High-Concentration Band Profiles and System Peaks for a Ternary

Injection Technique for Generating Accurate Adsorption Isotherm Data Using the Elution by Characteristic Points Method. Jörgen Samuelsson and Torgny ...
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Anal. Chem. 2000, 72, 1495-1502

High-Concentration Band Profiles and System Peaks for a Ternary Solute System Igor Quin˜ones, John C. Ford,† and Georges Guiochon*

Departments of Chemistry and Chemical Engineering, University of Tennessee, Knoxville, Tennessee 37996-1600, and Division of Chemical and Analytical Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6120

High-concentration HPLC band profiles of single solutes and the individual band profiles of the components of binary and ternary mixtures are reported for benzyl alcohol, 2-phenylethanol, and 2-methylbenzyl alcohol. These solutes were eluted from a C18 column by a binary mobile phase (MeOH:H2O ) 1:1, v/v). High-concentration system peaks were obtained using mixtures of benzyl alcohol and 2-phenylethanol at different relative concentrations as the feed and 2-methylbenzyl alcohol as the strong mobile phase additive. Band profiles and system peak profiles were calculated using the equilibriumdispersive model of chromatography. The adsorption equilibrium in the multicomponent system was characterized by the competitive Langmuir model. Excellent quantitative agreement was found between the experimental and the calculated profiles. This work confirms that extremely unusual system peak profiles can be obtained even when the adsorption behavior is quite simple. Under certain circumstances, the use of a properly chosen additive could markedly increase the separation between bands and hence the production rate, the recovery yield, and/or the purity of the fractions. Simulated moving-bed chromatography and batch elution chromatography have found widespread use in the pharmaceutical industry. The time required by method development, scale-up, and optimization of these preparative techniques is relatively long and contributes significantly to the cost of the process. Conventional trial-and-error methods could be improved by the application of appropriate models of the process. The main goal of these models is the quantitative prediction of the individual band profiles that arise in multicomponent separations.1 Both analytical and preparative liquid chromatography separations are often carried out by employing multicomponent mixtures of solvents. The multicomponent mobile phase usually contains a weak solvent and a strong additive that actively competes with the solutes for the adsorption sites in the stationary phase. The presence of the additive in the mobile phase is essential to control the retention of the separated solutes and to achieve proper resolution.2 As a result of the strong interference between the † Current address: Department of Chemistry, Indiana University of Pennsylvania, Indiana, PA 15705. (1) Guiochon, G.; Golshan-Shirazi, S.; Katti, A. M. Fundamentals of Preparative and Non-linear Chromatography; Academic Press: Boston, MA, 1994.

10.1021/ac9909406 CCC: $19.00 Published on Web 02/25/2000

© 2000 American Chemical Society

solutes and the additive, extremely unusual band profiles or system peaks are obtained in both analytical and preparative applications.1 Thus, understanding the underlying phenomena producing the system peaks is important for method development. For these reasons, system peaks have received much attention from the perspective of both analytical3,4 and preparative chromatography.1 Previous theoretical studies have shown how system peaks arise as a result of the competitive interactions between the separated solutes and the strong additive of the mobile phase. Theoretical results were presented for one5 and two solutes6 eluted by a binary mobile phase containing a strong additive. In these studies, the competitive interactions among the components of the system were accounted for by a multicomponent Langmuir model. The band profiles were calculated using the equilibriumdispersive model of chromatography.1 Experimental studies6,7 showed good qualitative agreement with the previous theoretical predictions. A quantitative comparison between experimental and theoretical results was not possible because of the lack of the relevant multicomponent adsorption equilibria in the systems under consideration. In a later theoretical study, a set of rules was proposed in an attempt to rationalize the conditions under which system peaks originate.8 Afterwards, the elution of a single solute band by a binary eluent in a reversed-phase ion-pair system was studied.9 In the latter work, the single solute isotherm data for the compounds involved were correlated by the bi-Langmuir model. The competitive isotherms of these compounds were assumed to be described also by the bi-Langmuir model. Competitive adsorption data were not measured for mixtures of the solute and the additive. Accordingly, the parameters in the competitive model were estimated only from the single solute adsorption data and from additive data at low concentrations. Nevertheless, good quantitative agreement was obtained between the experimental and the calculated system peak profiles. Recently, large concentra(2) Schoenmakers, P. J. Optimization of Chromatographic Selectivity; Journal of Chromatography Library, Vol. 35; Elsevier: Amsterdam, 1986. (3) Fornstedt, T. Distortions of Analyte Peaks due to Large System Peaks in Ion-Pair Adsorption Chromatography. Ph.D. Dissertation, Uppsala University, 1992. (4) Golshan-Shirazi, S.; Guiochon, G. Anal. Chem. 1990, 62, 920. (5) Golshan-Shirazi, S.; Guiochon, G. J. Chromatogr. 1989, 461, 1. (6) Golshan-Shirazi, S.; Guiochon, G. Anal. Chem. 1989, 61, 2373. (7) Golshan-Shirazi, S.; Guiochon, G. Anal. Chem. 1989, 61, 2380. (8) Fornstedt, T.; Guiochon, G. Anal. Chem. 1994, 66, 2116. (9) Fornstedt, T.; Guiochon, G. Anal. Chem. 1994, 66, 2686.

