MODELING OF ION-EXCLUSION AND VACANCY ION-EXCLUSION CHROMATOGRAPHY ON A STRONGLY ACIDIC CATION-EXCHANGE RESIN IN THE H + FORM

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1 ACTA CHROMATOGRAPHICA, NO. 15, 2005 MODELING OF IONEXCLUSION AND VACANCY IONEXCLUSION CHROMATOGRAPHY ON A STRONGLY ACIDIC CATIONEXCHANGE RESIN IN THE H + FORM K. Kaczmarski 1, *, M. Mori 2, B. Głód 3, T. Kowalska 4, and K. Tanaka 2 1 Faculy of Chemisry, Technical Universiy of Rzeszów, Al. Powsańców Warszawy 6, Rzeszów, Poland 2 Naional Insiue of Advanced Indusrial Science and Technology a Seo, 110, Nishiibaracho, Seo, , Japan 3 Mea and Fa Research Insiue, Jubilerska 4, Warsaw, Poland 4 Insiue of Chemisry, Silesian Universiy, 9 Szkolna Sree, Kaowice, Poland ABSTRACT Ionexclusion chromaography (IEC) can someimes be used for separaion of he weak acids using pure waer as mobile phase. Characerisic leading (i.e. fronally ailing) peaks are obained and reenion depends on he concenraion of solues. I was recenly shown ha his order could be reversed. In vacan ion exclusion chromaography (viec) sample flows as mobile phase and pure waer is injeced as he sample. Symmerical peaks are obained; his is believed o be because of selfbuffering of he solues in he sample. The aim of he work discussed in his paper was o describe he mechanism of reenion in IEC and viec by using he modified equilibrium dispersive (ED) model. I was found ha he reenion imes and peak shapes prediced by he derived equaions are in good agreemen wih experimenal daa. These equaions also predic new feaures of viec, and hese were confirmed experimenally. I was shown ha in viec, in conras wih IEC, symmerical peaks are obained even for a single analye. INTRODUCTION Ion exclusion chromaography (IEC) is a chromaographic echnique used for separaion of parially ionized molecules [1 5]. When he pure ionexclusion mechanism of reenion is involved, reenion volumes of mediumsrengh elecrolyes are proporional o heir dissociaion consans. Srong and weak elecrolyes are separaed, he firs a he beginning 66

2 of he eluion order and he laer a he end. As wih oher chromaographic echniques, he name IEC is derived from he predominan mechanism of reenion, i.e. ion exclusion. Oher mechanisms (e.g. adsorpion on he resin, he screening effec, or size exclusion) enable separaion of sugars or alcohols [6 8]. The dead volume (volume of mobile phase) and he inner volume of he chromaographic column (he oal volume occupied by he waer in a column) can be deermined from he dependence of reenion volumes on dissociaion consans [9]. The reenion mechanism in IEC has been described using he socalled global hermodynamic equaions and by compuaional modeling of he column, using he Craig mehod [1]. The characerisic feaure of IEC is he same charge on he dissociaed funcional groups of he ionexchange resin and on he solue. Negaively charged ions (e.g. dissociaed acidic compounds) are herefore separaed on caionexchange resins wih anionic funcional groups, usually sulfonic acid groups. Alhough he same column can be used for boh IEC and ionexchange chromaography, rue ionexchange reacions are no involved in IEC. For he specific requiremens of IEC a large ionexchange capaciy is preferred. An increase in his capaciy can be achieved by increasing he column dimensions or he concenraion of funcional groups, or by using srong exchangers. Waer molecules accumulae, as hydraion spheres, around he dissociaed funcional groups of he suppor. Conained in he resin pores and in he hydraion spheres, hey are immobilized, forming a saionary phase. Neural, uncharged molecules penerae ino he resin whereas similarly charged coions are repelled by he presence of he dissociaed funcional groups immobilized in he resin skeleon. Similarly o he Donnan membrane equilibrium, he hydraed resin nework behaves as a semipermeable membrane beween he saionary and he mobile phases. Wih he excepion of he covalenly bound funcional groups, all oher species are freely exchanged hrough his hypoheical membrane. In IEC dilue sulfuric acid is frequenly used as mobile phase. The small amoun of sulfuric acid prevens peak ailing, which is frequenly observed when pure waer is used. Anoher mehod of avoiding ailing is o employ vacancy ion exclusion chromaography (viec). In his echnique a mixure of analyes is used as mobile phase and pure waer is injeced as he sample [10 14]. In he same way as in IEC, in viec he main reenion mechanism, based on exclusion of ions, can be coupled wih complemenary adsorpion of an analye by he resin skeleon. The aim of his paper is o describe he mechanism of reenion in IEC and viec, using he equilibrium dispersive (ED) model. The effec on 67

