Teaching Simulation and Computer-Aided Separation Optimization in

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Teaching Simulation and Computer-Aided Separation Optimization in Liquid Chromatography by Means of Illustrative Microsoft Excel Spreadsheets S. Fasoula, P. Nikitas, and A. Pappa-Louisi* Laboratory of Physical Chemistry, Department of Chemistry, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece S Supporting Information *

ABSTRACT: A series of Microsoft Excel spreadsheets were developed to simulate the process of separation optimization under isocratic and simple gradient conditions. The optimization procedure is performed in a stepwise fashion using simple macros for an automatic application of this approach. The proposed optimization approach involves modeling of the peak shapes in order for the simulation of predicted chromatograms to be possible. The performance of the selected optimization procedure was tested by means of experiments performed on a reversed-phase column that produced Gaussian peaks for all solutes, providing benefits for computational simplicity. The separation optimization by Microsoft Excel especially with simple and easily implemented macros is a challenging pedagogical tool for advanced analytical chemistry courses. An illustrative video given in the Supporting Information supports a novice Excel practitioner in following the proposed separation optimization procedure. KEYWORDS: Graduate Education/Research, Upper-Division Undergraduate, Analytical Chemistry, Computer-Based Learning, Internet/Web-Based Learning, Chromatography, HPLC

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INTRODUCTION The pedagogical potential of using Microsoft (MS) Excel spreadsheets has been highlighted in several applications reported in recent papers (see, e.g., refs 1−4). Moreover, the capability of the calculations performed in MS Excel spreadsheets, easily automated by macro subroutines, was recently demonstrated with respect to simulating chromatography. In particular, illustrative MS Excel spreadsheets were developed to model the movement of analytes on a chromatographic column and to visualize zone movements on column during chromatography5 or zone broadening/compression in chromatography.6 The computational movement of an analyte down the column has also been implemented in MS Excel, permitting simulation of isocratic and simple gradient elution as well as the simulation of nonideal chromatographic processes.7 Moreover, MS Excel-based numerical simulations of mass transport processes quantitatively predict the observed behavior of conductometric detection of volatile weak acids in a suppressed anion chromatography system,8 whereas MS Excel-based calculations can assist in the isocratic separation optimization of the data collected from experiments using an HPLC simulator.9 In our recently published work,10 a package of Excel VBA macros was developed for modeling and optimization of a mixture of analytes under multilinear single or double gradient elution conditions by changing the organic modifier(s) content and/or eluent pH. The proposed package and accompanying spreadsheets can be adopted by chromatographers for professional separations of complex mixtures of analytes under multilinear gradient conditions, but they may not be transparent to a beginner analyst/chromatographer and have no pedagogical merit. Consequently, it was desirable to create a simplified version of our previous work for separation optimization intended primarily for students and/or novice © XXXX American Chemical Society and Division of Chemical Education, Inc.

chromatographers who are not familiar with the use of algorithms in a separation optimization procedure. This technical report presents a series of illustrative MS Excel spreadsheets that were developed for separation optimization of a mixture of solutes under isocratic and simple linear organic modifier gradient conditions mostly for pedagogical purposes. These spreadsheets are designed to visualize the resolution as well as the retention time of the last eluted solute under different chromatographic conditions for the selection of the optimal separation conditions to be possible. Moreover, the developed Excel spreadsheets give one the ability to accurately simulate chromatograms as long as the retention parameters of analytes as well as their peak shape parameters are known. The implementation of the whole chromatographic separation process in a user-friendly and widespread software platform such as MS Excel may be more attractive for didactic purposes than that reported in other commercial or academic software.11−13 The separation of a mixture of nine solutes on a reversedphase column was considered as a representative and pedagogical example for testing the accuracy of the proposed optimization procedure. All of the solutes analyzed in this study appeared as narrow Gaussian peaks in recorded chromatograms, which simplified the simulation of the selected optimization procedure.

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LABORATORY RESULTS The separation of a mixture of nine solutes on a reversed-phase core−shell silica column (Kinetex 2.6 μm XB-C18 100 Å, 150 Received: February 8, 2017 Revised: May 19, 2017

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DOI: 10.1021/acs.jchemed.7b00108 J. Chem. Educ. XXXX, XXX, XXX−XXX

Journal of Chemical Education

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Figure 1. Appearance of the MS Excel spreadsheet “retention fit” used for fitting the experimental isocratic retention data to a quadratic retention model. See the text and the spreadsheet instructions for details.

