Instrumentation
J. L. Glajch J. J. Kirkland E.I. du Pont de Nemours and Company Central Research and Development Department Experimental Station Wilmington, Del. 19898
Optimization of Selectivity in Liquid Chromatography Mobile phase, stationary phase, and pH and other ionic effects are most useful in optimizing an LC separation Use of modern liquid chromatogra phy (LC) has increased so dramatical ly in the past decade that in many lab oratories it is now a routine method for solving many practical analytical and preparative problems. Along with this surge in application, advances have been made in the fundamental understanding of various LC separa tion mechanisms. Despite this, most routine LC analyses are still being de veloped in a nonsystematic manner, and very often the results are not as good as might be expected from this powerful technique. Optimizing the separation is an especially important goal for any rou tine LC method. Although one should . not attempt to optimize all separa tions—such as one-time-only samples or separations that are trivial to per form—the advantages of an optimum separation for quality control or other repetitive analyses are clear. Increased accuracy and precision, as well as sav ings in analysis time, often justify the effort spent in developing optimum LC separating conditions. In LC, as with any technique, the primary question is, What should be optimized? Generally, separation quality is the most useful criterion for all components in a mixture or for cer tain components of interest in the sample. Often of interest is a related 0003-2700/83/0351-319A$01.50/0 © 1983 American Chemical Society
optimization factor—separation time—especially when a large number of samples is to be analyzed. Sampleloading capacity for the system also can be important in preparative work, and detectability is especially crucial in trace analysis. However, these latter two factors are of less general interest and, therefore, will not be discussed in this treatment.
Effects Influencing Separation There are two major effects that in fluence the LC separation mechanism: physical and chemical. Physical ef fects relate to factors such as column efficiency, generally measured by plate count, N, and column capacity, described by the capacity factor, k'{l). The well-known resolution equation describes these effects:
*-^·(ΐ&)-*-» efficiency factor
capacity factor
«>
selectivity factor
where, JV is the column plate count calculated by (ί«/σ) 2 , k' is the capaci ty factor calculated by (ÎR — t())/to, a = k'2/k'i for peaks 1 and 2, σ is the standard deviation of the peak, tu is
the retention time of the solute peak, and to is the retention time of an unretained peak. Both the efficiency and capacity factors of the resolution ex pression in Equation 1 are well under stood from a theoretical standpoint (1). With respect to physical effects, well-packed, small-particle (3-10 μιη) columns operated to give solute k' val ues of about 1-10 (1 ) provide excellent resolution. Chemical effects, as described by a, the selectivity factor in Equation 1, are not as well understood, nor are they as predictable as physical effects. It is usually not possible from basic principles to predict the influence of mobile-phase composition or tempera ture on the relative retention charac teristics of different compounds. How ever, changes in chemical selectivity are the single most important variable leading to adequate separations, as predicted in Equation 1. Chemical Selectivity Effects A large number of operating vari ables can be used to change the chemi cal selectivity in an LC system. Al though not inclusive, the five most useful variables are mobile-phase composition, stationary-phase compo sition, temperature, pH or other ionic effects, and secondary chemical equi-
ANALYTICAL CHEMISTRY, VOL.. 55, NO. 2, FEBRUARY 1983 · 319 A
(a)
(b)
1 (1.0.0)
4 (0.5, 0.5, 0)
8
pH
5 (0, 0.5. 0.5)
X
7
χ 7 (0.333, 0.333, 0.333) 6
2 > (0.1,0)
6 (0.5, 0, 0.5)
3 (0. 0, 1)
30
35
40
45
50
Temperature
Figure 1. (a) Mixture design experiments used in mobile-phase optimization strategy, (b) Factorial design experiments used for examining temperature and pH effects
libria. These five factors are listed roughly in the order of general appli cability to all LC systems, although in certain specific instances the latter two parameters can be the most im portant in producing the desired sepa ration. Effects of mobile phase on chemical selectivity have been well documented for reversed-phase {2-5), normal bonded-phase (6"), and adsorption (7, 8) chromatographic systems. The solvophobic theory of Horvath (9) strongly suggests that mobile-phase effects are the most important in the separation mechanism of reversedphase chromatography. The systemat ic approaches initiated by the solvent selectivity triangle concept (10) have
been instrumental in the development of optimization strategies based on mobile-phase composition. Stationary-phase effects are also important in LC separation selectivi ty, as exhibited by the development of bonded-phase packings with a variety of functional groups, especially for reversed-phase separations. Recent studies (//, 12) have adequately dem onstrated these stationary-phase ef fects. However, the number of station ary phases needed in LC is relatively small compared to those used in gas chromatography, due in part to the fact that selectivity effects provided by changing the mobile phase are not significant in gas chromatography. Changes in temperature have not
been used extensively to change selec tivity in LC. However, Snyder {13) and others (14) have pointed out the potential for changing separation se lectivity by varying temperature, pri marily because of effects on the extent of ionization with certain molecules. Optimization of pH and other ionic ef fects has also been carried out by sim ple statistical approaches and shown to be quite useful in specific analyses (15). Secondary chemical equilibrium effects have also received increased at tention (/6'). This approach usually involves addition of a small amount of a particular selective agent into the mobile phase to alter the chemical equilibria that exist for solutes in the mobile and stationary phases.
