I 2 .o
I
2.5
, s 3.0
3.5
E(eV)
Figure 3. Comparison of different smoothing techniques applied to the artificially noisy data of Figure 2, as described in the text. The vertical axis scale is the same as that of Figure 2 (1) Chebyshev smoothing: (2) combined Chebyshev/Fourier smoothing: (3) Fourier smoothing remainder obtained by subtracting a straight line joining end points: (4) Fourier cosine smoothing: (5)Fourier smoothing remainder obtained by subtracting a third-order polynomial matching average endpoints and derivatives
used in the Chebyshev smoothing example, after first subtracting the Chebyshev polynomials of order u = 1, . . . , 4. The smoothing in this case is effective in a uniform manner over the entire curve. The third curve shows the result obtained by Fourier smoothing the remainder with the same truncation function following subtraction of a straight line joining the end points ( 3 ) .This procedure forces the derivatives of the smoothed curve to be equal a t the end points and induces a minor distortion a t the ends, but a better result is still obtained near the ends than with Chebyshev smoothing alone. The result of Fourier cosine smoothing (Equations 8-10), followed by truncation with the (equivalent) function exp[-(n - 6)2/52], n 2 7, is given by the fourth curve. Here, end-point distortion occurs because the derivatives of the smoothed curve must be zero a t the end points. The final curve was calculated by applying the Fourier method to the remainder obtained by subtracting a third-order polynomial, smooth on the scale of Figure 3, with coefficients chosen to give visual "best"-fit end-point and deriuatiue values to the data. This latter procedure is a minor extension of the technique of Ref. ( 3 ) . In general, each method yields basically the same lineshape, with relative advantages and disadvantages which must be considered with respect to the intended application. We have used the Chebyshev approach in numerous situations including smoothing raw dielectric function data and numerically calculated derivatives, and have found that it gives excellent results.
LITERATURE CITED substantially reduces both end-point and derivative discontinuity effects in Fourier sine/cosine smoothing in a systematic way, since odd-order Chebyshev polynomials provide end-point discontinuity reduction, and even-order polynomials, derivative discontinuity reduction. A comparison of Chebyshev and combined Chebyshev/ Fourier smoothing procedures with other techniques is shown in Figure 3, where each method considered is applied to the artifically noisy data of Figure 2. The curve smoothed by the Chebyshev procedure and given in Figure 2 is reproduced a t the top. The second curve shows the result of Fourier smoothing the remainder with the truncation function exp[-(n - 3 ) 2 / 2 . 5 2 ]n, 2 4, equivalent to that
(1) A. Savitzky and M. J. E. Golay, Anal. Chem., 36, 1627 (1964). (2) G. Horlick, Anal. Chem., 44, 943 (1972). (3) J. W. Hayes, D. E. Glover, D. E. Smith, and M. W. Overton, Anal. Chern., 45, 277 (1973). (4) C. A. Bush, Anal. Chem., 46, 890 (1974). (5)U. W. Hochstrasser. in "Handbook of Mathematical Functions", M. Abramowitz and I. A . Stegun, Ed., (Nat. Bur. Std. ( U S . ) Appl. Math. Ser., 55, 1964), pp 771 ff. (6)R . W. Hamming, "Introduction to Applied Numerical Analysis", McGrawHill, New York, 1971, pp 297 ff. (7) P. J. Davis and I. Polonsky, Ref. 5,pp 878-9. (8) J. W. Cooiey and J. W. Tukey, Math. Cornput. 19, 297 (1965). (9) D.E. Aspnes, Opt. Comrnun., 8 , 222 (1973). (10) D. E. Aspnesand A. A. Studna, Appl. Opt., 14, 220 (1975).
RECEIVEDfor review October 31, 1974. Accepted February 21, 1975.
Kinetic Assay of Nitric Esters S. K. Yap, C. T. Rhodes, and Ho-Leung Fung' Department of Pharmaceutics, School of Pharmacy, State University of New York at Buffalo, Buffalo, NY 142 14
A number of assay methods are currently available for the determination of nitric ester antianginal drugs such as nitroglycerin, erythrityl tetranitrate, pentaerthrityl tetranitrate, and mannitol hexanitrate in commercial dosage forms. Cornpendial assays ( I , 2 ) of these drugs are tedious and time-consuming in that they require extraction of the drug followed by colorimetric determination of the nitrated products of phenoldisulfonic acid. Other reported analytical methods such as IR (3, 4 ) , gas-liquid chromatography Author to whom inquiries should be directed.
