Chern. Anal. (Warsaw), 41, 899 (1996) Derivative UV-VIS Spectrophotometry in Analytical Chemistry by Stanislaw Kus, Zygmunt Marczenko and Norbert Obarski REVIEW Department of Analytical Chemistry, Technical University of Warsaw, 00-664 Warszawa, Poland Key words: derivative spectrophotometry, numeric differentiation, review The paper deals with theoretical and instrumental aspects connected with derivative spectrophotometry. Ideal absorption spectra and their derivatives from 1st to 6th order are consequently discussed. The influence of intensity and width of peaks and relative position of the bands of the analyzed substances on the quality of the derivative spectra obtained has been discussed (choice of derivative order and measurement technique). Next, the dependence of the apparatus parameters on the course of derivative curves is described. Methods of obtaining derivatives with particular consideration of the Savitzky- -Golay numeric differentiation technique are presented. The dependence of the number of spectrum points and degree of polynomial fit on the smoothness and differentiation of spectra is described. Possibilities of improving the selectivity and sensitivity of determination using derivative spectrophotometry are presented. Examples of applying this technique for the determination of inorganic and organic analytes are shown. Artykul przedstawia zagadnienia teoretyczne i aparaturowe ze spektrofotome- Omowiono idealne widma absorpcji i ich pochodne od 1. do 6. rZ<;du. Przedyskutowano wplyw intensywnosci i szerokosci pikow oraz wzajemnego polozenia pasm analizowallych substancji na jakosc otrzymywanych widm pochodnych (wybor rZ<;du pochodnej i techniki pomiaru). Omowiono z kolei wptyw parametrow aparaturo- wych na przebieg krzywych pochodnych. Z'prezentowano sposoby otrzymywania po- chodnych ze szczegolnym uwzglltdnieniem numerycznej techniki rozniczkowania wedlug algorytmu Savitzkyego i Golaya. Opisano wplyw liczby punktow widma oraz stopnia wielomianu dane na gladzenie i rozniczkowanie widm. Poka- zano mozliwosci wzrostu selektywnosci i czulosci oznaczen przy uzyciu spektrofotometrii pochodnej. Podano przyklady zastosowa6 tej techniki do oznaczania nieorganicznych i organicznych allalitow.
The paper deals with theoretical and instrumental aspects connected with derivativespectrophotometry. Ideal absorption spectra and their derivatives from 1st to 6th orderare consequently discussed. The influence of intensity and width of peaks and relativeposition of the bands of the analyzed substances on the quality of the derivative spectraobtained has been discussed (choice of derivative order and measurement technique).Next, the dependence of the apparatus parameters on the course of derivative curves isdescribed. Methods of obtaining derivatives with particular consideration of the Savitzky-Golay numeric differentiation technique are presented. The dependence of the numberof spectrum points and degree of polynomial fit on the smoothness and differentiationof spectra is described. Possibilities of improving the selectivity and sensitivity ofdetermination using derivative spectrophotometry are presented. Examples of applyingthis technique for the determination of inorganic and organic analytes are shown.
Artykul przedstawia zagadnienia teoretyczne i aparaturowe zwi~zane ze spektrofotometri~ pochodn~. Omowiono idealne widma absorpcji i ich pochodne od 1. do 6. rZ<;du.Przedyskutowano wplyw intensywnosci i szerokosci pikow oraz wzajemnego polozeniapasm analizowallych substancji na jakosc otrzymywanych widm pochodnych (wyborrZ<;du pochodnej i techniki pomiaru). Omowiono z kolei wptyw parametrow aparaturowych na przebieg krzywych pochodnych. Z'prezentowano sposoby otrzymywania pochodnych ze szczegolnym uwzglltdnieniem numerycznej techniki rozniczkowaniawedlug algorytmu Savitzkyego i Golaya. Opisano wplyw liczby punktow widma orazstopnia wielomianu aproksymuj~cegodane na gladzenie i rozniczkowanie widm. Pokazano mozliwosci wzrostu selektywnosci i czulosci oznaczen przy uzyciu spektrofotometriipochodnej. Podano przyklady zastosowa6 tej techniki do oznaczania nieorganicznych iorganicznych allalitow.
900 S. Kus, Z. Marczenko and N. Obarski
The origin of derivative spectrophotometry is connected with the appearance ofspectrophotometers enabling recording of derivative spectra [1-5). Initially, 1st orderderivatives were of interest. The development of apparatuses, especially of spectrophotometers interfaced with computers, caused that higher order derivatives weredealt with, which gave much more interesting possibilities from the point of view ofchemical analysis [6-10). Analog (electronic) and digital (numeric) differentiationare used when higher order derivatives are needed. The Savitzky-Golay algorithm[11,12] is the most frequently used digital algorithm for obtaining derivatives ofspectra.
There has been an intense development of derivative spectrophotometry duringthe last 15 years. This spectrophotometric technique permits carrying out a numberof determinations much faster than the classic spectrophotometry, and in applicationswhere the classicai technique cannot be used. Generally speaking, by differentiationof a zero order spectrum and obtaining consecutive derivative spectra the separationof overlapping peaks is achieved, increasing selectivity without separation of theanalytes. Generally, an increase in the sensitivity of the determination is achievedwith an increase in the order of derivatives.
The application of derivative spectrophotometry concerns both "inorganic andorganic substances. The more important published determination methods arepresented at the end part of this paper, including those developed in our laboratory.
A monograph on UV-VIS derivative spectrophotometry appeared in 1994 [13].The author, G. Talsky, contributed considerably to the development of the theory andpractice of this technique. Attention should be drawn to review articles devoted toderivative spectrophotometry [14-36].
GENERAL ASPECTS OF DERIVATIVE SPECTROPHOTOMETRY
UV-VIS spectrophotometry deals with absorption spectra resulting from electrontransitions between energy states in a molecule. Such a transition is accompanied byabsorption of a quantum of energy in the UV-VIS region, which is represented byan absorption curve on the intensity of radiation-wavenumber (wavelength) plot. Thevalue of the transition energy is connected with the respective location of the bandin the ultraviolet region or visible light, usually characterized as "-max. The intensityof the band is connected with the probability of an electron transition from the groundstate to the excited state and molar absorptivity is the band parameter connected withthis transition. These parameters characterize the system qualitatively ("-max) andquantitatively (E) in classical molecular spectrophotometry. The molar electrontransitions are not so narrow as atomic transitions. The reason for this is e.g.overlapping of the ground state energy, oscillation energy and rotational energy ofmolecules as well as the interaction of the substance molecules with the solvent. Thewidth of the peak, a band parameter very important in derivative spectrophotometry,is characterized by the so called half-width (L), i.e. peak width at half of its height[6, 7, 13, 17, 19, 21).
