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Journal of Chromatography A, 1216 (2009) 3992–4004

Contents lists available at ScienceDirect

Journal of Chromatography A

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

nvestigation of the adsorption mechanism of a peptide in reversed phaseiquid chromatography, from pH controlled and uncontrolled solutions

nna Andrzejewskaa,b, Fabrice Gritti a,b, Georges Guiochona,b,∗

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

r t i c l e i n f o

rticle history:eceived 18 December 2008eceived in revised form 2 March 2009ccepted 6 March 2009vailable online 13 March 2009

eywords:cid–base equilibrium adsorptionechanism

etention of acido-basic compounds RPLCripeptides

a b s t r a c t

The single-component equilibrium adsorption of the tripeptide Leucyl-Leucyl-Leucine (LLL) on a high-efficiency Jupiter Proteo column (C12) was investigated experimentally and modeled theoretically. Theexperimental equilibrium isotherms of LLL for adsorption on a C12 packing material from an aqueoussolution of methanol (48%) and trifluoroacetic acid (0.1%) were measured by frontal analysis (FA). The FAmeasurements were done with two solutions, one in which the pH was controlled, the other in which itwas not. Two solutions of LLL in the mobile phase were prepared (4.3 and 5.4 g/L) and their pH measured(2.94 and 2.88), respectively. The first solution was titrated with TFA to match the pH of the mobile phase(2.03), so its pH was controlled. The pH of the other solution was left uncontrolled. In both cases theisotherms could be modeled by a bi-Langmuir equation, a choice consistent with the bimodal affinityenergy distribution (AED) obtained for LLL. The isotherm parameters derived from the inverse method

(IM) of isotherm determination under controlled pH conditions (by fitting calculated profiles to exper-imental breakthrough profiles) are in a good agreement with those derived from the FA data. Underuncontrolled pH conditions, the application of IM suggests the coexistence of two different adsorptionmechanisms. According to the isotherm parameters found by these three methods (FA, AED and IM), theC12-bonded silica can adsorb around 500 and 70 g/L of LLL under controlled and uncontrolled pH condi-tions, respectively. The adsorption of LLL on the C12 material strongly depends on the pH of the mobile

y of T

phase and on the quantit

. Introduction

Reversed-phase liquid chromatography (RPLC) is a powerfulethod of identification, characterization, and purification of pep-

ides and peptide mixtures. High quality silica particles withhemically bonded alkyl chains are efficient packing materials usedor the separation, purification, and analysis of peptides. By adjust-ng the parameters of the separation, such as the mobile phaseomposition (organic modifier, buffer, salt and ion-pairing agent),he pressure, the temperature, or the elution mode (isocratic orradient), the separation of small or large molecules from environ-ental, pharmaceutical or food samples can easily be performed.lthough RPLC is widely used, the retention mechanism is still dis-

uted [1–7]. To understand solute behavior in preparative RPLC, aetter, more detailed understanding of these complex systems isecessary. This is the key to the prediction of the overloaded bandrofiles and the optimization of the chromatographic processes.

∗ Corresponding author at: Department of Chemistry, University of Tennessee,noxville, TN 37996-1600, USA. 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.2009.03.014

FA added, which plays the role of an ion-pairing agent.© 2009 Elsevier B.V. All rights reserved.

The influence of many experimental parameters like the nature ofthe buffer added to the mobile phase and the buffer capacity in thepresence of highly concentrated samples must be understood froma thermodynamic point of view.

Retention of ionogenic analytes, e.g., peptides, in RPLC is knownto strongly depend on the eluent pH. The retention factor, k, of anon-dissociated form of an acid or a base may be 10–20 times largerthan that of the corresponding dissociated form for a given mobilephase composition [8,9]. This phenomenon would provide a con-venient means to adjust the separation of ionizable compounds ifa proper theoretical model were available. This theory was pre-sented and validated first for isocratic systems in buffered aqueousmobile phases by Horvath et al. [10]. Later, van de Venne et al. [11]extended the relationships between the eluent pH and the analyteretention to methanol–water mobile phases. A complete mathe-matical model of retention in isocratic RPLC as a function of themobile phase pH and composition was proposed by Lopes-Marques

and Schoenmakers [12].

Rules of selection of the mobile phase pH to optimize the separa-tions of mixtures of analytes were recently reported by Snyder andco-workers [13]. The results of exhaustive studies on the effectsof the organic modifiers and their concentrations on acid–base

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A. Andrzejewska et al. / J. Chro

quilibria in mobile phases along with a cogent, comprehensiveritical review of the vast amount of literature on the subject wereresented by Roses and Bosch [14,15]. An excellent up-to-date pre-entation of the subject was recently been published by Barbosand co-workers [16]. The effect of the pH on the retention of basesas also recently discussed by LoBrutto et al. [17].

The acid modifier serves several functions. At low pH, peptidesave a net positive charge, which is particularly useful for theirnalysis in positive ion electrospray MS, the silanol effects due torotonation of the exposed hydroxyl groups are suppressed, andotential ion-pairing effects are generated causing simultaneous

nteractions between analytes and the functional groups bonded tohe adsorbent surface. It was reported that the type and concentra-ion of the acidic modifier used in RPLC has significant effects on theelectivity of peptide separations [18–20]. Hancock et al. and Guot al. first described the effects of three different acidic modifiersphosphoric acid, trifluoroacetic acid, and heptafluorobutyric acid)n the retention and selectivity of mixtures of synthetic peptides.wo models were proposed to explain the mechanism of ion-paireparations. In one model, the acidic modifier first forms an ion pairith the analyte in solution, which is retained [21,22]. In an alter-ative model, the acidic modifier is first retained on the column,nd the analyte binds with the adsorbed modifier via counter-ionxchange [11,23].

All the literature reports discussing the influence of the pH onetention assume that the pH remains constant during the wholehromatographic run. However, for obvious economical reasons,reparative HPLC must be conducted at finite concentrations, nott infinite dilution as analytical chromatography. Buffers have aimited solubility and, at high sample concentrations, the amountf acidic modifier may be insufficient, causing the pH of the elu-nt to change during elution, affecting the retention mechanism ofeptides.

Sabharwal and Chase [24] measured the adsorption isotherms ofovine and porcine insulin on a RPLC adsorbent, Whatman BioPrep4, by frontal analysis and studied the influence of the mobile phaseomposition on their characteristics. Liu et al. [25] determined thedsorption isotherms of Lispro, recombinant human, and porcinensulins on YMC-ODS C18 by frontal analysis (31% acetonitrile and.1% TFA in water). The elution order of these insulin variantsas tentatively explained on the basis of the hydrophobic binding

trength, the chromatographic contact region, and conformationalhanges. The experimental isotherm data fit best to the Tóth equa-ion. The chromatographic behavior of human and porcine insulinsere found to be close and slightly different from that of Lispro

n terms of retention factor, saturation capacity, and heterogeneityarameters. The high concentration breakthrough profiles exhibit ahoulder on their rear diffusive front. The importance of this shoul-er decreases with increasing insulin content. Similar findings wereeported in this work. The authors explained this abnormal behav-or of the rear part of the breakthrough profiles of insulin in frontalnalysis by the presence of insulin aggregates, which may formuring the sample injection into the column and then dissociater be renatured during the elution process. Excellent agreementas observed between experimental and calculated breakthroughrofiles in frontal analysis and band profiles in elution.

