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Journal of Chromatography A, 1216 (2009) 3175–3184

Contents lists available at ScienceDirect

Journal of Chromatography A

journa l homepage: www.e lsev ier .com/ locate /chroma

and profiles of reacting acido-basic compounds with water–methanol eluents atifferent S

WpHs and ionic strengths in reversed-phase liquid chromatography

abrice Gritti, Georges Guiochon ∗

epartment of Chemistry, University of Tennessee, 413 Buehler Hall, Knoxville, TN 37996-1600, USA

r t i c l e i n f o

rticle history:eceived 12 December 2008eceived in revised form 26 January 2009ccepted 3 February 2009vailable online 11 February 2009

eywords:PLC of acido-basic compoundsPLC

a b s t r a c t

Overloaded band profiles of aniline (25 �L injection of a 30.5 mM solution) eluted with a methanol-aqueous buffer solution (30/70, v/v) were recorded at the exit of a 150 mm × 4.6 mm column packed with3.5 �m XBridge-C18porous particles. The S

W pH of the mobile phase was adjusted with phosphate (SW pH ∼

2.7 and SW pH ∼ 7.5) or acetate buffers (S

W pH ∼ 5.3) of different concentrations (11, 56, and 278 mM). Theelution times and profiles of the bands observed at low ionic strength were succesfully accounted forusing the extended Debye–Hückel theory to estimate the activity coefficients of the ions in the bulkphase and a simple non-competitive Langmuir adsorption model, the adsorption of pure aniline or pureanilinium onto XBridge-C18 being described by a Langmuir isotherm. The band profiles were calculated

Bridge-C18

ctivity coefficientsxtended Debye–Hückel theoryethanol–water mobile phasepH

onic strength

using this adsorption model and the equilibrium-dispersive model of chromatography. The calculatedand the experimental band profiles are in excellent agreement at all buffer pH and ionic strength. Thisdemonstrates that the elution times and the band profiles are controlled by the chromatographic dilutionprocess and by the reaction of aniline with the buffer solution.

© 2009 Elsevier B.V. All rights reserved.

angmuir adsorption isothermniline

. Introduction

The profiles of elution bands of solutes that cannot react with theobile phase is completely predicted by the equilibrium isotherm

f the corresponding compound between the bulk liquid phasend the solid adsorbent [1]. Convex upward isotherms produceailing bands while convex downward isotherms lead to frontingands. S-shaped isotherms gives both effects, often character-

zed as mixed isotherm behavior. A convex upward isotherm isbtained when the coverage of the adsorbent surface increasesore slowly than the mobile phase concentration while a con-

ex downward isotherm takes place when the stationary phaseoncentration increases faster than the bulk phase concentra-ion. Thus, in the RPLC mode, in which a polar mobile phases in equilibrium with an apolar surface, the band profiles ofpolar solutes such as alkylbenzenes are fronting at high con-entrations while those of polar solutes such as alkylphenols are

ailing. Compounds of intermediate polarity, like alkylbenzoates,ive peaks that are tailing or fronting, depending on the concen-ration injected [2]. In summary, the peak shape of non-reactingolutes is controlled by the chemical nature of the solute studied,

∗ Corresponding author. Fax: +1 865 974 2667.E-mail address: guiochon@utk.edu (G. Guiochon).

021-9673/$ – see front matter © 2009 Elsevier B.V. All rights reserved.oi:10.1016/j.chroma.2009.02.013

hence its unique distribution between the bulk and the adsorbedphases.

The peak profile of a solute that can react and be transformedinto another one during its elution along the column is less straight-forward to explain. In practice, the only possible type of reaction isdue to the dilution process associated with chromatography affect-ing the relative concentration of different associated species inthe bulk mobile phase, as takes place in acid–base equilibria. Thedifferent associated species of a single compound are always inequilibrium in the bulk and the exchange rate between them maybe assumed to be infinitely fast compared to the LC characteristictime. However, their adsorption properties may differ consider-ably from one to the other. The resulting band profiles of suchkind of compounds is usually difficult to predict and very unusualband profiles may be observed for compound that seem to haveadsorption isotherms that are inconsistent with the observed pro-file.

This general problem of the elution of a reacting compound inliquid chromatography is illustrated by the elution of acido-basiccompounds under experimental conditions that allow the progres-

sive transformation of either the acidic or the basic species into theother one when their total concentration changes, due to the elutionprocess. A series of experimental studies have already demon-strated this type of behavior [3–5] and shown the reproducibility ofthe results, the stability of the process, and its control by adsorption

3 matog

tfctcbtriicttf

cdmsTl

teatoTotbtadpsp

2

2

utmtaffbfi

D

wacaos

wp

ing the recording of the pH was set at 0.250 mL/min.

