Optimization of HPLC and GC Separations Using Response Surfaces Three Experiments for the Instrumental Analysis Laboratory David T. H a ~ e y ' ,Shannon Byerly, Amy Bowman, and Jeff Tomlin DePauw University, Greencastle, IN 46135 ~
~
A common characteristic of modern experimental chemiatry is an increased reliance on instrumental methods of analvsis. With the increased availabilitvand use of instrumentation in the general, organic, inorganic, and introductory analytical laboratory courses, students entering the instrumental analysis laboratory often have substantial experience in the basic operation of a department's instrumentation. Although these students will be aware of the utility of instrumentation in solving a variety of chemical problems, their limited experience will have provided a seriously incomplete picture of modern instrumental analysis. Early exposure to instrumentation is usually of a "black-box" nature in which, for example, a sample mixture is injected into a HPLC and a separation of desired resolution appears. As a result of this simple, routine use of instrumentation, many students will n o t have developed an appreciation for the difficulty of optimizing instrumental and experimental parameters to obtain thebest analvtical results. The goal of instrumental optimization is to maximize the response of the system, whether it is signal intensity in spectrophotometry or the base-line separation of a mixture in chromatography. Typically this is accomplished by varying instrumental or experimental parameters one a t a time until the optimum response is produced. For example, Sawyer et al. (1) describ; an exp;riment in which the atomic absorption signal for Cu is maximized by independently optimizing the burner height, the fuel pressure, and the oxidant pressure. A collection of responses as a function of experimental parameters is called a response surface (2).Since changing the value of a parameter is the same as movine alone the response surface, a one-parameter-at-a-time optimization can eventually be achieved, provided that movement is always toward a greater response. This strategy, however, is not very efficient. Recently, there has been a growing interest in developing more efficient approaches to locating the optimum on a response surface. Methods include the simplex method (2-4), the development of empirical models of the response surface through least-squares fitting of appropriate polynomial equations (3), and the development of theoretical models of the response surface (5). ~
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Resented. In part. at the 2191 Central Regional Meeting of the American Chemical Society. May 31J u n e 2, University Helghts. OH. ' Author to whom correspondence should be addressed.
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Journal of Chemical Education
Few experiments have been published that provide an introductfon to instrumental opGmization through response surface methodolom. Shavers et al. (6)and Stiea (7)have written laboratory~xperimentsin which the simplex method is used to optimize absorbance in colorimetric measurements, while s-angsila et al. (8) used the simplex method to optimize the hydride generation atomic absorption determination of As. No experiments have been published recently that involve the use of either empirical or theoretical models nf the resnonse surface. This article describes three experiments designed to provide an introduction to all of the above-described aooroach.. es to instrumental optimization. The optimization of chromatomanhic separations was chosen because the effect of instr&&ntal and experimental parameters on retention characteristics are. in most cases, easilv understood. In addition, there is an abundance of lit&aturedescribing optimization strategies in HPLC (9, IO), GC ( 1 1 , 12), and planar chromatography (13). ~
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Experiment I: Theoretical Modeling-Window Dlagram Optimization In HPLC The optimization of HPLC separations by varying the composition of the mobile phase often is complicated by changes in the order of peak elution. Because of the possibility of peak crossings, the resolution between every possible peak pair must be evaluated. Thus. for an n-com~onent kixt&e, this means that n!l(2(n- %!) response s;rfaces must be generated. The intersection of these multiple response surfaces defines a single, new response surface that represents the most difficult peak pair separation under any sei of experimental paramet&. ~ ; c hresponse surfaces are known as window diagrams (5). Berridge (9) has summarized the application of window diagramming to HPLC separations. Examples cited include one-, two., and three-parameter models involving the optimization of mobile phase pH, organic modifier content, column temperature, and the concentration of ion-pairing reagents. This experiment is based on an earlier study by Demine and Turoff (14) in which the reverse-phase seoaration ofseveral henzoic &ids was optimized byadjusting the mobile ohase pH. This svstem was chosen because the relationship between mobilebhase pH and retention time is well developed and because one-parameter window diagrams are easy to construct and interpret.
w r y
In a buffered mobile phase, organic weak acids will exist in both their conjugate weak acid (HA) and conjugate weak base (A-) forms, each of which will possess its own partition coefficient between the mobile and stationary phases. Because the equilibrium between HA and A- is rapid with resnect to the eauilibrium. ~artitionine of HA and A- across -. the mobile phaselstationary phase interface, the retention times of oreanic weak arids ( t a )will b e a weiehtedaveraaeof the i n d i v i h retention times of the conjugate weak acid (tHA)and the conjugate weak base ( t ~ - ) .Since the distrihution between HA and A- varies with pH, the retention time of an organic weak acid will be pH dependent. Deming and Turoff (14) derived a simple expression relating retention time and mobile phase pH: t,, t,Kr tR = (1) 1+Kr
.~~~~~~.
