Journal of Chromatography A, 1101 (2006) 136–152

Thermodynamic analysis of the heterogenous binding sites ofmolecularly imprinted polymers

Hyunjung Kima,b, Krzysztof Kaczmarskia,b,c, Georges Guiochona,b,∗a Department of Chemistry, University of Tennessee, Knoxville, TN 37996-1600, USA

b Division of Chemical Sciences, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6120, USAc Faculty of Chemistry, Rzeszow University of Technology, 35-959 Rzeszow, Poland

Received 1 August 2005; received in revised form 23 September 2005; accepted 27 September 2005Available online 2 November 2005

Abstract

The thermodynamic interactions of two polymers, one Fmoc-L-Trp-imprinted (MIP), the other one an unimprinted reference (NIP), with thetwo Fmoc-tryptophan enantiomers were studied by frontal analysis, which allows accurate measurements of the adsorption isotherms. Theseisotherms were acquired at temperatures of 40, 50, 60, and 70◦C, for sample concentrations ranging between 0.005 and 40 mM. The mobile phaseu uir isothermmN isotherm datat al and thec electivity doesn increasingt ctions (i.e.,t ch identifiedts doesn©

K res; Over

l

1

atcnpTmcp

, andinedendsta-

ers intud-

ycolula

eat-toeffi-d uponnaryof

ts ofally,

0d

sed was acetonitrile with one percent acetic acid as an organic modifier. Within the measured concentration ranges, the tri-Langmodel accounts best for the isotherm data of both enantiomers on the MIP, the bi-Langmuir model for the isotherm data of Fmoc-L-Trp on theIP. These isotherm models were selected using three independent processes: statistical tests on the results from regression of the

o different isotherm models; calculation of the affinity energy distribution from the raw isotherm data; comparison of the experimentalculated band profiles. The isotherm parameters obtained from these best selected isotherm models showed that the enantiomeric sot change significantly with temperature, while the affinity of the substrates for both the MIP and the NIP decrease considerably with

emperatures. These temperature effects on the binding performance of the MIP were clarified by considering the thermodynamic funhe standard molar Gibbs free energy, the standard molar entropy of adsorption, and the standard molar enthalpy of adsorption) for eaype of adsorption sites, derived from the Van’t Hoff equation. This showed that the entropy of transfer of Fmoc-L-Trp from the mobile to the MIPtationary phase is the dominant driving force for the selective adsorption of Fmoc-L-Trp onto the enantioselective binding sites. This entropyot change significantly with increasing temperatures from 40 to 70◦C.2005 Elsevier B.V. All rights reserved.

eywords: Fmoc-L-tryptophan imprinted polymers; Frontal analysis; Isotherm parameters; Affinity distribution; Heterogeneous binding sites; Temperatu-

oaded band profiles; Enantiomer selectivity; Van’t Hoff plot; Entropy; Enthalpy

. Introduction

MIPs are chemically and physically very stable polymers thatdsorb selectively the molecules of the species present in solu-

ion during their polymerization (i.e., the template). The mostommonly used strategy to prepare MIPs involves the use ofon-covalent interactions between a target molecule (the tem-late) and some suitable functional groups of the monomers.hese interactions allow the formation of template-functionalonomer complexes in solution before and during their poly-

ondensation. These complexes are then immobilized into theolymer matrix by copolymerization with a high concentration

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

of cross-linking monomers. Complementary size, shapefunctionalities toward the template in the MIPs can be obtaby extracting the template from the polymer matrix after theof the polymerization process. The MIPs are thermally stabletionary phases that are used for the separation of enantiomhigh-performance liquid chromatography (HPLC). Recent sies on the thermal stability of methacrylic acid–ethylene gldimethacrylate imprinted copolymers (the most typical formfor MIPs) showed no loss of affinity for the template after trment at 150◦C for 24 h[1]. Therefore, it may be most usefuloptimize the temperature of the column. Improved columnciency, selectivity, and separation speed have been reporteincreasing the temperature of other thermally stable statiophases[2]. To explore the optimization of the temperatureMIPs in HPLC, we need to understand how better the effectemperature on the binding characteristics of MIPs. Basic

021-9673/$ – see front matter © 2005 Elsevier B.V. All rights reserved.oi:10.1016/j.chroma.2005.09.092

H. Kim et al. / J. Chromatogr. A 1101(2006) 136–152 137

there are two major effects of temperature that can affect the per-formance of stationary phases in chromatography[3–6]. First,the viscosity of the mobile phase decreases and the diffusioncoefficients of the analytes in both the mobile and the station-ary phases increase with increasing temperature. Thus, the masstransfer kinetics becomes faster and the separation times can bereduced. The effects of the temperature on the mass transfer ki-netics can especially benefit the chromatographic performanceof MIPs which are known to exhibit slow mass transfer kineticsand to produce serious peak tailing (particularly for the tem-plate). Second, and for completely different reasons, tempera-ture affects the retention and the separation factors. Althoughthe first effect is general (retention factors almost always de-crease with increasing temperature), the effect of temperatureon the separation factor depends much on the nature of the sys-tem studied and there are no general rules[7–10]. This is partlydue to a lack of understanding of how temperatures affect thechanges of thermodynamic functions, such as entropy, enthalpy,and free energy, that are associated with the transfer of the so-lutes from the mobile to the stationary phases in different sys-tems. The phenomenon is particularly complex in the case ofmixed mechanisms.

This work had several purposes. First, we wanted to deter-mine how should be selected the most appropriate isothermmodel that accounts best for the isotherm data obtained forthe system studied. Second, we wanted to investigate howt enat inet sitest thisi n tht n, wi etico er).T ms otr asea atef stant

2

n asw uilibr MIPp rs orf d ont tionso s exp tentw eous ationo videu enat d isd

Obviously, in this work, as in all applications of thermody-namics to chromatography, we assume that the rates of the differ-ent contributions to the mass transfer kinetics across the columnsare sufficiently fast and that the data derived from frontal anal-ysis measurements are adsorption data. This is justified in theexperimental problem studied here[20].

2.1. Isotherm models

The isotherm models used in this work are the bi- and thetri-Langmuir models:[11]

q = qs1b1C

1 + b1C+ qs2b2C

1 + b2C(1)

q = qs1b1C

1 + b1C+ qs2b2C

1 + b2C+ qs3b3C

1 + b3C(2)

whereqs1, qs2, andqs3 are the saturation capacities for the first,the second, and the third types of sites on a heterogeneous sur-face, respectively; andb1, b2, andb3 are the corresponding ad-sorption constants. Each of these terms has the form of a Lang-muir isotherm and corresponds to one type of sites.

2.2. Affinity energy distributions

The affinity energy distribution (AED) of a surface is the dis-t areao of theM iffer-e hencehA ism acesct row.I lved,a tionf erm.D s ont EDso theirA usedd ermd them s onM iono ntali dingt thodi

2

bandp ith as odeld idity

emperature affects the isotherm parameters and theiomeric selectivity of a MIP. Third, we wanted to determhe thermodynamic functions of each type of adsorptionhat we had identified on the surface of the MIP and usenformation better to understand the temperature effects ohermodynamics of the separation. In a separate publicationvestigate how temperature affects the mass transfer kinn a MIP and on its reference (i.e., non-imprinted polymo achieve our goals, we measured the adsorption isotherhe Fmoc-Trp enantiomers on a Fmoc-L-Trp MIP and on theeference polymer (NIP), in an organic-based mobile pht different temperatures. The isotherm parameters estim

rom the isotherm data for each system were used to underhe temperature effects on the MIP and the NIP.