176 F. Gritti, G. Guiochon / J. Chro

hermodynamics only, because the exchange rate between the dif-erent species present in the solution is much faster than any of thehromatographic kinetic processes. The peak observed correspondso the elution of an apparently single component but its shape is notonsistent with the adsorption isotherm of each individual speciesecause an equilibrium takes place in the mobile phase. By nature,he experimental conditions are unusual as they require the use ofelatively low buffer capacity (because either the mobile phase pHs set too far from the buffer pKa and/or the buffer concentrations too low compared to the sample concentration). However, theseonditions are often found in LC/MS analyses when analysts needo minimize the amount of buffer sent to the ion source, in ordero minimize its pollution by salts and/or to enhance the sensitivityor trace components.

The interpretation of the shapes of the recorded peaks is stillontroversial. Some believed that these unusual profiles could beue to the adsorption of eluent components onto the packingaterial (silica-C18) [6] and/or to the effect of the buffer ionic

trength on the adsorption mechanism of ionizable compounds.he buffer electrolytes could possibly compete with charged ana-

ytes for adsorption onto the adsorbent surface.The goal of this work is to clarify these controversies and

o demonstrate that the complexity of these profiles that, nev-rtheless, seem to correspond to a single compound is simplyccounted for by the combination of the adsorption behaviors ofhe two conjugated species and to the variation of the degreef advancement of their equilibrium during the elution process.his thesis is illustrated by the analysis of the chromatogramsbtained upon injection of 25 �L samples of a 30.5 mM solu-ion of aniline (pKS) in nine different buffers: two phosphateuffers (pKa,1 and pKa,2) and an acetate buffer (pKa), each ofhese buffers being used at three different concentrations (11, 56,nd 278 mM). The extended Debye–Hückel theory was used toescribe the thermodynamics in the bulk mobile phase and a sim-le co-adsorption model was assumed for the acid and the basepecies. The calculated and experimental peak shapes are com-ared.

. Theory

.1. Calculation of chromatographic band profiles

The overloaded band profiles of the two acido-basic compoundssed in this work (anilinium and aniline) were calculated usinghe equilibrium-dispersive model (ED) of chromatography [1]. This

odel assumes instantaneous equilibrium between the mobile andhe stationary phases and a finite column efficiency that is due to anpparent axial dispersion coefficient, Da. This coefficient accountsor both the axial dispersive phenomena (molecular and eddy dif-usion) and the consequences of a finite mass transfer kineticsetween the two phases in the column. The axial dispersion coef-cient is

a = uL

2N(1)

here u is the mobile phase linear velocity, L the column length,nd N the number of theoretical plates or apparent efficiency of theolumn measured under linear conditions, i.e., with samples thatre so small that the column efficiency is completely independentf the sample size. In this model, the mass balance equation for aingle component is written as

∂CT

∂t+ u

∂CT

∂z+ F

∂qT

∂t− Da

∂2CT

∂z2= 0 (2)

here qT and CT are the total stationary phase and the total mobilehase concentrations of the acido-basic compound at equilibrium

r. A 1216 (2009) 3175–3184

(i.e., are the sums of the concentrations of the conjugated acidicand basic species), respectively, t is the time, z the distance alongthe column, and F = (1 − �t)/�t is the phase ratio, with �t the totalcolumn porosity. qT is related to CT through the isotherm equation,qT = f (CT ).

2.1.1. Initial and boundary conditions for the ED modelAt t = 0, the concentrations of the solute and the adsorbate in the

column are uniformly equal to zero and the stationary phase is inequilibrium with the pure mobile phase. The boundary conditionsused are the classical Danckwerts-type boundary conditions [1,7]at the inlet and outlet of the column. The peak area is proportionalto the sample size.

2.1.2. Numerical solutions of the ED modelThe ED model was solved using a computer program based on

an implementation of the Rouchon method [1,8–10]. The relativeand absolute errors of the numerical calculations were 1 × 10−6

and 1 × 10−8, respectively.

3. Experimental

3.1. Chemicals

The mobile phase was a solution of methanol and water(30/70, v/v), both HPLC grade from Fisher Scientific (Fair Lawn,NJ, USA). The mobile phase was filtered before use on asurfactant-free cellulose acetate filter membrane, 0.2 �m poresize (Suwannee, GA, USA). The compound used in this work wasaniline (S

W pKS

= 4.5). Phosphoric acid (85% H3PO4), potassiumdihydrogenphosphate (KH2PO4), dipotassium hydrogenphosphate(K2HPO4), acetic acid (>99.5%) and potassium acetate (KCH3COO),all from Fisher Scientific, were used to prepare the buffer solutions(see Table 1 for the S

W pH of the buffers and their concentra-tions).

3.2. Materials

An Agilent 1090 liquid chromatograph was used to perform themeasurements. This instrument includes a ternary solvent deliverysystem, an auto-sampler with a 250 �L sample loop, a diode-arrayUV detector (cell volume 1.7 �L), a column oven, and a data sta-tion running the HP data software. From the needle seat to thecolumn inlet and from the column outlet to the detector cell, thetotal extra-column volume of the instrument is 45 �L, measured asthe apparent hold-up volume of a zero-volume union connector inplace of the column.