Proton Acceptor
20 '
MTBE 1.5
MeOH
Rs 1.0
CH?CI?
mm
0.5
CHCI3 Proton Donor
χ
„
Dipole Interaction Reversed-Phase Normal Phase
0.0 0
5 k'
10
Figure 2. Resolution of a pair of peaks as a function of k1. Plate count, N, is 10 000 and « = 1.04
Figure 3. Preferred modifying solvents for use in reversedand normal-phase LC optimization. Xe, Xd, and Xn are selec tivity effects for proton acceptor, proton donor, and dipole in teraction, respectively. Adapted from Reference 5, with per mission
320 A · ANALYTICAL CHEMISTRY. VOL. 55. NO. 2, FEBRUARY 1983
Optimization Strategies 1-2
fls
> 1.5
fls
> 1.5
6-7
2-3
fis
> 1.5 fis
3-4
fis
To optimize any LC system, three factors must first be specified: 1) the type of variables important in effecting the separation, 2) the optimization strategy that is the most appropriate to those variables, and 3) an accurate method to measure the performance of the separation for the quantitative comparison of different separation approaches. The chemical parameters described above that are the most important in LC can be conveniently grouped into two categories— related variables and discrete variables. Related variables are those that by their nature directly affect each other. For example, mobile-phase composition must total 100% for all components at all times, so individual mobile-phase solvents are related variables. A similar situation exists for stationary-phase composition.
5-6
> 1 •5s
7-8
> 15
fls
> 1.5
8-9
4-5
fls > 1.5
fls
> 1.5
Figure 4. Resolution maps for all eight peak pairs in a mixture of substituted naphthalenes. White areas represent solvent mixtures that will result in Rs > 1.5. Reprinted with permission from Reference 5
.Optimum , 2.5
f MeOH
ACN
0.0
THF
Figure 5. Overlapping resolution map (ORM) obtained from resolution maps in Figure 4 322 A · ANALYTICAL CHEMISTRY, VOL. 55, NO. 2, FEBRUARY 1983
By contrast, temperature, pH, and secondary equilibrium effects can be considered discrete variables since they have little direct effect on each other or on the other mobile-phase or stationary-phase components. It is possible, for example, to carry out LC separations in a temperature range of 30-70° C and an apparent pH range of 3-8, with all possible combinations of these two variables. On the other hand, it is not possible to carry out separations with methanol ranging from 0-100% with acetonitrile also simultaneously ranging from 0-100% in the mobile phase. Definition of these two types of variables provides two distinct optimization strategies of experimental design. The mixture design statistical approach for mobile-phase optimization is illustrated in Figure la. This approach is well-known in the statistical literature (77). Seven experiments are employed to fit experimental retention (k') data to a second-order polynomial equation with respect to the three mobile-phase modifiers. In the case of reversed-phase LC, the mobile-phase carrier, water, is modified with methanol, acetonitrile, and tetrahydrofuran (5). Figure l b illustrates a factorial design for combined temperature and pH effects in LC that employs nine experiments to fit the k' data to an equivalent secondorder equation. It is also possible to combine the mixture design and factorial approaches for both related and discrete variables such as mobilephase composition, pH, and secondary equilibrium effects. However, in many cases, adequate separation selectivity can be obtained by utilizing only organic mobile-phase modifier effects. This approach is usually simpler and more easily predicted than the other chemical effects altering selectivity.
