Chemical Engineering Science 61 (2006) 1122–1137www.elsevier.com/locate/ces

Intraparticle mass transfer kinetics on molecularly imprinted polymers ofstructural analogues of a template

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

bDivision of Chemical Sciences, Oak Ridge National Laboratory, Oak Ridge, TN, 37831-6120, USAcFaculty of Chemistry, Rzeszów University of Technology, 35-959 Rzeszów, Poland

Received 20 May 2005; received in revised form 1 August 2005; accepted 6 August 2005Available online 23 September 2005

Abstract

The intraparticle mass transfer kinetics of the structural analogues of a template on a Fmoc-L-Tryptophan (Fmoc-L-Trp) imprinted polymer(MIP) and on the corresponding non-imprinted polymer (NIP) were quantitatively studied using the lumped pore diffusion model (POR) ofchromatography. The best equilibrium isotherm models of these compounds were used to calculate the high-concentration band profiles ofdifferent substrates on the MIP and the NIP with the POR model. These profiles were compared to experimental band profiles. The numericalvalues of the intraparticle pore and surface diffusion coefficients were adjusted to determine those that minimized the differences betweencalculated and experimental profiles. The results of this exercise show that surface diffusion is the dominant intraparticle mass transfer processfor the substrates on the polymers and that the energetic heterogeneity of the surface should be considered in accounting for the surface diffusionof the L-enantiomers on the MIP. The surface diffusion coefficient increases with decreasing overall affinity of each substrate for the polymers.� 2005 Elsevier Ltd. All rights reserved.

Keywords: Fmoc-L-tryptophan imprinted polymers; Frontal analysis; Tri-Langmuir isotherm model; Lumped pore diffusion model; Intraparticle mass transfer;Peak profiles; Surface diffusion model; Isosteric heat of adsorption

1. Introduction

Molecularly imprinted polymers (MIPs) are popular func-tional polymers used as effective separation media in chro-matography and in solid-phase extraction, due to their highselectivity toward the molecule(s) present in solution duringtheir polymerization (the template). The most commonly usedstrategy to prepare MIPs is the use of non-covalent interac-tions between a target molecule (the template) and some suit-able functional groups. These interactions allow the forma-tion of template-functional monomer complexes in solution.These complexes are then immobilized into a polymer ma-trix by copolymerization with a high concentration of cross-linking monomers. A MIP exhibiting adsorption sites withsize, shape, and functionalities complementary of those of the

∗ Corresponding author. Tel.: +1 865 974 0733; fax: +1 865 974 2667.E-mail address: guiochon@utk.edu (G. Guiochon).

0009-2509/$ - see front matter � 2005 Elsevier Ltd. All rights reserved.doi:10.1016/j.ces.2005.08.012

template can be obtained by extracting the template from thepolymer matrix after the end of the polymerization process.

One of the major problems encountered in using MIPs asseparation media in chromatography is the serious peak tailingobserved, especially for the bands of the template. This tailinghas often been attributed to a wide distribution of the adsorp-tion energy on the MIP surface and to a slow intraparticle masstransfer kinetics (MIP, 2001). These explanations suggests thatthe chromatographic performance of MIPs can be improved ei-ther by achieving a narrower distribution of the binding sites orby increasing their accessibility. Attempts to achieve more ho-mogeneous binding sites have included chemical modificationsof these sites (Umpleby et al., 2001) and imprinting inside den-drimers (Zimmerman and Lemcoff, 2004). Attempts to achievefaster accessibility of the sites were directed toward developingdifferent formats of imprinted polymers and locating the bind-ing sites on the polymer surface (Sulitzky et al., 2002; Biffiset al., 2001; Perez et al., 2001; Ye et al., 2000; Yilmaz et al.,

H. Kim et al. / Chemical Engineering Science 61 (2006) 1122–1137 1123

2000). Although many studies reported on different strategiesto improve the binding performance of MIPs, there are few sys-tematic studies as far as we know, on how these strategies im-prove the kinetic characteristics of MIPs (Sajonz et al., 1998;Miyabe and Guiochon, 2000a; Kim et al., 2005a). In order todevelop a clear strategy aiming at improving the performanceof MIPs, we need systematic measurements of the kinetic pa-rameters and of the adsorption energy distributions on the MIPsurface.

In a previous study (Kim and Guiochon, in press(a)), wereported equilibrium data for the adsorption of structural ana-logues of a template on a Fmoc-L-Trp MIP and on the corre-sponding NIP. These analogues were Fmoc-L-tyrosine (Fmoc-L-Tyr), Fmoc-L-serine (Fmoc-L-Ser), Fmoc-L-phenyalanine(Fmoc-L-Phe), Fmoc-Glycine (Fmoc-Gly), Fmoc-L-tryptophanpentafluorophenyl ester (Fmoc-L-Trp(OPfp)), and their an-tipodes. These substrates have different numbers of functionalgroups that can interact with the 4-vinylpyridine groups of thepolymer. These substrates have also different partition coef-ficients (log Pow) in the octanol-water system (from 7.61 forFmoc-Trp(OPfp) to 1.48 for Fmoc-Ser). This study showed thatthe surfaces of the MIP and NIP are mosaics of two or threerelatively homogeneous types of sites. It also showed a con-siderable extent of cross-reactivity of the structural analogues,particularly for the structural analogues that have the samestereochemistry as the template. This cross-reactivity increaseswith increasing number of functional groups on the structuralanalogue. In contrast, the cross-reactivity of the enantiomersof these substrates increases with increasing hydrophobicity ofthe substrate, as indicated by the values of log Pow.

In this study, we report on the intraparticle mass transferkinetics of the different substrates considered in the previousstudy on the Fmoc-L-Trp MIP, as well as on its reference poly-mer (NIP), using mixtures of organic solvents as the mobilephase. Using the isotherm parameters derived earlier (Kim andGuiochon, in press(a)) and the lumped pore diffusion model(POR), we calculated the profiles of high concentration bands,compared them to experimental profiles, and determined thevalues of the intraparticle diffusion coefficient and of the otherkinetic parameters for each substrate. The results of this studywill be used for a quantitative characterization of the masstransfer mechanism of the substrates on the MIP and NIP.

2. Theory

2.1. Modeling method

The lumped POR was used to calculate the intraparticle masstransfer kinetics of different substrates in the MIP and the cor-responding NIP. The method consists in using the isotherm pa-rameters previously measured (Kim and Guiochon, in press(a))and determining the intraparticle diffusion coefficient that mini-mizes the difference between the calculated and the experimen-tal profiles of high-concentration elution bands. This methodsgives the overall mass transfer coefficient (ki) from which theintraparticle diffusion coefficient (Deff) can be calculated.

The POR model consists of the following two mass balanceequations: one for the fluid phase percolating through the sta-tionary phase, the other for the stagnant fluid impregnating thepores of the stationary phase

�e�Ci

�t+ u

�Ci

�z

= �eDL

�2Ci

�z2− (1 − �e)kiap(Ci − Cp,i(r = R)), (1)

�p�Cp,i

�t+ (1 − �p)

�qi

�t= kiap(Ci − Cp,i(r = R)), (2)

where �e is the external porosity, �p is the internal (or particle)porosity and calculated by (�t − �e)/(1 − �e), where �t is thetotal porosity, Ci, Cp,i and qi are the average concentrationsof the solutes in the mobile phase, in the particle pores, andadsorbed on the stationary phase, respectively, t is the time, z isthe distance along the column, R is the diameter of the column,u is the superficial linear mobile phase velocity, DL is the axialdispersion coefficient, ap(=3/Rp) is the external surface areaper unit volume of the particles, Rp is the equivalent particleradius (in this study, we assume that all particles are sphericaland that their average size is 31.5 �m), and ki is the overallmass transfer coefficient for the solute, which is obtained fromthe modeling method and given by

ki =[

1

kext+ 1

kint

]−1

(3)

with

kint = 10Deff

dp

, (4)

where kext is the external mass transfer coefficient, and kint isthe internal mass transfer coefficient which is derived from theestimated ki from the modeling method.

The effective diffusivity Deff is calculated from the followingequation (Gubernak et al., 2004):

Deff = �pDp

�+ (1 − �p)Ds

q

Cp

, (5)

where

�(tortuosity factor) = (2 − �p)2

�p.

