Peak shapes of acids and bases under overloaded conditions in reversed-phase liquid chromatography, with weakly buffered mobile phases of various pH: A thermodynamic interpretation

Journal of Chromatography A, 1216 (2009) 63–78

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Journal of Chromatography A journal homepage: www.elsevier.com/locate/chroma

Peak shapes of acids and bases under overloaded conditions in reversed-phase liquid chromatography, with weakly buffered mobile phases of various pH: A thermodynamic interpretation Fabrice Gritti a,b , Georges Guiochon a,b,∗ a b

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

a r t i c l e

i n f o

Article history: Received 1 May 2008 Received in revised form 3 November 2008 Accepted 7 November 2008 Available online 14 November 2008 Keywords: Overloaded band profiles Acids and bases compounds C18 reversed-phase columns Weak buffer capacity Nonlinear chromatography Competitive adsorption isotherms Column heterogeneity Silanol activity Silica

a b s t r a c t We measured overloaded band profiles for a series of nine compounds (phenol, caffeine, 3-phenyl 1propanol, 2-phenylbutyric acid, amphetamine, aniline, benzylamine, p-toluidine, and procainamidium chloride) on columns packed with four different C18 -bonded packing materials: XTerra-C18 , Gemini-C18 , Luna-C18 (2), and Halo-C18 , using buffered methanol–water mobile phases. The SW pH of the mobile phase was increased from 2.6 to 11.3. The buffer concentration (either phosphate, acetate, or carbonate buffers) was set constant at values below the maximum concentration of the sample in the band. The influence of the surface chemistry of the packing material on the retention and the shape of the peaks was investigated. Adsorbents having a hybrid inorganic/organic structure tend to give peaks exhibiting moderate or little tailing. The retention and the shape of the band profiles can easily be interpreted at SW pHs that are well above or well below the SW pKa of the compound studied. In contrast, the peak shapes in the intermediary pH range (i.e., close to the compound SW pKa ) have rarely been studied. These shapes reveal the complexity of the competitive adsorption behavior of couples of acido-basic conjugated compounds at SW pHs that are close to their SW pKa . They also reveal the role of the buffer capacity on the resulting peak shape. With increasing SW pH, the overloaded profiles are first langmuirian (isotherm type I) at low SW pHs, they become S-shaped (isotherm type II), then anti-langmuirian (isotherm type III), S-shaped again at intermediate S pHs, and finally return to a langmuirian shape at high SW pHs. A new general adsorption isotherm model W that takes into account the dissociation equilibrium of conjugated acidic and basic species in the bulk mobile phase accounts for these transient band shapes. An excellent agreement was achieved between experimental profiles and those calculated with a two-sites adsorption isotherm model at all SW pHs. The neutral species adsorbs strongly on a first type of sites that have a high density while the ionic species adsorb preferentially on a second type of sites that have a very low density. The evolution of the peak shape when the SW pH changes from acidic to basic is well explained by the weak buffer capacity of the mobile phase used compared to the concentration of the eluted compounds. © 2008 Elsevier B.V. All rights reserved.

1. Introduction Recent major progresses in column technology have resulted in highly efficient columns that provide excellent separations between neutral compounds. Columns packed with small particles (sub 2 ␮m) or with porous shell particles are now widely available. In contrast, analyses of samples containing ionic analytes remain difficult. The problems encountered are essentially of thermodynamic origin and are related to the surface chemistry of the

∗ Corresponding author at: Department of Chemistry, University of Tennessee, Knoxville, TN 37996-1600, USA. Fax: +1 865 974 2667. E-mail address: [email protected] (G. Guiochon). 0021-9673/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.chroma.2008.11.020

silica-C18 bonded phases used in reversed-phase liquid chromatography (RPLC). To alleviate the consequences of these problems, column manufacturers have developed the hybrid particle technology. Organic moieties such as methyl or ethyl groups are inserted into the silica matrix or in the region close to the surface of these particles. This confers to the particles of these new packing materials stronger mechanical and chemical resistances, so that the columns can withstand ultra-high pressures (about 1000 bar) and very basic SW pHs (up to 12). Despite all these improvements in column technology, serious band deformation can still occur under certain experimental conditions. These problems are often caused by the thermodynamics of adsorption of analytes onto the solid phase, particularly at finite dilution. Significantly distorted band profiles, however, have been

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F. Gritti, G. Guiochon / J. Chromatogr. A 1216 (2009) 63–78

reported even at extremely low sample concentrations. The contributions to tailing due to the injection profiles, which systematically tail, to a slow adsorption–desorption kinetics, or to the radial heterogeneity of the column packing are rarely the source of this problem. Nefarious losses in column efficiency have been observed on some of the most efficient columns available on the market [1–9] when certain ionizable compounds are analyzed. The source of this decrease in column performance was first explained by the inevitable surface heterogeneity of C18 -bonded silica adsorbents [10]. Strong, selective interactions take place between some analytes and certain regions of the surface of the packing material. They are the main origin of peak tailing in RPLC because the concentration of the strong adsorption sites is very small. Therefore, these sites become saturated at low or even very dilute concentrations, the adsorption isotherm is strongly nonlinear, leading to a strong concentration dependence of the migration velocity of the compound [10]. This thermodynamic phenomenon was explained in detail elsewhere [11]. The literature dealing with the retention mechanisms of ionizable compounds concludes that the retention time of a neutral species is larger than that of its conjugated, charged species (whether acid or base). More interesting, hold, are the results regarding the band shapes. To avoid the elution of bands having complex shapes, Fornstedt et al. [12] recommended that protonated bases be eluted with basic mobile phases, if possible. Neue et al. [13–16] showed the influence of the presence of ionized silanol groups on the surface of RPLC packing materials on the retention of ionizable compounds in linear and in preparative chromatography. These authors demonstrated the important role played by the pKa distribution of the surface silanols on the peak shape of ionizable compounds. In an earlier publication, we reported that the elution band profiles of propranololium cations under overloaded conditions can be modified by changing the valence of the counter-anions introduced into the mobile phase, either as supporting salts [17–21] or as buffers [22–25]. The counter-anions pair up with the positively charged analyte molecules, which may considerably change their interaction energy with the stationary phase. Peak tailing or fronting were observed with monovalent or trivalent anions, respectively. Intermediate, broadly symmetrical profiles were usually observed with bivalent anions. These results illustrate the importance of adsorbate–adsorbate interactions on peak shapes under nonlinear conditions and show that the mobile phase composition (and not only the heterogeneity of the stationary phase surface) can drastically affect the peak shapes. This work deals with the origin of the retention and of the peak shape of acido-basic compounds, whatever the relative values of the mobile phase SW pH and the sample SW pKa (SW pH  S pK , S pH  S pK , or S pH ∼ S pK ). Nine different compounds W W W W a W a a having SW pKa ranging from ca. 4 to more than 14 were chosen. Depending on the mobile phase SW pH, these compounds may experience partial or total conversion into their conjugated form. So, five different mobile phases were prepared from pure water buffered with phosphate, acetate, and carbonate buffers at W pH = W 2.15, 4.01, 5.93, 7.87, and 10.1. Four different columns packed with two categories of packing materials were chosen: Gemini-C18 and XTerra-C18 , are both hybrid organic/silica particles but they have significantly different specific surface area (375 versus 176 m2 /g, respectively). Luna-C18 and Halo-C18 are both conventional endcapped silica-C18 stationary phases, but have also quite different specific surface area (426 m2 /g versus 156 m2 /g, respectively). The relative influences on the experimental band profiles of the charge of the solute and of the organic–inorganic hybrid nature of the packing material will be discussed.