Derivative UV-VlS spectrophotometry 901
Ideal peaks and their derivatives
The absorption curve can be similar to the Gaussian curve, the Lorentzian curve(ofvery narrow central part of the peak) orbe of an intennediate character [4,6,13,21).Ideal absorption peaks and their derivatives are shown in Fig. 1. The central part ofa peak in derivatives of even orders is narrower than the basic peak and hence theseparation of overlapping peaks is easier. Narrowing of the central part of peaks ismore pronounced in the case of the Lorentzian type peak derivatives. For the peakspresented, the size of the derivative signal decreases with an increase in the order ofthe derivatives; however, the peak derivatives of a Lorentzian type have higher values(except the first derivative). The ratio of maximum Lorentzian peak derivatives tothose of the Gaussian type are 0.91, 1.25, 2.07, 3.66 and 7.66 for 1st, 2nd, 3rd, 4thand 5th derivatives, respectively. The values of the peaks mentioned are calculatedfrom function relations, due to which ideal derivatives are obtained ofknown zeroing,and also placing and values of maxima and minima. Such operations give an idea ofthe relations occurring between the basic spectrum and its spectra obtained bydifferentiation. Spectra of varying parameters are obtained using e.g. a Microsoft Excel5.0 worksheet. Curves are drawn in arbitrary units (AU) using the nonnalizing factor W:
W -I At,.p)~~ AendIwhere Abegin, Aend denote spectrum range wavelengths, ~A - interpoint distance(distance between the points of the spectra). In other words, the coefficient Wis thenumber of points of the spectrum to which arbitrary unit values from the -W/2 to+W/2 range differing between each other by 1 can .be assigned (step of calculatingthe band or derivative curve). Due to the coefficient applied, the derivative valuescalculated from the functional relationships and those from the increments give thesame results. For simplicity, the intensity of the simulation spectra is assumed asequal to 1. Comparison of amplitude values (difference between the maximal andminimal value of the curve) of the derivative of the 1st to 6th order indicates that forbroad spectra the derivative intensity systematically decreases with an increase in thederivative order, both for the Gaussian (PG) and Lorentzian (PL) type of peak. Forexample, for a peak ofhalf~width0.1 AU the derivative values are 0.14, 0.02, 0.0045,0.00093, 0.00026 and 0.00007 (PG) and 0.13, 0.025, 0.0093, 0.0034, 0.002 and0.0011 (PL) for the 1st to 6th order derivatives, respectively. For sharp peaks thecourse of these changes is different. With an increase in the derivative order itsderivative value first decreases (acquiring minimum for the 2-nd derivative)and thenincreases to exceed for the Lorentzian peak the value equal to that of the basicspectrum. For example, for a peak of a half-width 0.025 AU the derivative values are0.57, 0.32, 0.27, 0.24, 0.25 and 0.26 (PG) and 0.48, 0.40, 0.57, 0.79, 1.19, and 4.51(PL) for the 1st to 6th order derivatives, respectively. These data permit to draw theconclusion that by using derivative spectrometry for flat spectra no increase in thesignal measured will be obtained, contrary to sharp spectra, where the signalmeasured after differentiation is greater than the basic signal, especially for derivatives of higher orders.
Figure 1. Ideal Gaussian (a) and Lorentzian (b) peaks and their 1st-5th order derivatives. The half width(L) and heigth of both peaks are identical. The expansion of derivatives value scale was madeautomatically'
Derivative UV-VIS spectrophotometry 903
Ideal Gaussian or Lorentzian curves are symmetric only in the wavenumberscale, and in the wavelength scale they lose their symmetry. The introduction of anormalizing factor and arbitrary unit of scale permits to avoid the problem connectedwith the comparison of spectra registered as a function of the wavelength with thoseobtained as a function of the wavenumber. I ,
Simulation of ideal spectra and then diff~rentiation of them pennits to check thecorrectness of the differential algorithm used. Having exact data calculated fromfunctional relationships one can determine the error made by using a given algorithmfor differentiation of of the real spectrum of a shape similar to the simulationspectrum. Much attention has been given to this in the literature [5, 6, 15, 17, 21].
Properties of derivative spectrophotometry
The most important properties of derivative spectrophotometry, similarly as inclassic spectrophotometry, is the dependence of the derivative value on concentrationand its additivity. By differentiating the expression for the Lambert-Beer law overthe wavelength the following equation is obtained [7, 13, 21]:
dnA dng n--=-xcx[=DdAn dAn
n~Order derivative of molar absorptivity over wavelength calculated at ~'(;itledstandard conditions could be a measure of sensitivity in methods applying derivativespectrophotometry (by analogy to molar absorptivity in classical spectrophotometry).
For a mixture of x components the derivative value of their mixture is a sum ofthe derivative values of each of them [6, 7, 21, 31]: .
D~ixture = D'i + D~+·"+ D~
This property is taken advantage of for the detennination of several (x) components in a mixture by measuring the derivative value of the mixture at several (minimumx) wavelengths. The measurement is carried out at those wavelengthS at which thederivative spectra of particular components undergo zeroing [25-27, 30].
The relationship between the signal value and half-width of the peak L is aspecific property of derivative spectrophotometry [13, 21]:
vn = P" x A max x L-D
where P" denotes polynomial depending on the derivative order.For two peaks Aand B of the Aand B peaks half-widths LA andLB, the derivative
values ratio is expressed by the equation: .
D~ AmaX,A(LB)nD~ = Amax,B LA
Derivative spectrophotometry provides an increase in sensitivity and selectivityof the methods in comparison with the classical derivative spectrophotometry basedon the same colour system. An increase in selectivity in the derivative spectrophoto-
904 s. Kus, Z. Marczenko and N. Obarski
metry results from the fact that differentiation permits to obtain a larger amount ofinformation contained in the basic absorption spectrum. Due to this it is possible totake advantage of the differences in the position of the peaks (different A.max) and inthe peak half-width (different L values) [7, 13, 20, 21 J.
In Figure 2 are presented two models of absorption bands Aand B (correspondingto substances Aand B), differing in intensity (Amax,AIAmax,a =115), half-width (LAlLa =115) and position (A.max,A ¢ A.max,a). These bands overlap and thus by simple measurement of absorbance it is impossible to determine the components of the mixture-curve C.
The situation changes when differentiation of the spectra is carried out. Alreadythe first derivative pennits to determine substance B in the presence of substance Aby the fact of the zeroing of the band A derivative. The derivative values of themixture and of substance B are equal to each other (Ha segment) for this wavelength,where the derivative of substance A crosses the zero line. It can be noted that
Dfi,1-.o = Dt,1-.o
where D denotes derivative value, 1 - derivative order, B, C - substance (or band)detennined, A.o - coordinate of the substance A derivative zeroing. This measuringtechnique is called "zero crossing" [6, 10, 13, 21 J.