3 reenion of wo facors in paricular, he dissociaion consan and he concenraion of he solue, will be discussed. The chromaographic sysem was chosen in such a way as o avoid adsorpion of analyes on resin skeleon. THEORY Reenion of Acids in IonExclusion Chromaography wih Very Dilue Soluions To model peak reenion in analyical chromaography, i generally suffices o develop an equaion for he reenion facor, k. In he simples model of ionexclusion chromaography, when analye adsorpion can be negleced and assuming oal exclusion of coions from he waer occluded in he adsorben pores, he reenion facor can be expressed by he equaion [15]: k = = C V r 0 S,HR S 0 CHRVm + C V R m where V m is he volume of he mobile phase (he socalled dead volume), V S is he volume of liquid inside he resin in he column (he saionary liquid phase), C HR is he concenraion of acid in he mobile phase, C S,HR is he concenraion of he acid in he saionary liquid phase, C R is he concenraion of ion R in mobile phase, r is he reenion ime, and 0 is he dead ime (i.e. he eluion ime of species oally excluded from adsorben pores). For a wider discussion i is convenien o define several variables [16,17] including he exernal porosiy (bulk porosiy, voidage), ε e = V m /V k, where V k is he column volume, he paricle porosiy (inernal porosiy of he paricles), ε p = V S /V a, where V a is he adsorben volume (he sum of he skeleon resin volume and he saionary phase), and he oal porosiy oal volume occupied by eluae in column ε =. column volume I is easy o verify ha he following relaionship ε = ε e + (1 ε e )ε p is valid. Taking ino he accoun definiion of exernal porosiy, he dead ime can by expressed by he equaion: L u e 0 = ε (2) (1) 68

4 where u is he superficial velociy. Inroducing definiion of porosiy o eq. (1), he expression for reenion ime can be wrien as: C ε (1 ε ) C ε ε S,HR p e S,HR e r = = 0 1+ CHR + C ε e CHR C R + ε R e I is assumed ha equilibrium beween HR and R in he mobile phase is esablished immediaely, i.e.: C K C C HR a = + R H and ha resisance mass ransfer of he acid from he bulk phase o he resin can be ignored, i.e.: C S,HR = C HR Then, aking ino he accoun eqs (2), (4), and (5), eq. (3), can be rewrien as: r L ε ε = + u 1+ C e ε e (6) Ka + H The reenion imes of peaks in IEC can be calculaed from eq. (6), in which he dependency of reenion ime on acid concenraion is clearly visible. The error in he calculaion of reenion ime by use of his equaion increases wih increasing acid concenraion and i canno herefore be used for calculaion of reenion for high concenraions of analyes in IEC and viec, because of changes in ion concenraions in he course of migraion of he acid peaks or acid vacancies along he column. To calculae he reenion ime, an appropriae mass ransfer equaion mus be solved. The Mass Transfer Model Reenion ime in chromaography depends mainly on he hermodynamics of adsorpion, whereas he shape of he peak profile is a funcion of dispersion and resisance o mass ransfer in he bulk phase and on he adsorben. In IEC he reenion is also a funcion of exernal and he paricle porosiy. The general rae model akes all hese facors ino accoun [16 18]. When massransfer resisance is no exremely low, he lumped porediffusion model (POR) is recommended [18]. Finally, when mass (3) (4) (5) 69

