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A New Version of the Internal Standard Method In Quantitative Thin Layer Chromatography Valery N. Aglnsky
Key Words: Quantitative TLC Internal standard Peak signal ratio Relative response factor (RRF) Mass-Independent RRF Precision
Summary A new version of the internal standard method for use in quantitative thin layer chromatography is introduced in thls paper. In comparison with the existing method, the proposed technique enables significant enhancement of the accuracy and precision of quantitation. The reasons for this are considered. The technique described enables the calculation of the relative response factor of a sample component relative to an internal standard; within the calibration range the relative response factor is independent of the masses of the component and standard.
In memoriam Prof. Dr. H. Jork Pioneer of Quantitative Thin-Layer Chromatography
is that this method can produce imprecise and inaccurate quantitative data because it "assumes" a directly proportional relationship between the signal from an optical detector and the amount of a substance (analyte, standard) in a separated chromatographic zone; for TLC this can be considered as a rather crude approximation only. This paper describes a new approach to the use of the IS method in quantitative TLC, which enables significant enhancement of the accuracy and precision of the method.
Software for the technique is available.
1 Introduction In chromatographic analysis the internal standard method is based on comparison of the measured chromatographic peak signal (area or height) for the substance being quantitatively determined (the analyte) with that of the peak of the internal standard (IS), a known quantity of which is added to the sample to be analyzed. The well-known advantages of the IS method (the results of the analysis are not affected by variations in the volume of sample introduced to the chromatographic system, and/or partial losses of the analyte during extraction, derivatization, and other stages of sampling, e.g. during transfer of the analyte from the sample to the solution which is analyzed) lead to its wide application in gas and high performance liquid chromatography. Despite these advantages, this method is not often used in quantitative thin layer chromatography {TLC). One reason
V.N. Aginsky, Forensic Science Center of the Ministry of the Interior, 22 Raspletina Street, Moscow 123060, Russia.
Journal of Planar Chromatography
2 Determination of the Mass-Independent Relative Response Factor (RRF): The Principle of the Method Proposed When the IS method is used in chromatographic analysis, the procedure of plotting a calibration curve involves adding a fixed amount of an IS to a series of standards containing increasing concentrations of the analyte, and chromatographic separation of the mixtures obtained. Finally, the ratio of the peak signal of the analyte to that of the IS is plotted against the known concentration of the analyte. This, for gas and high performance liquid chromatography, usually gives a straight line calibration plot where the slope of the plot is equal to the response of the analyte relative to that of the IS. Using this mass-independent RRF value, the unknown concentration of the sample component can be easily calculated. In TLC, however, the situation is more complex since the response of a sample component relative to that of an IS is usually mass-dependent; the relationship between the above-mentioned peak signal ratio and the concentration of the analyte is usually non-linear and is rarely a straight line passing through the origin. Because of this, when the IS VOL. 7, JULY/AUGUST 1994
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method has been used in TLC [1,2] RRF values have not been used. The problem which arises can be clarified with the help of an example. If a solution contains the same concentrations of the analyte (A) and IS (B) (i.e. in this example, the ratio of the concentrations of these substances is equal to unity) and different volumes of the solution are applied to a TLC plate as narrow bands, development of the plate and scanning of the resulting chromatograms could furnish the data shown in Figure 1, where lines A and B approximately represent the relationship between the peak signal (area or
stant (SA 1 : S81 < SA 2 : S82 ; see also eq. (9), below) but increases as the amounts of these substances per zone increase. This simple example clearly demonstrates the mass dependence of the RRF in TLC and explains why the conventional IS method can produce unreliable quantitative data. The method proposed in this paper enables calculation of mass-independent RRF values. The method uses two series of calibration standards, each characterized by a certain value of the ratio [content of analyte] : [content of IS]. Figure 2 shows a typical scheme for applying calibration standards according to the proposed method.
Different ';'Oiumes
Calibration standards
Sample
atone and the same solution
-----A
Analyte
----A
Analyte Internal Standard
----3
-----3
lnlemaJ Standard
Start
Start
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Figure 2
Mass-dependence ol the relative response factor.