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mm × 4.6 mm) was used as a representative example for the performance of the separation optimization procedure developed in this study and implemented in MS Excel spreadsheets. The solutes were a mixture of three benzenes (benzene (B), toluene (T), and ethylbenzene (EB)) and six phenols (3-bromophenol (3-BP), 2,4-dibromophenol (2,4DBP), 2,4,6-tribromophenol (2,4,6-TBP), 2-bromo-4-nitrophenol (2B-4NP), 4-bromo-2-nitrophenol (4B-2NP), and pentachlorophenol (PCP)). The working solutions with single solutes or solute mixtures were prepared at a concentration of 60 μg mL−1 for benzenes and 20 μg mL−1 for phenols. The liquid chromatography system consisted of a Shimadzu LC-20AD pump, a Shimadzu DGU-20A3 degasser, a model 7125 syringe-loading sample injector fitted with a 5 μL loop, and a Shimadzu UV−vis spectrophotometric detector (model SPD-10A) operating at 215 nm. The column was thermostated at 25 °C using a CTO-10AS Shimadzu column oven. The chromatographic behavior of the solutes was investigated in mobile phases consisting of aqueous phosphate buffers with a total ionic strength of 0.02 M and a fixed pH of 5.9 modified with acetonitrile (ACN). Four isocratic runs were performed in hydro-organic eluents with different ACN volume fractions (φ = 0.4, 0.45, 0.5, and 0.6), and four gradient runs were performed by linearly increasing the ACN content in the mobile phase from an initial volume fraction φ0 = 0.4 to a final one φf = 0.6. In all of the gradients, a linear elution program was applied with the same starting time (tin = 0 min) but with different gradient durations (tG = 5, 10, 15, and 20 min). Some of the above isocratic or gradient runs were used as initial data for the fitting procedure, whereas others were utilized to confirm the validity of the optimization procedure proposed in the present study. The hold-up time and the dwell time were estimated to be t0 = 1.3 min and tD = 0.68 min, respectively, with the flow rate set at 1.0 mL min−1.

SEPARATION OPTIMIZATION PROCEDURE A computer-assisted optimization of the separation of a mixture of solutes comprising a visualization of predicted chromatograms involves the following steps: 1. An initial experimental study of the chromatographic behavior of solutes obtained by the least number of chromatographic runs adequately selected. 2. Fitting of the experimental retention data of each solute to a retention model in order to determine its adjustable parameters. 3. Modeling of the peak shape of analytes in the form of a preferred function. 4. Determination of the optimal separation conditions, i.e., the conditions that lead to the best separation of the solutes under consideration, based on the abovedetermined retention and peak shape parameters of the solutes. 5. Comparison of the simulated chromatogram plotted under the optimal predicted conditions with the corresponding experimental chromatogram recorded under the same conditions in order to test the accuracy of the optimization process. An Excel file with the name “Isocr&GradSeparation Optimization” was created for the whole separation optimization procedure performed in the above stepwise fashion (this file is provided in the Supporting Information). Separations of a mixture of nine solutes under isocratic conditions and under single linear gradients are considered as illustrative examples for the separation optimization proposed in this study and implemented on different MS Excel spreadsheets in the file Isocr&GradSeparationOptimization. Fitting of Isocratic Retention Data

The spreadsheet “retention fit” is designed to fit experimental isocratic retention data for solutes to a retention model. Figure 1 depicts this Excel worksheet, which is available in Isocr&GradSeparationOptimization. The original experimental B



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Figure 2. Sreenshot of the MS Excel spreadsheet “BLcor.” used for baseline correction of experimentally recorded chromatograms. See the text and spreadsheet instructions for details.

Figure 3. Screenshot of the MS Excel spreadsheet “peak shape fit” used for fitting Gaussian peaks of solutes to a retention-time-dependent function. See the text and the spreadsheet instructions for details.

Modeling of Peak Shapes

retention data for the solutes, tR(exp), obtained under different isocratic conditions are fitted to the most popular retention model for a reversed-phase-type elution mode, which is the quadratic polynomial14,15 ln k = c0 + c1φ + c 2φ 2

A prerequisite for modeling of the peak shapes of solutes that appear in a chromatogram is a nonsloping zero baseline, i.e., first the chromatographic responses should be baselinecorrected. Baseline correction of experimentally recorded chromatograms is simple to do. Within the frames of the present work, this may be done using the macro BLC. An example is given in Figure 2, which is a screenshot of the spreadsheet with the name “BLcor.” available in Isocr&GradSeparationOptimization. The spreadsheet instructions provide more details on how to use the “BLcor.” spreadsheet for