In this entire work, the buffer capacity was purposefully made weak, the sample being slightly less concentrated than the buffer, in order for the ratio of the base to the acid concentrations to change during elution of the band. This leads to unusual experimental band profiles that experience a complex evolution with increasing pH. The interpretation of these profiles and their changes requires a correct understanding of the adsorption mechanism of acido-basic compounds in RPLC. All calculations of elution band profiles necessitate a prior, accurate measurement of the column hold-up time. Any error made in the estimate of this time may lead to significant errors on the parameters of the equilibrium isotherm or even to erroneous assumptions regarding the best isotherm model to use for the problem studied [26,27]. The origins of the unexpected band profiles observed when the mobile phase SW pH is close to the compound SW pKa and the buffer capacity is relatively low was carefully investigated. The experimental and calculated band profiles in a wide range of pH were compared discussed. 2. Theory 2.1. Influence of adsorption thermodynamics on peak tailing Generally, band asymmetry is due to the dependance of the migration rate of the analyte concentration on its local concentration, which takes place under nonlinear conditions [11]. At low concentrations, this phenomenon is usually the consequence of the adsorbent surface being heterogeneous and the density of the highenergy adsorption sites being low. At low analyte concentrations, most of the low-energy adsorption sites remain unoccupied while the population of the high-energy sites (also called active sites) increases with increasing analyte concentration, until these sites are close to saturation. In such cases, at low analyte concentrations, the adsorption isotherm equation simplifies to q = HW C + qS,A

bA C 1 + bA C

(1)

where C is the bulk analyte concentration, HW is the Henry’s constant of adsorption onto the weak adsorption sites that cover most of the adsorbent surface, qS,A is the saturation capacity of the strong active adsorption sites, and bA is the equilibrium constant of the analyte on these active sites. At low analyte concentrations, the weak adsorption sites (W) remain poorly populated, although they occupy a large fraction of the adsorbent surface area. The behavior of the adsorption isotherm of the analyte on these sites remains linear. In contrast, the adsorption isotherm of the analyte on the active adsorption sites (A) is accounted for by a simple Langmuir isotherm. When C tends toward 0, the ratio q/C tends toward HW + bA qS,A to which the retention factor is directly related [11]. Usually, for strong active sites, qS,A is very small, but bA is large and their product is often larger than HW . Consider a fixed concentration C0 . According to the theory of characteristics [28], the time t(C0 ) necessary for this concentration to reach the column outlet is equal to: t(C0 ) =

L u0



1+F

 

dq   dC C0

=

L u0



1 + FHW +



FqS,A bA (1 + bA C0 )

2

(2)

where L is the column length, u0 is the chromatographic linear velocity, F is the column phase ratio, VS /VM , and dq/dC|C0 is the slope of the adsorption isotherm at concentration C0 . Under linear, ideal conditions, the elution band of a rectangular pulse injection has the same profile as the injection. The slope of the rear boundary of the band is −dC0 /dt = ∞. Under nonlinear, ideal conditions, the slope of rear boundary of the band is the limit of −dC0 /dt when C0 tends toward 0 and the intensity of the peak

F. Gritti, G. Guiochon / J. Chromatogr. A 1216 (2009) 63–78 Table 1 Physico-chemical properties of the five columns given by the manufacturer. Neat silica

Halo 2.7 ␮m

XTerra 5 ␮m

Luna 5 ␮m

Gemini 5 ␮m

Particle size [␮m] Pore diameter [Å] Surface area [m2 /g]

2.70 90 156

5 121 176

5 100 426

5 110 375

Bonded phase analysis

Halo-C18

XTerra-C18

Luna-C18 /C6

Gemini-C18

Total carbon [%] Surface coverage [␮mol/m2 ] Endcapping

?? 3.50 Yes, ??

15.2 2.17 Yes, TMS

17.5 2.88 Yes, TMS

14 ?? Yes, TMS

Serial number Packed column analysis Dimension (mm × mm) Total porosity a External porosity b Particle porosity

USFH001289

T30431G03

233512

280136-2

4.6 × 150 0.506 0.423 0.144 c 0.192 d

3.9 × 150 0.625 0.383 0.392

4.6 × 150 0.630 0.372 0.411

4.6 × 150 0.645 0.380 0.427

65

low adsorption-energy sites will play no role in the band shapes observed. Their profiles depend only on the degree of overloading of the high-energy adsorption sites (so-called sites A in Section 2.1). These sites are far fewer than the low-energy adsorption sites and, therefore, their actual loading factor is much larger, which explains the characteristically overloaded shapes of the peaks recorded. 2.3. Modeling of overloaded band profiles The profiles of the overloaded bands of aniline 2-phenylbutyric acid were calculated using the equilibrium-dispersive (ED) model of chromatography [11]. This model assumes instantaneous equilibrium between the mobile and the stationary phases and a finite column efficiency that is due to an apparent axial dispersion coefficient, Da , which accounts for both axial dispersive phenomena (molecular and eddy diffusion) and the consequences of a finite mass transfer kinetics between the two phases in the column. The axial dispersion coefficient is

a

Measured by pycnometry (CH3 OH-CH2 Cl2 ). Measured by inverse size exclusion chromatography (polystyrene standards). c Particle porosity including the volume of the solid core of the Halo particle. d Particle porosity omitting the volume of the solid core (only the volume of the porous shell is considered). b

tailing is related to this slope. Under actual, nonideal conditions, the rear boundary is smoothed by axial dispersion due to the finite column efficiency. Differentiating Eq. (2) and taking the limit of the reciprocal fraction gives: lim −

C0 →0

dC0 1 u0 = dt qS,A b2A FL

(3)

According to Eq. (3), the degree of peak tailing generally increases with increasing equilibrium constant, i.e., when the interaction energy between the analyte and the high-energy sites increases. In conclusion, the stronger the interaction energy between analyte and active sites (bS,A ), the stronger the peak tailing. More quantitatively, the peak tailing is mostly controlled by the product qS,A b2S,A : the larger this term, the stronger the peak tailing. This is no longer true, however, when significant adsorbate–adsorbate interactions take place, because these interactions tend to linearize the adsorption isotherm. 2.2. Condition of column overloading: loading factor Moderately overloaded bands were recorded for this work and their shapes are discussed. The degree of column overloading is measured by the loading factor, Lf , or ratio of the sample size to the monolayer capacity of the column [11]: Lf =

Cmax Vinj (1 − t )LSqS

(4)

where Cmax is the concentration of the injected sample (0.05 M or from 4.7 g/L for phenol to 13.6 g/L for procainamide HCl), Vinj is the injected volume (10 ␮L), t is the total porosity of the column (from 0.50 for Halo-C18 to 0.65 for Gemini-C18 , see Table 1), L and S = R2 are the length and the cross-section area of the column (L = 150 mm and R = 1.95 or 2.3 mm), respectively, and qS is the total monolayer saturation capacity of the column (in g/L). For lowmolecular weight compounds, qS varies from 100 g/L (caffeine on Halo-C18 ) to 400 g/L (phenol on Gemini-C18 ) [40]. As a result, the maximum loading factor will be obtained for procainamide HCl (M = 271.8 g/mol) on the Halo-C18 column (qS = 100 g/L). Numerical application of Eq. (15) gives Lf,max = 1.1 × 10−3 . As a consequence, it should be emphasized that all the columns were weakly overloaded (with Lf < 0.1%) and that the

Da =

uL 2N

(5)

where u is the mobile phase linear velocity, L the column length, and N the number of theoretical plates or apparent efficiency of the column measured under linear conditions, i.e., with sample sizes that are so small that the efficiency is independent of the sample size. In this model, the mass balance equation for a single component is written ∂CT ∂2 CT ∂CT ∂qT =0 +u +F − Da ∂t ∂z ∂t ∂z 2

(6)

where qT and CT are the total stationary and the total mobile phase concentrations of the acido-basic compound at equilibrium (i.e., the sum of the concentrations of the acidic and the basic species), respectively, t is the time, z the distance along the column, and F = (1 − t )/t is the phase ratio, with t the total column porosity. qT is related to CT through the isotherm equation, qT = f (CT ). 2.3.1. Initial and boundary conditions for the ED model At t = 0, the concentrations of the solute and the adsorbate in the column are uniformly equal to zero, and the stationary phase is in equilibrium with the pure mobile phase. The boundary conditions used are the classical Danckwerts-type boundary conditions [11,29] at the inlet and outlet of the column. 2.3.2. Numerical solutions of the ED model The ED model was solved using a computer program based on an implementation of the Rouchon method [11,30–32]. The relative and absolute errors of the numerical calculations were 1 × 10−6 and 1 × 10−8 , respectively. 3. Experimental 3.1. Chemicals The mobile phases used in this work were all mixtures of methanol and water at different concentrations, between 10% and 50% methanol (v/v) depending on the hydrophobicity of the analyte, both solvents are HPLC grade and were purchased from Fisher Scientific (Fair Lawn, NJ, USA). Dichloromethane, HPLC grade, was used to estimate the column hold-up volume (by pycnometry, the second solvent being methanol) and was purchased from Fisher Scientific. This method was chosen because it is relatively fast and very accurate. The error made in the calculation of the band profiles

