Optimization of Reverse-Phase Liquid Chromatographic Separation of Weak Organic Acids Stanley N. Deming” and Michael L. H. Turoff Department of Chemistry, University of Houston, Houston, Texas 77004
Figure l ) ,it can be shown that
The effect of aqueous carrier solvent pH upon the high performance reverse-phase liquid chromatographic separation of several benzoic acids is studied. A semiempirical optimization strategy is demonstrated: retention times of the weak acids of interest are measured at three or more values of pH in an appropriate buffer, models are fit to the data, and the model parameters are used to construct window diagrams from which the optimum pH can be estimated.
where Km and K H B are the acid dissociation constants of HA and HB, K = KHA/KHB, and r = ([B-]/HB]). In a reversephase system, species HA and A- will each have individual affinities for both the aqueous (polar, mobile) phase and the organic (nonpolar, stationary) phase. At extreme values of p H where either HA or A- predominate, the relative affinities for the stationary phase are indicated by the retention times tH.4 and tA-. Because the equilibrium between HA and A- is very fast with respect to the separation process, a t intermediate values of p H the retention time t of the single observed peak might be expected to be a weighted average of the individual retention times
It has long been suggested that liquid chromatography should be a more versatile analytical tool than gas chromatography, in part because of the larger number of variable factors associated with the mobile liquid phase-e.g., in reverse-phase liquid chromatography, it is possible to vary pH, ionic strength, polarity, counterion concentration, etc. ( I ) . To date, however, there have been few studies suggesting a systematic means of adjusting these factors to provide optimum liquid chromatographic performance. R e present here a strategy for seiecting a value of one of these factors, pH, to achieve optimum resolution of simple organic acids in reverse-phase chromatographic systems.
The parameters tHA, tA-, and K can be estimated from experimental data obtained by measuring t for a t least three different values of r. Different weak acids would be expected to give different sets of values for these three parameters because of their different affinities for the mobile and stationary phases, and because of their different acid dissociation constants.
THEORY The optimization of chromatographic resolution is especially difficult hecause of the existence of multiple optima (2). The intentional variation of system conditions (e.g., temperature or p H ) can often cause peaks to “cross” one another. Conditions for which two or more peaks of interest are eclipsed clearly represent minimum performance from the system (no separation). Conditions for which all peaks are separated from each other represent maximum performance. In chromatographic systems, there are often many sets of conditions that give rise to local maxima. T h e problem, then, is to predict the location in factor space of these local maxima and to choose the best (or global) maximum, often within certain constraints such as maximum allowable analysis time. Once this desirable region of factor space has been approximately located, local optimization procedures can be used to find the exact location of the maximum ( 3 ) . Laub and Purnell have presented a series of papers (4-7) in which “window diagrams” are used to locate optima in gas chromatographic systems for which the composition of a mixed stationary phase is a variable factor. We have found the concept of window diagrams to be equally useful for locating optima in reverse-phase liquid chromatographic systems for which p H is a variable factor. T h e following derivation is similar to those of Horvath e t al. (8)and Pietrzyk and Chu
EXPERIMENTAL Chromatograph. All separations were carried out using a Model 6000A pump (Waters Associates, Milford, Mass. 017571, a U6K injector (Waters), a Model SP8200 detector (Spectra Physics, Santa Clara, Calif. 95051) operated at 254 nm, and a Model 281 strip chart recorder (Soltec, Encino, Calif. 91316). A 10-cm section of 2-mm i.d. Bondapak CIB/Corasil(Waters) was used as a precolumn to a 30-cm X 4-mm i.d. pC,, Bondapak high efficiency column. A flow rate of 2.0 mL m i d was used throughout the study. Injection volumes were 5 pL or less. The time equivalent of the void volume (1.65 min) was measured by noting the small change in detector signal after injecting a water sample. Solvents. Nine buffer solutions were prepared as shown in Table I using 1.00 M acetic acid (HAC,Mallinckrodt Chemical Works, St. Louis, Mo. 631471, 1.00 M NaOH (Fisher Scientific Co., Fairlawn, N.J. 074101, and 1.00 M NaCl (Fisher) to provide a set of solvents for which the ionic strength was essentially constant (0.06 M) as the r value ranged from 0.111 to 9.00. Weak Acids. Solutions of five weak organic acids-benzoic acid, ?-aminobenzoicacid, 4-aminobenzoic acid, 4-hydroxybenzoic acid, and 1,4-benzenedicarboxylic acid-were prepared by dissolving 50 mg of the weak acid in 10 mL distilled water and filtering through a 0.45 i.lm filter (type GA-6, Gelman, Ann Arbor, Mich. 48106). A mixture of all five weak acids was prepared by combining appropriate amounts of the individual solutions.