The purpose of our work is to measure the adsorption of a tripep-ide under two different pHs conditions: when the pH of the eluentemained constant during elution of the most concentrated sample,ue to a sufficient concentration of TFA, and when the eluent pH wasot kept constant. The theory of nonlinear chromatography affords

everal models allowing the accurate calculation of the individualand profiles of the feed component [26]. The model parame-ers can be derived from a limited number of experiments. Theeneral rate (GR), the lumped pore diffusion (POR), the equilibrium-ispersive (ED), and the transport-dispersive models can be used,

gr. A 1216 (2009) 3992–4004 3993

depending on the importance of the mass transfer resistances andthe kinetics of adsorption/desorption [27–32]. The general ratemodel accounts for all the sources of nonideal behavior, i.e., molec-ular diffusion, eddy diffusion, and the kinetics of the various stepsinvolved in the mass transfer process. However, too many parame-ters must be measured to calculate the elution band profiles, so weused here the simple ED model, which provides equivalent resultsin the case studied.

2. Theory

Among the many different methods used to measure equilib-rium isotherm data, chromatographic ones proved to be highlyaccurate and to need modest amounts of sample. The one mostlyused are frontal analysis (FA), frontal analysis by characteristicpoints (FACP), elution by characteristic points (ECP), perturbationmethod (PM), and inverse method (IM). The choice of the method isspecific to the problem studied and depends on the type of equip-ment available, the possible requirement for detector calibration,and the cost and availability of the chemicals studied. In our studywe chose FA, which is highly accurate, does not require detectorcalibration, and gives results that do not depend on the columnefficiency.

The selection of the method in which the FA adsorption data arehandled is most critical to determine an adsorption isotherm modelthat is consistent with the whole set of data collected and makesphysical sense regarding the chromatographic system studied. Spe-cific representations of the adsorption data (e.g., Scatchard plot),statistical analysis of the data (using e.g., multi-linear regressionanalysis and/or the Fisher parameter), calculation of the adsorptionenergy distribution (using the expectation-maximization method),and comparison of calculated and experimental overloaded bandprofiles permit the selection of the best model, the derivation of thebest estimates of its parameters, and the validation of the isothermobtained. The adsorption isotherms found by involving differentexperimental conditions (e.g., mobile phase composition or mobilephase pH) permits a better understanding of the retention mecha-nisms in RPLC.

2.1. Determination of single-component isotherms by frontalanalysis

The adsorption data of LLL used in this work to illustrate theeffects of the sample composition were acquired by the frontal anal-ysis method [21]. The details and systematic steps followed in thismethod were described elsewhere [26]. The breakthrough curvesthat are recorded during the FA experiments provide the values ofthe stationary phase concentration, q, in equilibrium with the inletconcentration, c0. These values are derived from the retention timeof the front shock of the breakthrough curve, which is estimated bythe equivalent area method.

q = c0 · Fv(tshock − text − t0)

�r2in

L − Fvt0(1)

where Fv is the mobile phase flow rate, tshock the elution time of thefront shock of the breakthrough curve, text the extra-column hold-up time (measured from the elution time of the inflection pointof the same breakthrough curve injected with no column), t0 thehold-up time, rin the internal radius of the column tube, and L thelength of the column.

2.2. Models of single-component adsorption isotherm

Adsorption isotherms are the critical physicochemical propertythat accounts for liquid–solid equilibria of any compound in HPLC.

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994 A. Andrzejewska et al. / J. Chro

sotherms can be broadly sorted out into three kinds, correspondingespectively to ideal adsorption (adsorbate molecules do not inter-ct) on homogeneous surfaces, ideal adsorption on heterogeneousurfaces, and nonideal adsorption (adsorbate molecules inter-ct). To investigate the adsorption mechanism of the Leu-Leu-Leunto RPLC packing materials, we used several isotherm equations,.e., the Langmuir, the Jovanovic, the BET, the bi-Langmuir, theangmuir–Freundlich, the Moreau, the Langmuir–Moreau, and theóth isotherms, which are simple models corresponding to thesehree types of adsorption behavior.

The Langmuir isotherm equation [33] is the simplest model ofdeal adsorption on homogeneous surfaces:

= qsbc

1 + bc(2)

here qs is the monolayer saturation capacity and b the equilib-ium constant at infinite dilution, related to the adsorption energy= b0eε/RT , with b0 the pre-exponential factor that can be derived

rom the molecular partition functions in the bulk and the adsorbedhases, R is the universal gas constant, T the absolute temperature.his equation was originally developed on the basis of reasonablehysical assumptions regarding monolayer adsorption on an idealurface at constant temperature.

In contrast with the assumption generally made in chromatog-aphy, actual surfaces are not homogeneous. Different alkyl chainsnd silanol groups coexist on these surfaces, so analytes may adsorbn more than one type of adsorption sites. Sander et al. [34] showedow order and disorder in alkyl stationary phases influence their

nteractions with analytes. Using a Monte-Carlo simulated model ofPLC, Rafferty et al. [35] illustrated the great complexity of the inter-ctions between a silica substrate bonded to octadecyl chains andonpolar and polar solutes. They showed that both partitioning anddsorption may take place in retention, which explains why RPLChases behave differently from a bulk hydrocarbon phase. Interac-ions with the methylene groups of the alkyl chains are lipophilic.hose with silica are polar and affect the polar compounds more.olute may be retained either at the bulk mobile phase interfaceith the layer of alkyl ligands, between these ligands, or at the

nterface between silica and ligands. The electrostatic environmentf these three locations are entirely different. A full identificationf the chemical nature of the different types of sites has not beenchieved yet.

The surface of typical RPLC adsorbents contains adsorption siteshat differ by their saturation capacity, the nature and energy ofhe interactions between these adsorption sites and the analyte

olecules, and their steric accessibility, related to the shape andolume of the sites [36–39]. Specific interactions can also occuretween solutes and free silanol groups on the silica surface. Thedsorption energy of such sites could be quite high. On the basis ofolecular dynamics, Lippa et al. [7,40] suggested that free spaces

ould be located between clusters of bonded alkyl chains, espe-ially at low surface coverages. One type of such sites is hydrophobicnd related to the bonded alkyl chains, another is hydrophilic andelated to residual silanol groups. Taking into account the chemicalature of the tripeptide used in this work, i.e., the presence of differ-nt functional groups, the Langmuir isotherm may account for thequilibrium behavior of the solute on each type of sites. In such aase, the total amount adsorbed is equal to the sum of the amountsorresponding to each term of the bi- or multi-Langmuir isothermquation.

b c b c

= qs11

1 + b1c+ qs2

2

1 + b2c(3)

here the subscripts 1 and 2 correspond to the concentrationsdsorbed on the two different types of adsorption sites. In mostases, the coefficient b1 of one type of site is larger than b2 and the

gr. A 1216 (2009) 3992–4004

coefficient qs1 smaller than qs2. The monolayer capacity of the mostabundant type of sites is much larger than that of the less abundantones and the equilibrium constant on these sites lower.

