232
ANALYTICAL CHEMISTRY, VOL. 50, NO. 2, FEBRUARY 1978
Direct Potentiometric and Titrimetric Determination of Methadone in Urine with Plastic Electrodes Selective for Hydrophobic Cations Songsak Srianujata, Wesley R. White, Takeru Higuchi, and Larry A. Sternson" Department of Pharmaceutical Chemistry, University of Kansas, Lawrence, Kansas 66044
Methadone was determined in acidified (pH 2 to 3 ) urine samples by using a miniaturized hydrophobic-cation-selective plastic membrane electrode. The selectivity of this electrode M in urine permitted the determination to be made at 5 X samples without prior separation. Determinations of about f15% accuracy were possible with a single potential measurement; better than f2% accuracy could be obtained by titrating the sample with a solution of sodium tetraphenylboron and monitoring the decrease in methadone activity potentiometrically.
T h e use of methadone in opiate-addiction treatment programs has created a need for rapid, simple, yet accurate analytical methods for monitoring drug levels in biological fluids, in order to evaluate patient compliance. Some of the earlier reported (1-5) clinical methods for the drug lacked the specificity required to obtain meaningful results. Beckett (6) has described a gas-liquid chromatographic technique for analysis of methadone and its metabolites in microsomal homogenates, and Valentine (7) reports an alternative GLC procedure for quantitation of the analyte in human urine samples. These methods, while highly specific, are time consuming and require substantial sample manipulation. They are not ideally suited for routine monitoring of methadone levels in an outpatient setting. What is needed is a direct method, requiring a minimal number of steps and time to specifically detect and quantitate the drug in urine. Urine was chosen as the test biological fluid because of its ready accessibility and because a significant fraction of the drug is eliminated intact by the kidney. Structurally, methadone is a y-keto-tertiary amine. In this report we describe a clinically applicable method for methadone, based on its hydrophobicity and ability to form cationic species a t low pH. Higuchi (8) has described an ion-selective membrane electrode, which responds preferentially to hydrophobic cations. The membrane is composed of a poly(vinylch1oride) (PVC)-dioctylphthalate (DOC) mixture. The selective response of the electrode for cations is made possible by specific anionic sites in the membrane (9),while the preference for hydrophobic species is derived from the hydrophobicity of the membrane itself, Le., response is related to the difference in chemical potential of the analyte in the aqueous vs. membrane phase. The potential of this electrode is directly related to the activity of hydrophobic cations in aqueous solution (8) and response is Nernstian. Although these characteristics seem to make the electrode a useful probe for drug analysis, the cumbersome nature of the original assembly prevented application of the electrode to clinical analysis. Coated-wire ion-selective electrodes have been further discussed by Freiser et al. (10, 11). This report describes the design of a modified version of this electrode which is smaller, less fragile, more stable, and
provides a faster response time. This electrode was then used to monitor urinary levels of methadone, a hydrophobic drug which is made cationic a t low p H because of protonation of the amine. Measurement could he made either by direct potentiometric monitoring of acidified urine samples or by potentiometric titration of the analyte in urine with tetraphenylboron (TPB). EXPERIMENTAL Apparatus. Potential measurements were made with an Orion Model 801 Ionalyzer. Materials. Tetraphenylboron (sodium salt) was purchased from Matheson, Coleman and Bell Chemical Company and methadone hydrochloride was obtained as 10-mg tablets (Dolophine) from Eli Lilly Inc. Dolophine tablets (10 mg) were crushed, a portion of the resulting powder was weighed, and the weight of methadone calculated assuming that the average weight of methadone hydrochloride per tablet in the sample taken is exactly 10 mg. The electrode membrane was prepared with poly(vinylch1oride) (PVC) resin [(BakeliteQYKV Blend 1)Union Carbide Corp.], PVC (molding resin) purchased from Diamond