Research Article
Application of van Deemter Diagrams and Golay Equation in Optimization of a GCMS Method to Pesticides Analysis
Pablo Gordiano Alexandre Barbosa^{1}, Renata de Oliveira Silva^{1}, Paulo H. M. Theophilo^{1}, Dafne A. Cavalcante^{1}, e Pollyana C. V. de Morais^{2}, Ronaldo Ferreira do Nascimento^{1}^{1}Department of Analytical and Physical Chemistry Chemistry, Federal University of Ceará (UFC), Av. Humberto Monte S / N Campus do Pici, Bl 935. CEP 60451970 FortalezaCE, Brazil
^{2} Institute of Marine Sciences, Federal University of Ceará, Av. Abolição, 3207, Meireles, CEP 60165 081, FortalezaCE, Brazil
Ronaldo Ferreira do Nascimento, Department of Analytical and Physical Chemistry Chemistry, Federal University of Ceará (UFC), Av. Humberto Monte S / N Campus do Pici, Bl 935. CEP 60451970 FortalezaCE, Brazil, Email: ronaldo@ufc.br
Keywords:Optimization, Chromatography, van Deemter, Golay, Pesticides
This paper presents an optimization study of the GCMS chromatographic method for the determination of pesticides in pineapple fruits by applying the van Deemter diagram and Golay equations in the investigation of the optimal flow of the mobile phase, aiming to improve performance of the method.The target compounds were the atrazine, simazine, trifluralin and chlorothalonil (internal standard).The mobile phase optimal flows for trifluralin, simazine and atrazine were 57.7, 42.2 and 49.0 cm s1, corresponding to the flow rates of 1.7, 1.2 and 1.4 mL min1.The selected flow rate for the final method was 1.2 mL min1, which allowed an increase of 1.20 to 1.70 in the peak resolution between the pesticides simazine and atrazine, providing a 42% improvement in the efficiency of separation without compromising the separation of the trifluralin and chlorothalonil compounds. Additionally, the terms of longitudinal diffusion (B) and mass transfer in the mobile phase (CM) were calculated for trifluralin (B = 0.196 cm2 s1 and CM = 5.89 x 105 s) for simazine (B = 0.151 cm2 s1 and CM = 8.57 x 105s) and for atrazine B = 0.149 cm2 s1 and CM= 6.22 x 105 s.
Modern chromatographic techniques, including gas chromatography (GC) and high performance liquid chromatography (HPLC), are longstanding analytical tools for analyzing complex samples in several branches of chemistry and related areas, such as biochemistry, environmental sciences, food science, toxicology, forensic science, natural products, pharmaceutical area, petrochemical, among others [1,2].
In the development of efficient chromatographic methods, in addition to selecting a column with a stationary phase suitable for the separation of the compounds, the chromatographers need to adjust and optimize a variety of chromatographic parameters associated with the separation efficiency to obtain symmetric and well defined chromatographic peaks in shorter analysis times [13]. The efficiency of a chromatographic column is affected by a variety of factors that may compromise it, according to the chromatographic run conditions and the column dimensions. The low column efficiency is expressed by deformations in the morphology of the chromatographic peaks and low resolutions, visualized in the chromatogram obtained under certain conditions of analysis, which can drastically impair the qualitative and quantitative analysis of the sample.
In 1956, van Deemter, Zuiderweg & Klinkenberg published a paper that has as its essence the development of a kinetic theory to describe the band enlargement processes in nonideal linear chromatography, as well as column efficiency. The theory of van Deemter et al. bases the processes of bandwidth expansion in the processes of longitudinal molecular diffusion, turbulent diffusion (preferential paths) and nonideal mass transfer processes between the mobile and stationary phases, in packaged columns [4]. The van Deemter model establishes column efficiency based on Martin and Synge's (1941) plate theory(1941), correlating column efficiency with the equivalent height of a theoretical plate (H), being called the van Deemter equation [47]. With the development of the capillary columns (open tubular) for GC, by Marcel Golay (1957) the description of efficiency for these columns disregards the effects of turbulent diffusion, with a simplification of the van Deemter model, being this model called the Golay equation.
The mathematical treatment developed by Golay provided viable expression to evaluate quantitatively the height of plates (H) in open tubular columns in GC to express of separation efficiency [3,6,8]. The models of van Deemter and Golay can be applied in the optimization of drag gas flow in the development of GC methods, considering that this parameter, in the form of the linearmigration speed of the mobile phase (μ), has great influence on Processes that affect column efficiency. The van Deemter diagrams are powerful tools in the investigation of the optimum linear velocity and consequently of the optimal mobile phase flow (F) [3,6,8,9]. In spite of the relevance of the mentioned theories for the studies of column efficiency in chromatography, we still observe a modest number of studies that apply these concepts, as well as little use by the professionals who work in the area of chromatographic analysis.