Schematic presentation ol the procedure lor determining the mass- in· dependent relative response !actor.
height) and the amounts of analyte and IS, respectively, applied to the plate. (In this example it is, for simplicity, assumed that for amounts of analyte and IS, per zone, within a certain range, the relationship between signal and amount is linear; in general, these lines can be considered to be the linear regions of the corresponding calibration curves for A and B). It is readily apparent from this figure that although the ratio of the contents of the zones remains constant (CA 1 : C81 = CA 2 : C82 = 1), the ratio of the peak signals corresponding to the analyte and the IS is not con-
One series of calibration standards (the lst series in Figure 2) is applied at the origin of a TLC plate either as narrow bands, by spraying different volumes of one and the same calibration solution, or as spots, by application of similar aliquots of a series of solutions, such that the ratio [concentration of analyte] : [concentration of IS] spans a calibration range which includes the amounts of sample component expected. The other series of calibration standards (the 2nd series in Figure 2) characterized by a different ratio [concentration of
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analyte] : [concentration of IS] is applied to the TLC plate so that the amounts of analyte and IS per zone lie within the range spanned by the amounts per zone obtained for the 1st calibration series.
obtained for these substances in such a manner that their ratios become mass-independent (eqs (1)-(3) and eqs
Figure 2 also shows that one of the lines, A or B can be moved up or down until, on back extrapolation the line which has been moved (line A') intersects the stationary line (line B) at a point (designated "b") on the abscissa. This point corresponds to the situation when the ratio of the transformed (according to eq. (I 1), q.v.) peak signals from the analyte and IS calculated for the standards of the 1st calibration series, becomes mass-independent for a given ratio of the contents per zone of these substances. The massindependent value of the RRF can thus be calculated (eqs (3) and (II)).
Quantitation of the sample component by use of the RRF value determined (eqs (4) and (5) and eqs (4') and (5'))
Further, the densitometric data obtained for the 2nd series of calibration standards are used to move the lines A' and B down until, by back extrapolation, they intersect at the origin of the graph (lines A" and B' in Figure 2). This corresponds to a change of the value of the peak signals of the analyte and IS such that their ratio becomes mass invariant (i.e., a value independent of the amounts of these substances per zone). This makes it possible to quantify the analyte by use of the value of the RRF (eqs (2')-(5')). It should be remarked that Figures 1 and 2 (and eqs
(1')-(5')) illustrate the situation when, within the calibration range, the relationship between signal and zone content for both analyte and IS are satisfactorily approximated by straight lines (A and BIn the figures). The proposed method is also applicable if the relationships are better approximated by non-linear rather than linear functions (eqs (1)-(5)). The steps of the proposed technique can be illustrated by the Row sequence shown below.
Addition of substance employed as internal standard (IS) to a sample to be analyzed which contains a component to be quantitatively determined
L Preparation of two series of calibration standards (or, if the sample is to be sprayed on to the plate as narrow bands, two solutions) so that each series (solution) differs by the ratio of the concentrations of analyte and IS
L Application of samples and calibration standards to TLC plate
L Development and scanning (reflectance mode) of the TLC plate
L Determination of response factor (RRF) of the analyte relative to the IS by transforming the peak signals Journal of Planar Chromatography
(I ')-(3'))
L
The capabilities of the technique are compared with those of the conventional method [I ,2] in the example considered below.
3 Experimental 3.1 Samples
Acid anthraquinone brilliant blue (the substance to be quantitatively determined, or analyte) and acid brilliant blue Z (the internal standard), obtained from NPO Niopik (Moscow, Russia), were used as model samples for comparing the capabilities of the conventional and proposed IS methods. The dyes were used to prepare two series of calibration standards (four solutions in each series) in 50 % aqueous methanol. In the first series of calibration standards the ratio of the concentration of the analyte to that of the IS was unity and the concentrations of the internal standard (and thus the analyte also) were I, 2, 3, and 4 mg/ml. In the second series of standards the ratio of the concentration of the analyte to that of the IS was 3 and the concentrations of the internal standard were 1.1, 1.2, 1.25, and 1.3 mgjml.
