A contribution to the derivative ratio spectrum method

ELSEVIER Analytica Chimica Acta 317 (1995) 83-93

ANALmcA CHIMICA ACTA

A contribution to the derivative ratio spectrum method

J.M. Garcia, 0. Hernbdez, A.I. JimCnez, F. Jimknez, J.J. Arias *

Departamento de Q&mica Analitica, Bromatologia y Toxicologia, Facultad de Q&mica, Universidad de La Laguna, E-38204 La Laguna, Tenerije, Spain

Received 21 February 1995; revised 6 July 1995; accepted 11 August 1995

Abstract

The performance of two graphical methods (the derivative ratio spectrum method and its variant with normalized divisor) for the determination of the resolution of several binary mixtures of analytes is compared. This paper demonstrates that normalized spectra used as divisors facilitate optimization of the working conditions and diminishes quantitation errors. The additional use of diode array spectrophotometers allows quantitation of second order derivative ratio spectra. In order to validate the proposed approach to derivative ratio spectra, two binary mixtures, acetylsalicylic acid-salicylamide and imipramine-perphenazine, were assayed. The results obtained by using the proposed method in its conventional and modified variants are discussed. On the other hand, a multi-wavelength regression method is suggested for the determination of several metal ions by using an organic reagent as chelating agent. It was shown that it is possible to determine the analytes without any previous knowledge of stoichiometry of the complexes involved and how the contribution from excess of chelating agent can be eliminate. The method has been validated on several binary mixtures of Fe(U), Cu(II) and Z&I) by using 4-(1’H-1’,2’,4’-trizolyl-3’-azo)-2-methylresorcinol (TrAMeR) as chelating agent.

Keywords: Multiwavelength regression; Derivative ratio spectrum method

1. Introduction effects as well. Also, the subsequent inception of

The use of spectrophotometric analytical methods for the simultaneous determination of several analytes with no prior separation has grown enormously in the last few years. Initially, they entailed solving

an equation system established from absorbance spectra for the mixture recorded at as many wavelengths as analytes present in it; the goodness of the results was obviously limited by the extent of spectral overlap. Derivative spectrophotometry succeeded in correcting many of the problems posed by absorbance spectra, and in suppressing some matrix

* Corresponding author.

diode array spectrophotometers allowed the typically low signal-to-noise ratios of derivative spectra pro- vided by early spectrophotometers to be substantially boosted. At a later stage, methods for obtaining

analytical signals for a mixture depending on a sin- gle analyte (e.g., the zero-crossing method [ll, which has widely been used for resolving binary mixtures [2-41) were reported. Blanco et al. [5] developed a multi-wavelength regression method that measures the absorbance at more wavelengths than analytes present in the sample, thereby providing an overdi- mensioned system that can only be solved graphi- cally. Salinas et al. [6] modified the original equations of Blanc0 et al. by derivation of the spectrum

0003-2670/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDIOOO3-2670(95)00426-2

84 J.M. Garcia et al. /Analytica Chimica Acta 317 (199.5) 83-93

obtained as the ratio of that for the mixture and a

standard spectrum for one of its components; in this way, the signal obtained was absolutely independent

of the species whose spectrum was used as divisor. This method is known as the derivative ratio spec-

trum method and has so far been used for the simultaneous resolution of mixtures of two [6-91 and three components involving a variety of analytes; in

any case, ternary mixtures require the joint use of the zero-crossing method [lo]. The most serious pitfall

of this methodology arises from the need to empiri- cally determine the standard spectrum that provides the best results. In addition, in the absence of a diode

array spectrophotometer, derivative spectra must be filtered, which detracts from reproducibility. Also, the high spectral noise of rudimentary spectrophotometers precludes use of derivative spectra of the

second or higher order. This paper demonstrates that normalized spectra

used as divisors facilitate optimization of the work-

ing conditions and diminishes quantitation errors; the additional use of diode array spectrophotometers allows quantitation of derivative ratio spectra of the

second order. In order to validate the proposed approach to

derivative ratio spectra, we assayed two binary mixtures, viz. acetylsalicylic acid-salicylamide and imipramine-perphenazine. The results obtained by using the derivative ratio spectrum method in its

conventional and modified variants are discussed. One of the major constraints to determining metal

ions by formation of coloured complexes with a common reagent arises from the need to use excess chelating agent in order to ensure complete chelation and to accurately know the stoichiometry of each

complex in order to obtain its pure spectrum. In this work we developed a new method based on dividing the spectra for the complex solutions with reagent in excess into a standard spectrum for the reagent, and subsequently deriving the resulting spectra; in this way, a signal that is independent of the concentration of excess reagent is obtained without the need to know the stoichiometry of the complexes involved. The analytes are quantified by multi-wavelength regression. The proposed method was applied to the resolution of binary mixtures of Fe(III), Cu(l1) and Zn(I1) by using 4-(l’H-1’,2’,4’-triazolyl3’-azo)-2- methylresorcinol (TrAMeR) as chelating agent.