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tion system peaks were obtained when the same species, 3-phenyll-propanol, was used both as the solute and as the strong additive of the mobile phase.10 In this case, only the single solute adsorption isotherm of 3-phenyl-l-propanol was needed to perform the necessary calculations. Very good agreement was obtained between the experimental and calculated band profiles. So far, the quantitative description of the system peaks arising during the elution of a binary solute mixture by a binary eluent containing a strong additive has not been possible. This is a natural result of the lack of available ternary solute adsorption data for a system of chromatographic interest. The goal of this study is to compare experimental profiles of system peaks at high concentrations and those derived from the theory of nonlinear chromatography. The calculation of the latter requires a model accounting properly for the adsorption data of all single solutes and of binary and ternary mixtures of three compounds in a typical chromatographic system. We will use data recently acquired with benzyl alcohol (BA), 2-phenylethanol (PE), and 2-methylbenzyl alcohol (MBA) in solution in a 1:1 (v/v) mixture of methanol and water.11 The adsorbent was a C18 bonded porous silica for reversed-phase chromatography. The multisolute adsorption data were accurately described by the competitive Langmuir model.12 Methanol adsorption in this system is negligible,13 and the role of this solvent is merely to allow proper adjustment of the retention of the solutes to reasonable values by modifying their solubility, not by competing for adsorption. Accordingly, the mobile phase can be considered as a pure liquid in the thermodynamic study of the phase equilibrium, as previously demonstrated.7 THEORY Multisolute Adsorption Equilibria. The adsorption isotherm relates the equilibrium concentrations of the studied component in the bulk liquid phase, C, and in the adsorbed phase, q. Several isotherm models have been applied to the description of multisolute adsorption equilibria associated with preparative liquid chromatography applications.14,15 The Langmuir isotherm model is the simplest model available.1 This model considers that the adsorption process takes place on a surface composed of a fixed number of adsorption sites of equal energy, one molecule being adsorbed per site until monolayer coverage is achieved. The single solute Langmuir model is16

q)

qsKLC 1 + KLC

(1)

where qs is the monolayer capacity and KL is the Langmuir equilibrium constant. The competitive Langmuir model for a multicomponent mixture is1,12

qi )

qsiKLiCi Ns

1+

∑K

(2)

L

iCi

i)1

where the indices 1, 2, and 3 will correspond to BA, PE, and MBA, (10) Sajonz, P.; Yun, T.; Zhong, G.; Fornstedt, T.; Guiochon, G. J. Chromatogr., A 1996, 734, 75. (11) Quin ˜ones, I.; Ford, J. C.; Guiochon, G. Chem. Eng. Sci. 2000, 55, 909.