For assessment of the conventional IS method (e.g. [1]), four calibration solutions were prepared containing 2 mg;ml of IS and l, 2, 3, and 4 mg/ml of analyte. The analyte (200 mg) was dissolved in 50% aqueous methanol (50 ml) containing IS (2 mg/ml). This solution (containing 4 mg;ml of analyte and 2 mg/ml of IS) was designated the "unknown" sample (Sample I) which was to be analyzed. In order to estimate which method, that proposed herein or the conventional procedure, was less mass-dependent, 25 % and 50 % losses of both dyes during sampling were simulated by diluting Sample I by 25 % (Sample 2) and 50 % (Sample 3). Thus in all three samples the ratios of the concentrations of analyte and IS was equal to two, the concentrations of analyte and IS in the samples being 4 and 2, 3 and 1.5, and 2 and l mgjml, respectively. Four aliquots of each sample were analyzed by the conventional and proposed techniques. 3.2 Chromatography
I ,ul of the calibration solutions and four aliquots (I ,ul) of each sample, 1, 2 and 3, were spotted on precoated 20 x 20 em silica gel60 F 254 TLC plates (without fluorescent indicator; Merck, FRG) by means of a Camag (Muttenz, SwitzerVOL. 7, JULY/AUGUST 1994
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land) Micro-Applicator I. The plate was developed to a distance of ca 3.5 em by the linear ascending mode in a Camag twin-trough chamber, without saturation. The eluent was ethyl acetate - isopropanol - water - acetic acid, 30 + 15 + 10 + 1 (vjv). The plate was dried at room temperature in a stream of cold air. Two compact colored zones were apparent on the resulting chromatograms; the RF values were approximately 0.21 for the IS and 0.45 for the analyte. The plate was scanned in absorbance reflectance mode at A. = 582 nm using a Camag TLC/HPTLC scanner connected to an SP4100 integrator (Spectra-Physics, USA). All 24 tracks were measured with positioning at each run in order to minimize positioning error. An HP 86B computer (Hewlett-Packard, USA) and software developed by the author were used for calculations.
4 Results The peak heights calculated by the integrator for the separated substances, analyte and IS, are shown in Table 1. According to the proposed technique the concentration of analyte in the "unknown" sample was calculated in the following manner. (a) Eq. (1) was used to calculate the peak signals ratio for each of the four densitograms, i, obtained from the four standards of the 1st calibration series (Table I, row I) (I)
where SAN and S15 are the measured signals (in this example, peak heights) of the chromatographic peaks of the analyte and the IS, respectively; i is the index of the chromatographic track of the standard of the 1st calibration series (in this example, i = I, ... , 4); C1 is a coefficient (determined by using an iterative technique [3]) which changes the values of 1/(SAN)i so that the dispersion of the (Z 1)i values is minimized. (b) Eq. (2) was used to calculate the peak signals ratio for each of the four densitograms, j, obtained from the four standards of the 2nd calibration series (Table I, row 2).
(Zz)i = [1/(SAN)i- C1- C2 · Zt)/[(1/Sts)j- Cz]
(2)
where Z 1 is the mean value of the values of 2 1, C 1 is the coefficient calculated using eq. (1), j is the index of the chromatographic track of the standard of the 2nd calibration series (in this example}= 1, ... , 4); C 2 is a coefficient (determined by using an iterative technique) which is used to minimize the deviation of (Z2 )i from a quantity Q, where
Q = RRF/ R 2
(3)
where RRF, = R 1 · Z 1, is the response factor of the analyte relative to the IS; and R 1 and R 2 are the ratios of the masses of these substances in the 1st and 2nd calibration series, respectively. An alternative means of performing the calculations is by using eqs ( 1'}-(3'): (Zt)i = ((SAN)i- Kt] · (Sts)i (Z2)j = [(SAN)i- Kt - K2 · Zt')/[(Sts)i- Kz] Q' = R 2 • RRF
(1') (2') (3')
where K 1 and K 2 are coefficients determined as described for coefficients C 1 and C 2 ; and (RRF)', = (Z 1)'/Rt. is the response factor of the analyte relative to the IS. Eqs (1) and (1') were derived from Michaelis-Menten and linear functions, respectively (eqs (7) and (9)). More complex approximation functions, e.g. those based on signal conversion according to the Kubelka-Munk equation, have also been adopted for use in the proposed technique, but are beyond the scope of this paper. In every instance of the use of the proposed method, both these sets of equations were tested in order to choose that giving more precise data (e.g., in the terms of coefficients of variation) for the standards of both calibration series. In the example described in this paper, calculations based on eqs (1}-(3) gave more precise results than those based on eqs {I '}-(3'). In some instances, however, e.g. analysis of nanogram quantities of analyte, or when the analyte could be monitored by fluorescence, eqs (1'}-(3') can produce more precise quantitative data, because in these instances the relationship between the measured chromatographic peak signal and the content of the chromatographic zone often is
Table 1 Results from scanning of chromatograms.
No.
