlinear least-squares technique. This ester was chosen for two reasons: (a) The para position is protected from attack by the alkyl radical. (b) Of the esters studied the toluate radical anion decomposed most rapidly. This allowed a measurement of the radical anion decomposition rate with minimal complications due to the electroactive
0
0.2
0.4
0.6
0.8
1
relative time Flgure 3. Nonlinear least-squares EC fit to data obtained by finite difference simulation based on an ECE DISP1 mechanism. Step reversal time was 0.12 s. The experiment parameters correspond to experiment C in Figure 1: k = 9.9 c',cox = 1.05 mM, and D = 1.26 X cm2 s-l. It is assumed that charge transfer properties of the starting material are as described for the EC irr mechanism, all species have equal diffusion coefficients, and the formal potential for the electroactive species generated by the homogeneous reaction is far EC fit (-). positive of both E , and E,: simulated data (..e);
species generated by homogeneous reactions involving the tert-butyl radical. (See the coulometry results discussed below.) Independent determinations of the homogeneous rate constant were obtained for three different step times 7 = 0.03 s, 0.06 s, and 0.12 s, giving k = 10.8 s-l, 10.5 s-l, and 9.9 s-l, respectively. As apparent in Figures 1 and 2, good fits were obtained for both current ratio vs. time plots and the corresponding current vs. time plots. Coulometric experiments on the toluate ester at a mercury pool electrode (14) gave a 65% yield of the toluate anion and an overall n value of 1.3. This suggests that about a third of the toluate species are involved in a two-electron process. Since this is not consistent with the EC irr mechanism used to analyze the potential step data, Q vs. t'Iz plots were prepared from forward step current data. If subsequent homogeneous reactions produce species which are electroactive at the applied voltage (i.e,, at &), these plots are curved (e.g., for an ECE DISPl (17,18) mechanism). However, even for the longest step time, the Q vs. t1i2plots remained linear. The slopes varied only slightly as the step time lengthened slopes C cm-2 s-l12,and 4.16 C cm-2 s-lIz, 4.07 x = 4.06 x
Anal. Chem. 1984, 56, 1229-1236
lo4 C cm-2 for T = 0.03 s, 0.06 s, and 0.12 s, respectively. (This gives a diffusion coefficient of 1.26 X cm2 s-l for tert-butyl p-toluate). This indicates that the process responsible for the second electron observed in the coulometry experiments is negligible in the potential step experiment. The discrepancies between the two experiments are probably due to different time scales and initial ester concentrations: 50 mM and 2 h for coulometry vs. 1.05 mM and 0.12 s for the longest potential step experiment. A better indication of the validity of an assumed mechanism is obtained by analyzing numerous current ratio points from each experiment. Using parameter values similar to those found assuming an EC mechanism, ECE DISPl data files were simulated and then analyzed by the EC nonlinear least-squares method. As shown in Figure 3, the resulting "best fit" did not match the simulated data. Even worse matches were obtained for simulated ECE data. Registry No. tert-Butyl p-toluate, 13756-42-8. X
LITERATURE CITED (1) Schwarz, W. M.: S h a h I. J. Phys. Chem. 1965, 69, 30. (2) Marcoux, L.; O'Brlen, T. J. P. J. Phys. Chem. 1972, 76, 1666.