This work presents an optimization study of the chromatographic method (GC) for the determination of pesticides in pineapple fruits, applying the van deemter diagrams and Golay equation in the optimum flow investigation, to evaluate the improvement of the method performance, considering the system suitability.
Analytical standards and reagents
The target pesticides were trifluralin, simazine and atrazine, and the chlorothalonil compound was used as the internal standard (IS).The analytical standards of atrazine, simazine and trifluralin were purchased from SigmaFluka, with purity of 98.5% for atrazine and 99.0% for simazine and trifluralin, and the analytical standard of chlorothalonil was purchased from Accustandard with purity of 99.7%.From the solid analytical standards were prepared stock solutions of each pesticide at 1000 μg mL1in methanol spectroscopic UV/HPLC grade. With stock solutions, a mixed solution of the compounds was prepared at 5 μg mL 1 in ethyl acetate: cyclohexane 1: 1.
For the preparation procedures of the sample, acetonitrile UV/HPLC spectroscopic grade from Tedia (USA), ethyl acetate and cyclohexane spectroscopic UV/HPLC grade from Vetec (Brazil) were used. Anhydrous magnesium sulfate (MgSO4), trisodium citrate dihydrate (C6H5Na3O7•2H2O), disodium hydrogen sulphatesesquihydrate(C6H6Na2O7 •1.5H2O), all from SigmaAldrich, primary/secondary amine sorptive phase Supelcoclean bonded silica (PSA) and graphitized carbon black (GCB) Supelcoclean ENVICARB 120/400, both from Supelco (USA).
Preparation of the test samples by QuEChERS method
The samples were prepared according to the modified QuEChERScitrate method [10,11]. Approximately 10.0 g of processed pineapple was weighed into a 50 mL PTFE tube and then 10.0 mL acetonitrile solvent was added, followed by stirring for 1 min on a vortex shaker.After stirring, 4.0 g of anhydrous magnesium sulfate, 1.0 g of sodium chloride, 1.0 g of tribasic sodium citrate and 0.5 g of sodium hydrogen citrateses quihydrate were added, followed by manual stirring of the tube to avoid formation of nodules.After manual stirring, agitation was promoted for 1 min on a vortex stirrer followed by centrifugation for 10 min at 3000 rpm. To obtain the final extract, a 4.0 mL aliquot of the acetonitrile liquid phase was withdrawn.
In the cleanup phase by dispersive solidphase extraction (DSPE), 600 mg of magnesium sulfate, 100 mg of PSA sorbent, 30 mg of graphitized black carbon Supelcoclean ENVICARB 120/400, and followed by stirring for 1 min to promote dispersion of the sorbent in the primary extract of the matrix. Then, an aliquot of 3.0 mL of the postclean up extractwas transferred to a ground flask. The extract was taken to a rotary evaporator at 40 ° C to remove the acetonitrile from the extract. After evaporation, the extract was resuspended in 3.0 mL cyclohexane: ethyl acetate 1:1. The final extract free of the compounds was stored in vial for later fortification with standard solution of the pesticides to obtain the test sample.
GCMS analysis
For the beginning of the studies of development and optimization of the chromatographic method, initial chromatographic conditions were defined for the experiments of evaluation of the temperature programming. These conditions are described below.
Temperature programming
Four temperature programming were tested to verify the best condition for separation of the compounds. The chromatographic analysis was conducted in a gas chromatograph GCSQ/MS DSQII model, Thermo FisherScientific (USA). Chromatographic conditions for temperature programming were based on an injection volume of 1.0 µL, splitless injection mode, inlet temperature 250 ° C and carrier gas flow 1.0 mL / min. The column was 30m x 0.25 mm i.d. and 0.25 µm of film thickness with OV5(5% phenyl, 95% polydimethylsiloxane) stationary phase. The MS detector operated with transfer line temperature 280 °C and ionization mode of electron impact. The criterion for the selection of the best method was based on the chromatographic resolution (Rs) between the simazine and atrazine compounds, which presented problematic separation, as will be discussed in the results section (Table1).
Programming 1 
Programming 2 
Initial temp.: 100 °C (1 min) 15°C/min até 180°C 10°C/min até 280°C (5 min) 
Initial temp.:100 °C (1 min) 7°C/min até 280°C (5 min)

