In the Laboratory
Optimizing Chromatographic Separation: An Experiment Using an HPLC Simulator R. A. Shalliker,* S. Kayillo, and G. R. Dennis Nanoscale Organization and Dynamics Group, School of Natural Sciences, University of Western Sydney, NSW, Australia; *
[email protected] Analytical chromatographic separations are usually optimized by varying experimental conditions until the components in the mixture are resolved with the best achievable resolution in a minimum run time. The criteria of minimum run time defines the term “limiting resolution” or “limiting selectivity”, which is, the resolution measured between the two most poorly resolved peaks. Usually the lowest value acceptable for the limiting resolution is unity if the aim is quantitative analysis of the components. The resolution of a separation, Rs , provides a quantitative measure of the separation of analytes and is related to the retention factor of the eluting species (k), the separation selectivity (α), and the number of theoretical plates (N): Rs 1 4 N
B 1 B
k k 1
(1)
Each of the variables is essentially independent and hence resolution of a separation can be improved by altering either N, k, or α via changes in the stationary or mobile phase. However, since the analyst is also attempting to optimize run time of an analysis, this puts important constraints on the range that these variables may have. In general, an analyst selects a particular column with a nominal particle diameter and column length; hence the number of theoretical plates is essentially fixed. Separation selectivity depends on the variation in the interactions between pairs of solutes and the mobile and stationary phases. Changing the type of mobile phase, column temperature, and the type of stationary phase can lead to a change in selectivity, albeit with little predictability (1). Therefore, usually the first step in optimization is to alter the solvent strength, which varies the retention factor, k, and is defined as t t0 k r (2) t0 where tr is the retention time of the solute under investigation and t0 is the void time, that is, the retention time of an unretained solute in the system under investigation. Selectivity, α, is defined as k B 2 (3) k1 where k1 and k2 are the retention factors of adjacent peaks, and k1 elutes before k2. In many instances separation can be significantly improved by increasing k through a decrease in solvent strength, with the optimum range being between 2 and 5 (2), but the limit can be increased to between 1 and 10, particularly for more complex separation problems. However for a retention factor of greater than 5, very little gain in resolution is achieved for a subsequent large increase in separation time. While the α and k terms are considered to be independent, they are not always so. Hence some selectivity changes may also take place as a function of the
solvent strength. In fact, it is often observed that the elution order for components varies significantly as the solvent composition is varied. Hence the limiting resolution or selectivity at any particular solvent composition is not necessarily always going to be between the same two compounds of a complex mixture. Care should be taken to confirm the identity of each component during the optimization process. The aim of the present experiment is to demonstrate the optimization of separation through an understanding of the relationship between solvent strength and resolution. To achieve this, the simulation software provided by JCE Software (3) is an invaluable tool because the appropriate number of experiments required for an optimization may be conducted in the time frame of a typical laboratory session, that is, 3 hours. The data collected from the simulation experiments can be used to calculate log k as a function of the solvent composition, and a spreadsheet can then be used to determine the optimum solvent composition that yields the best separation conditions. Basic Theory To quantify the retention behavior of small solutes in LC, the retention factor, k, may be expressed as a function of the mobile phase composition, Φ
log k log k w S '
(4)
where kw is the extrapolated value of k in a poor solvent such as water and S is the rate of change of log k with the solvent composition. Plots of log k versus Φ are generally linear, and this relationship may be used to measure the relative retention of a set of solutes and also assess selectivity changes that may be occurring in a given separation. These plots are also suitable for predicting the best solvent compositions to use for a particular separation, rather than adopting a “trial-and-error” approach that could be painstakingly slow in real-life, especially since after changing the mobile phase to each new solvent composition the column would require re-equilibration of at least five column volumes before the next analysis. Points of intersection in the plots of log k and Φ represent solvent compositions of co-elution. Therefore, maximizing the differences between log k and Φ for a group of analytes contained within a sample results in a value for the most efficient separation conditions, at least with respect to resolution. Experiment The HPLC Simulator The HPLC simulator represents the basic instrumentation of an automated LC system capable of binary gradient operation (4). Three types of solvents are available, as listed under the solvent icon. These solvents are delivered through a HPLC column using the solvent delivery control panel (accessed through the control panel icon). Adjustments may be made to the flow rate,
© Division of Chemical Education • www.JCE.DivCHED.org • Vol. 85 No. 9 September 2008 • Journal of Chemical Education
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In the Laboratory
1.5 1.0
log k
benzene 2,5-xylenol p-cresol phenol p-nitrophenol
toluene phenetole anisole methyl benzoate
2.0
0.5
ene. These standards were used to measure the retention times of each sample across four different methanol/water mobile phase compositions (80/20, 75/25, 70/30, 65/35). These data were used to calculate log k and then a series of log k versus Φ plots were constructed and analyzed to give the optimal solvent composition for separation. Hazards
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This is a computer simulation experiment and as such involves no chemical hazards.