~
~
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+
where K is the ratio (KHB&A) of acid dissociation constants for the analyte (HA) and the buffer (HB), and r is the ratio ([B-]/[HB]) of the conjugate weak base and the conjugate weak acid concentrations of the buffer. Logarithmic values of r are simply offset pH values where log r = pH ~ K H BThe . parameters A HA, t ~ -and , K a r e used as adjustable ~ a r a m e t e r sfor fitting ea 1 to experimental retention data iecorded for a t least i i e e buffered mobile phases. Equation 1can then be used to predict the separation between any two components a t any $3.
bases predominate, which, because of their lesser affinity for the oreanic stationarv Dhase. results in shorter retention times.'klthough the r;&ntion times of all four components increase as the pH of the mobile phase decreases, the separation at pH 3.65 (Fig. la) is no better than the separation at DH 5.01 (Fie. lb) because the retention time of terephthalic k i d is affected more by the change in mobile phase acidity than the retention times of p-aminobenzoic acid and phydroxybenzoic acid. An optimum pH, however, should exist between these two pH extremes. The retention times in Table 1were fit to eq 1using HA, tA-,and K as adjustable parameters. Several different initial messes for the adiustable ~ a r a m e t e rwere s chosen t o ensure ;hat the final vaiues of t6e parameters were reproducible. Results of the curve-fitting are shown in Table 2. Values for HA and t ~ are - substantially different from those reported by Deming and Turoff (14) due to the use of different columns. Values for KHAare, with the exception of terephthalic acid, in good agreement with values reported by Deming and Turoff (14). As noted by Deming and Turoff (14), however,
Experimental Chromatogramswere obtained using a Varian model 5M)OHPLC equipped with a rheodyne 10-& injectionloop, a Varian model 2050 variable-wavelength UV detector operated at 254 nm, and a Varian model 4290 integrator. The column was a 10-cm MicroPak MCH-10 C18 bonded phase column. All separations were carried out at aflow rate of 2.0 mllmin. In general, experimental procedures followed Deming and Turoffs earlier work (14). Acetic acidlacetate buffers were prepared by diluting appropriate volumes of 1 M acetic acid and 1 M NaOH. Enough 1M NaCl was added to each buffer to ensure an essentially constant ionic strength of 0.6 M. The pH of each buffer was measured with a Markson model 611p pH meter. Values of r were calculated using a KHBfor acetic acid of 1.95 X 10V (14). The sample to be separated was a four-component mixture of benmir acid (HA), p-hydroxybenzoic acid (pH),p-aminohenzuic scrd (PAL and tere~hthalicacid (TI'). This mixture was prepared from k&dard solu~ionsof each acid. which. in turn, were . irebared . by liltcrinp: saturated solutions of each arid in distilled water Equation I was fit to the recentiondata using animplea nonlinear Ieast-squar~aprogram written hy Jurs (1.5). A window diagram was then c&trueted&d the optimum pH selected. ~~~
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Resuns Typical experimental results are shown in TaQe 1.At the more acidic pH's, the weak acids exist primarily in their conjugate weak acid form and, consequently, show a relatively high affinity for the organic stationary phase. At the more basic pH's, the negatively charged conjugate weak
Table 1.
Figure 1. HPLC ch:omatogam of me sample mixture at (a) pH 3.65 and (b) pH 5.01. Camponentsfor the mixtureare ( I ) terephthalicacid.(2)paminobenroic acid. (3) phydroxybenrolc add, and (4) benzolc acid.
Experimental Retention Tlmer for the Weak Aclds Table 2.
Buffer
r
pH
BA'
1 2 3 4 5
0.087 0.195 0.347 0.513 0.832 1.288 1.995
3.85 4.00 4.25 4.42 4.63 4.82 5.01
39.68 29.74 23.58 18.41 13.88 11.01 7.85
6 7
'AbtmvMIons given In tsxt.