. Theoretical background

The principle of our approach consists of measuring, iide a concentration range as possible, the adsorption eq

ium isotherm data of the template and of its antipode on theolymer (MIP) and the similar data for one of the enantiome

or the racemic mixture for the NIP. These data are modelehe one hand, used to calculate the affinity energy distribuf the two solutes on the two polymers, on the other hand. Alained elsewhere[11], the data for both polymers are consisith heterogeneous surfaces paved with different homogenurfaces having markedly different properties. The combinf the results of these thermodynamic determinations proseful clues regarding the surface heterogeneity and the

ioselectivity of MIPs. The fundamental basis of the methoiscussed elsewhere[12–14].

n-

ees

f

,dd

-

-

s

sn-

ribution of the values of the association constants over thef this surface. The heterogeneous nature of the surfaceIPs and NIPs mean that these surfaces are covered with dnt types of sites, each type being nearly homogeneous,aving a narrow affinity adsorption energy distribution[11].ccordingly, the distribution for the whole polymer surfaceultimodal. The adsorption energy distributions of the surf

orresponding to the isotherm models in Eqs.(1) and (2)displaywo or three isolated peaks which should be infinitely narn practice, these modes are merely narrow, well resond their small width does not cause any significant devia

rom the langmuirian behavior of each terms of the isothetailed investigations of the properties of the binding site

he surface of MIPs are possible only by determining the Af the template and its enantiomer and comparing them toED on the NIP. Among the several possible methodsirectly to derive the AED from the set of experimental isothata (q(C)), the expectation maximization (EM) method isost successful for the investigation of the binding siteIPs [11,15–18]. The EM method allows the direct calculatf the adsorption energy distribution from the raw experime

sotherm data, without making any prior assumption regarhe isotherm model nor the shape of the AED. The EM mes described, justified, and validated elsewhere[19].

.3. Modeling of peak profiles

The degree of agreement between the experimentalrofiles obtained for large samples and those calculated wuitable model of chromatography and the best isotherm merived from the set of adsorption data informs on the val

138 H. Kim et al. / J. Chromatogr. A 1101(2006) 136–152

of the selected isotherm model. Thus, this comparison is criticalto validate the results of the determination of the isothermmodel and the AED. We used in this work the POR model,for reasons detailed elsewhere[20]. Band profiles calculationswere made using known methods[20–23].

2.4. Van’t Hoff equation

The standard molar Gibbs free energy of adsorption,�G◦, isthe difference between the molar standard Gibbs free energy ofthe adsorbed and the dissolved molecules, at constant tempera-ture. Under equilibrium, the standard molar Gibbs free energy ofadsorption is related to the equilibrium constant at temperatureT(K), by

�G◦ = −RT ln K = −RT ln a (3)

whereR is the universal gas constant (1.9872 cal/mol/K) andK = a = qsb (whereqs is the saturation capacity andb is theassociation constant) is the thermodynamic equilibrium constant[24].

Since the coefficients of the bi- and the tri-Langmuirisotherms are thermodynamic equilibrium constant, the classi-cal thermodynamic functions of the different sites can be de-rived from the temperature dependency of the correspondingequilibrium constant, itself derived from the Gibbs–Helmholtzequation, following classical thermodynamic relationships[25].

3

t aren ils ot d cab

3

p de-s itht oa ew anicm (w o thc ea-s thep colu taldp mnsr

3

datp f thes lum

at equilibrium with a stream of mobile phase at a given con-centration[11]. The column is flushed with pure mobile phasebetween successive FA experiments. Measurements were car-ried out at four different temperatures (40, 50, 60, and 70◦C)with acetonitrile containing 1% acetic acid (organic modifier) asthe mobile phase, in a concentration range extending from 0.005to 40 mM. this broad width is necessary to achieve a sufficientaccuracy of the AED. The concentration of the compounds in themobile phase was adjusted by mixing two stream, one of puremobile phase the other of a suitable mother solution and settingthe flow-rate fractions delivered by the two pumps at constanttotal flow rate (1 mL/min), for a set time interval. Sufficient in-jection time (10–40 min) at each injected solute concentrationwas allowed to ensure that the composition of the eluate wasthe same as that of the injected solutes. This was checked bythe plateau of the breakthrough curve lasting more than 5 min.Between the successive breakthrough curves, a long delay time(60 min) was allowed for re-equilibration of the column with thepure mobile phase. The signal was detected, depending on theconcentration range, at a wave-length between 260 and 310 nm,to avoid recording any signals above 1500 mAU. Each obtainedbreakthrough curve gives one data point of the isotherm (theamount of adsorbed substrate (q, mM) versus the concentrationof the substrate in the mobile phase (C, mM) [11].

The isotherm data were fitted to a langmuirian type of theisotherm model (Eqs.(1) and (2)) and the quality of the fitse hermp quares[

omt ) al-g ons con-s romt ri-b f thecp ant oft

filesa oc-T asa ted.T poly-m r eachs re in-j gingb d be-t e ab-s ing ac

4

eriesm aseb rough

. Experimental

We describe briefly here the experimental conditions thaecessary to understand our analytical results. Other deta

he experimental conditions and the theoretical backgroune found in previous publications[11,15–17].

.1. Chromatographic conditions

The synthesis of the Fmoc-L-tryptophan (Fmoc-L-Trp) im-rinted polymer (MIP) and its non-imprinted polymer wascribed previously[11]. The polymeric stationary phase, whe particle sizes ranging between 25 and 38�m, was packed int

stainless steel column (10 cm× 0.46 cm). The mobile phasas acetonitrile with one percent of acetic acid as an orgodifier. The hold-up times of the MIP and NIP columnst0)ere measured by injecting a small amount of acetone intolumn. The extra-column volume from the pump was mured by injecting a small amount of the substrate fromump into a zero dead-volume connector instead of themn. A value oftx = 0.94 min was obtained. The experimenata have all been corrected by subtractingtx. The total columnorosities were 0.73 and 0.75 for the MIP and the NIP coluespectively.

.2. Procedures

Frontal analysis (FA) was used to measure adsorptionoints. The retention time of the breakthrough curves oolute considered provides the amount adsorbed in the co

nn

e

-

,

a

n

stimated by calculating the standard deviation of each isotarameter, the Fisher parameter, and the residual sum of s

20].The affinity energy distributions (AED) were calculated fr

he isotherm data, using the expectation-maximization (EMorithm [11,15–18]. The AED gives the density of adsorptiites (qs(bj)) as a function of the corresponding associationtant (lnbj). The isotherm parameters were also derived fhe AEDs, the values ofqs comprising one mode of the distution were summed up to obtain the saturation capacity oorresponding type of adsorption sites; the value of lnbj for theeak maximum was used to calculate the adsorption const

he corresponding type of sites.Systematic comparisons of the experimental peak pro

nd those calculated under the same conditions for FmL-rp and Fmoc-D-Trp on the MIP and the NIP were donelast check on the validity of the isotherm model selec

he experimental peak profiles of the substrate on theer were recorded at each temperature, immediately afte

et of frontal analysis measurements. The substrates weected from the pump, at six different concentrations ranetween 0.1 and 40 mM. The band profiles were recorde

ween 260 and 310 nm (depending on their size) and thorbance was converted into concentration units (mM) usalibration curve.