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' Figure 1. Plot of log k versus Φ for the nine components in methanol/ water mobile phases on the Dupont C18 column.
% solvent composition, and the injection volume. Five columns may be selected under the column icon. Samples are detected using either a variable wavelength detector or a photodiode array detector (DAD), which may be useful for identifying the eluted compounds through matching their UV spectrum to that of the known standard substance. A total of nine standard solutions are available by accessing the sample icon. The injection and recording of a chromatogram is obtained through the computer data system, and a run can be initiated and the resulting chromatogram integrated to give information on retention time and peak area. Chromatographic Separation Since all columns are either C8 or C18, the retention behavior of the nine-component mixture is essentially the same. Therefore, while any column could be selected for this purpose, the DuPont C18 column was chosen. This experiment could have been conducted with any of the three aqueous or organic systems available, but for demonstration purposes we illustrate the optimization using methanol/water. Separations of a ninecomponent mixture were performed using an isocratic mode, at a flow rate of 1.0 mL/min, and an injection volume of 10 μL. To determine the void time of the system, phenol was injected using 100% tetrahydrofuran as the mobile phase. Preparation of the Nine-Component Sample Mixture A “virtual” nine-component sample was prepared from p-nitrophenol, phenol, p-cresol, 2,5-xylenol, benzene, methyl benzoate, anisole, phenetole, and toluene at concentrations between 10 and 40 mg/mL (for ease of detection at 254 nm, the later eluting components were prepared at higher concentrations). The simulator assumes that the Beer–Lambert law is obeyed; that is, a linear response is measured irrespective of the sample concentration, therefore sample concentration is not important except for maintaining adequate peak height for easy identification. To facilitate the easy identification of the nine components, three “virtual” standard mixtures were prepared, each containing three different components that were selected to yield the maximum separation of each component in each sample. Standard A contained phenol, 2,5-xylenol, and benzene; standard B contained p-nitrophenol, methyl benzoate, and phenetole; and standard C contained p-cresol, anisole, and tolu1266
Results and Discussion A plot of log k versus Φ for the nine-components using the DuPont C18 column is shown in Figure 1. These plots illustrate that changes in elution order occurred as the solvent composition was altered. They also show which compounds would prove most difficult to resolve and the likely regions where separation would be expected to be the best. For example, for the compounds benzene, methyl benzoate, and anisole, their retention is quite similar with the minimum selectivity between them at around 70/30 MeOH/H2O. For toluene and phenetole, their retention is similar at 80/20 MeOH/H2O, but a decrease in the mobile phase composition leads to an increase in the separation between the two compounds. In contrast, p-nitrophenol and phenol have significant retention differences at 80/20 MeOH/H2O but exhibit a decrease in selectivity as the mobile phase becomes weaker. A quantitative assessment of the retention behavior can be obtained if the selectivity of adjacent bands is systematically measured across all solvent compositions. This would be an arduous task if undertaken manually, but with the aid of a spreadsheet such calculations are fast. The advantage of performing an optimization strategy is that the student becomes familiar with the terms retention factor and selectivity and thus should be able to relate these parameters to separation. Such an optimization procedure is also a simple task and does not distract from the concepts behind the separation process. The application of spreadsheets for process optimization is also introduced into the classroom. A Spreadsheet Approach to Separation Optimization The objective of the optimization is to maximize the selectivity between the two least resolved components of the complex mixture. The following process using a spreadsheetbased calculation can assist in the optimization of separation, and a typical spreadsheet for Excel 2003 is included in the online materials.
1. The retention data obtained from the chromatograms are entered into a spreadsheet as a function of the solvent composition. Four solvent compositions are adequate for describing the relationship between log k and Φ, and even three is viable, but the linear regression becomes less reliable as the number of data points decreases. Since a total of 16 injections would be easily undertaken in a single day using a HPLC system, this number of injections was used in this simulation and optimization.