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respectively. Thus, all the parameters of the competitive isotherm can be derived from measurements made with the single solutes, which is very convenient from the experimental point of view. For thermodynamic consistency, the multicomponent Langmuir model requires that the values of the saturation capacities for all the components in the system be the same.17 For practical purposes, however, it is possible to allow these values to be different as long as the model, used only as a means of empirical correlation, provides a good representation of the whole set of multisolute adsorption data. This latter approach is used in the present study. The multisolute adsorption data used in this work and their detailed analysis are presented elsewhere.11 Suffice it to report here that the competitive Langmuir model (eq 2) accounts very well for the experimental data. Multisolute Band Profiles. For HPLC columns, which usually possess a high efficiency, the equilibrium-dispersive model is a good approximation to the solution of the system of mass balance equations that governs the separation process in the column.1 In this case, the mass transfer in the column is assumed to be relatively fast and the effects produced by the different resistances to mass transfer are lumped into an apparent axial dispersion coefficient (Da). For each component i in the column, the equilibrium-dispersive model is represented by18

∂Ci ∂2Ci 1 -  ∂qi ∂Ci + +u ) Da,i 2  ∂t ∂t ∂z ∂z

(3)

where z and t are the length and time coordinates, respectively,  is the void fraction, and u is the interstitial mobile phase velocity. The equilibrium-dispersive model assumes that qi and Ci are the equilibrium values related by the multicomponent adsorption isotherm. The value of Da is related to the column height equivalent to a theoretical plate (H) by

Da,i )

Hiu 2

(4)

Suitable boundary conditions are needed to solve eq 3. The column is assumed to be empty at the beginning of the process (Ci(z,0) ) 0), and the experimental injection profile at the column inlet is introduced into the calculations. The set of eqs 3 for different components is solved numerically using a finite-differences algorithm. In this study, we apply a forward-backward finite difference procedure based on the Godunov scheme.19 A detailed discussion of the application of the equilibrium-dispersive model to the study of system peaks in chromatography can be found elsewhere.6 EXPERIMENTAL SECTION Equipment. Experimental band profiles and system peaks were acquired using an HP 1100 series modular liquid chromato(12) Schwab, G. M. Ergebnisse der exacten Naturwissenschaften; Springer: Berlin, 1928; Vol. 7. (13) McCormick, R. M.; Karger, B. L. Anal. Chem. 1980, 52, 2249. (14) Quin ˜ones, I.; Guiochon, G. Langmuir 1996, 12, 5433. (15) Quin ˜ones, I.; Guiochon, G. J. Chromatogr., A 1998, 796, 15. (16) Langmuir, I. J. Am. Chem. Soc. 1916, 38, 2221. (17) LeVan, M. D.; Vermeulen, T. J. Phys. Chem. 1981, 85, 3247. (18) Rhee, H.; Bodin, B. F.; Amundson, N. R. Chem. Eng. Sci. 1971, 26, 1571. (19) Rouchon, P.; Valentin, P.; Schonauer, M.; Guiochon, G. Sep. Sci. Technol. 1987, 22, 1793.

graph (Hewlett-Packard, Palo Alto, CA) composed of an isocratic pump, a vacuum degasser, a variable-wavelength detector, and a thermostated column compartment. HP-Chemstation PC-based software was used to control these modules and to acquire and process the UV signal. The system was complemented by a Rheodyne (Cotati, CA) 7725i injector and a Gilson (Middletown, WI) model 203 fraction collector. The collected fractions were further analyzed using an HP 1090 series liquid chromatograph (Hewlett-Packard, Palo Alto, CA) equipped with a ternary solvent delivery system, an automatic sample injector with a 25 µL loop, a diode-array UV detector, and the same PC-based data acquisition/processing system. Materials. A 150 × 3.9 mm i.d. Symmetry C18 column (Waters, Mildford, MA) was used to measure the relevant data. The average particle size was 5 µm, and the void fraction of the column was 0.59, determined using thiourea as the nonretained marker. The solvents employed were of HPLC grade, purchased from Fisher Scientific (Pittsburgh, PA). The solutes employed were 99+% benzyl alcohol, ACS reagent (Aldrich, Milwaukee, WI), 99+% 2-phenylethanol (Fluka, Ronkonkoma, NY) and 99+% 2-methylbenzyl alcohol (Fluka, Ronkonkoma, NY). A similar C18bonded silica column and the same mobile phase were used to analyze the collected fractions. Procedures. Multisolute adsorption data in the ternary system of BA, PE, and MBA were measured by frontal analysis. The experimental details and associated calculations are detailed elsewhere.11 The band profiles were acquired at 30 °C. The solutions were prepared and used on the same day. The detector signal was recorded at 275 nm. The single solute band profiles were derived from the detector trace, converted to units of concentrations using a calibration curve determined by pumping directly into the detector solutions of known concentration of the sample in the mobile phase. The nonlinear detector response was converted using a fourth-order polynomial. The multisolute profiles were obtained by collecting and analyzing successive fractions of the column effluent. Fractions were collected every 3 s (ca. 50 µL) and diluted prior to analysis. For quantitation, a linear calibration graph based on the area of the peak was established for each compound, via the external standard method. The analysis of the samples was performed at 27 °C. The injected amount was 2 µL. The flow rate was 1 mL/min. The signal was detected at 220 nm. The change in wavelength is explained by the need to carry out the frontal analysis measurements at higher concentrations than those for the band profile acquisition: chromatography is a dilution process. Because proper calibration was made at both wavelengths, this cannot affect the agreement between calculated and experimental band profiles. Calculations. Regression of the experimental adsorption data to the Langmuir isotherm model was performed using a corrected Gauss-Newton method. The algorithm is implemented in the NAG Library.20 The procedure calculates the values of the isotherm parameters which minimize the residual sum of squares between experimental and calculated values for each set of single solute data. (20) The NAG Fortran Library Manual, Mark 16; The Numerical Algorithms Group Ltd.: Downers Grove, IL, 1993.

