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The Resolution of Dye Binary Mixtures by Bivariate Calibration and wavelengths selection
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This article was downloaded by: [Michigan State University]On: 04 February 2015, At: 16:37Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number:1072954 Registered office: Mortimer House, 37-41 Mortimer Street,London W1T 3JH, UK
Analytical LettersPublication details, including instructions forauthors and subscription information:http://www.tandfonline.com/loi/lanl20
The Resolution of DyeBinary Mixtures byBivariate Calibration UsingSpectrophotometric DataP. L. López-de-Alba a , L. López-Martínez a , K.Wróbel-Kaczmarczyk a , K. Wróbel-Zasada a & J.Amador-Hernández aa Instituto de Investigaciones Científicas ,Universidad de Guanajuato , 36000, MéxicoPublished online: 22 Aug 2006.
To cite this article: P. L. López-de-Alba , L. López-Martínez , K. Wróbel-Kaczmarczyk , K. Wróbel-Zasada & J. Amador-Hernández (1996) The Resolutionof Dye Binary Mixtures by Bivariate Calibration Using Spectrophotometric Data,Analytical Letters, 29:3, 487-503, DOI: 10.1080/00032719608000413
To link to this article: http://dx.doi.org/10.1080/00032719608000413
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ANALYTICAL LETTERS, 29(3), 487-503 (1996)
THE RESOLUTION OF DYE BINARY MIXTURES BY BIVARIATE
CALIBRATION USING SPECTROPHOTOMETFUC DATA
Key Words: Bivariate Calibration, Dye Mixtures, Spectrophotometry
Ldpez-de-Alba, P. L. *, Ldpez-Martinez, L., Wrdbel-Kaczmrczyk, K.,
Wrdbel-Zasada, K., and Amador-Herndndez, J.
Instituto de Investigaciones Cientificas, Universidad de Guanajuato, 36000
Mexico
ABSTRACT
A new, simple spectrophotometric method for resolution of dye binary mixtures is
proposed in this work. A simple mathematical algorithm was designed, in which the data
are used from four linear regression calibration equations: two calibrations for each
component at two selected wavelengths. The method of Kaiser was applied for the
selection of the optimum two-wavelength sets for all mixtures under study. The recovery
experiments were carried out in ten mixtures of the following dyes: Tartrazine, Amaranth,
Erythrosin B, Sunset Yellow and Allura Red. The obtained results were compared with
the results of a commonly used derivative spectrophotometric procedure (zero-crossing
technique). The statistical evaluation of the method bias was performed and it was
concluded that the proposed methodoloa may be competitive with the derivative
procedure for the resolution of such dye binary mixtures.
* Author to whom the correspondence should be addressed.
487
Copyright @ 1996 by Marcel Dekker, Inc.
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4xx LOPEZ-DE-ALBA ET AL
INTRODUCTION
Several natural and artificial dyes are widely used as alimentary additives. For
many commercial products, two or more different dyes are added and legislation exists
to control the quality of such dyes and their content in the alimentay products'**. Thus,
analytical procedures are needed to rapidly and reliably determine the dyes in food
products. Spectrophotometric methods are most frequently used for such purposes. For
the simultaneous spectrophotometric determination of two sample components, the choice
of an analytical procedure is strictly related to the observed resolution between the
individual absoi-ption peaks of these components. Such a determination is not
problematic, if the absoi-ption peaks are satisfactorily resolved, but if the individual
component signals are partly or totaly overlapped, then chemometric techniques are
needed. There exist several powerful, well established multivariate calibration techniques
which can be used in the modem spectrophotometry: classical least squares (CLS),
inverse least squares (ILS). pi-incipal component regression (PCR) or partial least squares
(PLS)'". These techniques have been widely used for the simultaneous determination of
the two or more components of the sample and excellent analytical results have been
reported. On the other hand, derivative spectrophotometry has also been satisfactorily
applied for such kind of analyses6-'*. However, most of the techniques mentioned above
require full-spectrum infonnation and the spectral data have to be processed using highly
specialized software. In many cases, especially for dye mixtures, there is no need to use
such sophisticated and expensive techniques.