2. The retention factor, k, for each of the nine components is calculated at each solvent composition.
Journal of Chemical Education • Vol. 85 No. 9 September 2008 • www.JCE.DivCHED.org • © Division of Chemical Education
In the Laboratory
4. A graph (similar to Figure 1) of log k versus Φ is plotted for visual inspection.
5. The line of best fit for each of the nine components is determined. This can be done through the spreadsheet commands, that is, LINEST(Y1:Y3,X1:X3). 6. A new data table is created that has theoretical log k values calculated using the linear regression coefficients calculated in step 5 at all mobile phase compositions available within the simulation program, that is, from 40% organic modifier to 100% organic modifier at 1% increments.
7. The theoretical retention factors, k, are calculated by taking the exponential of these theoretical log k values.
8. The data must be sorted so that the retention factors increase in magnitude for each solvent composition. This can be done using RANK combined with nested IF statements or by using RANK and then a LOOKUP function (strategy used in the example spreadsheet)
9. The selectivity factor (α) is then calculated for each adjacent pair of peaks.
10. At this stage, a graph of α versus Φ can be plotted (Figure 2). Tracing along the lower edge of this graph yields the condition of limiting resolution (selectivity) for each solvent composition. However, interpretation of this graph would not be easy for students.
Alternatively, a simpler method is to examine a graph of the minimum values of the selectivities at each solvent composition (using the MIN spreadsheet function) plotted against solvent composition (Figure 3). This allows the critical values of the selectivities to be examined and identification of the possible solvent compositions for achieving the best separation. An example of a plot of α versus Φ for all nine components is shown in Figure 2. In this figure there are eight curves each of which correspond to the selectivity between adjacent bands (k2/k1). Note that the selectivity plots do not necessarily represent the selectivity that occurs between the same two components, but rather, the selectivity between adjacent bands. It is important to stress that the identity of these adjacent bands changes as the solvent composition is varied. The plot of the minimum values of the selectivities against solvent composition in Figure 3 illustrates that this curve is essentially an expansion of the lower boundary region of Figure 2. The global maximum of α is located at 57/43 MeOH/H2O or at 75/25 MeOH/H2O, which are indicated by the arrows in Figure 2. Also, included in Figure 2, is a deliberate error associated with data entry. The purpose of including this data point was to show how obvious mistakes can be readily identified. This error is shown by (E). Chromatographic Separation of the Nine-Component Mixture The next step in the procedure is to test whether the optimal solvent compositions predicted from the selectivity data meets the resolution requirements for all of the components of the mixture. This was tested using the simulator when the ‘"virtual" nine-component mixture was injected into the system using 57/43 MeOH/H2O and then 75/25 MeOH/H2O as the mobile phase compositions. Figures 4 and 5 show the chromatograms using these conditions. In the separation shown in Figure 4, the limiting resolution is between phenol and p-nitrophenol,
2.00
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B
3. The log of the retention factor, log k, is computed.
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57/43
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'
75/25
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(E)
Figure 2. Plot of α versus Φ for each of the nine peak pairs (eight selectivity plots). Error in data entry is labeled as (E). 1.10
global optimum
local optimum
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Limiting B
1.06 1.04 1.02 1.00 0.4
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' Figure 3. Minimum selectivities (α) versus Φ for the nine-component mixture.
limiting resolution
Figure 4. Illustration of the separation of the nine-component mixture using the mobile phase conditions of 57/43 methanol/water on the DuPont C18 column. Grid lines are at 1 min intervals.
limiting resolution
Figure 5. Illustration of the separation of the nine-component mixture using the mobile phase conditions of 75/25 methanol/water on the DuPont C18 column. Grid lines are at 1 min intervals.