Shamrock Corp., dioctylphthalate (DOC) (Analabs Chemical Co.), and 1,2-dichloroethane (obtained from Fisher Scientific Co.). Electrode Construction. Silver wire ('/2-inch, No. 0 gauge) was soldered to a shielded wire connected to a standard glass electrode plug. A glass tube ('/,-inch diameter) was used as the electrode body and the wire was sealed into the tapered end of the tubing with epoxy resin so that the silver wire protruded about 3 mm from the tube. The protruding silver wire was then melted into a ball point (Figure 1). The entire electrode was then coated with a nonsensitive hard plastic (prepared by dipping the electrode in a solution prepared by dispersing 20 g of PVC in 200 mL of 1,2-dichloroethane,heating at 60" for 6 h, then adding a few drops of DOC and heating for an additional hour) to obtain a coating of ca. 0 5 m m thickness. One and one-half millimeters of plastic were removed from the tip of the wire (Figure 1). The exposed tip was then chloridized electrolytically for 30 min in 0.1 N HC1 solution (121,after which the electrode tip was immersed in 0.1 M KC1 solution. The sensitive polymer membrane solution was prepared as a 1:l mixture of PVC (Diamond Shamrock) and DOC in 1,2-dichloroethanemaintained at 60 "C. The Ag/AgCl electrode tip was then dipped into this polymer solution a total of 4 to 6 times, and allowed to dry after each treatment. The electrode was finally equilibrated with 0.1 M KC1 solution for 12 h before use. Analysis for Methadone in Urine. Crine samples containing methadone were diluted with one volume of water and acidified to pH 2-3 with 5 M H2S04. The electrode assembly was then introduced into the solution and the mixture titrated with a 4.98 X lo4 M solution of tetraphenylboron (sodium salt). Alternatively, the urine samples were assayed by a single direct potentiometric measurement. RESULTS AND DISCUSSION Electrode Design. A simplified version of a hydrophobic cation specific electrode was constructed by affixing a PVC-DOC membrane onto a silver wire coated with AgC1. Effective construction depends on developing electrical contact between the metal and polymer membrane surfaces, which in turn establishes a constant potential which is responsive
0003-2700/78/0350-0232$01.00/00 1978 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 50, NO. 2, FEBRUARY 1978
233
SHIELDED WIRE
ELECTRICAL L E A D POLYETHYLENE OR GLASS TUBING HARD PLASTIC COAT
SILVER WIRE
-5
-4
-3 LOG
LYMER MEMBRANE
-2
-I
0
O K *
Figure 3. Response of two coated wire plastic electrodes in potassium chloride aqueous solutions. The line drawn is a theoretical line with slope of 59 mV
AI
Figure 1. (A) Miniaturized electrode bodies for coated wire electrodes.
(6)Magnified view of the tip of a coated wire electrode 300
-> 200 .J
5 W z
x
IOC
I-
1
1
0
'
'
I
10.'
16' [KCd
C
-8
-7
-6
-5
-3
-4
16'
IO"
IO0
M
Figure 4. Response of a coated wire plastic electrode towards tetrapentylammonium bromide 1 X IO4 M (0)and benzalkonium chloride M (0) in distilled water, in the presence of varying 1.38 X concentration of potassium chloride
-2
LOG [OUAT]
Figure 2. Response of a coated wire plastic electrode towards tetrabutylammonium bromide (0)and tetrapentylammonium bromide (0) in distilled water. The lines drawn are theoretical lines with slope of 59 mV
to the external solution. I t is unlikely that such contact takes place directly, because of large differences in the physical properties of the metal surface and hydrophobic membrane. I t is assumed t h a t electrical contact between these surfaces is made through a thin layer of aqueous salt solution, which originates from transfer of water through the thin membrane by diffusion and from the established osmotic gradient. The potential develops through the aqueous phase between the wire-membrane interface. The most reproducible and stable electrode configuration was acquired by immersing the Agi AgCl wire in a 0.1 M KCl solution after coating it with the polymeric membrane. A reproducible aqueous interphase was thus generated. The resulting electrode, shown in Figure 1, has an internal reference solution and is in a less fragile, more stable configuration than the electrode previously described (8). A typical cell used for measuring the potentials developed was:
Ag'AgC1
I
!plastic
KC' membrane
I1
1
R N SCE test soln.