Retention Time (mln) pHe PA' 13.36 11.57 10.08 8.43 7.04 5.60 4.08
9.10 8.54 8.07 7.12 6.45 5.42 4.11
TP. 18.10 7.73 4.45 2.92 1.84 1.33 0.93
(mln) tr- (rnin) &A
K
Slmplex Cune-FlHlng R e s u b for Retention Data BA'
PHs
PA'
TPa
53.07 2.78 4.25
15.02 0.75 1.58
9.61 0.67 0.88
1% 0.076 100.1
Abbrevlatlonsglvm In text. a Calculated uslng Kns = 1.95 X 10-5.
'Lnerature values repotted by Dsmlng end Turoft (l*).
Volume 68 Number 2
February 1991
163
values of ÿ HA and K for terephthalic acid are subject to substantial uncertainty because all of the experimental data is collected under conditions where the conjugate weak base is the predominate species. Figure 2 shows that the theoretical curves calculated using eq 1 provide a good fit to the retention data. Although it is clear from Figure 2 that there are regions of mobile phase pH where a separation is possible, the optimum pH is not directly evident. A window diagram (Fig. 3) can he constructed for this se~arationbv drawine resoonse surfaces for each of the six possible peak pairs using the separation factor (9) as the response. The separation factor (S) is defined as
-
where t~ and t . are the retention times of the two comoonents being compared, chosen such that t b is always the later elutine"comoonent. Values of S are thus alwavs ereater than . or equal to zero, with a value of zero indicating ;hat the two components elute simultaneously. Each of the six curves in Figure 3 is a response surface for the separation of a particular peak pair as a function of
' b, 45
Table 9. Comparlm of Experimental and Calculated Retention Tllll88 at pH 4.11
40
Retention Time (min)
mobile obase DH. The intersection of these individual response surfaces, which is shown by the darkened line, is the overall resoonse surface, defining the oeak oair that limits the sepa&ion of the mixture for a& mobile phase pH. Thus, for pH's less than 3.54 or greater than 4.09, the separation of the mixture is limited by the resolution between p aminoheuzoic acid andp-hydroxybenzoic acid. For pH's between 3.54 and 3.86 the separation of the mixture is limited by the resolution between p-hydroxybenzoic acid and terephthalic acid. Finally, for pH's between 3.86 and 4.09 the separation is limited by the resolution between p-aminobenzoic acid and terephthalic acid. Each peak in the overall response surface represents a reeional ootimum orovidine the best overall. se~aration for a . limited range lor "windbw3').In this case, regional optima are found at pH's 3.50,3.86,4.09, and 5.10, with the best overall separation occurring at the mobile phase pH corresponding to the top of the tallest window. From Figure 3, the best separation occurs at a pH of 3.50 (S= 0.20). However, at this pH the retention time for benzoic acid will be greater than 40 min. The next best separation occurs at a pH of 4.09 (S= 0.14). The resulting separation is shown in Figure 4 (actual pH of 4.11). Experimental and calculated retention times are compared in Table 3. Al-
,,
..
weak Acida
tea,p (min)
t ~ ~ l i l ~
BA PH
26.32 10.70
27.10 10.97
PA
8.16 5.96
8.31 6.04
TP
imln)b
Abbreviations glven In text. a CBIcuIatBd uslng eq 1 and parsmeters from Table 2.
15
10 5
\
0
Flgura 2. Retention time vs. DH f a the ComDonents ot the samde mixture. P&S are experlmentsl retention data f a (.j terephlhalic acid, ix) pamino. benzolc acid. (A) phydror,+enzoic acid, and (t) benzoic acld. Solid curves are theoretical retention times.
Separation Factor
Figwe 3. Window diagam t w ihe sample mixture. individual curves are responseslrrtaces for the separation between: (a) benzoic acid and phydroxybanmlc acid, (b) benzoic acid and paminobenzoicacid. (c) benzolc acld and terepmhalic add. (d) phydmxybenroic acid and paminobenzoic acid. (e) p hydroxybenzolcacid and terephthalic acid, and (f) paminobsnzoic acld and terephmslic acid.