An increase in the order of the derivative leads to a flattening of the band Bderivative and increase in the band A derivative signal. As can be seen in Fig. 2f, forthe 5th order derivative the derivative spectra of substance A and the mixture arenearly identicaL One can note
Di,"-t-~=Dt,"-t-~
where D is derivative value, 5 - derivative order, A, C - substance (or band)determined, 1..1-1..2 - coordinates of places, where the 5th order derivative of substance A gains maximum and minimum. The measuring technique applied here iscalled peak-to-through [13, 16, 21 J. The dimension of the HA segment correspondsto the concentration of substance A in solution. The differentiation of the mixturespectrum pennits to eliminate the influence of the intense band B on the determination of the substance of band A.
The value of the signal in derivative spectrophotometry depends precisely on theshape of the basic spectrum. Spectra of sharp peaks are preferred, in which the signalvalue after differentiation increases with that of the derivative order, contrary tospectra of flat peaks, for which the signal decreases. The ratio of signals dependsinversely proportional to the ratio of peak half-width in an order equal to that of thederivative. This pennits to expose a small sharp peak overlapped by a flat, evenintense band, from the total basic spectrum. The value of the sharp peak d,erivativeis then several times greater than that of the broad peak. The derivative valueincreases with a decrease in the half-width of a given spectrum [7, 10, 13, 21 J.
IYA > D1J when La >LA
Derivative UV-VlS spectrophotometry 905
+
o
+
o
6th
4th
f
e
1st
+
Ol---=:;;~----'~"~l-------~-
•ocas..Q
o•..Q-<
a
Arbitrary units
Figure 2. Dependence of selectivity on shape of peaks and derivative order. Comparison of derivativesignal for two peaks (curves A and B) and their mixture (curve C). LB: LA = 5 : 1;Amax.B : A max• A =5 : 1
906 s. Ku§, Z. Marczenko and N. Obarski
In the case of spectra of similar half-widths a measurement can be taken of thederivative value ofthe substance determined at a wavelength for which the disturbingsubstance derivative crosses the zero line (reaches zero value, and thus does not affectthe derivative value of the substance determined).
Measurement techniques of the derivative value
The derivative spectrum of any order results from the differentiation of a zeroorder (basic) spectrum of a mixture of components. The differentiation of a spectrumis performed by various methods, usually by analog or numeric methods. The result,irrespective of the mode of differentiation, may be presented graphically on paper or'registered in a computer memory. The detennination of the derivative values iscarried out by means of one of the three methods describe below. The derivative valuedetennination can be carried out graphically or numerically.
Graphic measurement consists in recording on paper (by using a XY-registereror plotter) a derivative spectrum and zero line (Fig. 3a). The wavelength f... (wavenumber) at which the derivative value will be measured is then marked, and at thispoint a line, perpendicular to the zero line, is drawn. The AB segment length is the
II
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I,I
!I
lA.u
• b+ IJAl 'It
, ,0 "
I .',I I ", : : .,
HaI I I,I I •,I II I I• i I ---- .. ~--- 6• B.: , • •• • I • •
II I
I . I •I)I II I I::::J I I •"i : I
> :A.u !~I
I) :1&>~l:~ aa
+
0
Wavelength, nm
Figure 3. Graphic (a) and numeric (b) methods of derivative signal measurement. HAl - a measure ofcurve Asignal exactly at experimental point AA1; H A2 - a measure of curve Asignal betweentwo experimental points (interpolated value); H B - a measure of curve B signal at point wherecurve A crosses the zero line
Derivative UV-VIS spectrophotometry 907
derivative value expressed in length units (e.g. mm). The length of measured segments is usually increased by signal amplification (amplificaton factor). The curvedrawn by an XY-recorder is electronically smoothed and interpolated through thediscreet point spectrum. Each spectrum registered in the memory during measurement is of a discreet fonn, i.e. consists of points distant from each other by a certainconstant value called interpoint distance or sampling interval (L\A). This valuedepends on the working parameters of a scanning spectrophotometer, such as integration time, scan speed, range of spectrum registered. The spectrum outlined by therecorder is continuous, which is an advantage of this type of treatment. A disadvantage, however, is an inaccuracy of measurement, especially when performed on thesteep side of the curve (the perpendicular line crosses the derivative spectrum underan acute angle). This disadvantage can be eliminated by detennining the derivativevalue numerically.
Numeric measurement of the derivative values is carried out by reading thederivative value at a given wavelength (wavenumber) from a set of points (wavelength-derivative value). Such a set is obtained as a result of spectrum differentiationusing an appropriate numerical algorithm for obtaining of derivatives. When lookingat the derivative spectrum, e.g. on a computer monitor linked to the spectrophotometer, one can exactly read the. derivative values at wavelengths changingstepwise. If at a given wavelength A(Fig. 3b) there are no points, then, knowing thevalues of the points before and after the wavelength determined, it is possible tocalculate the derivative values by interpolating the nearest points with a straight lineor any polynomial. Such a solution should be realized in the software at an enlargement of a segment of part of the spectrum (often occurring option "zoom").
Both graphical and numerical measurements of the derivative value differ fromthe absorbance value measurement in a traditional spectrophotometer and cannot beperformed by means of a spectrophotometer for point measurements. In a derivativespectrophotometry a measurement is made always on the basis of a registered anddifferentiated absorption spectrum.
The zero-crossing technique [6, 10, 13,21] consists in measuring the derivativevalue at a wavelength (wavenumber), at which the derivative of the interferingcomponent accepts value zero - crosses the zero line (Fig. 4a). Curve A crosses thezero line at point Z, and curve B at point P - the derivative accepts value zero at thesepoints. In this way there is no effect of one component on the other one. The derivativevalue of component B at the zeroing point of component A (point Z) is equal to thesegment HB. Curve C shows a sum of components A and B. At a wavelengthcorresponding to point Z the derivative values of curves Band C are the same andcomponent A does not affect component B at this place. The same occurs at point P.Segment H A is the derivative value of component A. This technique is applied whenthe zero order differentiated spectra differ in the position of the absorbance maximum, or one of the spectra (determined) has an inflection point.
The zero-crossing technique permits to eliminate the influence of the componentinterfering with the component detennined. A disadvantage of this measuring technique is a not too great precision of measurements. T4is is noticeable in the graphic
908 S. Ku8, Z. Marczenko and N. Obarski
b
mode of detenninillg the derivative value by measuring the length of segments H A
and HB' An error then occurs connected with the detennination of the crossing pointof the straight line with the derivative spectrum (the measurement takes place on thesteep side). The zeroing point of the derivative should be detennined for at least twoconcentrations.