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F. Gritti, G. Guiochon / J. Chromatogr. A 1216 (2009) 63–78

Fig. 1. Chemical structures of the nine compounds studied in this work.

is minimum. Potassium dihydrogenophosphate (KH2 PO4 ), dipotassium hydrogenophosphate (K2 HPO4 ), sodium acetate (NaCH3 COO), acetic acid (CH3 COOH), potassium hydrogenocarbonate (KHCO3 ), and dipotassium carbonate (K2 CO3 ) were used to buffer the mobile phase. They were purchased from Aldrich (Milwaukee, WI, USA). The solvents used to prepare the mobile phase were filtered before use on an SFCA filter membrane, 0.2 ␮m pore size (Suwannee, GA, USA). The analytes studied were phenol, caffeine, 3-phenyl-1propanol, 2-phenylbutyric acid, aniline, p-toluidine, benzylamine, amphetamine, and procainamide hydrochloride. They were all purchased from Fisher Scientific and used as received with no further purification. The selection of the species purchased (acid, salt, or base) was made for practical reasons (purity and cost). All these chemicals were at least 99% pure, according to the manufacturer. The structures of the analytes are given in Fig. 1. 3.2. Columns The four columns used in this study were XTerra-MSC18 (Waters, Mildford, MA), Gemini-C18 and Luna-C18 (2) (Phenomenex, Torrance, CA), and Halo-C18 (Advanced Materials Technology, Wilmington, DE). These columns were generously offered by their respective manufacturers. The main characteristics of the packing materials used and of their bare porous silica matrix are summarized in Table 1. There are significant differences between the specific surface areas of the two types of columns. Halo-C18 and XTerra-C18 have rather small specific surface area (< 200 m2 /g) while Luna-C18 and Gemini-C18 have large specific surface areas, of the order of 400 m2 /g. The hold-up volumes of these four columns were measured by pycnometry, using methanol and dichloromethane as the two eluents. The precision of this static method is better than 0.5% and its accuracy with respect to other dynamic methods such as the minor disturbance method is about −3% [33]. The error possibly made on the measurement of the hold-up volume (note that there are actually as many hold-up volumes as there are methods used to measure it, since each method

is based on a different property of the column) will not seriously affect the determination of the adsorption isotherms in the present case because the differences between the adsorption energies of the ionic and neutral species is large (> 10 kJ/mol) [34] and their respective saturation capacities differ by more than one order of magnitude. 3.3. Mobile phases and samples The mobile phases were mixtures of a buffered water solution and methanol. The buffer solutions were prepared by mixing the appropriate volumes of 50 mM acid and basic solutions of pH = 2.1, 5.9, and 7.9), acetate (W pH = 4.0), or carphosphate (W W W bonate buffer (W pH = 10.1). The addition of e.g., 10%, 30%, and W 50% methanol dilutes the buffer concentration by a factor of e.g., 0.9, 0.7, and 0.5, respectively. Regarding the elution of aniline (30% methanol), the three successive phosphate SW pKa , SW pKa,1 , SW pKa,2 , and SW pKa,3 , were taken as 2.5, 7.5, and 12.5, respectively [38], after

the addition of methanol. The SW pKa of acetic acid was taken as 5.2. These SW pKa are slightly different from the corresponding values in pure water (W pKa ), due to the influence of the presence of 30% W methanol in the mobile phase (see Table 3) [38]. The relative proportion of methanol was adjusted for each compound to achieve a retention factor between 1 and 20. Table 2 Preparation of the buffer solutions in pure water. vA and vB are the volumes of the acid and the base solutions, respectively. Buffer solution

Acid [A]

Base [B]

vA (mL)

vB (mL)

pH

1 2 3 4 5

H3 PO4 0.05 M CH3 COOH 0.05 M KH2 PO4 0.05 M KH2 PO4 0.05 M KHCO3 0.05 M

KH2 PO4 0.05 M CH3 COONa 0.05 M K2 HPO4 0.05 M K2 HPO4 0.05 M K2 CO3 0.05 M

560 830 910 90 500

440 170 90 910 500

2.1 4.0 5.9 7.9 10.1

F. Gritti, G. Guiochon / J. Chromatogr. A 1216 (2009) 63–78

67

Table 3 pKa in water, SW pKa in mobile phase mixture), the mobile phase composition (H2 O/MeOH), Summary of data concerning the 10 analytes injected (molecular weight MW, W W solution SW pH after adding methanol. T = 295 K. The five pH of the 50 mM buffer before the addition of the organic modifier methanol was pHw w = 2.1, 4.0, 5.9, 7.9, and 10.1. Sample introduced

MW (g/mol)

W pKa W

MeOH (%,v/v)

S pKa W

S pH1 W

S pH2 W

S pH3 W

S pH4 W

S pH5 W

Acid AH 3-Phenyl 1-propanol Caffeine Phenol 2-Phenylbutyric acid

136.2 194.2 94.1 164.2

15 14 9.9 4.3

50 30 30 50

∼ 16 ∼ 14.5 ∼ 10.5 ∼ 5.5

3.1 2.6 2.6 3.1

4.9 4.5 4.5 4.9

7.1 6.5 6.5 7.1

9.0 8.6 8.6 9.0

11.3 10.9 10.9 11.3

Base B Aniline p-Toluidine Benzylamine Amphetamine

93.1 107.2 107.2 135.2

4.6 5.2 9.3 9.8

30 30 30 30

∼ 4.3 ∼ 4.9 ∼ 8.5 ∼ 9.0

2.6 2.6 2.6 2.6

4.5 4.5 4.5 4.5

6.5 6.5 6.5 6.5

8.6 8.6 8.6 8.6

10.9 10.9 10.9 10.9

Acid BH+ Procainimide HCl

271.8

9.2

10

∼ 8.5

2.3

4.1

6.1

8.1

10.3

A total sample concentration CT = 50 mM is prepared by dissolving the correct amount of compound in 25 mL of the 35 mM buffer solution (i.e., in the mobile phase). 3.4. Apparatus The overloaded band profiles of the nine compounds studied were acquired with a Hewlett-Packard (now Agilent, Palo Alto, CA, USA) HP 1090 liquid chromatograph. This instrument includes a multi-solvent delivery system (tank volumes, 1 L each), an auto-sampler with a 250 ␮L sample loop, a diode-array UVdetector, a column thermostat and a data station. Compressed nitrogen and helium bottles (National Welders, Charlotte, NC, USA) are connected to the instrument to allow the continuous operations of the pump, the auto-sampler, and the solvent sparging. The flow-rate accuracy was controlled by pumping the pure mobile phase at 22 ◦ C and 1 mL/min during 50 min, from each pump head, successively, into a volumetric glass of 50 mL. The relative error was less than 0.4%, so we can estimate the long-term accuracy of the flow-rate at 4 ␮L/min at flow rates around 1 mL/min. All the measurements were carried out at 22 ◦ C, a temperature kept constant by the laboratory air-conditioner. The daily variation of the ambient temperature never exceeded ±1 ◦ C.

4. Results and discussion The total loading factor corresponding to the injection of 10 ␮L of a 50 mM sample was always lower than 0.1% (see Section 2.2). This value of Lf is reported to the saturation capacity of the abundant low-energy adsorption sites [10,11]. Accordingly, the distortion of the band shape that is observed is essentially due to the overloading of the high-energy adsorption sites that are present at low concentration on the surface of the adsorbent. These sites are some times visualized as cracks within the C18 bonded layer that can accommodate solute molecules [35]. The presence of organic eluents such as methanol, acetonitrile, or tetrahydrofuran in the mobile phase does not disturb the arrangement of the C18 chains, as was shown by Kazakevich et al. [36], who measured the hold-up volumes of a series of silica-C18 bonded phases by the minor disturbance method with aqueous mixtures of these organic solvents and found no change in these volumes when the nature or concentration of the organic modifier were altered. This shows that the C18 layer is not miscible in any proportion with aqueous solutions of organic modifiers and that the alkyl chains remain in a collapsed state, which explains the origin of the surface heterogeneity. The access to the underlying bare silica is then possible through these cracks, provided that the size of the analyte molecules matches the dimension of these cracks in the C18 layer. This could explain the formation of sites on which adsorption-energy is much higher than on the surface of the C18 bonded layer [37].

