Anal. Chem. 2000, 72, 3581-3589
Liquid Chromatographic Separations with Mobile-Phase Additives: Influence of Pressure on Coupled Equilibria Lisa M. Ponton, Shirley M. Hoenigman,† Mei Cai, and Christine E. Evans*
Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055
On the basis of equilibrium thermodynamics, pressure can cause a shift in equilibrium for any interaction that exhibits a change in partial molar volume. This shift in equilibrium can be observed in liquid chromatography as a pressure-dependent shift in solute retention. In this paper, the impact of pressure on liquid chromatographic separations with mobile-phase additives is examined from both theoretical and experimental perspectives. The theoretical development for coupled-equilibria separations shown here is general and can be applied to any separation using mobile-phase additives. Predictions indicate that the coupled nature of these equilibria leads to pressure-induced perturbations in partitioning and complexation that can either compete with or complement one another. Using positional isomers and enantiomers as model solutes, experimental retention observations are fully consistent with these predictions, showing the diminution of individual pressure effects for competing cases and enhanced pressure effects for complementary cases. When pressure-induced changes in capacity or retention factor differ between individual solutes, changes in solute selectivity are predicted and observed. Using a C18 stationary phase with β-cyclodextrin as the mobile-phase additive, solutes studied here exhibit changes in selectivity ranging from -7 to +10% for a change in average pressure of ∼215 bar. Perhaps the most dramatic change in selectivity is observed for the separation of positional isomers where pressure-induced changes in selectivity actually reverse solute elution order. Mobile-phase additives are frequently used in liquid chromatography to enhance the selectivity by introducing additional interaction mechanisms.1-5 When mobile-phase additives are used, retention is still governed by interaction of the free solute with * Corresponding author: (e-mail)
[email protected]; (fax) 734-647-4050. † Current address: Department of Chemistry, Newman University, Wichita, KS 67213. (1) Hinze, W. L. Sep. Purif. Methods 1981, 10, 159-237 and references therein. (2) Armstrong, D. W.; Nome, F.; Spino, L. A.; Golden, T. D. J. Am. Chem. Soc. 1986, 108, 1418-1421 and references therein. (3) Sybilska, D.; Zukowski, J.; Bojarski, J. J. Liq. Chromatogr. 1986, 9, 591606. (4) Husain, N.; Christian, A. Y.; Warner, I. M. J. Chromatogr., A 1995, 699, 73-83. (5) Morin, N.; Guillaume, Y. C.; Rouland, J.-C. Chromatographia 1998, 48, 388394. 10.1021/ac000094v CCC: $19.00 Published on Web 06/21/2000
© 2000 American Chemical Society
the stationary phase, but the availability of free solute is mediated by interactions with the mobile-phase additive. As a result, this approach can increase column utility and often eliminate the need for multiple specialty columns. For example, cyclodextrins have been used as mobile-phase additives to achieve discrimination for a wide range of solutes including prostaglandins,2 chiral barbiturates,3 polynuclear aromatic hydrocarbons,4 and imiadazole enantiomers.5 Incorporation of mobile-phase additives also affords a convenient method for the determination of binding or complexation constants.6-10 Binding constants of cyclodextrins to various drugs,6 anthracene and pyrene,7 and terpenes8 have been determined chromatographically by varying the cyclodextrin concentration in the mobile phase. This method has also been used to examine biologically important binding interactions including protein binding of small molecules.9,10 Although pressure is an inherent parameter in all of these separations, the impact of pressure on solute retention for coupled-equilibria separations has been largely overlooked. The impact of pressure on liquid chromatographic separations involving the single mechanisms of adsorption, partitioning, or complexation has been established over the past several years.11-18 It is known that the bulk properties of polar liquids are not significantly perturbed in the pressure regime of HPLC (18 MΩ). Control of mobile-phase pH was accomplished using Tris base (Sigma), and pH was adjusted using HCl (high-purity grade, EM Science; Gibbstown, NJ). For the study of hexobarbital and mephobarbital, the mobile-phase solutions were prepared using