Optimization in LC differs from ap proaches used for other analytical methods in that data are taken at specified values of the key variables, fitted to a polynomial equation (gen erally second-order), and interpolated to search for an optimum response re gion. Such a simple method is feasible since the response of LC separations to variable changes is usually continu ous and regular. Other analytical tech niques (e.g., atomic spectroscopy) rely on different optimization routines (e.g., simplex algorithms) to handle
data that are less regular in form. Perhaps the most crucial step in op timization is deciding upon a measure of system performance. Various meth ods have been proposed to assign a single value of separation quality to a chromatogram (18). However, these methods have the inherent disadvan tage that much of the chromatograph ic information is either lost or ob scured. An extension of the "windowdiagram" approach (19) based on min imum separation factor plots has been used (20-22) to provide information
MeOH
C-8 THF
ACN
Previous use of a values to measure separation quality is probably due, in part, to the simplicity of having to measure only k' (or corrected reten tion time) values, rather than having to determine both the retention time and peak widths that are required for calculating accurate resolution values (see Equation 1). However, measure ment of Rs can be simplified by using the expression (23)
MeOH
MeOH
CN ACN
ACN
. THF
on separation performance. However, this approach can be limited since in formation based on a (at constant col umn plate count) does not take into account the important influence of the capacity factor k' values. We prefer to use the resolution function (Rs) as a separation perfor mance criterion, since this is directly related to the actual separation re quired. A representation of the differ ence in performance information pro vided by a and Rs is shown in Figure 2. A column of plate count = 10 000 and α = 1.04 for two components would give an Rs = 1.8 at k' = 10. However, the same a value would pro vide only Rs = 1.0 at k' = 1. Thus, practical separation performance is in adequately described by a values alone, since the ability to separate one component from another is a function of how long these compounds are re tained on the column as measured by capacity factor k' values, and peak sharpness as measured by column plate count values, N.
THF
Figure 6. Experimental design for combined mobile-phase and stationary-phase optimization
Rs =
[N^/2][(k2-kl)/ (2 + ky + k2)\
(2)
Equation 2 can be rigorously derived from the fundamental resolution ex pression (Equation 1) by making the reasonable first-order assumption of constant plate count for all peaks in an LC chromatogram (1 ) . We current ly use Equation 2 for all our isocratic mobile-phase optimization calcula tions. Once the separation variables, opti mization strategy, and system perfor mance criteria have been selected, one can quickly define the proper set of experimental conditions necessary for an optimum separation. Examples of various LC optimization approaches will now be described to illustrate the potential for each method.
Minimum Rs Calculated—1.1 Actual—1.1
Mobile-Phase Effects
0.0
3.5
7.0
10.5
14.0 Time (min)
17.5
21.0
24.5
28.0
Figure 7. Isocratic separation of 20 PTH-amino acids. Experimental details in Reference 26 326 A · ANALYTICAL CHEMISTRY, VOL. 55, NO. 2, FEBRUARY 1983
Several studies have shown that op timization of mobile-phase selectivity is probably the single most useful ef fect in LC. One of the first systematic studies of mobile-phase optimization was illustrated by the reversed-phase separation of nine substituted naph thalenes on a C-8 hydrocarbon bonded-phase column (5). To obtain
useful selectivity changes leading to improved resolution, modifiers of the carrier mobile-phase solvent were se lected using the Snyder solvent selec tivity triangle approach (10). This or ganization of solvent selectivity de scribes the major effects of proton ac ceptor, proton donor, and dipole inter actions of solvents with compounds to be separated. Preferred modifying sol vents for both reversed- and normal bonded-phase systems are shown in Figure 3. In reversed-phase LC, the carrier solvent is water, while ra-hexane or 1,1,2-trifluorotrichloroethane (FC-113) (24) is the preferred carrier solvent in normal-phase systems. Methanol, acetonitrile, and tetrahydrofuran are effective proton acceptor, proton donor, and dipole solvents, re spectively, for reversed-phase separa tions, while methyl tert- butyl ether, chloroform, and methylene chloride are effective counterparts in normal bonded-phase LC. The experimental design used to se lect the optimum solvent system (Fig ure la) is based on the report of Snee (25). Retention (k') values are mea sured for each compound in the mix ture using the seven mobile-phase sol vent mixtures depicted in Figure la. These data are then fitted to a secondorder polynomial to obtain retention or k' value maps for each solute. Using Equation 2, the resolution of each peak pair in the system also can be mapped in this way. Once the resolu tion maps are obtained, the solvent compositions that allow a certain min imum resolution can be determined for each peak pair. Figure 4 shows this for eight peak pairs of Reference 5, where the white areas in each small triangle represent solvent composi tions that will resolve the particular peak pair to a resolution of at least 1.50. These resolution maps of all con straining peak pairs are then overlaid and the resulting overlapping resolu tion map (ORM) can be used to define the optimum solvent mixture (or sol vent mixture region) to obtain a cer tain minimum resolution for all peak pairs in the mixture, as shown in Fig ure 5. In this case, the optimum mo bile phase corresponding to the χ in the figure is 32% acetonitrile, 16% tetrahydrofuran, and 52% water. This produces a minimum resolution of 2.5 for all peaks in the mixture.
