Retention of Ionizable Compounds in Reversed-Phase Liquid

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Anal. Chem. 2004, 76, 4779-4789

Retention of Ionizable Compounds in Reversed-Phase Liquid Chromatography. Effect of the Ionic Strength of the Mobile Phase and the Nature of the Salts Used on the Overloading Behavior Fabrice Gritti and Georges Guiochon*

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

The retention mechanism of the protonated cation in propranolol chloride on C18-Xterra was investigated using mobile phases of various compositions. Accurate adsorption data were measured by frontal analysis, with a mixture of methanol and water (25% methanol), with no salt, as the mobile phase. The experimental isotherm has at least two inflection points, at concentrations of about 0.2 and 6.0 g/L, respectively. This precludes the modeling of these data with a simple convex-upward isotherm (e.g., Langmuir). The adsorption energy distribution or relationship between the number of sites on the adsorbent surface and the energy of adsorption on these sites was calculated by assuming Moreau isotherm behavior (Sshaped isotherm). This model has never been applied to describe the surface heterogeneity of any RPLC adsorbent. The calculation converged toward a bimodal energy distribution. Accordingly, the bi-Moreau model is the simplest theoretical model accounting for the adsorption data of propranolol from a mobile phase without salt. The complex-overloaded band profiles of propranolol measured in the presence of increasing concentrations of a supporting salt (KCl) in the mobile phase demonstrate that the same isotherm model applies also under these conditions, as was merely assumed in a previous work. The elution band profiles of propranolol calculated with the bi-Moreau isotherm model for solutions of salts of different natures (CaCl2, CsCl, Na2SO4) in the same mobile phase agree very well with the experimental band profiles. Ionogenic compounds are most important in the biochemical, biomedical, pharmaceutical, and environmental fields. Their analysis and separation is currently of great interest. Among the various methods used for that purpose, one of the most widely used to perform their separation, purification, or quantitative analysis is reversed-phase liquid chromatography (RPLC).1 The * To whom correspondence should be addressed. Fax: 865-974-2667. Email: [email protected]. (1) Dorsey, J. G.; Cooper, W. T.; Wheeler, J. F.; Barth, H. G.; Foley, J. P. Anal. Chem. 1994, 66, 500. 10.1021/ac0304121 CCC: $27.50 Published on Web 07/09/2004

© 2004 American Chemical Society

separation challenges that keep arising from the constantly evolving practical applications encountered in these areas have led to the use of increasingly complex experimental conditions. In most cases, care should be taken to use the appropriate mobilephase composition that keeps the analyte in its desired ionic form and allows the optimization of the separation. Mobile phases are often the combination of complex solution mixtures. Gradient elution chromatography, temperature adjustment, and the addition of suitable buffers or supporting salts are common approaches used to optimize separations. Accordingly, RPLC has become a successful empirical method using eclectic chromatographic systems to achieve specific goals, but the results are often contradictory, at least in appearance, and the interpretations given in the literature for the mechanisms of retention, separation, or both, are confused. Insights into the fundamentals of the adsorption of ions onto hydrophobic surfaces and the origin of the separation observed in RPLC are strongly needed. Numerous authors have worked to further our understanding of the retention mechanisms of ionizable compounds in RPLC.2-10 Most of these studies deal with linear conditions, although a model taking into account the repulsive surface potential of the adsorbent was proposed and investigated under nonlinear conditions.11,12 Basically, however, chromatographic separations depend on the equilibrium thermodynamics of the analyte between the stationary and the mobile phase.13-15 Knowledge of the entire equilibrium (2) Rose´s, M.; Canals, I.; Allemann, H.; Siigur, K.; Bosch, E. Anal. Chem. 1996, 68, 4094. (3) Bosch, E.; Bou, P.; Allemann, H.; Rose´s, M. Anal. Chem. 1996, 68, 3651. (4) Bosch, E.; Espinoza, S.; Rose´s, M. J. Chromatogr., A 1998, 824, 137. (5) Canals, I.; Portal, J. A.; Bosch, E.; Rose´s, M. Anal. Chem. 2000, 72, 1802. (6) Espinoza, S.; Bosch, E.; Rose´s, M. Anal. Chem. 2000, 72, 5193. (7) Rose´s, M.; Oumada, F. Z.; Bosch, E. J. Chromatogr., A 2001, 910, 187. (8) McCalley, D. V. J. Chromatogr., A 1996, 738, 169. (9) McCalley, D. V. Anal. Chem. 2003, 75, 3072. (10) A. Me´ndez, E. Bosch, M. Rose´s, U. D. Neue, J. Chromatogr., A 2003, 986, 33. (11) Ha¨gglund, I.; Ståhlberg, J. J. Chromatogr., A 1997, 761 3. (12) Ha¨gglund, I.; Ståhlberg, J. J. Chromatogr., A 1997, 910, 11. (13) Guiochon, G.; Golshan-Shirazi, S.; Katti, A. M. Fundamentals of Preparative and Nonlinear Chromatography; Academic Press: Boston, MA, 1994. (14) Ruthven, D. M. Principles of Adsorption and Adsorption Processes; Wiley: New York, 1984. (15) Suzuki, M. Adsorption Engineering; Elsevier: Amsterdam, The Netherlands, 1990.