In the present work a new, simple procedure is proposed for the resolution of
binary dye mixtures. The recovery experiments results are compared with the results
obtained by commonly used derivative speckophotometric procedure and the method bias
is evaluated.
OUTLINE OF THE BIVARIATE METHOD PROPOSED
ln the ideal (error-fiee conditions), the absoiption of t h o component mixture (A and
B) at one chosen wavelength may be described accoiding to the Lambert-Beer law, by
the equation
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DYE BINARY MIXTURES 489
A,= Eibc,+ E;bc,, (1)
where: Am is the absorbance value of the mixture at this wavelength; E,, E, are molar
absorption coefficients of components A and B at this wavelength; c,, c, are the molar
concentrations of both components and b is the optical path length.
However, in real conditions, when the individual responses A, and A, are affected by
the analyt~cal and measurement errors, the calibration curve formulas for each component
at one selected wavelength (Ai), are:
A, = mAi' C, + eAi (2)
where: m,, mB, are the slope values of linear regressions; C,, C, are the concentrations
of both components (for practical reasons the concentration units of mg L-' were used in
this work) and e,, e,, are the intercept values, which reflect the differences between the
model and the real system.
If the measurements of the binary mixture are performed at two selected wavelengths
( 1 and 2), we have two equations:
where eml, e,,are the sum of the intercepts of linear calibration at two wavelengths (e,,
= eAi + %,). The resolution of such equations set allows the evaluation of,C an4C
values:
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400 LOPEZ-DE-ALBA ET A L
This simple mathematic algorithm allows the resolution of the binary mixture by
measuring the absorbance of the mixture at two selected wavelengths and using the
parameters of the linear regression functions evaluated individually for each component
at these same wavelengths
In such a procedure the problem arises of which set of wavelengths should be
selected to assure the best sensitivity and selectivity of the determination. In this work,
the method of Kaiser" was applied for the selection of the optimum wavelengths. A
series of sensitivity matrices, K, was created for each binary mixture:
where mA1, m, are the sensitivity parameters of the component A at two selected
wavelengths (1, 2) and mRI, mRZ are these parameters for the component B. It was decided
to use the values of the linear regression calibration slope evaluated for one component
at h, as the sensitivity factor. The determinants of these matrices were calculated and the
obtained values were used as the optimization criterion: the wavelength set selected was
the one for which the highest matrix determinant value was obtained.
All calculation were performed using a simple GWBASIC program.
EXPERIMENTAL
Appurutus
A Spectronic 3000 Diode Array Milton Roy spectrophotometer with 0.35nm
resolution was used which was coupled to a 486 PC and User data Version 2.01 Milton
Roy Inst. Co software for spectral data acquisition, storage and manipulation. All data
treatment operations were carried out using an Hewlett Packard Vectra 486/66 VL
microcomputer equipped with the GRAMS/386 tm software package, version 3.01A
(Galactic Ind. Co., Salem, USA)
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DYE BINARY MIXTURES 49 1
Reagents
All chemicals were of analybcal-reagent grade.
The dyes: Tartrazine (FD&C Yellow-5, YS), Amaranth (FD&C Red-2, R2) and
Erythrosin B (FD&C Red-3, R3) were obtained &om Aldrich Chemical Company and the
dyes: Sunset Yellow (FD&C Y6) and Allura Red (FD&C R40) were from "Quimica
I.R.S.A. de Mexico".
The buffer solution (2molL-', pH 4.6) was prepared by mixing acetic acid and
sodium acetate in molar ratio 1: 1 and adjusting pH with hydrochloric acid lmol.L-'.
Stock solutions containing 250mg-L-' of the dye were prepared. These solutions
were stable approximately one month14, the working solutions were prepared daily by
appropriate dilution.