Eq. (5) assumes that the diffusional mass flux inside the particlecan be depicted by two parallel fluxes, the molecular flux insidethe fluid phase that fills the adsorbent pores, and the surface fluxof which the driving force is the gradient of chemical potential(Krishna, 1990; Kaczmarski et al., 2002).

The initial condition for Eqs. (1) and (2) are

Ci(t = 0, z) = C0i (z),

Cp, i(t = 0, z) = C0p, i(z),

qi(t = 0, z) = q0i (z). (6)

1124 H. Kim et al. / Chemical Engineering Science 61 (2006) 1122–1137

The boundary conditions for Eq. (1) are the Danckwerts con-dition (Danckwerts, 1953):

• For t > 0 and z = 0:

uf Cf,i − u(0)Ci(0) = −�eDL

�Ci

�z,

Cf,i = C0f,i for 0 < t < tp,

Cf,i = 0 for tp < t . (7)

• For t > 0 and z = L:

�Ci

�z= 0.

2.2. Calculation of the necessary parameters

The external mass transfer coefficient (kext, see Eq.(3)) was determined using the empirical correlation of theWilson–Geankoplis equation (Wilson and Geankoplis, 1996):

Sh = 1.09

�eSc1/3Re1/3. (8)

This equation relates the Sherwood number, Sh, a function ofthe external mass transfer coefficient, to the Schmidt (Sc) andthe Reynolds (Re) numbers. These numbers are defined by Reidet al. (1997):

Re = �udp/�,

Sc = �/�Dm,

Sh = kextdp/Dm, (9)

where � and � are the viscosity and the density of the mobilephase filling the pores and u and dp are the superficial linearvelocity of the mobile phase and the average particle size, re-spectively.

The molecular diffusion coefficient, Dm, was calculated ac-cording to the Wilke–Chang equation (Gidding, 1965):

Dm = 7.4 × 10−8T(�AMS)0.5

�́V 0.6A

, (10)

where T is the absolute temperature of the column (K), VA

is the molar volume of the solute at its normal boiling point(calculated from Le Bas correlation) (Reid et al., 1997), MS isthe molecular weight of the fluid, �́ is the fluid velocity (cP),and �A is the association factor for the fluid which accountsfor solute–solvent interactions and was assumed to be 1 in thisstudy.

The axial dispersion coefficient, DL (see Eq. (1)) can bederived from the Gunn equation (Gunn, 1987):

�eDL

dpu=

[ReSc(1 − p)2

4�21(1 − �e)

+ (ReSc)2p(1 − p)2

16�41(1 − �e)2

× exp

[−4�2

! (1 − �e)

p(1 − p)ReSc

]− 1

]

× (1 + �2v)

2 + �2v

2+ �e

�ReSc, (11)

where �1 is the first root of the zero-order Bessel function,Jo(x), which is equal to 2.4048, �v is the dimensionless vari-ance of the distribution of the ratio of the local fluid linear ve-locity and the cross-section average velocity, a variances which,in this work, is assumed to be equal to zero, � is the tortuosityfactor (for dispersion in a bed of spheres � = 1.4), and p is aparameter defined in Gunn (1987):

p = 0.17 + 0.33 exp(−24/Re). (12)

The POR model was solved using a computer programsbased on an implementation of the method of orthogonal collo-cation on finite elements (Berninger et al., 1991; Kaczmarski etal., 1997). The set of discretized ordinary differential equationswas solved with the Adams–Moulton method, implemented inthe VODE procedure (Brown et al.,). The relative and absoluteerrors of the numerical calculations were equal to 1×10−6 and1 × 10−8, respectively.

2.3. Isotherm models

The calculation of numerical solutions of the POR model re-quires an appropriate isotherm model accounting for the equi-librium behavior of the solute between the two phases of thesystem. Several isotherm models were fitted to the experimen-tal isotherm data of each substrate on the MIP and the NIP. Thebest isotherm model selected for each substrate on the NIP andon the MIP was the tri-Langmuir isotherm model (see equationbelow), with the only exception of Fmoc-L-Trp(OPfp) on theMIP and the NIP, in which case the simple Langmuir isothermmodel accounts best for the isotherm data (Kim and Guiochon,in press(a)).

q = qs1b1C

1 + b1C+ qs2b2C

1 + b2C+ qs3b3C

1 + b3C. (13)

In this equation, qs1, qs2 and qs3 are the saturation capacitiesfor the first, the second, and the third types of adsorption sites,respectively; and b1, b2, and b3 are the corresponding adsorp-tion constants.

3. Experimental

3.1. Chemicals

The substrate used were Fmoc-L-tryptophan (Fmoc-L-Trp, 98 + percent), Fmoc-D-tryptophan (Fmoc-D-Trp,98 + %), Fmoc-L-tryptophan pentafluorophenyl ester (Fmoc-L-Trp(OPfp), 98 + %), Fmoc-L-phenylalanine (Fmoc-L-Phe,99 + %), Fmoc-L-tyrosine (Fmoc-L-Tyr, 95 + %), Fmoc-L-serine (Fmoc-L-Ser, 98 + %), Fmoc-D-serine (Fmoc-D-Ser,98 + %, Fmoc-glycine (Fmoc-Gly, 97 + %) were purchasedfrom Novabiochem (San Diego, CA). Fmoc-D-phenylalanine(Fmoc-D-Phe, 99 + %) and Fmoc-D-tyrosine (Fmoc-D-Tyr,95+%). They were all purchased from Bachem (Torrance, CA).Ethylene glycol dimethacrylate (EGDMA), 4-Vinylpyridine(4-VPY), and 2,2-azo-bis(isobutyronitrile) (AIBN) were ob-tained from Aldrich (Milwaukee, WI). 4-VPY and EGDMA

H. Kim et al. / Chemical Engineering Science 61 (2006) 1122–1137 1125

were distilled under vacuum (60 mm Hg, 75 ◦C, and 60 mm Hg,120 ◦C, respectively). All other chemicals and solvents usedwere commercially available, of analytical or HPLC grade, andwere used as is.

3.2. Preparation of the stationary phase and packing of thecolumn

A polymeric chiral stationary phase imprinted with Fmoc-L-tryptophan (dp, 25–38 �m) was prepared by thermal poly-merization of 4-vinylpyridine (as the functional monomer) andethylene glycol dimethacrylate (as the crosslinking monomer)in a solution of the template in acetonitrile (the porogen). TheNIP was prepared by the same procedure, omitting the template.

Stainless steel columns (10 cm ×0.46 cm) were packed witheach polymer. The hold-up time of the columns (t0) at a flowrate of 1 mL/min was measured by injecting a small amount ofacetone into the column with the autosampler. After subtract-ing the contribution of the extra-column volume from the au-tosampler to the column (tx = 0.007 min), the total porosity ofthe column (volume of mobile phase divided by the geomet-rical volume of the column) was calculated from t0. The val-ues obtained were 0.759 for the MIP column and 0.78 for theNIP column. The external porosity of the column was derivedby inverse size exclusion chromatography, from the retentiontimes of polystyrene standards. Accordingly, the phase ratio isF = 0.318. The mobile phase used was acetonitrile with onepercent of acetic acid, as the organic modifier.

3.3. Experimental measurement of the breakthrough curves,and porosities of the columns

3.3.1. Breakthrough curvesThe isotherm data were obtained by the frontal analysis

method (FA), using a Hewlett-Packard (Palo Alto, CA, USA)HP 1090 liquid chromatograph. This instrument is equippedwith a multi-solvent delivery system (tank volumes, 1 L each),an auto-sampler with a 250 �L sample loop, a diode-array UVdetector, a column thermostat and a computer data acquisitionstation. The microcomputer of this system was used to programthe series of breakthrough curves needed. The three pumps ofthe HP 1090 solvent delivery system were used to obtain thesebreakthrough curves for the different solutes on the two sta-tionary phases studied. One of the pumps delivered the puremobile phase, each of the other two pumps delivered differentstock solutions of the compound studied. The concentration ofthe studied compound in the mobile phase was determined bythe concentration of the stock solution and the flow-rate frac-tions delivered by the two pumps at a constant total flow rate(1 mL/min) for a set time interval. Three consecutive break-through curves were acquired under any set of experimentalconditions, in the concentration range from 0.005 to 50 mM.Data in this 10 000 dynamic range are needed for the properconvergence of the calculations of the affinity energy distribu-tion (AED).