Figure 4. The "zero crossing" (a), "peak-to-through" or "peak-to-peak" (b) and "baseline--to-peak" (c)measurement techniques of derivative signal. Curves A and B - peaks of analyte and interference, curve C - sum
The "peak-to-peak" technique [6] consists in measuring the derivative value atsuch wavelengths where the ratio of the derivative values HA of the componentdetennined A to the derivative values HB of the interfering component B reaches thelargest value. (Fig. 4b). The determination is carried out by measuring the amplitude(from the maximum to minimum of the curve). The peak-to-peak technique is usedwhen the spectra differentiated of zero order differ considerably in half-widths,component A has a smaller half-width than component B. When differentiating suchspectra, flattening of the component B derivative with respect to the component Aderivative occurs.
Derivative UV-VlS spectrophotometry 909
o
or
The "baseline-to-peak" technique [6, 13,21] consists in measuring the deriva~
tive value at such a wavelength where the ratio of the derivative value HA of thecomponent determined Ato the derivative value HB of the interfering compon'ent Breaches the greatest value (Fig. 4c). The measurement is carried out from maximumto the zero line Oi" from minimum to the zero line. This technique is a version of thepeak-to-peak technique, in comparison with which it is less sensitive (the ratio of thederivativevalues is smaller here).
OBTAINING OF DERIVATIVE SPECTRA
Obtaining of a spectrum of any order is preceded by a selection of parameters,·on which the shape and position of characteristic points of the derivative (zeroingpoint, maxima, minima) depend. Each of the parameters described below can affectthe course of the derivative, independently or dependently of the others. The shapeof the zeroth order spectrum is decisive of the course of parameter optimization.
The absorption spectrum derivative is obtained mostly by two methods: by analog(electronic) differentiation of the detector output signal, or by numerical (digital)differentiation of the absorption spectrum registered in the computer memory.
In the analog technique [7, 13, 15, 16, 18, 21] a suitable electronic circuit(derivative unit) is employed, connected between the spectrophotometers (detector)outputand recorders input. In Figure 5 a simple electronic circuitscheme is presented.
R
C~'000--_1 ,.OPinput U(t) • output .!!.!:!..
\ i 0 dt
-Figure 5. Simplified diagram of analogue differentiation circuit: C - capacitor, R - resistor, OP
operational amplifier
The output voltage of the spectrophotometer, which is proportional to the absorbance,is differentiated with respect to time to give the derivative signal. The derivative withrespect to wavelength is related to the time derivative signal as follows:
dA dA dA.-=-x-dt dA. dt
where dA./dt is scanning speed, usually a constant value [13, ,IS, 16].This derivative unit works on-line and its advantage is the possibility of electronic
amplification of a signal by simultaneously lowering the noise. n-Order derivativespectra can be obtained in the analogue technique with omission of the zeroth orderspectra and lower order derivative spectra. The order of the derivative obtaineddepends on the number of the derivative circuits [13, 16, 18].
Derivative units are commercially available, e.g. Hitachi 200-0576 or Philips PyeUnicam TLB 600.
910 s. Xu§, Z. Marczenko and N. Obarski
A development of the numeric differentation of spectra technique is presentlyobserved. The real absorption spectrum, consisting of points described by a pair ofcoordinates wavelength-absorbance is burdened with some noise, the value ofwhichdepends on the working conditions of the spectrophotometer registering the spectrum. How close the points of the spectrum are collected (interpoint distance L\A.) alsodepends on these parameters. The derivative spectrum can be calculated from simpleincrements in absorbance per a wavelength unit increase. In Figure 6 is shown asimulation of an ideal spectrum (Gaussian curve) and a curve with small noise(Gaussian curve + noise) and their 1st order derivatives. In the case of an idealspectrum the derivatives calculated mathematically and those from the absorbanceincreases overlap. The derivative of the spectrum with noise calculated from increments is irregular and a clear influence of noise is visible (Fig. 6b).
•.2CII>•>~~•"
•ocCII.0olIII.0<
•r--------------------------IIIIII
Arbitrary units
Figure 6. Comparison of numeric differentiation method for ideal Gaussian curve (1) and ideal curvewith noise (2). a) fundamental spectra, b) 1st derivative spectra; 1 - ideal first derivative, la,2a - point-point differentiation, Ib, 2b - Savitzky-Golay algorithm (2nd degree polynomial,9-points window)
Derivative UV-VIS spectrophotometry 911
The application of the Savitzky-Golay methods [11, 12] in numerical differentiation causes a considerable decrease of the noise influence on the derivativespectrum shape (Fig. 6b, curve 2b). Due to numerical fiItration this method permitsto increase the signal/noise ratio (SNR). The derivative value for a given point of thespectrum is calculated considering the weights and values of absorbance of anappropriate number of adjacent points (part of spectrum), usually symmetricallydistributed with respect to the central point (Fig. 7). A polynomial of respective orderis fitted through these points with the best mean-square method, from which aderivative can be calculated with an order not larger than the polynomial degree. Theresult of calculations depends on the interpoint distance !J.'A, number of points of thespectrum fragment on which the polynomial is concerned and the order of thepolynomial applied. The simultaneous fitting of all the.points of the spectrum wouldrequire a polynomial of a very high order. Therefore, only a fragmentofthe spectrumis considered, choosing a determined number 2m+ 1 experimental points from -m to+m (in Fig. 7 m = 3). The first seven points of original spectrum gives a first point ofderivative spectrum. Repetition of this process for 2-8 point of spectrum gives asecond point of derivative spectrum. Then the seven-points window moves on theright by one point and a successive point of derivative spectrum is calculated. Thisprocedure is called a convolution. It is repeated until the next seven points (k-7 - k)
Figure 7. Presentation of a 7-points convolute (2m+l group of experimental data) for calculation of 2ndderivative by the least-squares method using3rd degree polynomial
~12 s. Kus, Z. Marczenko and N. Obarski.
original spectrum. An exemplary equation fOf the calculation of the 1st derivative forthe central point of 7 points fragment spectrum and 2nd polynomial degree assumingIi/...= 1 is as follows [11, 12]:
1 -3Y-3 - 2Y-2 - Y-l +Yl + 2Y2 + 3Y3Do= 28
where: 3, 2, 1, 1, 2, 3 are weights of suitable points, 28 - nonnalizing factor.The common use of spectrophotometers interfaced with computers and the
possibility of multiple processing of the spectrum registered causes that numericaldifferentiation is more convenient than analogue differentiation. On the other hand,the facility of obtaining derivative spectra (especially of lower order ones), possibility of hardware filtering, lowering the noise and signal amplification makes theanalog differentiation technique still attractive. The quality of derivative spectraobtained in both differentiation techniques is comparable; however, the course ofderivative spectra slightly differ. Numeric differentiation provides greater possibilities in'the optimization of the algorithm for obtaining the derivative.