2. Theory

Beer’s law for a mixture M of two substances A

and B at j different wavelengths can be expressed as

AMj = cAjcA + es,cB (1)

where l A and mu are the molar absorptivities of the

analytes and C, and C, their concentrations. Divid- ing Eq. 1 into a standard spectrum for analyte A at

concentration Cl and deriving the resulting expres-

sion yields

(2)

As can be seen from Eq. 2, the derivative ratio spectrum for a mixture of A and B is independent of the concentration of species A (C,) as it is the sole

function of the concentration of species B (C,) and that for the standard spectrum used as divisor (Ci), which is known. Dividing Eq. 1 into the standard

spectrum for B (Ci) yields an expression similar to Eq. 2 that allows C, to be calculated. Salinas et al. [6] choose the standard spectrum resulting in the best possible resolution of synthetic samples. However, using a spectrum recorded at a concentration (;YC~ (where (Y is a constant) as the divisor yields

(3)

which coincides with the expression obtained by

multiplying Eq. 1 times l/a; in other words, decreasing the concentration at which the divisor spectrum is recorded has the same effect as decreasing LY (i.e., increasing the signal). As a result, the calibration graphs obtained have greater slopes but provide no sensitivity improvement because the signal-to- noise ratio also increases in parallel. The ratio between the slopes of two calibration curves coincides with that between the reciprocals of the concentrations used to obtain the divisor spectrum.

The goodness of the results obtained in the resolution of synthetic samples does not depend on the concentration of the standard spectrum used as divisor, but rather on the experimental or instrumental errors made in the process. This can readily by seen by dividing a Gaussian curve, which is a reliable simulation for a spectrum, into another three curves

J.M. Garcia et al. /Analytica Chimica Acta 317 (1995) 83-93 85

.c A La

c. c

A - .3 A _i

-0.02 Wavelength

Fig. 1. Residuals of first-derivative ratio spectrum obtained by

using the noiseless spectrum and each of the noisy spectra ( A, o .

0 ) or their average ( n ).

of the same type including random noise. As can be seen from Fig. 1, which shows the differences between the derivative ratio spectrum obtained by using the noiseless spectrum and each of the noisy

spectra (or their average), averaging signals results in substantially reduced residuals.

Therefore, in order to minimize errors and expe-

dite implementation of the method, we suggest using as divisor the normalized spkctrum for each substance obtained by dividing the spectra for several standards of variable concentration into the corresponding concentration and subsequently averaging them, in order to obtain a spectrum of unit concentration (normalized spectrum).

Deriving Eq. 2 yields

(4)

based on which the mixed spectrum continues to exclusively depend on the concentration of one species. This allows such a species to be determined in a binary mixture with the added advantage that the number of peaks increases with the derivative order.

On the other hand, the expression of Beer’s law for a mixture of (n - 1) metals reacting with a common reagent n to give coloured complexes is given by

A;, = elic, -t czjc2 + . . . +E,_~~c,_~ + E,,~c, fc,

(5)

In order to be able to apply multi-wavelength regres-

sion to this system, one must know the stoichiometry of the metal-reagent complex so as to subtract the excess reagent concentration and obtain the pure

standard component for each complex. Alternatively, normalized ratio spectra can be used for systems of unknown stoichiometry. Thus, dividing Eq. 5 into

the standard spectrum for the reagent at concentration c,” and deriving yields

‘n-1 d 'n-lj +...+-- -

( ) c; dh enj

1 d e,

+,“dh c n ( ) n1 (6)

which shows that the mixture absorbance is indepen-

dent of the reagent concentration. Eq. 6 can be rearranged to

~=cc,Xj,+C2X,2+...+C,_1Xj,_,+E; (7)

or, in matrix form:

Y=KC+E (8)

Finally, the metal concentrations that minimize the summation of the squared residuals

i

i n-1

cq=c Y,- c c (Xj”C,) I (9) j=l n=l

can be calculated by least-squares regression.