high-purity, 95% ethanol/water (ACS spectrophotometric grade, Aldrich; Milwaukee, WI), sodium acetate (Aldrich), and distilled, deionized water. The apparent pH of these solutions was then adjusted using glacial acetic acid (Aldrich). Chromatography. A custom-designed HPLC system was used for study of the pressure-induced changes in solute partitioning and coupled-equilibria separations. Separations were performed on three individual monomeric C18 columns (dp ) 5 µm; 2.1 mm i.d., 10 cm; model Spherisorb S5ODS2; Higgins Analytical Inc.; Mountain View, CA). These columns are designated as columns 1, 2, and 3 for the purpose of discussion. Solvent delivery utilized a single-piston reciprocating pump (model 110B; Beckman; Fullerton, CA) with pressure monitored independently (model 4.5PG10; High-Pressure Equipment; Erie, PA) at the column inlet. Samples were introduced with a 10-µL external injection loop (model C6W; Valco; Houston, TX) and solute detection used a variable-wavelength absorbance detector (model UVIS-205; Linear; Chicago, IL) fitted with a high-pressure capillary flow cell (76-µm i.d. and 357-µm o.d.; Polymicro Technologies, Inc.; Phoenix, AZ). Optimization resulted in a 254-nm absorbance wavelength for the nitrophenols and 220-nm absorbance wavelength for both hexobarbital and mephobarbital. In the mobile-phase additive studies, the average pressure on the column was controlled via a capillary flow restrictor attached at the end of the chromatographic column. In this way, the pressure at the column exit is increased without altering the pressure gradient along the column or the mobile-phase linear velocity. For the pressure conditions examined here, the pressure gradient is linear along the column, ranging from 11.7 to 14.1 bar/ cm. Moreover, the mobile-phase linear velocity was maintained constant for all controlled-pressure studies at 17 cm/min. Using this approach, the average pressure is controlled directly from separation to separation but maintained constant during a separa-
Table 1. Separation Conditions mobile phasea 18:82 EtOH/acetate 10 mM β-CD 20:80 MeOH/Tris pH 7.5 3 mM β-CD 20:80 MeOH/water pH 6.6 3 mM β-CD
column
∆Pav (bar)
P gradient (bar/cm)
T (K)
1
193 ( 2
14.1 ( 0.1
296.7 ( 0.1
1 2 1 3
237 ( 1 210 ( 1 218 ( 3 203 ( 6
12.7 ( 0.1 11.7 ( 0.1 12.1 ( 0.03 13.4 ( 0.1
295.3 ( 0.2 297.3 ( 0.1 296.0 ( 0.4 295.6 ( 0.3
a A more detailed description of the mobile phases is included in the Experimental Section.
tion. Pressure gradients (bar/cm) and average pressure-controlled changes (∆Pav) are given in Table 1 for each separation. The positional isomers of nitrophenol were studied in unbuffered 20: 80 (v/v) methanol/water (apparent pH 6.6) and 20:80 (v/v) methanol/10 mM aqueous Tris buffer (apparent pH 7.5), each with 3 mM β-cyclodextrin added to the mobile phase. Racemic hexobarbital and mephobarbital were studied in 18:82 (v/v) ethanol/10 mM aqueous acetate buffer (apparent pH 5.0) with 10 mM β-cyclodextrin. A methanol spiked mobile-phase solution was used as the void marker throughout these studies. Pressure-induced changes in solute complexation were independently determined using a β-cyclodextrin bonded stationary phase (Cyclobond I 2000, Advanced Separations Technology; Whippany, NJ). Utilizing packed capillary columns containing β-cyclodextrin bonded stationary phase (dp ) 5 µm; 251-µm i.d., 360-µm o.d.), controlled-pressure studies of solute retention were directly related to the change in partial molar volume upon complexation (∆Vcomp).16-18 Except where noted, complexation constants at low pressure were determined chromatographically by varying the cyclodextrin concentration. RESULTS AND DISCUSSION In this study, the average pressure on the column is controlled, while the pressure gradient along the column (bar/cm) and the linear velocity (cm/min) for a given separation are maintained constant. All reported changes in average pressure (∆Pav) are between separations, and pressure conditions remain unperturbed during a given separation. Although expected to be small, temperature changes induced by frictional heating must also be considered. A constant pressure gradient (and linear velocity) is maintained along the column to limit any flow-induced temperature variations. The external temperature is also well-defined as reported in the Experimental Section. This approach allows the systematic control of the average pressure on the column during a separation. Moreover, this measurement scheme