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CHROMA-346795;
No. of Pages 7
Journal of Chromatography A, xxx (2006) xxx–xxx
Chromatographic quantitation at losses of analyte during sample preparation
Application of the modified method of double internal standard
Igor G. Zenkevich ∗ , Evgeny D. Makarov
St. Petersburg State University, Chemical Research Institute, Universitetsky pr. 26, St. Petersburg 198504, Russia
Received 12 May 2006; received in revised form 22 August 2006; accepted 30 August 2006
Abstract
Known methods of quantitative chromatographic analysis (calibration, external standard, internal standard and standard addition) require the
application of sample preparation techniques without significant losses of analytes. If this condition cannot be satisfied, the compensation of these
losses should be provided. The modification of known method of quantitative chromatographic analysis (double internal standard), implying the
addition of two homologues (previous and following) of target analytes as internal standards into initial samples is considered. This approach
permits us to compensate significant losses both analytes and standards at all stages of sample preparation. The advantages of this method are
demonstrated on the examples of liquid–liquid extraction, head space analysis (HSA), distillation of volatile compounds with volatile solvents
(concentration in condensates) and evaporation of volatile solvents (concentrating in the residues of solvents). In all cases the application of two
homologues as internal standards provides accurate results (the typical relative errors are within 1–6%) at the values of a factor of composition
distortion of initial samples (K , the definition is suggested) from 0.2 up to 4. These results are in accordance with general relationships between
variations in any physicochemical properties of organic compounds within homologous series. The single found exception was the evaporation of
volatile solvents (the open phase transition process) when to get the results with relative errors not more then +10% requires the minimal changes
in the composition of initial samples (K values should not be more then approximately 1.5).
© 2006 Published by Elsevier B.V.
Keywords: Chromatographic quantitation; Sample preparation; Losses of analytes; Double internal standard method; Homologous standards
1. Introduction
Various methods of quantitative chromatographic analysis
(including calibration [1–3], external standard [4], internal standard [5] and standard addition [6]) are used often for quantification of target compounds in probes obtained using different procedures of sample preparation. Most of these procedures (e.g.,
extraction, head space analysis (HSA), evaporation of volatile
solvents, distillation, solid phase extraction (SPE) and microextraction (SPME), etc.) are characterized by some changes in
the composition of initial samples caused by the partial losses
of analytes. It leads to the systematic errors of determinations
of their concentration measurements. Recently, it was demonstrated that the control of pesticides residues in plant materials (at
the level 1–10 mg/kg) using external standard method in accord
∗
Corresponding author. Tel.: +7 812 428 4045; fax: +7 812 428 6939.
E-mail addresses: izenkevich@mail15.com (I.G. Zenkevich),
edmakarov@yandex.ru (E.D. Makarov).
with standard procedure in Russian Federation [7] allows us to
quantify only 10–70% of analytes in model samples [8]. In real
samples (with smaller concentrations of pesticides) these errors
could be more significant.
Practically there are no ways to avoid analyte losses using
mentioned sample preparation techniques. Reasonable way to
provide accurate quantitation is a compensation of these losses.
It implies that reference compounds should be added directly
into initial samples. Only two quantitation procedures provide
such compensation: standard addition (i) and internal standard
(ii).
Standard addition method (i) exists in various modifications
and it seems to be a single way to measure the total amounts
of analytes in heterophaseous systems by analysis of one phase
(usually the phase containing smaller quantities of interfering
components should be chosen) [9,10]. The main disadvantage
of this method is the necessity to conduct chromatographic
measurements twice: before and after addition of reference compounds into initial samples with complete sample preparation,
thus increasing time and cost of analyses.
0021-9673/$ – see front matter © 2006 Published by Elsevier B.V.
doi:10.1016/j.chroma.2006.08.083
Please cite this article as: Igor G. Zenkevich, Evgeny D. Makarov, Chromatographic quantitation at losses of analyte during sample preparation,
Journal of Chromatography A (2006), doi:10.1016/j.chroma.2006.08.083
CHROMA-346795;
2
No. of Pages 7
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A quantitation method known as “isotope dilution” [11–16]
is used only with GC–MS techniques. It can be considered as a
modification of the method of addition, and also as a method of
internal standard. Isotopic analogues (D, 13 C, 15 N, 18 O, etc.) of
target analytes are used as quantitation standards. Physicochemical properties of these analogues are practically identical to those
of unlabeled organic compounds. Their ratios in prepared probes
directly correspond to their ratios in initial samples; there is
no dependence on compound losses during sample preparation.