3. Experimental

3.1. Apparatus and software

Absorption measurements were made on a Hewlett-Packard HP8452A diode array spectrophotometer furnished with quartz cell of 1 cm light

pathlength and interfaced to a Vectra ES computer and a Think Jet printer, also from Hewlett-Packard. The spectrophotometer’s bundled software was used to processed absorption, derivative and derivative ratio spectra.

86 J.M. Garcia et al. /Analytica Chimica Acta 317 (1995) 83-93

A Radiometer PHM84 digital pH meter furnished with a dual glass-saturated calomel electrode was used for pH measurements.

Multicomponent analysis was carried out by using

multi-wavelength regression has been performed with the MULTIC program [ll].

Calculations were made at a 386SX/AT personal

computer.

3.2. Reagents

Standard solutions containing 100 pg/ml acetylsalicylic acid were prepared by direct weighing of required amount from commercial products (Sigma) and standardized by volumetric methods [12]. A salicylamide (Sigma) standard of the same concentration was also prepared by dissolution in ethanol

(20%). Standard solutions containing 100 pg/ml

imipramine or perphenazine were prepared by direct weighing of the required amount of hydrochloride

(Sigma) and d issolution in deionized water and

ethanol, respectively. Sodium acetate-acetic acid buffer [total buffer

concentration (C,) = 1 M] of pH 5.0 was also used. Nitrates of copper, zinc and iron (Merck) were

prepared in water as 0.1 M solutions. In case of iron nitrate the solutions contained 0.1 M HNO, to pre-

vent hydrolysis. The concentrations of the solutions were checked by atomic absorption spectrometry. Standard solution containing 1.2 X 10e3 M 4-(l’H-

1’,2’,4’-triazolyl-3’-azo)-2-methylresorcinol (TrAMeR) synthesized and purified as described earlier [13] was also prepared by dissolution in methanol. The ionic strength was adjusted by adding suitable amounts of 2.5 M sodium nitrate. A 0.025 M sodium tetraborate-sodium hydroxide buffer solution was

used.

3.3, Procedure

Acetylsalicylic acid-salicylamide and

imipramine-perphenazine mixtures were prepared in triplicate by placing in a 25-ml volumetric flask 3 ml of HAcO-NaAcO buffer at pH 5.0, an amount of salicylamide and acetylsalicylic acid in the range 25-750 and 50-625 pg, respectively (or 25-750 pg of imipramine and 25-200 pg of perphenazine,

respectively), and ethanol to a final content of 20% (v/v) after dilution to the mark. The spectra for the mixtures were then recorded between 190 and 350 nm at an integration time of 1 s.

3.3.1. Determination of acetylsalicylic acid and salicylamide

The analysis of salicylamide in mixtures by the method of the derivative ratio spectra was performed

by dividing the absorption spectra of the mixtures by the standard spectrum obtained for 10 ,ug/ml of acetylsalicylic acid spectra. The resulting ratio spectrum was next derived and its height measured at 326 nm. On the other hand, to quantify the acetylsalicylic acid the same spectrum of the mixture was divided by the standard spectra for 25 ,ug/ml of

salicylamide and the signal measured on the derivative spectra at 258 nm.

Salicylamide was determined in mixtures with acetylsalicylic acid by using the derivative of ratio spectra according to modified variants by dividing the absorption spectrum for the mixture into the

normalized spectrum for the acetylsalicylic acid, which was then derived and its height at 326 nm in the first-derivative or 318 nm in the second-derivative spectrum measured. Similarly, acetylsalicylic acid was quantified by using the normalized spectrum for salicylamide as the divisor and measuring

the height of the spectrum at 258 nm (first order) or 260 nm (second order). By interpolation on the

calibration curves, the measured signals allowed the quantitative determination of both drugs.

3.3.2. Determination of imipramine and perphenazine

Imipramine and perphenazine were determined simultaneously by measuring the height at 286 and 264 nm, respectively (first-order derivative ratio spectrum), or at 278 and 270 nm, respectively (second-order derivative ratio spectrum). The normalized spectrum for the other substance was used as the divisor in each case.