T h e observed response of coated wire plastic electrodes toward varying concentrations of tetrabutylammonium
bromide (TBA) and tetrapentylammonium bromide (TPA) in water is illustrated in Figure 2. The electrode gave a good, apparently Nernstian response over a wide range of concentrations. The sensitivity limit appears to be approximately 1 X l o 4 M for TBA and 1 X M for TPA. These results are similar to those obtained with the original design of the electrode (8). Interference of common inorganic cations with electrode response was studied both in solutions containing the primary hydrophobic cation and in its absence. The electrode response to sodium ion and hydronium ion was essentially insignificant in the concentration range from 1 x lo-' M to 1 M. However, the response toward potassium ion in KC1 solution was appreciable (Figure 3), particularly at concentrations greater than 1X M, where a slope of about 48 mV per decade change in concentration was observed. However, in the presence of a hydrophobic cation, the interference from potassium ion was not appreciable (Figure 4). The slight change in potential for TBA ion a t higher KC1 levels may be due to changes in the ionic strength of the solution. In the cme of benzalkonium chloride, a t the 1 M KC1 level, the observed drop in potential may be accounted for by micellular aggregation of t h e ions. The electrode failed to respond to calcium ion at concentrations less than 0.5 M. Shatkay (13)previously found that a PVC membrane in which tributylphosphate and theonyltrifluoroacetone were incorporated could serve as a calcium ion selective electrode.
234
ANALYTICAL CHEMISTRY, VOL. 50, NO. 2, FEBRUARY 1978
-100
> I
W v)
vi > -I50
z
- 200
I 0
-250
0
0 5
10
TITRANT VOLUME l m l )
Figure 5. Typical potentiometric tiration curve of methadone in distilled
water, with graphical lines drawn for locating of the equivalence point, titrated with sodium tetraphenylboron The response time of the coated wire electrode towards 1 X M TBA in aqueous solution (taken as >98% of peak) was less than 50 s; after removal of the electrode from the test solution and immersion in “clean” buffer, the equilibrium potential was reestablished within 20 s. Response time was concentration-dependent, taking up to 3 min to obtain equilibrium potentials in very dilute solution, e.g., 1 x IO-’ M TBA. Response time was also dependent on the composition and thickness of the membrane and the time allowed for equilibration of the membrane with salt solution before use. D i r e c t Potentiometric Analysis for Methadone. The response of the coated wire plastic electrode towards varying concentrations of methadone hydrochloride in water was identical to that seen with TBA (Figure 2). A linear, Nernstian M to 1 X response was observed in the range from 1 x lo-’ M with a slope of 59 mV/decade change in concentration of methadone. Measurements for methadone were made in acidic solution to ensure protonation of the tertiary amine group. Standard curves, similar to those generated in aqueous solution, were obtained with known concentrations of methadone present in unprocessed, acidified urine. The electrode did not respond to any of the many cationic constituents of normal urine, presumably because they are too hydrophilic to influence the sensor, even when methadone was M. present at levels as low as 1 x The usefulness of the coated wire plastic electrode is still somewhat unsatisfactory for direct potentiometric measurement because of the need for frequent standardization of the electrode. However, for some applications, where the highest accuracy is not required, it might be possible to estimate the methadone concentration from a single potentiometric measurement. T i t r i m e t r i c Analysis for Methadone. Tertiary ammonium salts can be titrated with sodium tetraphenylboron (14),the resulting complex forming a stable precipitate. The specificity and sensitivity of the method is then dependent, in part, on the dissociation constant for the complex and the constants for potential interferents. This reagent was used to titrate the protonated form of methadone, the decrease in analyte activity being followed using the plastic electrode. A typical titration curve for the drug in aqueous solution, which results from plotting electrode potential vs. titrant volume, is shown in Figure 5. Potentiometric titration curves
1.0
05
I
TITRANT VOLUME I m l )
15
Figure 6. Potentiometric titration curve of methadone in patient’surine. Two mL of the urine sample, titrated with sodium tetraphenylboron solution, 4.98 X M
for methadone in acidified urine are shown in Figure 6. The curve shows a sharp equivalence point even though the sample was diluted with one volume of water before titration. The apparent equivalence point for these titrations was determined graphically as follows: Line A was drawn with minimum slope, tangent to the initial part of the titration curve; line B was then drawn parallel to A, tangent to the final portion of the titration curve; line C was then drawn with maximum slope tangent to the region of the equivalence point; lines D and E were drawn vertically so as to pass through the intersections of line C with A and B; line F was drawn from the intersection of lines A and E to the intersection of lines B and D. The intersection of lines F and C was then taken to be the equivalence point. The equivalence point of the titrations was alternatively determined by a computerized curve-fitting technique. The curve-fitting was performed on the HP 2100 computer by a modified version of the GCSL055-Omega nonlinear regression program developed at Goddard Computer Science Institute and distributed by Hewlett-Packard as Program No. 22188A. This program uses the Gauss-Newton (15) method to minimize the sum of the squares of the differences between the data points and the function being fitted. If it is assumed that the product of T P B and MH ion concentrations is a constant, an equation can be derived relating the electrode potential to the volume of T P B solution added [(Equation 1)Appendix].