The shape of the derivative calculated according to the Savitzky-Golay algorithmdepends on the order of derivative and chosen differentiation parameters, i.e. numberof points (2m+ 1), degree of the fitted polyn~mial and the way of obtaining thederivative of a given order [11, 13, 21].
Choice ofthe derivative order takes place by analysis ofconsecutive derivativesfrom 1st to n-th order obtained from the registered zeroth order spectrum (at givenregistering parameters). The basis of 'such an analysis is the determination of theminimal derivative order for which the component determined derivative value ismaximal and precision the highest with respect to the interfering components derivative value. Initial determination as to which type of "absorbing system the system"studied belongs permits to limit the seeking range.
In the case of a system in which the half-widths of spectra are similar, onlymeasurement of the derivative value by the "zero-crossing" method can be thesolution. The order of the respective derivative depends here on the distance betweenthe maxima of the spectra analyzed with respect to each other in relation to theirhalf-width. If the absorbance maxima are located with respect to each other at adistance equal about 1/4 of the spectra half-width, then the 1st order derivativeenables the detennination of both components simultaneously. If the absorbancemaxima of the spectra analyzed shift from each other, then the derivative order atwhich both components can be determined simultaneously increases. At a differencein location of the absorbance maxima by about 0.5 half-width, the 2nd order derivative is more appropriate.
The Savitzky-Golay algorithm provides for application of any odd number ofppints over which the polynomial is expanded [11-13]. The choice of the number ofpoints depends on the degree to which one wants to influence the derivative shape ofa given order. This choice depends also on the shape of the zeroth order spectrum. Itis generally assumed that an increase in the number of points causes a smoothing ofthe derivative and the derivative shape becomes more regular. In Figure 8 is presented
Derivative UV-VIS spectrophotometry 913
[37] a zeroth order spectrum of sulphur dioxide registered (beam spectral width 0.5 nm,interpoint distance 0.01 nm)so as the 'spectrum fine structure (oscillations) wasvisible. If a 1st order derivative is obtained from this spectrum by calculating with adifferent number of points from 5 to 305 (Fig. 8a-f), then it can be seen that anincrease in the number of points favours obtaining of a derivative of a more regularshape (not frayed). Hone does not want to take advantage of the oscillation spectrumcharacter and only of the broad peak with a maximum at 286 nm, then the derivativeshould be calculated using 305 points. Oscillations have been treated here as an
,interfering agent or noise overlapping the broad spectrum of large half-width [37].However, when a sharp peak is differentiated of a small half-width, one should
use a small number of points. In Figure 9a is presented a spectrum of nitrogen oxide[37]. An increase in the number of points from 5 to 25 favours obtaining a derivativeof a more regular course (Fig. 9b, c). A further increase in the number of points (Fig,9d-g) causes a change in the unfavorable derivative shape. For 305 points it loses itscharacter, undergoes a considerable shift towards negative values and a peak at 243 nmappears which does not correspond to any in the zeroth order spectrum.
The polynomial degree, fitted to experimental points, has an influence on theshape of derivative to a lesser degree than the number of points of the polynomial.The polynomial choice scope is small. The differences between the use in calculationsof a 2nd, 4th, 6th and 8th degree polynomial are presented for a broad spectrum, suchas that of sulphur dioxide in Figure 10 and for a sharp spectrum of nitrogen oxide inFigure 11 [37]. An increase in the polynomial degree from 2 to 8 (Fig. 10a-<1) causesan increase in irregularity of the broad spectrum derivative shape. For narrow spectraan increase in the polynomial degree (Fig. 10a-<1) causes an increase in the ratio ofthe determined component (NO) spectrum derivative value to the noise. This causesthe formation of sharp peaks in the derivative spectrum.
Polynomials of a relatively low degree should be used for the differentiation ofspectra of considerable half-width, and higher degree polynomials for that of spectraof small half-width. By choosing an appropriate, polynomial degree the influence ofthe narrow spectrum derivative on the broad spectrum deriv.ative can be limited.
The way of obtaining the derivative has a considerable effect on the shape ofthe derivative obtained. An n-th order derivative can be obtained directly from thezeroth order spectrum, or in stages, obtaining, e.g. first the k-th order derivative(k - any derivative order, but smaller than n), and then from this the n-th orderderivative. The influence of the mode of obtaining the derivative on the derivativeshape is shown on the example of the 4th order derivative of the permanganate ionspectrum ,(Fig. 12) [37, 52].
In Figure 12a the 4th order derivative ha's been obtained directly from the zerothorder spectrum. The spectrum is strongly frayed, irregular. Derivatives of the sameorder obtained by a lllultiple step way (Fig. 12b-<1) are of a more regular shape. Thisis best presented by the derivative obtained by consecutive differentiations 1st -+ 2nd-+ 3rd -+ 4th.
Smoothing means a mathematical processing of the experimental data registered(so called raw data) leading to the obtaining of a curve of a regular course (numeric
914 S. Kus, Z. Marczenko and N. Obarski
noise elimination). Smoothing is applied when a zeroth order derivative of a regularshape cannot be obtained by a choice of its registering parameters. It is also used
+305 points f
O.-.---------""Ir--------__::::::a_
•155 points
+OF-------~r-------__:::_-
+ dCD
0::Iti>CD>;;.2:•"0i 25 points
+0
+o
b
CD()c:ell.Q
o10.Q4(
240 280 280 300 320Wavelength, nm
a
340
Figure 8. Influence of points number (window) of least-squares polynomial fitting of experimental dataon the shape of the 1st derivative spectrum of sulphur dioxide (802), Interpoint distance - 0.1 nm,slit - 0.5 nm
Derivative UV-VIS spectrophotometry 915
; 1805 pmnllf
+ I 155 points •
~ I 1\fJWV'''J
CDocas.0o.a< IW, A
190 205 220 235Wavelength, nm
a
Figure 9. Influence of points number (window) of least-squares polynomial fitting of experimental dataon the shape of the 1st derivative spectrum of nitrogen oxide (NO). Interpoint distance - 0.1 nm,slit - 0.5 nm
when the derivative calculation algorithm (e.g. S-G) does not lead to a regular shapeof the curve. FFT (Fast Fourier Transformation)[13, 24] and Savitzky-Golay algorithm [11-13] are the most known numeric smoothing algorithms. The smoothingoptimization by S-G consists in a choice of a number of points and polynomialdegree. Tbe effect of sulphur dioxide spectrum smoothing is shown in Figure 13 [37].With an increase in the number of points (from 5 to 25) noises are eliminated and
916 S. Ku8, Z. Marczenko and N. Obarski
then (to 105 points)the oscillation structure of the spectrum. A spectrum of a linearcourse results from smoothing. A further increase in the number of points (to 305)does not change the shape of the curve. Too advanced smoothing leads to a changein the character of the spectrum (loss of information on the spectrum fine structure).
d
+o F""-~------bf-;r Ih-......---~-::;poo--
+CD.2 0..>CD~
ai~•"CI- b..-
+0
a+
O~"-------_---"~-------:::::==---
240 280 280 300 320 340
Wavelength, nm
Figure 10. Influence of polynomial degree of least-squares fitting of experimental data on the shape ofthe 1st derivative spectrum of S02' Interpoint distance - 0.1 nm, slit - 0.5 nm; a, b, c, d 2nd, 4th, 6th and 8th degree, respectively
The averaging out ofspectra by multiple registering is another way of eliminatingnoise. A multiple registering of spectra has also a positive effect on the reproducibility in determining the derivative zeroing point in the "zero-crossing" meas,uringtechnique.