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Journal of Chemical Education
0
20 TIME (MiN)
10
io
Figure 4. Optimum HPLC chmmatogram of the sample mixture at pH 4.11. Peak identification as in Figure 1.
though all four experimental retention times are shorter than the calculated retention times, agreement is fairly good with errors of 1-3%. Experlrnent 11: Ernplrlcal Modellng-Overlapping Resolution Maps In HPLC The optimization of the mobile phase pH in experiment I resulted in a nearly base-line separation of the four-component mixture. The necessity of working a t a relatively acidic pH, however, resulted in a fairly long separation time. The analysis time can be shortened by increasing the solvent strength of the mohile phase by adding methanol, acetonitrile, and/or tetrahydrofuran as organic modifiers to the buffered aaueous mobile ohase. In the adsence of a theoretical model describing the effect of oreanic modifiers on retention times, least-sauares fitting empirical polynomial model can be used to predict of retention times and to generate the appropriate response surface. Obviously the results will he limited by the suitahilitv of the empirical model. Since the optimzation of two b i t h e window diagram technique will result in a very complex three-dimensional response surface with many regional optima, individual response surfaces for each peak pair are simply divided into regions of acceptable and unacceptable separations. Such "maps:, for each peak pair, can then he overlaid to establish common conditions for achievine the desired separation. In this exoeriment. the o~timized separation t'rom experiment I is furiher optimizedwith the goal of shortening the analysis time toapproximately 6 min.
an
The empirical model describing the response surface for any peak pair must include all possible terms describing the effect of the individual modifiers on the separation, as well as all possible organic modifier interactions. Thus, for a system in which three organic modifiers are considered, an appropriate empirical model (9) is
strength, allowing the determination of the coefficients a,, a., and at. The three experiments along the sides of the triangle involve binary mixtures of the organic modifier/ buffer mobile phases, allowing the determination of a, amt, and sat. The final experiment is a ternary mixture of the organic modifierlhuffer mohile phases, allowing the deterOnce the coefficients have been determination of a., mined, theoretical separation factors can be calculated for any possible combination of the three organic modifierbuffer mobile phases. In this way maps of acceptable and unacceptahle mohile phases can he constructed. Further details about the use of overlapping resolution maps can be found in the text by Berridge (9). Experimental Chromatograms were obtained using the same system described in experiment I, with all separations carried out at a flow rate of 2.0 mL/min. The sample mixture and standards prepared in experiment I also were used. Isocratic mixtures of methanol, acetonitrile, or tetrahydrofuran and the optimized, buffered aqueous mobile phase determined in experiment I (pH 4.11) were run toestablish single organic modified huffer mixtures with analysis times of approximately 6 min far the elution of the last component.The binary and ternary combinations of the single arganc modifierbuffermixtures, described in Figure 5, were then run. In each case, after running the mixture,the retention time for each component was determined using the standard solutions. Separation factors were calculated for all peak pairs for all seven mobile phases. The coefficients were calculated and a response surface was generated using a program written by Berridge (9).
Results lsocratic mixtures of 208 methanol, 169 acetonitrile, and 109 tetrahydrofuran, with the pH 4.11 aqueous buffer from experiment I, were chosen for the vertices of the triangular
where S is the response (seoaration factor); and X,, X,, and Xt are, respectively, the volume fractions of the binary methanollhuffer, acetonitrilelhuffer, and tetrahydrofuranl huffer mohile phases. The coefficients in eq 3 are defined (9) as:
a,
= 27S,,,
- 12(S,, + S,, + S,) + 3(S, + Sa + S,)
(10)
where S is the response for the appropriate single, binary, or ternary organic iodifierlhuffer mobile phase.The optimization of a three-parameter system in which the rela$onship
x,+x,+xt=l always holds, can be shown graphically on triangular coordinates. Solving eqs 6 1 0 requires a minimum of seven experiments that are placed on the triangular coordinates using the simplex lattice design shown in Figure 5 (9). The experiments a t the three vertices involve single organic modifier1 huffer mohile phases of approximately equal solvent
A
0
100
0
T
0
0
100
MA
50
50
0
MT
50
0
50
AT
0
50
50
33.3 33.3
33.3
MAT
Flgure 5. Simplex latlice design for determining optimum ternary mobile phase wmpOsBion. Experlmemai mobile phase wmpositions (volumepercents)are listed in table. M = methanol, A = acetonitrile,and T = teIrahydmhmn. Volume 68 Number 2 February 1991
165
plot. As shown in Figure 6, these single organic modifier1 buffer mobile phases do not provide an adequate separation between the components of the mixture. Retention times for the weak acids for all seven mobile phases used in this experiment are shown in Table 4. Based on these retention times, only the separations between p-
Figure 8. HPLC chmmalDgram for single aganic modifier/buffer mobile phases: (a) 20% melhanol/buffer. (b) 16% aceionllrile/buffer, and (c) 10% tehahydrohlranmuffer.Peak identification as in Figure 1.
Table 4.