but these components are resolved in the 75/25 MeOH/H2O mobile phase (Figure 5). However, in the separation at 75/25 MeOH/H2O the limiting resolution is between benzene, methyl benzoate, and anisole, but the run time is greatly reduced. It is also important to examine the solvent compositions adjacent to both the 57/43 MeOH/H2O and the 75/25 MeOH/ H2O because of the inherent errors in the analysis of the data. In fact, the optimal conditions, were at either 56/44 MeOH/
© Division of Chemical Education • www.JCE.DivCHED.org • Vol. 85 No. 9 September 2008 • Journal of Chemical Education
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H2O (Figure 6), where baseline resolution between all peak pairs was maintained, or at 76/24 MeOH/H2O (Figure 7), where a substantial improvement in the limiting resolution compared to the separation at 75/25 MeOH/H2O was obtained. At 58/42 MeOH/H2O and 74/26 MeOH/H2O resolution decreased such that in both cases there was almost perfect co-elution of a peak pair (results not shown). An important consideration for the optimization is the run time. In the separation undertaken at 56/44 MeOH/H2O, the retention time of the last eluting peak is 23.9 minutes (k = 11.9). Such a long isocratic retention time results in significant band broadening of the latter eluting components. This would raise their limit of detection and decreases the reproducibility of their quantification. Furthermore, the retention factor range is outside the ideal limits (2 < k < 5) and even outside the range 1 to 10. As such, argument may be made that the separation at 76/24 MeOH/H2O����������������������������������������� may be more useful as the retention factors are maintained between 0.23 to 2.2, which provides better detection sensitivity of the latter eluting components, a substantial decrease in the overall analysis time (hence increasing the throughput), and a higher degree of precision in analysis because band broadening is less substantial. A disadvantage is that the resolution between the components—benzene, methyl benzoate, and anisole—is less than that which is suitable for quantification. Therefore if the analysis of these three components is essential, then the solvent composition at 56/44 MeOH/H2O is preferable. Another disadvantage at 76/24 MeOH/H2O is that the retention of the early eluting components is very short, hence increasing the possibility of significant variation in their retention times as a result of flow fluctuations. At this point the concept of peak capacity, analysis throughput, precision in analysis, and detection sensitivity can be discussed with the student and consequently gradient elution introduced into the separation strategy. Conclusion This simulated HPLC experiment allows the student to gain an appreciation of separation as a function of solvent strength. It also illustrates the concept of selectivity in separation, demonstrating that changes in elution orders can occur as the solvent strength changes. Furthermore, this simulation exercise allows a substantial number of experiments to be undertaken in a time frame that is a fraction required for the real experiment. This allows more detailed chromatographic problems to be investigated and studies such as separation optimization can be addressed in real laboratory sessions. An extension of the learning outcome is that the students should realize the importance of spreadsheet calculations in the manipulation of experimental data. This experiment has been used in the third-year analytical chemistry class. The experiment has evolved to the point where now the spreadsheet optimizer is a key component. Prior to the use of the spreadsheet optimizer the students tended to focus on the calculations rather than the meaning of the results. Therefore the example spreadsheet program allows the final results to be determined without detracting from the key learning aspects— resolution and optimization. In regards to the student’s concept of optimization, we quiz them in relation to their notion of the “real” time required to bring about the required separation. Students undertake the ex1268
Figure 6. Illustration of the separation of the nine-component mixture using the mobile phase conditions of 56/44 methanol/water on the DuPont C18 column. Grid lines are at 1 min intervals.
Figure 7. Illustration of the separation of the nine-component mixture using the mobile phase conditions of 76/24 methanol/water on the DuPont C18 column. Grid lines are at 1 min intervals.
periment without instruction regarding optimization strategies, they count their runs, add up the time (including 15 minutes between each mobile phase change) and then determine how long in "real-time" this would take. The result is compared to the time required for the optimization using the approach described in the simulator. Following this comparison, the student’s unanimously acknowledge the virtue of undertaking such a problem systematically. Some students even extend this learning process to include questions such as, can we implement such a process in a real separation problem when we leave university and can we take the spreadsheet with us. Acknowledgment The financial support of the School of Natural Sciences, University of Western Sydney is gratefully acknowledged. Literature Cited 1. Snyder L. R.; Kirkland, J. J. Introduction to Modern Liquid Chromatography, 2nd ed.; John Wiley and Sons: New York, 1979; Chapter 6. 2. Snyder L. R.; Kirkland, J. J. Introduction to Modern Liquid Chromatography, 2nd ed.; John Wiley and Sons: New York 1979; Chapter 2. 3. The HPLC program is part of the Advanced Chemistry Collection, JCE Software 2003, SP28. http://www.jce.divched.org/JCESoft/Programs/Collections/ACC/index.html (accessed Jun 2008). 4. Rittenhouse, R. C. J. Chem. Educ. 1995, 72, 1086.
Supporting JCE Online Material
http://www.jce.divched.org/Journal/Issues/2008/Sep/abs1265.html Abstract and keywords Full text (PDF)
Links to cited JCE articles
Supplement
Student handouts and instructor notes A typical spreadsheet for Excel 2003
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