The chromatographic column (150 mm × 4.6 mm packed withXBridge-C18 particles, average size 3.5 �m, average pore size136 Å, specific surface area 172 m2/g, bonding density 16.95% C,3.13 �mol/m2) was a generous gift from Waters (Milford, MA,USA). The total porosity �t = 0.637 of this column was esti-mated from pycnometric measurements (made using methanol anddichloromethane), giving a column hold-up volume of 1.588 mL.The packing material was endcapped according to a proprietaryprocess.

The pH of the mobile phase was measured with an AccumetpH-meter (Fischer Scientific), calibrated in pure water with twostandard aqueous solutions at pH 4.00 and 9.00. The flow rate dur-

The flow rate during the recording of the elution bands of ani-line was set at 0.500 ± 0.004 mL/min or 0.250 mL/min when thepH was simultaneously measured. The temperature was controlledat 297 ± 1 K using the laboratory air-conditioner, the column beingkept inside the oven compartment.

F. Gritti, G. Guiochon / J. Chromatogr. A 1216 (2009) 3175–3184 3177

Table 1Preparation of the nine buffer solutions. The measured masses of acid and bases were added to 450 mL of a mixture of methanol and water (30/70, v/v). The pH was calibratedat 23 ◦ C in pure water and measured directly in the methanol/water mixtures. The pHs measured after addition of 0.071 g of aniline into 25 mL of these buffer solutions aregiven in the last column.

Buffer Acid Base Cacid+base (mM) SW

pHbulk

[aniline] = 0 mM SW

pHinj

[aniline] = 30.5 mM

WeakPhosphate I 0.288 g 0.340 g 11 2.92 5.20

85% H3PO4 KH2PO4

Acetate 0.150 g 0.245 g 11 5.16 5.58CH3COOH CH3COOK

Phosphate II 0.340 g 0.435 g 11 7.62 7.65KH2PO4 K2HPO4

MediumPhosphate I 1.441 g 1.701 g 56 2.70 3.84

85% H3PO4 KH2PO4

Acetate 0.751 g 1.227 g 56 5.12 5.28CH3COOH CH3COOK

Phosphate II 1.701 g 2.177 g 56 7.44 7.47KH2PO4 K2HPO4

StrongPhosphate I 7.206 g 8.506 g 278 2.53 2.72

85% H3PO4 KH2PO4

Acetate 3.753 g 6.134 g 278 5.11 5.17CH3COOH CH3COOK

3

(T(sp(t(Tt(

3

ss9scuamwmC

SW

w

v

4

ow

Phosphate II 8.506 g 10.886 g 278KH2PO4 K2HPO4

.3. Buffer and sample preparation

Equimolar solutions of the acid and the conjugated base450 mL) were prepared by dissolving appropriate amounts (seeable 1) of phosphoric acid and potassium dihydrogenophosphateWW pH = 2.11), of dipotassium hydrogenophosphate and potas-ium dihydrogenophosphate (W

W pH = 7.19), and of acetic acid andotassium acetate (W

W pH = 4.77) into the methanol–water solution30/70, v/v). For each buffer solution, three different concentra-ions were chosen, 278 mM, 56 mM (ca. 1/5th dilution), and 11 mMwith two consecutive ca. 1/5th dilutions). The S

W pH are listed inable 1. 0.071 g of aniline was dissolved into 25 mL of each ofhese two buffer solutions. The total molar concentration injectedanilinium + aniline) was 30.5 mM.

.4. pH measurements

The SW pH values were measured directly in the methanol–water

olution (solution S), after calibrating the pH-meter with two pHtandard solutions in pure water (solutions W) at pH 4.00 and pH.00. The solution potential (mV), whether measured in aqueousolutions or in aqueous-organic solutions refer to the same andonstant reference electrode potential (Ag/AgCl electrode in sat-rated KCl solution). The solutions S and W having the same protonctivity aH+ generate the same electrode potential. S

W pH is a directeasure of the activity of the proton in the solution studied. In pureater, the proton H+ is present as hydroxonium ion H3O+, only. Inethanol–water solutions, it can also be solvated by methanol as

H3OH2+ and

pH = − log aH+ = − log(�H3O+ [H3O+] + �CH3OH+2

[CH3OH+2 ]) (3)

here �H3O+ and �CH3OH+2

are the activity coefficients of both sol-

ated forms of H+.

. Ressults and discussion

In the first section, we report and discuss our experimentalbservations. In the second, we propose a general adsorption modelhich is combined with the degree of advancement of the reac-

7.26 7.30

tion (protonation of aniline equilibrated with the dissociation ofanilinium) during the elution process. Finally, we compare theexperimental band profiles with those calculated using this modeland the ED model of nonlinear chromatography.

4.1. Experimental results

4.1.1. pH measurementsTable 1 lists the S

W pHs of the nine mobile phases used (3 dif-ferent pHs and 3 buffer concentrations). The values measured areclearly different from those expected in pure water at infinite dilu-tion (W

W pKa

= 2.11, 4.77, and 7.19). The SW pH values measured at

low concentration (at 11 mM, the activity coefficients are closeto one) are systematically larger, being equal to 2.92 (+0.81),5.16 (+0.39), and 7.62 (+0.43), respectively, in excellent agree-ment with the data and the model presented in [11]. This mirrorsthe role of methanol in the dissociation constant of weak acidsin methanol–water solutions. Weak neutral acids become weakerbecause the dielectric constant of methanol is smaller than that ofwater (� = 33.8 vs. 79.5 at 298.15 K). The dielectric constant of themethanol–water solution (70/30, v/v) is 65.6 at the same tempera-ture [12].