. Results and discussion

Frontal analysis (FA) was carried out using the step sethod, in which the column is flushed with pure mobile phetween two successive FA experiments to acquire breakth

H. Kim et al. / J. Chromatogr. A 1101(2006) 136–152 139

curves. Compared to the staircase method, where a series of suc-cessive steps is done without flushing the column between thesuccessive steps, the step series method has the advantage ofavoiding cumulative errors, even though a considerable time isrequired compared to the staircase method. In order to acquiredata in a broad concentration range (0.005–40 mM), the adsorp-tion isotherms at each temperature were measured using threedifferent mother solutions of the substrates. A total of 33 datapoints were acquired within the whole concentration range.

4.1. Equilibrium isotherm and Fitting models for theexperimental isotherm data

Figs. 1 and 2show the adsorption isotherm data obtainedfor the two Fmoc-Trp enantiomers on the MIP (Fig. 1), and forFmoc-L-Trp on the NIP (Fig. 2), at each different temperature.Figs. 1a and 2a show the data in the low concentration range(below 0.5 mM);Figs. 1b and 2b in the medium concentrationrange (below 5 mM); andFigs. 1c and 2c in the high concen-tration range (below 40 mM). A qualitative analysis of the ad-sorption curves shown inFigs. 1 and 2shows that temperature

does not affect the overall shape of the adsorption isotherms,which are all convex upward. This negative curvature of the ad-sorption isotherm characterizes langmuirian types of isotherms.We see also that at a given mobile phase concentration (C), in-creasing the temperature decreases the amount adsorbed (q) atequilibrium. For example, at a 0.1 mM mobile phase concentra-tion, increasing the temperature from 40 to 70◦C causes 36, 39,and 48% decreases in the amount of Fmoc-L-Trp, and Fmoc-D-Trp adsorbed on the MIP and Fmoc-L-Trp adsorbed on theNIP, respectively. These results show that increasing the temper-ature decreases the affinity of the substrates for either polymer.At the same temperature, the amount adsorbed at equilibriumdecreases in the order Fmoc-L-Trp on the MIP > Fmoc-D-Trpon the MIP > Fmoc-L-Trp on the NIP. The differences betweenthe behavior of the enantiomers are larger at low concentra-tions and decrease with increasing substrate concentration. Inthe high concentration range, no significant differences could beobserved in the amounts of enantiomers adsorbed (seeFig. 1aand c). However, the differences between the amounts adsorbedon the MIP and the NIP remain significant even at the high-est concentration measured (Figs. 1c and 2c). A similar trend

F(r

ig. 1. Adsorption equilibrium isotherms of Fmoc-L-Trp (solid symbols) and Fmtriangle-ups), and 70◦C (triangle-downs). The symbols represent the experimenange between 0.005 and 0.5 mM. (b) Concentration range between 0.005 an

oc-D-Trp (open symbols) on the MIP at 40◦C (circles), 50◦C (squares), 60◦Ctal data and the solid lines represent the best tri-Langmuir isotherms. (a) Concentrationd 5.0 mM. (c) Concentration range between 0.005 and 40 mM.

140 H. Kim et al. / J. Chromatogr. A 1101(2006) 136–152

Fig. 2. Adsorption equilibrium isotherms of Fmoc-L-Trp on the NIP at 40◦C (circles), 50◦C (squares), 60◦C (triangle-ups), and 70◦C (triangle-downs). The symbolsrepresent experimental data and the solid lines represent the best bi-Langmuir isotherms. (a) Concentration range between 0.005 and 0.45 mM. (b) Concentrationrange between 0.005 and 4.5 mM. (c) Concentration range between 0.005 and 35 mM.

can be seen in the curvatures of the isotherm data, especiallyin the low concentration range (Figs. 1a and 2a): the curvatureof the isotherm data decreases in the order Fmoc-L-Trp on theMIP > Fmoc-D-Trp on the MIP > Fmoc-L-Trp on the NIP. In thelow concentration range, the behavior of the isotherm data of thetwo enantiomers is already non-linear while that of Fmoc-L-Trpon the NIP is still linear.

The isotherm data were fitted to various isotherm models.The best isotherm model was selected based on the results from(1) statistical tests made on the results of the regression of thedata to the models; (2) calculation of the affinity energy distri-bution; and (3) comparison of the experimental and calculatedband profiles. The isotherm data of both enantiomers on the MIPfit best to the tri-Langmuir model while those of Fmoc-L-Trpon the NIP fit best to the bi-Langmuir model. The lines inFigs.1 and 2represent the best isotherm models for the isothermdata. The statistical results from the nonlinear regression of thedata are reported inTables 1 and 2. The best isotherm param-eters for the two Fmoc-Trp enantiomers on the MIP and forFmoc-L-Trp on the NIP are reported inTable 3. In each case,we assumed that the number of types of adsorption sites is inde-

Table 1Summary of the non-linear regression analysis

Polymer Substrate Model RSSa Fcalb

MIP Fmoc-L-Trp Langmuir 7.27 8.8Bi-Langmuir 0.239 212Tri-Langmuir 0.0257 2020Tetra-Langmuir 0.0267 2690

MIP Fmoc-D-Trp Langmuir 1.21 40.5Bi-Langmuir 0.0712 967Tri-Langmuir 0.0136 8570Tetra-Langmuir 0.0136 9670

NIP Fmoc-L-Trp Langmuir 0.561 69.1Bi-Langmuir 0.0556 2850Tri-Langmuir 0.0181 7930

a RSS: Sum of square of differences between experimental and theoreticaldata, where the weight for each data point for the non-linear regression was1/(qexp,i)2 (qexp,i is the experimentally determined concentration of adsorbedsubstrates at each mobile phase concentration of substrate).

b Fcal =(n−l)

∑n

i=1(qex,i−qex)2

(n−l)∑n

i=1(qex,i−qt,i)2

wheren is the number of data points,l the num-

ber of parameters,qex the experimental values of adsorbed substrates,qt,i thetheoretical values of adsorbed substrates and ¯qex is the mean value ofqex.

H. Kim et al. / J. Chromatogr. A 1101(2006) 136–152 141

Table 2Comparison of fitting from fitting each best isotherm model to isotherm data ofFmoc-Trp enantiomers on the MIP and to isotherm data of Fmoc-L-Trp on theNIP with and without assumption thatq is constant with temperature

Polymer Substrates Model q RSS

MIP Fmoc-L-Trp Tri-Langmuir Constant 0.0257Variable 0.0121

Fmoc-D-Trp Tri-Langmuir Constant 0.0136Variable 0.0120

NIP Fmoc-L-Trp Bi-Langmuir Constant 0.0556Variable 0.0500

pendent of the temperature. To estimate the isotherm parametersfrom the nonlinear regression of the adsorption data, we simul-taneously fitted all the sets of isotherm data at the five differenttemperatures to the corresponding tri-langmuir isotherm model.The tri-langmuir isotherm parameters in the model have differ-ent association constants but their saturation capacities were setequal and were let simultaneously to vary, in order best to fitthe isotherm data at the five temperatures. The standard devi-ations derived from the results of the nonlinear regression arealso reported inTable 3. Depending on the parameter, the rela-

tive standard deviation is between 5 and 10%, with a trend for therelative standard deviation of each parameter to increase fromthe type 1 to the type 2 and to the type 3 sites.