is fully consistent with detection at the column exit, where the resulting measurement of the solute retention or capacity factor is an average of the behavior along the column. Due to minimal mobilephase compressibility under these pressure conditions (10-300 bar), the pressure gradient along the column is well approximated by a linear relationship. Needless to say, for those cases where a pressure-induced change in solute retention is observed, the pressure gradient along the column will result in a solute retention gradient along the column. These retention gradients will be predicted and addressed later in this paper. Predictions of Pressure-Dependent Retention. The predicted influence of pressure on solute retention is conducted here
for a range of solutes and mobile-phase conditions using a C18 stationary phase with β-cyclodextrin as the mobile-phase additive. The pressure dependences of partitioning (∆Vpart) and complexation (∆Vcomp) are determined independently under identical mobile-phase conditions, and the coupled equilibria are assessed using eq 11. Not presently predictable on the basis of first principles, ∆Vpart is determined directly on the chromatographic column of interest. The retention or capacity factors for each solute of interest are evaluated at two different pressures (defining ∆Pav). Using eq 9, ∆Vpart is determined for each solute and mobile-phase condition. These values are shown in Table 2, where the ( values are the propagated error of at least three determinations each at low (P0) and high (P1) pressure. Comparison of different columns under the same mobile-phase conditions indicates significant differences in stationary-phase behavior. These differences are not expected for truly identical stationary phases, and highlight the difficulty in direct prediction of ∆Vpart based on a model stationary phase. Likewise, ∆Vcomp cannot be predicted on the basis of first principles and is determined from the retention factor at two different pressures using a β-cyclodextrin stationary-phase column. While this approach assumes that the free and surface-attached cyclodextrins have similar volumetric interaction properties, direct measurement of pressure-dependent binding constants is quite cumbersome and not always feasible.31,32 As a result, predictions here will assume that the ∆Vcomp is identical for free and surfaceattached cyclodextrins. Although this assumption is perhaps counterintuitive, its validity will be evaluated upon comparison of predicted and measured ∆Vapp values. Using eq 10, ∆Vcomp is evaluated for each solute and mobile phase and is shown in Table 2. As expected on the basis of differing solvation chemistry, ∆Vcomp values vary widely for different mobile-phase conditions. The presence of both positive and negative values indicates that differing mobile-phase solvation can lead to either an expansion or a contraction of the solvation shell upon complexation. Individual complexation constant values at low pressure are taken from the literature or determined chromatographically by varying the concentration of mobile-phase additive. For final predictions of ∆Vapp, the complexation constant at high (P1) pressure P1 (Kcomp ) is determined using eq 10 and cyclodextrin concentrations of 3 mM are assumed for all MeOH/aqueous separations and 10 mM for the EtOH/acetate separation. As shown in Table 2, predicted ∆Vapp values are both positive to negative, but all are qualitatively consistent with competitive and complementary predictions illustrated in Figure 1 (vide supra). Experimental Measurements of Pressure-Dependent Retention. Experimental measurements of ∆Vapp in the presence of mobile-phase additive and under separation conditions are identical to those utilized for predictions. Retention measurements are evaluated at low and high pressure, and ∆Vapp is determined using the first part of eq 11. Comparison of measured and predicted ∆Vapp values shows generally good agreement. While the errors on the measured values are in the range of 1-3 cm3/mol, the propagated errors for the predicted values are significantly higher. Capacity factor reproducibilities for these measurements are all (32) Hoenigman, S. M. Ph.D. Thesis, University of Michigan, Ann Arbor, MI, 1998.
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Table 2. Predicted and Experimental Values of ∆Vapp (cm3/mol)a individual contributions mobile phase 18:82 EtOH/acetate column 1
solute
∆Vcomp
∆Vapp pred
∆Vapp meas.