The conventional wide rectangular injection procedure wasfollowed. A solution of known concentration of the sample ispumped into the column until the plateau of the breakthroughcurve begins to elute (10–40 min). After the plateau has lastedfor at least 5 min, the adsorbed substrate is washed off the col-umn with a stream of pure mobile phase, until the UV ab-sorbance of the eluent has decreased to the same baseline asbefore, which takes 60–120 min. The next breakthrough time isthen measured under the same conditions as the previous one.After the third breakthrough curve is recorded (informing onthe precision of the measurement), the feed composition is in-creased for the acquisition of the next data point. The signalwas detected, depending on the compound used and its concen-tration range, at between 260 and 310 nm, to avoid recordingany signals above 1500 mAU. Because the return of the base-line below a threshold at the end of the re-equilibration periodis checked, there can only be small amounts of adsorbate leftin the column. Because the concentration is always increasedfrom one step to the next, the error on the isotherm data pointcaused by this residual can only be small. Even if the isothermparameters on the low energy sites were to be slightly over-estimated for this reason, they will be so for each system andthis would not affect conclusions based on a comparison of theisotherm parameters for each different solute on the stationaryphase. Finally, before changing the solute to acquire anotherseries of breakthrough curves, the column was washed with a4/1 methanol/acetic acid solution for at least two hours at aflow rate of 1.0 mL/min.

3.3.2. Porosities of the columnsThe hold-up time for the MIP columns (t0) was measured

by injecting a small amount of acetone from an auto-samplerinto the column. The extra-column volume from the pump wasmeasured by injecting a small amount of the substrate from thepump into a zero dead-volume connector instead of the column.A value of tx = 0.07 min was obtained. The experimental datahave been corrected by subtracting tx . The total porosity (�t )of the MIP and NIP columns was 0.75 and 0.78, respectively.

The external porosities (�e) of the MIP and NIP columnswere measured at temperatures of 23 ◦C and 40 ◦C from the re-tention data of polystyrene samples of narrow molecular sizedistributions and known average molecular mass, ranging be-tween 1780 and 1,877,000. The detailed procedure for measur-ing the external porosities on the MIP and NIP columns can befound in our previous study (Kim et al., 2005b). The externalporosities of the columns reported in this study are the averagevalues of the external porosities at each different temperature.The external porosity of the MIP and NIP columns were 0.368and 0.418, respectively.

3.4. Calculation of the isotherm data and isotherm modelselection

The adsorption isotherm data consist in a set of values ofthe amount of substrate (q, mmol/L) bound to the column fora series of mobile phase concentrations of the substrate (C,

1126 H. Kim et al. / Chemical Engineering Science 61 (2006) 1122–1137

mmol/L). To calculate this amount, q, from the FA data, thefollowing equation was used:

q = CVequ − V0

Va

,

where Vequ is the elution volume of the equivalent area ofthe solute, V0 is the hold-up volume and Va is the volume ofthe stationary phase. The value of Vequ of each breakthroughcurve was calculated using the equal area method (Sajonz etal., 1996a,b). The value of Va was calculated by subtracting V0from the geometrical volume of the column.

The best numerical values of the coefficients of the tri-Langmuir isotherm model were estimated by fitting the experi-mental isotherm data with weights (1/q2, where q is the exper-imentally measured amount adsorbed) to the model equations,using Marquardt–Levenbeg method. The quality of the fittingswas estimated by calculating the standard deviation of eachisotherm parameter, the Fisher parameters, and the residual sumof squares (Kim and Guiochon, in press(a); Seber, 1989).

3.5. Measurement of the band profiles

High concentration experimental band profiles of each sub-strate were recorded on the MIP and the NIP during the acqui-sition of the FA data. The injections of the large samples of thesubstrates were done from the pump, at six different concen-trations ranging between 0.1 and 30 mM.

The band profiles were recorded between 260 and 310 nmand the absorbances (mAU) were converted into concentrationunits (mM), using a second order polynomial function as cali-bration curve, obtained by minimization of the square root sumbetween the left and right sides of the following equation, us-ing n measured band profiles (with n� the polynomial degree(Kim et al., 2005a).

Cf tp =∫ +∞

0p1 × S(t) + p2 × S(t)2 dt ,

where Cf is the injected concentration of the substrates, tp isthe injection time, S(t) is the detector response, a function oftime, pi are the coefficients of the polynomial function.

4. Results and discussion

4.1. Adsorption equilibrium

The adsorption isotherm data on the NIP and on the Fmoc-L-Trp imprinted MIP for the different structural analogues ofthe template were measured by frontal analysis, using ace-tonitrile with 1% acetic acid as the mobile phase, at roomtemperature (Kim and Guiochon, in press(a)). The structuralanalogues of the template have a similar structure but dif-ferent numbers of hydroxyl groups that can interact with thefunctional 4-vinylpyridine groups of the polymers: there aretwo such functional groups in Fmoc-L-Tyr and Fmoc-L-Ser;one in Fmoc-L-Trp , Fmoc-L-Phe, and Fmoc-Gly; and none inFmoc-L-Trp(OPfp). For the substrates that have one functional

0 10 20 30 40 50 60 70

0

50

100

150

200

250

300

350

0.00 0.04 0.08 0.120

1

2

3

q s (

mM

)

C (mM)

q s (

mM

)

C (mM)

Fig. 1. Adsorption equilibrium isotherms on the non-imprinted polymerof Fmoc-L-Trp (•), Fmoc-L-Tyr (closed squares), Fmoc-L-Ser (closed trian-gle-ups), Fmoc-L-Phe (◦), Fmoc-Gly (open squares), and Fmoc-L-Trp(OPfp)(open triangle-ups). The lines represent the best-calculated tri-Langmuirisotherm for each substrate. The inset shows the adsorption isotherms of eachsubstrate in the low concentration range, between 0.005 and 0.12 mM.

group, the octanol-water partition coefficient (log Pow) (Kimand Guiochon, in press(a); log Pow,) decreases in the followingorder.

Fmoc-L-Trp (log Pow = 4.74) > Fmoc-L-Phe (log Pow =4.65) > Fmoc-Gly (log Pow = 2.53). The adsorption isothermsof the substrates on the NIP and the MIP are shown in Figs.1 and 2, respectively. The isotherm parameters for the sub-strates on the NIP and the MIP, estimated from the non-linearregression of the data to the tri-Langmuir isotherm model, aresummarized in Tables 1 and 2, respectively.

Fig. 1 shows the adsorption isotherm data for the differentsubstrates on the NIP. The symbols show the experimental data,the solid lines the curves that fit best the data to the tri-Langmuirisotherm model. The inset in this figure shows the data at thelowest concentration range (i.e., 0.005–0.12 mM) of each sub-strate. On the NIP, the amount of adsorbed substrate decreasesin the following order:

Fmoc-L-Tyr (�) > Fmoc-L-Ser (solid triangle-ups) > Fmoc-L-Trp (•) > Fmoc-L-Phe (◦) > Fmoc-Gly (open squares) >

Fmoc-L-Trp(OPfp) (open triangle-ups).A similar trend can be observed for the isotherm data for

the D-enantiomers on the MIP (see Fig. 2a). The amount ofadsorbed D-enantiomers decreases in the following order:

Fmoc-D-Tyr (squares) > Fmoc-D-Ser (triangle-ups) > Fmoc-D-Trp (◦) > Fmoc-D-Phe (triangle downs).

The adsorption isotherm data for the L-enantiomers and Glyon the MIP are shown in Fig. 2b. The adsorbed L-enantiomersdecreases in the following order:

Fmoc-L-Tyr (closed squares) > Fmoc-L-Trp (closed circles)> Fmoc-L-Ser (closed triangle-ups) > Fmoc-L-Phe (open cir-cles) > Fmoc-Gly (open squares) > Fmoc-L-Trp(OPfp) (opentriangle-ups).