In the non-linear regression, the experimental data were givena weight equal to 1/(qexp)2 whereqexp is the measured concen-tration of the substrate in the stationary phase.Table 1shows thestatistical results of the regression of the experimental isothermdata to each of these isotherm models. In most cases, the lowervalues of the residual sum of squares (RSS) was always obtainedfor the isotherm model with most fitting parameters. This is be-cause an increase in the number of model parameters gives amore flexible model, resulting in lower RSS values. To betterestimate the relative quality of the fitting of the data to differ-ent isotherm models, we calculated the Fisher parameters (Fcal)from the results of fittings the data to a pair of different isothermmodels. The calculated ratios of the Fisher parameters for thepair of models were then compared to the criticalF-value froma standardF-distribution table. The criticalF-value to comparethe eight-parameter tetra-Langmuir isotherm model to the six-parameter tri-Langmuir model is 2.98 at the 95% confidencelevel. The calculated ratios of the corresponding Fisher param-

Table 3Tri-Langmuir model fittings and Bi-Langmuir model fittings for Fmoc-Trp enantiomers on the MIP and Fmoc-L-Trp on the NIP, respectively, with the assumptionthatq is independent of the temperature

Polymer (isomer) Site T (K) qs (mM) b (mM−1) aa Enantiomer-selectivity (α)

MIP (L-Trp) 1 313 389± 20323 389± 20333 389± 20343 389± 20

2 313 7.75± 1.5323 7.75± 1.5333 7.75± 1.5343 7.75± 1.5

3 313 0.342± 0.04323 0.342± 0.04333 0.342± 0.04

67± 30 4± 3

343 0.342± 0.04

MIP (D-Trp) 1 313 422± 20323 422± 10333 422± 20343 422± 20

2 313 12.2 ± 2323 12.2 ± 2333 12.2 ± 2343 12.2 ± 2

3 313 0.064± 0.01323 0.064± 0.01

333 0.064± 0.01343 0.064± 0.01

NIP (L-Trp) 1 313 310± 25323 310± 25333 310± 25343 310± 25

2 313 3.47± 1.5323 3.47± 1.5333 3.47± 1.5343 3.47± 1.5

a a is the product ofqs andb.

0.032± 0.003 12.5 ± 1 1.1 ± 0.150.027± 0.002 10.5 ± 1 1.15± 0.150.022± 0.002 8.6 ± 0.9 1.1 ± 0.150.0195±0.002 7.8 ± 0.8 1.15± 0.15

1.5 ± 0.3 12± 3 1.4 ± 0.51.15± 0.2 9± 2 1.3 ± 0.50.99± 0.2 8± 2 1.7 ± 0.60.81± 0.15 6.4 ± 1.5 1.4 ± 0.5

110± 20 37± 8 6± 594± 15 31± 6 7± 667± 10 24± 4 20± 2046± 6 16± 3 7± 5

0.027± 0.002 11± 10.022± 0.002 9.2 ± 0.90.0185±0.0015 8.0 ± 0.70.0160±0.0015 6.7 ± 0.6

0.65± 0.1 8.5 ± 20.54± 0.09 6.6 ± 1.50.40± 0.06 4.8 ± 10.37± 0.06 4.5 ± 1

97± 50 6± 5

22± 15 1.2 ± 141± 15 2.5 ± 1.5

0.027± 0.003 8± 1.50.023± 0.003 7± 10.019± 0.002 6± 0.90.0155±0.002 5.0 ± 0.7

0.93± 0.3 2.7 ± 1.50.95± 0.3 2.7 ± 1.50.74± 0.2 2.0 ± 10.57± 0.15 1.8 ± 1

142 H. Kim et al. / J. Chromatogr. A 1101(2006) 136–152

eters were 1.33 and 1.13 for Fmoc-L-Trp and for Fmoc-D-Trp,respectively, on the MIP. This means that the data do not fitsignificantly better to the Tetra-Langnmuir model. By the sametoken, however, the data for both enantiomers on the MIP fitbetter to the tri-Langmuir than to the bi-Langmuir model at alltemperatures (seeTable 1). The converse is true for the isothermdata of Fmoc-L-Trp on the NIP and there is no significant differ-ence between the qualities of the bi- and tri-Langmuir models inaccounting for the isotherm data of Fmoc-L-Trp on the NIP atall temperatures. The simpler isotherm model should be chosen.

For each system studied, a statistical analysis of the resultsshowed that the number of sites of each type (qs,i) does notchange with the temperature. This result is reasonable consider-ing that these stationary phases are highly cross-linked polymers(90% of crosslinking monomers are used in the polymerizationformula) the morphology of which should not change signifi-cantly with increasing temperature. Experimental proof of thethermal stability on this kind of stationary phases has been re-ported[1]. Table 2compares the sums of residues from the fit-

ting of the experimental data to each isotherm model with theassumptions that (1)qs,i is constant, independently of the tem-perature; and (2)qs varies with the temperature. No significantdifferences in the residues can be observed.

4.2. Calculation of the affinity energy distribution

In the previous section, we discussed the results of the non-linear regression of the isotherm data and of the statistical testsmade on the results of these regressions to different isothermmodels. These results demonstrate that the surfaces of the poly-mers studied are not homogeneous. At least three different typesof sites were identified on the sureface of the MIP and two onthat of the NIP. These results should be compared to the affinityenergy distributions (AED) that are derived independently fromthe same experimental isotherm data. We used the expectation-maximization method (EM) to calculate the AEDs.

Fig. 3shows four successive stages of the calculation of theAED functions of Fmoc-L-Trp on the MIP, from the set of 33 ex-

FicF

ig. 3. Affinity energy distribution (AED) for Fmoc-L-Trp on the Fmoc-L-Trp imprintsotherm data points using the EM method. Four different numbers of iteratiorresponding to the second type of sites (as indicated inFig. 3a). (c) Expanded viig. 3a). The sites of types 1–3 correspond to the energy modes identified bas

ed polymer at a temperature of 40◦C. (a) AED calculation from 33 experimentalons were used as indicated on the graph. (b) Expanded view of the AED functionew of the AED function corresponding to the third type of sites (as indicated ined on the affinity energy distribution for Fmoc-L-Trp on the MIP.