-6.0 ( 2 -6.0 ( 2 -6.7 ( 1 -6.7 ( 1
-11.6 ( 4 -11.5 ( 4 -9.6 ( 1 -10.3 ( 1
4b
151 ( 131 ( 2b 112 ( 3b 101 ( 5b
1.1 ( 4 0.7 ( 3 -1.5 ( 3 -1.4 ( 5
-0.8 ( 3 -1.1 ( 3 -0.2 ( 1 -0.2 ( 1
∆Vpart
hexobarbital mephobarbital
coupled equilibria P0 Kcomp
20:80 MeOH/Tris pH 7.5 column 1
o-nitrophenol m-nitrophenol p-nitrophenol
8.6 ( 3 -0.1 ( 2 7.9 ( 5
38 ( 1c 12 ( 1c 21 ( 1c
42 ( 6 97 ( 9 269 ( 12
5.0 ( 3 -2.7 ( 4 -1.0 ( 6
3.3 ( 3 -4.3 ( 3 -1.5 ( 4
20:80 MeOH/Tris pH 7.5 column 2
o-nitrophenol m-nitrophenol p-nitrophenol
11.0 ( 1 3.4 ( 1 8.1 ( 1
38 ( 1c 12 ( 1c 21 ( 1c
42 ( 6 97 ( 9 269 ( 12
7.3 ( 3 0.8 ( 3 -0.8 ( 4
3.6 ( 1 -8.0 ( 1 -2.9 ( 1
20:80 MeOH/water pH 6.6 column 1
o-nitrophenol m-nitrophenol p-nitrophenol
-0.3 ( 5 -2.5 ( 5 -2.6 ( 5
7.5 ( 1c 10.5 ( 2c 13.5 ( 1c
56 ( 3d 107 ( 2d 146 ( 6d
-1.4 ( 10 -5.0 ( 6 -6.5 ( 8
-2.6 ( 2 -4.5 ( 2 -6.2 ( 2
20:80 MeOH/water pH 6.6 column 3
o-nitrophenol m-nitrophenol p-nitrophenol
-9.0 ( 0.3 -7.0 ( 0.7 -8.8 ( 0.9
7.5 ( 1c 10.5 ( 2c 13.5 ( 1c
56 ( 3d 107 ( 2d 146 ( 6d
a
-10.0 ( 1 -11.8 ( 1 -13.3 ( 2
All ∆V values are cm3/mol. See Table 1 for conditions. b Reference 3. c Calculated from ref 16. d Reference 27.
Table 3. Pressure-Induced Changes in Retention Factora ∆k/k (%) mobile phase
solute
∆Pav (bar)
kP0 av
pred
meas
20:80 MeOH/ Tris pH 7.5 column 1
o-nitrophenol 237 ( 1 10.4 ( 0.2 -4.7 ( 4 -3.1 ( 3 m-nitrophenol 10.1 ( 0.2 2.6 ( 5 4.2 ( 3 p-nitrophenol 2.75 ( 0.08 0.9 ( 7 1.5 ( 3
20:80 MeOH/ Tris pH 7.5 column 2
o-nitrophenol 210 ( 1 8.79 ( 0.04 -6.0 ( 2 -3.0 ( 1 m-nitrophenol 9.19 ( 0.04 -0.7 ( 3 7.1 ( 1 p-nitrophenol 2.20 ( 0.01 0.7 ( 3 2.4 ( 1
20:80 MeOH/ o-nitrophenol 218 ( 3 19.4 ( 0.2 water pH 6.6 m-nitrophenol 10.4 ( 0.1 column 1 p-nitrophenol 8.3 ( 0.1
1.2 ( 9 4.5 ( 6 5.9 ( 8
2.3 ( 2 4.0 ( 2 5.7 ( 2
20:80 MeOH/ o-nitrophenol 204 ( 6 9.28 ( 0.05 8.8 ( 8 8.8 ( 1 water pH 6.6 m-nitrophenol 5.11 ( 0.05 8.3 ( 4 10.4 ( 1 column 3 p-nitrophenol 3.66 ( 0.03 11.3 ( 7 11.8 ( 2 a
-10.1 ( 9 -9.5 ( 4 -12.7 ( 7
See Table 1 for details.