1229
(3) Cheng, H. Y.; McCreery, R. L. J. Elecfroanal. Chem. 1977, 85, 361. (4) Cheng, H. Y.; McCreery, R. L. Anal. Chem. 1978, 5 0 , 645. (5) Chrlstle, J. H.; Osteryoung, R. A.; Anson, F. C. J . Nectroanal. Chem. 1967, 13, 236. ( 6 ) Chllds, W. V.; Maloy, J. T.; Keszthelyi, C. P.; Bard, A. J. J. Elecfrochem. SOC. 1971, 118, 874. (7) Vlslnskl, B. M.; Dryhurst, G. J. Elecfroanal. Chem. 1976, 70, 199. (8) Hanafey, M. K.; Scott, R. L.; Ridgway, T. H.; Rellley, C. N. A n d . Chem. 1976, 5 0 , 116. (9) MacDonald, D. D. "Transient Techniques in Electrochemlstry"; Plenum Press: New York, 1977: Chapter 4. (10) Beilamy, A. J. Anal. Chem. 1980, 52, 607. (11) Woodard, F. E. Ph.D. Dissertation, University of North Carollna at Chapel Hill, 1982. (12) Woodard, F. E.; Woodward, W. S.; Rellley, C. N. Anal. Chem. 1981, 53, 1251A. (13) SavBant, J. M.; Tessler, D. J. Electroanal. Chem. 1975, 65, 57. (14) Feldberg, S. I n "Electroanalytical Chemistry"; Bard, A. J., Ed.; Marcel Dekker: New York, 1969 Vol. 3. (15) Hamming, R. W. "Numerical Methods for Scientlsts and Engineers"; McGraw-HIII: New York, 1962; pp 34 and 389. (16) Wagenknecht, J. H.; Goodin, R. D.; Kinlen, P. J.; Woodard, F. E. J. Electrochem. SOC., In press. (17) Hawley, M. D.; Feldberg, S. W. J. Phys. Chem. 1966, 70, 3459. (18) Amatore, C.; SavQant, J. M. J. Electroanal. Chem. 1977, 85, 27.
RECEIVED for review September 26,1983. Accepted February 21, 1984.
Gradient Liquid Chromatography/Mass Spectrometry Using Microbore Columns and a Moving Belt Interface M. J. Hayes,' H. E. Schwartz, Paul Vouros,* and B. L. Karger* Barnett Institute of Chemical Analysis and Department of Chemistry, Northeastern University, Boston, Massachusetts 02115
A. D. Thruston, Jr., a n d J. M. McGuire Athens Environmental Research Laboratory, US. Environmental Protection Agency, Athens, Georgia 30613
Hlghperfonnance gradlent microbore LC/MS Is demonstrated by use of spray deposition onto a moving belt surface. A slmpllfled nebulizer deslgn Is shown to provide convenlent operatlon and high transfer efflciency over a wide range of flow and solvent conditions. I t Is further shown that the extracolumn varlance of the LC/MS system is sufflclently small to allow the use of relatively short 5 pm and 7.5 pm reversed-phase microbore columns wlthout signlflcant loss in resolutlon. Relatlvely hlgh mlcrobore flow rates (-100 pL/mln) are posslble for fast analysls and sensltlvlly. The LC/MS technlque Is applied to the analysis of phenols In an aqueous coal gasiflcatlon sample. Detection llmlts for full scan LWEI-MS are found to be - 6 ng for some representative phenols.
In recent years, increasing interest has been shown in on-line liquid chromatography/mass spectrometry (LC/MS) for analysis of polar and/or nonvolatile compounds. Two major interface approaches have been developed based on direct liquid introduction (1) and moving belt (2) principles. At present, direct liquid introduction, including the promising thermospray technique ( 3 ) )has been shown to yield useful Current address: Drug Metabolism Subdivision, Ciba-Geigy Corp., Ardsley, NY 10502. 0003-2700/84/0356-1229$01.50/0
spectra of nonvolatile and thermally labile compounds. The moving belt interface is also a promising technique, allowing the selection of the ionization mode of choice, along with the potential for employing a variety of surface ionization techniques for the analysis of substances which are difficult to vaporize (4,5). Recently, we published an extensive study on the use of spray deposition, first reported by Smith and Johnson (6))for the optimization of the chromatographic performance of the moving belt system (7). It was shown that it is possible to perform on-line LC/MS with normal bore columns (4.6 mm Ld.), using either normal or reversed-phase LC. Extracolumn contributions to band broadening were sufficiently reduced to maintain chromatographic integrity of the peaks eluting from the column. Some difficulties remained, however, in the handling of mobile phases of high water content at the flow rates commonly used for normal bore columns (- 1mL/min). It was necessary to use reduced flow rates at the expense of analysis time and sensitivity or to split the effluent, again reducing sensitivity. Microbore columns have been utilized to overcome the flow rate problem with moving belt systems. The reduced flow rates required for rapid mobile phase velocities significantly decrease the problem of solvent removal. For example, Games et al. (8,9) have shown that LC eluents containing high water content can be successfully flowed onto the moving belt, although such eluents may require the addition of a miscible cosolvent, e.g., ethanol, to the belt. Microbore LC/MS has 0 1984 American Chemical Society