H. Kim et al. / J. Chromatogr. A 1101(2006) 136–152 143

Fig. 4. Affinity energy distribution (AED) for Fmoc-L-Trp on the reference polymer at temperature 40◦C. (a) AED calculation from 33 experimental isotherm datapoints using the EM method. Four different number of iterations were used as indicated on the graph. (b) Expanded view of the AED function corresponding tothe second type of sites (as indicated inFig. 5a). The sites of types 1 and 2 correspond to the energy modes identified based on the affinity energy distribution forFmoc-L-Trp on the NIP.

perimental isotherm data points obtained, at the temperature of40◦C. Similar AEDs were observed at all temperatures studied.These four stages correspond to an increasing number of itera-tions.Fig. 3a shows the AED obtained over the entire affinityenergy calculated. Due to the very large differences in the satu-ration capacities of the three types of sites identified, we show inFig. 3b and c expansion of the parts of the distribution that cor-respond to the two types of sites of higher energy, which havelow saturation capacities. The peak of the low energy type ofsites (with approximately−4 < ln b < 2.5) is illustrated inFig.3a, which shows also a divergence at low values of the interac-tion constant (lnb < −6). The peak corresponding to the type ofsites of intermediate energy (i.e., 0< ln b < 1.5) can be clearlyobserved inFig. 3b and the peak of the high energy type of sites(i.e., 3< ln b < 5) can be observed inFig. 3c. These figures il-lustrate how, as the number of iterations increases, the trimodalenergy distribution becomes clearer. The divergence observedat very low energies does not disappear with increasing numberof iterations. This shows that more data points would be neededat high mobile phase concentrations (above 40 mM) than wereacquired. Unfortunately, this was not possible for the lack of asufficient solubility of Fmoc-Trp in the acetonitrile-based mo-bile phase (with 1% acetic acid). The AEDs shown inFig. 3demonstrates that at least three different types of binding sitescoexist for Fmoc-L-Trp on the MIP, with the additional possi-bility of another type at very low energies. The AED similarlyc owt ts odesa re obse ce av

theM satur es o

sites identified were calculated, using the integrals of each iden-tified mode in the AED and the abscissa of the maximum peakheight, respectively. These values are summarized inTable 4.Comparing these values with the isotherm parameters estimatedfrom the non-linear fitting (Table 3), we observe that the satura-tion capacities of each type of sites calculated from the affinitydistribution are smaller than those derived from the isothermfitting (e.g., 211 mM versus 390 mM for the sites of type 1 forFmoc-L-Trp on the MIP at 40◦C). This discrepancy is largerfor the lower energy sites because the divergence observed inthe low energy range affects the accuracy of the values esti-mated from the AED functions and it affects more the accuracyof the parameters of the low energy sites. On the other hand,the values of the association constants estimated from the AEDat this lower energy site are higher than those derived from theisotherm fitting (e.g., 0.051 versus 0.032 mM−1 on site 1 forFmoc-L-Trp on the MIP at 40◦C). In summary, the accuracy ofthe isotherm parameters calculated from the AED is low whena divergence is observed, especially those corresponding to thelow energy sites. When this happens, additional data points athigher mobile phase concentrations should be obtained and thiswould improve the accuracy of the AED, but this is possibleonly if the solubility of the substrates allows it, which is not thecase here. Thus, the utility of the AEDs obtained in this studyis limited to qualitative comparisons of the AEDs of the studiedsystems. These are consistent with the selection of the isothermm

ner-g ture.T ergyt -t 0a d ath eb en-e ture.

alculated for Fmoc-D-Trp on the MIP at all temperatures shhe same trends as that of Fmoc-L-Trp on the MIP (data nohown): With a high number of iterations, three energy mnd the same additional divergence at very low energies weerved as well. In contrast, the AED of Fmoc-L-Trp on the NIPxhibits only a bimodal distribution and the same divergenery low energies (Fig. 4).

Figs. 5 and 6show the AEDs of the two enantiomers onIP and the NIP, respectively, at all four temperatures. The

ation capacities and the association constants of all the typ

-

t

-f

odels based on the isotherm fit.There are important affinity energy shifts towards lower e

ies for all the modes of the AEDs with increasing temperahese shifts are larger for the higher than for the lower en

ypes of sites. Although the AEDs of the Fmoc-D-Trp enaniomers on the MIP (dotted lines inFig. 6) are trimodal at 4nd 50◦C, the highest energy mode could not be detecteigher temperatures. The AEDs of Fmoc-L-Trp on the NIP arimodal at all temperatures. The modes exhibit large affinityrgy shifts toward lower energies with increasing tempera

144H

.Kim

etal./J.Chrom

atogr.A1101(2006)

136–152

Fig. 5. Affinity energy distributions for Fmoc-L-Trp (solid line) and Fmoc-D-Trp (dotted line) on the Fmoc-L-Trp imprinted polymer (MIP) at different temperatures. (a) 40◦C; (b) 50◦C; (c) 60◦C; (d) 70◦C. (a′–d′)are expanded views of (a–d), respectively. They show the high energy sites which have a low density. The insets in these four figures are expanded views of the highest energy mode. The indices 1–3, 1′–3′representthe energy modes identified based on the affinity energy distribution for Fmoc-L-Trp and for Fmoc-D-Trp, respectively, on the MIP.

H.K

imetal./J.C

hromatogr.A

1101(2006)136–152

145

Fig. 6. Affinity energy distributions for Fmoc-L-Trp on the reference polymer (NIP) at different temperatures. (a) 40◦C; (b) 50◦C; (c) 60◦C; (d) 70◦C. (a′–d′) are expanded views of (a–d), respectively. They showthe high energy sites which have a low density. The insets in these four figures are expanded views of the highest energy mode. The indices 1′ ′and 2′ ′represent the energy modes identified based on the affinity energydistribution for Fmoc-L-Trp on the NIP.

146 H. Kim et al. / J. Chromatogr. A 1101(2006) 136–152

Table 4Isotherm parameters for Fmoc-L-Trp and Fmoc-D-Trp on the MIP, and for Fmoc-L-Trp on the NIPa

Polymer(isomer) Site T(◦C) q (mM) b (mM−1)

MIP (Fmoc-L-Trp) 1 40 211 0.050950 187 0.050960 174 0.042370 443 0.0138

2 40 5.15 2.10550 5.12 1.45160 3.66 1.20570 23.5 0.226

3 40 0.392 72.250 0.407 49.860 0.667 9.3370 1.47 3.68

MIP (Fmoc-D-Trp) 1 40 170 0.050950 310 0.024260 250 0.029270 190 0.0351

2 40 11.8 0.47550 14.9 0.32860 6.62 0.57270 3.7 1.00

3 40 0.57 6.4350 1.13 1.7560 n.db n.d70 n.d n.d

MIP (Fmoc-L-Trp) 1 40 121 0.059350 269 0.020160 149 0.029270 134 0.0292

2 40 1.06 1.6950 8.57 0.39460 4.07 0.57270 1.98 0.689

a These isotherm parameters were calculated from the affinity energy distribution. The saturation capacity was calculated by the integral of the corre-sponding peak of the distribution and the association constant as the value othe association constant for the peak maximum.

b n.d: not determined.

In conclusion, the AEDs of the two enantiomers on the MIP andthe NIP are consistent with the choice of the isotherm modebased on the results of the statistical tests. At all temperatureat least three types of sites coexist for the enantiomers on thMIP and at least two types of sites for Fmoc-Trp on the NIP,within the measured concentration ranges.