5 ransfer resisance is negligible, he equilibrium dispersive (ED) [17] model is used. In his work, a suiable ED model was used for invesigaion of IEC. Adsorpion of he analye in he resin was ignored. I was convenien o develop he ED model used in his sudy from he POR model. The POR model applied o ionexclusion chromaography enables definiion of he mass ransfer equaion for he acid (HR) in he mobile phase and in he adsorben paricles, and for he R ions in he mobile phase only assuming he coions are oally excluded from he adsorben pores (i.e. from he saionary volume). Mass ransfer for he acid in he mobile phase is given by: ε z C z 2 e HR HR HR + u = εedl 1 2 e er ( ε ) k0,hrap ( CHR Cp,HR) ε HR where D L is he dispersion coefficien, a p = 3/R p, R p is he paricle diameer, k 0 is he overall massransfer coefficien, and r HR characerizes he dissociaion reacion: 1 1 r = k C C C = k C C 2 HR a HR + a HR R H R K a Ka where k a is he dissociaion rae consan, and he difference beween he concenraions of he R and H + ions was ignored. I is usually assumed ha he dissociaion reacion is infiniely fas. For he sake of convenience, for numerical soluion of his model a finie rae of dissociaion was assumed. I should, however, be noed ha for high enough values of k a he soluion obained for a finie value of he rae consan approximaes ha wih for an infinie rae consan wih negligible error only. In his work, he k a was chosen in such way ha he growh of is value did no affec he simulaed peak profiles. The mass balance for R ions in he mobile phase is given by: ε e 2 R R R + u = ε edl 2 + z C z ε r and he mass balance for HR in waer occluded in he adsorben s pores (i.e. in he saionary volume), ignoring adsorpion in he resin is given by: S,HR ε p = k0,hrap ( CHR CS, HR ) (10) e HR (7) (8) (9) 70

6 I was also assumed, ha mass ransfer resisances could be negleced. Wih his assumpion, concenraions of acid in he wo waer phases were equal: C HR = C S,HR. Afer eliminaion of he mass ransfer erms from eqs (7) and (10) i is easy o obain he equilibrium dispersive model (eqs 11 and 12) used in his work, remembering ha ε = ε e + (1 ε e )ε p : u ε C εe + = r HR (11) ε ε ε 2 HR HR e HR DL 2 z z C C C + = + r HR (12) ε 2 R u R R DL 2 e z z Model expressed by eqs. (11) and (12) were solved assuming he following iniial and boundary condiions: For IEC For = 0 and z > 0, C HR = C R = 0 For 0 < < injecion and z = 0, he inle concenraion of he nondissociaed acid and ion was calculaed from eq. (4) and from he relaionship C HR + C R = C inle ; For > injecion and z = 0, C HR = C R = 0 HR R For > 0 and z = L i was assumed ha: C 0 z = z = For viec For = 0, > injecion and z > 0, he concenraion of he nondissociaed acid and ion was calculaed from eq. (4) and from he relaionship C HR + C R = C inle For 0 < < injecion and z = 0 C HR = C R = 0 HR R For > 0 and z = L i was assumed ha C 0 z = z = The model expressed by eqs (11) and (12) were solved using he orhogonal collocaion mehod on finie elemens [19,20]. From hese models and afer he nex simplificaion, he reenion ime formula given by eq. (6) can also be developed. Assuming ha he dissociaion kineics are infiniely fas, and neglecing he dispersion erms and adding eqs (11) and (12), he following formula is obained: 71