3.3.3. Resolution of mixtures of Cu, Fe and Zn Copper-zinc and copper-iron mixtures were de-

termined by mixing in 25-ml volumetric flask in the following order an appropriate amount of metal ion, 2.5 ml of sodium tetraborate-sodium hydroxide


Table 1

Statistical data for calibration graphs

Analyte A (nm) Intercept Slope RSDa Irlh DLC Range

(%I ( wg/mI) ( fin/ml)

First-derivative ratio method

ASA 258 3.64. 10-s k 1.14-* 1.76 lo-’ + 6.00. lo- 5

S 326 0 2.96.10-’ +7.86.10-’

First-derivative ratio spectra (normalized spectra as divisor)

ASA 258 3.02.10-’ f 3.66. lo-* 1.24.10-‘*1.93.10-”

S 326 - 1.32 + 1.53 10-l - 2.35 + 1.42 lo- *

Second-derivative ratio spectra (normalized spectra as divisor)

ASA 260 -2.84. lo-* f 1.32. 1O-3 -2.53. K-* f 1.23. lo-”

S 318 -3.18. lo-* f 2.13. 1O-3 -2.50. lO-’ i 1.32 1O-3

First-derivative ratio spectra (normalized spectra as divisor)

I 286 0 - 1.02. lo-’ + 5.24. 1O-4

P 364 0 - 2.58 . 10-r f 3.41 lo- 3

Second-derivative ratio spectra (normalized spectra as divisor)

I 278 0 -2.52 lO-’ + 1.43 1O-4

P 270 0 2.39. lo-* + 3.58. 1O-4

3.12 0.9995 0.28 2.00-25.00

1.87 0.9987 0.24 1.00-30.00

1.79 0.9995 0.17 l.O(l-25.00

1.70 0.9996 0.10 1.00-30.00

1.70 0.9997 0.17 1.00-25.00

1.69 0.9999 0.09 1.00-30.00

1.17 0.9998 0.05 1.00-30.00 2.17 0.9996 0.03 1.00-7.00

1.23 0.9997 0.06 1.00-30.00 2.40 0.9992 0.03 1 .OO-7.00

a RSD = relative standard deviation.

b r = correlation coefficient.

’ DL = detection limit.

buffer, 8 ml of methanol, 2 ml of 1.2 X 10e3 M TrAMeR and 2.5 ml of 2.5 M NaNO,, and making to the mark with distilled water. In order to quantify

the metal ions, the absorption spectrum for the Cu-Zn

reagent for 1 X lop5 M and derived, the MUL-

TIC program was run over the wavelength ranges

480-540 and 470-540 nm for the Cu-Zn and Cu-Fe mixture, respectively.

or

1.

2.

Cu-Fe mixture was:

the MULTIC program was run over the wavelength ranges 410-600 and 480-600 nm for the Cu-Zn and Cu-Fe mixture, respectively; or

divided into the normalized spectrum of the

3.3.4. Determination of CM and Zn in metal alloys Accurately weighed amounts of metal alloy close

to 1 g were treated with 10 ml of concentrated HNO, to near-dryness tree times. The residue was diluted

Table 2

Simultaneous determination of acetylsalicylic acid (ASA) and salicylamide (S) by using the methods of Salinas et al. and the proposed

methods

Amount added ( pg/ml)

ASA S

Relative error (%o)

Salinas et al. Proposed methods

1st Derivative 1st Derivative 2nd Derivative

ASA S ASA S ASA S

10.0 10.0 - 1.0 2.8 - 2.5 3.8 - 2.2 2.8

20.0 4.0 -2.3 3.2 2.6 - 0.2 2.3 2.7

4.0 20.0 -3.2 1.1 1.0 -3.2 -0.5 I .4 20.0 2.0 - 2.6 7.5 2.6 -3.0 2.6 - 0.5

2.0 20.0 - 12.0 - 1.7 2.5 3.1 - 2.5 1.8 20.0 10.0 4.3 0.6 1.4 1.2 1.4 I .s 10.0 20.0 - 1.8 - 1.2 1.4 2.7 0.5 1.8

RSEP (o/o) *3.1 f 1.5 k2.2 + 2.9 +2.1 i_ 1.8

Overall error (%) k2.4 f 2.6 +2.0


-A

230 261 3w 230 290 350

WlvelUlglb(OO) wude~qnm)

Fig. 2. Second-derivative ratio spectra of different concentrations: (a) acetylsalicylic acid: (1) 5 pg/ml, (2) 10 pg/ml, (3) 15

pg/ml, (4) 20 pg/ml; and (b) salicylamide: (1) 5 pg/ml, (2) 10 pg/ml, (3) 15 pg/ml, (4) 20 pg/ml.

with 20 ml of deionized water and filtered across Whatman No. 41 paper. The solution was transferred to a lOO-ml volumetric flask and made up to the mark with deionized water. The volume required to obtain a Cu and Zn concentration within the linear range of the calibration graph on dilution to 25 ml was taken and analysed as described above.