Programming 3 
Programming 4 
Initial temp.: 100 °C (1 min) 7 °C/min até 190°C 2 °C/min até 220°C (2 min) 
Initial temp.: 100 °C (1 min) 7°C/min até 240°C (2 min) 
Table1. Temperature programmings tested in the development of the chromatographic method.
The peak resolution was calculated according to equation 1, in the separations where there was greater peak overlap, considering the peak width at half height (W1/2), and equation 2, considering peak width (W), when better separations were observed in the chromatograms [3,9].The terms tr correspond to the retention times of the compounds obtained in each condition tested.
Optimization of carrier gas flow via van Deemter diagram
The optimization of the carrier gas flow were conducted according to the van Deemter diagrams/curve model. The van Deemter diagram is a plot of theoretical plate height versus linear migration velocity of the mobile phase (H x μ) [3,4].Injections of test samples were conducted under the chromatographic conditions reported in Tables 2 and 3, with the best temperature programming considered, at the following mobile phase linear velocities (carrier gas flows): 17, 30, 34, 40, 50, 60, 70 and 85 cm s1. After obtaining the chromatograms relative to each linear velocity, the numbers of theoretical plates (N) associated to the column were calculated for the compounds trifluralin, simazine and atrazine, according to equations (3) and (4). Equation 3 was applied in cases where there was a low resolution between simazine and atrazine [3,9].
Once the values for theoretical plate numbers were reached, the theoretical plate equivalent heights (H), according to equation 5, were calculated and added to the column for each compound in each mobile phase flow. Finally, the graphs H versus μ were plotted. In equation 5, L corresponds to the column length.The optimal flow for separation of each compound was evaluated graphically, verifying the linear velocity (μotm) associated with minimum theoretical plate height (Hmin).
Estimating the terms of the Golay equation
The estimation of the terms of the Golay equation was conducted in order to know the magnitude of the effects of longitudinal molecular diffusion and the mass transfer processes between the phases, on the separation efficiency, in the form of terms B and C, respectively. The Golay equation in its simplified form is expressed as equation 6 [3,12].
The terms B and C were calculated according to equation 7 and 8 respectively, so that these mathematical relationships are demonstrated in the reference Grob & Barry (2004), based on equation 9, considering the knowledge of the optimal linear velocity μotm and the minimum plate height ( Hmin), obtained in the van deemter diagrams [5,8].
System suitability
In the evaluation of the systemsuitability were evaluated in addition to the parameters chromatographic resolution (Rs) and number of theoretical theoretical plates (equations 2 and 4), for the compounds simazine and atrazine, the parameters retention factor (k) and selectivity factor (α), calculated according to equations 10 and 11, respectively. In equation 11, kB represents the retention factor of the most retained compound. The dead time (tM) wasestimatedaccordingtoequation 12 [1,9].