Experimental Retention Times lor the Weak Adds
Mobile P h e S
BAb
M A T MA MT AT MAT
5.84 8.18 5.01 5.78 4.76 4.97 4.90
Reternion Time (min) pHa PAb 2.62 2.67 3.9 1 2.59 3.30 3.21 3.05
TPb
1.88 2.21 2.05 1.98 1.83 1.92 1.84
1.47 1.23 1.54 1.30 1.36 1.29 1.28
aminohenzoic acid and terephthalic acid, p-aminobenzoic acid andp-hydroxybenzoic acid, andp-hydroxybenzoic acid and benzoic acid need to be considered in determinine the optimum mobile phase composition. Separation factors, calculated usine ea 2 and the data from Table 4. for these three peak pairs &e shown in Table 5. Resolution maps for each of the three peak pairs included in Table 5 are shown in Figures 7a-c. Based on the chromatoerams from the seven initial experiments, separation factors greater than or equal to 0.20 prbvide acceptable separations. Overlavina these three resolution maps defines the range of mobile-phasecompositions where an adequate separation will be feasible (Fig. 7d). The separation of the mixture using amobile phase from this region (55%acetonitrile/ huffer, 30% tetrahydrofuranibuffer, 15% methanolibuffer) is shown in Figure 8. All four components are separated with nearly base-line resolution within the desired analysis time. Experimental and calculated separation factors are compared in Table 6. The good agreement between these values suggests that the empirical model used in this experiment provides a reasonable picture of the response surface for this separation.
T h e optimization of chromatographic separations through the use of theoretical or empirical models of the response surface has several advantages. If the model adeouatelv describes the resvonse of the svstem. a com~lete picture of the resulting response surface is obtained. This allows not only the identification of the global optimum but also the identification of regional optima, which may, due to other considerations, provide a more desirable set of analytical operating conditions. In addition, relatively few experiments are needed to describe the response surface (a minimum of three for the theoretical model used in experiment I, a minimum of seven for the empirical model used in experiment 11). Problems are encountered with modeling the response surface when more than two independent parameters are included in the model. For example, a model with three
dAbbre~iation9 given in Figure 5. Abbreviatim given In text.
Table 5.
SeDaratlon Factors lor Overlawlna Peak Palm
Mobile W e a M A T MA MT AT MAT
TP/PAb
PA/PHb
PH/BAb
0.122 0.285 0.142 0.207 0.147 0.200 0.179
0.164 0.094 0.312 0.132 0.297 0.251 0.247
0.381 0.397 0.123 0.383 0.191 0.215 0.233
Abbreviatim given in Figure 5. bAbbreviatimgiven in text.
Table 6.
Comparison ot Exprlmental and Calculated Separation Factors lor Chromatogram In Flgure 8
Peak PaiP TPIPA PAIPH PHIBA
SXP 0.209 0.229 0.259
Abbreulations glven in text. CBic~IatBdusing eqs 3-10 sM dam horn Table 5.
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Journal of Chemical Educatlon
%k5
0.209 0.220 0.259
Figwe 7. Resolution maps for (a) terephthallc acid and paminobenzoie acid. (b) paminobenzoic acid and phydroxybenzoic add, and ( 0 ) phydroxybenzoic acid and benzolc acid. The final overlapping resolution map is shown in (d). Key: (m) unacceptableseparation (S < 0.2): (O)acceplatle separation (S 2 0.2).
independent parameters will generate a 4-dimensional resnonse surface. which cannot be directlv visualized. Findine k e optimum response, in this case, wili require a n efficient searchine aleorithm. One orthemore powerful available search methods is the seauential simolex nrocedure. This is an efficient "hill-climbing" method that Lses simple rules to ensure that each new experiment will produce a better response. There are numerous examples of the application of the simplex method t o the optimization of HPLC and GC separations, many of which are included in the bibliographies published by Bayne and Rubin (2) and Berridge (9). This experiment is based on a n earlier study by Morgan and Deming (12) in which the GC separation of octane isomers was o~timizedhv adiustine the column temDerature . and carrier gas flow rate. A GC separation was selected over a HPLC senaratton because the more raoid eau~ltbrationof the GC & changes in instrumental pa&net& allows the optimization of the separation in a single Iab period.
.