4. Results and discussion

4.1. Derivative ratio spectrum method using normalized divisor

Based on the results obtained with various ratio spectra, there was no apparent relationship between

o.f-- -~ - ._.L

270 350

Wavelength

Fig. 3. Absorption spectrum of (1) 10 pg/ml imipramine, (2) 5 pg/ml perphenazine and (3) 10 kg/ml imipramine +5 pg/ml perphenazine.

the errors made and the concentration at which the divisor spectrum was obtained; consequently, the errors were not dependent on the divisor spectrum used, but only on the instrumental errors made by the operator who recorded the spectra. Therefore, there is no such thing as an absolute optimal spectrum since two different operators can obtain two different optimal divisor spectra - as noted earlier, trying to find one has no theoretical justification. In addition, testing various standard spectra as divisors is rather tedious. The use of the average of several spectra corresponding to the same concentration could lessen the quantitative errors, because most random noise through averaging is eliminated; however, it is preferable to divide the initial mixed spectra by normalized spectra involving the average of several spectra including concentration in the application range of the method.

Table 3 Simultaneous determination of perphenazine (P) and imipramine (I) by using the proposed methods

Amount added ( pg/ml) Relative error (%)

P I 1st Derivative 2nd Derivative

P I P I

5.0 5.0 -2.4 2.6 - 1.6 2.6 3.0 15.0 - 4.6 0.6 -2.0 0.3 2.0 15.0 -5.5 0.6 - 4.5 0.3 2.0 20.0 -4.5 1.5 - 4.0 0.3 1.0 12.5 - 7.0 0.2 6.0 0.5 RSEP (%) + 3.7 *Il.1 +2.6 rtO.6 Overall error (%) +1.3 + 0.7


Table 4

Results obtained for different mixtures of Cu(II)-Z&I) by using the derivative ratio spectrum method

Amount added Amount found ( pg/ml) Relative error Fitting parameters a

( pg/mI) + confidence interval (o/o)

cu Zn cu Zn cu Zn s x 102 rr

0.402 0.482

0.537 0.642

0.402 0.963

0.805 0.642

1.073 0.642

1.073 0.482

0.805 0.962

0.537 0.642

RSEP (%I

Overall error (o/o)

0.411 & 0.007 0.471 f 0.010

0.577 * 0.003 0.678 + 0.005

0.374 * 0.007 0.971 f 0.011

0.851 + 0.005 0.650 f 0.008

1.099 + 0.008 0.603 f 0.012

1.093 f 0.006 0.463 f 0.009

0.812 k 0.007 1.006 f 0.010

0.518 k 0.003 0.667 f 0.004

2.24

7.45

- 6.97

5.71

2.42

1.86

0.87

- 3.54

+_ 3.67

- 2.28

5.61

0.83

1.25

- 6.07

- 3.94

4.57

3.89

+ 3.89

+ 3.77

1.2 0.9992

0.6 0.9999

1.2 0.9996

0.8 0.9999

1.3 0.9998

2.2 0.9998

2.2 0.9998

0.4 0.9999

a s = Standard deviation; r = correlation coefficient.

In order to validate the proposed variant of the original method, we used the acetylsalicylic acid- salicylamide mixture. Thus, when the Salinas et al. method was used, it was found that the heights at 330 nm and 258 nm were proportional to the amount of salicylamide and acetylsalicylic acid present. In order to determine the divisor concentration resulting in the best mixture resolution, different solutions with concentration over the ranges 2-25 pg/ml for acetylsalicylic acid and l-30 pg/ml for salicylamide, were assayed. 10 vg/ml acetylsalicylic acid and 25 pg/ml salicylamide were chosen as optimum values.

L

210 285 -340 130 111 3411

wavclcllgtb(m) WaVder@h(m)

Fig. 4. First-derivative ratio spectra of different concentrations: (a)

imipramine: (1) 5 pg/ml, (2) 9 pg/ml, (3) 13 pg/ml, (4) 17

pg/ml; and (b) perphenazine: (1) 2 pg/ml, (2) 4 pg/ml, (3) 6

wg/ml, (4) 8 pg/mI.