Concentration ratios can be measured in single ion monitoring
(SIM) mode with MS detection. Depending on the chemical
origin of analytes this method provides the relative standard
deviation (RSD) of results in the range 0.5–20% (5–15% in most
practical cases) which is considered as appropriate error at low
contents of analytes.
Quantification using method of internal standard (ii) is based
on simple relationship:
qstand
qx = fx/stand Px
(1)
Pstand
where qx and qstand are masses (m) or concentrations (c = m/M,
M— mass of the initial sample) of compound under study (x)
and standard compounds respectively in the prepared probes; Px
and Pstand —parameters of chromatographic peaks (e.g., area);
fx,stand —calibration coefficient.
General recommendation of the choice of standard compounds is based on “chemical similarity of target and standard
compounds”. This can be illustrated by examples of numerous GC analyses, e.g., compounds of pharmaceutical interest
[17]. For example, the reported internal standards for quantification of chlorpheniramine (MW 274, retention index on
standard non-polar polydimethyl siloxane phases 2000 ± 18)
are non-substituted pheniramine (MW 240, RI 1794 ± 11) or
bromopheniramine (MW 318, RI 2082 ± 15). The selection of
analogues in accord with the rule H ↔ Cl ↔ Br, as well as in
accord with series H ↔ CH3 ↔ · · · ↔ Cn H2n+1 a priori provides
the appropriate chromatographic separation of these compounds
using different types of GC columns (packed or capillary), or
even in reversed-phase HPLC.
However, any structural analogues (excluding labeled by isotopes) are not completely chemically identical to target analytes.
Thus, if these standards are added to initial samples, their losses
during sample preparation could be different from losses of
target compounds leading to low quantitation accuracy of this
method.
One of possible approaches to overcome the low quantitation
accuracy is so-called double internal standard (DIS) method,
suggested by Vigdergaus and Krauze in 1985 [18]. The main
relationship of this method is similar to that of “traditional”
single internal standard procedure. It implies calculation the
average geometrical value of two sub-results obtained with each
standard:
fx/stand.1 qstand.1 fx/stand.2 qstand.2 1/2
qx = Px
(2)
Pstand.1
Pstand.2
where qx and qstand are masses (m) or concentrations (c = m/M,
M—mass of the initial sample) of compound under study
(x) and two standards (x − 1 and x + 1) in the prepared
probes; Px and Pstand —parameters of chromatographic peaks;
fx,stand —calibration coefficients for both internal standards.
Unfortunately, no recommendations on the selection of two
standards were suggested in original paper [18]. If two internal
standards are added to prepared probes, this method does not
demonstrate advantages comparing with single internal standard method. The differentiation of Eq. (2) provides a complex relationship for estimation of standard deviations of results
depending on standard deviations of chromatographic parameters, qx = f(Px , Pstand.1 , Pstand.2 ). Using this procedure
requires the area measurements for three chromatographic peaks
instead of two P-values. Thus, the relative standard deviations
of results obtained with double internal standards exceed those
for single internal standards procedure. At the same time, this
approach seems to be very effective in compensation of systematic errors of quantitation. However, this procedure is not used
in practical quantitation measurements.
The application of two internal standards represents effective way to compensate large losses of analytes at all stages of
sample preparation. These possibilities can be realized when
the previous (x − 1) and following (x + 1) homologues of target
compounds (x) are chosen as two internal standards.
The aims of this paper are as follows:
i. to model large distortions in the composition of analytes in
different samples using various procedures of their preparation for GC analyses, and
ii. to characterize of the possibilities of modified double internal
standard method to compensate the changes in composition
of samples.
The fundamentals of modified double internal standard procedure and examples of its application are considered.
2. Experimental
Low boiling organic compounds were chosen as model analytes and internal standards to provide the large distortions in
the composition of model mixtures at different stages of sample
preparation. Their physicochemical properties are presented in
Table 1.
Two sets of compounds represent normal linear homologues.
The third set represent so-called multi-linear homologues (the
number of methyl groups in the molecules is variable).