A simplex is a n n
+
-
+
1dimensional geometric figure on a n n 1 dimensional reawnse surface, where n is the number of independent para&eters being optimized. Thus, for a twoparameter system, the simplex is a triangle. Each vertex of the simplex represents the response for a set of parameter values. The simplex algorithm is designed to move the simplex away from regions of poor response, toward regions of optimum response. This is done by rejecting the vertex with the poorest response and replacing i t with a new vertex
chosen by following a simple set of rules. Further details regarding the mathematics of the simplex method are covered elsewhere (2,3,16). Experimental
Chromarograms were obtained using a Varian model 3300 GC equipped witha flame ionizarion detector and a stripchart recorder. The column was a 2-m by 'I-in.-0.d. stainless steel column containing 10%OV-101 on Chromosorb W-HP(801100mesh). The carrier gas was NI. The sample to be separated was a mixture of three octane isomers in methanol: 2,2,4-trimethylpentane, 2,3,4-trimethylpentane, and octane. All sample injections were made with a 10-WLsyringe. The only parameters varied during the optimization of the separation were the column temperature and carrier gas flow rates. The injector temperature was held at 250 'C, and the detector temperature was held at 300 T.All samples were 1.0-WLinjections. Column temperatures and flow rates were taken from the instrument settings. Simplex optimization was done using step sizes of 10 OC for the column temperature and 2.0 mL/min for the flow rate. The GC was allowed to equilibrate for at least 10min following the adjustment of parameters. Results Typical experimental results for the simplex optimization are shown in Table 7. The chromatographic response funcTable 7. Slrnvlex Ootlrnlratlon Resulls vertex Number
Column Temperature (OC)
Flaw Rate (mLlmin)
COF
~lgure8. optimum nPLc chmmamgam of me aemple mldurs obtalned wlth a 55% acwtonlblldbuffer.30% Fbure 9. GC chromato(~ramsof sam~femlmre at fa1vertex I. fbl vertex 2. fcl vertex 3; and (dj -~ teDahydrofuran/buffer.an0 15% nwthsnollbuner mobile optimum ssparatla at vertex 9. Components ol the mlnare are (1) 2.2,hlr metnylpentane. 12)2.3.6 Dlmelhylpsntaoe. and (3)octane. The Inttlal peak ins chromatogramsla tne solvent methanol. phew. Peak demlffcatlwas In Flpvrs 1 ~
Volume 68 Number 2 Februaw 1991
167
tion ( 9 , I O ) was used as the system response. For this experiment, the COF was defined as
.OF
=
2 h(2)
(12)
i-l
where n is the number of adjacent peak pairs, R i is the resolution of the ith peak pair, and R i d is the desired resolution, which was set t o 2.0 to ensure base-line resolution. The COF function is constrained such that when R i is greater than R i d , R i is set equal to R i d . Consequently, poor separations result in more negative values for the COF, while a COF of zero indicates a complete base-line separation of the mixture. The initial simnlex (vertices 1-3) was selected from a range of column temperatures and flow rates known to yield noor senarations. The desired hase-line senaration was then achieved after running only six additional experiments. Figure 9 shows the chromatograms for the initial simplex and for the optimized separation. Note to instructors
These three experiments can be run over a three-week period. In the author's lab, each student is responsible for gathering data for experiment I on one or two buffers during the first week. At the end of the week the class meets to pool data, to do the curve-fitting, and t o construct the window diagram. The optimum buffer is then prepared and analyzed as a group. Experiment I1 is started during the second laboratory period. As a class, the appropriate single organic modifierbuffer mobile phases are selected. Each student is
168
Journal of Chemical Education
then responsible for gathering data on a binary or ternary oreanic modifierbuffer mobile phase during the second w'ek. At the beginning of the third week, the class meets again to construct and interpret the resolution maps. Each student is then responsible for preparing a mobile phase from the optimum region for analysis. Experiment 111 requires relatively little time (no vertex requires more than 5 min of analysis time) and is run while the students are working on either experiment I or 11. Acknowledgment
Partial support for this work was provided by a DePauw Universitv Course Develonment Grant and a National Science ~o&dation-collegeAScience Instrumentation Grant (#CSI-8750039). Literature Cited
4. L&D. E.Anal. Chim.Acto 1969.46, 193-206. 5. Leub,R. J.: Purnell, J.H. A n d C h e m . 1976.48.799-803. 6. Shavers, C. L.: Psrsona, M . L.; Derning, S. N . J. Chsm.Educ. 1976.56.301-309. 7 . Stieg, S. J. Chem. Edue. 1986,63,547-548. 8. Sangsilia, 8.;Labinaz, G.; Poland, J. S.;vsnLwn, G. W .J Cham.Edue. 1989,66,351-