Figure 11. Influence of polynomial degree of least-squares fitting of experimental data on the shape ofthe 1st derivative spectrum of NO. Interpoint distance - 0.1 nm, slit - 0.5 nm. a, b, c, d 2nd, 4th, 6th and 8th degree, respectively
An unrestricted choice of numeric differentiation parameters is not possible inevery spectrophotometer adapted for obtaining of derivatives. There exist apparatuses with chosen differentiation parameters permanently set up, without a possibilityof changes. SPECORD M 40 is such a spectrophotometer with a Data Handling Icassette, where the derivative is calculated using only 9 points (the polynomial degreeis not given).
The result of spectra differentiation depends on many parameters. Therefore,applying a method elaborated for another apparatus may not give satisfactory effects.
918 s. Kus, Z. Marczenko andN. Obarski
d
Wavelength, nm
Figure 12. Influence of the way of obtaining derivative spectra on the shape of the 4th derivativespectrum of permanganate ion calculated by use of 2nd degree polynomial with 9-pointwindow. Interpoint distance - 1 nm, slit - 1 nm; a) direct Oth-4th:, b) Oth-3rd-4th,c) Oth-2nd-4th, d) Oth-lst-2nd-3rd-4th
A majority of spectrophotometers have generally a 1-4 order option of derivativecalculation in their data handling software. However, it is not known how it iscalculated. In order to fully reproduce the method elaborated it is necessary tointroduce a unified procedure.
The optimization of the numeric differentiation parameters can be carried outusing spectrophotometers ~nabling registering of the spectrum in the computermemory, and then derivative calculation with appropriate software. An exanlple ofsuch a program can be any calculation sheet, such as QUATRO PRO 4.0, EXCEL 5.0with a written in S-G algorithm of derivative calculation or specialistic program., e.g.GRAMS/386 GALACTIC CORPORATION.
Derivative UV-VlS spectrophotometry 917
+
o
d
e+
0CD:::Ia;>CD~a;~
CD b't'J +-:!0
~ 1 7 ~ L': ~=, :'J190 205 220
Wavelength, nm
a
235
Figure 11. Influence of polynomial degree of least-squares fitting of experimental data on the shape ofthe 1st derivative spectrum of NO. Interpoint distance - 0.1 nm, slit - 0.5 11m. a, b, c, d2nd, 4th, 6th and 8th degree, respectively
An unrestricted choice of numeric differentiation parameters is not possible inevery spectrophotometer adapted for obtaining of derivatives. There exist apparatuses with chosen differentiation parameters permanently set up, without a possibilityof changes. SPECORD M 40 is such a spectrophotometer with a Data Handling Icassette, where the derivative is calculated using only 9 points (the polynomial degreeis not given).
The result of spectra differentiation depends on many parameters. Therefore,applying a method elaborated for another apparatus may not give satisfactory effects.
Figure 12. Influence of the way of obtaining derivative spectra on the shape of the 4th derivativespectrum of permanganate ion calculated by use of 2nd degree polynomial with 9-pointwindow. Interpoint distance - 1 nm, slit - 1 nm; a) direct Oth-4th, b) Oth-3rd-4th,c) Oth-2nd-4th, d) Oth-lst-2nd-3rd-4th
A majority ofspectrophotometers have generally a 1-4 order option of derivativecalculation in their data handling software. However, it is not known how it iscalculated. In order to fully reproduce the method elaborated it is necessary tointroduce a unified procedure.
The optimization of the numeric differentiation parameters can be carried outusing spectrophotometers enabling registering of the spectrum in the computermemory, and then derivative calculation with appropriate software. An exaniple ofsuch a program can be any calculation sheet, such as QUATRO PRO 4.0, EXCEL 5.0with a written in S-G algorithm of derivative calculation or specialistic program., e.g.GRAMS/386 GALACTIC CORPORATION.
Derivative UV-VIS spectrophotometry 919
Zeroth order spectra
105 points e+o
2nd derivative spectra
105 points smooth j
55 points+
55 points smooth
e:;,
h25 points .. 25 points smoothe C :+0c
~...0 ·00 ~•.0 e-< '0
'0Cw
5 points 5 points smooth g
+0
~270 280 290 300 310
Wavelength. nm
+o~~::;~A/_[~V'V~270 280 290 300 310
Wavelength. nm
Figure 13. Influence of points number (window) of polynomial smooth on the shape of the zeroth orderspectrum and 2nd derivative spectrum of S02. Interpoint distance - 0.1 nm, slit - 0.5 nm.Derivative spectrum calculated using 2nd degree polynomial with 17 points window
INFLUENCE OF APPARATUS PARAMETERSON THE DIFFERENTIATION OF SPECTRA
Techniques of recording zeroth order spectra
An absorption spectrum is obtained by means of scanning or diode-array spectrophotometers [33].
920 S. Ku§, Z. Marczenko and N. Obarski
A scanning spectrophotometer records the spectrum by measuring the intensityof the monochromatic radiation (with changing in time wavelength from the begi1ll1ing to the end of the measuring range) passing through an absorption solution.Spectra with a different interpoint distance, various scanning speed and differentspectral beam width (which affects the shape of the spectrum recorded and itsderivatives) are obtained depending on the spectrophotometer design.
A diode-array spectrophotometer permits to obtain a zeroth order spectrumsimultaneously over the whole wavelength range for which the spectrophotometer isdesigned. Light is split after passing through the solution studied and directed on thearray of photodiodes. The construction features of this spectrophotometer limit thepossibilities of influencing, by selecting the parameters of recording, and on theabsorption spectrum shape (limited to the number of photodiodes covering the range,distributer, dA constants). An advantage is obtaining of consecutive spectra in shorttime intervals, which is useful in kinetic absorption systems or in flow systems. Bymeans of these spectrophotometers mainly organic compounds are detennined byderivative spectrophotometry. A spectrophotometer of simultaneous detection andderivative spectrophotometry are interfaced as a detector with liquid chromatography.