It is noteworthy that increasing the buffer concentration affectsthe S

W pH because the activity coefficients of ions become signifi-cantly smaller than unity, especially at concentrations larger than10 mM. The S

W pH decreases with increasing solution ionic strength,dropping by close to −0.04 when the acetate buffer concentrationincreases from 11 to 56 mM and by close to −0.22 and −0.18 forthe monovalent and the divalent phosphate buffers, respectively.Accordingly, increasing the ionic strength of the buffer solutionscauses an increase of the activity of the protons in the solution.

These observations suggest that the activity of the pro-tons of conventional acetate and phosphate buffers prepared inmethanol–water solutions at concentrations larger than 10 mM

could be accurately predicted if the calculation of the activity coef-ficients of the ions in solution accounts for both the presence ofmethanol in water and the ionic strength of the solution. We applythe extended Debye–Hückel theory for the calculation of the activ-ity coefficients of all ions in the different buffer solutions.

3 matogr. A 1216 (2009) 3175–3184

3tISWspcsobpercti

4

nfnstwwotTn

ctdttcmdmattttttmdtmpt

nplwptcpiia

Fig. 1. Elution band profiles of aniline with the XBridge-C18 column. The 25 �L injec-tion of a 30.5 mM solution of aniline were prepared in three buffer mobile phases

178 F. Gritti, G. Guiochon / J. Chro

The SW pH measurements were also performed with the nine

0.5 mM solutions of aniline in the different buffers (see Table 1)hat were injected into the column. The W

W pKa

of aniline is 4.60.n a 30/70 (v/v) methanol–water solution, it slightly decreases to

pKa

= 4.45, according to [11]. Aniline was introduced in the bufferolutions as the basic species. As expected, the pH of the bulk mobilehase is poorly affected by the presence of aniline when the bufferoncentration is about 10 times larger (278 mM) than that of theample, even in the most acidic buffer (+0.19). As the concentrationf the buffer is decreased to 56 mM, the pH of the aniline solutionecomes significantly larger than the pH of the most acidic mobilehase (+1.14). The presence of aniline controls the pH in the weak-st (11 mM) acidic buffer (+2.28). In these last two cases, anilineeacts with the buffer solution and is partially transformed into theonjugated species anilinium. When added to the neutral pH solu-ion (bivalent phosphate) aniline does not react. The S

W pKa

of anilines determined in a later section.

.1.2. ChromatogramsFig. 1A–C shows the chromatograms of aniline eluted with the

ine buffered mobile phases. These chromatograms were derivedrom the records of the UV absorbance as functions of time and fromine calibration curves obtained by measuring the UV absorbance ofolutions made by dissolving increasing concentrations of aniline inhe nine buffer solutions. Fig. 2A–C shows these calibration curves,hich are all quasi-linear, except when aniline is dissolved in theeak buffer solutions. In these last cases, as the total concentration

f aniline increases, aniline tends to impose its own pH, and thehree calibration curves in Fig. 2A converge toward the same limit.he absorptivity of the anilinium cation is smaller than that of theeutral aniline molecule.

When the buffer concentration is much larger than the totaloncentration of the injected sample (e.g., 278 mM vs. 30.5 mM),he molar fractions of anilinium and aniline in the solution do notepend on CT and their ratio can be considered as constant duringhe elution. The band profiles are conventional and exhibit a slightailing, due to column overloading (Fig. 1A). When the buffer con-entration decreases to 56 mM, the peak shapes recorded with theonophosphate buffer and the acetate buffer (Fig. 1B) are slightly

istorted, although their retention times remain unchanged. Thisirrors the increase of the relative concentration of aniline to

nilinium when CT increases. The distortion becomes obvious whenhe buffer concentration is only 11 mM, e.g., three times less thanhe injected sample concentration (Fig. 1C). The injected concen-ration to which we are referring is the sample concentration inhe injected solution. During its transit from the injection seat tohe column entrance and from the column exit to the detector cell,he sample experiences dilution. This extra-column dilution effect

ay affect the relative concentrations of the acid and the base. Weid not investigate here the effect of the extra-column volumes onhe observed peak shape. Nevertheless, it is important to keep in

ind that sample dilution in the extra-column volumes can affecteak shapes in certain cases in which the sample may react withhe buffer solution.

The goal of the next sections is to provide a fundamental expla-ation for these observations. We submit that the distorted bandrofiles result from the progressive evolution of the reaction of ani-

ine with the buffer during the elution. To calculate these profiles,e must first determine the molar composition of the bulk mobilehase everywhere along the column. The extended Debye–Hückelheory will be applied for this purpose. Then, we need the single

omponent adsorption isotherm of each individual species in thehase system. The isotherm parameters will be estimated using the

nverse method of chromatography. Finally, the model will be val-dated by recording the band profiles in different buffers (acetate)nd/or at different ionic strength I of the bulk mobile phase.