Solution analyzed
Integrator reading (peak height) Analyte
1 2 3 4 5 6
1st series 2nd series Calibration solutions•> Sample I Sample 2 Sample 3
43 590 70 790 43 782 74 974 69 918 58 236
59 805 73 754 58 934 76 125 70 267 58 759
69 918 74 800 70 999 76 195 70 441 59 282
Internal standard 76020 75 846 75 916 76 718 71 138 60 851
65036 69 046 94 712 93 805 80 554 62 595
96 072 72 708 96 090 93 980 81 774 64 338
109 149 74 451 95 759 95 374 81 862 64 949
122 749 77 764 94 904 95 549 82 995 66 396
" For these solutions, in accordance with the conventional IS method [1], the ratio [peak height of the analyte, PHA.N] : [peak height of IS, PHIS] was plotted against the concentration of the analyte (CANl· The regression equation obtained for the linear calibration graph was: PHA.N I PHIS = 0.3685 + 0.1142 ·CAN; the correlation coefficient (CC) was 0.9834. This equation was used to determine the concentration of analyte in the "unknown" sample (Table 2, column 2).
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better approximated by linear rather than non-linear functions.
(4)
areas) of the analyte (SAs) and IS (S15) are mass-dependent, i.e. they are not directly proportional to the corresponding ratios of the amounts of analyte (CAs) and IS ( C1s) in the scanned chromatographic zones; in general, when the relationships between the signal and the amount of substance per spot, or between the reciprocal values of the signal and the amount of substance per spot, can be satisfactorily approximated by straight lines, these lines do not pass through the origins of plots of signal against content (as shown in Figure 1) or reciprocal signal against reciprocal content (e.g. [3]).
(4')
To clarify this conclusion, a number of mathematical expressions and illustrations are given below.
Depending on which set of equations was chosen, eqs (4) and (5) or eqs (4') and (5') were used for quantification of the sample component of interest. (c) For each densitogram, i, obtained from the four aliquots of the sample analyzed (Table 1, rows 4-6) the value of the ratio, R,, of the masses of the analyte and IS was calculated: li(S,Ji-C2 (RJ· = RRF. ' liSJi-CI-C2·ZI , I (SJi- Kl- K2 · (Zl)' (RJi = (RRF)' . (S,Ji- K2
where SAN and S 1s are the measured chromatographic peak signals corresponding to the analyte and IS, respectively, and i is the index of the chromatographic track for the sample analyzed (in this example, i = 1, ... , 4).
In TLC, the relationship between signal output and the content of absorbing substance is often satisfactorily described by the non- linear Michaelis-Menten function (Figure 3, curves A and B for analyte and IS, respectively).
(d) Finally, the "unknown" concentration of the analyte, CAN• was calculated:
S = Smax · C/(K + C)
= (RAN)i. CIS
(5)
(CANX = (RAN);· C1s
(5')
(CAN)i
where C1s is the known value of the concentration of the IS in the sample analyzed (in this example, 2 mglml). The quantitative data obtained using eqs (l)-(5) are listed in Table 2 (columns 5 to 7).
Table 2 Results from quantitative determination of analyte.
Sample
I
2 3 •l b) <)
Proposed method
Conventional method (:")
Recoveryb)
CV")
[mg/ml]
[%]
[%]
3.80 4.32 4.81
95.0 108.0 120.3
1.2 1.0 1.5
X")
Recoverybl [%] [mg/ml] 4.08 4.17 3.87
102.0 104.3 96.8
CV")
where Sis the peak signal, Smax is the limit of the peak signal, K is a constant, and Cis the content of the separated zone. Linearization of this function results in: liS= KI(Smax ·C)
2.6 0.6 1.6
the mean value (n = 4) of the concentration of analyte in Sample l Recovery (%] = (X X 100)/C,_. (where = 4 mg/ml) coefficient of variation
c._.
+ IISmax
(7)
this can be depicted graphically as a line with the slope of KISmax and an intercept of liSmax (Figure 4, lines A and B for analyte and IS, respectively. It should be pointed out that for small ranges of spot content, relationships between S and C can be satisfactorily approximated by straight lines (as is shown in Figure 3, in the range C 1 to C 2 the regions A 1 to A 2 and B 1 to B 2 of curves A and B, respectively, are almost linear). These lines do not, however, usually converge at the origin of the plots of signal against content, i.e. they are described by eq. (8).