(1)

where k = (tR − t0)/t0 is the solute retention factor and φ is the volume fraction of ACN in the mobile phase. The values of the adjustable parameters obtained in this fitting procedure (for details, see the spreadsheet instructions in the Supporting Information) are shown in cells E18:M20 in Figure 1. C



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Figure 4. Screenshot of the MS Excel supplementary spreadsheet “isocr. optim.” used for isocratic separation optimization. See the text and the spreadsheet instructions for details.

baseline correction of experimentally recorded chromatograms in case they appear a nonzero or slanted baseline. After correction of the baseline of the experimental chromatograms, modeling of the peak shapes is straightforward. The spreadsheet “peak shape fit” in Isocr&GradSeparationOptimization is designed to fit the peak shapes of each solute recorded in different chromatograms to a preferred function. A chromatographic peak is time-dependent detector response data, i.e., an array of y values over the time band from t1 to t2, which depend on the peak width. A typical chromatographic Gaussian peak with a height h, a width parameter D (more precisely, a constant denoting the standard deviation of the Gaussian distribution), and a retention time tR is given by the equation16 ⎡ (t − t )2 ⎤ R ⎥ y = h exp⎢ − D2 ⎦ ⎣

instead of the quadratic one initially assumed in eq 3. Details on how to use the spreadsheet “peak shape fit” are given in the spreadsheet instructions. Optimization and Visualization of Isocratic Elution

After the retention times and peak shape parameters for all of the solutes studied under isocratic conditions have been estimated, the values of these parameters (i.e., c0, c1, c2, h0, h1, h2, D0, D1, and D2) are transferred into the spreadsheet “isocr. optim.” in Isocr&GradSeparationOptimization. A screenshot of this spreadsheet, which was created for isocratic separation optimization and simulation of chromatograms, is displayed in Figure 4. The inset Graph B in Figure 4 depicts a perfect similarity between the simulated chromatogram created for an eluent with φACN = 0.45 (plotted as the red line) and the original experimental one (plotted as the blue line), which shows that both models (the retention model, eq 1, and the peak shape model, eq 3) accurately predict any chromatogram that could be recorded under isocratic conditions in the studied range of mobile phase strength (φ between φ(min) = 0.4 and φ(max) = 0.6). Thorough instructions for simulating/predicting an isocratic chromatogram at each mobile-phase strength φ as well as for automatically optimizing the isocratic separation conditions using “isocr. optim.” are given in the Supporting Information. However, the selection of the optimal separation conditions is also possible from a good appreciation of the inset Graph A of Figure 4, which is automatically created as described in the spreadsheet instructions. As shown in this figure, tR(max) decreases with increasing organic content φ in the mobile phase (purple circle markers), as is expected for a reversed-phase-type elution. However, the dependence of Rs (the resolution of the least resolved pair of adjacent solutes) on φ (depicted by the green diamond markers) is rather peculiar: for example, the resolution in a mobile phase with φACN = 0.4 is worse than that in an eluent with φACN = 0.45 even though the separation time is longer. Consequently, the foreknowledge of the precise

(2)

where y is the detector response at time t. Assuming that the peak height as well as the peak width for each analyte recorded in different chromatograms obtained under similar conditions, like those used in this study, depend primarily on tR, we can write eq 2 as ⎡ (t − t )2 ⎤ R ⎥ y = h(t R ) exp⎢ − D(t R )2 ⎦ ⎣

(3)

2

where h(tR) = h0 + h1tR + h2tR and D(tR) = D0 + D1tR + D2tR2 if a quadratic dependence of both the peak height and peak width on tR is assumed. An example of using the spreadsheet “peak shape fit” is shown in Figure 3, which describes the fitting of the peak shapes of the four last-eluted solutes of the test mixture under isocratic conditions in eluents with φACN = 0.4 and 0.5 to eq 3. It should be noted that the data for two experimental chromatograms are enough for the above procedure since the peaks experimentally recorded in this study permit a linear dependence of both the peak height and peak width on tR D



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Figure 5. Screenshot of the MS Excel spreadsheet “grad. optim.” used for separation optimization under single linear gradient conditions. See the text and the spreadsheet instructions for details.

dependence of Rs and tR(max) upon φ enables the selection of the optimal eluent concentration.

spreadsheet instructions provide details on how to use the worksheet “grad. optim.”.