Considering heterogeneous surfaces, adsorbates that are suf-ficiently close may interact with each other when adsorbed onthe low-energy sites. On the other hand, it is highly probable thatadsorbates do not interact when adsorbed on strong adsorptionsites because these sites are randomly spread on the stationaryphase and remain relatively isolated from each other. To describeadsorption onto a heterogeneous surface and take into accountthe interactions between solute molecules, the Langmuir–Moreaumodel should be considered:

q = qs1b1c

1 + b1c+ qs2

(b2c + Ib22c2)

1 + 2b2c + Ib22c2

(4)

2.3. Determination of the adsorption parameters

Once the isotherm data have been determined, the isothermparameters are estimated by fitting them to the above adsorp-tion models, for which purpose a nonlinear regression analysis ofthe models was used. The fitting was done using the ORIGIN soft-ware, based on the Levenberg–Marquard’s algorithm [41], whichminimizes the sum-of-squares of the vertical distances betweenthe experimental data and the corresponding model data points.It is the most widely used algorithm in nonlinear least-squaresfitting. Points farther from the curve contribute more to the sum-of-squares. Points close to the curve contribute little, which is expectedfrom the nature of the scatter of the experimental data. In manyexperimental cases, the average absolute value of the distance ofthe data points from the curve corresponding to the true isothermis expected to be larger when the fitted function is also larger. Thehigh concentration data points, which have the largest value fortheir absolute scatter would provide the larger contribution to thesum-of-squares and thus dominate the results of the calculationsof the best isotherm coefficients. Because relative experimentalerrors tend to be constant, to restore an equal weighting to all thedata points, it is appropriate to weigh the data points as describedbelow.

The weighting method used in this work consists in weightingby 1/Y2 (making W = 1/Y2 the weight of each data point). It is con-venient to think of this method as minimizing the sum-of-squaresof the relative distances of the data from the theoretical curve. Thismethod is appropriate when a constant relative error of the datapoints is expected. Minimizing the sum of the squares of the relativedistances restores equal weighting to all data points.

2.4. Fischer parameter

In order to decide which of several possible models is the bestisotherm model the statistical Fisher parameter, Fp, is useful [42].

Fp = ND − P

ND − 1·

ND∑i=1

(qexp,i − qexp)2

ND∑i=1

(qexp,i − qtheor,i)2

(5)

In this equation, ND stands for the number of data points and Pfor the number of model parameters. The subscript exp, i denotesthe experimental values of the stationary phase concentration of

the adsorbate in equilibrium with a given liquid phase concentra-tion, ci, qexp is the mean value of the adsorption data, the subscripttheor, i represents the model adsorption isotherm data, which isderived from the equation of the isotherm model selected. A highervalue of Fp suggests a better fit to the experimental data. Fp increases

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A. Andrzejewska et al. / J. Chro

hen (ND − P) increases (more experimental data points is avail-ble), �(qexp,i − qtheor,i)

2 decreases with increasing goodness of the

t and �(qexp,i − qexp)2 increases with increasing width of the dataange. The Fisher parameter assumes that the residuals are nor-ally distributed. To determine if a model provides data that are

tatistically more accurate than another one, the ratio of the twoisher parameters corresponding to the data obtained with thisethod or model is calculated and compared to critical F-ratios

ound in most statistical books.

.5. Adsorption energy distribution

After the experimental adsorption isotherm data have beencquired, the next step in the study of the retention mechanismonsists in choosing a correct model of isotherm.

The adsorption energy distribution (AED) characterizes theehavior of a heterogeneous surface. It is derived from experi-ental isotherm data, using expectation–maximization method

36,43,44]. The adsorption behavior on the sites having the samenergy is described by an isotherm model valid for homogeneousurfaces, the Langmuir [33] or the Jovanovic [45] isotherm models.

detailed discussion of gas-solid physical adsorption on hetero-eneous surfaces was given by Jaroniec and Madey [46]. Theirreatment can be extended to liquid/solid equilibria [47]. The exper-mental isotherm on a heterogeneous surface is the sum of thesotherms on each of the homogeneous types of sites covering theurface. Under the condition of a continuous adsorption energyistribution and assuming a Langmuir local isotherm model, thexperimental isotherm can be written [46]:

(c) =∫ ∞

0

F(ε) · b(ε)c1 + b(ε)c

dε (6)

here q(c) is the total amount of solute adsorbed on the surfacet equilibrium with a concentration c, F(ε) is the adsorption energyistribution with unit of q(c), and b the equilibrium constant at infi-ite dilution, which is related to the adsorption energy, ε, throughhe relationship b = b0eε/RT , where b0 is the pre-exponential factorhat can be derived from the molecular partition functions in theulk and the adsorbed phases. R is the universal gas constant, T ishe absolute temperature. The parameter b0 is usually assumed toe the same, whatever the type of adsorption site [46].

The normalization condition for the AED is:

∞

0

F(ε)dε = qs (7)

here qs is the overall saturation capacity.The relationship between overall adsorption isotherm and AED

s given by an integral equation, the solution of which is not trivial.variety of methods have been suggested [43,46–48]. We used

he expectation–maximization method (EM) [43], a method thatses directly the raw experimental data, without introducing anydditional information into the AED computation. The distributionunction, F(ε), is discretized, using an N-grid points in the energypace. The energy space is limited by εmin and εmax, two energyoundaries that are respectively related to the maximum and theinimum concentrations within which the adsorption data have

een acquired, by using Eq. b = b0eε/RT (with bmin = 1/cM , bmax =/c1). The adsorbed amount q(cj) of solute at concentration cj is

stimated by iteration, through:

kcalc(cj) =

εmax∑i=εmin

Fk(εi)b(εi)cj

1 + b(εi)cj�ε; j ∈ [1, M]; i ∈ [1, N] (8)

gr. A 1216 (2009) 3992–4004 3995

and

�ε = εmax − εmin

N − 1; εi = εmin + (i − 1)�ε (9)

The subscripts i and j symbolize each energy and concentrationpoints, respectively. The index k indicates the k th iteration ofthe numerical calculation of the AED function. The initial guess(iteration k = 0) of the distribution function, F0(εi), is the uniformdistribution (over the N adsorption sites) of the maximum adsorbedamount that was observed experimentally [43].