Temperature is a physical variable of fundamental relevance in chromatographic separation processes. In the development of GC chromatographic methods, one of the critical steps is to establish column temperature programming. The temperature programming is a powerful tool in the configuration of GC methods, since it allows the manipulation of the retention times of the analytes, through the controlled and gradual elevation of the column temperature during the chromatographic run, in order to obtain the best resolutions in the shorter time [3,8,13]. In the development of the CGMS method the separation of the simazine and atrazine compounds was considered critical for the analytical efficiency. This difficulty was naturally expected, considering that they belong to the same chemical group of pesticides, the triazines, having high structural similarity between their molecules, according to Figure 1.
Compound 
Vapor pressure (25°C) (mPa)^{a} 
log K_{ow }(pH 7, 20°C)^{a} 
Trifluralin 
9.5 
5.27 
Simazine 
0.00081 
2.30 
Atrazine 
0.039 
2.70 
Chlorothalonil 
0.076 
2.94 
^{a}Pesticides Properties DataBase (PPDB), Hertfordshire University, 2015. 
Table 2. Physicochemical properties in the evaluation of the retention order of the compounds.
Is also observed that the elution order followed the trend of log Kow values, considering that the stationary phase of the column is predominantly nonpolar. The trifluralin, having a higher log Kow value, showed the shortest retention time in all tested conditions, while the chlorothalonyl compound with the lowest log Kow value presented the highest retention times.
The order of elution, based on vapor pressure, does not follow the trend of volatility (Table 2), at least for the case of the last three eluted compounds: simazine, atrazine and chlorothalonil. The polarity was, therefore, the predominant factor in the chromatographic separation. The chromatographic resolutions (Rs) obtained between simazine and atrazine in the four temperature programs tested were respectively 1.20, 1.25, 1.32 e 1.44. The programming 4 allowed the highest resolution (Rs = 1.44), with a running time of 23.00 min. Based on the mathematical modeling of the calculations associated with the chromatographic peaks, in Rs = 1.0 the degree of overlap of the bands evaluated is 4.0%, considering therefore that the peaks are reasonably separated if the amounts of the components in the sample are equal.However, for applications in real samples for quantitative purposes, the value Rs = 1.25 can be considered acceptable. Values for Rs ≥ 1.5 indicate almost complete separation of the chromatographic bands, with overlap of only 0.3% [1,9, 15]. In spite of the various temperatureprogramming tests, the best resolution achieved still did not contemplate the more restrictive criterion of Rs≥ 1.5, which would allow a better accuracy and precision in the quantifications of the compounds simazine and atrazine. In order to achieve resolution improvement, experiments were conducted based on the optimization of the mobile phase flow, adopting the temperature programming 4 (Figure 2).
Optimization of the carrier gas flow
The flow optimization of mobile phase in analytical chromatography, whether CL or GC, is a feasible measure to achieve improved chromatographic resolution efficiency. Obtaining an optimal flow condition provides greater column efficiency without the need for a drastic replacement procedure [1,9,15]. As already well established in the literature, the theoretical bases of the mobile phase flow optimization studies are essentially based on the van Deemter model and, in the case of capillary gas chromatography, this model is simplified, being called the Golay equation [3,4,9].The experimental procedure of the optimization process is relatively simple, however, calculations and data processing are laborious. Table 3 shows the results obtained in the optimization studies to obtain van Deemter diagrams for the analyzed compounds.
t_{r}(min) 
W (min) 
N 
H (mm) 
µ (cm s^{1}) 