The equations of the calibration graphs are given in Table 1.

The results obtained for a set of synthetic mixtures prepared containing different salicylamide and acetylsalicylic acid proportion are listed in Table 2. As can be seen, errors were less than 5% in all cases, except for salicylamide-acetylsalicylic acid ratios equal to 1O:l.

The ratio range over which the mixture can be resolved is expanded by using the derivative ratio spectrum method and normalized spectra as divisors. Thus, once the normalized spectrum for a 1 pg/ml

(b) ‘I

0 ,’

230 280 110 230 280 330

Wavclengtb(Mi) helcng$(nm)

Fig. 5. Second-derivative ratio spectra of different concentrations:

(a) imipramine: (1) 5 pg/ml, (2) 9 pg/ml, (3) 13 pg/ml, (4) 17

pg/ml; and (b) perphenazine: (1) 2 fig/ml, (2) 4 pg/ml, (3) 6

pg/ml, (4) 8 *g/ml.

90

Table 5

J.M. Garcia et al. /Analytica Chimica Acta 317 (1995) 83-93

Results obtained for different mixtures of Cu(II)-Z&I) by subtracting the excess of chelating agent

Amount added Amount found ( pg/ml)

( pg/ml) + confidence interval

CU Zn cu Zn

Relative error Fitting parameters a

(%)

cu Zn s x 102 r2

0.402 0.482

0.537 0.642

0.402 0.963

0.805 0.642

1.073 0.642

1.073 0.482

0.805 0.962

0.537 0.642

RSEP (o/o)

Overall error (%)

0.393 + 0.006 0.484 * 0.005

0.538 f 0.010 0.618 f 0.008

0.413 f 0.017 0.977 + 0.013

0.796 f 0.015 0.581 f 0.013

1.034 + 0.018 0.539 * 0.017

1.028 + 0.018 0.402 f 0.016

0.798 k 0.018 0.930 + 0.016

0.512 f 0.012 0.662 + 0.011

- 2.24

0.19

2.74

- 1.12

-3.63

-4.19

-0.87

- 4.66

k3.16


concentration of each drug was obtained from the spectra for 5 standards of variable concentration, the derivative ratio spectra were calculated; the mixed signals at 326 and 258 nm were found to correspond to the amounts of salicylamide and acetylsalicylic acid, respectively, present in the mixed solutions.

4.2. Second-order derivative ratio spectra

Conventional spectrophotometers entail filtering the ratio spectra prior to derivation owing to the high noise of the signals they provide [6-lo], which in turn precludes use of second-derivative spectra. On the other hand, diode array spectrophotometers allow

unfiltered ratio spectra to be derived [3]. Thus, Fig. 2a and b shows the second-derivative ratio spectra for various standards of acetylsalicylic acid and salicylamide, respectively; as can be seen, the spectra were noiseless in those regions where the analytes had a non-zero absorbance. Of all the peaks obtained, those at 260 and 318 nm resulted in the smallest quantitation errors for the acetylsalicylic acid and salicylamide, respectively. The corresponding calibration equations are given in Table 1.

Table 2 shows the results obtained in the resolution of 7 synthetic mixtures of the two drugs by using the above-described methods. As can be seen, the derivative ratio spectra method resulted in larger

Table 6

Results obtained for different mixtures of Cu(II)-Fe(III) by using the derivative ratio spectrum method

0.41

-3.74

1.45

- 9.50

- 16.04

- 16.60

- 3.33

3.12

+ 7.60

f 5.69

0.4 0.9999

0.6 0.9999

0.9 0.9993

0.9 0.9998

1.1 0.9996

1.1 0.9996

1.2 0.9997

0.8 0.9999

Amount added

( wg/mI)

cu Fe

Amount found ( pg/ml)

+ confidence interval

cu Fe

Relative error Fitting parameters a

(%o)

cu Fe s x lo2 r2

0.402 0.406

0.805 0.812

0.402 1.015 0.402 1.218

0.805 0.406 0.537 0.812

0.805 0.812

0.805 0.609

RSEP (o/o) Overall error (%)

0.403 * 0.004 0.383 + 0.002

0.790 + 0.011 0.799 f 0.005

0.412 f 0.012 0.999 f 0.006 0.399 + 0.018 1.163 + 0.008 0.765 f 0.006 0.419 + 0.003