Methods of modeling the various sample preparation procedures include liquid–liquid extraction from water solutions
(LLE, A), head space analysis (HSA, B), distillation of volatile
components with volatile solvent (concentrating in the condensates, C), and evaporation of volatile solvents (concentrating in
the residues of initial solutions, D). Details of preparation of
model samples are provided below:
A. Liquid–liquid extraction: Variable amounts (50–150 ␮l) of
target analytes were dissolved in 10 ml of water with adding
equal amounts (100 ␮l) of two internal standards. All v/v
concentrations were re-calculated into w/w values using ref-
Please cite this article as: Igor G. Zenkevich, Evgeny D. Makarov, Chromatographic quantitation at losses of analyte during sample preparation,
Journal of Chromatography A (2006), doi:10.1016/j.chroma.2006.08.083
CHROMA-346795;
No. of Pages 7
I.G. Zenkevich, E.D. Makarov / J. Chromatogr. A xxx (2006) xxx–xxx
3
Table 1
Principal physicochemical properties of model compounds and homologous internal standards
Component (x) [Tb , ◦ C; d420 ]
Standard (x − 1) [Tb , ◦ C; d420 ]
Standard (x + 1) [Tb , ◦ C; d420 ]
1-Propanol [97.2; 0.804]
2-Hexanone [127.2; 0.812]
m-Xylene [139.1; 0.864]
Ethanol [78.3; 0.789]
2-Pentanone [101.7; 0.809]
Toluene [110.6; 0.867]
1-Butanol [117.7; 0.810]
2-Heptanone [150.4; 0.816]
Mesitylene [164.7; 0.865]
erence data on densities of substances. The extraction of
these samples was carried out with 1–2 ml of suitable solvents. In extraction with the use salt additives the excess of
anhydrous Na2 SO4 was added to the water until observation of insoluble salt precipitation at the bottom of the vial
(solubility of this salt in the water at ambient temperature is
approximately 8.6%, w/w).
B. HSA was realized in the simplest form (without application
of special equipment). The samples of 10–50 ␮l of target
compounds and two standards in conventional non-volatile
solvent (n-tetradecane, 2 ml) were placed into glass bottles
(10 ml), followed by their heating up to 70 ◦ C and further
sampling of 1–2 ml of gas phase with gas syringe into gas
chromatograph.
C. Distillation of volatile compounds with volatile solvent was
carried out using solution of 50–150 ␮l of model compounds
and standards in relatively non-volatile solvents (50 ml) with
adding of low-boiling solvent (10 ml). Standard laboratory
equipment with dephlegmator (efficiency ca. 2 theoretical
plates) was used for distillation. Collected amounts of condensates were approximately 5–6 ml.
D. Evaporation of volatile solvent. Model compounds and
internal standards (50–150 ␮l) were dissolved in 10 ml
of ethanol (Tb 78.3 ◦ C), n-hexane (68.7 ◦ C), or n-heptane
(98.4 ◦ C). The evaporation was carried out from open glass
until obtaining sample volumes approximately 1–5 ml.
GC analysis was carried out using gas chromatographs
Tsvett-100 and Tsvett-500 series (Tsvett Inc., Dzerzhinsk, Russia) with FID at different conditions (the details are presented
separately for each case below). Both WCOT and packed
columns were used.
3. Results and discussion
3.1. Backgrounds and objectives
The general approach for sample preparation is a concentrating of analyte and also it includes a maximal removing of
interfering compounds from probes. However, it is practically
impossible to optimize concentrating and removal of interfering compounds simultaneously without losses of target analytes.
The decreasing or the compensation of these losses is the important analytical quantitation problem.
The selection of two homologues (previous and following)
as internal standards seems unfamiliarly “rigid” recommendation in chromatographic practice. However, it should be noted
that this choice (or even, if it is necessary, special synthesis
of these homologues) is much simpler and much less expensive than the use of labeled standards in the isotope dilution
method. For example, in odorant’s analyses D- or 13 C-labeled
compounds are used, namely 2-[␣-D2 ]-furfurylthiol, 2-[D3 ]methyl-3-furanthiol, 3-mercapto-2-[4,5-D2 ]-pentanone [4-D3 ]methional, 4-hydroxy-2,5-[13 C]-dimethyl-3(2H)-furanone, etc.