H. Kim et al. / Chemical Engineering Science 61 (2006) 1122–1137 1127

0 10 20 30 40 50 60 70

0

100

200

300

400

0.00 0.04 0.08 0.12 0.160

2

4

6

q (m

M)

0 10 20 30 40 50 60

0

100

200

300

400

0.00 0.04 0.08 0.120

2

4

6

q (m

M)q

(mM

)

q (m

M)

C (mM) C (mM)

C (mM) C (mM)

(a) (b)

Fig. 2. Adsorption equilibrium isotherms on the Fmoc-L-Trp imprinted polymer of (a) Fmoc-D-Trp (closed circles), Fmoc-D-Tyr (closed squares), Fmoc-D-Ser(closed triangle-ups) and Fmoc-D-Phe (closed triangle-downs). The dotted lines represent the best-calculated tri-Langmuir isotherm for each substrate, andthe inset in the figure shows the adsorption isotherms of each substrate at the low concentration range between 0.005 and 0.12 mM. (b) Fmoc-L-Trp (closedcircles), Fmoc-L-Tyr (closed squares), Fmoc-L-Ser (closed triangle-ups), Fmoc-L-Phe (open circles). Fmoc-Gly (open squares), and Fmoc-L-Trp(OPfp) (opentriangle-ups). The solid lines represent the best-calculated tri-Langmuir isotherm for each substrate, and the inset in the figure shows the adsorption isothermsof each substrate at the low concentration range between 0.005 and 0.12 mM.

Table 1Isotherm parameters for each substrate on the Non-MIP estimated by fitting data to the Tri-Langmuir isotherm model

Substrates Isotherm parameters

qs1 (mM) b1 (mM−1) qs2 (mM) b2 (mM−1) qs3 (mM) b3 (mM−1)

Fmoc-L-Trp 524 ± 13 0.0118 ± 0.0066 69.8 ± 30 0.157 ± 0.045 0.114 ± 0.059 33.9 ± 20Fmoc-L-Tyr 457 ± 9.1 0.0222 ± 0.0017 46.9 ± 6.3 0.297 ± 0.038 1.408 ± 0.25 7.27 ± 0.95Fmoc-L-Ser 598 ± 18 0.0168 ± 0.00099 20.91 ± 2.3 0.53 ± 0.061 0.216 ± 0.086 19.8 ± 7.1Fmoc-L-Phe 439 ± 87 0.0183 ± 0.0065 31.8 ± 11 0.278 ± 0.062 0.0757 ± 0.026 47.0 ± 18Fmoc-Gly 745 ± 43 0.00887 ± 0.00094 38.9 ± 5.6 0.164 ± 0.017 0.04088 ± 0.011 53.8 ± 16Fmoc-L-Trp(OPfp) 62.0 ± 14 0.0194 ± 0.0046

The solid lines in Figs. 1 and 2, represent the best isothermfor each system. The best isotherm model was selected fromstatistical tests (using the Fisher parameters and the residuals),the results of the calculations of the affinity energy distribu-tion, and a comparison between the experimental band profilesand those calculated assuming several different isotherm mod-els (i.e., the Langmuir, the bi-, the tri-, and the tetra-Langmuirisotherm models) (Kim and Guiochon, in press(a)). After com-pletion of the selection process, it was found that the bestisotherm model for the different substrates on the NIP and theMIP was the tri-Langmuir isotherm model, although the pos-sibility of the existence of one more type of sites cannot becompletely excluded (Kim and Guiochon, in press(a)). Therewas only one exception, Fmoc-L-Trp(OPfp) was found to ex-hibit no significant affinity for either the NIP or the MIP. Inthis cases, the simple Langmuir isotherm model was the bestisotherm model.

The best isotherm parameters (Tables 1 and 2) show thatthe retention of the substrates on the NIP increases with in-creasing number of functional groups and hydrophobicity ofthe substrates, the former having a larger influence on the re-tention. A similar retention behavior can be observed for the D-

enantiomers on the MIP. In contrast, the “imprinting process”of Fmoc-L-Trp on the MIP overcomes the stronger interactionswith the substrates which have larger number of −OH groups,as indicated by the higher overall affinity for Fmoc-L-Trp versusthat for Fmoc-L-Ser on the MIP. Comparing the isotherm pa-rameter on the highest energy type of sites shows that the affin-ity for Fmoc-L-Trp is higher than that for Fmoc-L-Tyr (20%)while the overall affinity for Fmoc-L-Tyr is slightly higher thanthat for Fmoc-L-Trp (3%). These changes of the affinity on theMIP with different substrates are primarily due to correspond-ing changes in the density of the highest energy sites (Kim andGuiochon, in press(a)).

4.2. Intraparticle mass transfer kinetics

The NIP and the MIP used for this study were made by bulkpolymerization of pre-polymerization mixtures in the presenceof acetonitrile as a pore-forming solvent. A previous study hasreported that the imprinted polymers (composed of EGDMAas a main polymer matrix) made with acetonitrile as a solventare mesoporous materials, with a pore volume of 0.60 ml/g and

1128 H. Kim et al. / Chemical Engineering Science 61 (2006) 1122–1137

Tabl

e2

Isot

herm

para

met

ers

for

each

subs

trat

eon

the

MIP

estim

ated

byfit

ting

data

toth

eT

ri-L

angm

uir

isot

herm

mod

el

Subs

trat

esL-e

nant

iom

ers

D-e

nant

iom

ers

qs1

b1

qs2

b2

qs3

b3

qs1

b1

qs2

b2

qs3

b3

(mM

)(m

M−1

)(m

M)

(mM

−1)

(mM

)(m

M−1

)(m

M)

(mM

−1)

(mM

)(m

M−1

)(m

M)

(mM

−1)

Fmoc

-L-T

rp55

0.2

±17

0.03

13±

0.00

2323

.1±

3.6

0.88

4±

0.13

0.70

54±

0.05

789

.8±

1052

6±

130.

0344

±0.

0025

10.4

±1.

91.

270

±0.

240.

128

±0.

036

75.8

±19

Fmoc

- L-T

yr56

2±

170.

0353

±0.

0025

32.7

±3.

81.

004

±0.

110.

351

±0.

037

148

±18

623

±17

0.02

89±

0.00

2138

.7±

4.8

0.63

8±

0.07

20.

3607

±0.

0704

41.2

±7.

2Fm

oc- L

-Ser

696

±13

0.02

23±

0.00

083

25.2

±1.

70.

731

±0.

044

0.14

3±

0.01

215

8±

2176

4±

140.

0197

±0.

0007

829

.5±

2.2

0.56

7±

0.03

80.

178

±0.

026

57.1

±9.

2Fm

oc-L

-Phe

496

±25

0.02

901

±0.

0026

19.0

2±

2.6

0.75

2±

0.08

40.

165

±0.

015

116

±12

496

±17

0.02

87±

0.00

159.

81±

1.07

0.96

07±

0.09

20.

0410

6±

0.00

9393

.4±

20Fm

oc-G

ly75

4±

340.

015

±0.

0012

12.7

±3.

00.

553

±0.

120.

106

±0.

027

59.5

±15

Fmoc

- L-T

rp(O

Pfp)

102.

4±

250.

0177

±0.

0045

a surface area of 256 m2/g (Sellergren and Shea, 1993). Inthis study, we used these mesoporous NIP and MIP to inves-tigate the intraparticle mass transfer kinetics of the differentsubstrates by comparing experimental band profiles with thosecalculated using the lumped POR. The experimental band pro-files were acquired for the different substrates on the NIP andthe MIP with sample concentrations between 0.1 and 50 mM.These profiles were compared with those calculated using thePOR model. Tables 3 and 4 list the parameters necessary toperform these calculations for the substrates on the NIP andthe MIP, respectively. These parameters are the total porosities(�t ), the external porosities (�e), the internal porosities (�p) ofthe columns, their tortuosities (�), the molecular diffusion co-efficients of the substrates in the bulk phase (Dm), and the axialdispersion coefficient (DL).