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isotherm may provide much new information regarding the retention mechanisms involved and the surface properties of the adsorbent used, e.g., its heterogeneity.16-20 This information cannot be derived from the retention time of a mere analytical injection. The retention factor of an analyte is often the sum of the contributions of several distinct elementary adsorption processes because all solid adsorbents have a heterogeneous surface. Measurements made in the concentration range from =0 (i.e., under analytical conditions) to close to the compound solubility (i.e., under nonlinear conditions) allow a deconvolution of these different contributions. This makes it possible to determine whether the solute is adsorbed on one or different sites and often allows the derivation of the adsorption energy distribution (AED) on the surface considered. A bimodal energy distribution is obviously inconsistent with a Langmuir, a Jovanovic, a Moreau, or a BET adsorption isotherm, models that all assume a homogeneous surface. On the other hand, to acquire detailed information on the surface properties of an adsorbent, it is necessary to measure accurately the equilibrium isotherm. The acquisition of accurate isotherm data, i.e., of the relationship between the concentration of the solute adsorbed at equilibrium and its concentration in the mobile phase, is best carried out using frontal analysis (FA) chromatography. The goal of this paper is to show how the measurement of accurate isotherm data and the proper modeling of these data inform on the retention mechanism of an ionizable compound, propranolol, on a RPLC column. The data were acquired on MS XTerra-C18, a packing material that contains practically no ionexchange sites. The method described involves four successive steps. First, FA adsorption data of propranolol were acquired with a saltless mobile phase. Second, these data were modeled by regression analysis on several model equations and the best model was validated by estimating the AED from the same adsorption data and by comparing experimental overloaded elution profiles and profiles calculated with the isotherm model. Third, overloaded band profiles were recorded at six different salt concentrations in the mobile phase and the best values of the isotherm parameters were determined using the inverse method (IM) of chromatography. The evolution of the values of these parameters as a function of the ionic strength of the solution was studied from a physicochemical point of view. Fourth, the validity of the results obtained is confirmed by the agreement between experimental and calculated band profiles at high concentrations, for different supporting salts. THEORY The determination of the adsorption isotherm of a compound by the FA and the IM methods, and the equilibrium-dispersive model of chromatography are described elsewhere.21,22 The isotherm used in this work and the method followed to calculate the AED are summarized below. (16) Stanley, B. J.; Guiochon, G. J. Phys. Chem. 1993, 97, 8098. (17) Gritti, F.; Go¨tmar, G.; Stanley, B. J.; Guiochon, G. J. Chromatogr., A 2003, 988, 185. (18) Gotmar, G.; Stanley, B. J.; Fornstedt, T.; Guiochon, G. Langmuir 2003, 19, 6950. (19) Stanley, B. J.; Krance, J. J. Chromatogr., A 2003, 1011, 11. (20) Stanley, B. J.; Szabelski, P.; Chen, Y. B.; Sellergren, B.; Guiochon, G. Langmuir 2003, 19, 772. (21) Gritti, F.; Guiochon, G. J. Chromatogr., A 2004, 1033, 43. (22) Gritti, F.; Piatkowski, W.; Guiochon, G. J. Chromatogr., A 2002, 978, 81.

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Model of Isotherm. The plot of the isotherm data obtained by FA is convex downward in part of the concentration range investigated (see later), showing that there are significant adsorbate-adsorbate interactions. The simplest isotherm model for a homogeneous adsorbent surface on which such interactions take place is the Moreau model.23 The results obtained by fitting the adsorption data to this model suggested that the adsorbent surface is not homogeneous. The data are better modeled by assuming that this surface consists of patches of two different types of sites and by using the bi-Moreau model, an extension of the Moreau model. This last model assumes that a different Moreau model applies to each of two different types of sites, considered as homogeneous and acting independently:

b1C + Ib12C2

b2C + Ib22C2

+ qs,2 (1) q* ) qs,1 1 + 2b1C + Ib12C2 1 + 2b2C + Ib22C2 where qs,1, qs,2, b1, and b2 are the monolayer saturation capacities and the equilibrium constants on sites 1 and 2, respectively, and I is the adsorbate-adsorbate interaction parameter in the monolayer. Note that this model is nearly identical to the Ruthven model developed for adsorption on zeolites14 and for which the relationships between the coefficients in the numerator and denominator are slightly different. The equilibrium constants b1 and b2 are associated with the adsorption energies a,1 and a,2 through the following equation:24

bi ) b0ea,i/RT

(2)

where a,i is the energy of adsorption on type i sites, R is the universal ideal gas constant, T is the absolute temperature, and b0 is a preexponential factor that could be derived from the molecular partition functions in the bulk and the adsorbed phases. b0 is often considered to be independent of the adsorption energy, a,i.24 The adsorbate-adsorbate parameter I is related to the interaction energy, AAg 0, between two neighbor adsorbed molecules of compound A (i.e., propranolol) through a similar relationship,23

I ) exp(AA/RT)

(3)

Calculation of the Adsorption Energy Distribution. Actual surfaces are neither homogeneous nor paved with homogeneous tiles, as is generally assumed in chromatography. Actual surfaces are characterized by an adsorption energy distribution that may have several more or less well-resolved modes, each mode having a finite width.25 The experimental isotherm on such a surface is the convolution of the AED and the local isotherm. In many instances encountered in RPLC, the AED has two or a few narrow modes, each one corresponding to a nearly homogeneous type of sites. The overall or experimental isotherm is the sum of the (23) Moreau, M.; Valentin, P.; Vidal-Madjar, C.; Lin, B. C.; Guiochon, G. J. Colloid Interface Sci. 1991, 141, 127. (24) Jaroniec, M.; Madey, R. Physical Adsorption on Heterogeneous Solids; Elsevier: Amsterdam, The Netherlands, 1988. (25) Umpleby II, R. J.; Baxter, S. C.; Chen, Y.; Shah, R. N.; Shimizu, K. D. Anal. Chem. 2001, 73, 4584.