(9).
Given a small amount of weak acid HA that dissociates to give conjugate base A- in a solution buffered by a more concentrated weak acid H B and its conjugate base B- (see 0003-2700/78/0350-0546$01.00/0
F
1978 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 50, NO. 4 , APRIL 1978
B ’ X
547
HB
+
II
II
-HA
Aqueous
A‘
Organic
Figure 1. Equilibria involved in the reverse-phase liquid chromatographic separation of weak acids
Table 1. Solvent Composition Solvent
a
mL 1.00 M HAC=
mL 1.00 M NaOHa
mL 1.00 M NaCP
rb
30.00 30.00 30.00 30.00 30.00 30.00 30.00 30.00 30.00
3.00 6.00 9.00 12.00 15.00 18.00 21.00 24.00 27.00
27.00 24.00 21.00 18.00 15.00 12.00 9.00 6.00 3.00
0.111 0.250 0.429 0.667 1.00 1.50 2.33 4.00 9.00
In 0 . 5 0 0 liters of solution.
-1.0
-0,s
b.1
O.b
1.0
UE([SI/( LMJ)1 Figure 2. Hetention time vs. log ( r ) for five weak acids. Solid lines are predicted behavior, dots are observed behavior
T h e relative net retention of two compounds X and Y is defined as (tx - t v ) / ( t y- tv), where tx and t y are the observed (uncorrected) retention times of X and Y, and t v is the time equivalent of the void volume. If the relative net retention is calculated to be less than unity, the reciprocal i s taken; thus. relative retention is always greater than or equal to unity. Figure 3 is a window diagram ( 4 ) showing relative net retention for all ten pairs of the five weak acids as a function of log (r). Those conditions giving a relative retention of unity for a pair of components represent minimum performance from the system (eclipsed peaks). Those conditions giving relative retentions greater than unity give improved separation for that pair. The tops of the “windows” indicate conditions for which the relative retentions of two pairs are equal-each of the two pairs is equally well separated. The tops of the windows thus represent conditions giving the best separation for the worst separated pairs-all other pairs will be better separated. In Figure 3, the best conditions occur at r = 0.54.
( [ B - ] / [ H B ] ) ;see text.
Calculations. The parameters of Equation 2 were fit to the data for each of the weak acids using a simplex nonlinear least-squares program similar to that described by O’Neill (10).
RESULTS Table I1 contains observed retention times for each of the five weak acids at each of the different solvent compositions. Replicates were carried out a t r = 0.111, 1.00,and 9.00. Using these experimental data, the parameters of Equation 2 were fit for each weak acid. The results are presented in Table 111. Figure 2 shows calculated and observed retention times as a function of log ( r ) (equivalent to an offset p H scale, where log ( r ) = 0 corresponds to pKHB). Table 11. Retention Times of Weak Acids
Retention time, min
Experiment
r 0.111
3 7 10 4 12 6 11 5 8 1 2 9
0.250 0.429 0.667 1.00 1.50 2.33 4.00 9.00
Benzoic acid
2-Aminobenzoic acid
58.10 58.20 44.30 35.40 27.40 22.15 20.50 17.55 13.70 10.15 7.00 6.86
26.50 25.80 25.15 23.65 22.45 20.35 19.05 18.40 16.70 12.15 8.42 8.11
4-Aminobenzoic acid
4-Hydroxybenzoic acid
1,4-Benzenedicarboxylic acid
16.25 15.40 14.85 14.15 12.90 11.15 11.15 10.05 8.50 6.40 4.29 4.26
25.25 25.60 21.95 19.40 16.35 13.60 13.30 11.45 9.10 6.75 4.42 4.32
25.30 27.27 14.15 8.8 c U
i2
0
le
7 -
w
11 RET"
ON T .E
SI
61
3 NJIE6
Figure 4. Chromatograms of mixture of five weak acids. Chromatogram A: r = 9 00 Chromatogram 6: r = 0 111. Chromatogram C: r = 0.54 -1.0