F0(εi) = q(cM)N

; ∀i ∈ [1, N] (10)

The only parameters, which have to be defined before the AED cal-culations, are M, N, bmin, bmax, and the number of iterations. Thefinal result is the distribution of the equilibrium constants (oftencalled the affinity distribution). The distribution function, Fk+1(εi),is updated after each iteration by:

Fk+1(εi) = Fk(εi)cmax∑

j=cmin

b(εi)cj

1 + b(εi)cj�ε

qexp(cj)

qkcalc

(cj)(11)

where qexp(cj) is the experimental isotherm data measured for abulk concentration cj, qk

calc(cj) is the estimated data at iteration k

via Eq. (8), �ε is the grid spacing around each energy point i, andthe sum is over the concentration points j.

2.6. Inverse method

The inverse method of isotherm determination estimates theparameters of an a priori selected isotherm model by determiningthe values of its parameters that best match the profiles of the over-loaded elution bands that can be calculated with this isotherm andthose actually recorded under the same set of experimental condi-tions. The overloaded band profiles are calculated with a suitablemodel of nonlinear chromatography. The measured and calculatedband profiles are compared by evaluating the following objectivefunction:

min∑

i

(Csimi − Cmeas

i )2

(12)

where csimi

and cmeasi

are the calculated and the measured concen-trations at point i. At the end of each loop, the isotherm parametersare changed to minimize the objective function, using an optimiza-tion routine.

Several mathematical models could be used to describe elutionof a sample band along a chromatographic column [26,49,50]. Thesimplest one is the equilibrium-dispersive model (ED). This modelis based on the ideal model of chromatography, but it takes the finitecolumn efficiency into account by introducing in the calculations anumerical dispersion that simulates the actual band dispersion dueto the combination of axial dispersion and mass transfer resistance[26]. The ED model can be successfully applied when the following

between the mobile and the stationary phase is fast.2. The contributions of all nonequilibrium effects (i.e., diffusion and

the mass transfer resistances) can be lumped into an apparentaxial dispersion coefficient (which means that their concentra-tion dependence is neglected).

3 matogr. A 1216 (2009) 3992–4004

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Table 1Characteristics of the C12-bonded Jupiter Proteo column and experimentalparameters.

Characteristics of the C12-bonded Jupiter Proteo columnColumn length (cm) 15Inner diameter of the column (mm) 4.6Particle size (�m) 4Pore size (Å) 90Surface area (m2/g) 450Particle shape sphericalCarbon load (%) 17Surface coverage (�mol/m2) 3.04pH range 1.0–10.0Hold-up volume (mL) 1.58Total porosity 0.6355Phase ratio 0.5736Endcapping Yes

Experimental parametersEfficiency 11860Flow rate (mL/min) 1Superficial velocity (cm/s) 0.1003Temperature (◦C) 30

996 A. Andrzejewska et al. / J. Chro

Accordingly, in the ED model of chromatography, the differentialass balance equation is written:

∂c

∂t+ F

∂q

∂t+ u

∂c

∂z= Da

∂2c

∂z2(13)

here F is the phase ratio (volume of the stationary phase dividedy the volume of the mobile phase or F = (1 − �)/�, with � the totalorosity of the column), u the linear mobile phase velocity, c and qhe solute concentrations in the mobile and the stationary phasest position z along the column, at time t. The surface concentration,, is related to the mobile phase concentration by the adsorptionsotherm equation (see Section 2.2). The apparent axial dispersionoefficient, Da, is related to the column efficiency by the followingquation:

a = HL

2t0= uL

2N(14)

here H and N are the height equivalent to a theoretical plateHEPT) and the number of theoretical plates in the column, respec-ively, L is the column length, and t0 is the hold-up time (t0 = L/u).onsistent with the ED model assumptions, the apparent axial dis-ersion coefficient does not depend on the concentration of theompound examined.

The initial condition c(z, 0) = 0 states that at t = 0 the columns equilibrated with the pure mobile phase. The boundary condi-ion is given by the inlet concentration profile. The true inlet profilean be determined by eliminating the column from the instrumentnd performing a large-volume injection. Ideally, the concentra-ion profile is a rectangular impulse but in reality it is smoothedy dispersion effects that occur in the extra-column volumes of thenstrument.

The ED differential mass balance equation was solved numer-cally, by means of an orthogonal collocation on finite elementlgorithm (OCFE) [26,51–53].

The set of differential equations obtained from the partial dif-erential equation of the ED model after application of the OCFE

ethod was solved with the VODE solver, with a relative error of× 10−6 and an absolute error of 1 × 10−8. The algorithm for no

tiff equation was used. The number of subdomains considered inhe OCFE method was set in such a way that there was no visiblescillation on the concentration profiles. The number of collocationoints for each subdomain was equal to 3.

. Experimental

.1. Apparatus

The overloaded band profiles were acquired using a Hewlett-ackard (now Agilent Technologies, Palo Alto, CA, USA) HP 1090iquid chromatograph. This instrument includes a multi-solventelivery system (volume of each tank, 1 L), an auto-sampler with250 �L sample loop, a diode-array UV detector, a column ther-ostat and a data station. A compressed nitrogen bottle (Nationalelders, Charlotte, NC, USA) is connected to the instrument to

llow the continuous operations of the eluent sparging, the pumpnd the auto-sampler. The extra-column volume from the solventixer to the detector is 0.59 mL, measured by recording the profile

btained without column. All the retention data used for adsorptionsotherms determination were corrected for these contributions. All

easurements were carried out at a constant temperature of 30 ◦C,aintained by the instrument thermostat.

The on-line pH profiles of the breakthrough curves were mea-

ured using the Micro Flow-through pH electrode from Lazaresearch Laboratories (Los Angeles, CA, USA). The micro pH elec-rode was calibrated with fresh buffers (4, 7 and 10). The internalead volume of the flow cell was 50 �L. The 16-channel Multi

Extra-column volume (mL) 0.59Concentration range of LLL stock solutions (g/L) 0.00054–5.4

and 0.00068–4.3

pH/Ion meter (Model KST101B, Kosentech, S. Korea) was employedto record the data.

The absorbance spectra were recorded with the Evolution 300UV–vis spectrophotometer (Thermo Scientific, Waltham, MA).

3.2. Chemicals

The mobile phase used in this study was a mixture of HPLC-grademethanol, water, and trifluoroacetic acid (48/51.9/0.1, v/v). Bothwater and methanol were of HPLC grade, purchased from Fisher Sci-entific (Fair Lawn, NJ, USA). Leucyl-Leucyl-Leucine, trifluoroaceticacid, phosphoric acid, and sodium phosphate were obtained fromAldrich (Milwaukee, WI, USA). All samples used in the experimentsreported were freshly prepared and filtered to remove suspendedparticles.

3.3. Column

The column used in our experiments was a Jupiter Proteo col-umn (Phenomenex, Torrance, CA). It was a gift from manufacturer.It is specially designed for the chromatographic analysis of smallpeptides. The main characteristics of these packing materials aresummarized in Table 1. The void volume of the column was deter-mined by the pycnometry method (1.58 mL). Taking into accountthe size of the tripeptide studied, 90% of the void volume is acces-sible for LLL.