7 C ε u u z z HR R HR R + εe + + = 0 or, aking ino he accoun ha, C C ε + ε + u H R H R e K a K a z and, finally: R C u 1+ K + H a + C + H ε + εe K a C C C + H = R HR we have: Ka (13) = 0 (14) R = 0 (15) z The second erm before he parial derivaive in eq. (15) represens he velociy of migraion of he par of he peak in which concenraion is C H +. Taking his fac ino accoun, eq. (6) can be obained. EXPERIMENTAL Insrumenaion and Procedure Ion separaion was performed wih Tosoh (Tokyo, Japan) Model IC2001 ion chromaograph equipped wih vacuum degasser, pump, column oven, auosampler, and conduciviy deecor. IEC and viec experimens were performed on a polysyrene divinylbenzenebased srongly acidic caionexchange resin column in he H + form (Tosoh TSKgel SCX; 150 mm 6 mm i.d., 5 µm paricle size, pore diameer 60 Å, 1.5 mequiv ml 1 caionexchange capaciy). The experimenal condiions were: column emperaure 40 C, flow rae 0.5 ml min 1, and injecion volume 30 µl. The separaion column was equilibraed unil sable mobile phase background conduciviy was obained (i.e. afer ca. 60 min). Reagens All reagens were of he analyical reagen grade from Wako (Osaka, Japan). Sandard soluions were prepared in disilled and deionized 72

8 waer. Appropriae amouns of analye samples a a concenraion of 0.1 M were dilued wih waer, as necessary. IonExclusion Chromaography The mobile phase was disilled and deionized waer. Injecion sample: 1 mm H 2 SO 4 as an indicaor of he dead volume (V m ) and 1 mm NaHCO 3 as an indicaor of he sum of dead volume and he volume of he mobile phase conained wihin he pores of he resin beads (inner column volume = V S + V m ) [21]. The sandard samples injeced ino he separaion column were 0.005, 0.05, 0.25, 0.5, 1.0, 2.0, 2.5 and 5.0 mm oxalic acid, and 0.5, 1.0, 2.5, 5.0 and 8.0 mm aceic acid. Vacancy IonExclusion Chromaography The mobile phase was 0.005, 0.05, 0.25, 0.5, 1.0, 2.0, 2.5, or 5.0 mm oxalic acid, or 0.5, 1.0, 2.5, 5.0, or 8.0 mm aceic acid. The sample injeced was he disilled and deionized waer. Model Daa For he calculaions relaing o IEC and viec dissociaion consans, K a, of and were used for oxalic and aceic acids, respecively [22]. Numerical values of u, ε, ε e, and D L necessary for soluion of he ED model expressed by eqs (11) and (12), were calculaed on he basis of he above menioned experimenal condiions. The superficial velociy was cm min 1 and he injecion ime was 0.06 min. Exernal porosiy, ε e, calculaed from he reenion of H 2 SO 4 was To calculae his from he measured reenion volume of sulfuric acid (1.172 ml) he numerical value of he exernal porosiy, an exra volume corresponding o he dead ime and equal o ml was subraced. In a similar way, he oal porosiy (ε = 0.876) was calculaed from he reenion of NaHCO 3 [21]. The measured NaHCO 3 reenion volume was 3.72 ml. To develop he equilibrium dispersive (ED) model, massransfer resisances were ignored. In pracice, however, mass ransfer resisances always exis and in he ED model hey are indirecly aken ino he accoun by formally regarding he dispersion coefficien (D L ) as he apparen dispersion coefficien [17], which includes he dispersion and he massransfer resisances. The apparen dispersion coefficien, calculaed by use of he formula N = ul/(ε D L )/2 [17] was D L = cm 2 min 1, where he number of he heoreical plaes (N) was esimaed from he H 2 SO 4 peak, using he half bandwidh mehod (N was approx. 2000). 73