0.529 + 0.009 0.832 f 0.003 0.808 + 0.007 0.808 + 0.004

0.812 + 0.004 0.599 f 0.002

0.25

- 1.86

2.49

- 0.75 - 4.97

- 1.49

0.37

0.87

+ 2.47

-5.67 0.7

- 1.60 2.1

- 1.58 2.3

- 4.52 3.3

3.20 1.1

2.46 1.3

- 0.49 1.7

- 1.64 0.7

+3.00

-+ 2.80

0.9998

0.9997

0.9997

0.9996

0.9998

0.9999

0.9998

0.9999



errors than the proposed method, especially above an analyte ratio of 1:lO. Also, second-derivative ratio spectra gave rise to even smaller errors.

On the other hand, the absorbance spectra for imipramine and perphenazine were strongly over- lapped (see Fig. 3). Nevertheless, their derivative

ratio spectra (Figs. 4 and 5) allowed the two drugs to be quantified simultaneously. Thus, perphenazine could be determined from the peak at 264 or 270 nm in the first- or second-derivative, respectively, of the ratio spectrum, whereas imipramine was quantified from the peak at 286 or 278 in the first- or second-

order ratio spectrum, respectively. The normalized spectrum for the corresponding analyte was used as the divisor spectrum in every case. The calibration equations obtained by using both methods are given in Table 1.

The above-mentioned methods were applied to the resolution of 5 synthetic mixtures of imipramine

and perphenazine. As can be seen from the results (Table 31, the use of derivative ratio spectra allowed the binary mixtures to be correctly resolved, even at high analyte ratios.

4.3. Elimination of the contribution from excess

chelating agent

Azo dyes have traditionally been used in the determination of metals on account of the high sensi-

525 650

Fig. 6. Absorption spectra yielded by the TrAMeR complexes

formed from 9.6X lo-’ M TrAMeR and 0.40 pg/ml Cu(II),

0.48 fig/ml Zn(II) and 0.41 pg/ml Fe(II1); (-1, TrAMeR; (-_),

TrAMeR-C&I); (- - -), TrAMeR-Z&I); (. .I, TrAMeR-Fe(II1);

(m n n ), TrAMeR-Cu(II) + TrAMeR-Z&I); (- - -), TrAMeR-

Cu(II) + TrAMeR-Fe(III).

Wavelength

Fig. 7. First-derivative ratio spectra yielded by the TrAMeR

complexes formed from 9.6 X 10e5 M TrAMeR and 0.40 pg/ml

Cu(II), 0.48 pg/ml Z&I) and 0.41 @g/ml Fe(II1) using normal-

ized spectra of 1 X 10e5 M TrAMeR as divisor; (--_), TrAMeR-

Cu(I1); (- -), TrAMeR-Z&I); ( ), TrAMeR-F&II);

( n n n ), TrAMeR-C&I) + TrAMeR-Zn(I1); (- - -), TrAMeR-

C&I) + TrAMeR-Fe(II1).

tivity with which the complexes they form can be quantified. Most such reagents are not specific, so

they can be used to simultaneously determine several metals with the aid of multi-wavelength methods

1141. Application of this multivariate calibration method entails using the pure standard spectrum for every species contributing to the overall signal.

Derivative ratio spectra allow multi-wavelength regression to be applied to these systems without the need to know the stoichiometry of the metal-reagent

complexes involved, thereby overcoming one of the serious limitations of this type of system. For this purpose, the spectra of the complexes are divided into the normalized spectrum for the reagent and subsequently derived in order to obtain a signal that

is independent of the reagent concentration. In order to test the proposed method, we assayed

the resolution of Cu-Fe and Cu-Zn mixtures by formation of coloured complexes with TrAMeR. Fig. 6 shows the spectra for the complexes formed by the pure metal ions, as well as those for their mixtures in the presence of excess TrAMeR; as can be seen, there was marked spectral overlap in every case.