Pure water of Milli-Q class (Labconco) was used throughout.
Procedures
A series of the dye solutions in the concentration range from 1 to 22 mg L-' were
prepared for one-component calibration.
All possible binary mixtures of the five dyes selected were studied: YS-Y6, Y5-
R2, YS-R3, Y5-R40, Y6-R2, Y6-R3, Y6-R40, R2-R3, R2-R40 and R3-R40. For each
mixture a series of ten solutions were prepared, which contained different concentrations
of the components (in the range 2 to 22 mg L" with the exception of R3, for which the
range of 2 to 12 mgL-' was used).
The spectra of all solutions were registered in the spectral range 350-65Om using
the buffer solution (5ml of 2M buffer solution diluted to 25mL) as the reference. The
absorbance values at selected wavelengths were obtained from these spectra.
First derivative spectra were calculated (AA=8.75nm) from the smoothed spectra
(25 experimental points) using the Savitsky-Golay procedure',.
RESULTS AND DISCUSSION
The individual absorption spectra of five dyes under study are presented in Fig. = 1. As can be observed, these spectra are partly overlapped (A,,, = 427.5nm,
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492 LOPEZ-DE-ALBA ET AL
0.6
0.4
0.2
0.0
350 415 480 545 610 Wavelength, nm
Figure 1. The absoipfion spectra of 1 - Tartraztne (Y5, 14mg L 'j, 2- Amaranth (R2.
ISmgL'), 3 - Erythrosm B (R3, 7mgL'), 4 - Sunset Yellow (Y6, 14mgL'),
5 - Allura Red (R40, 141ngL ') with the buffer solution as a blank
482.0nm,
binary mixtures using conventional methods is impossible.
= 522.0nn-1, Lac: = 527.5nm, = 499.0nm) and the resolution of
The analytical characteristics for one-component determination at wavelengths
corresponding to the absorption maximum were evaluated for Y5, Y6, R2, R3 and R40
and the obtained results are given in Table I . For the binaiy mixtures studies, the
concentration range for each dye was taken according to the linear range of the individual
calibration function.
The two wavelengths sets for the proposed bivariate procedure were selected using
the method of Kaiser. Nine wavelengths were chosen and the ( m , , A- component, i - wavenumber) slope values of the linear regression calibration were estimated for five
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DYE BINARY MIXTURES
420
427
43 7
449
474
491
511
521
53 1
493
0 17 67 167 667
0 51 I54 668
0 106 630
0 516
0
Table 1. The sensitivities evaluated for Y5 and R2 determination in one-component solutions at
nine selected wavelengths (q-the slope value of linear regression calibration of i-component),
A. m,,E-3 m,E-3
420 43.68 7.37
427
43 7
449
474
49 1
44.26
43 30
38 90
20 28
6 40
7.85
8.84
10.39
18.69
26.43
511 5.59 33.18
521 1.65 34.34
53 1 1.60 33.38
Table 2. Application of the method of Kaiser for the selection of the best wavelengths set: the
absolute values of determinants of sensitivity matrices (K).
a\A. I 420 427 437 449 474 491 511 521 531
1107
1120
1088
962
416
0
1408
I425
1387
1233
568
65
0
1488
1507
1472
1319
666
176
137
0
1446
1465
143 1
1282
647
171
134
0.1
0
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494 LOPEZ-DE-ALBA ET AL.