( 5 ) ,and polarography (6) also require a number of manipulative steps prior to assay, thus rendering them unsuitable for rapid analysis of nitric esters. Simpler methods such as that developed by Bell ( 7 ) ,which indirectly measure nitrite ions liberated by alkaline hydrolysis of nitric esters a t elevated temperatures, are subjected to interference by inorganic nitrites. In a recent communication (81, we reported preliminary data on a simple kinetic assay of nitroglycerin. This nitric ester was shown to degrade in alkaline methanolic soliItions in a consecutive manner producing a chromophoric, interANALYTICAL CHEMISTRY, VOL. 47, NO. 7, JUNE 1975 * 1183
-
Table I . Parameters for the Calibration Curves Found in the Direct Spectrophotometric and Kinetic Assays of Pentaerythrityl Tetranitrate and Mannitol Hexanitrate Coeff. of Slope
Pentaerythrityl tetranitrate Spectrophotometric assay Kinetic method Mannitol hexanitrate Spectrophotometric assay Kinetic method
\\\
W A V E IE N C T H ( n m )
Figure 1. Timedependent spectral changes of erithrityl tetranitrate in alkaline solution [NaOH] = O.O6M, [Erithrityl tetranitrate] = 4.96 X lO-'M. ance vs. time plot at 330 nm.
a
correlation
Q
2.16 x 103
0.999 (5)b
lo3
0.999 (6)
2.70 x 103
0.990 (5)
5.84 x l o 3
0.998 (6)
2.83
X
Absorbance/molar concentration. Number of data points.
Insert: Absorb-
of the appropriate concentration, followed sequentially by 1 ml of absolute methanol and 1 ml of the nitric ester standard solution. After complete mixing, the absorbances of the reaction mixture, as a function of time, were recorded. Absorbance maximum for erythrityl tetranitrate was followed a t 330 nm, whereas for pentaerythrityl tetranitrate and mannitol hexanitrate, absorbance readings a t 288 nm were recorded from 1 to 5 minutes after the initiation of the reaction. The solvent system used contained about 7% v/v of water in methanol. Kinetic assays of erythrityl tetranitrate in 40% v/v water in methanol were conducted by substituting 1 mi of distilled water for the absolute methanol in the above procedure.
RESULTS A N D DISCUSSION
Figure 2. Calibration curves for the kinetic assay of erythrityl tetranitrate at different sodium hydroxide concentrations and solvent compositions
(A)= O.O06M, (0) = O.O6M, (0) = 0.6M; all in 7 % v/v water in methanol. (0)= 0.06M NaOH and 40% v l v water in methanol. Ordinate: , ,A at 330 nm
mediate which has a peak absorption wavelength (Amax) a t about 328 nm. Under similar conditions, other nitric esters such as erythrityl tetranitrate, mannitol hexanitrate, and pentaerythrityl tetranitrate also showed significant absorbances (9).This communication presents the application of the kinetic assay to the analysis of these three nitric esters. Excellent correlations were observed between results obtained by the present kinetic technique and existing compendial methods. EXPERIMENTAL Apparatus. Absorbance measurements were made with a Coleman DB Hitachi 412 spectrophotometer and a Varian A26 recorder, using 1-cm cuvettes. Reagents. Except for the nitric esters, all reagents were of analytical grade quality, and were used without further purification. Nitric esters were obtained from commercially available tablets. Nitric Esters Standard Solutions. Five 16-mg erythrityl tetranitrate tablets (Burroughs Wellcome and Co.), five 10-mg pentaerythrityl tetranitrate tablets (Warner Chilcott Co.) and two 32-mg mannitol hexanitrate tablets (Merrell Co.) were separately dispersed in 20 ml of distilled water and made up to 100 ml with absolute methanol. After vigorous shaking for about five minutes, the aqueous methanolic solutions were centrifuged and the supernatents diluted with appropriate volumes of water and methanol to give standard solutions of the nitric esters a t differnt concentrations. Erythrityl tetranitrate and pentaerythrityl tetranitrate were determined by the current National Formulary assay method. Mannitol hexanitrate was assayed according to the procedure for pentaerythrityl tetranitrate published in the current National Formulary, using an equivalent factor of 0.7456 (IO). Procedure. The kinetic assay was performed by first pipetting into a 1-cm cuvette 1 ml of methanolic sodium hydroxide solution 1184
ANALYTiCAL CHEMISTRY, VOL. 47, NO. 7, JUNE 1975
Erythrityl tetranitrate, which has insignificant absorption above 300 nm, degrades in alkaline solutions (Figure 1) to give a chromophoric intermediate with a A,, of about 330 nm. The absorbance maxima (Amax)a t 330 nm (Figure 1 insert) observed during the reaction were directly proportional to the initial concentrations of erythrityl tetranitrate (1 X 10-4M to 8.8 X 10-4M) present, as separately determined by the compendia1 assay (Figure 2). This linear relationship held over a wide range of sodium hydroxide concentrations (0.006M to 0.6M) and in different solvent systems (7% and 40% v/v water in methanol). As is evident from Figure 2, the sensitivity of the kinetic assay of erythrityl tetranitrate was enhanced with increasing sodium hydroxide concentrations. This was probably due to an increase in the rate of production of the chromophoric intermediate, but not its degradation, a t higher alkali concentrations. The shorter time for appearance of A,,, (tmax) is consistent with this postulate. Sodium hydroxide concentrations greater than 0.06M were unsuitable for manual kinetic assays of this drug since extremely short tmar (