Figure 1. Adsorbed amounts of BA (a) and PE (b) determined via frontal analysis in mixtures containing BA, and PE. The abscissa is the total solute concentration in the bulk liquid phase (C1 ) CBA, C2 ) CPE). The mobile phase concentration is expressed via the relative composition of BA and PE. Experimental data are provided with the following symbols: data for a single solute, circles; data for the BA: PE (w/w) ) 3:1 mixtures (three parts of BA and one part of PE), squares; data for BA:PE ) 1:1 mixtures (equal parts of both components), diamonds; data for BA:PE ) 1:3 mixtures (one part of BA and three parts of PE), triangles. The lines are the adsorbed amounts calculated via the Langmuir model which uses the parameters determined from single solute data. Calculations are presented for the single solutes (solid lines), 3:1 mixtures (dotted lines), 1:1 mixtures (dashed-dotted lines) and 1:3 mixtures (dashed lines).

RESULTS AND DISCUSSION The single, binary, and ternary solute adsorption data measured by frontal analysis are presented in Figures 1-4. The equilibrium data (symbols) show very good thermodynamic consistency.11 The best values of the parameters obtained when the single solute adsorption data were fit to the Langmuir model are reported in Table 1. The correlation between the single solute adsorption data (symbols) and the isotherms calculated from these coefficients (lines) is also presented in Figures 1-4. Note that the model is able accurately to predict the binary and ternary solute data solely on the basis of the values of the parameters identified only from the single solute data. This result is a consequence of the fact that the activity coefficients of the species involved are nearly constant within the studied composition range.11 The calculation of nonlinear band profiles also requires knowledge of some of the characteristics of the separation at low concentrations, i.e., under analytical conditions. The heights equivalent to a theoretical plate (HETPs) for the three compounds, listed in Table 2, are nearly the same. They are used for the derivation of the apparent axial dispersion coefficient (eq 4). As demonstrated repeatedly in the literature,1 the effect of the HETP on high-concentration band profiles is negligible beyond a few thousand plates, which is the case here. So, the use of a common value for the axial dispersion coefficients of the three solutes is justified. Analytical Chemistry, Vol. 72, No. 7, April 1, 2000

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Figure 2. Adsorbed amounts of BA (a) and MBA (b) determined via frontal analysis in mixtures containing BA and MBA. The conventions are identical to those for Figure 1.