4.3. Comparison of calculated and experimental bandprofiles

A last check of the validity of the isotherms obtained is af-forded by a comparison of the experimental peak profiles withthose calculated, using an appropriate mass transfer modelchromatography and these isotherms[23]. It was shown that thelumped pore diffusion model (POR) accounts very well for themass transfer kinetics on the stationary phases used in this stud[20]. A discussion of the details of the calculation, using the PORmodel, of the mass transfer coefficients in the phase system use

is not within the scope of this paper. This issue was discussedelsewhere[20]. In this paper, we used the mass transfer coeffi-cient derived previously and calculate the elution band profilesusing each one of several different isotherm models. These cal-culated band profiles are then compared to experimental bandprofiles.

As an example, we compare inFig. 7 calculated and exper-imental peak profiles of Fmoc-L-Trp on the MIP for sampleof two widely different concentrations, 0.1 and 40 mM, at twodifferent temperatures, 40 and 70◦C. The band profiles were cal-culated using three different isotherm models, the bi-Langmuir;the tri-Langmuir; and the tetra-Langmuir models. The profilesderived from the bi-Langmuir model deviate strongly from theexperimental profiles at all temperatures, especially at low con-centrations (Fig. 7a and c). In contrast, there is good agree-ment between the experimental and calculated band profilesobtained with either the tri- or the tetra-Langmuir isothermmodels. Similar observations can be made by comparing theband profiles calculated and measured for Fmoc-D-Trp on theMIP (Fig. 8). Again, the peak profiles calculated with the bi-Langmuir isotherm model deviate much from the experimen-tal profiles, at all temperatures, especially at the lowest sampleconcentration (Fig. 8a and c). However, the experimental pro-files show similarly good agreement with the profiles calculatedeither with the tri-Langmuir or the tetra-Langmuir models. Fi-nally, the experimental peak profiles of Fmoc-L-Trp on the NIPa e bi-Lt tedp theN

o-fi ermm typei tem-p1 ,a ec s. Ine db e twop cen-t itherc quallyw , fora

bestf tisti-c of thei thes cal-c con-c therec n theM ec-t oret

-

f

ls,e

of

y

d

re in excellent agreement with those calculated with thangmuir isotherm model at all temperatures (Fig. 9). Using the

ri-Langmuir or the simpler Langmuir model gave calcularofiles in poor agreement with the experimental ones onIP.Finally, we compare inFig. 10 the experimental peak pr

les with those calculated with the different selected isothodels, assuming either that the number of sites of each

s independent of the temperature or that it changes witherature. The results for Fmoc-L-Trp on the MIP are inFig.0a and b, those for Fmoc-D-Trp on the MIP inFig. 10c and dnd those for Fmoc-L-Trp on the NIP inFig. 10e and f. Thesalculations were performed at two different temperatureach figure, the eluent concentration (y-axis) was normalizey the concentration of the injected sample, to compare throfiles obtained by injecting samples of very different con

rations (0.1 and 40 mM). The band profiles calculated in ease are very close, so both calculated profiles account eell for the experimental band profiles, at all temperaturesll systems studied.

In summary, the selection of the isotherm accountingor our isotherm data is consistent with the results of staal tests made on the results of the nonlinear regressionsotherm data; the affinity energy distributions derived fromame isotherm data; the comparison of experimental andulated band profiles at low (linear) and high (nonlinear)entrations. Within the concentration range investigated,oexists at least three types of sites for the enantiomers oIP and two types of sites for Fmoc-Trp on the NIP, resp

ively. However, the possibility of the existence of one mype of sites cannot be completely excluded.

H. Kim et al. / J. Chromatogr. A 1101(2006) 136–152 147

Fig. 7. Comparison between calculated and experimental peak profiles of Fmoc-L-Trp on the MIP at two different temperatures. The experimental peak profiles areshown as dotted bold lines. The calculated peak profiles were calculated using each one of three different isotherm models, as indicated in the graph. The injectiontime was 1 min; the inlet concentrations were (a) 0.1 mM and (b) 40 mM at a temperature of 40◦C, (c) 0.1 mM and (d) 40 mM at a temperature of 70◦C.

4.4. Thermodynamic functions from Van’t Hoff equation

Table 3illustrates the effects of the temperature on the affin-ity (a = qs × b) and the enantiomeric selectivity (α) of the dif-ferent types of sites identified for the two enantiomers on theMIP. With increasing temperature, a similarly large decreasein affinity is observed for each type of sites, for both enan-tiomers. For example, increasing the temperature from 40 to70◦C decreases the enantiomeric affinity on the lowest energysites (type 1) by about 40%. This decrease is more significantfor the higher energy sites. For example, increasing the temper-ature from 40 to 70◦C decreases the affinity of types 2 and 3sites by about 50 and 60%, respectively. In contrast with theselarge decreases in the enantiomer affinity with increasing tem-perature, no significant changes in the enantiomeric selectivityare observed. The enantiomeric selectivity on each site increasesslightly (by about 5%) when the temperature increases from 40 to70◦C.

To understand these temperature effects better, we calculatedthe thermodynamic functions by applying the Van’t Hoff equa-tion (Eq.(3)) to each binding type of sites of the MIP and the

NIP [24,25].

∂(ln ai)

∂(1/T )= −�H◦

i

R(4)

whereai coefficients are associated with each type of sites (withai = qs,ibi, seeTable 3) and�H◦

i is the corresponding stan-dard molar entalphy of adsorption.Fig. 11shows a plot of thelogarithm of theai coefficients versus the reciprocal of the tem-perature for Fmoc-L-Trp and Fmoc-D-Trp on the MIP (Fig. 11aand b, respectively), and Fmoc-L-Trp on the NIP (Fig. 11c). Thetotal length of each error bar is equal to the standard deviationafforded by the nonlinear regression. The solid lines show thebest linear fit of the data to the Van’t Hoff equation. The standardmolar enthalpy of adsorption,�H◦, for each site was derivedfrom the slope of the best straight line. The standard molar Gibbsfree energy of adsorption for the corresponding site,�G◦, wasdetermined by the following equation:

�G◦i = −RT ln Ki = −RT ln ai (5)

whereR is the universal gas constant (1.9872 cal/mol/K) andKi = ai = qs,ibi. The standard molar entropy of adsorption,

148 H. Kim et al. / J. Chromatogr. A 1101(2006) 136–152

Fig. 8. Comparison between calculated and experimental peak profiles of Fmoc-D-Trp on the MIP at two different temperatures. The experimental peak profiles areshown as dotted bold lines. The calculated peak profiles were obtained using each one of three different isotherm models, as indicated in the graph. Theinjectiontime was 1 min and the inlet concentrations were (a) 0.1 mM and (b) 40 mM at a temperature of 40◦C, (c) 0.1 mM and (d) 40 mM at a temperature of 70◦C.

�S◦, for the corresponding site was estimated from Eq.(6),using the values obtained from Eqs.(4) and (5):

�S◦i = − (�G◦

i − �H◦i )

T(6)

Since the equilibrium constants (a) on each type of site, foreach chromatographic system were obtained in this study, thethermodynamic functions,�G◦, �H◦, and�S◦ can be deter-mined separately for each type of sites. These values are reportedin Table 5which lists also the errors made on the estimationsof the best values of these parameters. The values of�G areprecise, with relative standard deviations (σ) of a few percent inmost cases. however, theσs are of the order of 5–15% on�H

and of 10–25% on�S. They are larger for the high energy sitesthan for the low energy ones.