isotherms on the different types of sites that cover the surface. These local isotherms are often Langmuir or Jovanovic isotherms, in which case, the overall isotherm is convex upward. However, all the experimental isotherms measured in this work are not convex upward, so a model of a local isotherm that is consistent with these results should be used, a model that could describe experimental isotherms having at least one, sometimes two inflection points. The Moreau isotherm is the simplest model that fulfills this requirement. We assume here that the surface is made of several types of homogeneous tiles, on which adsorbateadsorbate interactions can take place. The parameter I in the model must be arbitrarily fixed before the AED calculation can begin. Under the condition of a continuous adsorption energy distribution, and assuming a Moreau local isotherm model, the experimental isotherm can be written

q*(C) )

b()C + Ib2()C2

∫ F()1 + 2b()C + Ib ()C ∞

2

0

2

d

(4)

where q*(C) is the total amount of solute adsorbed on the surface at equilibrium with a concentration C,  is the binding energy between an adsorbed molecule and the surface of the adsorbent, and b is the binding constant related to  through eq 2. The normalization condition for the AED is

∫ F() d ) q ∞

0

s

(5)

where qs is the overall saturation capacity. The AED, F(), of the surface is derived from the set of experimental isotherm data points measured by FA. There are several procedures for that,24-27 but most of the methods used require a preliminary smoothing of the experimental data, e.g., by fitting them to an isotherm model or imposing a functional dependence to the AED. In both types of methods, some arbitrary information is injected into the determination of the AED. In this work, we used the expectation-maximization (EM) method,27 a computer-intensive method that directly uses the raw experimental data, without injecting any arbitrary information into the AED derivation. The principle of the EM method and the mathematical procedure used by this method to derive the AED are discussed in detail elsewhere.27 EXPERIMENTAL SECTION All details regarding the chemicals, the HPLC instrument, the reversed-phase column used, and the experimental conditions selected to acquire the breakthrough curves (for FA) and the overloaded band profiles (for IM) are given in ref 21. RESULTS AND DISCUSSION The main purpose of this work was to investigate the adsorption mechanism of propranolol, an amine ionizable into a cation at sufficiently low pH, on Xterra-C18, to determine the extent of the heterogeneity of this adsorbent, and to explain previous chromatographic results obtained on the same column and on (26) Toth, J. Adsorption; M. Dekker: New York, 2002. (27) Stanley, B. J.; Bialkowski, S. E.; Marshall, D. B. Anal. Chem. 1994, 659, 27.

Kromasil-C18. The commercial XTerra-C18 adsorbent was chosen because it exhibits almost no silanol activity, as demonstrated by the lack of retention of the cation Li+ in the pH range 3-11.10 When propranolol is dissolved in water, in the same concentration range as that used in this work, the solution pH varies by less than 0.5 pH unit, around pH 5.2. The pKa of propranolol is 9.45 in pure water, hence, pKa ) 8.8 in a 40:60 v/v methanol/water solution.28 Accordingly, we study the adsorption of an organic cation on a surface on which ionic exchanges between solute and surface are practically impossible. Adsorption Data of Propranolol on XTerra-C18 and the BiMoreau Adsorption Model. Figure 1 shows the adsorption data (isotherm plot, Figure 1A, and Scatchard29 plot, Figure 1B) of propranolol onto XTerra from the 25:75 methanol/water solution. The isotherm is clearly convex upward at high concentrations, above ∼7.5 g/L, and obviously convex downward at low concentrations, below 5 g/L. However, the isotherm is convex upward again at very low concentrations, below ∼0.2 g/L, as shown by the decreasing Scatchard plot at very low concentrations. The isotherm data must be fitted to an isotherm model that may have at least two inflection points. Obviously, neither the Langmuir nor any combination of Langmuir isotherm model is suitable because these are strictly convex upward and do not admit any inflection point. For the same reason, the modified Langmuir or Sta˚hlberg isotherm model, usually appropriate to describe the adsorption behavior of ionic species on charged surfaces, is inconsistent with our adsorption data. The simplest model consistent with these data is the Moreau model for a homogeneous surface or the simplest extension of this model to heterogeneous surfaces, the so-called bi-Moreau model (eq 1). The Moreau model accounts for adsorbate-adsorbate interactions through the parameter I. The best numerical values of the parameters were derived by regression analysis (Table 1), by minimizing the sum of the relative residuals squared, (1 - qi,calc/qi,exp)2. A relatively poor Fisher number was obtained with the Moreau model (F ) 2300) and a much higher one (F ) 33 600) for the bi-Moreau model. The latter model contains two more parameters than the Moreau model. According to the Student test and given the numbers of degrees of freedom of the two models (28 - 3 ) 25 and 28 - 5 ) 23, respectively), the bi-Moreau model is statistically better than the Moreau model with a 99% confidence level if the ratio of their respective Fisher numbers is larger than 2.69, a value that is markedly lower than the 14.6 ratio obtained. The bi-Moreau model is the better suggesting that the surface is heterogeneous. The best isotherm parameters were as follows: qs,1 ) 148.5 g/L, b1 ) 0.035 67 L/g, qs,2 ) 0.37 g/L, b2 ) 1.78 L/g, and I ) 5.191 (or AA =1.65RT). The ratios of the saturation capacities and adsorption constants of types 1 and 2 sites are about 400 and 1/50, respectively. The high-energy sites are thus responsible for 1/8th of the overall retention under linear conditions, despite their much lower density, which is all but negligible. Their presence explains the Langmuirian isotherm behavior observed at very low propranolol concentrations, because these sites are rapidly saturated. However, a careful look at the Scatchard plot of the data (symbols) and at the Scatchard plot derived from the best model (28) Rived, F.; Canals, I.; Bosch, E.; Rose´s, M. Anal. Chim. Acta 2001, 439, 315. (29) Andrade, J. D. In Surface and Interfacial Aspects of Biomedical Polymers; Andrade, J. D., Ed., Plenum Press: New York, 1985; Vol. 60, Chapter 1.