(phosphate I with SW

pH ∼ 2.7, acetate SW

pH ∼ 5.1, and phosphate II with SW

pH ∼ 7.5)at three different total buffer concentrations, 278 mM (A), 56 mM (B), and 11 mM(C). Flow rate: 0.5 mL/min. T = 297 K.

4.2. Determination of the SW pK

as of the buffer and the solute

In methanol–water solutions, the total concentrations of all thesolvated forms of the proton and of all the deprotonated species ofthe eluent are respectively

[H+] = [H3O+] + [CH3OH+2 ] and

[O−] = [OH−] + [CH3O−]

F. Gritti, G. Guiochon / J. Chromatogr. A 1216 (2009) 3175–3184 3179

Fsi∼

mwoO

a

K

Table 2Effective solvated diameter of organic and inorganic ions in water.

Ion ai (Å)

H+ 9.0C6H5NH2

+ 6.0K+ 3.0OH− 3.5CH3O− 3.5

ig. 2. Concentration-UV absorbance calibration curves of aniline in the nine bufferolutions (3 buffers × 3 buffer concentrations Cbuffer). Note the deviation from linear-ty when the buffer concentration is comparable to the sample concentration (1 g/L

11 mM) at low pH due to aniline protonation.

The autoprotolysis constant of the binary eluent containing 30%ethanol (v/v), KS

e = 10−14.07, is barely smaller than that of pureater (KW

e = 10−14) [11]. If we assume that the activity coefficientsf H O+and CH OH +on the one hand and the activity coefficients of

3 3 2H− and CH3O− on the other hand are equal (i.e., �H3O+ = �CH3OH+

2nd �OH− = �CH3O− ) then

Se = aH+ aO− = �H3O+ �OH− [H+][O−] (4)

H2PO4− 4.0

HPO42− 4.0

CH3COO− 4.5

The activity coefficients of any ion in solution, �i, are estimatedusing the classical extended Debye–Hückel equation, which is usu-ally valid for ionic strengths in the range of 10–100 mM

log �i = − Az2i

√I

1 + Bai

√I

(5)

where zi is the valence of the ion, A and B are two parameters thatdepend on the temperature and on the dielectric constant, �, of thesolvent, ai is the effective solvated diameter of the ion, and I is theionic strength of the solution. A and B write [11]:

A = 1.8246 × 106

(�T)3/2(6)

B = 50.29

(�T)1/2(7)

Accordingly, in a methanol–water solution containing 30%methanol (v/v), we have � = 65.6 and at 298.15 K, A = 0.667 and B =0.360. The effective solvated diameter, ai, depends on the nature ofthe ion i. The diameters of all the ions present in the buffer solutionused are listed in Table 2 [13]. The ionic strength is given by thefollowing summation over all the ions present in solution

I = 12

∑

i

z2i ci (8)

where ci is the molar concentration of the ion i in the solution.The complete equilibrium problem must be solved in order to

determine the equilibrium concentrations of all the species in thesolution, hence its ionic strength. We need to determine simulta-neously the activity of the protons (S

W pH) and the values of SW pK

a,1

and SW pK

a,2 for a given buffer. The solution of this problem is diffi-cult due to its circularity. Activity coefficients depend on the ionicstrength which, in turn, depends on the equilibrium concentrationsof all the ions. A method of successive approximations is appropri-ate. An initial guess is made for I, based on the amount of electrolytedissolved, and the set of equations is solved. At the end of thisstep, the resulting ionic strength is calculated and used as the ini-tial guess of another step. The process is continued until the ionicstrength remains constant. The set of equations to solve in the bulkphase was given elsewhere [4]. These equations include the ther-modynamic equilibria (eluent autoprotolysis, buffer and sampleacido-basic equilibria, buffer and sample mass conservation, andelectroneutrality).

The SW pK

a,1 and SW pK

a,2 values of the phosphate buffer are 2.75and 7.86, respectively, with a total buffer concentration of 11 mM(I1 = 6.9 mM and I2 = 22.2 mM). The S

W pKa,1 of acetate is 5.20 (I1 =

5.6 mM). The estimated SW pK

avalues at a buffer concentration of

56 mM are 2.71 and 7.87 for the phosphate buffers (I1 = 30.2 mMand I2 = 111.1 mM) and 5.21 (I1 = 27.8 mM), respectively. The valueof S

W pKa

for anilinium/aniline in the methanol–water solution wasestimated from S

W pH measured in a 30.5 mM solution of aniline inthe phosphate buffer (S

W pKa,1 = 2.75, S

W pKa,1 = 7.86, and S

W pH =

3180 F. Gritti, G. Guiochon / J. Chromatogr. A 1216 (2009) 3175–3184

Fig. 3. Calculated degree of advancement of aniline dissociation (or molar fractionof aniline, full squares) and solution S

WpH (empty stars) as a function of the total

cv2h

5

a4

iDb

4

(spc

oncentration of aniline (represented on a logarithmic scale) dissolved in the mono-alent phosphate buffer at three different concentrations, 11 mM (A), 56 mM (B), and78 mM (C). Note the reduced protonation of aniline at low buffer concentration andigh aniline concentration.