Figure 4. Adsorbed amounts of BA (a), PE (b) and MBA (c) determined via frontal analysis in mixtures containing BA, PE, and MBA. The abscissa is the total solute concentration in the bulk liquid phase. The mobile phase concentration is expressed via the relative mass composition BA:PE:MBA. Experimental data are provided with the following symbols: data for a single solute, circles; data for 1:1:1 mixtures (equal parts of BA, PE, and MBA), diamonds; data for 3:1:1 mixtures (three parts of BA, one part of PE, and one part of MBA), squares; data for 1:3:1 mixtures (one part of BA, three parts of PE, and one part of MBA), triangles; data for 1:1:3 mixtures (one part of BA, one part of PE, and three parts of MBA), stars. The lines are the adsorbed amounts calculated via the Langmuir model which uses the single solute determined parameters. Calculations are presented for the single solutes (solid lines), 3:1:1 mixtures (dotted lines), 1:1:1 mixtures (solid lines), 1:3:1 mixtures (dashed-dotted lines), and 1:1:3 mixtures (dashed lines). Table 1. Parameters of the Langmuir Model Identified from the Fit of the Single Solute Adsorption Data parameters

BA

PE

MBA

qs KL × 102

129.99 1.517

141.09 2.341

168.50 2.107

Table 2. Parameters of the Separation under Analytical Conditions Figure 3. Adsorbed amounts of PE (a) and MBA (b) determined via frontal analysis in mixtures containing BA and MBA. The conventions are identical to those for Figure 1.

At low concentrations, the distribution of the solute between the stationary phase and the mobile phase is characterized via the retention factor1

k′i )

tR,i - t0 t0

(5)

where k′i is the retention factor (equal to the product of the phase ratio and the initial slope of the isotherm), tR,i is the retention time of the ith solute, and t0 is the column holdup time. These 1498 Analytical Chemistry, Vol. 72, No. 7, April 1, 2000

parameters k′

BA

PE

1.274

2.160

MBA 2.440

N)L/H

Flow Rate 0.8 mL/min 8302 9019

9098

N)L/H

Flow Rate 1 mL/min 7396 8048

8228

parameters are determined from an analytical chromatogram of a mixture of the solutes and a nonretained compound. In this study, we used thiourea as the nonretained tracer. The relevant parameters are also presented in Table 2. The boundary condition or injection profile of the feed at the column inlet is also needed to calculate band profiles and system

Figure 5. Experimental injection profiles of solutes (a) and vacancies (b). The profiles are normalized in terms of concentrations, where C0 is the concentration of the solute present in the injected sample (a) or the concentration of additive initially present in the mobile phase (b). The solid line corresponds to a loop with a volume of 0.5 mL operated at 1 mL/min, the dashed-dotted lines correspond to a loop with a volume of 0.5 mL operated at 0.8 mL/min and the dashed lines correspond to a loop with a volume of 1.0 mL operated at 0.8 mL/ min.

peaks. It is customary to represent this boundary condition by a rectangular injection profile. However, experimental injection devices, like the one employed in this study to introduce the large amount of feed required, produce injection profiles that deviate significantly from the ideal, rectangular injection profile. The use of the correct boundary condition is necessary to achieve an accurate calculation of the bands under overloaded, nonlinear conditions.21 Experimental injection profiles (i.e., boundary conditions) corresponding to solutes not present initially in the column (i.e., under the conventional conditions of elution chromatography) have been reported.21 However, the study of system peaks requires special attention. The relevant boundary condition corresponds to the simultaneous injection of a feed sample and a vacancy of the strong additive on a concentration plateau of the strong additive. This is important to remember because the composition of the injected sample is usually different from that of the mobile phase and, accordingly, the injection produces a complex perturbation of the equilibrium established in the column prior to the injection.5 Injection profiles were recorded with the detector connected between the injection valve and the column, thus maintaining the same pressure drop (and presumably flow behavior) as that in the actual chromatographic experiment but replacing the column by a zero-volume connector. Recorded profiles corresponding to the different experimental situations encountered in the present study are shown in Figure 5. Note that, under the same experimental conditions, the injection of a certain amount of solute and that of an equivalent vacancy produce profiles which are (21) Katti, A. M.; Ma, Z.; Guiochon, G. AIChE J. 1990, 36, 1722.