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Figure 1. Adsorption isotherm data of propranolol on XTerra-C18 measured by FA. T ) 296 K; mobile phase methanol/water, 25:75, v/v. (A) FA adsorption isotherm data. (B) Scatchard plot representation of the FA data. Note the changes of the isotherm curvature from low to high concentrations (Langmuirian, anti-Langmuirian, and Langmuirian). (C) Scatchard representations of the best mathematical bi-Moreau isotherm model with the same adsorbate-adsorbate interaction parameter on each site (I1 ) I2 ) I), derived by MLRA from the adsorption data in the figure. Note the presence of three inflection points (I, II, III). (D) Zoom of the low concentration part of (C). (E) Scatchard representations of the best mathematical bi-Moreau isotherm model with independent adsorbate-adsorbate interaction parameters on each site (I1 * I2). Note, this time, the presence of only two inflection points, consistent with the experimental adsorption data in (A) and (B). (F) Zoom of the low concentration part of (E). Table 1. Best Moreau or Bi-Moreau Isotherm Parameters Derived by MLRA of the Adsorption Data of Propranolol on the C18-Bonded Xterra Column with a Mixture of Methanol and Water (25:75, v/v) as the Mobile Phasea Moreau

Fisher qs,1 (mmol/L) b1 (L/mol) qs,2 (mmol/L) b2 (L/mol) I1 I2

bi-Moreau (I1 ) I2 ) I)

bi-Moreau (I1 * I2)

MLRAb

MLRAb

EM (I)c

MLRAb

EM (I1)c

EM ((I1I2)1/2)c

EM (I2)*

2300 602 9.84

33600 571 9.27 1.4 462.7 5.191

33900 570 9.31 1.2 550.4 6.654 1.364

36200 553 8.40 7.1 213.7 6.654

41000 562 8.31 3.6 223.6 3.012

1040 622 10.4 no no 1.364

170 771 10.1 no no

3.839

a The table also compares these best estimated isotherm parameters to those obtained by the calculation of the AED by assuming different values of the adsorbate-adsorbate parameters I. b MLRA used the minimization of the sum of the square relative residuals. c EM procedure for the AED determination after 106 iterations.

(lines, Figure 1C and D) shows that the best isotherm model actually exhibits three inflection points and can be divided into four concentration domains. The isotherm is initially convex downward (0 < C < 0.15 g/L), then convex upward (0.15 < C < 0.70 g/L), then convex downward again (0.70 < C < 5.5 g/L), and finally convex upward (C g 5.5 g/L). In the lowest concentration range, type 2 sites are not yet saturated and both isotherm terms exhibit anti-Langmuirian behavior (Note that their adsorbateadsorbate interaction intensities are the same, I ) 5.191.). The first concentration range of Langmuirian behavior is the one in which type 2 sites are becoming saturated. In the third concentration range, type 2 sites are saturated and the anti-Langmuirian 4782 Analytical Chemistry, Vol. 76, No. 16, August 15, 2004

behavior of the isotherm results from the strong adsorbateadsorbate interactions on type 1 sites that are still far from saturation. The behavior of the isotherm becomes Langmuirian in the fourth concentration range because type 1 sites are becoming saturated. The Scatchard plot corresponding to this description is illustrated in Figure 1C and D (at different concentration scales). Unfortunately, this description of the best isotherm model is inconsistent with the experimental results. First, note that the initial anti-Langmuir behavior (first domain) is not observed on the experimental Scatchard plot in Figure 1B. In addition, the overloaded band profiles recorded upon injection of samples of

Figure 2. Correspondence between the experimental isotherm curvature and the shape of the overloaded band profiles recorded in the same conditions as in Figure 1. A shock and a diffuse part in the adsorption front are associated with a Langmuirian and anti-Langmuirian curvature of the isotherm, respectively. The reversed is observed for the rear part of the band profile. (A) High loading band profile. (B) Low loading band profile. (C) Comparison between experimental and calculated band profiles of propranolol on XTerra-C18 (methanol/water, 25:75, v/v) assuming the best bi-Moreau model consistent with the adsorption data (I1 * I2). The calculation uses the equilibrium-dispersive model of chromatography, rectangular injection profiles, and a column efficiency of 3000 theoretical plates. Note the very good agreement between experience and calculation in all the band shape details. High loading. (D) Same as (C) except low loading.