3.4. Measurements of LLL breakthrough curves

The mobile phase composition was adjusted in order to providea convenient retention of LLL. Peptide solutions used in FA wereprepared in two different ways. Known weights of LLL weredissolved in two 100 mL volumetric flasks in the mobile phase(methanol/water/TFA, 48/51.9/0.1). The solubility of LLL in thesolution is around 6 g/L, so, in order to avoid any precipitationof the solute in the instrument, the prepared solutions were lessconcentrated. The concentrations of these master solutions were

4.3 and 5.4 g/L; the pH of the mobile phase was 2.03, those of LLLsolutions, 2.94 and 2.88 respectively. A sufficient amount of TFAwas added to the first solution in order to match its pH to that ofthe mobile phase. This solution will be called the controlled pHsolution. The second solution was used as prepared and will be

matogr. A 1216 (2009) 3992–4004 3997

csT

mcspa1awacd

ec0tslwomofttpu

caricsrahdiai

4

tp

Fig. 1. Adsorption equilibrium isotherms of LLL onto Jupiter Proteo C12 from

TBm

M

qbqb

A. Andrzejewska et al. / J. Chro

alled the uncontrolled pH solution. 5 mL aliquots of these masterolutions were taken and diluted 20 times with the mobile phase.he procedure was repeated to prepare new dilute solutions.

FA measurements were carried out using the independent stepsode that consists in injecting series of plugs of solutions of the

ompound studied. The breakthrough curves were recorded with aufficiently long delay between them (25 min), to allow for the com-lete re-equilibration of the column with the pure mobile phasefter the elution of each sample plug. The flow rate was set atmL/min and the injection time of each plug was fixed at 5 min forll FA steps, in order to reach a stable plateau at the column outlet,hatever feed concentration was used. The signals were detected

t 210, 230, and 240 nm. A calibration curve was derived from theoncentration injected and the UV signal of the plateaus of the plugsetected at the column outlet.

FA measurements were made using the multi-solvent deliv-ry system. Three series of FA runs were carried out, in thease of the uncontrolled pH solution: 0.27–5.4, 0.014–0.27, and.00068–0.014 g/L, and two series of FA runs in the case of the con-rolled pH: 0.22–4.3 and 0.011–0.22 g/L. For this purpose, elevenolutions were prepared by diluting the master solutions in the fol-owing ratios 5, 10, 20, 30, 40, 50, 60, 70, 80, 90 and 100%. They

ere generated by the multi-solvent delivery system. One pumpf the HPLC instrument was used to deliver a stream of the pureobile phase (methanol/water/TFA, 48/51.9/0.1, v/v) while the sec-

nd pump delivered a stream of the master solution (100 mL). Theeed concentration in the FA stream is proportional to the concen-ration of the sample in the master solution and to the ratio ofhe flow rates delivered by the two pumps. The twenty-two dataoints were acquired for the controlled pH solution and 32 for thencontrolled pH one. FA was carried out at 30 ◦C.

The masses adsorbed during each of the consecutive steps arealculated independently of the other ones, which eliminates theccumulation of errors that takes place in step FA. This methodequires more time and more chemicals but it is very accuratef the temperature, the back pressure, and the flow rate are wellontrolled during the entire sequence. The method of independentteps must be preferred for the sake of data accuracy. Furthermore,ecording the complete breakthrough curve (i.e., the adsorptionnd the desorption profiles for each concentration step injected)as two important advantages. First, it allows the unambiguousetermination of the initial linear part of the isotherm, hence it

nforms on the possible need for the acquisition of additional datat lower concentrations. Second, the breakthrough profiles containmportant information regarding the mass transfer kinetics.

. Results and discussion

The goal of this study was to compare the isotherm parame-ers of LLL on C12-bonded silica under controlled and uncontrolledH conditions. For that purpose, three independent methods were

able 2est bi-Langmuir isotherm parameters accounted for by the adsorption of LLL on Jupiterethods.

ethod/parameters pH condition

Controlled (4.3 g/L)

FA AED IM

s1 (g/L) 426.7 ? 531.81 (L/g) 0.009091 ? 0.009642s2 (g/L) 2.347 ? 3.0062 (L/g) 1.281 ? 1.845

* The initial parameters for IM were taken from FA isotherm fit for controlled and unco

MeOH/H2O/TFA (48/51.9/0.1, v/v) measured by FA for a controlled (full squares) andan uncontrolled (full circles) pH solution at 30 ◦C. The solid lines represent the best fitof the experimental data to the bi-Langmuir isotherm model. The best-fit parametersare listed in Table 2.

employed to obtain the isotherm parameters. These methods were(1) the nonlinear fitting of the FA experimental isotherm data; (2)the calculation of the AED function from the raw isotherm data; and(3) the inverse method applied to the breakthrough curves.

4.1. Adsorption data

Fig. 1 compares the adsorption data measured by FA under con-trolled and uncontrolled pH conditions at 30 ◦C. The differencesare important but both isotherms are similarly convex upward. Thecurvature of the isotherm under controlled pH is strikingly less pro-nounced than the other one. Accordingly, at high bulk concentration(c > 4.3 g/L), the surface concentration of LLL on C12 is lower whenthe pH is uncontrolled than when it is while it is conversely higherat low concentrations (c < 4.3 g/L). In contrast with the uncon-trolled pH case, the isotherm measured for “regulated pH” solutionbehaves almost linearly at high concentrations.

The solid lines represent the best fit of the bi-Langmuir isothermmodel. The best-fit FA parameters are listed in Table 2. Several otheradsorption models were also used. The choice of the best isothermequation, in this case the bi-Langmuir model, was done on the basis

of the Fisher test values, listed in Table 3. These values for theLangmuir, the Jovanovic, the Langmuir–Freundlich, the Tóth, theMoreau, and the Langmuir–Moreau isotherm models are all lessthan 3000, more than 3 times less than for the bi-Langmuir modelTable 3. This shows a statistically significant difference between

Proteo C12 in controlled and uncontrolled pH conditions determined by different

Uncontrolled (4.9 g/L)

IMFA AED Initial parameters from FA*

Controlled pH Uncontrolled pH

66.93 68.94 719.2 89.60.04130 0.04532 0.007776 0.02897

11.21 9.774 1.904 8.7390.5635 0.6322 1.967 0.7503

ntrolled pH.

3998 A. Andrzejewska et al. / J. Chromato

Table 3Fisher parameter table.