Figure 6. Single solute band profiles of BA (a) and PE (b). C0 ) 25 g/L for each phenyl alcohol in the sample. The mobile phase is a mixture of methanol and water (1:1, v/v). The flow rate is 1 mL/min, and the volume injected is 0.5 mL. Presented are the experimental points (circles), the theoretical profiles which use a rectangular injection (dashed lines), and the theoretical profiles which use the experimental injection profiles (solid lines).

mirror images, as expected. There is a time delay of ca. 5 s from the time that the injection valve is actuated to the time that the front of the injection profile actually reaches the column inlet. This delay is in part due to the time needed to operate the valve, in part to the transit time (estimated to be less than 1 s from the connecting tube volume and the flow rate) and, probably, in part to the pressure excursion in the loop (from atmospheric pressure during filling to about 200 bar at the end of the injection) and to mixing of sample and mobile phase in the loop. Note, however that the front of the injection profile is steep, without any significant dispersion. On the other hand, the dispersion due to the Hagen-Poiseuille flow velocity distribution across the cross section of the loop produces a significant dispersion of the rear part of the injection profiles. Unfortunately, it is this very part of the injection profile that has the major influence on the final shape of the calculated profiles (see below). The injection profiles presented in Figure 5 have been normalized with respect either to the total concentration of solutes in the injected sample or to the initial concentration of the additive in the mobile phase (see figure caption). Accordingly, they can be used for mixtures of any composition. These profiles constitute the actual boundary conditions in band profile calculations. Single solute band profiles for BA and PE are presented in Figure 6. The calculated profile that assumes a rectangular injection (dashed line) produces a poor description of the rear, diffuse part of the experimental data. When the actual experimental injection profile is accounted for in the boundary condition (solid line), a better agreement between calculated and experimental (symbols) profiles is observed. The profiles of BA and PE presented here are typically Langmuirian, with a shock in the front and a diffuse rear. Analogous Langmuirian profiles are observed Analytical Chemistry, Vol. 72, No. 7, April 1, 2000

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Figure 7. Band profiles of a binary solute mixture of BA and PE (1:1, w/w) with a total solute concentration of 50 g/L (a) and of a ternary solute mixture of BA, PE, and MBA (1:3:1, w/w/w) with a total solute concentration of 50 g/L (b). The mobile phase is a mixture of methanol and water (1:1, v/v). The flow rate is 0.8 mL/min, and the volume injected is 0.5 mL. Presented are the experimental profiles for BA (circles), PE (squares), and MBA (triangles) along with the calculated profiles for BA (dashed lines), PE (dashed-dotted lines), and MBA (solid lines).

for the multisolute mixtures presented in Figure 7. For the binary mixture of BA and PE, two shocks are observed (Figure 7a). For the ternary mixture (Figure 7b), there are three shocks. There is a good agreement between the multisolute experimental (symbols) and calculated (lines) profiles. In all these cases, the mobile phase was a mixture of methanol and water (1:1, v/v). As reported previously, methanol is weakly adsorbed in this system (the retention factor of methanol in pure water is approximately 1). Accordingly, system peaks are not observed since the interactions of the solutes with the stationary phase are much stronger than those of methanol.22 When the mobile phase contains an additive which is retained, the injection of a feed sample causes a perturbation of the additive equilibrium between the two phases. Because of competition with the feed component, the amount of additive adsorbed decreases, to be restored later, when the feed components have moved on. This is the origin of additive peaks and system peaks.1 When the retention of the additive is higher but not much higher than that of the solutes, the profiles of system peaks become unusual or even strange.8 Thus, we decided to use 2-methylbenzyl alcohol, the most retained of the three solutes (see Table 2), as the strong additive of the mobile phase and to determine the profiles of the three components upon injection of a mixture of the other two solutes. In Figure 8 we present the band profiles corresponding to the injection of 0.5 mL of a mixture of BA:PE ) 3:1 (w/w) at a total concentration of 40 g/L. Excellent agreement between the experimental results (symbols) and those of the calculations (lines) was observed for this and for subsequent experiments (22) Golshan-Shirazi, S.; Guiochon, G. Anal. Chem. 1988, 60, 2634.

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Figure 8. Band profiles corresponding to the additive system peaks (a) and solute peaks (b) corresponding to the separation of a binary solute mixture of BA and PE (3:1, w/w) with a total solute concentration of 40 g/L. The mobile phase contains 10 g/L of MBA in a mixture of methanol and water (1:1, v/v). The flow rate is 0.8 mL/min, and the volume injected is 0.5 mL. Presented are the experimental profiles for BA (circles), PE (squares), and MBA (triangles) along with the calculated profiles for BA (dashed line), PE (dashed-dotted line), and MBA (solid line).