either a 15 or a 3 g/L solution of propranolol (Figure 2A and B, respectively) can hardly be consistent with any anti-langmuirian behavior at very low concentrations since a front shock layer is observed at these low concentrations, not a dispersive adsorption boundary. This suggests that there was an error in the model assumed initially and the adsorbate-adsorbate interactions are not equal when the analyte is adsorbed on type 1 or 2 sites. The isotherm data in Figure 1 and the profiles in Figure 2 suggest that only weak adsorbate-adsorbate interactions do take place on the type 2 sites, which would explain an isotherm with an inflection point at such a low concentration that it could not be observed. A multilinear regression analysis (MLRA) of the isotherm data was then made using a six-parameter bi-Moreau model (with I1 * I2), and the results are given in Table 1. They confirm that I2 is lower than I1 in the best numerical model (1.36 versus 6.65, respectively) and that these values give an isotherm shape that is consistent with the experimental results (Figure 1E and F). The numerical values of the isotherm parameters were

also validated by comparing the experimental and simulated overloaded band profiles. The latter were calculated with the equilibrium-dispersive model of chromatography, assuming a column efficiency of 3000 theoretical plates. The isotherm model introduced was the six-parameter bi-Moreau model. The agreement between the experiment and calculated profiles is excellent (Figure 2C and D), which demonstrates that this isotherm model describes all details of the shape of the experimental band profiles corresponding to the different curvature domains of the actual isotherm (Langmuirian, anti-Langmuirian, and Langmuirian). Although the isotherm must have a first inflection point at a concentration below 0.04 g/L (Figure 1F), axial dispersion is too important and prevents observation of the corresponding change in the profile of the band front (Figure 2A). Some other, independent confirmation of the presence of two types of adsorption sites on the adsorbent surface was desired because (1) the saturation capacity of the high-energy sites is very small, which could cast some doubts regarding the existence of Analytical Chemistry, Vol. 76, No. 16, August 15, 2004

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Figure 3. AED of propranolol (plot of the distribution of the logarithm of the equilibrium constant b) from the raw adsorption data measured by FA (Figure 1). Calculations were run using the EM procedure assuming the local Moreau isotherm model (see text). The four rows of graphs correspond to calculations made with different values of the adsorbate-adsorbate parameter I of the local isotherm. The agreement between the resulting adsorption isotherm and the experimental one is also shown in the right graphs graphs in rows B-D. (A) I ) 5.191, increasing number of iterations (103-107). (B) I ) 6.654. (C) I ) 3.012. (D) I ) 1.364. Note that a unimodal distribution cannot describe satisfactorily the adsorption of propranolol. 4784 Analytical Chemistry, Vol. 76, No. 16, August 15, 2004

such sites, and (2) the values of the parameters of type 2 sites depend strongly on assumptions made regarding the numerical value of I1 and I2 (see Table 1). The first experimental evidence of their existence is strong, however. It is the shape of the overloaded band profiles (Figure 2) and the initial front shock at low concentrations instead of the diffuse boundary that would correspond to a simple unimodal Moreau model. Using the expectation-maximization method, it was possible to determine the AED of the system directly from the raw adsorption data by assuming a local Moreau model. However, the structure of the EM program has the drawback that the distributions of the equilibrium constant, bi, and that of the adsorbate-adsorbate interactions, Ii, cannot be calculated simultaneously. The adsorbateadsorbate interactions have to be fixed arbitrarily to a constant value I, common to all the adsorption sites. If I ) 5.191, the best value of the parameter that is afforded by the regression analysis of the isotherm data to the bi-Moreau model with the same adsorbate-adsorbate interactions on both sites, the EM predicts a bimodal energy distribution (Figure 3A, in which the left and right graphs correspond to the low- and high-energy sites, respectively) and isotherm parameters that are consistent with those derived by the MLRA. When I ) 6.654, the best value of parameter I1 that was obtained by MLRA using the bi-Moreau model with different adsorbate-adsorbate interactions on each site, the EM predicts again a bimodal energy distribution (Figure 3B, left) and there is a very good agreement between the experimental isotherm data and the isotherm calculated from the AED (Figure 3B, right). The reason for this is that the number of type 2 sites is very small and a large overestimate of the actual adsorbate-adsorbate interaction parameter on these sites does not much affect the adsorption isotherm. On the other hand, if an arbitrary estimate is selected for the parameter I and it is lower than 5.191 (e.g., I2 ) 1.364 or (I1I2)1/2 ) 3.012), the EM gives an unimodal energy distribution (left graphs in Figure 3B and D), with numerical values that lead to a very poor agreement between the experimental adsorption data and the calculated isotherm (right graphs in Figure 3C and D). This is because the adsorbateadsorbate interactions on the most abundant type 1 sites are seriously underestimated and the isotherm becomes unsatisfactory. Unfortunately, the EM cannot be used to estimate simultaneously the equilibrium constants and the adsorbate-adsorbate interactions. However, the EM calculations demonstrate that a unimodal energy distribution cannot take place in our system because, when such a distribution is obtained (for I < 4.5), the calculated isotherm never matches well the FA adsorption data. This result also supports the conclusion that strong adsorbateadsorbate interactions do take place on the low-energy adsorption sites. Isotherm Determination by IM in the Presence of Salt in the Mobile Phase. In the preceeding section, we focused our attention on the determination of the best isotherm model accounted for by the adsorption data of the ionic species propranolonium, using a solution of methanol in water as the mobile phase (25% methanol, v/v) that contains no salt. We concluded that the isotherm model had to fulfill the following conditions: (1) The isotherm model is not strictly convex upward but has at least two inflection points (see Figures 1 and 2, the FA data, and