Apparatus parameters ofzeroth order spectra registration
The shape of the zeroth order absorption spectrum depends on the colour systemand on the recording spectrophotometer working parameters (beam spectral width,interpoint distance, scan speed, integration time, registration interval of spectrum)[13, 16, 18, 21, 27-29]. The first two parameters have a decisive influence on theshape of the spectrum. A relationship exists between the parameters (by increasingthe registration speed the integration time is decreased) which causes an increase inthe interpoint distance (smaller number of points in a given measuring range).
An appropriate selection of the width of spectral beam (slit width) incident onthe solution studied has a great effect on the shape of the spectrum of narrow peaks[13, 21, 26]. An increase in the slit width causes that the radiation beam is less andless monochromatic. Spectra of small half-width undergo flattening. This is shownby the example of the benzene vapor spectrum characterized by many sharp peaks(Fig. 14) [37]. An increase in the slit width from 0.1 nm (Fig. 14a) to 0.5 nm (Fig. 14b)causes a decrease in the value of peaks at maximum absorbance to half and increasein absorbance at minima, and the ratio of the peaks values with respect to each otherdecreases. A further increase in the spectral beam width causes a decay of thecharacteristic bands.
The use of smaller spectral beams widths is connected with an increase in noiseand is justified when, e.g. the spectrum analyzed has narrow peaks, and that of thesecond component is more flat. An increase in the gap width has a much greater effecton the spectrum of sharp peilks (flattens it) than that on flat spectrum. The effect ofthe second component spectra can be partially eliminated already when registeringthe zeroth order spectrum by choosing an appropriate value of the spectral beamwidth.
Derivative UV-VlS spectrophotometry 921
f
h
,
270
e
d
I
j
;-------~ Ii---~-........,...-~--
---;~ .-1I _ ~ I~ j~ A~"""";'_...~J\,",._:III~A _
~ ~~I., ~.~....---,.a
l ~ +1 ~O t Aa A. ~~ .,~..
t1~~ - J~230 240 250 260 270 230 240 250 260
•oc...ao•.a4(
Wavelength, nm Wavelength, nm
Figure 14. Influence of slit width on the shape of the zeroth (a-e) and 1st derivative (f-j) spectra of thegaseous benzene. Interpoint distance - 0.1 om, 1st derivative spectrum calculated using 2nddegree polynomial with 25 points window
Registration of the spectrum takes place by absorbance measurement with anappropriate scanning step (interpoint distance or sampling interval). Registrationwith a large interpoint distance gives an averaged spectrum, since the ~pectro
photometer detector registers radiation of a larger wavelength difference. At too largeinterpoint distance values spectra of narrow peaks may undergo clear deformation[6, 23]. The derivative zeroing points also undergo considerable shifts.
The scanning speed of the spectrum is switched respectively to the abilities of agiven spectrophotometer [16-18]. In a SPECORD M40 spectrophotometer the registration speed (SPEED) can be from 10 mm s-1 to 5 mm min-1 and is connectedwith the expansion of the wavenumber scale (EXP X), integration time (INT) andinterpoint distance at which the spectrum is registered. An increase in the registrationrate in the same region of wavenumber stretching is connected with an increase inthe interpoint distance of registration or decrease in the integration time (maintainingthe same interpoint distance). From the point of view of derivative spectrophotometrya change in the registration speed should not affect the end result while maintainingthe same interpoint distance. Integration time is then, however, the decisive factor.
922 s. Kus, Z. Marczenko and N. Obarski
Integration time is the time in which the spectrophotometer detector cumulatesthe absorbance value. A decrease in the integration time causes a decrease in theprecision of measurement, which results in an increased share of noise in the spectrumobtained.
The registration range of wavelength (wavenumber) depends on the algorithmused in calculating the derivatives, and also on the possibilities of the spectrophotometer. In the case of the Savitzky-Golay algorithm the zeroth order spectrumis registered over an appropriately larger wavelength range. When calculating thederivatives with a k point convolute a (k-l )/2 interpoint distance is added to thebeginning and end of the range required for the derivative. The derivative calculationprocedure disregards this [(k-l)/2] number of measuring points at each differentiationoperation. This problem has been eliminated in the most recent modifications of theS~G algorithm [35, 36].
In derivative spectrophotometry the component detennined is interfered by otherones, as a result of which the absorbance value measured corresponds to the sum ofabsorbances of all the components present in the solution studied. This is of greatimportance when using the peak-to-peak or baseline-to-peak techniques. The increase in the derivative value of the spectrum of smaller half-width is then takenadvantage of. This is used for the detennination of traces in the presence of aconsiderable share of the absorbing matrix. Therefore, the absorbance range for thestandard curve should consist of only part of the measuring possibilities of thespectro!Jhotometer. Measurements of large absorbance values are burdened withconsiderable errors. In the case of exceeding the absorbance measurement range ofa given spectrophotometer the results are erroneous.
ADVANTAGES AND DISADVANTAGESOF DERIVATIVE SPECTROPHOTOMETRY
Advantages of derivative spectrophotometry are: simultaneous detennination ofseveral components in a mixture, determination of traces without isolation andseparation from the matrix, elimination of background and turbidity of the sample,increase in the contrastive effect of reaction, identification of organic compounds ortheir confirmation on the basis of a derivative of a respective order (so calledfingerprint), exact detennination of the maximum absorbance wavelength and inflection points [7, 10, 13, 19,21]. Derivative spectrophotometry, in comparison withclassical spectrophotometry, in many cases leads to an increase in sensitivity andselectivity.
Susceptibility towards changes in the apparatus parameters are negative sides ofderivative spectrophotometry. Reproduction of the determination method elaboratedby this technique requires the use of the same type of apparatus or the adaptation ofthe method to the possessed spectrophotometer.
Derivative spectrophotometry has a limited scope of applications. It can be usedonly in some systems. It can be applied as a supplementary method to the existing
Derivative UV-VIS spectrophotometry 923
instrumental methods (where changes of a signal as a function is measured), e.g. asa detector in chromatography based on an array type spectrophotometer [33,38].
A not too high precision of determination when using the zero-crossing techniqueis also a disadvantage (derivative values measurements on a steep side, the derivativezeroing point of the interfering substance may undergo small shifts with a change inthe sample composition). This measurement technique is applied in multivariatespectral analysis [30, 31].
Errors in the registration of the zeroth order spectrum are the reason for non-reproducibility of the method [25-27, 32]. The wavelength (wavenumber) at which thederivative is measured should be determined (and at least checked) for each spectrophotometer. Small differences in the wavelength setting (during their aligning) havea great effect on the result, especially in the zero-crossing technique.