To interpret the overall mass transfer coefficient (ki), we as-sume that (1) the adsorption/desorption kinetics is fast; (2) theexternal mass transfer resistance (1/kext) is negligible; and (3)pore diffusion (Dp in kint) is the dominant mass transfer pro-cess for all the substrates in the packing materials used. Forthe imprinted polymers, recent publications show that the intra-particle mass transfer is the dominant contribution to the over-all mass transfer, not the external mass transfer nor the adsorp-tion/desorption kinetics on the adsorption sites (Sajonz et al.,1998; Miyabe and Guiochon, 2000a). In this case, the theoret-ical effective diffusivity, given in Eqs. (4) and (5) simplifies tothe following equation:

Deff = �pDp

�, (14)

the overall mass transfer coefficient can then be expressed as

ki = kint = 10Deff

dp

= 10(�pDp)

�. (15)

These equations were used to calculate the peak profiles ofthe substrates studied, using the POR model. The calculatedband profiles were compared to the experimental profiles.Examples are shown in Fig. 3, comparing experimental andcalculated peak profiles for Fmoc-L-Trp(OPfp) (Fig. 3a), Fmoc-Gly (Fig. 3b), and Fmoc-L-Tyr (Fig. 3c) on the NIP. For Fmoc-L-Trp(OPfp), which has only one type of adsorption sites onboth polymers and exhibits no selective interactions (see Tables1 and 2), there is a good agreement between the experimentalband profiles and those calculated with a constant value ofthe pore diffusion coefficient (Dp) in the whole concentrationrange, between ca. 0.1 and 17 mM (see Fig. 3a). In contrast,for the other substrates which show several types of adsorptionsites, hence a considerable degree of selective affinity for thepolymers (see Tables 1 and 2), the same good agreement be-tween the experimental and the calculated band profiles cannotbe obtained if a constant value of Dp is used for widely differ-ent concentrations (i.e., for 0.1 and 50 mM, as shown in Fig. 3band c). The best Dp value is the one that gives the best agree-ment between the experimental and the calculated profiles. Forall these substrates, this value decreases with increasing con-centration of the injected substrate. Similar observations are

H. Kim et al. / Chemical Engineering Science 61 (2006) 1122–1137 1129

Table 3Values of parameters for the substrates on the NIP used in the POR model

Substrate �t *1 �e*2 �p*3 Tortuosity*4 Dm*5 × 10−4 kext

*6 DL*7

(cm2/ min) (cm/min) (cm2/ min)

Fmoc-Trp 0.780 0.418 0.622 3.053 6.48 1.65 0.0484Fmoc-Tyr 0.780 0.418 0.622 3.053 6.27 1.62 0.0493Fmoc-Ser 0.780 0.418 0.622 3.053 7.25 1.78 0.045Fmoc-Phe 0.780 0.418 0.622 3.053 6.69 1.69 0.0474Fmoc-Gly 0.780 0.418 0.622 3.053 7.82 1.87 0.0428Fmoc-Trp(OPfp) 0.780 0.418 0.622 3.053 5.36 1.46 0.0541

∗1�1 total porosity.∗2�e external porosity.∗3�p internal porosity = (�t − �e)/(1 − �e).∗4Tortuosity = (2 − �p)2/�p .∗5Molecular diffusion coefficient of the solute in the mobile phase (see Eq. (10) in Theory section).∗6External mass transfer coefficient (see Eq. (8) in Theory section).∗7Dispersion coefficient (see Eq. (11) in Theory section).

Table 4Values of parameters used for the substrates on the MIP in the POR model

Substrate �t *1 �e*2 �p*3 Tortuosity*4 Dm*5 × 10−4 kext

*6 DL*7

(cm2/ min) (cm/min) (cm2/ min)

Fmoc-Trp 0.759 0.368 0.619 3.081 6.48 1.88 0.0520Fmoc-Tyr 0.759 0.368 0.619 3.081 6.27 1.84 0.0531Fmoc-Ser 0.759 0.368 0.619 3.081 7.25 2.023 0.0483Fmoc-Phe 0.759 0.368 0.619 3.081 6.69 1.92 0.0509Fmoc-Gly 0.759 0.368 0.619 3.081 7.82 2.13 0.0458Fmoc-Trp(OPfp) 0.759 0.368 0.619 3.081 5.36 1.65 0.0585

∗1�1 total porosity.∗2�e external porosity.∗3�p internal porosity = (�t − �e)/(1 − �e).∗4Tortuosity = (2 − �p)2/�p .∗5Molecular diffusion coefficient of the solute in the mobile phase (see Eq. (10) in Theory section).∗6External mass transfer coefficient (see Eq. (8) in Theory section).∗7Dispersion coefficient (see Eq. (11) in Theory section).

Fig. 3. Comparison of experimental and calculated peak profiles using pore-diffusion model on the non-imprinted polymer of: (a) Fmoc-L-Trp(OPfp) with porediffusion coefficient, Dp = 3.811 × 10−5 ± 2.1 × 10−1 (cm2/ min). (b) Fmoc-Gly with pore diffusion coefficient, Dp = 7.4 × 10−5 (cm2/ min) estimated fromthe peak at the highest concentration. (c) Fmoc-L-Tyr with pore diffusion coefficient, Dp = 5.0 × 10−5 (cm2/ min) estimated from the peak at the highestconcentration. The y-axis is normalized by dividing the elute concentration by the injected concentration of the samples. The injection time was equal to 1 minand the inlet concentrations for Fmoc-L-Trp(OPfp) were 0.0962, 0.192, 1.73, 3.46, 8.46, and 16.9 mM (peaks from right to left); the inlet concentrations forFmoc-Gly were 0.180 and 67.1 mM (peaks from right to left); the inlet concentrations for Fmoc-L-Tyr were 0.236 and 50.76 mM (peaks from right to left).

1130 H. Kim et al. / Chemical Engineering Science 61 (2006) 1122–1137

Fig. 4. Comparison of experimental and calculated peak profiles using pore-diffusion model on the Fmoc-L-Trp imprinted polymer of: (a) Fmoc-L-Trp(OPfp)with pore diffusion coefficient, Dp = 2.808 × 10−5 ± 1.9 × 10−7 (cm2/ min). (b) Fmoc-D-Tyr with pore diffusion coefficient, Dp = 5.0 × 10−5 (cm2/ min)

estimated from the peak at the highest concentration. (c) Fmoc-L-Tyr with pore diffusion coefficient, Dp = 4.8 × 10−5 (cm2/ min) estimated from the peak atthe highest concentration. The y-axis is normalized by dividing the elute concentration by the injected concentration of the samples. The injection time wasequal to 1 min and the inlet concentrations for Fmoc-L-Trp(OPfp) were 0.02305, 0.117, 0.932, 1.87, 8.27, and 17.0 mM (peaks from right to left); the inletconcentrations for Fmoc-D-Tyr were 0.126 and 49.6 mM (peaks from right to left); the inlet concentrations for Fmoc-L-Tyr were 0.125 and 53.0 mM (peaksfrom right to left).

made for the MIP. Fig. 4 compares the experimental and cal-culated band profiles for Fmoc-L-Trp(OPfp) (Fig. 4a), Fmoc-D-Tyr (Fig. 4b), and Fmoc-L-Tyr (Fig. 4c) on the MIP. Usinga constant value of Dp over the concentration range between0.1 and 17 mM for Fmoc-L-Trp(OPfp) provides a good agree-ment between experimental and calculated band profiles. Notethat the best value of Dp for Fmoc-L-Trp(OPfp) is 26% largeron the NIP than on the MIP, in agreement with the porosity ofthe NIP being higher than that of the MIP (see Tables 3 and4). On the other hand, a good agreement between the experi-mental and the calculated band profiles could not be obtainedwith a constant value of Dp in a wide concentration range (ca.0.1–50 mM) for the substrates which exhibit a considerable se-lective affinity for the MIP.

The decrease of the pore diffusion coefficient with increasingsubstrate concentration indicates that surface diffusion domi-nates the mass transfer process in the polymers. Returning toEq. (5), we see that if surface diffusion plays the dominant rolein mass transfer through the particles, we have

Deff = (1 − �p)Ds

q

C, (16)

ki = kint = 10(1 − �p)DsqC

dp

(17)

if we assume that the driving force for surface diffusion is thegradient of the chemical potential.