9 I should be noed ha, in conras wih oxalic and aceic acids, sulfuric acid does no penerae inside he adsorben paricles, so he number of he heoreical plaes can be overesimaed by use of he firs wo acids. In his sudy, however, his error was negleced. RESULTS AND DISCUSSION IonExclusion Chromaography Experimenal and calculaed reenion imes of he peak apexes are presened in Table I. The experimenal reenion imes were calculaed by subracing he exra volume dead ime (which was equal o min) from he measured ime. To calculae heoreical reenion imes and peak Table I The reenion imes of oxalic acid and aceic acid obained in IEC Concenraion of sample injeced (mm) Experimenal reenion ime (min) Oxalic acid Calculaed reenion ime (min) for ε = 0.70 Experimenal reenion ime (min) Aceic acid Calculaed reenion ime (min) for ε = profiles he model given by eqs (11) and (12) was solved. The reenion ime prediced for aceic acid was, however, ca. 1 minue longer han ha measured experimenally. This error can resul from an inaccurae value of he exernal or oal porosiy. Incorrec calculaion of he exernal porosiy was virually impossible under our experimenal condiions, because compleely dissociaed srong sulfuric acid is repelled from he adsorben. Use of NaHCO 3 for calculaion of oal porosiy can also be imperfec. I seems ha NaHCO 3 can slighly be adsorbed and, as a resul, he calculaed oal 74

10 (a) mM (b) C R mM mM mM 0.25mM [min] Fig. 1 Comparison of (a) experimenal peak profiles and (b) heoreical peak profiles for oxalic acid in IEC. The inle concenraions (c inle ) were 0.25, 0.5, 1.0, 2.5, and 5.0 mm porosiy can be overesimaed. The oal porosiy was finally esimaed by comparison of experimenal and he heoreical reenion imes of aceic acid for is inle concenraion of 8 mm. The esimaed value (ε = 0.70) was employed in all he subsequen calculaions. 75

11 From comparison of he reenion imes given in Table I for boh relaively srong oxalic acid and relaively weak aceic acid i is apparen ha he maximum error of predicion of he reenion imes was always less hen 4%. Very good agreemen was also obained beween experimenal and he simulaed peak profiles (Figs 1 and 2). (a) mM (b) C R mM mM mM 0.5mM [min] Fig. 2 Comparison of (a) experimenal peak profiles and (b) heoreical peak profiles for aceic acid in IEC. The inle concenraions (c inle ) were 0.5, 1.0, 2.5, 5.0, and 8.0 mm 76

12 Vacancy IonExclusion Chromaography Experimenal and he calculaed reenion imes of he peak apexes are presened in Table II. The experimenal reenion ime was correced by subracing he exra volume dead ime from he measured ime. Relaive differences beween experimenal and heoreical reenion imes for aceic acid are similar o hose observed for IEC. For oxalic acid, he relaive calculaion error of he reenion ime has increased o 10%. I seems, however, ha his increase in he error is parly because of experimenal error (for example, compare he experimenal reenion daa for oxalic acid concenraions of 1 and 2 mm). Table II Reenion imes of oxalic and aceic acids obained in viec, and he ph of he mobile phases Concenraion of sample injeced (mm) ph Oxalic acid Experimenal reenion ime (min) Calculaed reenion ime (min) for ε = 0.70 ph Aceic acid Experimenal reenion ime (min) Calculaed reenion ime (min) for ε = The heoreical peak profiles obained for he wo acids, presened in Figs 3 and 4, are again in good agreemen wih experimenal resuls. CONCLUSION In his paper a simple equilibrium dispersive (ED) model is proposed for predicion of reenion for wo nonadsorbed organic acids in he ionexclusion chromaography (IEC) and in vacancy ionexclusion chromaography (viec). The model was successfully esed by use of a sron 77

13 (a) mM C R mM (b) mM 0.25mM [min] 6 Fig. 3 Comparison of (a) experimenal peak profiles and (b) heoreical peak profiles for oxalic acid in viec. The mobile phase concenraions (c inle ) were 0.25, 0.5, 1.0, 2.5, and 5.0 mm gly acidic ionexchange resin, in he H + form, characerized by a small pore diameer, 60 Å. I was found ha reenion values and peak shapes prediced by use of he derived equaions were in good agreemen wih experi 78

14 (a) C R mM 5mM 2.5mM (b) mM 0.5mM 8 [min] Fig. 4 Comparison of (a) experimenal peak profiles and (b) heoreical peak profiles for aceic acid in viec. The mobile phase concenraions (c inle ) were 0.5, 1.0, 2.5, 5.0, and 8.0 mm menal daa for a wide range of concenraion of he analyes invesigaed. These equaions also predic new feaures of viec which were confirmed experimenally. For example i was found ha in viec, in conras wih IEC, symmerical peaks were obained even for a single solue. The model 79