The thermodynamic functions for the enantiomeric selectiv-ity on the MIP (i.e.,�(�H◦), �(�S◦), and�(�G◦)) were ob-tained as follows:

�(�H◦) = �H◦(Fmoc-L-Trp) − �H◦(Fmoc-D-Trp)

�(�S◦) = �S◦(Fmoc-L-Trp) − �S◦(Fmoc-D-Trp)

�(�G◦) = �G◦(Fmoc-L-Trp) − �G◦(Fmoc-D-Trp)

(7)

These values are reported inTable 6, together with the stan-dard deviation of the estimate provided by the regression.The precision becomes relatively poor, with values of theσsbeing of the same order as unity. We note that these ther-modynamic relationships are valid under the assumption thatthe binding of the substrates with each identifiable site onthe MIP is reversible and equlilibrium binding event and thatthe binding mechansim of the system does not change withtemperatures.

Negative values of�G◦ were observed for all the systemsstudied. The absolute values,|�G◦|, decrease with increasingtemperature for each type of sites identified, which reflects thedecreasing affinity of the enantiomers for the stationary phaseswith increasing temperatures. This decrease in|�G◦| is largeron the high energy type of sites than on the lower energy typesof sites. On the high energy sites, which are the most enantiose-lective sites, this decrease is larger for Fmoc-D-Trp on the MIPthan for Fmoc-L-Trp on the NIP, which in turn is larger than forFmoc-L-Trp on the MIP. For example,|�G◦| for Fmoc-D-Trpon the MIP decreases by 20 and 50% on types 2 and 3, respec-tively, when the temperature increases from 40 to 70◦C whilefor Fmoc-L-Trp on the MIP, it decreases for these same sites byapproximately 20%.

H. Kim et al. / J. Chromatogr. A 1101(2006) 136–152 149

Fig. 9. Comparison between calculated and experimental peak profiles of Fmoc-L-Trp on the NIP at two different temperatures. The experimental peak profiles areshown as dotted bold lines. The calculated peak profiles were obtained using each one of three different isotherm models, as indicated in the graph. Theinjectiontime was 1 min and the inlet concentrations were (a) 0.1 mM and (b) 40 mM at a temperature of 40◦C; (c) 0.1 mM and (d) 40 mM at a temperature of 70◦C.

Negative values of�H◦ were obtained for all the systemsstudied (Table 5). This indicates that the transfer of the enan-tiomers from the mobile phase to the surface of the MIP or theNIP is enthalpically favored. The absolute values are between13 and 39 kJ/mol (i.e., between 3 and 9 kcal/mol). These val-ues are consistent with the energies involved in the interactionsexpected between the pyridine groups of the polymers and thecarboxylic groups of the substrates (a few tens kJ/mol). As ex-pected, the absolute values|�H◦|, are larger for the high- thanfor the low-energy sites of the enantiomers on the MIP. For ex-ample,|�H◦| is 30% larger for Fmoc-L-Trp on the type 2 sites(the medium high affinity sites) of the MIP than on the type 1sites (the low affinity sites) and it is 80% larger for Fmoc-L-Trp on the type 3 sites (the highest affinity sites) of the MIPthan for the type 1 sites (the low affinity sites). A qualitativelysimilar variation of|�H◦| is observed for Fmoc-D-Trp on theMIP. For example,|�H◦| for Fmoc-D-Trp on the MIP is 40%larger on the type 2 sites than on the type 1 sites of the MIP.Although this trend seems to hold also for Fmoc-D-Trp on thetype 3 sites of the MIP, the large error made on the values of|�H◦| (ca 45%) prevents a formal conclusion. Finally, there isa surprisingly small difference between the values of|�H◦| on

the two types of sites identified on the NIP (Table 5). For allthe systems studied, negative values of�S◦ were observed. Theabsolute value|�S◦| is larger for Fmoc-D-Trp than for Fmoc-L-Trp, especially on the type 2 sites, on which it is about 15%larger.

Fig. 12 compares the values of�(�H◦), T�(�S◦), and�(�G◦) that characterize the enantiomeric separation (Table6) on the sites of type 1 (Fig. 12(a)), 2 (Fig. 12(b)), and 3 (Fig.12(c)). The contribution ofT�(�S◦) values to the values of�(�G◦) is larger than that of�(�H◦). Although the directcomparison of the numerical values does not lead to a definitiveconclusion, the fact is confirmed by the values of both�(�H◦)and�(�S◦) being positive in all cases while that of�(�G◦) isnegative at all temperatures. The absolute values|�(�G◦)| andthe positive values of�(�H◦) and�(�S◦) all increase withincreasing affinity of the sites, at all temperatures. Thus, theseresults show that the favorable free energy of adsorption of themolecules of the template on the MIP is entropically driven andthat the adsorption is more entropically favorable on the higheraffinity sites, which are the more enantioselective. A similar ob-servation was already made in a previous study[26] in whichthe authors measured by microcalorimetry and compared the

150 H. Kim et al. / J. Chromatogr. A 1101(2006) 136–152

Fig. 10. Comparison between calculated and experimental peak profiles of (a) Fmoc-L-Trp on the MIP at 40◦C; (b) Fmoc-L-Trp on the MIP at 70◦C; (c) Fmoc-D-Trpon the MIP at 40◦C; (d) Fmoc-D-Trp on the MIP at 70◦C; (e) Fmoc-L-Trp on the NIP at 40◦C; (f) Fmoc-L-Trp on the NIP at 70◦C. The experimental peak profilesare shown as dotted bold lines. The calculated band profiles in each figure were obtained by assuming that the number of sites does not change with the differenttemperatures (qs = constant, solid lines) or that the number of sites changes with the different temperatures (qs = variable, dotted lines). The injection time was 1 minand the inlet concentrations were 0.1 mM and 40 mM. To compare the profiles obtained at the two different concentrations, they-axis (i.e., the eluent concentration)was normalized by dividing with the inlet concentration.

thermodynamic functions of the adsorption of an enantiomer of2,4-dichlorophenoxyacetic acid (template) on the correspond-ing MIP and on its reference polymer, from an aqueous solution.They reported that entropy is the dominant driving force for theinteractions between the template and the imprinted polymer.Fig. 12andTable 6also show that the value of�(�S◦) doesnot change significantly with increasing temperature, which ex-plains why the enantioselectivity of the MIP does not vary sig-nificantly with temperature. It seems that increasing the temper-ature from 40 to 70◦C does not affect significantly the structure

of enantioselective binding sites obtained. The observation thatthe adsorption entropy ofL-Trp on the MIP is higher than that ofits antipode,D-Trp, indicates that the changes in the geometryof the binding sites on the MIP caused by their binding with thetemplate do cause a lesser drop in entropy than those caused bythe binding of its antipode to the MIP. This implies that the stericstructure of the cavities in which consist the binding sites is op-timized for binding with the template. In contrast the geometryof the binding sites does not permit their close match with thefunctional groups ofD-Trp. The observation that the adsorp-

Fig. 11. Van’t Hoff plot for the determination of the enthalpy of adsorption of (a) Fmoc-L-Trp on the MIP; (b) Fmoc-D-Trp on the MIP; (c) Fmoc-L-Trp on the NIP.The symbols represent the experimental data; the lines represent the best linear fits. The indices sites 1–3 correspond to the types of sites identifiedon the polymers

urface.