Figure 9. Band profiles for the same conditions as in Figure 8 except that the volume injected is 1.0 mL.

carried out under different experimental conditions (see Figures 9-11 ). The additive profile (Figure 8a) exhibits a typical shape,1 with a positive primary system peak followed by the negative vacancy peak. This pattern of the additive system peak roughly holds for all the chromatograms (see Figures 8a-12a). The band profile of BA, the lesser retained component, retains a Langmuirian shape, with a sharp front and a diffuse rear. It is quite similar to the one

Figure 10. Band profiles corresponding to the additive system peaks (a) and solute peaks (b) corresponding to the separation of a binary solute mixture of BA and PE (1:3, w/w) with a total solute concentration of 40 g/L. The mobile phase contains 10 g/L MBA in a mixture of methanol and water (1:1, v/v). The flow rate is 0.8 mL/ min, and the volume injected is 0.5 mL. Presented are the experimental profiles for BA (circles), PE (squares), and MBA (triangles) along with the calculated profiles for BA (dashed line), PE (dasheddotted line), and MBA (solid line).

Figure 11. Band profiles for the same conditions as in Figure 10 except that the volume injected is 1.0 mL.

observed for the band of pure BA (cf. Figures 6a and 8b), although it is wider and is eluted slightly later. By contrast, the band profile of PE is quite different from those in Figures 6a and 7; it is diffuse at both ends but mostly so at the front, the opposite of what is expected in the case of a Langmuirian behavior. The profile of PE could easily be ascribed to an anti-Langmuirian isotherm since this association is well-known in the case of single component bands.1 However, we do know that, in this particular separation,

Figure 12. Band profiles corresponding to the additive system peaks (a) and solute peaks (b) corresponding to the separation of a binary solute mixture of BA and PE (2:1, w/w) with a total solute concentration of 30 g/L. The mobile phase contains 20 g/L MBA in a mixture of methanol and water (1:1, v/v). The flow rate is 0.8 mL/ min, and the volume injected is 0.5 mL. Presented are the experimental profiles for BA (circles), PE (squares), and MBA (triangles) along with the calculated profiles for BA (dashed line), PE (dasheddotted line), and MBA (solid line).

the isotherm of PE is Langmuirian. The band profile of PE is the sole result of the competitive interactions among the three solutes in the system under consideration. The band of PE also exhibits two small “hills” with a shallow valley between them. This profile shape was obtained before in theoretical calculations.6 The results obtained with a twice larger injection (1 mL) of the same mixture are shown in Figure 9. Although the same features of Figure 8 are maintained, there are some striking changes which would not arise in the case of a binary feed sample analyzed with a pure mobile phase, with Langmuirian isotherm behavior. The top of the BA band is flat and wide, in sharp contrast of what is observed in the absence of additive, and the rear of the band is eluted later and is more diffuse. The small “hill” already observed at the front of the PE band in Figure 8 becomes more important and appears nearly as a well-identified peak (Figure 9b). The experiment, the results of which are illustrated in Figure 10, was carried out under the same experimental conditions as Figure 8, except that the mass ratio of BA and PE in the feed sample was reversed. The positive primary additive band becomes a doublet, in agreement with the experimental evidence. There is also a conspicuous, strong compression of the BA band due to the displacement caused by the additive band, which intercalates between the bands of BA and PE. The unusual symmetry of the PE band is also noteworthy. Again, this behavior is not typical of an overloaded Langmuirian band. Figure 11 illustrates the same separation as the one in Figure 10 but performed with a larger injection volume, 1.0 mL instead of 0.5 mL in Figures 8 and 10. Note that the doublet associated with the positive primary additive peak becomes a plateau. In the same time, two plateaus develop Analytical Chemistry, Vol. 72, No. 7, April 1, 2000