3.5. Overloading experiments S pH, W

each column, and each compound, For each mobile phase 10 ␮L of a 50 mM sample solution (i.e., 0.5 ␮ mol of compound) was injected at constant temperature of T = 22 ◦ C. First, 25 mL of a 50 mM sample solution were prepared by dissolving 1.25 mmol of the compound in 25 mL of buffered mobile phase. The UV wavelength at which the detector monitors the eluent was chosen so that the UV-absorbance recorded did not exceed 2000 mAU, which is close to the upper range of meaningful signals given by the detector. For each sample, a calibration curve f was determined (CT = f (mAU)) to derive the true concentration profiles from the recorded chromatograms. Four liters of buffer solution were prepared by dissolving the adequate masses of acid and base into water in a 1 L volumetric glass and adding 3 L of water to this solution mixture in a 4 L solvent bottle and thoroughly mixing them. The W pH of this solution was measured. The amount of W organic modifier required to elute the compound within reasonable elution times was added in a next step. The SW pH of this new solution was also measured. All experimental details regarding the prepapHs and/or SW pHs are summarized ration of the buffer and their W W in Tables 2 and 3.

4.1. Peak shape and retention time for SW pH distant from the region

S pK W a

The changes in elution times and band profiles of the nine analytes as a function of the mobile phase SW pH on the XTerra-C18 and the Halo-C18 columns are shown in Fig. 2 A–D (see supplementary Figs. S2E–I) and 3A (see supplementary Figs. S3B–I), respectively. These two columns have very close specific surface area ( 170 m2 /g) but quite different surface chemistry, the first having a hybrid methyl/silica matrix and the second a regular silica matrix. The figures are arranged in the order of decreasing value of the W pKa of the compound in pure water, e.g. 15 (3-phenyl W 1-propanol), 14 (caffeine), 9.9 (phenol), 9.8 (amphetamine), 9.3 (benzylamine), 9.2 (procainamide), 5.2 (p-toluidine), 4.6 (aniline), and 4.3 (2-phenylbutyric acid). The buffer concentration of water pHs of the mobile phases are was uniformly set at 50 mM. The W W given in Table 3. The methanol content (10, 30, and 50%, v/v) was fixed so that the retention factors of the compounds, at all the SW pHs, are all in a range consistent with easy and accurate measurement (1 < k < 20). The SW pHs of the mobile phases are given in Table 3. Because neither Luna-C18 nor Halo-C18 are stable in mobile phases

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Fig. 2. Evolution of the retention time and peak shape of the overloaded band profiles of four compounds (A–D) as a function of the SW pH of the mobile phase measured with the XTerra-C18 column. The mobile phase composition and SW pH are listed in Table 3. See the overloaded band profiles of five other compounds in supplementary Figs. S2E–I.

having a SW pH larger than 9, the mobile phase with W pH = 10.1 W was used only with the XTerra-C18 and the Gemini-C18 columns, which both exhibit a high stability at high pHs, due to the hybrid organic–inorganic structure of their silica matrix. The results illustrated in Fig. 2 A–D and 3A (see supplementary Figs. S2E–I and S3B–I as well) are similar in terms of the relative elution times and the peak shapes. For the sake of clarity, the figures had to be rotated around the vertical axis, some times with a large angle, and their orientations vary widely. This is not surprising since the two materials are endcapped C18 bonded matrices. Note, however, that the flow rates were set at 1.00 mL/min with the XTerra-C18 column and 0.50 mL/min with the Halo-C18 , due to the large difference in the column permeabilities (with dp 5.0 and 2.7 ␮m, respectively). As expected from the similar specific surface areas of both materials, the elution times measured on the XTerra-C18 columns are systematically about twice smaller than those measured with the Halo column, reflecting the difference in flow rates. The molecules of all the compounds studied are small, polar, and do not contain any large hydrophobic sites. As a result [10], all the

peak profiles observed are strictly langmuirian (type I isotherm) when the SW pH of the mobile phase differs sufficiently from the S pK of the compound eluted. All band profiles exhibit the front W a shock and the diffuse rear boundary that characterize the profiles of compounds having an adsorption isotherm that is convex upward at low concentrations. There is no exception to this rule, showing that the adsorption mechanism of either the basic or the acidic species follows a langmuirian adsorption isotherm behavior. Peak tailing is due to the overloading of the adsorption sites of highest energy, which are present on the surface of the stationary phase at small concentration (see later). These sites fill more rapidly than the more numerous low-energy adsorption sites, which is why even low bulk concentrations suffice to saturate them and to generate peak tailing. All our experimental results are consistent with the fact that compounds that are ionized in the mobile phase elute faster than their conjugated neutral specie, irrespective of whether they are acidic or basic. This is a normal consequence of operating in the RPLC mode with a hydrophobic stationary phase. Accordingly, the mobile phase SW pH does not directly control the elution time but

F. Gritti, G. Guiochon / J. Chromatogr. A 1216 (2009) 63–78

Fig. 3. Same as in Fig. 2 except with the column Halo-C18 and benzylamine as the compound (A). See the overloaded band profiles of eight other compounds in the supplementary Figs. S3B–I.

the nature of the species that is eluted, the acidic form at low the basic one at high SW pH. Whether the compound is negatively or positively charged (i.e., under very basic or very acidic conditions, respectively), the retention factor of all charged species rarely exceeds 1. Their Henry constant (the product of the saturation capacity and the equilibrium constant) are small, unless the surface silanols of the packing materials become ionized at a SW pH at which the cationic species predominate, such as with protonated bases. Ion-exchange mechanisms can then take place and significantly increase the retention of the ionized species [13]. This happens on the Halo-C18 column with amphetamine (supplementary Fig. S3E), benzylamine (Fig. 3 A), and procainamide hydrochloride (supplementary Fig. S3F). The retention factors of these three compounds significantly increase with increasing SW pH in the range 2 < SW pH < 6, which is well below their SW pKa ( 9). On the other hand, for the same SW pH variation, the retention factor increases barely with the XTerra-C18 column because the silanol groups present on this hybrid inorganic–organic surface are less acidic than those on Halo and they are not ionized under these SW pH conditions [15](see supplementary Figs. 2F–H). The same remark applies to Luna(2)-C18 (acidic silanols) and Gemini-C18 (less acidic silanol groups). Another important conclusion of our results (Figs. 2 A–D and 3 A, and supplementary Figs. S2E–I and S3B–I) on the elution of acidobasic compounds is the difference between the peak asymmetry of the acidic and the basic species. It was already observed that ionized compounds give peaks that tail systematically more strongly than neutral compounds [14]. In other words the initial curvature of the adsorption isotherm of the ionized analytes is larger than that of neutral analytes. Smaller concentrations of ionized compounds are generally required to saturate the few active sites. A first likely interpretation is the mutual repulsion that takes place between adsorbed ions, which cannot be packed as densely in the adsorbed monolayer as neutral molecules can. This explanation might be valid but only when ions are adsorbed on high-energy sites, e.g. when the concentration of the injected solutes does not exceed 5 g/L. Indeed, frontal experiments performed with propranololium or naphthalene sulfonate [21] on C18 -bonded phases at concentrations up to 50 g/L have shown that the total saturation capacity (including adsorption on the numerous low-energy S pH, W