Table 3. The analytical characteristics for the dye determination in a one-component solution at
I m a x
Detection Limit I inearity Range
(mgL.') (mg.L-') 12 (a=o 05) Dye
Y5 2 5E-2 2 - 22 0 9999
Y6 16E-2 2 - 2 2 0 9999
R2 3 1E-2 2 - 22 0 9997
R3 6E-3 2 - 12 0 9999
R40 2 OE-2 2 - 22 0 9999
Table 4. The selected two-wavelength sets for the binary mixture resolution by the bivariate
method proposed
Binary Mixture 1, (nm) 1 2 ( 4
Y5 - Y6 427 5 494 1
Y 5 - R 2 427 5 521 8
Y5 -R3 427 5 527 5
Y5 - R40 449 3 484 7
Y 6 - R 2 477 7 531 8
Y6 - R3 492 7 522 5
Y6 - R40 476 6 534 9
R2 - R3 516 7 527 6
R2 - R40 498 8 508 8
R3 - R40 493 8 527 5
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DYE BINARY MIXTURES 495
Table 5 . Linear regression calibration formulas used for the bivariate algorithm.
Calibration Equations Binary Mixture Component
J.1 J.2
Y5 A = 0.0442.C + 0.0023 A = 0.0049C + 0,0018
Y6 A = 0.0434.C + 0.0049
Y5 A = 0.0020C + 0.0016
R2 A = 0.0343.C + 0.0029
Y5 A = 0.0442.C + 0.0023 A=O
Y5-Y6 A = 0.0203C + 0.0002
A = 0.0442.C + 0.0023
A = 0 0079.C + 0.0005 Y5-R2
Y5-R3 R3 A = 0.0028.C - 0.0008 A = 0.0886.C - 0.0070
Y5 A = 0.01 1OC + 0.0017
R40 A=0.0174C - 0.0014 A=0.0375C +0.0013
Y6 A = 0.0105C + 0.0003
R2 A = 0.0203.C + 0.0018 A = 0.0332.C + 0.0037
Y6 A = 0.0226C + 0.0020
A = 0.0389.C + 0.0022 Y5-R40
A = 0.0448.C + 0.0030 Y6-R2
A = 0.0438.C + 0.0049 Y6-R3
R3 A = 0.0292.C - 0.0039 A=0.0819C - 0.0068
Y6 A = 0.0082C + 0.0002
R40 A 0.0324.C - 0.0002 A = 0.0293.C + 0.0290
R2 A = 0.0340C + 0.0033
A = 0 0445.C + 0.0029 Y6-R40
A = 0 0340.C + 0.0026 R2-R3
R3 A = 0.0652.C - 0.0062 A = 0.0886.C - 0.0070
R2 A = 0.0326.C + 0.0022
R40 A = 0 0408.C + 0.0102 A = 0.0384.C + 0.0193
A = 0 0295.C + 0.0022 R2-R40
R3 A = 0.0298.C - 0.0041 A = 0.0866.C - 0.0071 R3-R40
R40 A = 0.0403C + 0.0074 A = 0.03 14.C + 0.0344
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496 LOPEZ-DE-ALBA ET AI
Table 6. Recovery results for individual dyes in their binary mixtures obtained using the bivariate
method
Binary Mixtures
Y5 Y6
YS R2
YS R3
YS R40
Y6 K2
Y6 R3
Y6 R40
R 2 R3
R2 R40
R3 R40
Average Recovery Fi SD, %
First Component Second Component
9 0 0 k O 5
9 8 2 k 0 4 9 7 8 * 1 3
9 9 4 i 0 6 9 9 3 * 2 3
9 6 6 i 0 9 9 8 S i 0 9
100 5 + 0 7 9 5 0 k 3 2
101 2 * 0 5 101 4 * 1 9
1 0 2 6 * 10 1 8 6 8 * 8 3
9 6 9 * 0 6 9 7 6 i 2 2
8 9 7 i 7 3 1 0 1 0 1 7 3
100 2 * 0 7
S 8 2 5 3 6 1 0 4 0 i 5 2
dyes at these nine wavelengths (see Table 2, where the results obtained for Y5 and R2 are
presented as an example). Using the obtained data, the sensitivity matrices were created
for each mixture and the respective determinants were calculated. The sensitivity results
obtained for the mixture of Y5 and R2 are presented in Table 3, where it can clearly be
seen that the wavelengths 427 nm and 52 I nm should be used in the bivariate procedure.