11.51 
0.1090 
178,409 
0.168 
17 

9.95 
0.0660 
328,017 
0.091 
30 

8.98 
0.0590 
370,654 
0.081 
40 
Trifluralina 
8.63 
0.0530 
424,219 
0.071 
50 

8.38 
0.0510 
431,984 
0.069 
60 

8.16 
0.0550 
352,188 
0.085 
70 

12.45 
0.0975 
90,413 
0.332 
17 
Simazina 
10.18 
0.0472 
257,937 
0.116 
30 

9.67 
0.0352 
418,475 
0.072 
40 

9.29 
0.0376 
338,499 
0.089 
50 

12.56 
0.0913 
104,940 
0.286 
17 

10.28 
0.0409 
350,301 
0.086 
30 

9.77 
0.0344 
447,274 
0.067 
40 
Atrazina 
9.39 
0.0312 
502,254 
0.060 
50 

9.10 
0.0359 
356,283 
0.084 
60 
Table 3. Results obtained in the experiments to obtain van Deemter diagrams for the compounds trifluralin, simazine and atrazine, t_{r} = retention time; W = peak base width; W_{1 / 2 }= peak width at half height; N = number of theoretical plates; H = theoretical plate equivalent height.
Figure 3 shows the profiles of the van Deemter (H versus μ) diagrams for trifluralin, simazine and atrazine, all the compounds presented the theoretically expected profile of asymmetric hyperbole [3,4]. In the evaluation of figure 3 it can be observed that it is possible to estimate easily the optimal linear velocity of mobile phase (µotm) for the separation of each compound.
The optimal flow for the simazine and atrazine were more closely related due to their chemical similarity, while the optimal flow for the chromatographic separation of trifluralin was slightly more divergent, which can be justified by the greater difference in molecular structure and chemical properties when compared to triazines.
The optimal flow for the simazine and atrazine were more closely related due to their chemical similarity, while the optimal flow for the chromatographic separation of trifluralin was slightly more divergent, which can be justified by the greater difference in molecular structure and chemical properties when compared to triazines.
The optimal values for the linear velocity of the mobile phase were 57.7 cm s1 for trifluralin, 42.0 cm s1 for simazine and 49.0 cm s1 for atrazine, respectively corresponding to the flow values of 1.7, 1.2 and 1.4 mL min1. The criterion to define the optimal flow rate for the configuration of the final method considered the problematic separation between simazine and atrazine. The results showed that the optimal flow rate to achieve better separation efficiency between these compounds was between 1.2 and 1.4 mL min1.In order to consolidate the choice of the optimum flow rate for the final method in terms of contribution to system suitability, the variation of the simazine / atrazine peak resolution was evaluated as a function of the carrier gas flow, as shown in Figure 4.In this case is evident that a maximum resolution was reached between flows of 1.2 to 1.4 mL min1, these resolutions being of the order of 1.7. We observed a marked improvement in peak resolution between simazine and atrazine compounds when using 1.2 mL min1 flow, adjusting the resolution parameter to the criterion of Rs ≥ 1.5 for methods applied to the quantitative analysis. It is important to note that, the application of the optimal flow rate 1.2 mL min1 did not compromise the separation of the trifluralin and chlorothalonil compounds (internal standard). From these observations, the optimum flow rate for the separation of the target compound was 1.2 mL min1.
The influence of the mobile phase linear velocity (μ) on the separation efficiency is the result of its effect on the molecular diffusion and mass transfer processes between the mobile and stationary phases of the chromatographic system. This parameter can alter these phenomena in a more or less intense manner in the separation of a given analyte, affecting the terms of longitudinal diffusion B and mass transfer C (CM and CE), and, consequently, affecting H according to equation 6.In a more detailed perspective, the Golay equation can be expressed by expressing the terms of resistance to mass transfer to the mobile phase (carrier gas) CM and to the stationary phase CE, according to equation 13.
By critically evaluating equation 13, the direct influence of μ on the column efficiency in the form of H is clear, however, as stated earlier, this influence becomes even more important given the interdependence of terms B, CM and CE also with the velocity of the carrier gas.The term Bcan be mathematically defined as a function of the diffusion coefficient of the analyte in the mobile phase, in capillary columns in the form of equation 14.
The extent of occurrence of longitudinal diffusion during the chromatographic analysis is a direct consequence of the residence time of the analyte molecules in the mobile phase and the nature of the carrier gas, since the analyte will have different diffusion coefficients for each type of carrier gas. The effect of longitudinal diffusion is more intense under lower mobile phase linear velocity conditions and less important at relatively higher linear velocities [8].
As the general term associated with the process of molecular diffusion expressed as (B / μ), for higher values of μ, the lower the contribution of this term to the elevation of H (chromatographic bandwidth).This relationship between B and μ is explained by the fact that at higher linear velocities of mobile phase (higher flow rates), the residence time of the analyte molecules in the column is relatively smaller, reducing the time available for the occurrence of molecular diffusion [3,8].
The mass transfer processes are considered as the phenomena that most affect the separation efficiency, emphasizing the relevance of the control of the term C for column efficiency. This term, which expresses the resistance to mass transfer between the mobile and stationary phases, is constituted by the two components of resistance to mass transfer in both phases of the system, and are dependent, among other factors, of the diffusion coefficients in the Phases, according to equations 15 and 16 [3,8,12].
In equation 15 rc is the radius of the chromatographic column and k the retention factor, while in equation 16 df is the film thickness of the stationary phase. There is a proportionality relationship between CMand rc2, meaning that the resistance to mass transfer in the mobile phase tends to increase with increasing column diameter. There is an inverse proportional relationship between CM and the analyte diffusion coefficient in the mobile phase, so that, for higher DM values, the lower the mass transfer resistance in the mobile phase, contributing to higher column efficiency [3,8].