Figure 4. Comparison between the experimental profiles of propranolol (dotted line) and the best calculated profiles found by IM (solid line) on XTerra (methanol/water, 40:60, v/v, 15-s injection of a 30 g/L solution) at high column loading for different concentrations of potassium chloride salt in the mobile phase. T ) 296 K; flow rate 1 mL/min. The bi-Moreau model with independent adsorbateadsorbate interaction parameters was used in IM. Note that the simple bi-Langmuir model would have failed to describe the band profiles at low ionic strength solution (I < 0.05 M). (A) High loading. (B) Low loading.

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Table 2. Adsorption of Propranolol on the C18-Bonded Xterra Columna FA [KCL] qs,1 (mmol/L) b1 (L/mol) qs,2 (mmol/L) b2 (L/mol) I1 I2

0b 553 8.40 7.1 213.7 6.654 1.364

inverse method 0c 568 8.15 6.0 252.8 6.801 2.528

0d 436 3.01 6.6 119.7 15.22 4.25

0.002d 437 3.59 6.6 1179.4 11.07 0.33

0.010d 481 5.14 12.9 667.9 5.60 0.22

0.050d 519 7.83 24.2 412.8 1.59 0.52

0.100d 588 10.05 27.5 352.2 0.65 0.73

0.200d 738 11.21 29.7 312.7 0.25 0.97

a Best bi-Moreau isotherm parameters derived from frontal analysis data (MLRA) and from overloaded band profiles using the inverse method of isotherm determination. The table shows the evolution of those parameters when the concentration of the neutral salt KCl increases in the mobile phase. b Methanol/water, 25:75, v/v. c Methanol/water, 25:75, v/v. Arithmetic mean of the best isotherm parameters estimated by IM with the low and high loading profile. d Methanol/water, 40:60, v/v. Arithmetic mean of the best isotherm parameters estimated by IM with the lowand high-loading profile.

the experimental overloaded bands). When the concentration increases in the mobile phase, the curvature of the isotherm has to be successively Langmuirian, anti-Langmuirian, and Langmuirian. However, an anti-Langmuirian segment at very low concentrations cannot be ruled out. (2) The isotherm model does not have a unimodal AED (see Figure 3). The simplest way to satisfy these two conditions is to assume a two-site heterogeneous surface (with equilibrium constants b1 and b2) and different adsorbate-adsorbate interactions (I1 * I2) in the adsorbed monolayer (of saturation capacities qs,1 and qs,2). This physical model is implemented by the bi-Moreau isotherm equation. The best set of these parameters obtained by MLRA of the FA data is given in Table 1. The data there show that the results derived from the MLRA and from the EM method are in excellent agreement and that the bi-Moreau model with I1 * I2 is better than the other models, with a Fisher coefficient of 36 200. Now, we are interested in investigating the effect of the presence of a salt in the mobile phase on the adsorption behavior of the ionic compound. We assumed that the addition of the salt (here, potassium chloride) to the methanol/water solution used as the mobile phase, together with the increase in methanol concentration needed to compensate for the increased retention caused by the salt, does not qualitatively alter the retention mechanisms. The equilibrium isotherm behavior remains the same, still accounted for by the bi-Moreau model. The only effects of the changes made in the composition of the mobile phase are changes in the numerical values of its parameters. The basis for this assumption is that the addition of a salt that is entirely dissociated should not affect the dissociation or the adsorption equilibria of propranolol in the chromatographic system. The retention mechanism should not change abruptly, nor should the isotherm switch from one model to another when the salt is added to the mobile phase and its concentration is changed. There should be continuity in the behavior of the system. The equilibrium isotherms were determined by IM in six different mobile phases, solutions of KCl at increasing concentrations (0, 0.002, 0.01, 0.05, 0.1, 0.2 M) in methanol/water (40:60, v/v). To apply the IM method, two 15-s, 250-µL injections of two different propranolol solutions were made in each mobile phase, one at low (1.5 g/L) and the other at high (30 g/L) concentration. This procedure saved much time and chemicals. The advantage of performing two injections at very different concentrations arises from the fact that the high loading factor profile provides accurate information on the isotherm parameters of the low-energy type 4786 Analytical Chemistry, Vol. 76, No. 16, August 15, 2004