Model Uncontrolled pH Controlled pH

Langmuir 459 156Jovanovic 183 126BET 5545 2492Bi-Langmuir 9308 17931Langmuir–Freundlich 712 633TML

thasray

4

feitbpAtcrdttatct

FMrutti

óth 2177 1618oreau 800 163

angmuir–Moreau 447 134

hese models and the bi-Langmuir or the BET ones. On the otherand, we cannot decide whether the BET or the bi-Langmuir modelccounts better for adsorption from the uncontrolled pH solutionince the ratio of the respective Fisher test values is less than theequired threshold of 2.0. It is difficult at this stage to definitivelyscertain the physical meaning of the results of this statistical anal-sis.

.2. Adsorption energy distribution

To help in the choice between an adsorption isotherm modelor a homogeneous and a heterogeneous surface, the adsorptionnergy distributions were calculated on the basis of the raw exper-mental adsorption data. We used 350 grid points in the b-spaceo logarithmically digitize the range between bmin = 0.002 L/g andmax = 100 L/g (controlled pH) and bmax = 1500 L/g (uncontrolledH). The number of iterations was taken at 1 × 107. Fig. 2 shows theED functions calculated for of LLL under controlled and uncon-

rolled pH conditions. Unfortunately, the AED under controlled pHonditions has at least one unresolved site at low energy and oneesolved at high energy. The presence of this unresolved mode isue to the concentration used in this determination being too lowo permit the resolution of the high-energy site. For the uncon-

rolled pH solution, the AED exhibits two well-resolved peaks, onet low and one at high energy. Both AEDs show that the adsorp-ion isotherm used should be at least bimodal. This supports thehoice of the bi-Langmuir isotherm model to account for adsorp-ion of LLL on Jupiter Proteo C12. The bi-Langmuir parameters were

ig. 2. Adsorption energy distribution of LLL onto Jupiter Proteo C12 fromeOH/H2O/TFA (48/51.9/0.1, v/v) calculated by the expectation–minimization algo-

ithm from raw FA adsorption data measured for the controlled (solid line) andncontrolled (dashed line) pH solutions. 350 grid points in the b-space were usedo logarithmically digitize the range between bmin = 0.002 and bmax = 100 L/g (con-rolled pH solution) and bmax = 1500 L/g (uncontrolled pH solution). The number ofterations was set at 1 × 107. The AED adsorption parameters are listed in Table 2.

gr. A 1216 (2009) 3992–4004

estimated from the AED. They are compared with those obtainedfrom the best fit of the FA isotherm data in Table 2. In the case ofthe uncontrolled pH solution, the agreement between the two setsof adsorption parameters is very good. But in the other case, theadsorption parameters found have no physical meaning.

4.3. Inverse method

The inverse method was used to derive the best values of theisotherm parameters from the breakthrough curves for both thecontrolled and uncontrolled pH solutions. In this method the ini-tial choice of an isotherm model and a set of initial adsorptionparameters are required. We used the bi-Langmuir model and thevalues of the parameters obtained from the fitting of the FA data tobi-Langmuir isotherm model. These parameters were further opti-mized to minimize the difference between the experimental andthe calculated breakthrough curves.

4.3.1. Inlet profileThe inlet concentration profile influences considerably the

elution band profile of rectangular injection plugs. This profile con-stitutes the boundary condition of the mass balance equation, thusit should be accurately known. Ideally, this profile should be rect-angular but, in practice, significant deviations are observed [54].Axial dispersion, causing back-mixing, takes place in the tubes con-necting the injection port and the column, is enhanced by theconsequences of the Hagen–Poiseuille velocity profile in tubes.Thus, the inlet concentration profile is not sharp. Extra-columndispersion increases the spread of the band profile. The inlet pro-file can be determined by injecting a sample in the instrument inwhich the column has been removed and replaced by a zero-volumeconnector.

Due to the origin of the spreading of the band profile, this profilecan be accounted by the exponentially modified Gaussian (EMG)function, a model that is the convolution of a Gaussian profile andan exponential decay function. The former contribution describesband broadening in the connecting tubes while the latter modelsthe mixer-type extra volumes [55–57]. When the inlet profile is awide rectangular pulse, the true inlet concentration can be modeledby the convolution of the EMG function and a rectangular pulse oflength tp. The resulting profile is

c(t) = c0

2

{erfc

(m − t√

2

)− erfc

(tp + m − t√

2

)+ exp

(2

22+ m − t

t

)

×[

exp

(tp

)erfc

(√2

+ tp + m − t√2

)− erfc

(√2

+ m − t√2

)]}

(15)

where m is the residence time in the connecting tube, is theGaussian band width and is the time constant of the mixer-typeextra-column volume.

The measured inlet concentration profile for a 3 min injectionis reported in Fig. 3 (symbols). The fitted model described in Eq.(20) (solid line) follows remarkably well the measured concen-tration profile with the parameters: c = 0.1361 g/L, tp = 3.00 min,m = 0.5149 min, = 0.06663 min, = 0.1373 min. This inlet pro-file was used in all band profile calculations with properly changingthe values of tp and c.

4.3.2. Controlled pH solutionFig. 4 A shows the comparison of the breakthrough curve

recorded for the injection of the controlled pH solution at 0.8612 g/LLLL for 5 min and the one derived by inverse method. This curve isfully consistent with the thermodynamical data and with the pre-diction of the ED model, e.g., a front shock, followed, first, by a stableplateau and, finally, by a diffusive rear desorption profile. In Fig. 4

A. Andrzejewska et al. / J. Chromato

Fig. 3. Experimental and theoretical plots of the inlet concentration profile for tp = 3min injection of LLL solution, cLLL=0.136 g/L used in ED.

Fig. 4. (a) Comparison of the best-fit ED breakthrough profiles (solid line) and theexperimental ones for LLL (symbol) with tp = 5 min and cLLL=0.89 g/L; the best-fitbi-Langmuir parameters found by IM are listed in Table 2; (b) the theoretical EDbreakthrough profiles calculated with the parameters obtained by IM (solid line)and the experimental ones of LLL (symbol) for tp = 5 min and concentration rangecLLL=0.215–4.3 g/L; The best-fit bi-Langmuir parameters of FA adsorption data (con-trolled pH solution) were used as initial parameters in IM. Controlled pH condition.

gr. A 1216 (2009) 3992–4004 3999

B the comparison of other experimental band profiles for higherconcentration of the LLL solution (symbols) and the calculated ones(solid lines) is presented. Quantitatively, Fig. 4 shows that the shockof the breakthrough curves appears earlier when the concentrationincreases, in agreement with a decreasing retention time of LLL.However, the predicted diffuse rear parts are only slightly differentfrom experimental ones at highest LLL concentration. As is shownin Fig. 4, there is a very good agreement between experimental andcalculated band profiles. The values of the bi-Langmuir isothermparameters obtained by IM are summarized in Table 2. There islittle difference between the FA and IM isotherm parameters.