[19]. 2-[D3 ]-Ethyl-3,5-dimethylpyrazine(I) as D-labeled internal standard for quantitation 2-ethyl-3,5-dimethylpyrazine were
synthesized specially. On the other hand, two reference compounds in modified double internal standard method are easily available 2,3,5-trimethylpyrazine(II) and 3,5-dimethyl-2propylpyrazine(III) (Table 2).
3.2. Distortion factor for the composition of initial samples
Adding two internal standards directly into initial samples
allows us to characterize changes in their relative ratios by
factor K or K . Its value can be estimated by comparison
the peak areas of both standards (Sx+1 /Sx−1 ) in initial samples (symbols without asterisks) and prepared probes (with
asterisks):
K=
(Sx+1
/Sx−1
)
(Sx+1 /Sx−1 )
1/2
(3)
However, for real samples (before sample preparation) the
ratios (Sx+1 /Sx−1 ) usually cannot be directly measured and,
hence, their values should be estimated using mass ratios of two
internal standards (Sx+1 /Sx−1 ) ≈ (mx+1 /mx−1 ). Thus, the resulting relationship for the distortion factor for the composition of
Table 2
Structural formulas of D-labelled internal standard (I) recommended for quantitation of 2-ethyl-3,5-dimethylpyrazine by isotope dilution method and two homologues
(II, III) required for its quantitation by modified double internal standard method
Internal standard in isotope dilution method
Two reference compounds in modified double internal standard method
Please cite this article as: Igor G. Zenkevich, Evgeny D. Makarov, Chromatographic quantitation at losses of analyte during sample preparation,
Journal of Chromatography A (2006), doi:10.1016/j.chroma.2006.08.083
CHROMA-346795;
No. of Pages 7
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initial samples (K ) can be written as follows:
K ≈
(mx−1 Sx+1
)
(Sx−1 mx+1 )
3.4. Theoretical grounds of modiﬁed double internal
standard method
1/2
(4)
Square root is necessary to convert the ratio characterizing
homologues differing on two carbon atoms (x + 1) and (x − 1),
into ratio attributed with two neighbor members of series.
3.3. Variations of compositions of analytes for different
sample preparation procedures
The character of variations of the relative amounts of homologues (target analytes and two internal standards) depends on
the procedures of sample preparation and the origin of the considered properties of organic compounds.
The liquid–liquid extraction (A) is controlled by differences
in partition coefficients (Kp ) of organic compounds in heterophaseous systems. The dependence Kp values on number of
carbon atoms in the molecule (nC ) for homologues is as follows
[20]:
log Kp = knC + k0
(5)
Samples after extraction will be enriched by higher homologue; it is reflected by inequality K > 1.
Similar dependencies characterize distortions in the composition of initial samples prepared by evaporation of volatile
solvents (concentrating in the residues of solvents, D), because
vapor pressures of homologues (including partial vapor pressures) at constant temperatures (P) are related to nC by logarithmic relationship that is similar to (5) [21]:
log P = k nC + k0
(6)
Thus, prepared probes will be enriched by components
with higher molecular weights and by less volatile compounds
(K > 1).
As a result of the same dependence (6) in head space analysis (HSA, B) vapor phase is enriched by more volatile components of initial samples (K < 1) [22]. The ratios of volatile
components distilled with vapors of volatile solvents (concentrating in condensates, C) are also characterized by inequalities
K < 1.
Other sample preparation techniques, which are not considered in this paper, can be classified as those belonging to the
two mentioned cases above. For instance, various SPME sampling procedures [23] from liquid phases [24–27] in accord with
Eq. (5) are characterized by inequality K > 1, while the same
sampling technique from vapor phases [28–30] (Eq. (6)) by
inequality K < 1.
Current typical quantitation procedures used at SPME
include external calibration or standard addition techniques, i.e.
the preparation of calibration solutions with concentrations of
analytes close to those in analyzed samples [24], or adding
extra amounts of target compounds into original probes [28].
Of course, isotope dilution method remains to be applicable in
these cases [27].