-0.5
0.0
0.5
1.0
LUG( C6 I/[ HB 1) Figure 3. Window diagram for all ten pairs of five weak acids
An optimum solvent was prepared containing 30.00 mL 1.00 M HAC,10.50 mL 1.00 M NaOH, and 19.50 mL 1.00 M NaCl in 0.500 L and was used to separate a mixture of the five weak acids. Figure 4 shows chromatograms obtained a t r = 9.00,0.111, and 0.54. In chromatogram A (higher pH), 4-aminobenzoic acid and 4-hydroxybenzoic acid are eclipsed (see Figure 2 ) ; in chromatogram B (lower pH), 2-aminobenzoic acid, 4hydroxybenzoic acid, and 1,4-benzenedicarboxylic acid elute together; chromatogram C (optimum pH) shows baseline separation of all peaks. DISCUSSION At low values of r (relatively acidic conditions), the benzoic acids are protonated (uncharged) and have a greater affinity for the stationary nonpolar phase; their retention times are relatively long (see Figure 2 ) . A t higher values of r (relatively basic conditions), the acids are unprotonated (negatively charged) and have a greater affinity for the mobile polar phase; their retention times are relatively short. This behavior has been observed previously for other weak acids and bases (e.g., 8 , 9, 11, 1 2 ) . Because K = K H A / K H B , values of K H A can be calculated from the estimated values of K and a known value of KHB. Table I11 compares values of K m estimated in this study with values from the literature. The agreement is good except for 1,4-benzenedicarboxylic acid. (However, as can be seen in Figure 2, data for 1,4-benzenedicarboxylic acid correspond to predominantly ionized conditions for the acid. The estimates
of fHA and K are subject to significant uncertainty. Thus, the calculated value of KHA for 1,4-benzenedicarboxylic acid is an imprecise estimate, and the discrepancy between calculated and literature values of KHAis not highly significant from a statistical point of view.) CONCLUSION
A semiempirical optimization strategy has been demonstrated: retention times of the weak acids of interest are measured at three or more values of r in an appropriate buffer, models are fit to the data, and the model parameters are used to construct window diagrams from which optimum chromatographic conditions can be estimated. LITERATURE CITED (1) J. J. Kirkiand, "Modern Practice of Liquid Chromatography", Wiley, New York, N.Y., 1971, p 162. (2) S. L. Morgan and S. N. Deming, Sep. Pur? Methods, 5 , 333 (1976). (3) S. L. Morgan and S. N. Deming. J , Chromatogr., 112, 267 (1975). (4) R. J. Laub and J. H.Purnell, J. Chromatogr.. 112, 71 (1975). (5) R. J. Laub and J. H. Purnell, Anal. Chem.. 48, 799 (1976). (6) R. J. Laub and J. H. Purnell, Anal. Chem., 48, 1720 (1976). (7) R . J. Laub, J. H.Purnell. and P. S. Williams, J . Chromatogr., 134, 249 ( 1977). (8) C Horvath. W. Melander, and I. Molnar, Anal. Chem., 49, 142 (1977). (9) D. J. Pietrzyk and C. H. Chu, Anal. Chem., 49, 860 (1977). ( l o ) R. O'Neill, Appl. Statist., 20, 338 (1971). (11) R. A Hartwick and P. R. Brown, J . Chromatogr., 126, 679 (1976). (12) I. Molnar and C. Harvath, Clin. Chem. ( Winston-Salem, N.C ), 22, 1497 119761 I - I
(13) R T Morrison and R N Boyd, "Organic Chemistry", Allyn and Bacon, Boston, 1959, pp 454, 677
RECEIVED for review October 25, 1977. Accepted January 9, 1978. Financial support of Grant E-644 from the Robert A. Welch Foundation is gratefully acknowledged.