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Optimization and Visualization of Single Linear Gradient Elution

PEDAGOGICAL ASPECTS This article can be used as a basis for laboratory experimentation in an upper-level analytical chemistry course related to isocratic and gradient liquid chromatography separation optimization. The proposed MS Excel spreadsheet approach to separation optimization was taught for the third time in the 2016/2017 spring semester (during the course with the title Modeling and Optimization of Chromatographic Separations of the eighth semester belonging to the direction Chemical Analysis - Environment - Electrochemistry of the Bachelor Chemistry program. It should be noted that the undergraduate students were already familiarized with the basic principles related to both isocratic and gradient elution in reversed-phase liquid chromatography and also with fundamental skills required for the use of MS Excel spreadsheet calculations in the manipulation of experimental data. After working through the proposed optimization process, the students became familiar with a computer-aided separation optimization and realized the importance and the advantages of performing such an optimization approach compared with a trial-and-error optimization method. Moreover, students appeared to learn in depth modeling of both peak shapes and retention data additionally with the solution of the fundamental gradient elution equation, which is necessary for the prediction of solute retention times under gradient conditions. Finally, students were very enthusiastic when they realized that simulated chromatograms generated by the proposed Excel spreadsheet for selected different isocratic and/or single linear gradient conditions were almost identical to the experimental ones. Some students have even extended the capabilities of the present process, writing their own macros after graduation and implementing such a model-based optimization approach in real separation problems that appeared in their Master’s and/or Ph.D. studies.

A procedure similar to that described above for isocratic separation optimization and simulation may be also followed to optimize single linear gradient conditions and simulate chromatograms obtained under selected different gradient profiles. A screenshot of the spreadsheet “grad. optim.” created for the above purpose is depicted in Figure 5, where the predicted/simulated chromatogram in a gradient elution with a duration tG = 15 min is plotted as the red line in the inset Graph B. The aim of the worksheet “grad. optim.” is to determine the best value of tG for the linear variation of φACN between an initial volume fraction φ0 = 0.4 and a final one φf = 0.6 that leads to the optimum separation of the solutes of interest. The main difference between gradient and isocratic separation optimizations is that the solute gradient elution time tR cannot be determined directly by the retention model through an analytical expression such as tR = t0(1 + k) but rather demands the solution of the fundamental gradient elution equation17,18

∫0

tR − t0

dt =1 t0k(t )

(4)

where tR is the retention time of a solute under gradient conditions, t0 is the column dead time, and k(t) is the isocratic solute retention factor, which refers to each value of the mobile phase composition during the gradient run and is expressed as a function of time through the gradient profile. The solution of eq 4 is achieved in the worksheet developed for gradient separation optimization as explained in the relevant section of the spreadsheet instructions. As in the case of the isocratic separation optimization, the gradient separation of the sample mixture is easily automated by the macro separationG written for this purpose. The E



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STEPS TO INCORPORATING THE SPREADSHEET PROGRAM INTO COURSES AND ITS PEDAGOGICAL EFECTIVENESS Some potential ways that the proposed spreadsheet could be incorporated into courses would be the following: After some of the fundamental concepts of HPLC separation optimization are discussed, the spreadsheet program is introduced in class, giving step-by-step instructions on the operation of the software. In our experience, not one student expressed difficulty in using the spreadsheet program and making changes to the separation conditions. Students appreciated being able to see the effect of a change in separation conditions on the recorded chromatograms and to find a value of φ or tG that gives a good resolution of the sample under consideration. Furthermore, provided they are familiar with functions in Excel, students could reconstruct the spreadsheets of the workbook using for simplicity the same layout as that in the Supporting Information or any other layout. Selected examples with chromatographic data given by instructors or by request from the authors of this technical report provide the chance for students to easily optimize separation conditions of a sample of interest, which gives students a feel of confidence for HPLC before entering the lab in their future work.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