Using this surface diffusion model in the POR model, we canoptimize the surface coefficient of each substrate on each poly-mer to obtain the best possible agreement between calculatedand experimental band profiles. Fig. 5a shows the plot of thesurface diffusion coefficient (Ds) versus the concentration ofeach substrate injected on the NIP. Fig. 5b and c show the sameplot for the D-enantiomers and Gly, and the L-enantiomers, re-spectively, on the MIP. As on the NIP, the Ds values of the D-enantiomers and Gly on the MIP are independent of their con-centration, except that a slight dependency of Ds is observed

for Fmoc-D-Phe. Figs. 6 and 7 compare the experimental andcalculated band profiles of the different substrates on the NIPand of the D-enantiomers on the MIP, respectively. We usedEqs. (16) and (17) and, using a constant value of Ds for eachsubstrate, we obtained a good agreement between the experi-mental and the calculated band profiles. The optimized surfacediffusivities of the substrates are summarized in Table 5 for theL-enantiomers on the NIP and in Table 6 for the D-enantiomersand Gly on the MIP. These results confirm that surface diffu-sion is the main contribution to the mass transfer mechanismfor the L-enantiomers on the NIP and for the D-enantiomers onthe MIP, and that the driving force for surface diffusion is thegradient of the surface concentration.

In contrast to the results obtained for all the substrates onthe NIP and for the substrates that have the stereochemistryopposite to that of the template on the MIP, a strong dependencyof Ds on the concentration of each L-enantiomer is observed inFig. 5c. Ds increases rapidly with increasing concentration ofeach L-enantiomer. This concentration dependency of Ds can bemodeled by the heterogeneous surface diffusion model (Miyabeand Guiochon, 2000a; Kim et al., 2005a). In this model, surfacediffusion is an activated process, the temperature dependenceof which is accounted for by the Arrhenius equation:

Ds = Ds,0 exp

(−Es

RT

), (18)

where Ds,0 is the surface diffusivity at zero energy level, Es isits activation energy, T is the temperature in K and R is theuniversal gas constant.

The activation energy (Es) is assumed to be linearly corre-lated with the isosteric heat of adsorption (Qst), with

ES = �(−Qst), (19)

where � is an empirical parameter. Combining Eqs. (18) and(19) gives the surface diffusion coefficient as a function of the

H. Kim et al. / Chemical Engineering Science 61 (2006) 1122–1137 1131

0 10 20 30 40 50 60 702

4

6

8

10

12

14

Fmoc-Gly

Fmoc-L-PheFmoc-L-Trp

Fmoc-L-SerFmoc-L-Tyr

DS (

cm2 /

min

)*10

-6

-10 0 10 20 30 40 50 60 700.8

1.2

1.6

2.0

2.4

2.8

3.2

3.6

4.0

4.4

4.8

5.2

5.6

6.0

Fmoc-Gly

Fmoc-D-Phe

Fmoc-D-Trp

Fmoc-D-Ser

Fmoc-D-Tyr

Ds

(cm

2 /m

in)*

10-6

(cm

2 /m

in)

C (mM)

-10 0 10 20 30 40 50 60 700.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

Fmoc-L-Phe

Fmoc-L-Trp

Fmoc-L-Ser

Fmoc-L-Tyr

DS (

cm2 /

min

)*10

-6

(b)

(c)

(a) C (mM)

-10

C (mM)

Fig. 5. Plots of surface-diffusion coefficient (DS) of: (a) Each substrate (as indicated on the graph) on the non-imprinted polymer. (b) Each D-enantiomer andFmoc-Gly (as indicated on the graph) on the Fmoc-L-Trp imprinted polymer. (c) Each L-enantiomer (as indicated on the graph) on the Fmoc-L-Trp imprintedpolymer. The driving force for the surface diffusion was assumed to be the chemical potential. The same scale for the y-axis was used for each graph tocompare the changes in the surface diffusion coefficient with the concentrations.

isosteric heat of adsorption:

Ds = Ds,0 exp

(−�(−Qst)

RT

)= Ds,0 exp

(−�

T

(−Qst

R

)).

(20)

The isosteric heat of adsorption is determined at constantamount adsorbed (q), using the following equation:

−Qst

R=

[d(ln C)

d(1/T )

]q=constant

. (21)

The value of ln C at constant q value, at each different tem-perature, was calculated from the best parameters of the tri-Langmuir isotherm, for each L-enantiomer on the MIP, fromthe isotherm data measured at different temperatures. Qst wasderived from the average slope of the lines obtained (Kim andGuiochon, in press(b)). The exponential dependency of theisosteric heat of adsorption for each L-enantiomer adsorbed on

the MIP on the amount adsorbed (q) (Fig. 8) was correlated byusing a three-term exponential decay function (Eq. (22)).

(−Qst)

R= p1 + p2 exp(−p3q) + p4 exp(p5q). (22)

Fig. 8 illustrates also the validity of the best estimates of theparameters, since the solid lines derived from these parametersfor each L-enantiomer on the MIP are in excellent agreementwith the experimental data (symbols). The numerical values ofthe parameters (i.e., p1, p2, p3, and p4 in Eq. (22)) are givenin Table 7.

To calculate the surface diffusion coefficient, which indi-rectly incorporates the effects of the surface heterogeneity,we substituted Eq . (22) into Eq. (20), giving the following

1132 H. Kim et al. / Chemical Engineering Science 61 (2006) 1122–1137

Fig. 6. Comparison of experimental and calculated peak profiles on the non-imprinted polymer of: (a) Fmoc-L-Tyr with DS = 2.29 × 10−6 (cm2/ min). (b)Fmoc-L-Ser with DS = 3.77 × 10−6 (cm2/ min). (c) Fmoc-L-Trp with DS = 3.48 × 10−6 (cm2/ min). (d) Fmoc-L-Phe with DS = 4.29 × 10−6 (cm2/ min). (e)Fmoc-Gly with DS = 5.26 × 10−6 (cm2/ min). The y-axis is normalized by dividing the elute concentration by the injected concentrations of the samples. Theinjection time was equal to 1 min, and the inlet concentrations for Fmoc-L-Tyr were 0.251, 0.5207, 2.51, 5.027, 25.4, and 50.76 mM (peaks from right to left);the inlet concentrations for Fmoc-L-Ser were 0.153, 0.3064, 3.053, 6.108, 27.5, and 55.1 mM (peaks from right to left); the inlet concentrations for Fmoc-L-Trpwere 0.125, 0.251, 2.39, 4.77, 21.1 and 42.2 mM (peaks from right to left); the inlet concentrations for Fmoc-L-Phe were 0.129, 0.258, 1.26, 2.53, 9.92 and19.8 mM (peaks from right to left); the inlet concentrations for Fmoc-Gly were 0.180, 0.360, 3.43, 6.87, 33.6, and 67.1 mM (peaks from right to left).

equation:

Ds(Qst)

= Ds,0 exp

(−�

T(p1+p2 exp(−p3×q)+p4 exp(−p5q))

).

(23)

The surface diffusion coefficient so defined is introduced intoEq. (16), giving the effective diffusivity, and into Eq. (17), giv-ing the overall mass transfer coefficient, in order to calculatethe band profiles of each L-enantiomer on the MIP, at roomtemperature. The parameters Ds,0 and � were optimized, inorder to obtain the best possible agreement between experi-mental and calculated band profiles. The best values of Ds,0and � for each L-enantiomer on the MIP are listed in Table 8.Fig. 9 compares the experimental and calculated band profilesfor each L-enantiomer on the MIP. A good agreement is ob-served between these band profiles in all cases.