Stationary-Phase Effects
Optimization of bonded stationary phases in LC can be carried out in a manner similar to that for mobile phases, since both phases involve re lated or dependent variables (i.e., the sum of all components of a stationaryphase system must also total 100%). Differences in selectivity are usually
Phenylacetic Acid
I
Cinnamic Acid
ω Ε i-
e ο
"c ω Φ
DC
Figure 8. Retention time maps for phenylacetic acid and cinnamic acid as a func tion of pH and ion-interaction reagent (IIR). Adapted from Reference 2 1 , with per mission
not as great for the common chemical ly bonded stationary phases as for mo bile phases. However, the experimen tal design just described can be used as well for stationary phases in LC col umns to provide selectivity changes over and above those possible with only mobile-phase optimization. An example of this approach involves the use of both mobile- and stationaryphase effects for optimizing the isocratic separation of the 20 common phenylthiohydantoin (PTH) deriva tives of amino acids (26). The experi mental design uses the strategy shown
328 A · ANALYTICAL CHEMISTRY, VOL. 55, NO. 2, FEBRUARY 1983
in Figure 6 to examine the selectivity effects of three mobile-phase modifi ers in an acidic (pH = 2) aqueous solu tion together with three different sta tionary bonded phases. A total of 21 experiments (seven mobile phases for each of the three stationary phases) is required. The calculated optimum col umn and mobile-phase composition predicted by the ORM technique pro duced the chromatogram in Figure 7. This separation was completed in 22 min with a minimum resolution of 1.1 for all components, using a single mo bile phase. This separation time com-
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The use of pH and other ionic effects can be quite helpful in modifying separation selectivity, particularly in reversed-phase systems. Optimized separation of a nine-component mixture of weak acids, weak bases, and zwitterionic compounds has been demonstrated by this approach (21). In this case, the pH and concentration of octylamine hydrochloride ion-interaction agent were used as discrete variables, and a four-level two-factor (42) experimental design was employed to specify 16 mobile-phase compositions. These consisted of all combinations of four pH values (3.6, 4.4, 5.2, and 6.0) and four concentrations of octylamine hydrochloride (0, 1.5, 3.0, and 5.0 mM). From separations with these mobile phases, retention time maps were obtained for all nine species as a function of both pH and concentration of octylamine hydrochloride. Two of these maps are shown in Figure 8. A window diagram was used to determine the optimum set of experimental conditions. The resulting optimum mobile phase separated all nine components in 45 min at pH 3.7 and 0.75 mM octylamine hydrochloride. A similar experimental design has been used to examine the effects of mobile-phase strength, pH, concentration of a phosphate buffer, and concentration of camphorsulfonic acid ion-pairing agent for the separation of four alkaloids (15). Other Effects
Although not as generally applicable, changes in temperature also have been used to achieve selectivity optimization (13). Changes in relative retention values are often observed for ionizable compounds. Temperature optimization also can be combined with other effects, such as mobilephase and stationary-phase characteristics as well as pH effects, for more comprehensive optimization possibilities. Use of secondary chemical equilibrium (16) to affect selectivity could also be utilized in optimization schemes. Conclusion
Optimization in LC can be very powerful if care is taken to choose the proper parameters for change, and if a valid experimental design is selected. (continued on p. 336 A)
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332 A . ANALYTICAL CHEMISTRY, VOL. 55, NO. 2. FEBRUARY 1983
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(1) Snyder, L. R.; Kirkland, J. J. "An Introduction to Modern Liquid Chromatography," 2nd éd.; Wiley: New York, 1979. (2) Schoenmakers, P. J.; Billiet, Η. Α. Η.; deGalan, L.J. Chromatogr. 1979, 185, 179. (3) Tanaka, N.; Goodell, N.; Karger, B. L. J. Chromatogr. 1978,158, 233. (4) Bakalyar, S. R.; Mcllwrick, R.; Roggendorf, E. J. Chromatogr. 1977,142, 353. (5) Glajch, J. L.; Kirkland, J. J.; Squire, K. M.; Minor, J. M. J. Chromatogr. 1980, 199, 57.