APPLICATIONS OF DERIVATIVE SPECTROPHOTOMETRY
Each year the number of applications of derivative UV-VIS spectrophotometryincreases. A majority of published work concenlS the determination of organicsubstances. The development of the needed apparatuses and derivative spectrophotometry theory indicates that more advantageous from the chemical analysis point ofview is the use of derivatives of higher order [13, 20, 24] than derivatives of the firstorder initially applied.
A large number of bibliographic data on analytical applications is included in themonograph by Talsky [13] and the review article by Bosch Ojeda et aJ. [34].
Publications concerning the determination of numerous elements· in variousmaterials are summarized in Table 1. There are given the reagents used or forms ofdetermined elements and also the order of applied derivative spectra.
Table 1. Derivative spectrophotometry in inorganic analysis
Elements determined Reagent used or Derivative order Ref(in material) determination form (wavelength, nm)
Th, U, Zr Arsenazo III (oxalate) 3rd (673,659,673) 75
Th, Zr Arsenazo III 2nd (662, 649) 76
Ti (alloy steels) hydrogen peroxide 2nd (524) 77
Some organic compounds detennined with derivative spectrophotometry in pharmaceutical, biological and clinical samples and also in other organic materials, arecollected in Table 2. In this case, the ultraviolet region of radiation is most often used.
Tab
le2.
Der
ivat
ive
spec
trop
hoto
met
ryin
orga
nic
anal
ysis
Ana
lyte
sM
ater
ials
Der
ivat
ive
orde
rR
ef.
(wav
elen
gth,
nm)
4-H
ydro
xyph
enox
ymet
hyl-
peni
cill
ine
med
icam
ents
4th
(304
)78
Am
pici
llin
e,cl
oxac
illi
nem
edic
amen
ts2n
d(2
16,2
49)
79
Dia
zepa
m,
oxaz
epam
med
icam
ents
4th
(238
-245
,237
-242
)80
Par
acet
am
ol,
met
hoca
rbam
olm
edic
amen
ts2n
d(2
51,2
28)
81
Ace
tyls
alic
ylic
acid
,ch
lorm
ezan
one
med
icam
ents
4th
zero
-cro
ssilI
lgte
chni
que
82
p-H
ydro
xype
nici
llin
epe
nici
iiin
e4t
h(2
90)
83
Fla
vour
sen
hanc
ers
food
s2n
d84
Qui
nine
soft
drin
ks4t
h(2
53-2
61)
85
Sul
phat
hiaz
ol,o
xyte
trac
ycli
neho
ney
2nd
(290
,360
-393
)86
3rd
(275
,35
0)4t
h(2
85,3
63)
Sac
char
ine
swee
ts4t
h(2
86)
87
Nic
otin
eto
bacc
opr
oduc
ts2n
d88
Pig
men
tsm
ixtu
rein
OM
S4t
h(s
uita
ble
for
pigm
ent)
89
Fen
dili
nean
dre
late
dco
mpo
unds
2nd
90
Cep
halo
spor
ins
phar
mac
euti
calp
repa
rati
ons
2nd
91
Ben
zodi
azep
ines
and
thei
rm
etab
olit
esla
bor.
mix
ture
s2n
d92
Not
ript
ilin
e,pe
rphe
zine
4th
(240
,26
9)93
Aci
ddy
este
xtil
es1s
t,2n
dre
flec
tanc
esp
ectr
osco
py94
Tet
racy
clin
esph
arm
aceu
tica
lpr
epar
atio
ns2n
d(2
76-2
89;
342-
344)
95
t;:,
~ ~. ~. ~ ~ {3 ~ ~ "15 ::- a ~ ~ ~ \0 ~
Tab
le2
(con
tinu
atio
n)
Am
oxyc
iiii
ne2n
d(2
80)
96
4-A
min
ophe
nol
para
ceta
mol
2nd
(224
)97
Gli
benc
lam
ide,
meb
ever
ine,
c10p
amid
eth
eir
degr
adat
ion
prod
ucts
2nd
98
Am
oxic
illi
n,ce
phal
exin
buff
eriz
edm
ixtu
re2n
d(2
76,
267)
99
Chl
orpr
omaz
ine,
~-cyclodextrine
bind
ing
cons
tant
inaq
ueou
sso
luti
on2n
d(2
61,2
54)
100
Ant
ioxi
dant
sla
b.m
ixtu
res
3rd,
4th
101
Chl
orop
rom
azin
ean
dits
sulp
hoxi
deph
arm
aceu
tica
lpr
epar
atio
ns3r
d(2
59-2
67;
350-
361)
102
2,3-
and
3,4-
Dim
ethy
lphe
nols
wat
erso
luti
onaf
ter
extr
acti
on4t
h(3
07.3
);5t
h(3
07.9
)10
32,
6-an
d-'3
,4-D
ichl
orop
heno
ls1s
t(28
8.3)
;2n
d(2
92.0
)
Phe
nylb
utaz
one,
oxyp
henb
utaz
one
bloo
dpl
asm
a4t
h(2
93,
282)
104
Myo
glob
ine
haem
oglo
bine
1st,
2nd,
mul
tisp
ectr
alan
alys
is10
5
Hae
mog
lobi
ne,c
arbo
xyha
emog
lobi
nebl
ood
3rd
106
Clo
naze
pam
urin
e3r
d(4
18)
107
All
opur
inol
urin
e2n
d(2
84)
108
Fen
itro
thio
n,ne
opyn
amin
e,pe
rmet
hrin
,pi
pero
nyl
buto
xide
com
mer
cial
inse
ctic
ide
form
ulat
ions
2nd
(220
-330
;2
30
-24
0,2
00
-21
0,2
80
-30
0)
109
Pol
ycyc
lic
arom
atic
hydr
ocar
bons
envi
ronm
enta
lan
alys
is2n
d-5t
hm
ulti
spec
tral
anal
ysis
110
Try
ptop
han
and
tyro
sine
synt
heti
cpe
ptid
es2n
d11
1
Try
ptop
han,
tyro
sine
and
phen
ylal
anin
epr
otei
n2n
d11
2
Met
hion
ine,
hist
idin
eam
ino
acid
sm
ixtu
re1s
t,2n
d,3r
d11
3
\0 ~ ~ ~ "'~, ~ ~ ii ~ ~ Ii::l l ~ o g" ~ ;.;.. ....
Derivative UV-VlS spectrophotometry 927
The examples given in Tables demonstrate simultaneous determination of two ormore analytes, determination of small or trace amounts of analytes in the presenceof a matrix and identification of some analytes present in a mixture (without theirprevious separation). Tables 1 and 2 do not contain method of determinations basedon the 1st order derivatives. Recently, the I-st order spectra are often used forindentification of individual organic compounds in their mixtures [13, 29, 30, 105].
Acknowledgement
This work was supported by the State Committee for Scientific Research (grant no 2 P303 15804).
REFERENCES
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