Recently, it was demonstrated that variations of practically the all physicochemical properties of organic compounds
(A): (normal boiling points, critical temperatures, critical pressures, refractive indices, densities, viscosities, surface tensions, vapor pressures (Eq. (4)), dielectric constants, first
adiabatic ionization potentials, partition coefficients in heterophaseous systems (Eq. (5)), chromatographic retention times
and indices, etc.) within any homologous series are identical
and can be approximated by general linear recurrent equation
[31,32]:
A(n + 1) = a A(n) + b
(7)
where A(n) is the value of any constant for homologue with n
carbon atoms in the molecule; A(n + 1), the value of the same
constant for homologue with n + 1 carbon atoms; a, b are the
coefficients calculated by least squares method. The correlation
coefficients (ρ) in all cases are more then 0.999 [31,32].
Recurrent Eq. (7) has the following algebraic solution that
can be easily obtained using standard MAPLE software:
A(n) = kan +
b(an − 1)
(a − 1)
(8)
Depending on coefficients a and b, relationship (8) and,
correspondingly, initial recurrent Eq. (6) describe both arithmetical progressions (at a ≡ 1, b = 0; A(n) = k + bn], and geometric
progressions [at a = 0, b ≡ 0; A(n) = kan ). Thus, Eqs. (7) and
(8) unite these two mathematical progressions in a joint form
of arithmetical–geometric progressions. It is one of the reasons of high approximation power of recurrent relationships
in relation to different physicochemical properties of organic
compounds.
It is noteworthy that the losses of analytes during sample
preparation can be considered as the property of organic compounds. Thus, the use of suggested modification of double internal standard method is based on estimation of the constants for
any member of homologous series using data for “neighboring”
homologues. As a result that recurrent relationship possess the
properties of both arithmetical and geometrical progressions,
the estimation can be done by both arithmetical and geometrical averaging. The following relationship for A(n) = f[A(n + 1),
A(n − 1)] can be derived from Eq. (7):
A(n) =
[a A(n − 1) + A(n + 1)]
(a + 1)
(9)
Unfortunately, this arithmetical average value is weighted
value and it can be used only if the coefficient “a” is known or
preliminary determined. To avoid this restriction, average geometrical values can be used:
A(n) ≈ [A(n + 1) × A(n − 1)]1/2
(10)
In all cases the accurate results of quantification of target analytes with two homologues chosen as internal standards could be
calculated by geometric averaging of two sub-results obtained
Please cite this article as: Igor G. Zenkevich, Evgeny D. Makarov, Chromatographic quantitation at losses of analyte during sample preparation,
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No. of Pages 7
I.G. Zenkevich, E.D. Makarov / J. Chromatogr. A xxx (2006) xxx–xxx
with each of these standards. Note that this idea of averaging
was suggested empirically by authors of double internal standard method [18].
Finally, the relationship for modified procedure of double
internal standard can be presented in the following form:
qx = Px
qx−1
Px−1
qx+1
Px+1
1/2
(11)
where qx , qx−1 , qx+1 are masses (m) or concentrations (c = m/M,
M—mass of initial sample) of target analyte and two internal standards added directly into initial samples; Px Px−1 ,
Px+1 —corresponding areas of chromatographic peaks registered
for probes after sample preparation.
Eq. (11) does not include calibration coefficients fx/stand comparing with Eq. (2), because their dependence on number of
carbon atoms in the molecules within homologous series should
be monotonous and their differences will be also compensated
by general recurrent dependence (7).
Practical application of modified double internal standard
method appears to be simple. It requires adding of known
(approximately equal) amounts of two homological internal
standards for each analyte into initial samples. After that these
samples can be treated by any procedures of sample preparation
without effect on the accuracy of results. The single revealed
exception is the process of evaporation of volatile solvents (D),
when the values of distortion factor (K ) should be minimal (see
discussion below).
4. Examples of application
The application of suggested method is demonstrated on
five examples discussed below. The short description of each
case includes characterization of model sample, concentration of target analyte (C), conditions of GC analysis, number of replications (3–4), estimation the values of the factor
of distortion of initial composition of analytes (K ), determined concentration of target analyte (Cmeasured ), absolute
error of determination C = (Cmeasured − C) and corresponding relative error ␦C = C/C, %. Standard deviations of peak
areas (shown for two cases) are not necessary to keep into
account because the data from each chromatogram were processed separately for calculation Cmeasured , followed by their
averaging. To simplify calculation of K values, the ratios
of two internal standards were chosen close to 1:1 in most
cases.