.20) and in the acetate buffer (SW pK

a,1 = 5.20, and SW pH = 3.84) at

concentration of 11 mM. The best values of SW pK

afor aniline were

.48 (I1 = 11.1 mM) and 4.49 (I1 = 8.1 mM).These S

W pKa

values are in excellent agreement with the exper-mental values given in [11], which validates the choice of theebye–Hückel theory to account for the non-ideal behavior of theulk mobile phase.

.3. Determination of the degree of protonation of aniline

S

Based on the accurate and precise estimates of all the W pKas

phosphate and acetate buffers and compound aniline), it is pos-ible to estimate the degree of advancement of the reaction ofrotonation of aniline in any given buffer as a function of the totaloncentration CT of aniline initially dissolved into this buffer. We

Fig. 4. Same as in Fig. 3, except with the monovalent acetate buffer.

define this degree of advancement as

˛(CT ) = [R-NH2][R-NH2] + [R-NH+

3 ]= [R-NH2]

CT(9)

˛ is the ratio of the concentration of aniline to the total concentra-tion (aniline + anilinium) of sample in the bulk during elution. Itis estimated with the method described above, by considering thereal activity of the solution. The concentration of all the componentsare determined, S

W pH is estimated for the nine buffer solutions as afunction of the total concentration CT , and ˛ can then be calculatedfor all CT values between 0 and 30.5 mM. A CT value tending towardszero defines infinite dilution of aniline in the buffer solution.

Figs. 3 and 4 show the variation of ˛ and SW pH as functions of the

total concentration of aniline in the monovalent phosphate bufferand in the acetate buffer, respectively. Because aniline does not react

S

in the divalent phosphate buffer, ˛ ∼ 1 and W pH are constant overthe full range of concentrations CT .

When aniline is dissolved into the acidic phosphate buffer solu-tion, it is almost completely protonated at infinite dilution (97, 99,and more than 99% in the 11, 56, and 278 mM buffers, respectively)

matog

aromrc

bm

Fipc

F. Gritti, G. Guiochon / J. Chro

nd only partial at a concentration of 30.5 mM (18, 82, and, 98%,espectively). In the presence of the acetate buffer, the reactionf aniline is less quantitative. Only 18, 22, and 27% of the anilineolecules react at infinite dilution in the 11, 56, and 278 mM buffers,

espectively. These fractions decrease to 9, 16, and 24% when theoncentration of aniline is 30.5 mM.

The reaction of aniline in the acidic phosphate and the acetateuffers induces a change in the S

W pH of the eluent in the chro-atographic zone, which can be detected at the outlet of the

ig. 5. Comparison between the experimental band profiles of aniline (see Fig. 1) and tn Eq. (10) (A), (B), and (C) divalent phosphate buffer at three different ionic strengths ihosphate buffer at two different ionic strength in which aniline reacts quasi-quantitatiolumn efficiencies are given in Table 3.

r. A 1216 (2009) 3175–3184 3181

chromatographic column during elution. As shown in Figs. 3 and 4,a change in the solution pH is expected when aniline is eluted withthe weakest (11 mM) acidic phosphate buffer (S

W pH = 2.92).

4.4. Co-adsorption model of anilinium and aniline

We consider the simplest adsorption isotherm model ofanilinium–aniline solutions onto the BEH-C18adsorbent: (1) theadsorption isotherm of aniline is a Langmuir isotherm. It has

he best calculated band profiles performed to estimate the isotherm parametersn which aniline does not react (basic S

WpH ∼ 7.5, ˛ → 1). (D) and (E) monovalent

vely with the buffer (basic SW

pH ∼ 2.6, ˛ → 0). The best isotherm parameters and

3182 F. Gritti, G. Guiochon / J. Chromatogr. A 1216 (2009) 3175–3184

Table 3Best isotherm parameters (qS,N , bN , qS,I , and bI) and column efficiency N determined by the inverse method using the isotherm Eq. (10) and the reaction advancement (˛)represented in Figs. 3 and 4.

I (mM) qS,N bN N qS,I bI

Phosphate II 11 mM 22.2 230 0.0143 18,000 – –Phosphate II 56 mM 111.1 230 0.0145 17,500 – –Phosphate II 278 mM 555.6 230 0.0162 15,500 – –PP

bsctpatoaa

q

teudqlpl

F(s

hosphate I 56 mM 30.2 230 a

hosphate I 278 mM 142.4 230 a

a Parameter maintained fixed during estimation.