Fig. 10 compares the surface diffusivities calculated for theL-enantiomers on the NIP (Fig. 10a), for the D-enantiomerson the MIP (Fig. 10b), and for the L-enantiomers on the MIP(Fig. 10c). The surface diffusivities for the L-enantiomers on theNIP and those for the D-enantiomers on the MIP do not dependon the amount adsorbed (q). On the other hand, the surfacediffusivities for the L-enantiomers on the MIP increase withincreasing q value, due to the energetic surface heterogeneity

for the L-enantiomers on the MIP. The surface diffusivity ofeach substrate decreases in the following order:

L-enantiomers on the NIP > D-enantiomers on the MIP >

L-enantiomers on the MIP.For example, the surface diffusivities for Fmoc-L-Trp on the

NIP, and Fmoc-D-Trp and Fmoc-L-Trp on the MIP were 3.48,1.27, and between 0.8 and 1.24 × 10−6 cm2/ min, respectively.The surface diffusivity of the different substrates studied onthese polymers increases with decreasing overall affinity ofeach substrate with the polymers (see Fig. 10). To quantitativelytest our assumption that the external mass transfer resistance(1/kext) is negligible compared to the internal mass transferresistance (1/kint), we first calculated the values of kint usingEq. (17) with the surface diffusivities reported on Tables 5 and6 for the substrates on the NIP and D-enantiomers on the MIP.The surface diffusivities for L-enantiomers on the MIP can beestimated from Eq. (23) using each optimized value reportedon Tables 7 and 8. The average value of q/C was used in Eq.(17) to calculate kint. The results of these calculations showthat the values of kext are more than 10 times larger that thoseof kint for the substrates on the polymers, confirming that theexternal mass transfer resistance can be neglected. For example,kint values for Fmoc-L-Trp on the NIP and those for Fmoc-D-Trp on the MIP, and those for Fmoc-L-Trp on the MIP were0.0515, 0.0771, and 0.04095 cm/min, respectively. Comparison

H. Kim et al. / Chemical Engineering Science 61 (2006) 1122–1137 1133

Fig. 7. Comparison of experimental and calculated peak profiles on the Fmoc-L-Trp imprinted polymer of: (a) Fmoc-D-Tyr with DS =1.064×10−6 (cm2/ min).(b) Fmoc-D-Ser with DS =1.783×10−6 (cm2/ min). (c) Fmoc-D-Trp with DS =1.27×10−6 (cm2/ min). (d) Fmoc-D-Phe with DS =2.29×10−6 (cm2/ min).(e) Fmoc-Gly with DS = 2.56 × 10−6 (cm2/ min). The y-axis is normalized by dividing the elute concentration by the injected concentration of the samples.The injection time was equal to 1 min, and the inlet concentrations for Fmoc-D-Tyr were 0.126, 0.253, 2.50, 4.99, 24.8, and 49.6 mM (peaks from right to left);the inlet concentrations for Fmoc-D-Ser were 0.157, 0.315, 3.068, 6.14, 27.6, and 55.1 mM (peaks from right to left); the inlet concentrations for Fmoc-D-Trpwere 0.288, 0.481, 2.403, 4.24, 21.2 and 42.4 mM (peaks from right to left); the inlet concentrations for Fmoc-D-Phe were 0.133, 0.265, 2.47, 4.95, 9.92 and19.8 mM (peaks from right to left); the inlet concentrations for Fmoc-Gly were 0.167, 0.333, 3.37, 6.75, 33.7, and 67.4 mM (peaks from right to left).

Table 5Best values of the surface diffusion coefficient (Ds(q/c)) and overall affinitycalculated from the Tri-Langmuir isotherm parameters for each substrate onthe Non-MIP

Substrates (qb)t Ds (cm2/ min)

Fmoc-L-Tyr 34.3 ± 2.8 2.29 × 10−6 ± 1.2 × 10−8

Fmoc-L-Ser 25.4 ± 2.3 3.77 × 10−6 ± 1.4 × 10−8

Fmoc-L-Trp 21.006 ± 7.05 3.48 × 10−6 ± 2.9 × 10−8

Fmoc-L-Phe 20.43 ± 5.0 4.29 × 10−6 ± 2.2 × 10−8

Fmoc-Gly 15.2 ± 1.4 5.26 × 10−6 ± 2.6 × 10−8

Table 6Best values of the surface diffusion model (surface diffusion coefficient (Ds))and overall affinity calculated from the Tri-Langmuir isotherm parameters forD-enantiomers on the MIP

Substrates (qb)t Ds (cm2/ min)

Fmoc-D-Tyr 57.6 ± 4.5 1.064 × 10−6 ± 7.1 × 10−9

Fmoc-D-Ser 41.9 ± 1.9 1.78 × 10−6 ± 6.2 × 10−9

Fmoc-D-Trp 41.005 ± 4.0 1.27 × 10−6 ± 7.4 × 10−9

Fmoc-D-Phe 27.5 ± 1.7 2.29 × 10−6 ± 7.2 × 10−9

Fmoc-Gly 24.6 ± 2.6 2.56 × 10−6 ± 8.9 × 10−9

of these values to kext values for Fmoc-Trp on the NIP andthe MIP (1.65 and 1.88 cm/min as reported on Tables 3 and 4)

0 50 100 150 200 2501900

2000

2100

2200

2300

2400

2500

2600

-Qst

/R

q (mM)

Fig. 8. The dependency of isosteric heat of adsorption, (−Qst/R), on surfaceconcentration (q) for Fmoc-L-Trp on the MIP (closed circles), for Fmoc-L-Tyr(closed squares), for Fmoc-L-Ser (closed triangle-ups), for Fmoc-L-Phe (opencircles) on the Fmoc-L-Trp MIP. The solid lines represent best-fit parameterscalculated using Eq. (23), and the best parameters are reported in Table 7.

shows that the corresponding kint values for Fmoc-Trp on thepolymers are at least 20 times less that kext values.

1134 H. Kim et al. / Chemical Engineering Science 61 (2006) 1122–1137

Table 7Values of parameters p1, p2, p3, p4 and p5 for Eq. (23)

Substrate p1 p2 p3 p4 p5

Fmoc-L-Trp 2103 ± 0.57 153 ± 15 1.79 ± 0.15 338 ± 0.92 0.0339 ± 0.00025Fmoc-L-Tyr 2230 ± 0.57 −54.4 ± 7.6 0.379 ± 0.084 316 ± 3.4 0.0349 ± 0.00049Fmoc-L-Ser 2130 ± 0.27 128 ± 1.8 2.31 ± 0.047 93.09 ± 0.49 0.0322 ± 0.00048Fmoc-L-Phe 2270 ± 14 24.3 ± 6.3 0.0166 ± 0.026 291 ± 12 0.137 ± 0.0064

Table 8Values for parameters for Eq. (24) for L-enantiomers on the MIP

Substrates (qbt ) (qb)3 � Dso (cm2/ min)

Fmoc-L-Trp 100.99 ± 4.7 63.3 ± 2.0 0.9032 ± 0.0024 0.001094 ± 1.8 × 10−5

Fmoc-L-Tyr 104.6 ± 5.6 51.9 ± 1.3 0.87 ± 0.0035 0.001021 ± 2.5 × 10−5

Fmoc-L-Ser 56.5 ± 1.9 22.6 ± 0.56 0.636 ± 0.0026 1.50 × 10−4 ± 2.5 × 10−6

Fmoc-L-Phe 47.8 ± 2.9 19.1 ± 0.36 0.480 ± 0.0029 7.058 × 10−5 ± 1.5 × 10−6

Fig. 9. Comparison of experimental and calculated peak profiles, calculated using Eq. (24), on the Fmoc-L-Trp MIP of: (a) Fmoc-L-Tyr. (b) Fmoc-L-Trp.(c) Fmoc-L-Ser. (d) Fmoc-L-Phe. The y-axis is normalized by dividing the elute concentration with the injected concentration of the samples. The injectiontime was equal to 1 min and the inlet concentrations for Fmoc-L-Tyr were 0.125, 0.250, 2.52, 5.040, 25.2, and 50.3 mM (peaks from right to left); theinlet concentrations for Fmoc-L-Trp were 0.117, 0.238, 2.38, 4.75, 21.2, and 42.5 mM (peaks from right to left); the inlet concentrations for Fmoc-L-Serwere 0.170, 0.339, 3.068, 6.14, 27.6 and 55.1 mM (peaks from right to left); the inlet concentrations for Fmoc-L-Phe were 0.137, 0.274, 2.63, 5.25, 10.33 and20.67 mM (peaks from right to left). The best values of parameters used to calculate these peak profiles are summarized in Table 8.