The metals were quantified with the aid of a multi-wavelength regression program (MULTIC) by using as standards the normalized spectra for complexes, obtained from spectra of variable concentra-


Table 7

Results obtained for different mixtures of Cu(II)-Fe(III) by subtracting the excess of chelating agent

Amount added Amount found ( pg/mI) Relative error

( pg/ml) + confidence interval (%I

cu Fe cu Fe CU Fe

0.402 0.406 0.384 + 0.002 0.403 f 0.002 - 4.48 -0.74

0.805 0.812 0.747 + 0.004 0.807 + 0.004 - 7.20 - 0.62

0.402 1.015 0.380 f 0.004 1.014 + 0.004 -5.47 -0.10

0.402 1.218 0.390 + 0.007 1.185 + 0.007 - 2.99 -2.71

0.805 0.406 0.717 f 0.002 0.417 + 0.002 - 10.93 2.71

0.537 0.812 0.502 + 0.002 0.808 f 0.002 - 6.52 - 0.49

0.805 0.812 0.763 + 0.003 0.821 f 0.004 - 5.22 1.11

0.805 0.609 0.771 * 0.001 0.608 + 0.001 -4.22 -0.16

RSEP (o/o) f 6.94 + 1.61

Overall error (%) + 4.53


Fitting parameters a

s x 102 r2

0.7 0.9999

1.3 0.9999

1.6 0.9998

2.5 1.0000

0.7 1.0000

0.8 0.9999

1.2 0.9998

0.5 0.9999

tions of each metal after dividing them into the normalized spectrum for a reagent concentration of 1 X 10d5 M and deriving the resulting ratio spectra. As can be seen from Fig. 7, which shows the derivative ratio spectra for each metal, the signals above 565 nm were very noisy owing to the low reagent absorbance in that region. We tested various wavelength ranges and found the best results to be pro- vided by 480-540 nm for the Cu-Zn mixture and 470-540 nm for the Cu-Fe mixture.

Tables 4-7 show the results obtained for various synthetic Cu-Zn and Cu-Fe mixtures resolved by using the proposed method and multi-wavelength regression but quantifying the analytes using as standards the spectra for the pure complexes of each metal obtained after subtraction of the contribution of the excess reagent; to do this, it is necessary to know the stoichiometry of the complexes, and intro-

duce the reagent as another component in the model. As can be seen, the use of derivative ratio spectra resulted in acceptable, though slightly worse fitting parameters owing to the signal processing treatment involved in obtaining the derivative ratio spectra. On the other hand, the errors obtained for some mixtures - particularly that of Cu and Zn - were substantially smaller as the likely result of the shorter distance between the Zn and reagent signals relative to the others - the derivative ratio spectrum cancels the reagent signal and hence any potential interfer- ence from it.

The results obtained by applying the proposed method to the determination of Cu and Zn in a metal alloy are compared, in Table 8, with the certified composition of the alloy and with those obtained by atomic absorption spectroscopy. As can be seen from that Table, all the percentages are consistent, and

Table 8 Simultaneous determination of copper and zinc in metal alloys

Metal ion Certified (o/o) a Found (%o) f standard deviation

AAS MULTIC Proposed method

cu 58.61 58.37 f 1.52 48.39 + 1.39 57.21 + 2.87

Zn 29.09 29.12 + 0.56 21.84 + 0.66 30.04 + 1.00

a NBS 157A: Cu 58.61%; Zn 29.09%; Ni 11.82%; Mn 0.174%; Fe 0.174%; Pb 0.034%; Sn 0.021%, Co 0.022%; P 0.009% (Ni separated by precipitation with dimethylglioxime).

J.M. Garcia et al. /Analytica Chimica Acta 317 (199.~) 83-93 93

show that the proposed method provide better results than the multi-wavelength regression method (MUL- TIC) in spite of it is necessary a larger number of mathematic operations.

5. Conclusions

The derivative ratio spectrum method allows the resolution of binary mixtures of analytes with satis- factory results that are further improved by the use

of normalized spectra as divisor spectra and spectral derivative orders above one. Notwithstanding the

high potential of this methodology, it has some pitfalls; thus, substances with a very different ab-

sorbance can lead to considerably increased noise as a result of the large signals obtained by dividing into a near-zero spectral absorbance.

While using derivative ratio spectra narrows the linear range of the resulting calibration curves, the

use of normalized spectra as divisors largely solves the problem and even expands the initial range.

Finally, the use of derivative ratio spectra for determining metals in the presence of excess reagent allows their quantitation without the need to know

the stoichiometry of the complexes formed. Further- more, this method can be applied to the elimination

of the signal from one interferent present in a matrix to be analysed; thus, independent signals from the excipient in the pharmaceutical formulations, or from one additive in foods, could be obtained.

Acknowledgements

The authors wish to acknowledge the financial

support of this work by CICYT grant No. FAR90- 0045-CO2-02.

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A contribution to the derivative ratio spectrum method

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