een shown that the adsorption energy distribution of aniline onilica-C18 is clearly unimodal [14]. The saturation capacity of theolumn, qS,N , and the binding constant, bN , completely determinehe overloaded band profiles of aniline alone; (2) as demonstratedreviously, the ionizable species anilinium adsorbs on specific andctive sites that are present at low concentrations on the surface ofhe adsorbent [4]. The saturation capacity and the binding constantf anilinium are qS,I and bI , respectively; and (3) the total amountdsorbed, qT , is the sum of the adsorbed amounts of anilinium andniline for a given degree of advancement of the reaction, ˛(CT ):

T = qS,NbN˛(CT )CT

1 + bN˛(CT )CT+ qS,I

bI[1 − ˛(CT )]CT

1 + bI[1 − ˛(CT )]CT(10)

Accordingly, to predict the band profiles of aniline, we needhe four isotherm parameters qS,N , bN , qS,I , and bI . These param-ters are first estimated from the results of measurements madender such conditions that either anilinium or aniline is the pre-

ominant species in the bulk solution. For instance, the parametersS,N and bN were determined from the elution band profiles of ani-ine in the divalent phosphate buffer (S

W pH ∼ 7.5). The isothermarameters qS,I and bI were estimated from the profile of ani-

ine eluted in the monovalent phosphate buffer (SW pH ∼ 2.8). The

ig. 6. Comparison between the experimental and the calculated band profiles of anilineB) Acetate buffer at low ionic strength. (C) Acetate buffer at moderate ionic strength, anhape of the experimental band profiles for all types of buffer and all ionic strengths.

0.0143 a 10,000 0.28 0.660.0146 a 7,500 0.61 0.29

actual inlet band profile was recorded by replacing the columnwith a zero-volume union and was used in the estimation of theisotherm parameters. The best values obtained for the isothermparameters are listed in Table 3. The experimental and calculatedband profiles are compared in Fig. 5A–E. The results are consis-tent with the fact that the adsorption constant of the neutralspecies is small (bN ∼ 0.015 L/g) on all the available hydropho-bic sites (qS,N ∼ 230 g/L). In contrast, the ionizable aniliniumspecies is strongly adsorbed (bI > 0.3 L/g) onto the few active sites(qS,I < 1 g/L).

It is important to underline that the natures of the adsorptionsites of the neutral and the ionizable species are clearly different.The variations of the solution ionic strength I barely change thecharacteristics of the adsorption sites of aniline, which is typicalof reversed-phase mode mechanisms. The equilibrium constant,bN , increases from 0.0143 to 0.0162 L/g when the ionic strengthincreases from 0 to 0.5 M. This explains the shift in the retention

time of aniline with the three divalent phosphate buffers (S

W pH ∼7.5) in Fig. 1. On the other hand, increasing the ionic strength of themonophosphate buffer from 30 to 142 mM at (S

W pH ∼ 2.8) dimin-ishes the equilibrium constant bI of anilinium by half while thesaturation capacity of the active sites increases by nearly the same

(see Eq. (10) and Table 4). (A) Monovalent phosphate buffer at low ionic strength.d (D) acetate buffer at high ionic strength. Note how well the model predicts the

F. Gritti, G. Guiochon / J. Chromatogr. A 1216 (2009) 3175–3184 3183

Table 4Isotherm parameters used for the prediction of the band profiles.

I (mM) qS,N bN N qS,I bI

Phosphate I 11 mM 7.0 230 0.0143 15,000 0.23 0.71Acetate I 11 mM 5.6 230 0.0143 17,500 0.23 0.71A 0.0143 17,500 0.27 0.67A 0.0146 17,500 0.60 0.30

T

ra

ttivtretdctocs

dtpbmmabla

FeaSWsti

Ftb

Fig. 8. Comparison between the experimental S pH(t) profile of the eluent and the

cetate II 56 mM 27.8 230cetate II 278 mM 138.9 230

he reaction advancements a are those represented in Figs. 3 and 4.

atio, which is typical of an ionic exchange or an ion–dipole inter-ction mechanism.

Fig. 6A–D illustrates the agreement between the measured andhe calculated band profiles of aniline (the isotherm parameters andhe column efficiency are given in Table 4) under buffer conditionsn which the degree of advancement of the dissociation of aniline isery sensitive to the dilution process during chromatographic elu-ion. In all cases, the calculated profiles agree very well with theecorded elution band profiles. This validates the model describedarlier and means that it contains all the substantial elements ofhe adsorption of acido-basic compounds. Most probably, the smallifferences observed are related to the inaccurate calculation of theoefficient ˛ provided by the extended Debye–Hückel method. Yet,he graphs of ˛ in Figs. 3 and 4 provide an excellent descriptionf the bulk mobile phase composition when the total aniline con-entration dissolved inside the buffer and the ionic strength of theolution are changing with time during elution.

Finally, another validation of this model was performed byirectly measuring the pH of the mobile phase during the elution ofhe aniline/anilinium band. A pH electrode (cell volume 50 �L) waslaced downstream the UV detector. It was calibrated with aqueousuffer solutions at pH 4.00 and 9.00. The flow rate was set at 0.25L/min, so it takes 12 s to fill the electrode cell volume. One pHeasurement was done every second (1 Hz). A 250 �L sample of3.0 g/L solution of aniline dissolved in a 11 mM monophosphateuffer (S

W pH = 2.92) was injected into the column (the injectionasts 60 s). The UV absorbance and a calibration curve (see Fig. 2A)llow the calculation of the concentration CT during elution.