H. Kim et al. / Chemical Engineering Science 61 (2006) 1122–1137 1135

0 10 20 30 40 50

0.000001

0.000002

0.000003

0.000004

0.000005

0.000006

0.000007

Fmoc-Gly ((qb)t = 15.2)

Fmoc-L-Phe ((qb)t = 20.43)

Fmoc-L-Trp ((qb)t = 21.006)

Fmoc-L-Ser ((qb)t = 25.4)

Fmoc-L-Tyr ((qb)t = 34.3)

Ds

(cm

2 /m

in)

Ds

(cm

2 /m

in)

q (mM) q (mM)

0 10 20 30 40 50

q (mM)

0 10 20 30 40 500.0000005

0.0000010

0.0000015

0.0000020

0.0000025

0.0000030

Fmoc-Gly ((qb)t = 24.6)

Fmoc-D-Phe ((qb)t = 27.5)

Fmoc-D-Ser ((qb)t = 41.9)

Fmoc-D-Trp ((qb)t = 41.005)

Fmoc-D-Tyr ((qb)t = 57.6)

0.0000005

0.0000010

0.0000015

0.0000020

0.0000025

0.0000030

Fmoc-L-Trp ((qb)t = 100.99)

Fmoc-L-Tyr ((qb)t = 104.6)

Fmoc-L-Ser ((qb)t = 56.5)

Fmoc-L-Phe ((qb)t = 47.8)

Ds

(Qst

) cm

2 /m

in

(a) (b)

(c)

Fig. 10. The surface diffusion coefficients for: (a) L-enantiomers on the NIP. (b) D-enantiomers and Fmoc-Gly on the Fmoc-L-Trp MIP. (c) L-enantiomers onthe Fmoc-L-Trp MIP. In each figure, the corresponding substrate and its overall affinity on the polymers is indicated. Note that the surface diffusion coefficientsincrease with increasing overall affinity of the substrate on the polymers.

In summary, in agreement with results reported for the dif-ferent substrates on packing materials used in reversed phasechromatography (Miyabe and Guiochon, 2000b), our resultsshow that surface diffusion on the polymers is a mass transferphenomenon of the adsorbate molecules that takes place in theadsorbed state, and that an energy gain is required for the ad-sorbed substrate to jump from one adsorption site to anotherone. This gain is proportional to the affinity energy between thesubstrate and the adsorbent. For the L-enantiomers on the MIP,due to the energetic heterogeneity of the surface, the energyrequired depends on the concentration of substrate adsorbed.This explains why surface diffusivity increases with increasingconcentration adsorbed. On the other hand, the surface diffu-sivities of the L-enantiomers on the NIP and those of the D-enantiomers on the MIP are independent of the concentration ofadsorbed substrate, due to the relatively energetic homogene-ity of the surface toward them. Finally, we note that a previousstudy also reported that surface diffusion dominates the masstransfer kinetics of L- and D-phenylalanine anilide (PA) on L-PAimprinted polymers. In this case, the polymers were preparedusing chloroform as a pore-forming solvent in a EGDMA poly-mer matrix (total porosity, 0.613, external porosity, 0.40, inter-

nal porosity, 0.36, hence, phase ratio 0.631) (Miyabe and Guio-chon, 2000a,b). Considering the widely different pore structuresof the polymers used in this study (internal porosity, 0.618 andsurface area 256 m2/g) and in the previous study, it seems thatthe pore structure of the imprinted polymers has no significantinfluence on the mass transfer mechanism of the substrates onthe polymers. However, a larger amount of quantitative data onthe mass transfer kinetics on different types of imprinted poly-mers is necessary to confirm this speculation, particularly inthis case as other characteristics of this MIP, reported earlierelsewhere (Sellergren and Shea, 1993) might be inconsistentwith those stated above, a fact that is probably explained bythe former being measured on a column impregnated with ace-tonitrile (Miyabe and Guiochon, 2000a,b) while the latter weremeasured on the dry MIP (Sellergren and Shea, 1993).

5. Conclusion

The good agreement achieved between the experimental andthe calculated band profiles for each system studied confirmsthat surface diffusion is the dominant contribution to the overallmass transfer kinetics of those of the substrates studied that

1136 H. Kim et al. / Chemical Engineering Science 61 (2006) 1122–1137

exhibit a considerable selective affinity toward the MIP. Thesurface diffusion coefficients of the L-enantiomers on the NIPand those of the D-enantiomers on the MIP do not depend onthe amount adsorbed on the polymers.

However, in contrast, the surface diffusion coefficients (Ds)of the L-enantiomers increase with increasing amounts adsorbedon the MIP. This dependency of Ds on q is fairly well modeledby incorporating the effect of the surface heterogeneity into thesurface diffusion coefficients, using the dependency of the isos-teric heat of adsorption on the adsorbed amount. The surfacediffusion coefficients of each substrate is larger on the NIP thanon the MIP and it is larger on the MIP for the D-enantiomersthan for their L-enantiomers. This order coincides with the de-creasing order of overall affinity of each substrate for the poly-mers (i.e., the affinity of the substrates is higher for the MIPthan for the NIP and the affinity for the MIP is higher for the L-than for the D-enantiomers). Finally, the surface diffusivity ofthe different substrates increases with decreasing overall affin-ity of the substrate for each polymer. These results confirm themechanism of surface diffusion reported earlier (Miyabe andGuiochon, 2001).

Finally, we note that our results show that the unsymmet-rical peaks observed at low samples sizes with MIP columnsare most probably not due to a slow mass transfer kinetics inthe porous particles but to the heterogeneity of the surface ofthese adsorbents. The problem is the same as that recently il-lustrated in a study of the retention mechanism of amitriptylineand nortriptyline on several RPLC columns (packed with end-capped C18 bonded silica and eluted with aqueous solutions ofmethanol) (Gritti and Guiochon, 2005). This surface has twotypes of adsorption sites with a difference in their adsorptionenergies of 5 kJ/mole, too small to be explained by residualsilanols. When the surface of an adsorbent is heterogeneousand the concentration of a retained compound increases, itsmolecules are adsorbed first on the sites of highest adsorptionenergy. As long as the loading factor, Lf , or ratio of the sam-ple size to the column saturation capacity is small, the peaksobserved are Gaussian. When the loading factor exceeds a fewtenth of one percent, the band profile becomes unsymmetrical,Langmuirian in the case of a convex upward isotherm, its frontis a shock later, its rear is a diffuse boundary (Guiochon et al.,2005). The elution time of the front shock layer decreases fromk′

0 = F∑n

1 ai (with F , phase ratio, n number of different typesof sites on the surface, and ai adsorption constant on the sitesof type i) to k′

1 = ∑n−1i ai while the sites of type n become

saturated and the molecules of the sample begin to populatethe sites of type n−1 (Gritti and Guiochon, 2005; Guiochon etal., 2005). When the saturation capacity of the highest energysites is small, which is often the case, this phenomenon takesplace at very low sample sizes, possibly in a size range thatis lower than the detection limit, in which case symmetricalpeaks are never observed. In the case of the MIP studied here,for Fmoc-Trp, k′

0 = 32.1, k′1 = 12.0; the saturation capacity of

the highest energy sites (type 3 sites, Table 2) is 1.16 �mole.Hence the column would begin to exhibit an overload be-havior for sample sizes exceeding a nanomole or 0.5 �g ofFmoc-Trp.

Notation

ap ratio of absorbant particle external surface area tovolume

b association constantBi Biot number (kextdp/2Deff)

C concentration in the mobile phaseCp average concentration in the stagnant fluid phase

contained inside poresCf injected concentration of substratesdp equivalent particle diameterDm diffusion coefficientDeff effective (or inside-pore) diffusion coefficientDp pore diffusivityDs surface diffusivityDL dispersion coefficientki overall mass transfer coefficientkext external mass transfer coefficientkint internal mass transfer coefficientL column lengthM molecular massPe Peclet number (uL/DL�e)q concentration of the solute in the stationary phaseqs saturated amount absorbedRe Reynolds number (�udp/�)Rp particle radiusSc Schmidt number (�/�Dm)Sh Sherwood number (kextapL�e/u)S(t) the detector responset timetp injection timeT temperatureu average superficial velocity of the mobile phaseVA molar volumeVequ elution volume of the equivalent area of a soluteV0 hold-up volumeVa volume of the stationary phasez longitudinal distance along the column

Greek letters

� association factor

� tortuosity parameter�e external porosity�p internal porosity� viscosity� fluid density

Subscripts

f inlet value

i component indexs solid phase

Superscript

0 initial value

H. Kim et al. / Chemical Engineering Science 61 (2006) 1122–1137 1137

Acknowledgements

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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