69

adsorption sites) does not significantly differ from those measured for the corresponding neutral compounds. Adsorbate molecules are clearly not repelled from each other at high concentrations. The phenomenon of peak tailing being enhanced for charged compounds is observed only at low concentrations (C < 5 g/L), hence it is related to the nature of the active adsorption sites. When the concentration of the sample largely exceeds that of the buffer or the supporting salt in the mobile phase, the ionized compound is adsorbed as an ion-pair, together with its co-ion to respect the electroneutrality condition that should apply everywhere in the column. No exchange with another counter-ion is possible at such high concentrations. The mutual repulsion rational does not hold at low concentrations either. By definition, the density of these adsorbed ions is low, hence their mutual repulsion weak if not negligible. This interpretation would be inconsistent with the experimental results if it is assumed that both neutral and ionic species adsorb on the same adsorption sites. Indeed, if the saturation capacities were the same for both species, the ionic species would have a smaller adsorption-energy than the neutral species, hence its peak would tail less while experimental results show the opposite. There should be another interpretation. A second likely interpretation would be that ionic species adsorb specifically and very strongly on high-energy adsorption sites, which have a very low saturation capacity. The neutral species would adsorb on another type of sites, low adsorption-energy sites, which have a much larger saturation capacity. As described in Section 2, large equilibrium constants coupled with a small saturation capacity necessarily generate strong peak tailing with low retention times. This interpretation is consistent with the experimental peak shapes. The choice between these two hypothetical interpretations will be discussed later, after the variations of the band shape of acido-basic compounds with the mobile phase SW pH in a range encompassing the compound SW pKa values has been illustrated. The same interpretation of the band profiles should apply in the entire S pH range. W 4.1.1. Influence of the ionization state of the compound on its peak shape From the band profiles recorded, we determined the peak asymmetry at half-height of each pair of conjugated species at the two extreme SW pHs used ( 2.5 and 11), at which either the acidic or the basic species is predominant. The peak asymmetry characterizes the peak distortion at low concentrations, hence the initial nonlinear behavior of the adsorption isotherm. Conjugated species make an ideal pair of neutral/charged compounds in order to test the effect of the charge of a compound on the tailing of its peak. The most suitable compounds for this purpose are p-toluidine and 2-phenylbutyric acid, which have SW pKa of the order of 5. The peak Table 4 Comparison between the peak asymmetry (As ) and retention factors (k )of neutral and charged conjugated species (pKa ∼ 6) measured at pH ∼ 3 and pH ∼ 9. Columns

Ionization state

Samples p-Toluidine

XTerra-C18 Gemini-C18 Halo-C18 Luna(2)-C18

Charged Neutral Charged Neutral Charged Neutral Charged Neutral

2-Phenylbutyric acid

As

k

As

k

5.33 2.61 4.42 2.50 4.64 2.69 6.21 2.16

0.60 5.30 0.56 6.33 0.54 5.60 0.78 9.22

3.00 3.08 4.37 3.41 6.28 4.21 7.99 3.80

1.06 6.09 1.64 7.65 1.04 6.54 1.89 10.55

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F. Gritti, G. Guiochon / J. Chromatogr. A 1216 (2009) 63–78 Table 5 Comparison between the peak asymmetry (As ) and retention factors (k )of protonated bases (pKa ∼ 9) measured at pH ∼ 6. Columns

Amphetamine As

XTerra-C18 Hybrid silica 176 m2 /g Halo-C18 Silica 156 m2 /g Gemini-C18 Hybrid silica 375 m2 /g Luna(2)-C18 426 m2 /g

k



Benzylamine As

k



Procainamide As

k

5.17

1.11

2.30

0.23

5.93

1.84

5.08 5.43

1.15 0.74

2.42 2.30

0.27 0.09

6.97 8.72

1.59 1.58

8.35

1.55

4.04

0.29

10.6

3.15

with a SW pKa around 9), which can possibly interact with the ionized silanols. The presence of high-energy sites enhance peak tailing, as explained in Section 2. The results are listed in Table 5. There is not much difference in the peak asymmetries between XTerra and Halo, possibly due to the unknown nature of the proprietary endcapping of the Halo-C18 packing material. In contrast, significantly larger peak tailing is observed with Luna-C18 than with Gemini-C18 . Among all four columns, Luna(2)-C18 appears to be the column that has the largest number of accessible acidic silanol groups. Fig. 5 illustrates the peak shape recorded on Gemini-C18 and Luna(2)-C18 . The peak asymmetries measured for neutral compounds are listed in Table 6.

Fig. 4. Overloaded band profiles of p-toluidine recorded on the Luna(2)-C18 column at SW pH = 8.6 (top graph) and SW pH = 2.6 (bottom graph). Note the strong peak tailing when the protonated form of the compound is eluted.

asymmetries for the four columns are listed in Table 4. Overall, as already shown in the literature, peak tailing is stronger for ionic species than for neutral species. Fig. 4 illustrates this point. The difference between the asymmetries are significant on Halo and Luna, which have conventional solid silica matrix. The maximum concentration of charged analytes necessary to fill the high-energy adsorption sites is smaller that the concentration of neutral species required to fill the same sites. This is because the ionic species adsorbs more strongly on those high-energy adsorption sites than the neutral species does. Neutral species are weakly adsorbed on another type of adsorption sites present in large amounts. 4.1.2. Influence of packing material chemistry on peak shapes It is often shown in the literature that hybrid inorganic–organic packing materials benefit from a diminution of the silanol activity. In this work, we compare the peak asymmetry measured on XTerra and Halo, on the one hand, and on Gemini and Luna(2), on the other hand. This comparison is not biased by the difference between the specific surface area of the materials. For classical silica adsorbents, the SW pKa of residual silanols is often between 5 and 7. Inserting methyl groups in the silica matrix significantly increases the SW pKa of these silanol groups, typically up to 10. So, we compared the peak asymmetries at a SW pH close to 6 for protonated bases (amphetamine, benzylamine, and procainamide, all

Fig. 5. Overloaded band profiles of amphetamine measured on the Gemini-C18 and Luna-C18 columns at SW pH = 6.5. Note the lesser degree of peak tailing on the hybrid organic/silica packing material (Gemini), despite the slightly smaller specific surface area of Gemini (375 m2 /g) compared to Luna (426 m2 /g).

F. Gritti, G. Guiochon / J. Chromatogr. A 1216 (2009) 63–78 Table 6 Comparison between the peak asymmetry of neutral compounds measured on columns with different specific surface areas. Columns

3-Phenyl 1-propanol (pH 3)

Phenol (pH 3)

Aniline (pH 9)

XTerra-C18 Hybrid silica 176 m2 /g Gemini-C18 Hybrid silica 375 m2 /g Halo-C18 Silica 156 m2 /g Luna(2)-C18 426 m2 /g

1.56 1.65 2.91 1.92

2.10 2.32 3.39 2.62

1.55 1.41 2.07 1.14

4.2. Peak shape and retention time for transient SW pH close to the S pK W a In the previous section, we provided experimental data that show what are the most important parameters that affect peak asymmetry in RPLC on endcapped C18 -bonded phases. This part of the study was conducted with mobile phases the SW pH of which was at least three units above or below the solute SW pKa , so that the eluent contained only either the acidic or the basic species. The actual charge of the eluite and the chemistry of the bulk solid matrix were the two most important parameters affecting the peak shape, in that order. In this section, we study the profiles of the elution bands of acido-basic compounds when the mobile phase SW pH is close to the eluite SW pKa , so that both the acidic and the basic species do coexist in the bulk mobile phase. This problem is not new in linear chromatography. The influence of the solution SW pH on the peak retention was studied in a wide SW pH range, in which there is a complete conversion between the two conjugated species [13]. Much less attention has been given to the evolution of the band profiles under overloaded conditions, in the intermediate SW pHrange, and almost no attention was ever paid to interpreting the shape of the experimental band profiles when the SW pH of the mobile phase is let to vary upon injection of a concentrated sample. In the next section, this problem is discussed. 4.2.1. Experimental results Obviously, no investigation is needed for 3-phenyl 1-propanol and caffeine, which do not dissociate in water and exist only as a single species, even at SW pH ∼ 11. The seven remaining compounds of interest in this work are phenol, amphetamine, benzylamine, procainamide, p-toluidine, aniline, and 2-phenylbutyric acid. These compounds were first dissolved in mobile phases at SW pHs set at 10.9, 8.6, 8.6, 8.1, 4.5, 4.5, and 7.1, respectively. Then these samples were eluted with mobile phases having the same SW pH as their solvent. Unusual distortion of the shapes of the band profiles were observed (see Figs. 2 A–D and 3 A, and supplementary Figs. S2E–I and S3B–I), as the result of the dissociation (acid) or the reaction (base) of the compound with the buffer solution and of the change of the mobile phase SW pH during the elution of the band (due to the weak buffer capacity of the mobile phase). These SW pHs, listed in Table 3, were directly measured with a pH-meter calibrated in pure water. For all these compounds, on all the columns, the same consistent evolution pattern of the band profiles was observed. At SW pHs well below and well above the compound SW pKa , peak profiles are strictly langmuirian (isotherm type I). In the intermediate SW pH range, the profiles pass through three successive intermediate shapes. When the SW pH increases but it still lower than SW pKa , the band profiles become those corresponding to a S-shaped isotherm (isotherm type II, see Fig. 2 D and supplementary Figs. S2F, S2H, S2D, S3G, and S3I). Then, when SW pH SW pKa , the profiles correspond to an anti-Langmuirian isotherm behavior (Fig. 2 B, C and supplementary Figs. 2G, 2I, and 3H). Finally, when the SW pH increases well above