of sites (those that are being populated at high concentrations) while the low loading factor profile provides accurate data regarding the parameters corresponding to the high-energy type of sites. This is important in the present case because there is a large difference between the contributions of the two types of sites to the overall Henry constant. The 12 chromatograms recorded are shown in Figure 4 (dotted lines), in two panels corresponding to the low (Figure 4A) and the high (Figure 4B) column loadings. These experimental chromatograms are compared to the best ones derived using the IM method (solid lines). An excellent agreement is observed between these two sets of profiles. Obviously, the bi-Moreau model predicts very well the overloaded band profiles at low salt concentrations, when the front and the rear of the profiles are complex assemblies of shock layers and diffuse boundaries, as well as at high salt concentrations, when the profile exhibits a front shock and a diffuse rear boundary. Obviously, the higher the ionic strength of the mobile phase, the higher the band retention, whatever the loading factor. This is consistent with the common-ion effect, the addition of a salt to an aqueous solution reducing the solubility of organic compounds. In addition to this sharp increase of the retention time, there is an important, progressive change in the shape of the high-concentration band profiles (Figure 4B). At low potassium chloride concentrations (e.g., 0.002 M), the band front exhibits two concentration shock layers separated by a diffuse boundary, the same shape observed when there is no salt in the mobile phase (previous section). This effect, consistent with a two-inflection point isotherm, supports the continuity argument stating that the isotherm model does not change when salt is added to the mobile phase; only the parameters vary. This result also agrees very well with the values of the isotherm parameters determined by FA using a mobile phase containing no salt (see previous section and Table 2). When the potassium chloride concentration becomes large (typically beyond 0.05 M), the band profile becomes more conventional, similar to the profiles obtained for compounds having a convex upward, i.e., a Langmuirian isotherm. Actually, the bi-Moreau model accounts well for this kind of band profile with appropriate numerical values of the isotherm parameters since the bi-Langmuir isotherm model is a particular case of the bi-Moreau isotherm for which there are no adsorbate-adsorbate interactions; i.e., I1 ) I2 ) 0). The best values calculated for the six isotherm parameters are listed in Table 1. The reproducibility of these coefficients is

Figure 5. Best bi-Moreau isotherm parameters (qs,1, qs,1, b1, b2, I1, I2) using the IM procedure. Each parameter was derived as the arithmetic mean of the best values found by IM with the high and low loaded band profiles. Note the increase of saturation capacities and the decrease of adsorbate-adsorbate interactions with increasing salt concentration in the mobile phase. Surprisingly, the equilibrium constants evolve in opposite directions, suggesting different physical origin for sites 1 and 2.

characterized by a relative standard deviation of ∼1% for the coefficients of the first term and less than 5% for those of the second term. This accuracy and the close agreement between the results derived from the FA and IM isotherm data and between the results of the analysis of the isotherm data by isotherm fitting, Scatchard plots, and adsorption energy calculations lead to important conclusions regarding the retention mechanism of propranolol. The relationships between the isotherm parameters and the ionic strength of the mobile phase are illustrated in Figure 5. Two different types of adsorption sites coexist on the surface of Xterra-C18. They have different average energies and very different saturation capacities. Obviously, the higher energy sites are populated first at low propranolol concentrations. The equilibrium constant b2 of the less abundant high-energy sites and their adsorbate-adsorbate interaction coefficient decrease rapidly

with increasing ionic strength of the solution while their saturation capacity increases. The density of these high-energy sites increases by a factor of 4 when [KCl] increases from 0 to 0.2 M, but it tends toward a finite limit at high ionic strength, a limit of ∼10% of the total saturation capacity. This change is due to the decrease of the surface potential of the adsorbent. A strong decrease of the equilibrium constant is observed when the lowest amount of salt is added to the pure methanol/water solution. Rose´s and al.7 attributed the decrease in the retention of K+ and Na+ that they observed to an ion-exchange mechanism between these cations and some residual, unprotonated silanols. Such an ionexchange mechanism is unlikely on XTerra-C18, on which no evidence of residual silanols at a pH lower than 10 has ever been observed.11 Furthermore, the large fraction (10%) of the overall saturation capacity occupied by type 2 sites and the weak energy difference between the two types of sites (2 - 1 < 10 kJ/mol) Analytical Chemistry, Vol. 76, No. 16, August 15, 2004

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Table 3. Best Bi-Moreau Isotherm Parameters (Sites 1 and 2) of Propranolol Measured by the Inverse Method, on the Xterra-C18 Column with a Mixture of Methanol and Water (40:60, v/v) as the Mobile Phase Containing Different Salts at a Constant Ionic Strength of 0.2 Ma KCl 0.20 M

qs,i (g/L) bi (L/g) Ii (L2/g2) a

CsCl 0.20 M

CaCl2 0.0667 M

Na2SO4 0.0667 M

sites 1

sites 2

sites 1

sites 2

sites 1

sites 2

sites 1

sites 2

192 0.043 0.69

7.5 1.20 1.02

167 0.043 0.46

7.7 0.97 0.80

196 0.035 0.48

6.4 1.30 1.13

145 0.075 6.22

0.5 1.50 ∼0

The parameters calculated from the analysis of both the high- and low-loading band profiles (arithmetic average, 30 and 1.5 g/L).

Figure 6. Comparison between the experimental band profiles of propranolol on XTerra-C18 (mobile phase methanol/water, 40:60, v/v) with different salts, calcium chloride, cesium chloride, potassium chloride, and sodium sulfate, at constant ionic strength (0.2 M) and the best calculated band profile assuming the bi-Moreau model. Note that the ionic strength alone does not govern the position and shape of the band. Note also the versatility of the bi-Moreau model that can well describe the different profiles obtained with different salts.