(6) Antle, P. E. Chromatographia 1982, 75(5), 277. (7) Snyder, L. R.; Glajch, J. L.; Kirkland, J. J. J. Chromatogr. 1982,218, 299. (8) Glajch, J. L.; Kirkland, J. J.; Snyder, L. R. J. Chromatogr. 1982,238, 269. (9) Melander, W. R.; Horvath, C. In "High-Performance Liquid Chromatog raphy, Advances and Perspectives," Vol. 2; Academic Press: New York, 1980. (10) Snyder, L. R. J. Chromatogr. Sci. 1978 16 223 (11) Hube'r, j ' . F. K.; Hirz, R.; Markl, P. 5th International Symposium on Column Liquid Chromatography, Avignon, France, 1981; Paper C20. (12) Goldberg, A. P. Anal. Chem. 1982,54, 342. (13) Gant, J. R.; Dolan, J. W.; Snyder, L. R. J. Chromatogr. 1979,185, 153. (14) Hammers, W. E.; Theeuwes, A. G. M.; Brederode, W. C ; DeLigny, C. L. J. Chromatogr. 1982,234,321. (15) Lindberg, W.; Johansson, E.; Johans son, K. J. Chromatogr. 1981,2/7,201. (16) Karger, B. L. In "High-Performance Liquid Chromatography, Advances and Perspectives," Vol. 1; Academic Press: New York, 1980. (17) Cornell, J. A. "Experiments with Mix tures: Design Models and the Analysis of Mixture Data"; Wiley: New York, 1981. (18) Morgan, S. L.; Deming, S. N. Sep. Purif. Methods, 1976,5, 333. ( 19) Laub, R. J.; Purnell, J. H. J. Chroma togr. 1975,7/2,71. (20) Deming, S. N.; Turoff, M. L. H. Anal. Chem. 1978,50,546. (21) Sachok, B.; Kong, R. C ; Deming, S. N. J. Chromatogr. 1980, 799, 307, 317. (22) Hodgin, J. C ; Hathaway, C. D.; How ard, P. Y. 1980 Pittsburgh Conference on Analytical Chemistry and Applied Spec troscopy; Paper No. 307. (23) Said, A. S. "Theory and Mathematics of Chromatography"; Dr. Alfred Huthig Verlag: Heidelberg, 1981; p. 162. (24) Glajch, J. L.; Kirkland, J. J.; Schindel, W. G. Anal. Chem. 1982,54, 1276. (25) Snee, R. D. Chemtech 1979,9,702. (26) Glajch, J. L.; Kirkland, J. J., in prepa ration.
J. Jack Kirkland (left) received AB and MS degrees in chemistry from Emory University and a PhD in ana lytical chemistry from the University of Virginia in 1953. Since that time he has been with Du Pont, where he is currently engaged in basic research in separation science, including GC, HPLC, and field flow fractionation.
Joseph Glajch (right) received his AB in chemistry at Cornell and a PhD in analytical chemistry at the Universi ty of Georgia, the latter under the di rection of L. B. Rogers. He joined Du Pont in 1978, and is currently working on GC, LC, and instrumental automation in the Process Research and Catalysis group.
Physical effects in L C , such a s c o l u m n efficiency, a r e p r e d i c t e d well by t h e o ry; however, chemical selectivity effects a r e less well u n d e r s t o o d . Mobile phase, stationary phase, p H and other ionic effects, temperature, a n d secondary chemical selectivity in L C a r e all c a n d i d a t e s for o p t i m i z a t i o n proced u r e s , b u t t h e first t h r e e a r e generally m o r e useful in o b t a i n i n g t h e d e s i r e d s e p a r a t i o n . B o t h related a n d discrete variables c a n be o p t i m i z e d , a l t h o u g h different e x p e r i m e n t a l designs a r e req u i r e d . A m i x t u r e design statistical t e c h n i q u e is m o r e a p p r o p r i a t e for related variables, while a factorial d e sign is used for discrete variables. Resolution is generally preferred for meas u r i n g s y s t e m p e r f o r m a n c e , a n d overlapping resolution m a p s can be used to determine the optimum separation s y s t e m . A practical a d v a n t a g e of t h e s e s y s t e m a t i c o p t i m i z a t i o n t e c h n i q u e s is t h a t a u t o m a t e d i n s t r u m e n t a t i o n can be used t o develop t h e s e strategies a n d carry o u t t h e e x p e r i m e n t s if t h e c h e m i s t r y a n d statistics a r e well d e fined. References
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336 A · ANALYTICAL CHEMISTRY, VOL. 55, NO. 2, FEBRUARY 1983