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at the BA band as well as a significant tag-along effect, again in agreement with experimental results. Finally, all the previous experiments were performed with an additive concentration in the mobile phase of 10 g/L. In Figure 12, we show the results of a similar separation carried out with a mobile phase concentration increased to 20 g/L. Compared to their profiles determined in the previous experiments, nothing unusual is observed regarding the band shapes of BA and MBA. By contrast, the band of PE exhibits a typical anti-Langmuirian shape with a diffuse front and a sharp rear. Note also that the band of PE is strongly compressed at the end of the chromatogram and that the mixed band containing both BA and PE is considerably reduced compared to what is seen in Figures 7-11. Similar shapes have been reported,7 but no quantitative results were published. If properly exploited, the band compression effects underlined above and especially in Figure 12 could be very useful in preparative separations. Note that a minor component of a binary mixture, i.e., an impurity, can be compressed, eluted as a narrow band, and recovered at a high purity (and possibly concentrated to a degree, certainly less diluted than under conventional conditions), either in the front or in the rear of the main component, provided that the proper additive is used. Similar manipulations were made under other chromatographic conditions.23,24 Proper manipulations of the mobile phase composition allow the selective concentration of minor components of a binary mixture (and probably of more complex mixtures) into a specific region of the chromatogram. This procedure could greatly facilitate the recovery and purification of important impurities for further analysis. This problem often arises in stability studies of pharmaceutical candidates. CONCLUSIONS The excellent agreement between the experimental and the calculated band profiles of sample components and system peaks obtained at high concentrations confirms once more the validity of the theory of nonlinear chromatography and the practical value of the equilibrium-dispersive model. Of particular interest is the demonstration that the simplest adsorption behavior, one following the competitive Langmuir model, may lead to unusual band profiles. Such results are often observed, to be discarded as anomalous and suspect of being irreproducible. The demonstration of their consistency with the fundamentals of adsorption and chromatography should lend them credence and legitimize their systematic investigation. System peaks are considered as unimportant in conventional reversed-phase liquid chromatography (RPLC), which is the most popular preparative process because of the relatively low cost of the mobile phase components. This is because the strong solvents in RPLC, methanol and acetonitrile, act by increasing the mobile phase solubility of the feed components, not by competing with them for access to the stationary phase. Indeed, the retention (23) Katti, A. M.; Ramsey, R.; Guiochon, G. J. Chromatogr. 1989, 477, 119. (24) Frenz, J.; Bourell, J.; Hancock, W. S. J. Chromatogr. 1990, 512, 299.

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times observed for BA and PE in the experiments reported in Figures 8-12 exhibit only small changes, certainly small ones compared to the changes of the band profiles. Solubility issues often force the chromatographer to consider either nonaqueous reversed-phase or normal-phase chromatography and to use solvent systems in which the strong solvent acts as a competitor of the feed components. In such a case, the strong solvent and its concentration are selected essentially on the basis of considerations limited to the need to achieve the proper retention and separation under linear conditions, i.e., at low concentrations. More attention should be paid to nonlinear system peaks and their potential usefulness for the design of separation methods in which larger throughputs are achieved by concentrating the impurities into certain zones of the chromatograms. Thus, the possibility of adjusting system peaks provides the knowledgeable separation scientist with another degree of flexibility in the development of new methods to enhance production rate, recovery yield, and/or product purity. ACKNOWLEDGMENT This work was supported in part by Grant CHE-97-01680 from the National Science Foundation and by a cooperative agreement between the University of Tennessee and Oak Ridge National Laboratory. We acknowledge the support of Maureen S. Smith in solving our computational problems. J.C.F. was a participant in the NSF-funded Macro-ROA Program for Faculty Research Visits to the University of Tennessee, Knoxville, and gratefully acknowledges that support. NOTATION C ) equilibrium concentration in the liquid phase, g/L Da,i ) axial dispersion coefficient, m2/s Hi ) height equivalent to a theoretical plate, m KL ) Langmuir equilibrium constant, L/g Ns ) number of solutes in the system q ) equilibrium concentration in the solid phase, g/L qs ) monolayer capacity, g/L t ) time, s t0 ) column holdup time, s tR,i ) retention time of the solute, s u ) interstitial velocity, m/s z ) axial coordinate, m Greek letters  ) column porosity Subscripts 1 ) benzyl alcohol 2 ) 2-phenylethanol 3 ) 2-methylbenzyl alcohol i ) ith solute Received for review August 18, 1999. Accepted January 5, 2000. AC9909406