From the total concentration of aniline recorded, CT = f (t) (seeig. 7), it is possible to recalculate the elution profile of S

W pH duringlution, from the curve in Fig. 3A that gives the pH of solutions of

niline in the buffers (empty stars). Fig. 8 compares the recalculatedpH and the experimental S

W pH. The agreement is good if we con-ider that the cell volume of the pH meter (50 �L) is much largerhan the volume of the UV cell (1.7 �L). This explains why the exper-mental pH profile is smoother than the recalculated one, which is

ig. 7. Comparison between the experimental band profiles of aniline (250 �L injec-ion, flow rate 0.25 mL/min) and the predicted band profiles. Monovalent phosphateuffer at low ionic strength (Cbuffer = 11 mM, I = 5.6 mM).

WSW

pH(t) profile calculated from the concentration profile of aniline (Fig. 7). Mono-valent phosphate buffer eluent (I = 5.6 mM), XBridge-C18column, 250 �L injection,flow rate 0.25 mL/min, T = 297 K.

based on the UV detection data. The slight increase of pH startingbefore the hold-up time t0 of the chromatographic column corre-sponds to the perturbation consecutive to the sample injection. ThispH is slightly larger than the eluent pH, by 0.2.

5. Conclusion

The complexity of the elution profiles of reacting compounds inbuffered mobile phases was explained based on the combinationof the activity coefficients of the ions involved in the mobile phaseand of the adsorption isotherms of the two conjugated species.The activity coefficients of the ions in the bulk phase were derivedfrom the extended Debye–Hückel theory. The adsorption of thesample components follows non-competitive langmuirian behav-ior. Although all these components have adsorption isotherms thatare strictly convex upward, their band profiles can exhibit anti-Langmuirian or S-shaped isotherm behavior, depending on the pHof the buffered eluent and of the injected sample. The phenomenonis due to the dissociation of the compound studied to a degree thatvaries with its concentration during the elution of the band. Theaccurate prediction of the band profiles of any acido-basic com-pound in any buffer, at any pH and any ionic strength I is possible.The agreement between experimental and calculated band profilesdemonstrates that the interpretation given in this work contains allthe substantial elements needed to account for the observations.

This report clarifies several unanswered or debatable issues:the adsorption of ionizable samples in RPLC involves very few ion-exchange or ion–dipole adsorption sites (the density of free silanolgroups on modern RPLC adsorbents is very low) but strong bindingconstants that decrease with increasing ionic strength of the mobilephase. It would be hasty to conclude regarding the nature of these

active sites. However, the new hybrid organic-silica Xbridge BEH-C18 material contains few silanol groups and their pKa is ratherhigh. Ionized silanols cannot be responsible for the retention ofanilinium in this case. Most likely, the permanent dipole of the very

3 matog

fsiTaccatabpcoov

bhiooca

oult

[10] G. Guiochon, S. Golshan-Shirazi, A. Jaulmes, Anal. Chem. 60 (1988) 1856.

184 F. Gritti, G. Guiochon / J. Chro

ew accessible silanol groups bonded to the surface could interacttrongly with the ion charge. The adsorption of neutral compoundss barely affected by changes in ionic strength of the mobile phase.he shape and position of band profiles of ionizable compoundsre controlled by the distribution of the conjugated species of thisompound in the mobile phase and by their respective single-omponent adsorption isotherms. The overall adsorption isothermsre not competitive because the two species adsorb on differentypes of sites. The conventional model of charge repulsion betweendsorbed ions cannot satisfactorily explain the retention and theand shapes observed in RPLC for ionizable compounds in theresence of their conjugated neutral species. The low buffer con-entration does not entail system instability. The band distortionbserved is of purely thermodynamics origin and mirrors the effectf dilution of the compound during its elution and the correlativeariation of the molar fractions of the two species in equilibrium.

This work will soon be extended to the prediction of the elutionand profiles of compounds having several acid or basic functions,ence multiple pKa that are eluted in buffered eluents with low

onic strengths. Model compounds could be nicotine (one basic andne acid groups) or naphthalenedicarboxylic acid (2 acid groups)r various amino acids. Our results could also be applied to moreomplex samples such as small peptides containing several aminocid residues.

Finally, this work could be used to predict the elution profilesf overloaded bands of acido-basic compounds in preparative liq-id chromatography. Because the solubility of buffer salts is often

imited to ca. 0.5 M, the sample concentration is often larger thanhe buffer concentration, which causes significant changes of the

[[

[[

r. A 1216 (2009) 3175–3184

mobile phase pH during elution, affecting the production rate ofthe purification process. The framework developed in this work willbe used to calculate band profiles, cut points, production rates andyields and to optimize the process.

Acknowledgements

This work was supported in part by grant CHE-06-08659 of theNational Science Foundation and by the cooperative agreementbetween the University of Tennessee and the Oak Ridge NationalLaboratory.

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