A. Pappa-Louisi: 0000-0003-4690-7188 Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Flannigan, D. J. Spreadsheet-Based Program for Simulating Atomic Emission Spectra. J. Chem. Educ. 2014, 91, 1736−1738. (2) Ge, Y.; Rittenhouse, R. C.; Buchanan, J. C.; Livingston, B. Using a Spreadsheet To Solve the Schrödinger Equations for the Energies of the Ground Electronic State and the Two Lowest Excited States of H2. J. Chem. Educ. 2014, 91, 853−859. (3) Pye, C. C.; Mercer, C. J. On the Least-Squares Fitting of SlaterType Orbitals with Gaussians: Reproduction of the STO-NG Fits Using Microsoft Excel and Maple. J. Chem. Educ. 2012, 89, 1405− 1410. (4) Loyson, P. Teaching Kinetics Using Excel. J. Chem. Educ. 2010, 87, 998−998. (5) Gilar, M.; McDonald, T. S.; Roman, G.; Johnson, J. S.; Murphy, J. P.; Jorgenson, J. W. Repetitive injection method: a tool for investigation of injection zone formation and its compression in microfluidic liquid chromatography. J. Chromatogr. A 2015, 1381, 110−117. (6) Gilar, M.; McDonald, T. S.; Johnson, J. S.; Murphy, J. P.; Jorgenson, J. W. Wide injection zone compression in gradient reversed-phase liquid chromatography. J. Chromatogr. A 2015, 1390, 86−94. (7) Kadjo, A.; Dasgupta, P. K. Tutorial: Simulating chromatography with Microsoft Excel Macro. Anal. Chim. Acta 2013, 773, 1−8. (8) Liao, H.; Kadjo, A. F.; Dasgupta, P. K. Concurrent HighSensitivity Conductometric Detection of Volatile Weak Acids in a Suppressed Anion Chromatography System. Anal. Chem. 2015, 87, 8342−8346. (9) Shalliker, R. A.; Kayillo, S.; Dennis, G. R. Optimizing Chromatographic Separation: An Experiment Using an HPLC Simulator. J. Chem. Educ. 2008, 85 (9), 1265−1268. (10) Fasoula, S.; Zisi, Ch.; Gika, H.; Pappa-Louisi, A.; Nikitas, P. Retention prediction and separation optimization under multilinear gradient elution in liquid chromatography with Microsoft Excel macros. J. Chromatogr. A 2015, 1395, 109−115. (11) Molnar, I. Computerized design of separation strategies by reversed-phase liquid chromatography: development of DryLab software. J. Chromatogr. A 2002, 965, 175−194. (12) Hewitt, E. F.; Lukulay, P.; Galushko, S. Implementation of a rapid and automated high performance liquid chromatography method development strategy for pharmaceutical drug candidates. J. Chromatogr. A 2006, 1107, 79−87. (13) Boswell, P. G.; Stoll, D. R.; Carr, P. W.; Nagel, M. L.; Vitha, M. F.; Mabbott, G. A. An Advanced, Interactive, High-Performance Liquid Chromatography Simulator and Instructor Resources. J. Chem. Educ. 2013, 90 (2), 198−202. (14) Nikitas, P.; Pappa-Louisi, A.; Agrafiotou, P. Effect of the organic modifier concentration on the retention in reversed-phase liquid chromatography II. Tests using various simplified models. J. Chromatogr. A 2002, 946, 33−45. (15) Schoenmakers, P. J.; Billiet, H. A.H.; de Galan, L. Description of solute retention over the full range of mobile phase compositions in reversed-phase liquid chromatography. J. Chromatogr. A 1983, 282, 107−121. (16) Nikitas, P.; Pappa-Louisi, A.; Papageorgiou, A. On the equations describing chromatographic peaks and the problem of the deconvolution of overlapped peaks. J. Chromatogr. A 2001, 912, 13− 29.

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CONCLUSION The proposed separation optimization procedure gives benefits for an advanced analytical chemistry course since it is performed in an automatic and visual stepwise fashion using Excel spreadsheets and simple macros created for this purpose. Moreover, we believe that the implementation of the proposed optimization process in MS Excel, a universally available and easily understandable computational platform, has pedagogical merits. With this in mind, the layout of the created Excel spreadsheets in this tutorial allows one first to understand the fundamental principles of a separation optimization and second to generate simulated chromatograms of solutes under selected isocratic and single linear gradient conditions. Moreover, since this tutorial is intended primarily for students and/or beginner chromatographers regardless of their experience in programmable separation optimization procedures, the solute retention parameters are obtained from the analysis of isocratic data, whereas a Gaussian function is used to fit peak shapes for computational simplicity. Finally, the Excel spreadsheets may be modified by the users or the users may write their own macros to extend the capabilities of the present approach, whereas an illustrative video given in the Supporting Information supports a novice Excel practitioner in following the proposed separation optimization procedure.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available on the ACS Publications website at DOI: 10.1021/acs.jchemed.7b00108. Instructions for using the Excel-spreadsheet-based software (PDF) Excel-spreadsheet-based software “Isocr&GradSeparationOptimization” (ZIP) Illustrative video supporting a novice Excel practitioner in following the proposed separation optimization procedure (AVI) F



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(17) Snyder, L. R. Linear elution adsorption chromatography: VII. gradient elution theory. J. Chromatogr. A 1964, 13, 415−434. (18) Nikitas, P.; Pappa-Louisi, A. Expressions of the fundamental equation of gradient elution and a numerical solution of these equations under any gradient profile. Anal. Chem. 2005, 77, 5670− 5677.

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Teaching Simulation and Computer-Aided Separation Optimization in

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