15 can be direcly exended o examples in which several analyes are separaed and in which he analyes are adsorbed on he resin. Modeling hese paricular examples will be he subjec of our nex paper. REFERENCES [1] B.K. Głód, Neurochem. Res., 22, 1237 (1997) [2] B.K. Głód, Aca Chromaogr., 12, 122 (2002) [3] K. Tanaka and J.S. Friz, J. Chromaogr., 361, 151 (1986) [4] K. Tanaka, M. Mori, Q. Xu, M.I.H. Helaleh, M. Ikedo, H. Taoda, W. Hu, K. Hasebe, J.S. Friz, and P.R. Haddad, J. Chromaogr. A, 997, 127 (2003) [5] K. Io, Y. Takayama, M. Ikedo, M. Mori, H. Taoda, Q. Xu, W. Hu, H. Sunahara, T. Hayashi, S. Sao, T. Hirokawa, and K. Tanaka, J. Chromaogr. A, 1039, 141 (2004) [6] G. Iwinski and D.R. Jenke, J. Chromaogr., 392, 397 (1987) [7] K. Tanaka and J.S. Friz, J. Chromaogr., 409, 271 (1987) [8] K. Tanaka, K. Oha, J.S. Friz, Y.S. Lee, and SB. Shim, J. Chromaogr. A, 706, 385 (1995) [9] B.K. Głód and W. Kamala, J. Chromaogr., 366, 39 (1986) [10] K. Tanaka, M.Y. Ding, M.I.H. Helaleh, H. Taoda, H. Takahashi, W. Hu, K. Hasebe, P.R. Haddad, J.S. Friz, and C. Sarzanini, J. Chromaogr. A, 956, 209 (2002) [11] K. Tanaka, M.Y. Ding, H. Takahashi, M.I.H. Helaleh, H. Taoda, W. Hu, K. Hasebe, P.R. Haddad, M. Mori, J.S. Friz, and C. Sarzanini, Anal. Chim. Aca, 474, 31 (2002) [12] M.I.H. Helaleh, K. Tanaka, M. Mori, Q. Xu, H. Taoda, M.Y. Ding, W. Hu, K. Hasebe, and P.R. Haddad, J. Chromaogr. A, 997, 133 (2003) [13] M.I.H. Helaleh, K. Tanaka, M. Mori, Q. Xu, H. Taoda, M.Y. Ding, W. Hu, K. Hasebe, and P.R. Haddad, J. Chromaogr. A, 997, 139 (2003) [14] M. Mori, M.I.H. Helaleh, Q. Xu, W. Hu, M. Ikedo, H. Taoda, and K. Tanaka, J. Chromaogr. A, 1039, 129 (2004) [15] K.L. Ng, B. Paull, P.R. Haddad, and K. Tanaka, J. Chromaogr. A, 850, 17 (1999) [16] M. Suzuki, Adsorpion Engineering, Elsevier, Amserdam,

16 [17] G. Guiochon, S.G. Shirazi, and A. Kai, Fundamenals of Preparaive and Nonlinear Chromaography, Academic Press, Boson, MA, 1994 [18] K. Kaczmarski and D. Anos, J. Chromaogr. A, 756, 73 (1996) [19] A.J. Berninger, R.D. Whiley, X. Zhang, and N.H.L. Wang, Compu. Chem. Eng., 15, 749 (1991) [20] K. Kaczmarski, G. Sori, M. Mazzoi, and M. Morbidelli, Compu. Chem. Eng., 21, 641 (1997) [21] K. Tanaka and P.R. Haddad, Encyclopedia of Separaion Science, III Ion Exclusion Chromaography, Academic Press, London, 2000, pp [22] G. Korün, W. Vogel, and K. Andrussov (Ed.) Dissociaion Consans of Organic Acids in Aqueous Soluion, Buerworhs, London,