Example 1. Sample preparation: liquid–liquid extraction.
Sample: solution of 1-propanol in water (C 8.8 mg/ml).
Extragent: 1-hexanol (1:10, v/v).
Internal standards: ethanol (C 7.9 mg/ml), 1-butanol (C
8.1 mg/ml).
Partition coefﬁcients of target analyte and internal standards
in the system 1-hexanol/water: unknown.
Conditions of GC analysis: WCOT column 20 m × 0.53 mm
with CP Sil 13 CB (ChromPack), isotherm 50 ◦ C.
Number of replications: 3.
5
Results:
Component
Average peak areas, S (mV × ms × 10−3 )
Ethanol (standard, x − 1)
1-Propanol (target analyte, x)
1-Butanol (standard, x + 1)
1.84 ± 0.29
5.62 ± 0.52
13.24 ± 1.08
Factor of initial composition distortion: K = 2.7.
Determined concentration of 1-propanol: 9.1 ± 0.3 mg/ml.
Error: +0.3 (relative error +3.4%).
Example 2. Sample preparation: liquid–liquid extraction
using salt additives.
Sample: solution of 1-propanol in water (C 9.3 mg/ml).
Extragent: benzene (1:10, v/v); additives of Na2 SO4 until
formation of saturated water solution.
Internal standards: ethanol (C 7.9 mg/ml), 1-butanol (C
8.1 mg/ml).
Partition coefﬁcients of target analyte and internal standard in the system benzene/water (in the presence of Na2 SO4 ):
unknown.
Conditions of GC analysis: packed column 0.75 m × 3 mm
with Silipor 75 (LaChema), temperature programming from
50 ◦ C until 210 ◦ C, ramp 8◦ /min.
Number of replications: 4.
Results:
Component
Average peak areas, S (mV × ms × 10−3 )
Ethanol (standard, x − 1)
1-Propanol (target analyte, x)
1-Butanol (standard, x + 1)
13.4
47.4
143.1
Factor of initial composition distortion: K = 3.3.
Determined concentration of 1-propanol: 8.7 ± 0.5 mg/ml.
Error: −0.6 (relative error −6.4%).
Example 3. Sample preparation: head space analysis.
Sample: solution of 2-hexanone in n-tetradecane (C
8.2 mg/ml).
Standards: 2-pentanone (C 4.1 mg/ml), 2-heptanone (C
16.3 mg/ml).
Partition coefﬁcients of target analyte and internal standards
in the system tetradecane—vapor phase at 70 ◦ C: unknown.
Conditions of GC analysis: packed column 3 m × 3 mm with
SE-30 on Inerton N, isotherm 90 ◦ C.
Number of replications: 3.
Results:
Component
Average peak areas, S (mV × ms × 10−3 )
2-Pentanone (standard, x − 1)
2-Hexanone (target analyte, x)
2-Heptanone (standard, x + 1)
13.3
10.3
7.5
Factor of initial composition distortion: K = 0.38.
Determined concentration of 2-hexanone: 8.4 ± 0.2 mg/ml.
Error: +0.2 (relative error +2.4%).
Example 4. Sample preparation: distillation of volatile components (concentrating in condensate).
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Sample: solution of m-xylene in n-tetradecane, 50 ml (C
8.6 mg/ml).
Volatile solvent (added additionally): n-heptane, 10 ml.
Standards: toluene (C 8.7 mg/ml), 1,3,5-trimethylbenzene (C
8.6 mg/ml).
Vapor pressures of target analyte and internal standards at
boiling point of n-heptane (98.4 ◦ C): not evaluated and not taken
into account.
Volume of condensate: 6 ml.
Conditions of GC analysis: packed column 2 m × 3 mm with
10% Carbowax 20 M on Chromaton N AW, temperature programming from 70 ◦ C up to 140 ◦ C, ramp 7◦ /min.
Number of replications: 4.
Results:
Component
Average peak areas, S
(mV × ms × 10−3 )
Toluene (standard, x − 1)
m-Xylene (target analyte, x)
1,3,5-Trimethylbenzene (standard, x + 1)
1.13 ± 0.10
0.54 ± 0.04
0.26 ± 0.02
Factor of initial composition distortion: K = 0.48.