S [%]
(6)
=
aC
+ b
(8)
where the intercept b is not equal to zero. Figures 1-4 show that ratioing signals corresponding to analyte (A) and IS (B) gives values which are mass-dependent: (9)
SAl I Sal # SAz I Saz (Figures 1-3), and (IISAl) I (1/Ssl) # (IISAz) I (11Ssz)
(10)
(Figure 4)
5 Discussion The data of Table 2 clearly show that the proposed technique gave more accurate results than the conventional IS method; the relative error is < 5 % compared with values as high as 20 %. The reason for this lies in the principal differences between these techniques. In the conventional method the ratios of the measured chromatographic peak signals (heights or Journal of Planar Chromatography
Because of this, quantitative data obtained by using the conventional IS method always includes a systematic error. The size of this error is unpredictable and can vary within a wide range depending on the values of the slopes and intercepts of the approximating linear functions. The size of the error may be small (e.g., when errors arising from dif~ ferent sources are mutually compensating, quantitative data, in terms of the statistical parameters calculated, may look quite good) to very large (e.g. Table 2, column 3). VOL. 7. JULY/AUGUST 1994
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SIGNAL OUTPUT (5)
B "\
L 2nd step: ) lines A· ', 3
where i relates to any amount (C;, not shown in the figures) of the components, whether analyte or IS, for which eqs (II) and (12) are valid (at the very least, this applies to any value of C; which lies between C 1 and C2 in Figures 2-4). In the 2nd step of the procedure, the lines A' and B are moved down until, on being extrapolated backwards, both lines (lines ANand B' in Figures 2-4) intersect at the origin of the graph. In the proposed method this movement (line A-+ line A', and then line A'-+ line A" and line B-+ line B') is performed by using the iterative procedure executed according to eqs (l}-(3) or (l'}-(3') which have been derived as follows.
a
CONTENT (C)
b
Figure 3 Theoretical Mlchaells-Menlen type curves relating signal output (S) to the amounts (C) of analyte (A) and IS (B) In the sorbent layer. 1/5
Suppose, for a given densitogram, CA and C8 are the amounts of analyte and IS, respectively, in the chromatographic zones; using eqs (7) and (8) their ratio is given by eqs (13) and (13'), respectively: Cs/CA =(!/SA- 1/SAmaJ · ks · SAmaxf[(l/Ss- 1/SamaJ · · kA · SsmaJ (l3) (13')
1st step: . lines A·,
A' :
2nd step: lines A'',=
! IS.
For the series of calibration solutions for which the ratio (R) of the contents of analyte and IS is constant, SAmaxo Ssmax• kA, and k 8, or aA, a8, bM and b8 are empirical constants. So substitution of SA by SAN• and S 8 by S1s in eqs (13) and (13') results in eqs (l4) and ( 14'), respectively:
i/R = K · [i/(SAN);- K1J / [1/(S,s);- K2J
-·~
(14)
1/5 ..
11s
3
(14')
__ -·: -
=
115_~--
where SAN and S 1s are the chromatographic peak signals obtained for the analyte and the IS, respectively, and K, K 1 , and K 2 are constants.
1/C
Simple transformation of these equations (and the assumption that K 2 = 0) results in eqs ( l) and ( l '), respectively.
Figure 4 Linearization of Mlchaells-Menlen type curves.
A new approach developed to solve the problem discussed in this paper includes transforming peak signal values (with the help of the proposed equations and using an iterative procedure) in such a manner that their ratios become massindependent (or at least, much less mass dependent in comparison with the ratioing technique used in the conventional IS method [1,2,4]). The process is demonstrated graphically in Figures 2-4: in the I st step of the procedure one of the lines, A or B, is moved up or down until, on being extrapolated backwards, both lines (lines A' and Bin the figures) intersect at one and the same point on the abscissa of the graph (points "b" In the figures). When this is achieved: SA1'/Ss1 = SA2'/Ss2 = ... = SA//Ss;
(ll)
(Figures 2 and 3) (lfSA/)/(l/S81 ) = (l/SA2')/(l/Sd = ... = = (1/SA;')/(l/SsJ (Figure 4)
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5 Conclusion A new version of the internal standard method is proposed for use in quantitative TLC. The technique is easy to perform and is more precise and accurate than the conventional method. The appropriate software is available.
References
[I] Youichi Fujii, Yukari Ikeda, and Mitsuru Yamazaki, J. Liq. Chromatogr. 13 ( 1990) 1909-1919. [2] D. Jiinchen (Ed.), Camag Bibliography Service CBS-60, Muttenz, Switzerland ( 1987) 8-11. [3] V.N. Aginsky, J. Forensic Sci. 38 (1993) llll-1130. [4] J. Ripphahn and H. Halpaap, J. Chromatogr.l12 (1975) 81-96.
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Ms received: April 19, 1994 Accepted by HJ: May 3, 1994 Journal of Planar Chromatography