H. Kim et al. / J. Chromatogr. A 1101(2006) 136–152 151

Table 5Thermodynamic parameters for the Fmoc-Trp enantiomers on the MIP and on the NIP, derived from isotherm data using Van’t Hoff equation

Polymer (isomer) Site T (K) �G (kcal/mol) �H (kcal/mol) �S (cal/mol/K)

MIP (L-Trp) 1 313 −1.57± 0.06 −3.45± 0.3 −6 ± 1323 −1.51± 0.06 −3.45± 0.3 −6 ± 1333 −1.42± 0.07 −3.45± 0.3 −6 ± 1343 −1.40± 0.07 −3.45± 0.3 −6 ± 1

2 313 −1.5 ± 0.15 −4.2 ± 0.6 −9 ± 2323 −1.4 ± 0.15 −4.2 ± 0.6 −9 ± 2333 −1.4 ± 0.15 −4.2 ± 0.6 −9 ± 2343 −1.3 ± 0.2 −4.2 ± 0.6 −9 ± 2

3 313 −2.3 ± 0.15 −6.1 ± 0.9 −12± 3323 −2.2 ± 0.15 −6.1 ± 0.9 −12± 3333 −2.1 ± 0.1 −6.1 ± 0.9 −12± 3343 −1.9 ± 0.1 −6.1 ± 0.9 −12± 3

MIP (D-Trp) 1 313 −1.51± 0.0003 −3.7 ± 0.15 −6.9 ± 0.4323 −1.42± 0.0003 −3.7 ± 0.15 −6.9 ± 0.4333 −1.37± 0.0003 −3.7 ± 0.15 −6.9 ± 0.4343 −1.29± 0.0002 −3.7 ± 0.15 −6.9 ± 0.4

2 313 −1.33± 0.0007 −4.8 ± 0.8 −11± 2323 −1.21± 0.0006 −4.8 ± 0.8 −11± 2333 −1.03± 0.0005 −4.8 ± 0.8 −11± 2343 −1.02± 0.0005 −4.8 ± 0.8 −11± 2

3 313 −1.11± 0.0015 −9 ± 5 −24± 15323 −0.92± 0.0015 −9 ± 5 −24± 15333 −0.12± 0.0002 −9 ± 5 −26± 15343 −0.60± 0.0009 −9 ± 5 −24± 15

NIP (L-Trp) 1 313 −1.32± 0.09 −3.8 ± 0.15 −7.8 ± 0.7323 −1.3 ± 0.1 −3.8 ± 0.15 −7.7 ± 0.7333 −1.2 ± 0.1 −3.8 ± 0.15 −7.8 ± 0.7343 −1.1 ± 0.1 −3.8 ± 0.15 −7.8 ± 0.7

2 313 −0.7 ± 0.3 −3 ± 0.8 −7 ± 3323 −0.7 ± 0.3 −3 ± 0.8 −7 ± 3333 −0.6 ± 0.3 −3 ± 0.8 −8 ± 3343 −0.5 ± 0.3 −3 ± 0.8 −78± 3

tion entropy is independent of the temperatures indicates thatthe geometry of the binding sites on the MIP does not changesignificantly with the temperature, which also supports our as-sumption that the number of binding sites on the MIP does notchange with temperature.

Finally we note that a different dependency of the enantios-electivity on the temperature was reported in a previous study

[27] of the enantioselectivity of anL-phenylalanine anilide (L-PA) imprinted polymer, using an aqueous-based mobile phase(70/30, v/v mixture of acetonitrile and an aqueous buffer at pH5.8). A rapid decrease of the enantioselectivity with increasingtemperature was observed in that case. It dropped by 70% on thehighest energy sites identified in that study when the temperatureincreased from 40 to 70◦C.

Fig. 12. Plots of the temperatures versus the thermodynamic functions for the enantiomer selectivity (�(�H◦), T�(�S◦), and�(�G◦)) on (a) the site 1; (b) thesite 2; (c) the site 3. The sites 1–3 correspond to the types of sites identified on the polymer surface.

152 H. Kim et al. / J. Chromatogr. A 1101(2006) 136–152

Table 6Thermodynamic parameters for the enantiomer selectivity derived from isothermdata using Van’t Hoff equation

Site T (K) ��G (kcal/mol) ��H (kcal/mol) ��S (cal/mol/K)

1 313 −0.06± 0.06 0.2 ± 0.3 1± 1323 −0.08± 0.06 0.2 ± 0.3 1± 1333 −0.04± 0.07 0.2 ± 0.3 1± 1343 −0.1 ± 0.07 0.2 ± 0.3 1± 3

2 313 −0.2 ± 0.15 0.6 ± 1 3± 3323 −0.2 ± 0.15 0.6 ± 1 2± 3333 −0.3 ± 0.15 0.6 ± 1 3± 3343 −0.2 ± 0.2 0.6 ± 1 2± 3

3 313 −1.1 ± 0.15 3± 5 10± 15323 −1.3 ± 0.15 3± 5 10± 15333 −2.0 ± 0.1 3± 5 12± 15343 −1.3 ± 0.1 3± 5 10± 15

5. Conclusion

Investigating the influence of temperature on the binding per-formance of Fmoc-L-Trp imprinted polymers we showed thatit could be explained by considering the thermodynamic func-tions derived from the application of Van’t Hoff equation to theisotherm data acquired by FA. The modeling of the isothermdata, the statistical tests made on the results of the fits of thedata to various models, the adsorption affinity distributions ofthe enantiomers of Fmoc-L-Trp on the MIP and of Fmoc-Trp onthe NIP, and the comparison of the experimental and calculateband profiles demonstrated that the surface of the MIP is coverewith adsorption sites belonging to three well-defined interactiontypes and that of the NIP with only two. Thus, the adsorption dataon the MIP are best accounted for by a tri-Langmuir isothermmodel yet those on the NIP by a simpler bi-Langmuir isothermmodel. This conclusion is valid at all temperatures and the density of the sites of each type is independent of the temperature

These affinity of the substrates for the two surfaces, MIP andNIP, decreases sharply with increasing temperature but no significant changes were observed in the enantiomeric selectivitybetween 40 and 70◦C. The thermodynamic functions of bindingto the different types of sites were calculated by applying Van’tHoff equation to the adsorption data on each type of sites. Thbinding entropy seems to be the dominant driving force for theenantioselective binding of the template (Fmoc-L-Trp) on theM itht e

enantioselectivity on the MIP, in an organic based mobile phase,does not show any significant changes with increasing temper-ature in this range.

Acknowledgments

This work was supported in part by grant CHE-02-44693 ofthe National Science Foundation, by Grant DE-FG05-88-ER-13869 of the US Department of Energy, and by the cooperativeagreement between the University of Tennessee and the OakRidge National Laboratory.

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