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: [email protected] (I.G. Zenkevich), [email protected] (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 I.G. Zenkevich, E.D. Makarov / J. Chromatogr. A xxx (2006) xxx–xxx 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 4 I.G. Zenkevich, E.D. Makarov / J. Chromatogr. A xxx (2006) xxx–xxx 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, 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 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). 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 6 I.G. Zenkevich, E.D. Makarov / J. Chromatogr. A xxx (2006) xxx–xxx 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 References [1] E. Leibnitz, H.G. Struppe (Eds.), Handbuch der Gaschromatographie, Akademische Verlagsgesellschaft, Leipzig, 1984. [2] E. Katz (Ed.), Quantitative Analysis using Chromatographic Techniques, John Wiley & Sons, Chichester, 1987. [3] G. Guiochon, C. Guillemin, Quantitative Gas Chromatography (for Laboratory Analyses and On-line Process Control), Elsevier, Amsterdam, 1988. [4] L.R. Snyder, J.J. Kirkland, J.L. Glajch, Practical HPLC Method Development, second ed., J. Wiley & Sons, New York, 1997, p. 643. [5] L.R. Snyder, S. Van der Wal, Anal. Chem. 53 (1981) 877. 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