71

S pK , W a

a symmetrical evolution takes place and the band profiles become those corresponding to an S-shaped isotherm again (type II), before returning to a langmuirian profile. In the next section we propose a simplified competitive adsorption model to account for this evolution of the band profiles. Then, we discuss its validity by comparing band profiles calculated with this model and the experimental profiles recorded and reported above.

4.2.2. A simple competitive adsorption model When the mobile phase SW pH is remote from the SW pKa of the studied compound, only one of the two conjugated species has a finite concentration. The band profile can be calculated using the ED model (Section 2.2) and the adsorption equilibrium isotherm of the only species present [11]. In the intermediate SW pHrange, the two conjugated species coexist. Hence, the elution band profile will depend on the competitive adsorption isotherm of the two conjugated species. However, their relative concentration depends on the SW pH. If the buffer concentration of the mobile phase is insufficient, the SW pH of the solution depends on the degree of dissociation, hence the SW pH varies with the concentration of the compound in the mobile phase. We assume that acid–base equilibria are fast compared to adsorption–desorption equilibria, so that the two conjugated compounds are always at equilibrium. We first derive the model in the case when adsorption takes place on a homogeneous surface, so the adsorption isotherms of the conjugated acid and basic species of the compound studied follow competitive Langmuir behavior. These adsorption isotherms are qI (C) for the charged species and qN (C) for the neutral species. When the SW pH is very different from the SW pKa : qI = qS,I

bI CI 1 + bI CI

qN = qS,N

bN CN 1 + bN CN

(7A) (7B)

where bI and bN are the adsorption–desorption equilibrium constants of the ionic and the neutral species, respectively, and qS,I and qS,N are the saturation capacities of the ionic and neutral species on these sites. Due to the possible mutual repulsion between two charged adsorbate molecules in the adsorbed phase, the inegality qS,I < qS,N should also be respected. Let define the constant ˇ < 1 as qS,I = ˇqS,N

(8)

When the two species compete for adsorption on the stationary phase, the classical kinetic competitive adsorption model writes as follows: bI CI (1 − I − N ) = I

(9A)

bN CN (1 − I − N ) = N

(9B)

where I =

qI qS,I

and N = (qN /qS,N ) are the surface fraction occupied

by the adsorbed ionic and neutral species, respectively. The solution of the system of Eqs. (9A) and (9B) writes: qI = ˇqS,N qN = qS,N

bI CI 1 + bI CI + bN CN

bN CN 1 + bI CI + bN CN

(10A) (10B)

Eqs. (10A) and (10B) give the competitive adsorption isotherm between the two independent components (I and N) in the mobile phase. However, when an ionogenic compound is eluted through the column, the concentrations of the two conjugated species are not independent, due to their equilibrium. They depend on the local

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Fig. 6. Calculated variation of the mobile phase SW pH (methanol/water, 30/70 (v/v), 35 mM buffer concentration given in Table 2) as a function of the total concentration of aniline dissolved. (A) buffer SW pH = 2.6, (B) buffer SW pH = 4.5, (C) buffer SW pH = 6.5, (D) buffer SW pH = 8.6. Note the increasingly wide range of the SW pH change when the buffer SW pH decreases.

S pH of the solution. The S pH of the mobile phase changes along the W W

column if the buffer strength of the mobile phase is not sufficient to prevent the consequences of an increase in the concentration of the ionic species. Let define CT as the total concentration of the compound and ˛ as the ratio of the concentration of the neutral species to the total concentration, e.g.: CT = CI + CN

(11A)

CN ˛= CT

(11B)

Combining Eqs. (11A) and (11B) leads to the relationship between the concentration CI and CT : CI = (1 − ˛)CT

(12)

The total amount adsorbed at equilibrium, qT = qI + qN , writes as a function of the total concentration CT : (ˇ(1 − ˛)bI + bN ˛)CT qT = qS,N 1 + (1 − ˛)bI CT + ˛bN CT

(13)

Obviously, the coefficient ˛ depends on the total concentration of the compound, CT , dissolved into the mobile phase. The function ˛(CT ) can be easily determined numerically, knowing the SW pKa of the sample and the SW pKa,i of the buffer used (here, phosphate, acetate, or carbonate).

4.2.2.1. Calculation of the band profiles. In this section we list the experimental parameters needed to calculate overloaded band profiles, based on the competitive adsorption model in Eqs. (10A) and (10B) that was derived in the previous section. The derivation attempts to match as closely as possible the experimental conditions used to record the elution band profiles of aniline. The SW pKa of aniline in a 70/30 methanol/water mixture is taken as 4.3 [38]. The S pH of the four mobile phases used were 2.6, 4.5, 6.5, and 8.5. The W data regarding the XTerra-C18 column were considered (Table 1). The description of the injected solution are given in Section 3.4. In the calculations, we assumed that both the acidic and the basic species have the same detector response factor. Then, the signal recorded is simply the sum of the two concentrations CI and CN at the column exit. This assumption is not always valid. All experimental chromatograms were recorded at a wavelength sufficiently close to the isosbestic point of the acido-basic compounds, for which the acid and the base have nearly the same molar absorptivity. The UV spectra of a 50 mM acid–base solution were recorded in the most acidic buffer solution, on the one hand, and in the most basic buffer solution, on the other hand. The wavelength selected to record the band profiles was the one at which both solutions had the same absorbance. 4.2.2.2. Determination of the coefficient ˛. The coefficient ˛ was calculated by solving numerically the following set of equations which

F. Gritti, G. Guiochon / J. Chromatogr. A 1216 (2009) 63–78

73

Fig. 7. Variation of the coefficient ˛, ratio of the concentration of the neutral species (aniline) to the total sample concentration in the bulk liquid phase.

state successively the acido-basic equilibrium, the mass conservation of the compound, and the electroneutrality of the bulk mobile phase at any time and anywhere in the column. Acido-basic equilibria: [ACID] ⇔ [BASE] + [H3 O+ ] + [H3 PO4 ] ⇔ [H2 PO− 4 ] + [H3 O ] − 2− [H2 PO4 ] ⇔ [HPO4 ] + [H3 O+ ] 3− + [HPO2− 4 ] ⇔ [PO4 ] + [H3 O ]

pKS pKa,1 pKa,2 pKa,3

or [CH3 COOH] ⇔ [CH3 COO− ] + [H3 O+ ] [H2 O] ⇔ [OH− ] + [H3 O+ ]

pKa,1 pKe

Mass conservations: 2− 3− [H3 PO4 ] + [H2 PO− 4 ] + [HPO4 ] + [PO4 ] = CBuffer

or [CH3 COOH] + [CH3 COO− ] = CBuffer [ACID] + [BASE] = CT Electroneutrality: [CATIONS] = [ANIONS] Figs. 6 A–D show how the mobile phase SW pH changes with increasing total concentration of aniline, CT . Fig. 7 A–D show the

corresponding variations of the coefficient ˛, the fraction of the neutral species in the solution. Note that aniline (SW pKa ∼ 4.3) is practically not dissociated at S pH = 6.5 and 8.5, which is consistent with the two identical chroW matograms shown in Fig. 2 C, which were recorded with the mobile phases made from the phosphate buffer solutions at these two pHs. At the low SW pHs of 4.5 and 2.6, the retention times of the aniline band decreases with increasing SW pH because the proportion of the ionic acid, anilinium, increases in the mobile phase with increasing H + concentration. 4.2.2.3. Comparison of calculated and experimental band profiles. The parameters qS,N and bN in Eq. (13) are easily derived from the experimental band profiles recorded at SW pH = 6.5 and 8.5. Under these conditions, ˛ 1, only the neutral species is present in the solution and the adsorption isotherm simplifies to the singlecomponent Langmuir adsorption isotherm: qT bN CT qS,N 1 + bN CT