Determined concentration of m-xylene: 8.7 ± 0.2 mg/ml.
Error: +0.1 (relative error +1.2%).
The last case of sample preparation presented below (evaporation of volatile solvents, accompanied by losses of volatile
components from residues) should be discussed in more detail.
Model experiments included the evaporation of low-boiling solvents (n-hexane, n-heptane, ethanol) from samples containing
2-alkanones CH3 COCn H2n+2 (3 ≤ n ≤ 5) as target analyte and
internal standards. They indicate the strong monotonous nonlinear behavior of relative errors upon values on the factor of
initial composition distortion K . In all cases the determined
concentrations of analytes strongly exceeded those in model
samples.
K
Relative error of quantitation (%)
1.5
1.8
2.3
2.6
3.9
+10
+21
+32
+40
+86
Such dependence indicates that the assumed model of regular variations in homologues’ properties (that is the basis for
DIS-method) seems incorrect in this case. The evaporation of
volatile solvents is classified in physical chemistry as so-called
open phase transition process. This procedure represents stationary processes of phase transition when one of phases (e.g.,
vapors of volatile solvents) undergoes by continuous removing
with the contact with another phase [33]. During open evaporation the losses of volatile constituents of initial samples are
linearly related with their partial vapor pressures and, hence,
molar concentrations in the solutions. However, they are not
constant during this process. As a result, the behavior of open
evaporation cannot be described by recurrent relationships (7).
The application of DIS-method in such cases requires further
improvement of physicochemical models and algorithm of data
processing. However, if the level of the change of initial samples composition is not large (K < 1.5), the relative errors are
less then approximately +10%. Thus, it is also possible to use
the double internal standard method in these cases.
Example 5. Sample preparation: evaporation of volatile solvent (concentrating the less volatile compounds in the residues
of solvent).
Sample: solution of 2-hexanone in n-hexane (C 8.0 mg/ml).
Standards: 2-pentanone (C 8.1 mg/ml), 2-heptanone (C
8.2 mg/ml).
Initial sample volume: 10 ml; sample volume after evaporation: approximately 5 ml.
Losses of volatile compounds during solvent evaporation:
unknown.
Conditions of GC analysis: packed column 2 m × 3 mm with
10% Triton X-305 on Chromaton N AW, isotherm 75 ◦ C.
Number of replications: 4.
Results:
Component
Average peak areas, S (mV × ms × 10−3 )
2-Pentanone (standard, x − 1)
2-Hexanone (target analyte, x)
2-Heptanone (standard, x + 1)
0.395
0.649
0.920
Factor of initial composition distortion: K = 1.5.
Determined concentration of 2-hexanone: 8.8 mg/ml.
Error: +0.8 (relative error +10%).
5. Conclusion
Chromatographic quantification using double internal standard method suggested at the middle of 1980s can be recommended for accurate measurements even at the significant
changes in the initial samples composition, caused by losses of
analytes and standards after application of various procedures
of sample preparation. These possibilities can be realized with
special selection of two homologues (previous and following)
of target analytes as two internal standards. Losses of analytes
and standards are described by the general regularities for various properties of homologous series of organic compounds. It
allows us to compensate these losses at the stage of processing
of results.
The main limitation of this method is the presence of homologues of target analytes in real samples that makes its application impossible. Thus, the suggested procedure is preferably
applicable for the analyses of individual compounds in complex
mixtures containing no homologues of target analytes.
Another limitation of this approach is the necessity of the
use of two homologues of target analytes instead of one. Further
development of this method implies its simplification just in
relation the solution of this problem.
Acknowledgements
This work is supported by grant of the President of Russian
Federation No. MK-1316.2005.3.
Please cite this article as: Igor G. Zenkevich, Evgeny D. Makarov, Chromatographic quantitation at losses of analyte during sample preparation,
Journal of Chromatography A (2006), doi:10.1016/j.chroma.2006.08.083
CHROMA-346795;
No. of Pages 7
I.G. Zenkevich, E.D. Makarov / J. Chromatogr. A xxx (2006) xxx–xxx
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Please cite this article as: Igor G. Zenkevich, Evgeny D. Makarov, Chromatographic quantitation at losses of analyte during sample preparation,
Journal of Chromatography A (2006), doi:10.1016/j.chroma.2006.08.083