E=
EO
1,
+ x RT -x F f -t( v- Veq)+ \lt2(Ve, V)2 + 4 K ( V + W)’ 2CO( v + W ) -
111 (
where E is the electrode potential, Co is the standard state concentration of MH, ,?3“ is E at @, x is the electrode response factor, t is the titrant concentration, Vis the titrant volume, V, is V at the equivalence point, K is the product of MH and T P B ion concentrations, W is the initial volume in the titration vessel, and R , T, and F have their usual meanings. This equation was fitted to each of the titration curves by allowing Eo, Veq, and K to vary, taking Co to be 1 M. In Table I the results of a typical fitting are shown in comparison with actual titration data. In all cases, the computerized fitting was quite successful; the standard deviation of the fitted equation from the actual
ANALYTICAL CHEMISTRY, VOL. 50, NO. 2, FEBRUARY
Table I. Results of Curve-Fitting the Data from a Typical Titration of Methadone in Aqueous Solution Using Nonlinear Regression Analysis* *b.c Titrant volume, mLd 0.00 0.10
0.14 0.18 0.22 0.26 0.30 0.34 0.38 0.42 0.44 0.48 0.49 0.50 0.52 0.54 0.56 0.58 0.60
Potential, mV
Predicted potential, mV
Error, mV
-105.0 - 112.6 - 115.8 - 118.6 -121.8 - 126.1 - 130.5 - 136.5 - 142.8 - 152.5 - 157.8 - 163.2 - 168.1 - 174.8 - 180.1 -185.1 - 189.7 - 193.4 - 196.5
-105.18 -111.79 -114.86 -118.24 -122.03 -126.32 -131.26 -137.07 - 144.04 - 152.55 -157.45 -162.76 - 168.34 -174.00 - 179.50 - 184.65 -189.36 - 193.61 -197.43
0.18 -0.81 -0.94 -0.36 0.23 0.21 0.76 0.57 0.12 0.48 -0.35 -0.44 0.24 -0.80 -0.60 - 0.45 -0.34 0.21 0.93
Volume Standard taken, added, Concentration Recovery, mL mg/mLa found,mg/mL % 0.0435 98.2 5.0 0.0443 Aqueous 0.0420 94.8 2.0 0.0443 Aqueous 0.0420 94.8 2.0 0.0443 Aqueous Sample type
Urine Urine Urine
Sample type Aqueous Aqueous Aqueous Aqueous Urine Urine Urine Urine
soln. soln. soln. soln.
5.0 2.0 2.0 2.0
0.485 0.384 0.750 1.520
0.4897 0.3849 0.7595 1.5526
0.5e
5.0 2.0 2.0 2.0
... 0.430 0.815 1.600
0.5066 0.4445 0.8502 1.6346
1.0e
2.0e 4.0e
* All titrations were carried out at 25 "C. The potential of the plastic electrode (vs. the reference solution) was monitored using an Orion Ionanalyzer Model 801Digital pH meter. Titrant was a standardized solution M) of sodium tetraphenylboron. Volume (4.98 X of sample used for titration. Volume of titrant necessary to reach equivalence point; e uivalence point determined as described in the text. ? Volume of 9.67 X M stock solution of methadone hydrochloride used; diluted t o 1 0 m L with water. e Volume of 9.67 X M stock solution of methadone hydrochloride used; diluted to 1 0 m L with urine acidified to pH 2-3 with 5 M sulfuric acid. data was less than a millivolt. The standard deviation was calculated as follows (Equation 2)
where u is the standard deviation, d, is the difference between t h e data point and the function a t corresponding values of t h e independent variable (volume), and N is the number of data points. Since the uncertainty in the potential measurement is approximately mV, almost all of the standard deviation can be ascribed to this phenomenon. The fitted equation
0.0211 0.0211 0.0211
0.0219 0.0217 0.0217
103.8 102.8 102.8
Table IV. Comparison of Single Potentiometric and Titrimetric Determinations of Methadone in Aqueous and Urine Samples
Aqueous Aqueous Aqueous Aqueous Patient's urine Patient's urine Patient's urine Patient's urine Patient's urine
vesc
0.5d 1.Od 2.0d 4.0d
2.0 2.0 2.0
a Calculated on the basis that one methadone tablet contained exactly 1 0 mg of methadone hydrochloride
Titration of 5 m L of 4.8 x lo-'M solution of methadone hydrochloride with 4.98 X M solution of sodium tetraphenylboron. K (1:1 complex) = 1.89 x lo-"; E" = 164.3 m V ; x = 1.053. From Equation 2: u = 0.558 mV. 4.98 X M solution of sodium tetraphenylboron.