(14)

The best isotherm parameters were derived using the inverse method [39]. Accordingly, qS,N = 46.1 g/L and bN = 0.079 L/g. The excellent agreement between calculated and experimental profiles is illustrated in Fig. 8. Consider now the intermediate band profile (Fig. 2C) recorded at SW pH = 4.5. Because the elution time of the anion anilinium is

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F. Gritti, G. Guiochon / J. Chromatogr. A 1216 (2009) 63–78

(anilinium) has to be smaller in order to give a smaller retention time. Should we assume that the SW pKa of aniline is equal to 4.51 and fit the new set of values of the function ˛(CT ) to the same type of expression, we obtain the following function: ˛(CT ) = 0.4823 +

0.23533CT 1 + 0.58224CT

(16B)

From this function, we calculate a band profile that is now in excellent agreement with the experimental one, as shown in Fig. 9 B. Finally, the band profiles were calculated for SW pH = 2.6. Values of ˛(CT ) were calculated according to the SW pKa of aniline, assumed to be equal to 4.51. These values were fitted to the following sigmoidal function: ˛(CT ) = −0.01591 +

0.70731 1 + exp((2.65318 − CT )/0.63695)

(17)

Fig. 10 illustrates the excellent quality of the fit. Eq. (17) was used to calculate the band profile of aniline at SW pH = 2.6 (see Fig. 11) by keeping the same values of qS,N (46.1 g/L) and bN (0.079 L/g) as in the previous calculation at SW pH = 4.5. Surprisingly, the best estimate for the ratio ˇ = (qS,I /qS,N ) is 0.8% while the equilibrium constant bI is about 15 times larger than bN (1.15 L/g). This confirms, as indicated earlier, that the adsorption sites on which the ionic compound is preferentially adsorbed are chemically different from those on

Fig. 8. Comparison between the experimental and the calculated band profiles of aniline at SW pH = 6.5 (top graph) and SW pH = 8.6 (bottom graph). The adsorption isotherm in Eqs. (11A) and (11B) was used in the calculations. The efficiency was set at N = 3100. The best parameters found were qS,N = 46.1 g/L and bN = 0.079 L/g.

close to the column hold-up time, we may assume in the band profile calculation that (1 − ˛)bI  ˛bN . Then, the adsorption isotherm simplifies to: qT bN ˛(CT )CT qS,N 1 + ˛(CT )bN CT

(15)

This adsorption isotherm equation is that of a Langmuir isotherm with a non-constant equilibrium constant, bN ˛(CT ), a function of the local mobile phase concentration. The values of ˛ were calculated using the SW pKa of aniline taken as 4.3 (see Fig. 7B). Fig. 9 A compares the experimental and the calculated band profiles obtained by fitting ˛(CT ) to the following empirical function: ˛(CT ) = 0.6215 +

0.16695CT 1 + 0.55532CT

(16A)

Note that Eq. (16A) is an empirical correlation, which is not based on any physico-chemical argument but is a simple function that best approximates the values of ˛ calculated from equilibrium thermodynamics. We note that the shape of the calculated band profile match very well that of the experimental band, although the retention times of the two bands differ by about 15 s. This offset may arise from an incorrect value of the SW pKa of aniline in the 30/70 methanol/water mixture used. The actual SW pKa of aniline should be larger because the relative amount of the neutral (aniline) to the charged species

Fig. 9. Comparison between the experimental and the calculated band profiles of aniline at SW pH = 4.5. The adsorption isotherm in Eq. (12) was used in the calculations. The coefficient ˛ was given by Eq. (13)(A) (top graph, SW pKa = 4.3) and by Eq. (13)(B) (bottom graph, SW pKa = 4.51). The efficiency was set at N = 2100. Same other isotherm parameters as those given in this figure.

F. Gritti, G. Guiochon / J. Chromatogr. A 1216 (2009) 63–78

Fig. 10. Comparison between the numerical ˛ values and the best curve obtained by fitting Eq. (14) at SW pH = 2.6 with a SW pKa of aniline equal to 4.51.

which the neutral species are adsorbed. The one-site competitive adsorption isotherm model would have been acceptable if ˇ had been slightly less than 1 and bI smaller than bN . With the values actually determined, this one-site adsorption model is not valid. The ˇ value is much too small and the equilibrium constant bI too large to describe an adsorption behavior involving only one type of adsorption sites. This result shows that the actual overall adsorption isotherm is more likely a two-sites adsorption isotherm. The assumption (1 − ˛)bI  ˛bN cannot hold anymore because it contradicts the last result of the inverse method, the one obtained at SW pH = 2.6. As a result, the isotherm model in Eq. (13) is not valid in the whole SW pH range and some adjustment is necessary. We propose a more consistent model in the next section. 4.2.3. Extension of the model to a two-sites non-competitive adsorption model In the previous section, we used a model assuming the presence of a single type of adsorption sites on which both the ionic

Fig. 11. Comparison between the experimental and the calculated band profiles of aniline at SW pH = 2.6. The adsorption isotherm in Eq. (10A) and (10B) was used in the calculations. The efficiency was set at N = 1600. The best parameters found were ˇ = 0.008 and bI = 1.15 L/g. The coefficient ˛ was given by Eq. (14). Same other isotherm parameters as those given in Fig. 9.

75

and the neutral species compete for adsorption. We showed that this model permits the calculation of band profiles of acido-basic compounds that agree very well with experimental profiles only when the mobile phase SW pH is very different from the compound S pK . In contrast, when the S pH of the mobile phase differs from W W a the SW pKa of the compound by less than one to two units, the experimental band profiles differ considerably from those calculated with our model. This conclusion is consistent with that of our earlier discussion, that the band profiles of ions tail more than those of neutral compounds and that their retention times are smaller. These conclusions are clearly inconsistent with one small equilibrium constant, bI , and one single, large saturation capacity, qS,N . Such an isotherm model would have a negligible initial curvature and the calculated bands would be nearly gaussian in contrast with experimental results. The only possible solution of this conundrum is the assumption that the surface of the adsorbent is heterogeneous and covered with two types of patches, one having a saturation capacity that is extremely small but a very large equilibrium constant, the other one having a large saturation capacity and a small equilibrium constant. Accordingly, the general adsorption isotherm should be written: qT = qS,I

(1 − ˛)bI CT ˛bN CT + qS,N 1 + (1 − ˛)bI CT 1 + ˛bN CT

(18)