4.3.3. Uncontrolled pH solutionIn the case of the uncontrolled pH solution, we decided to

use two sets of initial parameters in the solution of the inversemethod and to compare the results. First, the FA isotherm parame-ters obtained for the uncontrolled pH solution were used (Table 2,column 4). The best-fit curve is shown in Fig. 5 A and the best-fitparameters are listed in Table 2(column 7). As seen in Fig. 5 B, theagreement between the calculated profiles and the experimentalbreakthrough curves in this range of concentration is very good.The shock parts of the band profiles are also well predicted. Forconcentrated solutions (Fig. 5C), the fit is not as good as the previ-ous ones. The front shocks are predicted to elute slightly too earlywhile their rear parts do not follow the experimental ones at all.

When other sets of initial parameters were used in the inversemethod to fit the 0.2722 g/L breakthrough curve, namely theisotherm parameters obtained from the FA data fit of the controlledpH solution, (Table 2, column 1), we found a good agreement for lowconcentration breakthrough curves (Fig. 6 B) but at high LLL concen-trations (Fig. 6C) the results are quite different from those shownin Fig. 5. The shock fronts are predicted to elute much later thanthey actually do and the rear diffuse boundary is not predicted well.The adsorption parameters found in this way are listed in Table 2(column 6).

It seems there are two different adsorption processes for onecompound, meaning that neither of the models is correct. Figs. 5C and 6 C show breakthrough curves for high LLL concentrationswith the pH of the LLL solution being nearly one unit higher (2.88)than that of mobile phase (2.03). The shape of the elution curvesfor the controlled pH solutions (Fig. 4B) is most different from thatof the uncontrolled pH solutions (Figs. 5 C and 6C). On the curvescorresponding to concentrations higher than 1.6 g/L, an extra peakis observed. The higher the LLL concentration, the larger the humppreceding elution of the plateau. The origin of this peak is obviouslyrelated to the pH excursion of the eluent, which required a detailedexplanation.

4.4. The origin of the extra peak on uncontrolled pH breakthroughcurves

Fig. 7 compares the experimental FA breakthrough curves athigh LLL concentrations for the controlled pH and uncontrolled pHsolutions. When the pH of the LLL solution is stabilized by the addi-tion of TFA to match the pH of the mobile phase, the extra peak atthe beginning of the plateau disappears and the retention of thepeptide increases. The net charge of LLL depends on the pH (seeFig. 8), which shows that two different forms of LLL exist in solu-tion, one at high (2.88, the pH of LLL dissolved in the mobile phase),one at low pH (2.03, the pH of the pure mobile phase). The LLLnet charge at pH 2 is around 0.7, the functional carboxyl group of

LLL is fully protonated and the amino group mostly positive. Thepositively charged ionic form of LLL at pH around 2 interacts withthe negative trifluoroacetate ion (ion-pairing effect). At pH 2.9, theLLL net charge is around 0.2 and the peptide becomes neutral (orrather a zwitterion). The dependence of the pH of an LLL solution

4000 A. Andrzejewska et al. / J. Chromatogr. A 1216 (2009) 3992–4004

Fig. 5. (a) Comparison of the best-fit ED breakthrough profile (solid line) and theexperimental ones for LLL (symbol) with tp = 5 min and cLLL=0.2722 g/L; the best-fitbi-Langmuir parameters found by IM are listed in Table 2(column 7); (b) the theo-retical ED breakthrough profiles calculated with the parameters found by IM (solidline) and the experimental ones of LLL (symbol) for tp = 5 min and concentrationrange cLLL=0.0136–0.2722 g/L, and (c) cLLL=0.2722–4.9 g/L; The best-fit bi-Langmuirparameters of the FA adsorption data (uncontrolled pH, Table 2, column 4) were usedas initial parameters in IM. Uncontrolled pH condition.

Fig. 6. (a) Comparison of the best-fit ED breakthrough profile (solid line) and theexperimental one for LLL (symbol) with tp = 5 min and cLLL=0.2722 g/L; the best-fit bi-Langmuir parameters found by IM are listed in Table 2(column 6); (b) thetheoretical ED breakthrough profiles calculated with the parameters found by IM(solid line) and the experimental ones for LLL (symbol) with tp = 5 min and theconcentration range cLLL=0.0136–0.2722 g/L, and (c) cLLL=0.2722–4.9 g/L; The best-fit bi-Langmuir parameters of FA adsorption data (controlled pH, Table 2, column 1)were used as initial parameters in IM. Uncontrolled pH condition.

A. Andrzejewska et al. / J. Chromatogr. A 1216 (2009) 3992–4004 4001

Ft

odatkeFcssAcTiTctm

oup

solution at 31% acetonitrile (0.1% TFA) as the mobile phase. Heused the same concentration of TFA in his mobile phase as we did.

ig. 7. Comparison of the experimental FA breakthrough curves at high LLL concen-rations for uncontrolled (solid line) and controlled (dashed lines) pH solutions.

n its concentration is shown in Fig. 9. When 0.1956 g of LLL wasissolved in 50 mL of mobile phase (48/51.9/0.1, MeOH/H2O/TFA)nd the pH of this solution was measured, it was 2.76 while that ofhe mobile phase was 2.02. This LLL solution was diluted by addingnown volumes of the mobile phase and the pH was measured. Thexperiment was repeated 3 times. The mean values were plotted inig. 9 that shows the parabolic dependence of the pH on the LLLoncentration. At concentrations below 0.5 g/L of LLL, the pH of theolution does not change with increasing peptide concentration. Iteems that the amount of TFA is enough to keep the pH constant.t higher concentrations, the pH increases with increasing peptideoncentration and the TFA molecules are completely dissociated.he dissociation equilibrium of TFA moves toward the formation ofons as a result of “uptake” of protons by the peptide. The amount ofFA at an LLL concentration of 0.5 g/L is insufficient to keep the pHonstant. All TFA molecules are dissociated at that moment. Whilehe peptide concentration increases further, the LLL species uptakes

ore protons and the pH keeps increasing.

The experimental results show that the pH has a serious impact

n the retention time of peptides, as illustrated in Fig. 10. In this fig-re, the mobile phase was different, with 48% methanol and 52% of ahosphate buffer used instead of the water/TFA mixture. Small vol-

Fig. 8. Dependence of the LLL net charge on the pH.

Fig. 9. Dependence of the pH of LLL solution in the mobile phase (48/51.9/0.1,MeOH/H2O/TFA, v/v) on the LLL concentration. The line illustrates the general trendof the experimental results.

umes of three LLL solutions were injected (5 �L). The difference inretention between the two pH (2.03 and 2.88) is about one minute.When the pH of the solution increases, the retention time of LLLdecreases and LLL is eluted earlier.

The width of the extra peak depends on the volume injected,Vinj , as illustrated in Fig. 11 in which profiles obtained with Vinj = 5,10, and 15 mL of the same uncontrolled pH solution are compared.The longer the injection time, the wider the extra peak, while thewidth of the rear plateau (a rear shoulder) remains the same anddoes not depend on the volume injected.