Standard Volume added, taken, CurvemL mLb Graphical Fitting
235
Table 111. Accuracy of the Titration of Methadone Solution with Tetraphenylboron
a
Table 11. Summary of Titration Resultsa
1978
- 105 63.8 -46.8
0.497 0.319 0.718 1.566
0.490 0.385 0.760 1.553
0.985 1.207 1.057 0.991
-77.7
0.474
0.488
1.029
-67.4
0.658
0.694
1.056
-59.1
0.854
0.892
1.045
-47.2
1.207
1.252
1.037
-32.5
1.616
2.135
1.321
- 88 -
Obtained from initial potential measurement and solving Equation 3. Calculated by curve fitting of data from potentiometric titration with tetraphenylVqb (curve fit)/V,," (single potential boron. measurement ), a
would have described the data even better if the uncertainties in the volume measurements had been taken into account in the fitting procedure. However, the procedure was more than adequate for identifying the equivalence point, so no more refined mathematical analysis was attempted. T h e results of the graphical analysis and curve-fitting are presented in Table 11. Any small (about 1%) difference between the two techniques appears to be well within expected experimental error. Methadone can be determined titrimetrically to levels of 5 X M in urine samples without prior separation, with an accuracy of f 5 % (Table 111) and precision of ca. 1%. Standard addition curves for aqueous and urine solutions of methadone were constructed by plotting concentration of analyte found vs. amount added. The curves were linear with slopes very nearly equal to one, indicating the absence of any important interference in any of the samples. Identical lines resulted when either graphically or computer-generated equivalence points were used in constructing these plots. Potassium ion did not interfere in t h e titration, since the solubility product of potassium tetraphenylborate exceeds that of methadone tetraphenylborate by a factor of lo5. Thus all the methadone present in the sample is titrated well before potassium tetraphenylborate concentration approaches the solubility product. For some applications, where highest accuracy is not acquired, it is possible to estimate methadone concentration from a single potentiometric measurement. In Table IV are presented the initial potential measurements for all the ti-
236
ANALYTICAL CHEMISTRY, VOL. 50, NO. 2, FEBRUARY 1978
trations in this study, and the equivalence point volumes calculated from these potentials, using the values of Eo and n found in the curve-fitting for that titration in the following equation:
w x,=-xe t
(E
This cubic equation can be solved to give a function of B'; the concentration of B+ is obtained by dividing the positive root of Equation 3A by the total volume in the titration cell as in Equation 4A.
- EO)F nRT
(3)
In all cases the agreement between V,, (calculated) and Veq (curve-fit) agree within 15%, and for some applications, this is adequate. Presumably, if care were taken to maintain uniform p H and ionic strength from one sample to the next, and if the electrode were standardized periodically, Eo and n could be maintained sufficiently constant so that by making a single potentiometric measurement, the methadone content of a sample could be calculated, or read off a calibration curve. Thus, in conclusion a miniaturized plastic electrode is described which selectively responds to hydrophobic cations. This probe was used t o monitor methadone levels directly in urine either by direct potentiometric measurement or by potentiometric titration with sodium tetraphenylboron.