At this point, we have an apparent contradiction, considering that, previously, we affirm that relatively higher values of DM, provide band enlargement, due to the processes of molecular diffusion. This remains true. However, it is necessary to keep in mind that a compromise between all the factors that affect column efficiency is necessary, so that this compromise has dependence on the properties of the analytes to be separated.
The flow optimization study was able to define the chromatographic condition in which the diffusion coefficient of the analytes in the carrier gas contributes as little as possible to the longitudinal molecular diffusion without drastically affecting the mass transfer processes in the mobile phase. Regarding the mass transfer in the stationary phase, we have the dependence of CE with the film thickness of the stationary phase df and with the diffusion coefficient of the analyte in the stationary phase DE. In general, the resistance to mass transfer in the stationary phase can be minimized by the use of columns with lower film thickness of approximately 0.20 μm, as is the case in this study. Considering the film thickness of 0.25 μm of the capillary column employed, it characterizes a thin film, the mass transfer processes for mobile phase are preponderant for the band enlargement. The term C in the Golay equation consists, basically, of the term CM. Thus, for this specific study, we can present the Golay equation in the form below.
Since the chromatographic column was the same in the experiments, and the diffusion coefficients are inherent properties of the target compounds, the manipulation of the CM and CE values was driven by varying the k values through the variation of the mobile phase flow μ.
Estimating the terms of the Golay equation
After the conclusion of the mobile phase flow optimization studies and interpretation of the results according to the Golay equation, it was decided to explore the estimation of the terms of this equation for each target compound, considering equations 7 and 8 [8]. The estimated values for the terms of the Golay equation for the analytes, as well as the theoretical plate height values obtained based on the experimental study by van Deemter diagram. The values were B = 0.196 cm2 s1, CM= 5.89x105 s and H = 0.068 mm to trifluralin, B = 0.151 cm2 s1, CM= 8.57x105 s and H = 0.072 mm to simazine, B = 0.149 cm2 s1, CM= 6.22x105 s and H = 0.061 mm to atrazine. As expected, there were similarities of the Bvalues associated with the compounds simazine and atrazine, confirming that the effects of longitudinal molecular diffusion on the molecules of these two compounds have very close extensions.On the other hand, the effects of resistance to mass transfer to the mobile phase appear to act with very close extension over the three target compounds, given the proximity between CM values, with a slightly higher intensity for simazine, followed by atrazine and trifluralin.
System suitability
System suitability in chromatography is a fundamental requirement for analytical method validation procedures as it is a technical certification that the whole system has adequate performance to provide results with acceptable accuracy and precision [16].
the results obtained for some system suitability parameters, recommended by the United States Food and Drug Administration (FDA), to be measured during the development of the chromatographic method, for the method configured with a flow rate of 1.2 mL min1 and temperature programming 4, considering the problematic separation compounds[17].The retention factors (k) for simazine and atrazine were respectively 7.06 and 7.14, while the selectivity factor (α) observed was 1.01, peak chromatographic resolution 1.7 and average number of theoretical plates 432,875.
From the observed results for the parameters it is observed that the developed method presents good chromatographic performance. The retention factor for the most retained compound (atrazine) was in the range 2.0
The results showed that, although it is possible to obtain improvements in the GC chromatographic resolution, through the manipulation of the temperature programming, a significant optimization of the column efficiency is possible, together with studies of flow optimization / mobile phase flow, by applying the van Deemter diagrams and Golay equation. The optimization of temperature and drag gas flow (1.2 mL min1) by van Deemter and Golay models provided an increase from 1.20 to 1.70 in the chromatographic resolution between simazine and atrazine. This increase is equivalent to a resolution improvement of approximately 42%, without compromising the separation of the other compounds (trifluralin and chlorothalonil).
The application of the van Deemter theory and the Golay equation made it possible to evaluate the separation of the target compounds at a deeper level with respect to the effects of longitudinal molecular diffusion and mass transfer processes between the phases of the chromatographic system, means of estimating terms B and C of the Golay equation. The practical relevance of the optimizations in the conscientious development of the chromatographic method was verified by the determination of the values of the parameters of system suitability, emphasizing a significant improvement of the chromatographic resolution among compounds with similar chemical properties. These improvements are fundamental to later processes of validation of the analytical method.
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Citation: Barbosa PGA, Silva RDO, Theophilo PHM, Cavalcante DA, de Morais ePCV, et al. (2017) Application of van Deemter diagrams and Golay equation in Optimization of a GCMS method to pesticides analysis. J Mol Applied Bioanalysis 1:004.
Published: 10 November 2017
Reviewed By : Dr. Afsaneh Mollahosseini, Dr. Linda Xiao,
Copyright:
© 2017 Barbosa et al. . This is an openaccess article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.