Liu et al. [25] showed similar breakthrough curves for a largerpeptide, insulin. He determined the adsorption isotherms of threerecombinant proteins, human insulin, porcine insulin, and Lispro,by frontal analysis on a YMC-ODS C18 column with an aqueous

These authors found that high-concentration breakthrough profilesexhibit a shoulder on their rear diffuse front. The importance of

Fig. 10. Dependence of the LLL retention time on the pH of the mobile phase (48:52,MeOH:Phosphate buffer). The line illustrates the general trend of the experimentalresults.

4002 A. Andrzejewska et al. / J. Chromatogr. A 1216 (2009) 3992–4004

FuT

to

tntstnteiiuiwtcHe

aetpt

4

dtp1atsptteFpd

Fig. 12. FA breakthrough profiles of three different injected volumes of LLL solution

ig. 11. Comparison of the FA breakthrough profiles for three different injected vol-mes of LLL solution (cLLL=4.9 g/L), 5, 10, and 15 mL for the uncontrolled pH solution.he profiles were recorded at � = 240 nm.

his shoulder decreases with decreasing insulin concentration. Webtained the same result.

A slight negative signal is eluted between the hold-up time andhe shock of the elution curve in Fig. 11. The duration of this signal isearly the same as the length of the rear plateau. This corresponds tohe elution of the solvent injected with the LLL sample. This negativeignal could be associated with a component of the mobile phasehat would be missing or be eluted at a concentration lower than itormally has in the mobile phase. The only possible component ofhe mobile phase which could give such a signal is the trifluoroac-tate anion. TFA is a rather strong acid (p Ka � 0.27 in water and 1.5n 50/50 methanol/water solutions). It is thus fully dissociated (98%)n an aqueous solution at pH 2 but only at 80% in the mobile phasesed in this work. At this pH, the peptide is positively charged and it

nteracts with the negative TFA anion which is apparently adsorbedith the peptide. When the LLL concentration is small, the nega-

ive signal is not observed because the difference between the TFAoncentration in the eluent and in the mobile phase is too small.owever, when the LLL concentration increases, there is no longernough TFA anions and some LLL molecules are not paired.

Finally, the negative signal of the breakthrough curve beginsround the hold-up time (Fig. 11, first dotted arrow). The extra peaksnd exactly 5, 10, and 15 min later, the duration of the injectionime (Fig. 11, the other dotted arrows), suggesting that the secondlateaus begins when the fresh mobile phase begins to exit fromhe column.

.5. The pH profiles of the uncontrolled pH solution eluate

To understand better what actually happens in the columnuring the elution of these large sample plugs, we recorded simul-aneously a breakthrough curve of a concentrated, uncontrolledH solution of LLL (cLLL=4.9 g/L) and the eluent pH for 5, 10 and5 min injections, at a flow rate of 1 mL/min. The profiles obtainedre shown in Fig. 12. The dashed lines represent the pH profile. Allhe pH curves show that the eluent pH begins to increase when theample begins to elute, at the hold-up time. A sudden pH drop takeslace when the mobile phase (instead of the sample solvent) beginso elute. We can divide the elution of the breakthrough curve into

wo regions: one eluted earlier, at high pH (the extra peak) and oneluted later, at the initial mobile phase pH (the rear plateau). Fromig. 12 it is obvious that the elution of the FA plugs of uncontrolledH, concentrated LLL solutions takes place in two different pH con-itions. When the pH changes, so does the adsorption mechanism.

(cLLL=4.9 g/L), (a) 5 mL, (b) 10 mL, and (c) 15 mL (solid lines), and online pH profiles(dashed lines) measured simultaneously with the FA breakthrough curves for a sam-ple of the uncontrolled pH solution. The flow rate was 1 mL/min. The profiles wererecorded at � = 240 nm.

Finally, Fig. 12 shows that a small pH drop takes place whenthe peptide begins to elute, when the shock of breakthrough curveelutes. This response of the electrode is due to a fast change in itsenvironment. When the flow rate is reduced ten times (Fig. 13, Fv =0.1 mL/min, Vinj = 10 mL) no such drop is observed.

The two different absorbance plateaus on the breakthrough

curves of LLL (Figs. 11–13) are due to the presence of two differentforms of the peptide in these two regions. Fig. 14 shows theUV spectra of LLL recorded in two methanol/phosphate bufferssolutions (48/52, v/v) at pH 2 and 3, within a wavelength range

A. Andrzejewska et al. / J. Chromato

Fig. 13. FA breakthrough profile of LLL solution (cLLL = 4.9 g/L), Vinj = 10 mL, (solidlines), and online pH profile (dashed lines) measured simultaneously with FA break-through curve for a sample of the uncontrolled pH solution. The flow rate was0.1 mL/min. The profile was recorded at � = 240 nm.

Fm

2(ttflc

5

msasatct

ts

[

[[[[[

[

[

[[[[[[

[

[

[[

[

[[[[

ig. 14. Absorbance spectra of solutions of 4.3 and 4.1 g/L LLL in two differentethanol/phosphate buffer mixtures (48/52, v/v) of pH 2 and 3, respectively.

00–400 nm. As shown in this figure, at a wavelength of 240 nmthe wavelength used to record the chromatograms in Figs. 11–13)he LLL absorbance is higher at pH 3 where the neutral form ofhe peptide (−LLL+) dominates than at pH 2 where the protonatedorm of the peptide (LLL+) does. In contrast, TFA−does not absorbight significantly at wavelengths above 210 nm [58–60]. This isonsistent with our previous assumptions.

. Conclusion

Our results demonstrate that the retention mechanism of lowolecular mass peptides in nonlinear chromatography depends

trongly on the pH of the mobile phase, specially when the pH isffected by the very compound eluted. When the pH of the LLLolution was kept equal to that of the mobile phase, we observedstronger adsorption then if it was not. In both cases, adsorption

akes place on a heterogeneous surface but the maximum surface

oncentration of the adsorbate is one order of magnitude larger forhe controlled pH solution.

When the pH of the LLL solution was controlled by TFA additiono match the mobile phase pH, breakthrough curves of conventionalhapes were obtained, that were easy to predict using the data

[[[[[[

gr. A 1216 (2009) 3992–4004 4003

afforded by the inverse method. When the pH was not fixed butleft to vary with the sample concentration, the peptide was elutedlater and the inverse method could not predict the experimentalresults. The results of IM depend strongly on the initial parametersused. If these parameters are those found by fitting the FA isothermdata points to the bi-Langmuir model, the front shocks of the break-through curves were correctly predicted. But we showed that thesecurves correspond to the desorption of the non-protonated pep-tide LLL. The results are quite different if the adsorption parametersdetermined by fitting the bi-Langmuir equation to the FA isothermdata measured for the controlled pH solution are used as initialones in IM. In this case, the equilibrium-dispersive model predictsthe adsorption of protonated LLL molecules or/and of ion pairs ofLLL and trifluoroacete anions.

Further work will explore the theoretical description of the influ-ence of the pH and of the buffering of the mobile phase used for theelution of peptides in nonlinear chromatography.

Acknowledgement

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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