< 2% relative standard deviation, but relatively large errors are propagated in the evaluation of differences in natural logarithms. On the basis of the good agreement in most cases, this error propagation appears to overestimate the error in predicted ∆Vapp. This agreement also provides support for the validity of evaluating ∆Vcomp using surface-attached cyclodextrins. As shown in Table 3, pressure-induced perturbations in solute retention can also be expressed in terms of the relative change in capacity factor (%∆k/ k). Perhaps more easily envisioned than changes in partial molar volume, these percent changes in solute retention are shown with the corresponding difference in the average pressure (∆Pav). Pressure-induced changes in this representation are convoluted with the absolute capacity factor values and must be considered together with the capacity factor at low pressure. This pressure dependence of solute retention further indicates the presence of a spatial retention gradient along the chromatographic column. That is, the spatial pressure gradient that is inherent in all separations using pressure-driven flow gives rise to a spatial retention gradient along the column. The expected 3586
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retention gradient can be readily calculated using eq 11, assuming a linear pressure gradient. For example, the ortho isomer separated in MeOH/water on column 3 is predicted to exhibit a capacity factor at the column inlet (P ) 134 bar) of 9.53 ( 0.06 and at the outlet (P ) 1 bar) of 9.03 ( 0.06. In this case, a change in retention factor of 0.5 is predicted over the column length, a decrease of 5% over 10 cm. The impact of such capacity factor gradients on retention reproducibility is mediated in most typical separations by the measurement of the average capacity factor at the column exit. Nonetheless, these pressure-induced retention gradients can play a significant role in ultrahigh pressure and highspeed separations where the pressure gradient may be substantial. Moreover, the retention gradient described above shows a decrease in solute retention along the column. This negative retention gradient would be expected to result in an increase in solute band broadening as the solute traverses the chromatographic column. In addition to the normal band broadening mechanisms, this negative retention gradient will decrease separation efficiency simply because the front of the solute band is moving faster than the back of the band. Although beyond the scope of this paper, this additional band-broadening effect is expected not only for coupled-equilibria separations but whenever the ∆V for the separation interaction is negative. Alternatively, positive ∆V values are expected to create a positive retention gradient along the column, effectively increasing chromatographic efficiency. As particle sizes are decreased in an effort to improve chromatographic efficiency, the resultant pressure/retention gradient will become increasingly important. Competitive and Complementary Behavior. The influence of pressure on these coupled-equilibria separations can be further evaluated in a qualitative manner. As shown earlier in this paper, just as mobile-phase additives act to mediate solute retention, so the pressure dependence of solute-additive complexation acts to mediate the pressure dependence of solute partitioning into
the stationary phase. This effect is qualitatively illustrated in Figure 1, where different combinations of partial molar volume values are expected to lead to pressure-induced perturbations that are either complementary (cases 1 and 2) or competing (cases 3 and 4). Evaluating the data in Table 2 in this light shows both complementary and competing behavior are experimentally observed. The most significant competition is seen in the separation of hexobarbital and mephobarbital racemates. These compounds exhibit a negative change in the partial molar volume of both partitioning and complexation (Figure 1, case 3). For a negative ∆Vpart, increasing pressure acts to increase the solute capacity factor. Simultaneously, the negative ∆Vcomp indicates that pressure acts to shift the complexation equilibrium toward the complex. Indeed, in this separation, the quantitative predictions are quite striking (Table 2). Although both ∆Vpart and ∆Vcomp are significant, direct competition between the pressure dependence of complexation and partitioning effectively cancels any pressure dependence in the coupled-equilibria separation (∆Vapp ∼ 0). This prediction is experimentally observed in the pressure-controlled separation with β-cyclodextrin added to the mobile phase. In contrast to previous studies,17,18 the pressure-dependent behavior of these individual enantiomers is very similar, indicating no significant differences in enantiomeric partial molar volumes for either complexation or apparent measurements. Similar competitive behavior is observed for the positional isomers of nitrophenol in the Tris mobile phase (pH 7.5). In contrast to the previous example, these separations exhibit changes in partial molar volume that are positive for both partitioning and complexation (Figure 1, case 4). As predicted, all solutes show ∆Vapp values that are more negative than the initially positive ∆Vpart alone. As a result, predictions show that competition acts to diminish the pressure dependence of solute retention relative to separations with no mobile-phase additive. The possibility that this mediation could actually change the direction of the pressure effect is illustrated by the para isomers, where the sign of ∆V changes from positive for partitioning alone to slightly negative for the coupled-equilibria separations. Although the prediction is only slightly negative, these results highlight the potential for competition to actually change the directionality of capacity factor pressure dependence. The potential for this behavior is dependent not only on the relative magnitude of the ∆V values but also on the weighting of the coupled-equilibria separation toward complexation. That is, the magnitude of the complexation constant acts to weight solute retention. This effect is shown in comparing the behavior of the ortho and para isomers. While the pressure dependence of complexation is greater for the ortho isomer, the greater complexation constant of the para isomer serves to weight not only the magnitude of the solute capacity factor but also the resultant pressure dependence for the coupledequilibria separation. In general, experimental measurements show good agreement with the predicted behavior for this competitive case. Interestingly, separations studied using two different columns (same manufacturer, containing the same monomeric C18 stationary phase) with the same buffered mobile phase show generally similar pressure-dependent behavior even though solute retention and elution order differ. The influence of pH is shown in the separation of nitrophenol isomers on two columns using the same mobile phase, but at
Figure 2. Effect of pressure on solute selectivity of the nitrophenol isomers. Notation: 1, 2, and 3 refer to the specific separation column, water and Tris refer to 20:80 (v/v) methanol/water (pH 6.6), and 20: 80 (v/v) methanol/aqueous Tris buffer (pH 7.5), respectively. All other conditions as given in text or cited in Table 1.