APPENDIX Derivation of the Equation Representing the Titration Curve for the Computer Curve Fitting Model. For the titration of Bf with A-, if it is assumed that the product of the concentrations of B+ and A- is constant, the amount of the anion A- in the titrating solution can be expressed as:
where K,, = the ionic product of B+ and A', W = initial volume of the titer solution, and V = volume of the titrant added. The amount of the cation Bt present in the titrating solution a t any time can be expressed as:
B'= V,;tV e t + A(2A) where t is the concentration of the titrant. Substituting Afrom Equation 1A in Expression 2A and rearranging yields Equation 3A.
B'2 - (V& - V ) * t * B ' - &,(W
+ V)*= 0
(3A)
[B']
(Veq - V ) t =
+ d(Veq - V)2t2+ 4K,,(W + 2(W + V )
V)'
(4A)
Assuming that the electrode responds only to the cation B+, an equation can be written relating the electrode potential to the volume of the titrant added (Equation SA).
E = El
+ X FR T X 1'
(V,, - V ) t + d (
In
v,,- v y t 2 + K,,(W
[
2(W+ V)
1
4- VI2
(5A)
where E is the electrode potential, Eg/ is the standard potential of the electrode a t 1 M concentration of B+, x is the electrode response factor, and R , T , and F have their usual meanings.
LITERATURE CITED (1) E. J. McGonigle, Anal. Chern., 43, 966 (1971). (2) J. E. Wallace, H. E. Hamilton, J. T. Pay%, and K. Plum, J . Pbarrn. Scl., 81, 1397 (1972). (3) R. C. Baselt and L. J. Casarett, Clin. Pharmacol. Ther., 13, 6 4 (1972). (4) J. C. Rickards, G. E. Boxer, and C. G. Smith, J . Pharmacol. Exp. Ther., g8, 380 (1950). (5) E L Way, E. T Signorotti, C. H. March, and C. Peng, J . f h a r m c o i . ~ x p Ther., . 101, 249 (1951). (6) A . H. Beckett, M. Mltcharo, and A. A. Shlhab, J . Pharrn. Pharmacol., 23. 347 11970). (7) J. L. Valentine; P. E. Wiegart, and R. L. Charles, J . Pharrn. Sci., 81, 796 (1972). (8) T. Higuchi, C. R. Illhn, and J. L. Tossounlan, Am/. Chern., 42, 1674 (1970). (9) J. R. Luch, P h D Thesis, University of Kansas, Lawrence, Kansas, (1976): manuscript in preparation. (10) R. W. Cattrall and H. Frelser, Anal. Chern., 43, 1905 (1971). (1 1) R . W. Cattrall, S. Tribuzio, and H. Frelser, Anal. Chern., 48, 2223 (1974). (12) D. J. G. Ives and G. J. Janz, "Reference Electrode, Theory and Prectlce", Academic Press, New York, N.Y., 1961, pp 203-207. (13) A. Shatkay, Anal. Chern., 30, 1056 (1967). (14) C. E. Moore, Crlt. Rev. Anal. Chern., 2 , 111 (1971). (15) H. 0. Hartiey, Technornetrlcs, 3 , May 1961.
RECEIVED for review September 7,1977. Accepted November 7, 1977.
Controlled-Potential Coulometric Determination of Plutonium Michael K. Holland," Jon R. Weiss, and Charles E. Pietri New Brunswick Laboratory, United States Department of Energy, 9800 South Cass Avenue, Building 350, Argonne, Illinois 60439
A non+mpiricai method for the controlled-potential coulometric determination of plutonium has been proposed. The method utilizes an application of the Nernst equation to reduce the determlnatlon time by 4 0 % without loss in precision or accuracy. A fraction greater than 99% of the total plutonium content was accurately determined and corrected for background current and for the fraction not electrolyzed. One hundred thirty-five standards from eleven preparations were assayed yielding a mean recovery of 100.01 % with a standard deviation of 0.06 % using an electrical calibration factor. 0003-2700/78/0350-0236$01 .OO/O
Following the proposal of analysis using controlled-potential coulometry by Hickling in 1942, early investigations required electrolysis times in excess of one hour (1-7). These long electrolysis times initiated the development of various time-saving improvements such as predictive and empirical end-point determinations as well as cell and stirrer modifications. Predictive end-point methods based on the exponential current decay equation eliminate the need for electrolysis to completion (4-8). However, the time required in calculating 0 1978 American Chemical Society