Note that, in this case, we neglect the competition between the two species for adsorption on each type of sites because the equilibrium constant of the ionic species on the low-energy type of sites (qS,N ) should be small and the equilibrium constant of the ionic species on the second type of sites (qS,I ) is much larger than that of its conjugated neutral species. To check the validity of this model, we compared the band profiles calculated using the model in Eq. (18) and the four experimental band profiles. The SW pKa of aniline is taken as 4.51 and Eqs. (16B) and (17) are used for the calculation of ˛. We have qS,N = 46.1 g/L, qS,I = 0.008 × 46.1 = 0.369 g/L, bI = 1.15 L/g, and bN = 0.079 L/g. The results of the calculations are shown in Fig. 12. The agreement is excellent at all SW pHs, except at SW pH = 4.5, for which it is still very good but with a slight shift in the retention times between experimental and calculated band profiles. The fact that the peak shape calculated is very similar to the experimental one means that the proposed model contains the essential features needed to predict the change in peak shape from SW pH = 2.6 to S pH = 8.6. Slight adjustments of all the parameters (the S pK of W W a aniline and the isotherm parameters) may be required in order to achieve a better agreement between experimental and calculated profiles in all four cases. Overall, however, the agreement observed suggests that the adsorption model given in Eq. (18) might well account for the elution of acido-basic compounds in the whole SW pH range, from low to high SW pH, in which the compound experiences a complete conversion from the acidic to the basic species. The model in Eq. (18) accounts for the overloaded band profiles of all the acido-basic compounds studied in this work, in the widest S pH range, from very low to very high S pH. The model accounts W W for the variation of the SW pH during the elution of the peak when the buffer capacity is limited. All the band profiles recorded in the transient SW pH region are well accounted for by our model. However, its use requires accurate information regarding the SW pKa of the studied compounds and of the buffer used, and the complete resolution of the thermodynamic problem in the bulk phase. 4.2.4. Summary and generalization The experimental results (see Section 4.1, Figs. 2 A–D, 3 A, 4 and supplementary Figs. S2E–I and S3B–I) show that the retention

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time of the ionized species is systematically smaller than that of the conjugated neutral species. At the same time, the peak of the ionized compound is more unsymmetrical than that of the neutral compound. Lets assume that the surface of the adsorbent is homogeneous and that both species have the same saturation capacity qS . The saturation capacity of a compound is directly related to its size and slightly to its shape, the parameters that determine a possible exclusion from the smallest mesopores. Because conjugated species have similar size, they necessarily have the same access to the surface area. What differentiates between them is simply the bulk concentration required to form the complete monolayer, because their adsorption constant is different. Accordingly, the adsorption constant of the ionic species should be smaller and the rear part of its peak should tail less than that of the neutral species (see Eq. (3)). But the opposite is true. This contradiction demonstrates that the initial assumption was wrong: The surface of the adsorbent is heterogeneous. The ionic species necessarily adsorbs more strongly onto few highenergy sites (qS,I  qS,N , bS,I  bS,N , and qS,I bS,I < qS,N bS,N ) while the neutral species adsorbs weakly onto a large number of distinct low-energy sites. The large adsorption constant of the ionized compound compensates for its small saturation capacity, and, overall,

the retention time of the ionic species is only slightly smaller than that of the neutral species. This also explains why its peak tailing is stronger. It is noteworthy that, as a first approximation, the competition between the two conjugated species on each of the two types of sites can be neglected (see Eq. (18)). Thus, the model that we proposed accounts very well for the experimental band profiles of aniline recorded with a mobile phase at SW pH = 6.5 (see Fig. 12). In order to generalize the validity of this adsorption isotherm model, we fitted the experimental band profile of 2-phenylbutyric acid measured with a mobile phase at SW pH = 7.1 and the Halo-C18 column to the following adsorption model: qT = qS,I

˛bN CT + (1 − ˛)bN,I CT (1 − ˛)bI CT + qS,N 1 + (1 − ˛)bI CT 1 + ˛bN CT + (1 − ˛)bN,I CT

(19)

where bN,I denotes the new adsorption constant of the ionic species onto the low-energy sites, e.g. the term that accounts for the competition between the acid and the base for their adsorption on these low-energy sites. The best optimized parameters were: qS,I = 0.65 g/L, bI = 1.45 L/g, qS,N = 14.8 g/L, bN = 0.53 L/g, and bN,I = 0.022 L/g. The new function ˛ were fitted to the calculated data points shown in Fig. 13 A.

Fig. 12. Comparison between the experimental and the calculated band profiles of aniline at SW pH = 2.6, 4.5, 6.5, and 8.5. The adsorption isotherm in Eq. (15) was used in the calculations. The efficiency was set at N = 1600, 2100, 3100, and 3100, respectively. The best parameters were qS,I = 0.369 g/L, qS,N = 46.1 g/L, bI = 1.15 L/g, and bN = 0.079 L/g. The coefficient ˛ was equal to 1 for SW pH = 6.5 and 8.5, and was given by Eq. (13)(B) and Eq. (14) for SW pH = 4.5 and 2.6, respectively.

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Fig. 13. (A) Variation of the bulk phase SW pH (empty circles) and coefficient ˛ (full stars) as a function of the total sample concentration of 2-phenylbutyric acid. (B) Comparison between the experimental and the calculated band profiles of 2-phenylbutyric acid (10 ␮L, 50 mM) eluted with a mobile phase at SW pH = 7.1 (phosphate buffer). The adsorption isotherm in Eq. (19) was used in the calculations. The efficiency was set at N = 4500. The best parameters are listed in the text.

It is noteworthy that the model Eq. (19) can also account for the apparent S-shaped adsorption behavior (isotherm type II) shown in Fig. 13 B. The distortion of the band at high concentrations (anti-langmuirian shape or type III isotherm) is directly related to the increasing concentration of neutral acid species relatively to the ionized basic species when the total sample concentration increases in the bulk at SW pH = 7.1. 5. Conclusion The complex influence of the mobile phase SW pH on the overloaded band profiles of acido-basic compounds in RPLC was investigated using a simple thermodynamic approach, involving the acid/base equilibrium dissociation and the adsorption–desorption of the two species. The first results of this work are consistent with the fact that the peak shape is controlled by the relative concentrations of the acid and base species that coexist at equilibrium in the mobile phase. Knowing the adsorption behaviors of both species from their behavior at either ends of the SW pH scale, at very low S pH, where the compound is present only under the acidic form, W and at very high SW pH, where it is present only under the basic

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form, allows the derivation of an adsorption isotherm model that accounts quantitatively well for the band profiles recorded at any intermediate SW pH. Our model describes satisfactorily how the experimental peak shape passes successively from a langmuirian shape (type I isotherm), to an S-shaped (type II isotherm), an anti-langmuirian shape (type III isotherm), then to an S-shaped again, and finally to a langmuirian shape when the SW pH of the weakly buffered mobile phase continuously increases from low to high values. The experimental results show that ionic species, whether basic or acidic, adsorb very strongly on high-energy sites that have a very low density on the stationary phase surface. This explains why their peak shapes strongly tail at low sample sizes and why their retention factors are small. On the other hand, the conjugated neutral species are adsorbed rather weakly on a large number of low-energy adsorption sites, which explains why their band profiles tail less and why their retention factors are higher. The influence on band profiles of the competition for adsorption between the ionic and the neutral species appears to be negligible. Obviously, our model could be refined to take this competition into account but this would introduce new parameters, which might be difficult to measure by solving the inverse problem of chromatography and to estimate accurately. Our results showed that it is not necessary to do so in order to account properly for the observed overloaded band profiles of aniline. The validity of the adsorption model presented in this work needs to be further tested by changing the buffer concentration and keeping constant the injected sample concentrations. Possibly, the saturation capacity of the sites responsible for the adsorption of the ionic species will vary with the buffer concentration. This experimental work will be presented in a forthcoming work using more efficient columns having a particle size of 3.5 ␮m (instead of 5 ␮m). This work provides a simple tool to predict the band profiles of acido-basic compounds under any SW pH conditions, in a range of sample concentrations that exceeds the buffer concentration. It also provides simple rules for analysts easily to predict the shapes and the retention times of the peak of ionogenic compounds, knowing their SW pKa , that of the buffer and its concentration. This might be particularly useful in LC/MS applications when no or small buffer concentrations are necessary. Conversely, simple LC experiments like those described in this work should permit the accurate determination of the SW pKa of an unknown acido-basic species, knowing the SW pH and the concentration of the buffer used in the mobile phase. Another interesting problem is the one of compounds having two or more pKa , such as amino-acids, peptides, or other low molecular weight pharmaceutical compounds and the analysis of their overloaded band profiles using weak buffer capacity. This work will be carried out in a near future.

Acknowledgments This work was supported in part by grant CHE-06-08659 of the National Science Foundation, by Grant DE-FG05-88-ER-13869 of the US Department of Energy, and by the cooperative agreement between the University of Tennessee and the Oak Ridge National Laboratory.

Appendix A. Supplementary Data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.chroma.2008.11.020.

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