different pH values. As expected based on electrostriction,24 decreased ionization acts to decrease the magnitude of ∆Vcomp, with the apparent exception of the meta isomer whose ionization state is not appreciably changed in this pH range.16 For studies using column 1, the ∆Vpart values are statistically zero; therefore, the predominant pressure-dependent interaction is complexation (Figure 1, case 1 or 4 with little partitioning component). In this case, no competition or complementarity is expected and the pressure effect of complexation alone is predicted to increase solute retention. This is quantitatively shown in Table 2 with predicted ∆Vapp values that are more negative than partitioning alone, ∆Vpart. In contrast with column 1, column 3 exhibits a negative ∆Vpart coupled with the positive ∆Vcomp (Figure 1, case 1). This represents the complementary case where pressure acts to increase the impact of either independent mechanism. In this case, the overall or apparent change in the partial molar volume (∆Vapp) is exacerbated relative to partitioning alone, resulting in a predicted ∆Vapp that is more negative than ∆Vpart. This prediction illustrates the presence of both competing and complementary behaviors for pressure-dependent solute retention in coupledequilibria separations. Again, experimental observations for separations with mobile-phase additives are in good agreement with theoretical predictions. Thus, although these two columns exhibit significantly different retention behavior, predictions of their pressure-dependent behavior agree well with experimentally measured observations. Pressure-Dependent Solute Selectivity. Not only is solute retention in these coupled-equilibria separations affected by pressure but solute selectivity may also be pressure dependent. To the extent that pressure-induced changes in retention differ between solutes, pressure can act to either increase or decrease selectivity. As illustrated in Figure 2, both positive and negative perturbations in selectivity are predicted and observed. The relative change in solute selectivity (% ∆R/R) for a ∼215 bar increase in pressure ranges from -7 to +10% for the separations shown here. As illustrated by the chromatograms in Figure 3, Analytical Chemistry, Vol. 72, No. 15, August 1, 2000
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Figure 3. Chromatograms illustrating the effect of average pressure on mobile-phase additive separations of nitrophenol isomers. Mobile phase: 20:80 (v/v) methanol/10 mM aqueous Tris buffer (pH 7.5). Top: separation on column 1 at low and high pressure. Bottom: separation on column 2 at low and high pressure. Note: arrows highlight the direction of the pressure-induced shift in retention.
perhaps the most notable pressure-induced changes in selectivity occur in the buffered mobile-phase separations. The partial molar volume, and hence the solute retention, trends shown in Table 2 are quite similar for columns 1 and 2. However, the arrows in Figure 3 illustrate that the ortho and meta isomers are moving in opposite retention directions in response to pressure and the para isomer does not change appreciably. For column 1, the initial elution order and pressure-induced change is such that the pressure-induced shifts in capacity factor actually reverse the ortho/meta elution order! We believe that this is the first direct observation of pressure-induced changes in solute elution order. As selectivity is defined in eq 12, this pressure-induced selectivity change is -7.1%. If, however, the selectivity is measured independently in each chromatogram, the selectivity is not appreciably altered, and only the elution order is perturbed. In contrast, column 2 shows a similar capacity factor shift with pressure, but with quite different results. The initial elution order is opposite for the ortho and meta isomers relative to column 1, and pressure now acts to increase solute selectivity such that o- and mnitrophenol become fully resolved at high pressure. Thus, columnto-column variation in the pressure dependence of solute retention can produce significantly different chromatographic outcomes, but results remain consistent with fundamental predictions. Clearly, even the relatively modest pressures encountered in HPLC can have a profound impact on key separation factors including retention, selectivity, and elution order. 3588 Analytical Chemistry, Vol. 72, No. 15, August 1, 2000
Figure 4. Effect of cyclodextrin concentration on ∆Vapp for the nitrophenol isomers. Conditions: column 3, 20:80 methanol/water. Other separation conditions as cited in text or Table 1. Note: no response is predicted for ∆Vapp for 0 mM cyclodextrin because ∆Vapp is exactly equal to ∆Vpart in this case.