The two-wavelength sets evaluated for all dye mixtures under study are given in Table
4. At these selected wavelengths the one-component calibration curves were obtained. For
the linear response range, in each case, the linear regression calibration function (9 >
0.9990) was calculated and q, e, values were taken for the bivariate algorithm (Table 5).
Then, the resolution of the binary mixtures was performed. For each mixture type, the
recovery experiments were carried out in ten solutions containing the two components in
varying concentration ratios (from 1 : 1 1 up to 1 1 : I , and the mixtures containing R3 from
1.6 up to 6 : l ) . In Table 6 the obtained results are presented, where each value was
calculated as the average recoveiy of one component in ten binary solutions prepared. As
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DYE BINARY MIXTURES 497
0.008
0.004
0.000
-0.004
-0.008
-0.012
350 41 5 480 545 61 0 Wavelength, nrn
Figure 2. The first-derivative spectra of. 1 - Tartrazine (Y5, 14mgL"), 2- Amaranth
(R2, 18mgL-'), 3 - Erythrosin B (R3, 7mgE ), 4 - Sunset Yellow (Y6,
14mgL-'), 5 - Allura Red (R40, 14mgL ) with the buffer solution as a
blank.
can be observed in tlus Table, satisfactory results (recoveries in the range 88 -104%) were
obtained for all binary mixtures.
In further development these same binary mixtures were resolved using the first
derivative spectra (the derivative spectra of all five dyes are given in Figure 2). The zero-
crossing measurement method was applied. The selected wavelengths and the formula of
caIibration function for each component in ten mixtures studied are presented in Table
7. Using the equations obtained, those same recoveiy experiments were repeated, as in
the bivariate procedure. The obtained results are presented in Table 8. In this case, poorer
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4Y8 LOPEZ-DE-ALBA ET AL
Table 7. The calibration formulas for the individual dyes in their binary mixtures obtained using
the zero-crossing method for the derivative spectra.
Binary Mixture Component h(nm) Calibration Equation ?(a=0.05)
Y5-Y6
Y5-R2
Y5-R3
Y5-R40
Y6-R2
Y6-R3
Y6-R4O
R2-R3
R2-R40
Y5
Y6
Y5
R2
Y5
R3
Y5
R40
Y6
R2
Y6
R3
Y6
R40
R2
R3
R2
R40
R3
482 7
536 8
377 0
572 9
382 7
539 3
49s 8
553 2
522 I
575 5
572 2
482 7
49s 8
575 4
576 9
522 I
498 8
522 1
49s 8 R3-R40
R40 527 + 572 ID = -2.709E-4.C - 3 65E-5
'D = -3 047E-4.C + 2.88E-5
'D = -2.417E-4.C
ID = 2.190E-4.C - 2.7E-6
'D = -2.266E-4.C - 8.08E-5
'D = 2 110E-4.C - 5.7E-6
'D=-I.5416E-3.C + 1.288E-4
ID = -1 240E-4.C + 8.1E-6
ID = -2.692E-4.C - 4.080E-4
'D = -5.143E-4.C - 6.66E-5
ID = -2 239E-4.C - 8.55E-5
ID = -4.689E-4.C-6 11E-5
ID = 3.587E-4.C-4 85E-5
'D=-9.713E-5.C -1.96E-5
ID = - I 2 18E-4.C + 2.44E-5
ID = -2 21 1E-4.C - 4 11E-5
ID = 7.717E-4.C - 4.09E-5
ID = 1.361E-4.C - 8.8E-6
ID = - 1 2 1 OE-4.C + 9.09E-5
ID = 2.441E-4.C - 5.30E-5
0 9998
0 9994
0 9996
0 9995
0 9996
0 9999
0 9987
0 9924
0 999s
0 9994
0 999s
0 9993
0 9980
0 9981
0 9994
0 9997
0 9991
0 9967
0 9989
0 999s
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DYE BINARY MIXTURES 499
Table 8. Recovery results for the individual dyes in their binary mixtures (n = 10) obtained using
derivative spectrophotometric method.