do not support the existence of a cation-exchange mechanism on some acidic sites. The adsorbate-adsorbate interaction energy on the high-energy sites becomes close to zero as soon as some salt is added to the mobile phase, although the high ionic strength limit of I2 does not seem to be 0 (by contrast with the limit of I1). The equilibrium constant, b1, and the saturation capacity, qs,1, of the dense, low-energy sites increase with increasing ionic strength of the solution while the energy of the adsorbateadsorbate interactions decreases. The increase of the equilibrium constant is related to the decrease of the solubility of propranolol, caused by the common-ion effect, and connected with the addition of the chloride anion (the co-anion of propranolonium in the sample). The adsorption on type 1 sites probably involves dispersive interactions between the naphthyl group of propranolol and the C18-bonded chains. This effect shows that the chemistry of the sites of types 2 and 1 is certainly different. The saturation capacity increases by a factor of 1.6 when [KCl] increases from 0 to 0.2 M, a result that is consistent with the progressive decrease of the repulsive interactions between the charges of the adsorbed organic cations and the decrease of the surface potential of the C18-bonded phase with increasing salt concentration. This effect has the same origin as the correlative increase of qs,2, the reduction 4788

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of the surface potential. The coefficient of the adsorbateadsorbate interactions (I1) decreases with increasing ionic strength of the solution and tends toward zero, an effect explained by the decrease of the π-π staking intermolecular interactions between the naphthyl moieties of the propranololium cation. Versatility of the Bi-Moreau Model. A last important issue is whether the ionic strength is the fundamental factor controlling the adsorption of propranolol from an aqueous solution of methanol. Accordingly, the nature of the salt was changed while keeping the ionic strength of the solution constant. Figure 6 summarizes the overloaded band profiles (dotted lines) recorded after injection of the same high-loading amount of propranolol as used in the experiments reported in the previous sections (see Figure 4B). The ionic strength of the solution was kept constant, at 0.2 M. Obviously, the ionic strength of the solution alone cannot explain the whole variation of the retention time and of the shape of the bands. The nature of the ions used is important. Table 3 summarizes the best values of isotherm coefficients for the different salts studied. Small but significant changes of the numerical values of the isotherm parameters are observed for the other monovalent anions. The number of high-energy sites is still important (∼5%) and the adsorbent-adsorbent interactions remain weak. When a bivalent anion like SO42- was used, the shape and the position of the bands are drastically modified. Strong adsorbate-adsorbate interactions (with AA increasing from e 0 to ∼2RT) now take place on the low-energy sites whose adsorption energy is markedly increased (from 0.043 to 0.075 L/g). The saturation capacity of the low-energy sites decreases by 20%, to 145 g/L, and that of the high energy sites drops suddenly to almost zero. Accordingly, the front part of the band now exhibits first a diffuse front, followed with a shock layer, while the rear is composed of a diffuse boundary followed by a shock layer to the zero concentration. This behavior is typical of an antiLangmuir/Langmuir isotherm that possesses one inflection point. The bi-Moreau isotherm equation can account well for this new physical model. This suggests that the retention mechanism, although complex and affected in various ways by changes in the experimental conditions, remains fundamentally unaltered in all the experiments discussed in this report. CONCLUSION This work demonstrates the power, the generality, and the effectiveness of a general method of study of the adsorption behavior of a compound in a liquid-solid-phase system. This new method combines three successive steps. First, a sufficient number of accurate adsorption data are measured by FA under a

selected set of experimental conditions. Second, these data are carefully modeled, selecting the isotherm model on the basis of the information provided by the results of the calculation of the adsorption energy distribution. Third, one or several experimental parameters, e.g., the temperature or the composition of the mobile phase, are varied systematically and the coefficients of the isotherm model are determined with the IM method of isotherm measurements. These variations provide a better, more profound, and more detailed understanding of the often complex mechanisms of adsorption in the phase system studied than mere measurements of the retention factor and its variations with the experimental conditions. This method proved particularly useful in the case in point of an ionizable compound on a nonpolar adsorbent surface commonly used in RPLC. Our results demonstrate the strong influence on the adsorption isotherm of an ionizable compound of the nature and concentration of other ionic species dissolved in the mobile phase while these other ions are inert toward nonionic compounds.37 The presence of a salt does not change the isotherm model accounting for the adsorption of propranolol, but adding a salt as simple as KCl and changing its concentration modifies considerably the values of the isotherm parameters. The adsorption of propranolol is best accounted for by assuming that the adsorbent surface is covered with two types of adsorption sites having different adsorption constants and saturation capacities and on which adsorbateadsorbate interactions of different energies take place. This model accounts well for all the adsorption data and predicts accurately the low- and high-concentration band profiles recorded. The relative values of the parameters of the model change significantly with the salt concentration and with the nature of the salt. This

explains the important changes in the band profiles observed. The model applies to each salt investigated, whatever the number of inflection points of the adsorption isotherm. The two types of sites correspond most probably to two different environments in or around the alkyl ligands bonded to the adsorbent surface. Because the saturation capacity of the lowenergy sites is large, these sites correspond most probably to simple interactions with an alkyl group bonded to the surface. The involvement of free silanol groups at the silica surface in the formation of the high-energy sites is unlikely for three reasons. First, the difference in adsorption energy between the low- and the high-energy sites is too small to be explained by interactions between these free silanols and the propranololium ions. Second, the saturation capacity of the high-energy sites is too high compared to that of the low-energy sites and to the low density of these silanol groups. Finally, the adsorbent used is known for having an extremely low content of residual silanol groups. ACKNOWLEDGMENT This work was supported in part by Grant CHE-02-44693 of the National Science Foundation and by the cooperative agreement between the University of Tennessee and the Oak Ridge National Laboratory. We thank Uwe Neue (Waters Corp., Milford, MA) for the generous gift of the XTerra MS C18 column used in this work and for fruitful and creative discussions.

Received for review December 11, 2003. Accepted May 18, 2004. AC0304121

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