Concentration of Mobile-Phase Additive. Finally, it is interesting to note that the pressure dependence of retention in coupled-equilibria separations is predicted to be a function of the mobile-phase additive concentration (eq 11). With increasing additive concentration, the apparent capacity factor is more substantially influenced by additive interactions. Concomitantly, the pressure dependence of the apparent capacity factor is increasingly affected by the pressure dependence of the soluteadditive interactions. For the separation of nitrophenol isomers, Figure 4 shows that the apparent partial molar volume becomes increasingly negative with CD concentration. Although the error bars shown in Table 2 would effectively negate these systematic perturbations, as discussed earlier, error propagation likely overestimates this error. Moreover, the close agreement between prediction and experimental measurement that is shown in Figure 4 merits further discussion. Indeed, this increasingly negative apparent partial molar volume with CD concentration is observed for both theoretical predictions and experimental measurements. This trend is consistent with the positive ∆Vcomp for all isomers, effectively increasing the negative magnitude of ∆Vapp with CD concentration. In the case of the para isomer, the pressure dependence is nearly doubled for a 3 mM CD concentration (eq 11). Not shown here, more complete examination of the range of impact for common separation conditions indicates predicted
changes in solute capacity factor of up to 40% for a 250 bar change in pressure and numerous opportunities for elution order reversal.32 Together, these results have important implications for the practice of liquid chromatography using mobile-phase additives. Separations using mobile-phase additives to enhance chromatographic resolution are expected to be more susceptible to pressure variations from analysis to analysis. This pressure dependence may be causing some of the retention variability now experienced for these separations. This increased role of pressure will become even more important for ultrahigh pressure separations using mobile-phase additives. Optimization of selectivity in these cases can expect the combination of additive concentration and pressure to play a significant role in governing chromatographic performance. CONCLUSIONS When considered as an explicit parameter in coupled-equilibria separations, pressure is demonstrated to influence all figures of merit describing solute migration. Theoretical predictions are derived for coupled-equilibria separations and show that the pressure dependence of individual mechanisms can act in either a complementary or a competing manner. As a result, the change in partial molar volume for each interaction determines whether the overall pressure dependence of solute retention is exacerbated or diminished relative to separations with no mobile-phase additive. For the separations studied here, experimental agreement with theoretical predictions is generally good, and both competing and complementary cases are observed. Moreover, when pressure-induced changes in retention differ between solutes, chromatographic selectivity is also predicted to be
pressure dependent. Theoretical predictions and experimental observations demonstrate that pressure can increase, decrease, or have no effect on solute selectivity. In fact, chromatographic selectivity has been sufficiently perturbed for the solutes investigated here to achieve pressure-induced baseline resolution in one case. Predictions and observations also demonstrate that both pressure-induced changes in solute retention and selectivity are dependent on the cyclodextrin concentration added to the mobile phase. As a result, pressure is expected to play an increasing role in resolution optimization as the concentration of mobile-phase additive increases. Indeed, pressure in coupled-equilibria separations is demonstrated to have a widely ranging impact on solute migration, including the first pressure-induced shift in elution order to be observed to our knowledge. Together these results provide the theoretical and experimental framework for prediction of pressure-induced perturbations in coupled-equilibria separations. In light of these results, both the optimization of separations and the chromatographic determination of binding constants and stoichiometry using mobile-phase additives will need to be reassessed. ACKNOWLEDGMENT The authors acknowledge the National Science Foundation (Grant CHE-9707513) for support of this work.
Received for review January 31, 2000. Accepted May 5, 2000. AC000094V
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