Average Recovery Ti SD, %
First Component Second Component
Binary Mixture
Y5 Y6 93.4 f 1.5 104.9 f 3.1
Y5 R2 96.6 f 3.3 90.3 f 7.2
Y5 R3 99.4 f 2.3
Y5 R40 81.0 f 22.3
Y6 R2 98.9 f 0.6
97.3 f 1.0
97.6 f 4.0
96.7 * 8.7
Y6 R3 9 8 0 + 1 5 105 1 f 1 8
Y6 R40 104 8 f 49 6 1 0 8 9 f 9 1
R2 R3 1 1 2 9 1 13 1 9 8 5 5 1 9
R2 R40 1077* 1 6 117 0 f 20 8
R3 R40 1 1 2 9 f 1 6 6 I04 0 f 5 9
average recoveries were obtained (in the range 80-1 13%) as compared with the results
of the bivariate procedure (see Table 6).
To study the observed differences in more detail, the individual recovery results
obtained in ten solutions (containing different dye ratios) were considered for each binary
mixture under study. In Figure 3 the relationship is given between the real and the found
concentrations of Y5 and R40 in their mixture. As can be seen, much better results were
obtained for each composition of the mixture using the bivariate procedure (Fig.3a) than
using common derivative procedure (Fig.3b).
The obtained results suggest that the proposed bivariate procedure could be
competitive to the derivative spectrophotometric method in applications involving the
resolution of dye binary mixtures. The evaluation of method bias was camed out using
statistical tests. The F- and T- tests were performed for the results obtained for each
component in each mixture, and the difference between the results obtained in two
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500 LOPEZ-DE-ALRA 6T AL
J
I ! 1 n 1 '2 T 16
Figure 3. The relation between the real and the found concentrations of Y5 and R40
in their mixtures: (.4) bivariate procedure
(B) first derivative procedure.
procedures tested were considered statistically significant only in the case when for both
components the t orf value was higher than the theoretical valueI3. First the F-test was
performed, andfq <Aeor ( a=0.05) were found for the mixtures: Y6-R2, Y6-R3, Y6-R40,
Y2-R3, Y2-R40, R3-R40, while for the mixtures: Y5-Y6, YS-W, Y5-R3, Y5-R40,
signifigant differences in precision were detected between both procedures under study.
Better precision is obtained using the bivariate procedure, (see Tables 6 and 8). For the
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DYE BINARY MIXTURES 50 1 - real c , rug. L-'
Y.5
16 12 8 4 0
12 1; 8 1 4 -
-
0 I I 1 I I I I I
- 0
3 9 - 12
c
- It5
0 4 8 12 16
real cR,, , mg.~- ' .. #
Figure 3. Continued
former group of mixtures, the parametric T-test was applied and for the latter group the
non-paramehic test of Wilcoxon was applied. The results obtained indicate that for the
mixtures Y5-Y6 and Y6-R3 there exists statistically signifigant differences between
results obtained by the two procedures tested (texp > t,e,n). Better recoveries are obtained
by the bivariate procedure (see Tables 6 and 8).
CONCLUSIONS
In this work, a new bivariate procedure was proposed for the resolution of the two-
component mixtures of dyes. The results of the recovery experiments carried out in ten
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502 LOPEZ-DE-ALBA ET AL.
binary mixtures and the results of the statistical evaluation of method bias indicate that
this procedure may be competitive and, in some cases, even superior to commonly used
first derivative spectrophotometric procedure as applied to the resolution of the binary
mixtures of the dyes. Simplicity is an important advantage of the presented procedure.
There is no need for full-spectrum information and no spectral data processing is
required.
ACKNOWLEDGEMENTS
The authors gratefully acknowledge financial support from the CONACyT
(MCxico), project 3 179-E9307.
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Received: 22 August, 1995
Accepted: 20 October, 1995
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